Simxpert R3.2 Thermal Workspace Guide

Introduction 1

Thermal Workspace Guide Introduction This introduction briefly covers enough topics to familiarize the user with the capabilities of MSC SimXpert Thermal. The topics covered are • Overview of workspace applications • Workspace capabilities and supported solution types • Types of elements • Types of materials • Thermal loads and boundary conditions • Imaging • Overview of typical steps to do an analysis • Geometry

2 Overview of Workspace Applications

Overview of Workspace Applications The MSC SimXpert Thermal Workspace supports the full range of heat transfer analysis capabilities available in MD Nastran Thermal. These capabilities include: • Conduction in one, two, and three dimensions • Fundamental convection • One dimensional advection • Radiant exchange with space • Radiant exchange in enclosures • Specified temperatures • Surface and volumetric heat loads • Elements of thermal control systems

MD Nastran Thermal can span the full range of thermal analysis from system-level analysis of global energy balances to the detailed analysis associated with temperature and thermal stress limit levels. Within the integrated MSC SimXpert Thermal/MD Nastran Thermal environment, it is possible to simulate steady-state or transient, linear or nonlinear thermal behavior. Loads and boundary conditions can be applied either on the model’s geometry or on its finite element entities. MD Nastran Thermal’s sophisticated solution strategy automatically addresses the existence and extent of nonlinear behavior and adjusts the solution process accordingly.

Introduction 3 Workspace Capabilities and Supported Solutions

Workspace Capabilities and Supported Solutions The Main Menu for SimXpert Thermal is shown as follows:

MSC SimXpert Thermal has two solution methods • Steady-state • Transient

Steady-state Analysis A steady-state problem has constant specific energy (energy per unit mass) at each location in the conduction part of the model (interior to the boundary conditions). This is what causes the solution to achieve a constant temperature at each point in the conduction material. The boundary conditions can be • Convection • Free • Forced (SimXpert R4) • Radiation • To space • In radiation enclosure • Temperature • Constant • Temperature coupling (set one temperature equal to another)

The thermal loads can be • Heat flux to a surface • Directional heat flux from a distant source • Volumetric (internal) heat generation • Power into a node

4 Workspace Capabilities and Supported Solutions

The part of the MSC SimXpert Thermal GUI that deals with the specification of a steady-state analysis is shown as follows:

The Analysis dialog is used to specify what Case Control and Executive section entries are written to the MD Nastran Bulk Data file.

Transient Analysis Unlike a steady-state model, a transient model will not have constant specific energy at each location in the conduction part of the model. The temperature may change at the locations in the model. The boundary conditions and thermal loads can be those mentioned above for stead-state models. In addition to those it is possible to have nonlinear transient loads (four forms for them). The boundary conditions can be • Convection • Free • Forced (SimXpert R4) • Radiation • To space • In radiation enclosures • Temperature • Constant or time varying • Temperature coupling (set one temperature equal to another)

The thermal loads can be • Heat flux to a surface • Directional heat flux from a distant source • Volumetric (internal) heat generation • Power into a node

Introduction 5 Workspace Capabilities and Supported Solutions

The part of the MSC SimXpert Thermal GUI that deals with the specification of a transient analysis is shown as follows:

The Analysis dialog is used to specify what Executive Control Section and Case Control Section entries are written to the MD Nastran Bulk Data file.

6 Types of Elements

Types of Elements There are several types of elements, some being finite elements, that can be used to define a thermal model (steady-state or transient). There are conduction elements, elements that must be used to define boundary conditions; i.e. free convection, radiation to space; elements that must be used to define thermal loads; i.e. thermal flux from a distant source, heat flux applied to a surface; and “special” elements used to define simple thermal resistors, complex elements, and thermal capacitance.

Conduction Elements 1D, 2D, 3D, and axisymmetric finite elements are available to model the material that will undergo conduction.

1-D

2-D

3-D

CBAR

CQUAD4

CHEXA

CBEAM

CQUAD8

CPENTA

CBEND

CTRIA3

CTETRA

CONROD

CTRIA6

AXISYM CTRIAX6

CROD CTUBE

Special Elements There are a few types of elements that are used to define • Simple resistive components (simple thermal resistors) • More complex elements using direct matrix input or transfer function • Lumped thermal capacitance

Elements for Boundary Condition and Heat Flux to a Surface Boundary conditions for convection and radiation, and certain types of heat flux to surface, are applied to conduction elements (i.e. surface, solid) using 2D geometric (non-conduction type) surface elements - the boundary condition or heat flux are applied to the 2D geometric elements which are connected to the conduction elements, so energy is transferred to the conduction elements via the geometric elements. These interfacing element types are named CHBDYE, CHBDYG, and CHBDYP, as opposed to conduction elements named like CQUAD4 and CHEXA.

Introduction 7 Types of Materials

Types of Materials Several types of materials can be specified for conduction, convection, radiation.

Conductivity Thermal conductivity is an intrinsic property of all materials and in the absence of any other mode of heat transfer, provides the proportionality constant between the flow of heat through a region and the temperature gradient maintained across the region (Fourier’s Law). Thermal conductivity is generally a mild function of temperature, decreasing with increasing temperature for solids and generally increasing with increasing temperature for liquids and gases. Additionally, within a solid, thermal conductivity can vary due to material orientation (anisotropy). Preferential paths for heat flow can result. MSC SimXpert Thermal/MD Nastran Thermal allows for temperature-dependent and directional dependent thermal conductivity. • Isotropic • Constant property • Temperature dependent property • Anisotropic • Constant property • Temperature dependent property

Specific Heat and Heat Capacitance Specific heat is another intrinsic material property. When multiplied by the volume and density of material, the quantity of interest is referred to as heat capacitance or heat capacity. Given a closed thermodynamic system, heat capacitance provides the proportionality constant between heat added or subtracted from the system and the resultant temperature rise or fall of the system ( Δq = C ⋅ ΔT ) . Since heat capacitance only multiplies the time derivative of temperature in the heat conduction equation, specific heat is usually only relevant in the solution of transient thermal phenomena. It will noted later that advection introduces a pseudo-transient flavor even in steady-state analysis and therefore the specific heat and density of the advecting fluid are needed in these calculations. Specific heat is also slightly temperature dependent. However, in typical heat transfer problems, the largest variations in specific heat are generally attributed to materials changing phase • Isotropic • Constant property • Temperature dependent property • Anisotropic • Constant property • Temperature dependent property

8 Types of Materials

Density For the purpose of conserving mass, the density cannot be allowed to vary with temperature. Since node points are fixed in space in a MD Nastran Thermal analysis, if the density were to change with temperature, Density*Volume would also be changing, thus altering the system mass. • Isotropic • Constant property only • Anisotropic • Constant property only

Convection Coefficient Convection heat transfer involves the transfer of energy from a solid material, e.g. ceramic, to a moving fluid, e.g. gas, or vise versa. There are two types of convection, 1) free convection, where the fluid is heated or cooled because of the temperature difference between the solid material and the fluid; as a result of the heating or cooling the density of the fluid changes in the vicinity of the solid surface, thus causing the fluid to flow either up or down solely because of the difference of fluid density (the fluid is not driven by a pump), 2) forced convection, where the fluid is forced, e.g. pumped, inside of a duct or over a surface. Free Convection One material property, H, must be supplied • Isotropic • Constant property • Temperature dependent property • Anisotropic • Not available

Forced Convection Several material properties;

μ, C p , and K; are needed

• Isotropic • Constant property • Temperature dependent property • Anisotropic • Not available

Introduction 9 Types of Materials

Currently MSC SimXpert Thermal supports the free convection capability in MD Nastran Thermal. However, the forced convection capability in MD Nastran Thermal is not supported by MSC SimXpert Thermal; this will be supported in the near future (SimXpert R2).

10 Thermal Loads and Boundary Conditions

Thermal Loads and Boundary Conditions MD Nastran supports a full range of thermal boundary conditions and heat loads, starting with simple temperature constraints and heat flux boundary conditions, and moving on to more complicated heat transfer mechanisms associated with convection and radiation. All of the thermal boundary conditions can be modeled as functions of time. Thermal boundary conditions can be applied to finite element entities as well as geometric entities and include the following:

Thermal Loads There are several types of loads, from flux to internal heat generation. Temperature at nodes is treated as a load, even though some may consider it a boundary condition. Temperature Boundary Conditions Temperature constraints can only be applied to model nodes. They can be defined as constant, spatially varying, or time varying. Normal Heat Flux Normal heat flux is defined using the nodal, element uniform, or element variable loading operations. As with temperature boundary conditions, heat flux loads can be made to vary with space or time. Directional Heat Flux MD Nastran supports vector heat flux from a distant radiant heat source. This capability allows you to model phenomena such as diurnal or orbital heating. The required input for this capability includes: • The magnitude of the flux vector • The absorptivity of the surface on which the flux is being applied • The vector components of the flux vector

The absorptivity can be dependent on temperature. The magnitude and components of the heat flux can be defined as constant, spatial varying, or time varying. Nodal Source Heat can be applied directly on nodal points (or “grid points” in MD Nastran terminology). Nodal source heat can be defined as constant, spatially varying in a global sense, or time varying. Volumetric Heat Generation Volumetric heat can be applied to one or more conduction elements and can be defined as constant, spatially varying, or time varying. The MD Patran MD Nastran interface also includes a heat generation multiplier for specifying temperature dependence. The multiplier feature is available in the input form used to specify the material property data.

Introduction 11 Thermal Loads and Boundary Conditions

Thermal Boundary Conditions Boundary conditions consist of convection; free or forced, including advection; and radiation, to space or in enclosures. Basic Convection Basic convection boundaries can be defined. The approach to basic convection heat transfer in MD Nastran is to define the basic convection via a heat transfer coefficient and associated ambient temperature. The film coefficient is user specified and is available from a number of sources, including Reference 1. (p. 14). The film coefficient can be defined as a function of temperature; the ambient temperature can be defined as a function of time. Advection, Forced Convection Advection, forced convection, is a complicated heat transfer phenomenon that includes aspects of heat transfer as well as fluid flow. MD Nastran supports 1D fluid flow, which allows for energy transport due to streamwise advection and diffusion. Heat transfer between the fluid stream and the surroundings may be accounted for through a forced convection heat transfer coefficient based on locally computed Reynolds and Prandtl numbers; see Reference 1. (p. 14) and Reference 2. (p. 14) for more information on the underlying theory of this type of convection. The input for forced convection includes: • the mass flow rate of the fluid • the diameter of the fluid pipe • the material properties of the fluid

The calculation of the heat transfer coefficient between the fluid and the adjoining wall requires the specification of a film temperature. By default, this temperature will be internally calculated as the average of the temperatures of the fluid and the adjoining wall. Additional forced convection inputs consist of the type of convection relationship used to calculate the energy transport and the method of calculating the heat transfer coefficient at the tube wall. There are two choices with respect to the energy transport. The default method includes advection and streamwise diffusion, and its theoretical basis is the Streamwise-Upwind Petrov-Galerkin method, or SUPG. There are also two choices for picking the method for calculating the heat transfer coefficient that applies between the fluid and the adjacent wall. The default method uses the following equation:

h = Coef ⋅ Re

Expr

⋅ Pr

Expp

The second method, chosen by picking the alternate formulation option, uses the following equation:

k Expr Expp h =  --- ⋅ Coef ⋅ Re ⋅ Pr d

12 Thermal Loads and Boundary Conditions

where:

h

=

the heat transfer coefficient between the fluid and the adjacent wall (internally calculated)

Coef

=

a constant coefficient

Re

=

the Reynolds number based on the diameter (internally calculated)

Pr

=

the Prandtl number (internally calculated)

Expr

=

the Reynolds number convection exponent

Expp

=

the Prandtl number convection exponent

k

=

the fluid conductivity

d

=

the tube diameter

Currently MSC SimXpert Thermal supports the free convection capability in MD Nastran Thermal. However, the forced convection capability in MD Nastran Thermal is not supported by MSC SimXpert Thermal; this will be supported in the near future (SimXpert R4). Radiation to Space Radiation to space is a boundary condition that defines radiant exchange between a surface and blackbody space. The inputs required for radiation to space are the absorptivity and emissivity of the surface, the ambient temperature of space, and the radiation view factor between the surface and space (usually equal to 1.0). The absorptivity and emissivity can both be temperature dependent. The ambient temperature can vary with time. The exchange relationship is defined to be: 4

4

q = σ ⋅ View fac ⋅ ( ε e T e – α e T amb ) where:

q

=

the net energy flux in W/m2 (internally calculated)

σ

=

the Stefan-Boltzmann constant which has the value 5.668x10-8 W/m2 oK4 [0.1714x10-8 Btu/hr ft2 oR4]

View fac =

the view factor

εe

=

the emissivity

αe

=

the absorptivity (usually α e

= εe )

Introduction 13 Thermal Loads and Boundary Conditions

Te

=

the temperature of the element (internally calculated)

Tamb

=

the ambient temperature of space (user specified)

Calculation of radiation exchange requires that the temperatures be defined on an absolute scale (Kelvin or Rankine). If the temperatures input in a problem involving radiation are either Celsius or Fahrenheit, an internal conversion can be defined. Radiation Enclosures Radiation Enclosure exchange is similar to the Radiation to Space boundary condition; however, this type of boundary condition takes into account the radiation exchange between discrete surfaces. As a result, subsequent to building a finite element mesh, the geometric relationship (view factor) between individual finite element surfaces must be determined. For enclosure radiation the view factors between surfaces are internally calculated. Also, for enclosure radiation, the absorptivity is taken as being equal to the emissivity (Kirchhoff’s Identity). Calculation of the radiation view factors can be the most computational intensive operation in heat transfer analysis. MD Nastran has implemented a unique set of algorithms for solving this problem which provides for both reasonable performance while maintaining an accurate calculation. To help facilitate this calculation, the Can Shade and Can Be Shaded options have been added for those situations where the shading is known. These options can help reduce the calculation time for radiation enclosures. MD Patran also allows you to define multiple radiation enclosures. The view factors within each Radiation Enclosure will be independently calculated from the view factors of the other enclosures. In general, good view factor calculations require a reasonable surface mesh. Since the accuracy of the view factors tends to decrease as the distance between elements is reduced and becomes on the order of the element size, a mesh which prevents this sizing issue is recommended and is generally not too restrictive. MSC SimXpert Thermal supports both the radiation to space and radiation in enclosures capability in MD Nastran Thermal.

14 Overview of Typical Steps Used

Overview of Typical Steps Used Following is a brief discussion of what might be some steps taken to create thermal models. The first set of steps is for a steady-state model. MD Nastran Thermal has transient capability, but it is not currently supported by MSC SimXpert Thermal; it will be supported in the near future.

Steady-state Thermal Model Steps Import a parasolid surface

Parasolid surface

Introduction 15 Overview of Typical Steps Used

Create material property

16 Overview of Typical Steps Used

Create element property

Create elements (mesh)

Introduction 17 Overview of Typical Steps Used

Create a fixed temperature boundary condition

18 Overview of Typical Steps Used

Create a flux on the surface mesh

Now, the model is complete. Perform the steady-state analysis.

Introduction 19 Geometry

Geometry Geometry consists of • Point • Curve • Surface • Solid

It can be imported from a CAD source or created in SimXpert

Import Geometry Currently the types of CAD geometry files that can be imported into MSC SimXpert are • STL • Parasolid • CATIA • IGES

It is possible to import FEM models from • MD Nastran • Dyna

Create Geometry Currently is possible to create geometry by doing • Geometry: Curve / Arc/Circle • Geometry: Curve / Polyline/Spline • Geometry: Plane / XYZ • Etc.

Units for the Model MSC SimXpert Thermal uses all data, imported or created in MSC SimXpert, as being defined with a single consistent system of units, as specified in MSC SimXpert. It is important to specify the appropriate units prior to importing any unitless analysis files, such as an MD Nastran bulk data file, or creating materials, element properties, or loads. This is so that the MSC SimXpert user will be assisted in being

20 Geometry

consistent with the use of numerical quantities that have units. The system of units is specified in a dialog accessed by selecting Tools: Units Manager.

If a file is imported, e.g. from CAD, whose entities (numbers) have associated units, MSC SimXpert will convert them, the entities (numbers), so they have the units specified in the Unit Manager. For example, if the dimension/length of a curve, to be imported, is 1.0 in, and the length L unit, Basic Length unit in Unit Manager, is mm, the length of the curve, as seen in MSC SimXpert, will be 25.4.

Steady-State Thermal Analysis 21

Steady-State Thermal Analysis The topics discussed in this section are. • Overview of heat transfer, in brief • Presentation of heat transfer equations, in brief • Geometry, import and create • Thermal material properties • Element properties • Meshing geometry • Loads and boundary conditions • Performing steady-state thermal analysis • Viewing results • Example of a steady-state thermal analysis

22 Overview and Formulation

Overview and Formulation Thermal problems can be categorized as steady-state or transient, linear or nonlinear. Transient analyses are characterized by solution evolution over time, and in addition to energy exchange with the environment, involves thermal energy storage. Steady-state analyses are concerned with state point solutions to fixed boundary condition problems. Nonlinearities enter into both steady-state and transient solutions due to several influences. The most common nonlinearity is associated with temperature dependent material properties, in particular thermal conductivity and specific heat. Other nonlinearities are introduced from application of boundary conditions principally convection and radiation. All nonlinear analyses necessarily involve solution iteration, error estimation, and some form of convergence criteria. MD Nastran attempts to do this as efficiently and trouble free as possible.

Formulation Steps of Solution Process in Brief The familiar conduction heat transfer equation is

q· 1 ∂T 2 ∇ T + --- = --α ∂t k where:

T

=

temperature

=

Laplacian operator

=

rate of heat generation per unit volume

k

=

thermal conductivity of solid material

α

=

thermal diffusivity

t

=

time variable

∇ q·

2

A transition is made from this equation (strong form) to a variational formulation (weak form). The matrix equation corresponding to the variational formulation is

· M {T} + K {T} = {F}

Steady-State Thermal Analysis 23 Overview and Formulation

where:

{T}

=

temperature vector

· {T}

=

first derivative of temperature vector

M

=

heat capacity matrix

K

=

heat conductivity matrix

{F}

=

heat supply vector

The MD Nastran Thermal steady-state equation derived from this equation is 4

[ K ] { T } + [ ℜ ] { T + T abs } = { P } + { N } where:

{T}

=

temperature vector

{Tabs}

=

absolute temperature vector

K

=

heat conduction matrix

[ℜ]

=

radiation exchange matrix

{P}

=

applied heat flow vector

{N}

=

nonlinear heat flow vector that is temperature dependent

The user may refer to the MD Nastran Thermal Analysis User’s Guide for a detailed description of the above and following mentioned algorithms. This is a nonlinear matrix equation. It is solved using the Newton-Raphson iteration scheme. A residual load vector function is defined as the difference between the applied thermal load vector and the thermal load vector due to element temperature. 4

{ R } = ( { P } + { N } ) – ( K { T } + [ ℜ ] { T + T abs } ) The residual load vector function is equal to zero for the solution temperature vector. The task is to determine the solution temperatures. The residual load vector function is approximated by its first-order Taylor series expansion about the temperature vector from the i-th iteration.

24 Overview and Formulation

i

i ∂{R} { R ( { T } ) } ≅ { R ( { T } ) } + ------------- ( { T } – { T } ) ∂{ T} i

The Taylor series expansion is evaluated at the temperatures for the (i + 1)-th iteration, and set equal to zero.

{R({ T}

i+1

i

i+1 i ∂{ R} i – {T} ) = {0} ) } ≅ { R ( { T } ) } + ------------- ( { T } ∂{T }

From this the following equation is arrived at: i

i

K T { ΔT } = { R }

i

where: i

{ ΔT } = { T } i

KT

i+1

– {T}

i

i

∂{R} = – ------------- is the tangent heat conduction matrix. ∂{T }

An approximate representation is used as follows: i

KT

i ∂{N } i i ≅ ( K + 4 [ ℜ ] { T + T abs }3 ) – ------------∂{T }

i

The residual load vector function for the i-th iteration is given by i

i

i

{ R } = ( { P } + { N } ) – ( K { T } i + [ ℜ ] i { T i + T abs }4 ) This is an iterative process. Start with i = 0. Thus, the first equation to be solved is 0

0

K T { ΔT } = { R } From

0

0 { ΔT } the next temperature vector is found from

1

0

{ T } = { T } + { ΔT }

0

Next, use i = 1. The next equation to be solved is

Steady-State Thermal Analysis 25 Overview and Formulation

1

1

K T { ΔT } = { R } From

1

1 { ΔT } the next temperature vector is found from

2

1

{ T } = { T } + { ΔT }

1

This process is repeated until a converged solution is obtained, {T}m. Since matrix decomposition is time consuming, MD Nastran does not update the left-hand side matrix at each iteration. The tangential matrix is updated only when the solution fails to converge or the iteration efficiency can be improved. However, the residual vector is updated at each iteration. In concert with the Newton-Raphson method, the following options are provided to improve the efficiency of the iteration process: • Tangential matrix update strategy • Line search method • Bisection of loads • Quasi-Newton (BFGS) updates

These options are specified on NLPARM (steady-state analysis) or TSTEPNL (transient analysis) Bulk Data entries; this will be discussed later in the section on steady-state analysis. In general, if the solution process diverges, a line search algorithm, a bisection of loads method, or the quasi-Newton update method are implemented in an effort to improve the solution obtained. If the solution still fails to converge using all the above methods, the tangential stiffness matrix is updated, and the iteration is resumed. The user may refer to the MD Nastran Handbook for Nonlinear Analysis for a detailed description of the above mentioned algorithms.

26 Geometry Parts and Create Geometry

Geometry Parts and Create Geometry Currently, access to geometry is through • Importing geometry, e.g. Parasolid surface • Creation of only basic geometric shapes, e.g. create plane

The form that is used to import geometry is

As can be seen it is possible to import geometry that is • STL • Parasolid • CATIA • IGES

It is also possible to import FEM from • MD Nastran

Steady-State Thermal Analysis 27 Geometry Parts and Create Geometry

Import a Parasolid Solid

The image of the imported Parasolid solid is

Create a Local Coordinate System There are several ways to create a coordinate system

28 Geometry Parts and Create Geometry

• One node to specify a local coordinate system • Select a point (e.g. node) or specify a location of the origin. • Specify the basic X-, Y-, or Z-axis to have the local 3 axis, of the local coordinate system to

be created, aligned with. • This is only for a fixed coordinate system. • Two nodes to specify a local coordinate system • The first point (e.g. node) selected or location specified is for the origin. • The second point will be on the local w-axis. • This is only for a fixed coordinate system. • Three nodes to specify a local coordinate system • The first point (e.g. node) selected or location specified is for the origin. • The second point will be on the local x-axis. • The third point will be on the local y-axis. • This is for either a fixed or moving coordinate system.

A sample of creating a local cylindrical coordinate system for a Parasolid solid is shown as follows:

To access the form to create the local coordinate system use the following:

Steady-State Thermal Analysis 29 Geometry Parts and Create Geometry

This is the pick panel and form. They are used to specify the locations of the points, or the pick panel is used for selecting existing nodes or points on elements.

30 Geometry Parts and Create Geometry

After picking several nodes the cylindrical coordinate system is created.

Steady-State Thermal Analysis 31 Materials

Materials A material form appears when one is selected from the Material menu that is in the MSC SimXpert Thermal main menu. The selections made under the Material menu will determine which material form appears, and ultimately, which MD Nastran Thermal material will be created. The following pages give a description of the Material forms and details of all the material property definitions supported by MSC SimXpert Thermal. Only material records/data that are referenced by an element property region will be written out of MSC SimXpert Thermal. The following topics are covered for materials: • Supported materials for steady-state analysis • Required material properties to define a model • Units • Method of creation of materials • Use of fields for material definition

Supported Materials for Steady-state Analysis The material properties are for modeling conduction, convection, and radiation. • Conduction • Thermal conductivity of solid material • Isotropic, temperature independent • Isotropic, temperature dependent • Anisotropic, temperature independent • Anisotropic, temperature dependent • Convection • Free convection heat transfer coefficient • Isotropic, temperature independent • Isotropic, temperature dependent • Radiation • Absorptivity of radiating surface • Emissivity of radiating surface • Temperature independent • Temperature dependent

32 Materials

Required Material Properties The above covered the possible material properties that can be created in MSC SimXpert Thermal for MD Nastran Thermal. Now, the material properties that are needed (a must) for specific types of steadystate analysis are discussed. Conduction Steady-state conduction thermal behavior only needs thermal conductivity, K, to model it. So, the MatIsotropic form is needed for isotropic material, and the MatAnisotropic form is needed for anisotropic material.

Notice that only the thermal conductivity field, K, has data. Convection Steady-state convection thermal behavior needs properties that depend on the type of convection. Free convection needs the free convection heat transfer coefficient, H. This is input using the CONVECTION form.

Steady-State Thermal Analysis 33 Materials

Radiation Radiation to space steady-state thermal behavior needs the surface absorptivity and emissivity to model it. So, the RadMat form is needed to specify these.

Units The following table lists the units that correspond to the fields of the MatIsotropic or RadMat forms.

Parameter

Description

Consistent Units

K

Thermal conductivity

W/(m*C)

CP

Specific heat at constant pressure

J/(kg*C)

RHO

Density

kg/m3

H

Free convection heat transfer coefficient

W/(m2*C)

MU

Dynamic viscosity

N*sec/m2

HGEN

Volumetric internal heat generation

W/m3

REFENTH

Reference enthalpy

J/kg

TCH

Lower temperature limit for phase change

C

TDELTA

Temperature domain for phase change

C

QLAT

Latent heat

J/kg

ABSORP

Surface absorptivity

Unitless

EMISi

Surface emissivity

Unitless

Creation Methods The types of material for which their method of creation are shown are: • Isotropic • Anisotropic • Isotropic, temperature dependent

34 Materials

Conduction There are four types of material models. Two are for temperature independent properties, and two are for temperature dependent properties. First, is for isotropic, temperature independent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears:

Data can be specified in this form, as is shown below.

Second, is for anisotropic, temperature independent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

Steady-State Thermal Analysis 35 Materials

When this is used the following form appears:

Third, is for isotropic, temperature dependent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears (this is the same form whose image was shown previously):

To use this form click in the check box for conductivity, T(K). Double click in the T(K) cell, and select Select or Create. For this example select Create.

36 Materials

The following form for selecting the material entry type appears.

Steady-State Thermal Analysis 37 Materials

Select a table type to specify the temperature dependent material property, e.g. TABLEM1.

Enter data into the Graph.

38 Materials

• For details on creating a graph see Chart in the Charting Document.

The final MatIsotropic form looks like the following:

The process is similar for the MatAnisotropic form.

Steady-State Thermal Analysis 39 Materials

Convection The material properties for convection can be specified using the same forms that are used for conduction. The difference is that the form is used to specify properties of the fluid. The properties that are defined are • Thermal conductivity of the fluid • Heat capacity of the fluid • Dynamic viscosity of the fluid

The MatIsotropic form might be filled-out as follows:

Radiation The material properties for radiation are specified using the RadMat form. The form is accessed in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears:

40 Materials

Data can be specified in this form, as is shown below.

Steady-State Thermal Analysis 41 Properties for Elements

Properties for Elements An element property form appears when one is selected from the Property menu that is in the MSC SimXpert Thermal Model tree browser. The selections made under the Property menu will determine which Property form appears. There are several options available when creating element properties. The following pages give a description of a few of the Property forms and details of all the element property definitions supported by MSC SimXpert Thermal. This section deals with creating properties that correspond to topological shapes called elements. The topological shapes do not represent finite elements until they have associated element properties. An example of this is a four noded quadralateral shape.

It could be used to represent a 2D plate or 2D solid finite element. Shell property To create a property, to be associated to a 2D topological shape, use the following in MSC SimXpert Thermal: (right click Property)

42 Properties for Elements

When this is used the following form appears:

Data can be specified in this form as follows:

First, double click in the data cell MID, and select Create.

Steady-State Thermal Analysis 43 Properties for Elements

Specify the thermal conductivity, specific heat, and density.

Create the PSHELL element property. This property can be used during creating a 2D shell element mesh. Solid property Now, the steps in MSC SimXpert needed to create a property set corresponding to a 3D topological shape are shown. (right click Property)

44 Properties for Elements

When this is used the following form appears:

Data can be specified in this form as follows:

First, double click in the data box MID, and select Create.

Steady-State Thermal Analysis 45 Properties for Elements

Specify the thermal conductivity, specific heat, and density.

Create the PSOLID element property.

Supported Element Types and Uses There are several types of elements • Conduction elements • Special elements • Simple resistive components • User defined complex element types • 2D elements for coupling applied heat flux, convection, and radiation to conduction surfaces

Conduction Elements There are 1D, 2D, 3D, and axisymmetric conduction finite elements.

1-D

2-D

3-D

CBAR

CQUAD4

CHEXA

CBEAM

CQUAD8

CPENTA

CBEND

CTRIA3

CTETRA

CONROD

CTRIA6

AXISYM CTRIAX6

CROD CTUBE The heat flow through these elements is in the parametric directions of the elements. • 1D element • Heat flow is only along the centerline of the element, not normal to the centerline of the

element • 2D element • Heat flow is only in the plane of the element, not normal to the plane of the element

46 Properties for Elements

• 3D element • Heat flow is in all three directions of the element • Axisymmetric element • Heat flow is only in the radial or centerline direction of the element, not in the circumferential

direction So, do not use an element that does not have a parametric coordinate in a direction that heat flow must be modeled The performance of linear finite elements, e.g. CQUAD4 element, is as good as that of parabolic finite elements, e.g. CQUAD8 element, for 2D or 3D. Recommendations • Use linear elements, unless have substantial curvature and desire to minimize the number of

elements • If doing thermal analysis (calculate temperatures) to structural analysis (stress analysis) mapping

(loads are temperatures from thermal analysis), it is best to use the same type of element that is to be used for the structural analysis, e.g. Tet10, and not Tet4. • Loads and boundary conditions do not affect which type of element should be used

Special Elements This category is for elements that are not finite elements, but of course they can be used in modeling a thermal process. There are two types of special elements. They are. • CELASi (scalar spring) -- simple resistive component

L ΔT = q·  ------ = q· R kA • DMI or DMIG (direct matrix input) -- complex component

name = X ij Boundary Condition or Heat Flux Surface Elements To apply convection, radiation, or heat flux to a conducting surface (2D element, e.g. CQUAD4) or face (3D element, e.g. CHEXA) it is necessary to apply them to a geometric surface, which in turn is

Steady-State Thermal Analysis 47 Properties for Elements

connected to conducting elements. The geometric surfaces are named CHBDYE, CHBDYG, or CHBDYP, or to simplify, CHBDYi. This is shown conceptually as follows.

The user does not explicitly create the CHBDYi elements. They are created from within MSC SimXpert Thermal as a result of creating the loads and boundary conditions.

Use of Fields to Model Variable Element Properties Some examples of variable element properties are • Variable element thickness, t(x,y,z)

These types of parameters can be represented using Fields.

48 Properties for Elements

The Fields creation form is accessed using the following dropdown menu: (right click Fields)

Under Fields there are several inputs and choices that can be made. • Name • Method • Function • Tabular • Discrete FEM • Value Type • Scalar • Vector • String • Function or Table • Scalar Function • Vector Function; Component 1, 2, 3 • Table with Active Independent Variables X, Y, Z and Values

Steady-State Thermal Analysis 49 Properties for Elements

• Table with Nodes and Values

An example of the creation and use of a scalar Field follows:

50 Properties for Elements

Now, select the field in this form for F_T. This deselects the field T that is used for input of a constant value of thickness, and activates the field F_T that is used for selecting the Field named “thickness”.

Now, double click in the field (cell) F_T to select the Field named “thickness”.

Select the Field named thickness.

Steady-State Thermal Analysis 51 Properties for Elements

Now, complete entering information into the PSHELL form.

52 Meshing and Element Creation

Meshing and Element Creation Once the following has been done • Import the geometry, or create the geometry in MSC SimXpert • Create material property • Create element property, with it associated to the material property

the geometry can be meshed, with the resulting topological shapes associated to the element property.

Meshing Following is a brief presentation on how to mesh a surface. Import the geometry

Create the material property.

Steady-State Thermal Analysis 53 Meshing and Element Creation

Create the element property, using the material property.

Display “Collection” form to be able to see the Part list (contains the “parts” of the model). To do this right-click over the MSC SimXpert Thermal main menu area, and select “Collection”.

The “Part” form appears, as shown.

There is only one Part, it is named “P2”. It is not active (entities created, e.g. elements created by meshing, are not automatically assigned to it, Part P2). This is observed backaches the label P2 is not in the list box titled “Current:” at the top of the form.

54 Meshing and Element Creation

To make the Part P2 active mouse-click with the middle button on the name “P2” in the Part form.

Now, the previously imported surface can be meshed, with the mesh being associated to the Part “P2”. However, before the surface is meshed it is necessary to associate the previously created element property to Part “P2”. This is done by mouse-clicking with the right button on the name “P2”, and selecting Modify. The Modify Part form appears.

Double click in the 2D_PROP cell, and select Select.

Steady-State Thermal Analysis 55 Meshing and Element Creation

Select the property named PSHELL_1. The following form, named Modify Part, appears as follows:

Now, mesh the imported surface. This is done by accessing the form for Mesher.

56 Meshing and Element Creation

Using this causes the Mesher pick panel and Mesher form to appear.

The first thing to do is to select the entities, e.g. surfaces, to be meshed. This can be done using the Advanced button (Extended Pick Dialog), but since there is only one surface to be meshed it is only necessary to pick the button “All” in the Mesher Pick Panel, or screen picking the geometric surface directly. The surface ID, 1, appears in the Mesher form. Then, enter the desired element size under Element Size in the Mesher form. After doing this, pick the button “Done” in the Mesher Pick Panel or OK in the Mesher form.

Steady-State Thermal Analysis 57 Meshing and Element Creation

The mesh obtained is shown as follows:

The 2D element mesh will have been created. Upon exporting the model from MSC SimXpert Thermal, 2D CQUAD4 elements will be created; the following MD Nastran entries will be created. • GRID (nodes) • CQUAD4 (2D shell elements) • MAT4 (isotropic material property) • PSHELL (shell element property)

Mesh Control Using the previous model, create a new mesh using control of element size. Use the following to change the size of elements that are created as a result of meshing. First, delete the existing mesh that is on the surface. Next, change the size of the elements to be created by using the following pick:

58 Meshing and Element Creation

Using this causes the Mesh Size pick panel and Mesh Size form to appear.

Steady-State Thermal Analysis 59 Meshing and Element Creation

Select the button All to select all the edges of the surface, with 1, 2, 3, 4 entered into Support in the form Mesh Size. Enter 5 in Pitch, then click OK. Then, mesh the surface as before.

Merge Coincident Nodes For many analysis it is necessary to have adjacent elements connected. The elements (adjacent) created by meshing a single geometric entity, e.g. surface, are automatically connected. The elements at geometric interfaces (where different geometric entities meet) are not automatically connected. This allows the user to decide if those elements should be connected, depending on if the analysis model needs to include nonlinear contact. When elements at geometric interfaces need to be connected this can be done in MSC SimXpert Thermal. First, import or create two adjacent geometric surfaces.

60 Meshing and Element Creation

Mesh both surfaces using the same element size for both meshes.

Show where the elements are not connected using the following, View: Highlight FE Boundary:

Steady-State Thermal Analysis 61 Meshing and Element Creation

Following, is the image of the display before the adjacent elements, at the geometric interface, are connected:

The elements at the interface are connected by merging the nodes at the interface using Node: Merge Coincident Nodes.

62 Meshing and Element Creation

The following Merge Coin. Nodes pick panel and form appears:

Select All, then Done. The form for specifying the merging tolerance follows.

Following is the image of the display after the adjacent elements, at the geometric interface, are connected.

Steady-State Thermal Analysis 63 Loads and Boundary Conditions, and LBC Sets

Loads and Boundary Conditions, and LBC Sets Now, that the mesh(s) has been created, along with material and element properties, the remaining part of the model to define is the loads and boundary conditions. This section deals with • Thermal loads • Heat flux applied to surface elements • Heat flux applied to an area defined by nodes • Directional heat flux from a distant source • Volumetric internal heat generation • Thermal boundary conditions • Convection, free (SimXpert R1.1) • Convection, forced (SimXpert R2) • Radiation, to space (SimXpert R1.1) • Radiation, in enclosure (SimXpert R2) • Temperature • Load and boundary condition set • Combination of loads and boundary conditions • Scale factors • Priority of loads and boundary conditions

Sample of Loads and Boundary Conditions Forms A few MSC SimXpert load and boundary condition (LBC) forms are shown, and their use described. A simple model is used to do this. The model was imported into MSC SimXpert Thermal from an MD Nastran bulk data file.

Three LBCs are to be applied to the model.

64 Loads and Boundary Conditions, and LBC Sets

The location of a LBC is established by selecting (picking) nodes/elements as the LBC is created. This is shown below. First, a heat flux is to be applied to the bottom surface of the model. The form and pick panel to do this with is accessed using BC: Create BC / Segment BC / FLUX.

The following form appears.

Now, enter a value for Q0 (heat flux into element), say 2020.0

Click Store, then Exit.

Steady-State Thermal Analysis 65 Loads and Boundary Conditions, and LBC Sets

The next thing to do is to select a set of nodes at the bottom of the model. In the pick panel Create FLUX select Nodes.

Then, change from Single picking to Rectangular Window picking.

Select the nodes at the bottom of the model.

Click Done, then click Exit in the Create FLUX pick panel.

66 Loads and Boundary Conditions, and LBC Sets

Now, apply radiation to the top surface of the model. The form and pick panel to do this with is accessed using BC: Create BC / Segment BC / RADIATION.

The following form appears.

Enter the following • For TAMBIENT 490.0 • For FAMB 1.0 • Click checkbox for MID_ID, then double click in MID_ID cell, and enter, in RadMat form, 0.3

for ABSORP, and 0.5 for EMIS1. Click Store, then click Exit.

Steady-State Thermal Analysis 67 Loads and Boundary Conditions, and LBC Sets

The next thing to do is to select a set of nodes at the top of the model. In the pick panel Create RADIATION select Nodes.

Select the nodes at the top of the model.

Click Done, then click Exit in the Create RADIATION pick panel.

68 Loads and Boundary Conditions, and LBC Sets

Now, apply free convection to the side surfaces of the model. The form and pick panel to do this with is accessed using BC: / Create BC / Segment BC / CONVECTION.

The following form appears.

Enter the following • For TAMBIENT enter 490.0 • For H enter 0.006

Click Store, then click Exit.

Steady-State Thermal Analysis 69 Loads and Boundary Conditions, and LBC Sets

The next thing to do is to select a set of nodes on the sides of the model. In the pick panel Create CONVECTION select Nodes.

Select the nodes on the sides of the model.

Click Done, then click Exit in the Create CONVECTION pick panel. Now, there are three LBCs.

70 Loads and Boundary Conditions, and LBC Sets

LBC Set for Sample LBC forms Example Using the three LBCs just created, a LBC Set will be created. Subsequently, this set will be accessed for defining an MD Nastran Thermal job. The form for doing this is accessed using BC: Create LBC Set.

The following form appears for creating a LBC Set using • Heat flux • Radiation, to space • Convection, free

Do the following: • Enter a name in the list box LBC Set Name • Select all three of the LBC names under Select Existing LBCs: FLUX_1, CONVECTION_1,

RADIATION_1

Steady-State Thermal Analysis 71 Loads and Boundary Conditions, and LBC Sets

The form will look like the following:

Click OK to create the LBC Set. These three LBCs can be used for an analysis by using this LBC Set.

Supported Load Types As previously mentioned the thermal load types are • Thermal loads • Heat flux applied to surface elements • Heat flux applied to an area defined by nodes • Directional heat flux from a distant source • Volumetric internal heat generation

Comments about the various load dialogs follows:

72 Loads and Boundary Conditions, and LBC Sets

Heat Flux Applied to Surface Elements -- QBDY1 Entry

The form for creating a QBDY1 entry follows:

As described previously, a value for Q0 must be entered, click Store, then Exit. In the pick panel select the application region/domain entities over which the heat is to be applied. This is done by picking nodes using the pick panel.

Steady-State Thermal Analysis 73 Loads and Boundary Conditions, and LBC Sets

Units

Parameter Q0

Description Heat flux into an element

Consistent Units W/m2

Heat flux Applied to an Area Defined by Nodes -- QHBDY Entry

A form appears.

The entries for this form are. • FLAG = POINT, LINE, REV, AREA3, AREA4, AREA6, AREA8 • POINT, LINE, REV, AREA3, AREA4, AREA6, AREA8 uses 1, 2, 2, 3, 4, 4-6, 5-8 points,

respectively, to define an area for the heat flux. • Q0 is the magnitude of thermal flux onto the “face” • AF is the area factor • Areas that are defined with 1 or 2 points, for which an area cannot be calculated using the

location of the points, must have an AF value specified. For other areas, e.g. AREA4, the area is calculated by MD Nastran.

74 Loads and Boundary Conditions, and LBC Sets

The pick panel for creating a QHBDY entry follows. This is used to select the model nodes.

Units

Parameter

Description

Consistent Units

Q0

Magnitude of thermal flux into face

W/m2

AF

Area factor; depends on FLAG

m2, m, N/A

Directional Heat Flux from a Distant Source -- QVECT Entry

Steady-State Thermal Analysis 75 Loads and Boundary Conditions, and LBC Sets

A form appears.

The entries for this form are. • Q0 = magnitude of thermal flux onto the “face”. • TableQ -- table used to define flux vs time. • TSOUR = temperature of the radiant source. • CE -- coordinate system ID number for thermal vector flux. • Ei -- vector components (direction cosines in coordinate system CE) of the thermal vector flux. • ABSORP -- 0.0 <= absorptivity <= 1.0 • TableA -- table used to define absorptivity vs time. • EMIS -- 0.0 <= emissivity <= 1.0 • FACE_OPT -- surface option, FRONT or BACK. • MID_ID -- wavelength and/or temperature dependent surface properties ID.

The pick panel for creating a QVECT entry follows. This is used to select the model nodes.

76 Loads and Boundary Conditions, and LBC Sets

Units

Parameter

Description

Consistent Units

Q0

Magnitude of thermal flux vector onto face W/m2

TSOUR

Temperature of radiant source

K

Volumetric Internal Heat Generation -- QVOL Entry

A form appears.

The entries for this form are. • QVOL = power input per unit volume produced by heat conduction elements • TableQ -- table used to define power input per unit volume vs time. • CNTRL -- control point ID used for controlling heat generation

Steady-State Thermal Analysis 77 Loads and Boundary Conditions, and LBC Sets

The pick panel for creating a QVOL entry follows. This is used to select the model elements.

Units

Parameter QVOL

Description Power input per unit volume produced by a heat conduction element

Consistent Units W/m3

Supported Boundary Condition Types As previously mentioned the thermal boundary condition types are. • Temperature • Convection, free • Radiation, to space

Comments about the various boundary condition forms follow:

78 Loads and Boundary Conditions, and LBC Sets

Temperature Applied to Model Nodes -- TEMPBC Entry

A form appears.

The entries for this form are. • T is the temperature at model nodes • SID is the set ID • TYPE is the type of temperature boundary condition • STAT -- constant • TRANS -- time varying

Steady-State Thermal Analysis 79 Loads and Boundary Conditions, and LBC Sets

The pick panel for creating a TEMPBC entry follows. This is used to select the model nodes.

Units

Parameter T

Description Temperature at model nodes

Consistent Units C

The TEMPBC boundary condition can be used to enforce constant temperature at nodes, or it can be used to enforce time varying temperature. Like TEMPBC, the SPC boundary condition can be used to enforce constant temperature at nodes, however, the temperature cannot vary, it can only be constant. Initialization Temperature Applied to Model Nodes -- TEMP Entry For the solution procedure there must be a temperature specified at each node, some being constant and others just to begin the solution process. Some nodes will have their temperature specified as constant using the TEMPBC or SPC entry. These temperatures will remain unchanged throughout the solution process. The other nodes must have a specified initialization temperature just to begin the solution procedure. This is done using the TEMP entry.

80 Temperature Specification (SOL 400)

Temperature Specification (SOL 400) Overview Temperature specification can be done for several reasons. • Specifying temperature boundary conditions. They can be either constant or time dependent. • Specifying initial conditions. The term initial refers to two things. • For steady-state heat transfer analysis, the temperature for conduction material properties. • For steady-state heat transfer analysis, the starting temperature for the iteration process. • Specified temperature set is used to determine equivalent static loads from external loads,

thermal loads, and element deformations. • Both the thermal loading and temperature dependent material properties are to use the same

temperature set. • Specifying the temperature set for the temperature dependent material properties.

Uses of Temperature LBC for Heat Transfer GUI More detailed information about what temperature sets the Temperature LBC GUI can be used to create for heat transfer analysis is given below. Temperature Boundary Condition This is for creating a temperature boundary condition. The information that must be provided is • Application region -- list of nodes for which the temperature is to be specified. • Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function). • Temperature versus time scaling function -- the selected time dependent function (table, e.g.

TABLED1) is multiplied by the temperature.

Uses of 0D, 1D, 2D Initial Temperature for Heat Transfer Analysis To specify the initial (starting) temperature for steady-state heat transfer analysis, this is applicable. Initial Conditions If it desired to specify the temperature set for conduction material properties and the starting temperature for the iteration process, for steady-state heat transfer analysis, the following input is required. • Application region -- list of nodes for which the temperature is to be specified.

Steady-State Thermal Analysis 81 Temperature Specification (SOL 400)

• Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function).

Uses of 0D, 1D, 2D Material Temperature Dependency Temperature Dependent Material Properties Specify the temperature set for temperature dependent material properties. • Application region -- list of elements for which the temperature is to be specified. • Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function).

Units

Parameter T

Description Temperature at model nodes

Consistent Units C

Free Convection to Ambient Temperature -- CONV Entry Convection heat transfer occurs whenever a body is placed in a fluid at a higher or a lower temperature than that of the body. As a result of the temperature difference, there is heat transfer between the body and the fluid. This causes a change of density of the fluid adjacent to the surface of the body where the convection is occurring. This change of fluid density results in the movement, upward or downward, of the fluid. If the motion of the fluid is caused solely by differences of fluid density, and not by a pump or fan adding to the fluid motion, the heat transfer is called natural or free convection. Following is a picture showing conceptually a free convection example.

82 Temperature Specification (SOL 400)

To create a free convection, to an ambient temperature, boundary condition use the BC: Create BC / Segment BC / CONVECTION dropdown menu.

The following form appears for creating the thermal free convection boundary condition:

The entries for this form are. • TAMBIENT -- ambient temperature • TableT -- table used to define ambient temperature vs time • H -- free convection coefficient • TableH -- table used to define convection coefficient vs time • FORM -- used to specify the type of formula used for free convection • For FORM = 0, 10, or 20, EXPF is an exponent of (T- TAMB), where the convective heat

transfer is represented by

q = H ⋅ u CNTRLND ⋅ ( T – TAMB )

EXPF

⋅ ( T – TAMB )

• For FORM = 1, 11, or 21

q = H ⋅ u CNTRLND ⋅ ( T

EXPF

– TAMB

EXPF

)

where T is the elemental node point temperature, and TAMB is the associated ambient temperature.

Steady-State Thermal Analysis 83 Temperature Specification (SOL 400)

Further: • For FORM = 0 or 1, the reference temperature is the average of element node temperatures

and the ambient temperatures. • For FORM = 10 or 11, the reference temperature is the surface temperature (average of

element node temperatures). • For FORM = 20 or 21, the reference temperature is the ambient temperature (average of

ambient temperatures). • EXPF -- free convection exponent • T(H) -- free convection coefficient versus temperature • To activate click in the checkbox

The pick panel for creating a CONVECTION entry follows. This is used to select the model nodes.

Units

Parameter

Description

Consistent Units

TAMBIENT

Ambient temperature

C

H

Free convection coefficient

W/(m2*C)

84 Temperature Specification (SOL 400)

Radiation to Space -- RADBC Entry This form of radiant exchange is solely between a set of surface elements and a blackbody space node. There is no radiant exchange involving radiation in enclosures. Following is a picture showing conceptually a radiation to space example:

To create a radiation, to space, boundary condition use the BC: Create BC / Segment BC / RADIATION dropdown menu.

The following form appears for creating the thermal radiation to space boundary condition:

The entries for this form are. • TAMBIENT -- ambient temperature. • TableT -- table used to define ambient temperature vs time. • FAMB -- radiation view factor. • TableF -- table used to define view factor vs time. • ABSORP -- absorptivity.

Steady-State Thermal Analysis 85 Temperature Specification (SOL 400)

• EMIS --emissivity. • FACE_OPT -- surface option, FRONT or BACK. • MID_ID -- wavelength and/or temperature dependent surface properties ID.

The pick panel for creating a RADIATION entry follows. This is used to select the model nodes.

Units

Parameter

Description

Consistent Units

TAMBIENT

Ambient temperature

C

FAMB

View factor between face and ambient pt.

Unitless

ABSORP

Surface absorptivity

Unitless

EMISi

Surface emissivity

Unitless

Special Applications There are several modeling tools that can be used to assist in the creation of a thermal model. MPC Otherwise known as a multipoint constraint. This constraint can be used to specify a node point temperature to be a weighted combination of any number of other node point temperatures.

86 Temperature Specification (SOL 400)

This is accessed using.

A form appears.

The entries for this form are. • DOFO is for the degree-of-freedom of the dependent node • WTO is for the weighting factor for D0F0 • DOFi is for the degree-of-freedom of the i-th independent node • WTi is for the weighting factor for DOFi

The pick panel for creating an MPC entry follows. This is used to select the model nodes.

Steady-State Thermal Analysis 87 Temperature Specification (SOL 400)

Units

Parameter T

Description Temperature at model nodes

Consistent Units C

88 Perform Steady-State Analysis

Perform Steady-State Analysis Several topics are discussed in this section. • How to define a steady-state analysis, including the forms used • The parameters used for the definition of the analysis • The parameters used to control convergence of the nonlinear process

Define a Steady-state Analysis Once a thermal model has been completely defined. • Conduction elements • Material properties • Element properties • Boundary conditions • Material properties • Thermal loading

The steady-state thermal analysis can be performed. A MSC SimXpert Thermal analysis is setup as follows:

Expand Analysis by clicking on the “+”.

Right click Nastran Jobs.

Steady-State Thermal Analysis 89 Perform Steady-State Analysis

Click Create New Job.

Enter a title under Job Name, and select Steady State Heat Transfer (SOL 153).

Right click General Parameters, then click Properties.

90 Perform Steady-State Analysis

Input the needed values. Specifying a value for Default Init Temperature will cause a TEMPD MD Nastran entry to be created.

Right click Cases. There are two possible items to choose. • Add Common Case • Specifications that will be common to all subcases, unless over-ridden by specifications for

subsequently defined subcases • Add Subcase • Specifications for individual subcases

Click Add Common Case.

Enter titles and label. Now, proceed to the second item under Case, that of Add Subcase. • Add Common Case • Specifications that will be common to all subcases, unless over-ridden by specifications for

subsequently defined subcases • Add Subcase • Specifications for individual subcases

Steady-State Thermal Analysis 91 Perform Steady-State Analysis

Click Add Subcase.

Select LBC Set 1 under Select LBC Set.

Right click Subcase: LBC Set 1, then click Add Output Requests.

Right click Output Requests.

Select Add Temperatures, then click Apply.

92 Perform Steady-State Analysis

Click Close.

Right click Subcase Parameters, then click Properties.

Steady-State Thermal Analysis 93 Perform Steady-State Analysis

The entries for this form are discussed later in this section.

Right click Output File, then click Properties.

94 Perform Steady-State Analysis

Convergence of Nonlinear Steady-state Solution Process The form, whose entries are used to specify control of the nonlinear steady-state solution process, is repeated here for convenience. MD Nastran parameter (alpha) names are shown in the MSC SimXpert GUI

entry lists, e.g. “NINC” in “Number of Load Increments” list, instead of numerical values to make it easy to associate the MSC SimXpert Thermal inputs with MD Nastran Thermal inputs. Convergence Criteria The convergence criteria are characterized by the dimensionless error functions and the convergence tolerances. To ensure accuracy and efficiency, multiple criteria with errors measured about temperatures, loads, and energy are provided. Temperature error function Since the error in temperatures is not known, a contraction factor q is introduced to formulate the temperature error function, which is defined as

ui + 1 – ui Δu i ------------------q = -------------------------= ui – ui – 1 Δu i – 1 The final form of the temperature error function is obtained by introducing a weighted normalization. The result is

Steady-State Thermal Analysis 95 Perform Steady-State Analysis

 ωj Δuj

q ω ⋅ Δu q j E u = ------------ -------------------- = ------------ -----------------------1–q ω⋅u 1–q  ωj uj j

where the weighting function { ω } is defined as the square root of the diagonal terms of the tangent matrix [ K T ] , i.e.,

ωj =

K Tjj

Load error function The load error function is defined as

 R j uj

j R⋅u E p = ---------------- = --------------------P' ⋅ u  P'j uj j

where:

{ P' } = { P ld } + { ΔP ld } where { P ld } is the applied thermal load at the previous load step, and { ΔP ld } is the incremental load. Energy error function The energy (or work) error function is defined as

 Rj Δuj

R ⋅ Δu j E w = ------------------- ------------------------P' ⋅ u  P'j uj j

Using the error functions At every iteration, error functions are evaluated and the results printed in the convergence table under the headings EUI, EPI, and EWI. The convergence test is performed by comparing the value of the error functions with the convergence tolerances, e.g.

96 Perform Steady-State Analysis

E u < EPSU ( default = 10 –3 ) E p < EPSP ( default = 10 –3 ) E w < EPSW ( default = 10 – 7 ) where the value of EPSU, EPSP, and EPSW are tolerances specified in the NLPARM Bulk Data entry. The solution has converged if these tests are satisfied. Note that only those criteria selected by the user (specified in the CONV field of the NLPARM entry) are used to checked for convergence. The tolerances should not be too restrictive so that many more iterations are performed than need to be, or too unrestrictive so that there is poor accuracy. It is recommended that the default values be used until better values are found through iteration experience. Iteration Control The incremental and iterative solution processes are controlled by the parameters specified on the NLPARM Bulk Data entry, with the data format and default values described as follows:

1

2

NLPARM

3

4

5

6

7

8

9

ID

NINC

DT

KMETHOD

KSTEP

MAXITER

CONV

INTOUT

EPSU

EPSP

EPSW

MAXDIV

MAXQN

MAXLS

FSTRESS

LSTOL

MAXBIS

MAXR

10

RTOLB

In thermal analysis, the arc-length method (specified by NLPCI command) is disabled. The DT, FSTRESS, MAXR, and RTOLB fields are also ignored and should be left blank for heat transfer. The ID field specifies an integer selected by the Case Control request NLPARM. For each subcase, load and SPC temperature changes are processed incrementally with a number of equal subdivisions defined by the NINC value. The KMETHOD and KSTEP fields specify the tangential matrix update strategy. Three separate options for KMETHOD may be selected. • AUTO • The program automatically selects the most efficient strategy based on convergence rates. At

each iteration, the number of steps required to converge as well as the computing time with and without matrix update are estimated. The tangential matrix is updated if (a) the estimated number of iterations to converge exceeds MAXITER, (b) the estimated time required for convergence with current matrix exceeds the estimated time to converge with matrix update, or (c) the solution diverges. The tangential matrix is also updated on convergence if KSTEP is less than the number of steps required for convergence with the current matrix. • SEMI • This option is identical to the AUTO option except that the program updates the tangential

matrix after the first iteration.

Steady-State Thermal Analysis 97 Perform Steady-State Analysis

• ITER • The program updates the tangential matrix at every KSTEP iteration and on convergence if

KSTEP < MAXITER. However, the tangential matrix is never updated if KSTEP > MAXITER. Note that the Newton-Raphson method is obtained if KSTEP = 1, and the modified Newton-Raphson method is selected by setting KSTEP = MAXITER. The number of iterations for a load increment is limited to MAXITER. If the solution does not converge in MAXITER iterations, the load increment is bisected and the analysis is repeated. If the load increment cannot be bisected (i.e., MAXBIS is reached or MAXBIS = 0) and MAXDIV is positive, the best attainable solution is computed, and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated. The convergence criteria are defined through the test flags in the CONV field and the tolerances in the EPSU, EPSP, and EPSW fields. The requested criteria (combination of temperature error U, load error P, and energy error W) are satisfied upon convergence. The INTOUT controls the output requests for temperatures, heat fluxes, and heat flows. If the option ALL or YES is selected, the output requests specified in the Case Control Data are processed for every computed load increment. If the option is NO, the output requests are processed only for the last load step of the subcase. The MAXDIV limits the divergence conditions allowed for each iteration. The divergence rate is defined as the ratio of energy errors before and after the iteration

{ Δu i } T { R i } E i = -----------------------------------{ Δu i } T { R i – 1 } Depending on the divergence rate, the number of diverging iterations NDIV is incremented as follows:

If E i ≥ 1 or E i < –10 12, then NDIV = NDIV + 2 If – 10 12 < E i < – 1, then NDIV = NDIV + 1 The solution is assumed to diverge when NDIV ≥ MAXDIV . If the solution diverges and the load increment cannot be bisected (i.e., MAXBIS is reached or MAXBIS = 0), the tangential matrix is updated and the analysis is continued. If the solution diverges again and MAXDIV is positive, the best attainable solution is computed, and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated on the second divergence. The BFGS update is performed if MAXQN > 0. As many as MAXQN quasi-Newton vectors can be accumulated. The BFGS update with these QN vectors provides a secant modulus in the search direction. If MAXQN is reached, the tangential matrix is updated, and the accumulated QN vectors are purged. The accumulation resumes at the next iteration. The line search is performed if MAXLS > 0. In the line search, the temperature increment is scaled to minimize the energy error. The line search is not performed if the absolute value of the relative energy error is less than the tolerance LSTOL or if the number of line searches reaches MAXLS.

98 Perform Steady-State Analysis

The number of bisections for a load increment is limited to |MAXBIS|. Different actions are taken when the solution diverges, depending on the sign of MAXBIS. If MAXBIS is positive, the tangential matrix is updated on the first divergence, and the load is bisected on the second divergence. If MAXBIS is negative, the load is bisected every time the solution diverges until the limit on bisection is reached. If the solution does not converge after |MAXBIS| bisections, the analysis is continued or terminated depending on the sign of MAXDIV. Iteration Output At each iteration, the related output data is printed under the following headings:

Parameter

Description

ITERATION

Iteration i

EUI

Relative error in terms of temperature

EPI

Relative error in terms of load

EWI

Relative error in terms of energy

LAMBDA

Rate of convergence

DLMAG

Absolute norm of the residual vector

FACTOR

Final value of the line search parameter

E-FIRST

Divergence rate, initial error before line search

E-FINAL

Error at the end of line search

NQNV

Number of quasi-Newton vectors appended

NLS

Number of line searches performed during the iteration

ENIC

Expected number of iterations for convergence

NDV

Number of occurrences of probable divergence during the iteration

MDV

Number of occurrences of bisection conditions during the iteration

( Rl i )

The solver also prints diagnostic messages requested by DIAG 50 or 51 in the Executive Control Section. DIAG 50 only prints subcase status and NLPARM data, while DIAG 51 prints all data at each iteration. In general, the user should be cautioned against using DIAG 51, because it is used for debugging purposes and the volume of output is significant. It is recommended that DIAG 51 be used only for small test problems. The diagnostic output is summarized as follows: For each entry into NLITER, the following is produced: • Subcase status data • NLPARM data • Core statistics (ICORE, etc.) • Problem statistics (g-size, etc.)

Steady-State Thermal Analysis 99 Perform Steady-State Analysis

• File control blocks • Input file status • External load increment for subcase:

{ ΔP ld }

• Initial nonlinear force vector: { F g } . In thermal analysis, { Fg } is the heat flow vector

associated with nonlinear conduction, convection (CONV and CONVM), and boundary radiation (RADBC), i.e., •

{ F g } = [ K g ] nl { u g } – { N g } CONV – { N g } CONVM – { N g } RADBC

• Initial sum of nonlinear forces including follower forces: { F l } . In heat transfer, { F l } is the heat

flow vector associated with nonlinear conduction, convection, radiation, and nonlinear thermal loads (QBDY3, QVECT, and QVOL), i.e., •

4

{ F l } = [ K l ] nl { u l } + [ ℜ l ] { u l + T abs } – { N l }

• Initial temperature vector: • KFSNL • DELYS:

{ ul }

[ K f s ] T { Δu s }

• Initial residual vector:

{ Rl }

For each iteration, the following is produced: • Temperature increment: • Initial energy:

{ Δu l }

{ Δu l } T { R l }

• New temperature vector: • Nonlinear force vector:

{ ug }

{ Fg }

• Sum of nonlinear forces including follower forces: • New temperature vector: • New residual vector: • Denominator of EUI • Denominator of EPI • Contraction factor: • Remaining time

q

{ ul }

{ Rl }

{ Fl }

100 Perform Steady-State Analysis

For each quasi-Newton vector set, the following is produced: • Condition number:

λ2

• Quasi-Newton vector:

δ

• Quasi-Newton vector:

γ

1 • Energy error: z = --------T δj γj

For each line search, the following is produced: • Previous line search factor: • Previous error:

αk

Ek

• New line search factor:

αk + 1

Recommendations The following are recommendations, designed to aid the user. • Initial temperature estimate: • For highly nonlinear problems, the iterative solution is sensitive to the initial temperature

guess. It is recommended to overshoot (i.e., make a high initial guess) the estimated temperature vector in a radiation-dominated problem. • Incremental load: • Incremental loading reduces the imbalance of the equilibrium equation caused by applied

loads. The single-point constraints (temperature specified by SPC in the Bulk Data) and the applied loads (specified by QBDY1, QBDY2, QBDY3, QHBDY, QVECT, and QVOL) can be incremented. If the solution takes more iterations than the default values of the maximum number of iterations allowed for convergence (MAXITER), the increment size should be decreased. For linear problems, no incremental load steps are required. • Convergence criteria: • At the beginning stages of a new analysis, it is recommended that the defaults be used for all

options. However, the UPW option may be selected to improve the efficiency of convergence. For problems with poor convergence, the tolerances EPSU, EPSP, and EPSW can be increased within the limits of reasonable accuracy. The user may refer to the MD Nastran Thermal Analysis User’s Guide for a detailed description of the above mentioned algorithms.

Steady-State Thermal Analysis 101 Results

Results The results menu (set of forms) allows the user to process any results that have been accessed (imported or attached) by MSC SimXpert. The basic things that can be done under Result in MSC SimXpert are • Display in the computer screen • Deformation • Fringe • Vector • Write out from MSC SimXpert • Results report file

The Result dropdown menu that allows the user access to all the forms is

As can be seen there are two choices • Chart • This is for creating X-Y plots • State Plot • This is for creating on model result plots in the MSC SimXpert screen/viewport

State Plot Look at creating a State Plot type plot first. The form to do this with is shown as follows:

The first thing to select is an item under Plot type, e.g. Fringe Two possible choices will be looked at

102 Results

• Fringe • Vector

Fringe Now, set to creating a Fringe plot.

Select a result case under Result Cases

Select a Result Type.

Click Update Plot button to obtain a state plot.

Steady-State Thermal Analysis 103 Results

To clear the display of the fringe plot click Clear Plot button.

If necessary, select a layer. A form appears for picking a layer.

If needed, an Option can be used.

104 Results

To select only certain finite element entities (a subset of the results) to display the Fringe results on use the following part of the form:

Now, change to selecting Display attributes for the Fringe plot. There are four parts of this. • Fringe attributes • Element Edge display • Spectrum Range • Labels (Font, Title, Model, Legend)

Steady-State Thermal Analysis 105 Results

Sometimes it is necessary to apply a coordinate transformation to the Fringe data. This can be done using the next part of the Fringe form, Data transforms.

The Coordinate transformations are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system • Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems

106 Results

It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Fringe form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged • All entities -- all element results at the common node are averaged

Steady-State Thermal Analysis 107 Results

• Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

108 Results

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Fringe / Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value Vector Change to creating a Vector plot.

Steady-State Thermal Analysis 109 Results

Select a result case under Result Cases.

Select a Result Type.

Click Update Plot button to obtain a vector plot.

To clear the display of the vector plot click Clear Plot button.

110 Results

If necessary, select a layer. A form appears for picking a layer.

If needed, an Option can be used.

To select only certain finite element entities (a subset of the results) to display the Vector results on use the following part of the form:

Change to selecting Display attributes for the Vector plot. There are five parts of this. • Vector attributes • Display on • Spectrum Range

Steady-State Thermal Analysis 111 Results

• Vector component colors • Labels (Font, Title, Model, Legend)

Sometimes it is necessary to apply a coordinate transformation to the Vector data. This can be done using the next part of the Vector form, Data transforms.

The Coordinate transformations are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system

112 Results

• Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Vector form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

Steady-State Thermal Analysis 113 Results

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged • All entities -- all element results at the common node are averaged • Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

114 Results

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value

Steady-State Thermal Analysis 115 Results

Chart Plot Next, look at creating a Chart (X-Y) plot. The form to do this with is shown as follows:

This first thing to select is a result case under Curve Data / Result Cases.

Select a Result Type.

116 Results

Screen pick a set of nodes (along a path).

Click Add Curves button.

Steady-State Thermal Analysis 117 Results

If necessary, select a layer. A form appears for picking a layer.

If needed, an Option can be used.

To specify a type of finite element entity to display the X-Y plot data results for use the following part of the form:

Now, change to specifying the Transforms for the Chart data.

There are five types of Transforms. • Coordinate transforms • Scale factor

118 Results

• Filter • Result averaging • Result extrapolation

Sometimes it is necessary to apply a coordinate transformation to the Chart (X-Y) data. This can be done using the following form:

The Coordinate transforms are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system • Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems The data can be filtered as follows:

Steady-State Thermal Analysis 119 Results

It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, and 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Chart / Transforms form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged • All entities -- all element results at the common node are averaged

120 Results

• Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

Steady-State Thermal Analysis 121 Results

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Chart / Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value

122 Results

Transient Thermal Analysis 121

Transient Thermal Analysis The topics discussed in this section are. • Overview of heat transfer, in brief • Presentation of heat transfer equations, in brief • Geometry, import and create • Thermal material properties • Element properties • Meshing geometry • Loads and boundary conditions • Performing transient thermal analysis • Viewing results • Example of a transient thermal analysis

122 Overview and Formulation

Overview and Formulation Thermal problems can be categorized as steady-state or transient, linear or nonlinear. Transient analyses are characterized by solution evolution over time, and in addition to energy exchange with the environment, involves thermal energy storage. Steady-state analyses are concerned with state point solutions to fixed boundary condition problems. Nonlinearities enter into both steady-state and transient solutions due to several influences. The most common nonlinearity is associated with temperature dependent material properties, in particular thermal conductivity and specific heat. Other nonlinearities are introduced from application of boundary conditions principally convection and radiation. All nonlinear analyses necessarily involve solution iteration, error estimation, and some form of convergence criteria. MD Nastran attempts to do this as efficiently and trouble free as possible.

Formulation Steps of Solution Process in Brief The familiar conduction heat transfer equation is

q· 1 ∂T 2 ∇ T + --- = --α ∂t k where: T

=

temperature

=

Laplacian operator

q·

=

rate of heat generation per unit volume

k

=

thermal conductivity of solid material

α

=

thermal diffusivity

t

=

time variable

∇

2

A transition is made from this equation (strong form) to a variational formulation (weak form). The matrix equation corresponding to the variational formulation is

· M {T} + K {T} = {F}

Transient Thermal Analysis 123 Overview and Formulation

where:

{T}

=

temperature vector

{ T· }

=

first derivative of temperature vector

M

=

heat capacity matrix

K

=

heat conductivity matrix

{F}

=

heat supply vector

The MD Nastran Thermal transient equation derived from this equation is 4 [ B ] { T· } + [ K ] { T } + [ ℜ ] { T + T abs } = { P } + { N }

where: {T}

=

temperature vector

· {T}

=

first derivative of temperature vector

{Tabs}

=

absolute temperature vector

B

=

heat capacity matrix

K

=

heat conduction matrix

[ℜ]

=

radiation exchange matrix

{P}

=

applied heat flow vector

{N}

=

nonlinear heat flow vector that is temperature dependent

The user may refer to the MD Nastran Thermal Analysis User’s Guide for a detailed description of the above and following mentioned algorithms. This is a nonlinear matrix equation. It is solved using the Newton-Raphson iteration scheme. A residual load vector function is defined as the difference between the applied thermal load vector and the thermal load vector due to element temperature and temperature rate. 4 { R ( t ) } = ( { P } + { N } ) – ( [ B ] { T· } + K { T } + [ ℜ ] { T + T abs } )

124 Overview and Formulation

The residual load vector function, at a given time, is equal to zero for the solution temperature vector at that time. The task is to determine the solution temperatures as a function of time. The residual load vector function is approximated by its first-order Taylor series expansion about the temperature vector from the i-th iteration, for the n+1 time point (the solution is known for time point n).

∂{R} i { R n + 1 } ≅ { Rn + 1 } + ------------∂{T}

i

i

( { Tn + 1 } – { Tn + 1 } )

n+1

The Taylor series expansion is evaluated at the temperatures for the (i + 1)-th iteration, and set equal to zero.

{ Rn + 1 }

i+1

∂{R} ≅ { R n + 1 } + ------------∂{T } i

i

( { Tn + 1 }

i+1

i

– { Tn + 1 } ) = { 0 }

n+1

From this the following equation is arrived at:

∂-------------------( – { R } -) ∂{T}

i

i

{ ΔT n + 1 } = { R n + 1 }

i

n+1

or

K˜ T

i

i

n+1

{ ΔT n + 1 } = { Rn + 1 }

i

where i

{ ΔT n + 1 } = { T n + 1 }

i+1

– { Tn + 1 }

i

Note:

{ Tn + 1 }

i+1

i

= { T n + 1 } + { ΔT n + 1 }

i

where (continued)

K˜ T

i n+1

∂ ( –{ R } ) = --------------------∂{T}

i n+1

i 1 = --------- [ B ] + KT θΔt n+1

where the approximation for the time derivative is given by i i 1 1 { T· n + 1 } ≅ --------- ( { T n + 1 } – { T n } ) +  1 – --- { T· n } θ θΔt

Another approximate representation is used as follows:

i

1 ≅ --------- [ B ] + K T n + 1 θΔt n

n

Transient Thermal Analysis 125 Overview and Formulation

KT

n

≅( K

n

∂{N} 3 + 4 [ ℜ ] n { T n + T abs } ) – ------------∂{T }

n

The residual load vector function for the i-th iteration is given by i

i

{ Rn + 1 } = ( { Pn + 1 } + { Nn + 1 } ) – ( B

{ T· n + 1 } + K n+1 i

i

i n+1

i

{ Tn + 1 } +

i4

i

[ ℜ ] n + 1 { T n + 1 + T abs } ) This is an iterative process. Start with i = 0. Thus, the first equation to be solved is

K˜ T From

0

0

n+1

{ ΔT n + 1 } = { R n + 1 }

0

0 { ΔT n + 1 } the next temperature vector is found from 1

0

{ T n + 1 } = { T n + 1 } + { ΔT n + 1 }

0

Next, use i = 1. The next equation to be solved is

K˜ T From

1

1

n+1

{ ΔT n + 1 } = { R n + 1 }

1

1 { ΔT n + 1 } the next temperature vector is found from 2

1

{ T n + 1 } = { T n + 1 } + { ΔT n + 1 }

1

This process is repeated until a converged solution is obtained, {Tn+1}m. The process is repeated for the next time point, n+2 (tn+2 = tn+1 + Δtn+1). Set {Tn+2}0 = {Tn+1}m. Since matrix decomposition is time consuming, MD Nastran does not update the left-hand side matrix at each iteration. The tangential matrix is updated only when the solution fails to converge or the iteration efficiency can be improved. However, the residual vector is updated at each iteration. In concert with the Newton-Raphson method, the following options are provided to improve the efficiency of the iteration process: • Tangential matrix update strategy • Line search method • Bisection of loads • Quasi-Newton (BFGS) updates

126 Overview and Formulation

These options are specified on NLPARM (steady-state analysis) or TSTEPNL (transient analysis) Bulk Data entries; this will be discussed later in the section on transient analysis. In general, if the solution process diverges, a line search algorithm, a bisection of loads method, or the quasi-Newton update method are implemented in an effort to improve the solution obtained. If the solution still fails to converge using all the above methods, the tangential stiffness matrix is updated, and the iteration is resumed. The user may refer to the MD Nastran Handbook for Nonlinear Analysis for a detailed description of the above mentioned algorithms.

Transient Thermal Analysis 127 Geometry Parts and Create Geometry

Geometry Parts and Create Geometry Currently, access to geometry is through • Importing geometry, e.g. Parasolid surface • Creation of only basic geometric shapes, e.g. create plane

The form that is used to import geometry is

As can be seen it is possible to import geometry that is • STL • Parasolid • CATIA • IGES

It is also possible to import FEM from • MD Nastran

128 Geometry Parts and Create Geometry

Import a Parasolid Solid

The image of the imported Parasolid solid is

Create a Local Coordinate System There are several ways to create a coordinate system

Transient Thermal Analysis 129 Geometry Parts and Create Geometry

• One node to specify a local coordinate system • Select a point (e.g. node) or specify a location of the origin. • Specify the basic X-, Y-, or Z-axis to have the local 3 axis, of the local coordinate system to

be created, aligned with. • This is only for a fixed coordinate system. • Two nodes to specify a local coordinate system • The first point (e.g. node) selected or location specified is for the origin. • The second point will be on the local w-axis. • This is only for a fixed coordinate system. • Three nodes to specify a local coordinate system • The first point (e.g. node) selected or location specified is for the origin. • The second point will be on the local x-axis. • The third point will be on the local y-axis. • This is for either a fixed or moving coordinate system.

A sample of creating a local cylindrical coordinate system for a Parasolid solid is shown as follows:

To access the form to create the local coordinate system use the following:

130 Geometry Parts and Create Geometry

This is the pick panel and form. They are used to specify the locations of the points, or the pick panel is used for selecting existing nodes or points on elements.

Transient Thermal Analysis 131 Geometry Parts and Create Geometry

After picking several nodes the cylindrical coordinate system is created.

132 Materials

Materials A material form appears when one is selected from the Material menu that is in the MSC SimXpert Thermal main menu. The selections made under the Material menu will determine which material form appears, and ultimately, which MD Nastran Thermal material will be created. The following pages give a description of the Material forms and details of all the material property definitions supported by MSC SimXpert Thermal. Only material records/data that are referenced by an element property region will be written out of MSC SimXpert Thermal. The following topics are covered for materials: • Supported materials for transient analysis • Required material properties to define a model • Units • Method of creation of materials • Use of fields for material definition

Supported Materials for Transient Analysis The material properties are for modeling conduction, convection, and radiation. • Conduction • Thermal conductivity of solid material • Isotropic, temperature independent • Isotropic, temperature dependent • Anisotropic, temperature independent • Anisotropic, temperature dependent • Convection • Free convection heat transfer coefficient • Isotropic, temperature independent • Isotropic, temperature dependent • Radiation • Absorptivity of radiating surface • Emissivity of radiating surface • Temperature independent • Temperature dependent

Transient Thermal Analysis 133 Materials

Required Material Properties The above covered the possible material properties that can be created in MSC SimXpert Thermal for MD Nastran Thermal. Now, the material properties that are needed (a must) for specific types of steadystate analysis are discussed. Conduction Steady-state conduction thermal behavior only needs thermal conductivity, K, to model it. So, the MatIsotropic form is needed for isotropic material, and the MatAnisotropic form is needed for anisotropic material.

Notice that only the thermal conductivity field, K, has data. Convection Steady-state convection thermal behavior needs properties that depend on the type of convection. Free convection needs the free convection heat transfer coefficient, H. This is input using the CONVECTION form.

134 Materials

Radiation Radiation to space steady-state thermal behavior needs the surface absorptivity and emissivity to model it. So, the RadMat form is needed to specify these.

Units The following table lists the units that correspond to the fields of the MatIsotropic or RadMat forms.

Parameter

Description

Consistent Units

K

Thermal conductivity

W/(m*C)

CP

Specific heat at constant pressure

J/(kg*C)

RHO

Density

kg/m3

H

Free convection heat transfer coefficient

W/(m2*C)

MU

Dynamic viscosity

N*sec/m2

HGEN

Volumetric internal heat generation

W/m3

REFENTH

Reference enthalpy

J/kg

TCH

Lower temperature limit for phase change

C

TDELTA

Temperature domain for phase change

C

QLAT

Latent heat

J/kg

ABSORP

Surface absorptivity

Unitless

EMISi

Surface emissivity

Unitless

Creation Methods The types of material for which their method of creation are shown are: • Isotropic • Anisotropic • Isotropic, temperature dependent

Transient Thermal Analysis 135 Materials

Conduction There are four types of material models. Two are for temperature independent properties, and two are for temperature dependent properties. First, is for isotropic, temperature independent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears:

Data can be specified in this form, as is shown below.

Second, is for anisotropic, temperature independent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

136 Materials

When this is used the following form appears:

Third, is for isotropic, temperature dependent thermal properties. This is created in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears (this is the same form whose image was shown previously):

To use this form click in the check box for conductivity, T(K). Double click in the T(K) cell, and select Select or Create. For this example select Create.

Transient Thermal Analysis 137 Materials

The following form for selecting the material entry type appears.

138 Materials

Select a table type to specify the temperature dependent material property, e.g. TABLEM1.

Enter data into the Grapher.

Transient Thermal Analysis 139 Materials

• For details on creating a graph see Chart in the Charting Document.

The final MatIsotropic form looks like the following:

The process is similar for the MatAnisotropic form.

140 Materials

Convection The material properties for convection can be specified using the same forms that are used for conduction. The difference is that the form is used to specify properties of the fluid. The properties that are defined are • Thermal conductivity of the fluid • Heat capacity of the fluid • Dynamic viscosity of the fluid

The MatIsotropic form might be filled-out as follows:

Radiation The material properties for radiation are specified using the RadMat form. The form is accessed in MSC SimXpert Thermal as follows: (right click Material)

When this is used the following form appears:

Transient Thermal Analysis 141 Materials

Data can be specified in this form, as is shown below.

142 Properties for Elements

Properties for Elements An element property form appears when one is selected from the Property menu that is in the MSC SimXpert Thermal Model tree browser. The selections made under the Property menu will determine which Property form appears. There are several options available when creating element properties. The following pages give a description of a few of the Property forms and details of all the element property definitions supported by MSC SimXpert Thermal. This section deals with creating properties that correspond to topological shapes called elements. The topological shapes do not represent finite elements until they have associated element properties. An example of this is a four noded quadralateral shape.

It could be used to represent a 2D plate or 2D solid finite element. Shell property To create a property, to be associated to a 2D topological shape, use the following in MSC SimXpert Thermal: (right click Property)

Transient Thermal Analysis 143 Properties for Elements

When this is used the following form appears:

Data can be specified in this form as follows:

First, double click in the data cell MID, and select Create.

144 Properties for Elements

Specify the thermal conductivity, specific heat, and density.

Create the PSHELL element property. This property can be used during creating a 2D shell element mesh. Solid property Now, the steps in MSC SimXpert needed to create a property set corresponding to a 3D topological shape are shown. (right click Property)

Transient Thermal Analysis 145 Properties for Elements

When this is used the following form appears:

Data can be specified in this form as follows:

First, double click in the data box MID, and select Create.

146 Properties for Elements

Specify the thermal conductivity, specific heat, and density.

Create the PSOLID element property.

Supported Element Types and Uses There are several types of elements • Conduction elements • Special elements • Simple resistive components • User defined complex element types • Lumped thermal capacitance • 2D elements for coupling applied heat flux, convection, and radiation to conduction surfaces

Conduction Elements There are 1D, 2D, 3D, and axisymmetric conduction finite elements.

1-D

2-D

3-D

CBAR

CQUAD4

CHEXA

CBEAM

CQUAD8

CPENTA

CBEND

CTRIA3

CTETRA

CONROD

CTRIA6

AXISYM CTRIAX6

CROD CTUBE The heat flow through these elements is in the parametric directions of the elements. • 1D element • Heat flow is only along the centerline of the element, not normal to the centerline of the

element • 2D element

Transient Thermal Analysis 147 Properties for Elements

• Heat flow is only in the plane of the element, not normal to the plane of the element • 3D element • Heat flow is in all three directions of the element • Axisymmetric element • Heat flow is only in the radial or centerline direction of the element, not in the circumferential

direction So, do not use an element that does not have a parametric coordinate in a direction that heat flow must be modeled The performance of linear finite elements, e.g. CQUAD4 element, is as good as that of parabolic finite elements, e.g. CQUAD8 element, for 2D or 3D. Recommendations • Use linear elements, unless have substantial curvature and desire to minimize the number of

elements • If doing thermal analysis (calculate temperatures) to structural analysis (stress analysis) mapping

(loads are temperatures from thermal analysis), it is best to use the same type of element that is to be used for the structural analysis, e.g. Tet10, and not Tet4. • Loads and boundary conditions do not affect which type of element should be used

Special Elements This category is for elements that are not finite elements, but of course they can be used in modeling a thermal process. There are two types of special elements. They are. • CELASi (scalar spring) -- simple resistive component

L ΔT = q·  ------ = q· R kA • DMI or DMIG (direct matrix input) -- complex component

name = Xij • TF -- dynamic transfer function • CDAMPi (scalar damper) -- lumped thermal capacitance

Boundary Condition or Heat Flux Surface Elements To apply convection, radiation, or heat flux to a conducting surface (2D element, e.g. CQUAD4) or face (3D element, e.g. CHEXA) it is necessary to apply them to a geometric surface, which in turn is

148 Properties for Elements

connected to conducting elements. The geometric surfaces are named CHBDYE, CHBDYG, or CHBDYP, or to simplify, CHBDYi. This is shown conceptually as follows.

The user does not explicitly create the CHBDYi elements. They are created from within MSC SimXpert Thermal as a result of creating the loads and boundary conditions.

Use of Fields to Model Variable Element Properties Some examples of variable element properties are • Variable element thickness, t(x,y,z)

These types of parameters can be represented using Fields.

Transient Thermal Analysis 149 Properties for Elements

The Fields creation form is accessed using the following dropdown menu: (right click Fields)

Under Fields there are several inputs and choices that can be made. • Name • Method • Function • Tabular • Discrete FEM • Value Type • Scalar • Vector • String • Function or Table • Scalar Function • Vector Function; Component 1, 2, 3 • Table with Active Independent Variables X, Y, Z and Values

150 Properties for Elements

• Table with Nodes and Values

An example of the creation and use of a scalar Field follows:

Transient Thermal Analysis 151 Properties for Elements

Now, select the field in this form for F_T. This deselects the field T that is used for input of a constant value of thickness, and activates the field F_T that is used for selecting the Field named “thickness”.

Now, double click in the field (cell) F_T to select the Field named “thickness”.

Select the Field named thickness.

152 Properties for Elements

Now, complete entering information into the PSHELL form.

Transient Thermal Analysis 153 Meshing and Element Creation

Meshing and Element Creation Once the following has been done • Import the geometry, or create the geometry in MSC SimXpert • Create material property • Create element property, with it associated to the material property

the geometry can be meshed, with the resulting topological shapes associated to the element property.

Meshing Following is a brief presentation on how to mesh a surface. Import the geometry

Create the material property.

154 Meshing and Element Creation

Create the element property, using the material property.

Display “Collection” form to be able to see the Part list (contains the “parts” of the model). To do this right-click over the MSC SimXpert Thermal main menu area, and select “Collection”.

The “Part” form appears, as shown.

There is only one Part, it is named “P2”. It is not active (entities created, e.g. elements created by meshing, are not automatically assigned to it, Part P2). This is observed backaches the label P2 is not in the list box titled “Current:” at the top of the form.

Transient Thermal Analysis 155 Meshing and Element Creation

To make the Part P2 active mouse-click with the middle button on the name “P2” in the Part form.

Now, the previously imported surface can be meshed, with the mesh being associated to the Part “P2”. However, before the surface is meshed it is necessary to associate the previously created element property to Part “P2”. This is done by mouse-clicking with the right button on the name “P2”, and selecting Modify. The Modify Part form appears.

Double click in the 2D_PROP cell, and select Select.

156 Meshing and Element Creation

Select the property named PSHELL_1. The following form, named Modify Part, appears as follows:

Now, mesh the imported surface. This is done by accessing the form for Mesher.

Transient Thermal Analysis 157 Meshing and Element Creation

Using this causes the Mesher pick panel and Mesher form to appear.

The first thing to do is to select the entities, e.g. surfaces, to be meshed. This can be done using the Advanced button (Extended Pick Dialog), but since there is only one surface to be meshed it is only necessary to pick the button “All” in the Mesher Pick Panel, or screen picking the geometric surface directly. The surface ID, 1, appears in the Mesher form. Then, enter the desired element size under Element Size in the Mesher form. After doing this, pick the button “Done” in the Mesher Pick Panel or OK in the Mesher form.

158 Meshing and Element Creation

The mesh obtained is shown as follows:

The 2D element mesh will have been created. Upon exporting the model from MSC SimXpert Thermal, 2D CQUAD4 elements will be created; the following MD Nastran entries will be created. • GRID (nodes) • CQUAD4 (2D shell elements) • MAT4 (isotropic material property) • PSHELL (shell element property)

Mesh Control Using the previous model, create a new mesh using control of element size. Use the following to change the size of elements that are created as a result of meshing. First, delete the existing mesh that is on the surface. Next, change the size of the elements to be created by using the following pick:

Transient Thermal Analysis 159 Meshing and Element Creation

Using this causes the Mesh Size pick panel and Mesh Size form to appear.

160 Meshing and Element Creation

Select the button All to select all the edges of the surface, with 1, 2, 3, 4 entered into Support in the form Mesh Size. Enter 5 in Pitch, then click OK. Then, mesh the surface as before.

Merge Coincident Nodes For many analysis it is necessary to have adjacent elements connected. The elements (adjacent) created by meshing a single geometric entity, e.g. surface, are automatically connected. The elements at geometric interfaces (where different geometric entities meet) are not automatically connected. This allows the user to decide if those elements should be connected, depending on if the analysis model needs to include nonlinear contact. When elements at geometric interfaces need to be connected this can be done in MSC SimXpert Thermal. First, import or create two adjacent geometric surfaces.

Transient Thermal Analysis 161 Meshing and Element Creation

Mesh both surfaces using the same element size for both meshes.

Show where the elements are not connected using the following, View: Highlight FE Boundary:

162 Meshing and Element Creation

Following, is the image of the display before the adjacent elements, at the geometric interface, are connected:

The elements at the interface are connected by merging the nodes at the interface using Node: Merge Coincident Nodes.

Transient Thermal Analysis 163 Meshing and Element Creation

The following Merge Coin. Nodes pick panel and form appears:

Select All, then Done. The form for specifying the merging tolerance follows.

Following is the image of the display after the adjacent elements, at the geometric interface, are connected.

164 Loads and Boundary Conditions, and LBC Sets

Loads and Boundary Conditions, and LBC Sets Now, that the mesh(s) has been created, along with material and element properties, the remaining part of the model to define is the loads and boundary conditions. This section deals with • Thermal loads • Heat flux applied to surface elements • Heat flux applied to an area defined by nodes • Directional heat flux from a distant source • Volumetric internal heat generation • Thermal boundary conditions • Convection, free (SimXpert R1.1) • Convection, forced (SimXpert R2) • Radiation, to space (SimXpert R1.1) • Radiation, in enclosure (SimXpert R2) • Temperature • Load and boundary condition set • Combination of loads and boundary conditions • Scale factors • Priority of loads and boundary conditions

Sample of Loads and Boundary Conditions Forms A few MSC SimXpert load and boundary condition (LBC) forms are shown, and their use described. A simple model is used to do this. The model was imported into MSC SimXpert Thermal from an MD Nastran bulk data file.

Three LBCs are to be applied to the model.

Transient Thermal Analysis 165 Loads and Boundary Conditions, and LBC Sets

The location of a LBC is established by selecting (picking) nodes/elements as the LBC is created. This is shown below. First, a heat flux is to be applied to the bottom surface of the model. The form and pick panel to do this with is accessed using BC: Create BC / Segment BC / FLUX.

The following form appears.

Now, enter a value for Q0 (heat flux into element), say 2020.0

Make the heat flux a function of time. To do this click in the check box for TableQ.

166 Loads and Boundary Conditions, and LBC Sets

Double click in the cell for TableQ, and select Create.

The grapher form, having been modified with data and labels, is shown as follows:

Click Modify, then click Exit in the grapher form.

Transient Thermal Analysis 167 Loads and Boundary Conditions, and LBC Sets

In the Defaults For FLUX form click Store, then Exit. The next thing to do is to select a set of nodes (where the flux is to be applied) at the bottom of the model. In the Create FLUX pick panel select Nodes.

Then, change from Single picking to Rectangular Window picking.

Select the nodes at the bottom of the model.

Click Done, then click Exit in the Create FLUX pick panel.

168 Loads and Boundary Conditions, and LBC Sets

Now, apply radiation to the top surface of the model. The form and pick panel to do this with is accessed using BC: Create BC / Segment BC / RADIATION.

The following form appears.

Enter the following • For TAMBIENT 490.0 • TableT (table used to define ambient temperature vs time), null. • For FAMB 1.0 • TableF (table used to define view factor vs time), null. • Click checkbox for MID_ID (scroll to right in form), then double click in MID_ID cell, and

enter, in RADM form, 0.3 for ABSORP, and 0.5 for EMIS1. Click Store, then Exit.

Transient Thermal Analysis 169 Loads and Boundary Conditions, and LBC Sets

The next thing to do is to select a set of nodes at the top of the model. In the Create RADIATION pick panel select Nodes.

Select the nodes at the top of the model.

Click Done, then click Exit in the Create RADIATION pick panel.

170 Loads and Boundary Conditions, and LBC Sets

Now, apply free convection to the side surfaces of the model. The form and pick panel to do this with is accessed using BC: / Create BC / Segment BC / CONVECTION.

The following form appears.

Enter the following • For TAMBIENT enter 490.0 • TableT (table used to define ambient temperature vs time), null. • For H enter 0.006 • TableH (table used to define convection coefficient vs time), null.

Click Store, then click Exit.

Transient Thermal Analysis 171 Loads and Boundary Conditions, and LBC Sets

The next thing to do is to select a set of nodes on the sides of the model. In the Create CONVECTION pick panel select Nodes.

Select the nodes on the sides of the model.

Click Done, then click Exit in the Create CONVECTION pick panel. Now, there are three LBCs.

172 Loads and Boundary Conditions, and LBC Sets

LBC Set for Sample LBC forms Example Using the three LBCs just created, a LBC Set will be created. Subsequently, this set will be accessed for defining an MD Nastran Thermal job. The form for doing this is accessed using BC: Create LBC Set.

The following form appears for creating an LBC Set using • Heat flux • Radiation, to space • Convection, free

Do the following: • Enter a name in the list box LBC Set Name • Select all three of the LBC names under Select Existing LBCs: FLUX_1, CONVECTION_1,

RADIATION_1

Transient Thermal Analysis 173 Loads and Boundary Conditions, and LBC Sets

The form will look like the following:

Click OK to create the LBC Set. These three LBCs can be used for an analysis by using this LBC Set.

Supported Load Types As previously mentioned the thermal load types are • Thermal loads • Heat flux applied to surface elements -- MD Nastran entry QBDY1 • Heat flux applied to an area defined by nodes -- MD Nastran entry QHBDY • Directional heat flux from a distant source -- MD Nastran entry QVECT • Volumetric internal heat generation -- MD Nastran entry QVOL

Comments about the various load dialogs follows:

174 Loads and Boundary Conditions, and LBC Sets

Heat Flux Applied to Surface Elements -- QBDY1 Entry

The form for creating a QBDY1 entry follows:

As described previously: • Q0 -- heat flux into element • TableQ -- table used to define flux vs time

Click Store, then click Exit.

Transient Thermal Analysis 175 Loads and Boundary Conditions, and LBC Sets

In the pick panel select the application region/domain entities over which the heat is to be applied. This is done by picking nodes using the pick panel.

Units

Parameter

Description

Consistent Units

Q0

Heat flux into an element

W/m2

TableQ

Function of time

Unitless

Heat flux Applied to an Area Defined by Nodes -- QHBDY Entry

176 Loads and Boundary Conditions, and LBC Sets

The Defaults For QHBDY form appears.

The entries for this form are. • FLAG = POINT, LINE, REV, AREA3, AREA4, AREA6, AREA8 • POINT, LINE, REV, AREA3, AREA4, AREA6, AREA8 uses 1, 2, 2, 3, 4, 4-6, 5-8 points,

respectively, to define an area for the heat flux. • Q0 is the magnitude of thermal flux onto the “face” • AF is the area factor • Areas that are defined with 1 or 2 points, for which an area cannot be calculated using the

location of the points, must have an AF value specified. For other areas, e.g. AREA4, the area is calculated by MD Nastran. The pick panel for creating a QHBDY entry follows. This is used to select the model nodes.

Transient Thermal Analysis 177 Loads and Boundary Conditions, and LBC Sets

Units Parameter

Description

Consistent Units

Q0

Magnitude of thermal flux into face

W/m2

AF

Area factor; depends on FLAG

m2, m, N/A

Directional Heat Flux from a Distant Source -- QVECT Entry

The Defaults For VECFLUX form appears.

The entries for this form are. • Q0 = magnitude of thermal flux vector onto the “face”. • TableQ -- table used to define flux vs time. • TSOUR = temperature of the radiant source. • CE -- coordinate system ID number for thermal vector flux. • Ei -- vector components (direction cosines in coordinate system CE) of the thermal vector flux. • ABSORP -- 0.0 <= absorptivity <= 1.0 • TableA -- table used to define absorptivity vs time. • EMIS -- 0.0 <= emissivity <= 1.0 • FACE_OPT -- surface option, FRONT or BACK. • MID_ID -- wavelength and/or temperature dependent surface properties ID.

178 Loads and Boundary Conditions, and LBC Sets

The pick panel for creating a QVECT entry follows. This is used to select the model nodes.

Units Parameter

Description

Consistent Units

Q0

Magnitude of thermal flux vector onto face W/m2

TableQ

Table used to define flux vs time

Unitless

TSOUR

Temperature of radiant source

K

ABSORP

Value of absorptivity

Unitless

TableA

Table used to define absorptivity vs time

Unitless

Volumetric Internal Heat Generation -- QVOL Entry

Transient Thermal Analysis 179 Loads and Boundary Conditions, and LBC Sets

The Defaults For QVOL BC form appears.

The entries for this form are. • QVOL = power input per unit volume produced by heat conduction elements. • TableQ -- table used to define power input per unit volume vs time. • CNTRL -- control point ID used for controlling heat generation.

The pick panel for creating a QVOL entry follows. This is used to select the model elements.

Units Parameter

Description

Consistent Units

QVOL

Power input per unit volume produced by a heat conduction element

W/m3

TableQ

Table used to define power input per unit volume vs time

Unitless

180 Loads and Boundary Conditions, and LBC Sets

Supported Boundary Condition Types As previously mentioned the thermal boundary condition types are. • Temperature -- MD Nastran entry TEMPBC, or SPC • Convection, free-- MD Nastran entry CONV • Radiation, to space -- MD Nastran entry RADBC

Comments about the various boundary condition forms follow: Temperature Applied to Model Nodes -- TEMPBC Entry

The Defaults For TEMPBC BC form appears.

The entries for this form are. • T is the temperature at model nodes • SID is the set ID • TYPE is the type of temperature boundary condition • STAT -- constant • TRANS -- time varying

Transient Thermal Analysis 181 Loads and Boundary Conditions, and LBC Sets

The pick panel for creating a TEMPBC entry follows. This is used to select the model nodes.

Units Parameter T

Description Temperature at model nodes

Consistent Units C

The TEMPBC boundary condition can be used to enforce constant temperature at nodes, or it can be used to enforce time varying temperature. Like TEMPBC, the SPC boundary condition can be used to enforce constant temperature at nodes, however, the temperature cannot vary with time, it can only be constant. Initialization Temperature Applied to Model Nodes -- TEMP Entry For the solution procedure there must be a temperature specified at each node, some being constant, some being time dependent, and others given a value just to begin the solution process. Some nodes will have their temperature specified using the TEMPBC or SPC entry. These temperatures will remain unchanged or change following a time dependent function throughout the solution process. The other nodes must have a specified initialization temperature just to begin the solution procedure. This is done using the TEMP entry. Units Parameter T

Description Temperature at model nodes

Consistent Units C

182 Temperature Specification (SOL 400)

Temperature Specification (SOL 400) Overview Temperature specification can be done for several reasons. • Specifying temperature boundary conditions. They can be either constant or time dependent. • Specifying initial conditions. The term initial refers to two things. • For steady-state heat transfer analysis, the temperature for conduction material properties. • For steady-state heat transfer analysis, the starting temperature for the iteration process. • Specified temperature set is used to determine equivalent static loads from external loads,

thermal loads, and element deformations. • Both the thermal loading and temperature dependent material properties are to use the same

temperature set. • Specifying the temperature set for the temperature dependent material properties.

Uses of Temperature LBC for Heat Transfer GUI More detailed information about what temperature sets the Temperature LBC GUI can be used to create for heat transfer analysis is given below. Temperature Boundary Condition This is for creating a temperature boundary condition. The information that must be provided is • Application region -- list of nodes for which the temperature is to be specified. • Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function). • Temperature versus time scaling function -- the selected time dependent function (table, e.g.

TABLED1) is multiplied by the temperature.

Uses of 0D, 1D, 2D Initial Temperature for Heat Transfer Analysis To specify the initial (starting) temperature for steady-state heat transfer analysis, this is applicable. Initial Conditions If it desired to specify the temperature set for conduction material properties and the starting temperature for the iteration process, for steady-state heat transfer analysis, the following input is required. • Application region -- list of nodes for which the temperature is to be specified.

Transient Thermal Analysis 183 Temperature Specification (SOL 400)

• Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function).

Uses of 0D, 1D, 2D Material Temperature Dependency Temperature Dependent Material Properties Specify the temperature set for temperature dependent material properties. • Application region -- list of elements for which the temperature is to be specified. • Temperature -- a constant value of temperature, or a spatially (x,y,z) varying temperature field

(function).

Free Convection to Ambient Temperature -- CONV Entry Convection heat transfer occurs whenever a body is placed in a fluid at a higher or a lower temperature than that of the body. As a result of the temperature difference, there is heat transfer between the body and the fluid. This causes a change of density of the fluid adjacent to the surface of the body where the convection is occurring. This change of fluid density results in the movement, upward or downward, of the fluid. If the motion of the fluid is caused solely by differences of fluid density, and not by a pump or fan adding to the fluid motion, the heat transfer is called natural or free convection. Following is a picture showing conceptually a free convection example.

184 Temperature Specification (SOL 400)

To create a free convection, to an ambient temperature, boundary condition use the BC: Create BC / Segment BC / CONVECTION dropdown menu.

The following form appears for creating the thermal free convection boundary condition:

The entries for this form are. • TAMBIENT -- ambient temperature • TableT -- table used to define ambient temperature vs time • H -- free convection coefficient • TableH -- table used to define convection coefficient vs time • FORM -- used to specify the type of formula used for free convection • For FORM = 0, 10, or 20, EXPF is an exponent of (T- TAMB), where the convective heat

transfer is represented by

q = H ⋅ uCNTRLND ⋅ ( T – TAMB )

EXPF

⋅ ( T – TAMB )

• For FORM = 1, 11, or 21

q = H ⋅ u CNTRLND ⋅ ( T

EXPF

– TAMB

EXPF

)

where T is the elemental node point temperature, and TAMB is the associated ambient temperature.

Transient Thermal Analysis 185 Temperature Specification (SOL 400)

• Further: • For FORM = 0 or 1, the reference temperature is the average of element node temperatures

and the ambient temperatures. • For FORM = 10 or 11, the reference temperature is the surface temperature (average of

element node temperatures). • For FORM = 20 or 21, the reference temperature is the ambient temperature (average of

ambient temperatures). • EXPF -- free convection exponent • T(H) -- free convection coefficient versus temperature • To activate click in the checkbox

The pick panel for creating a CONVECTION entry follows. This is used to select the model nodes.

Units Parameter

Description

Consistent Units

TAMBIENT

Ambient temperature

C

TableT

table used to define ambient temperature vs time

Unitless

H

Free convection coefficient

W/(m2*C)

TableH

table used to define convection coefficient vs time

Unitless

186 Temperature Specification (SOL 400)

Radiation to Space -- RADBC Entry This form of radiant exchange is solely between a set of surface elements and a blackbody space node. There is no radiant exchange involving radiation in enclosures. Following is a picture showing conceptually a radiation to space example:

To create a radiation, to space, boundary condition use the BC: Create BC / Segment BC / RADIATION dropdown menu.

The following form appears for creating the thermal radiation to space boundary condition:

The entries for this form are. • TAMBIENT -- ambient temperature. • TableT -- table used to define ambient temperature vs time • FAMB -- radiation view factor. • TableF -- table used to define view factor vs time

Transient Thermal Analysis 187 Temperature Specification (SOL 400)

• ABSORP -- absorptivity. • EMIS --emissivity. • FACE_OPT -- surface option, FRONT or BACK. • MID_ID -- wavelength and/or temperature dependent surface properties ID.

The pick panel for creating a RADIATION entry follows. This is used to select the model nodes.

Units Parameter

Description

Consistent Units

TAMBIENT

Ambient temperature

C

TableT

table used to define ambient temperature vs time Unitless

FAMB

View factor between face and ambient pt.

Unitless

TableF

table used to define view factor vs time

Unitless

ABSORP

Surface absorptivity

Unitless

EMISi

Surface emissivity

Unitless

Special Applications There are several modeling tools that can be used to assist in the creation of a thermal model.

188 Temperature Specification (SOL 400)

MPC Otherwise known as a multipoint constraint. This constraint can be used to specify a node point temperature to be a weighted combination of any number of other node point temperatures. This is accessed using.

The Defaults For MPC BC form appears.

The entries for this form are. • DOFO is for the degree-of-freedom of the dependent node • WTO is for the weighting factor for D0F0 • DOFi is for the degree-of-freedom of the i-th independent node • WTi is for the weighting factor for DOFi

Transient Thermal Analysis 189 Temperature Specification (SOL 400)

The pick panel for creating an MPC entry follows. This is used to select the model nodes.

Units Parameter T

Description Temperature at model nodes

Consistent Units C

190 Perform Transient Analysis

Perform Transient Analysis Several topics are discussed in this section. • How to define a transient analysis, including the forms used • The parameters used for the definition of the analysis • The parameters used to control convergence of the nonlinear process

Define a Transient Analysis Once a thermal model has been completely defined. • Conduction elements • Material properties • Element properties • Boundary conditions • Material properties • Thermal loading

The transient thermal analysis can be performed. A MSC SimXpert Thermal analysis is setup as follows:

Expand Analysis by clicking on the “+”.

Right click Nastran Jobs.

Transient Thermal Analysis 191 Perform Transient Analysis

Click Create New Job.

Enter a title under Job Name, and select Transient Heat Transfer (SOL 159).

192 Perform Transient Analysis

Right click General Parameters, then click Properties.

Input the needed values. Specifying a value for Default Init Temperature will cause a TEMPD MD Nastran entry to be created.

Right click Cases. There are two possible items to choose. • Add Common Case • Specifications that will be common to all subcases, unless over-ridden by specifications for

subsequently defined subcases

Transient Thermal Analysis 193 Perform Transient Analysis

• Add Subcase • Specifications for individual subcases

Click Add Common Case.

Enter titles and label. Now, proceed to the second item under Case, that of Add Subcase. • Add Common Case • Specifications that will be common to all subcases, unless over ridden by specifications for

subsequently defined subcases • Add Subcase • Specifications for individual subcases

Click Add Subcase.

194 Perform Transient Analysis

Select LBC Set 1 under Select LBC Set.

Right click Subcase: LBC Set 1, then click Add Output Requests.

Right click Output Requests.

Select Add Temperature, then click Apply.

Transient Thermal Analysis 195 Perform Transient Analysis

Click Close.

Right click Subcase Parameters, then click Properties.

196 Perform Transient Analysis

The entries for this form are discussed later in this section.

Right click Output File, then click Properties.

Automatic Time Stepping MSC.Nastran estimates optimal time stepsize and the stepsize evolves based on the convergence condition. The time step is doubled ( Δtn + 1 = 2Δtn ) as { Δu n } = { u n – u n – 1 } becomes small, i.e.,

Transient Thermal Analysis 197 Perform Transient Analysis

u· n --------------< UTOL ( default = 0.1 ) u· max

where u·

max

is the maximum value of the norms computed from previous time steps and UTOL is a

tolerance on the temperature increment specified on the TSTEPNL Bulk Data entry. If the temperature increment exceeds the tolerance, a proper time step size can be predicted from the following calculation where ω n is the inverse of the characteristic time. T

T { Δu n } [ K T n ] { Δu n } { Δu n } { F n – F n – 1 } ω n = -----------------------------------------------≅ -------------------------------------------------T T { Δu n } { ΔH n } { Δu n } { ΔH n }

In thermal analysis, { F n } is the heat flow vector associated with conduction, convection (CONV and CONVM), and radiation (RADBC and RADSET), i.e., 4

{ F n } = [ K n ] { u n } + [ ℜ n ] { u n + T abs } – { N n }CONV – { N n }CONVM – { N n }RADBC

The next time step is adjusted by

Δt n + 1 = f ( r )Δt n where r is a scaling factor defined as

1 2π 1 r = --------------------  ------  -------- MSTEP ω n Δt n

198 Perform Transient Analysis

with f

= 0.25 for r < 0.5 • RB

f

= 0.5 for 0.5 • RB < r < RB

f

= 1.0 for RB < r < 2.0

f

= 2.0 for 2.0 < r < 3.0/RB

f

= 4.0 for r > 3.0/RB

Values of MSTEP and RB are specified on the TSTEPNL Bulk Data. If MSTEP is not specified, the default value is estimated by the stiffness ratio defined as T

{ Δu n } { F n – F n – 1 } λ = -------------------------------------------------T { Δu n } [ K Tn ] { Δu n } The default value of MSTEP is determined based on the following criteria:

λ * = λ if λ ≥ 1 λ * = --1- if λ < 1 λ and

MSTEP = 20 for λ * < 5 MSTEP = 40 for 5 ≤ λ * < 1000 No Adjust for λ * ≥ 1000 The adjusted time step size is limited to the upper and lower bounds, i.e.,

DT DT MIN  -------------------, ------------------ ≤ Δt ≤ MAXR ⋅ DT  2 MAXBIS MAXR where DT is the user-specified time increment and MAXR and MAXBIS are user-defined entries specified on the TSTEPNL entry. The time step is set to the limit if it falls outside the bounds. When the time marches to a value close to the last time specified by the user, the adaptive stepping scheme stops for the current subcase. The termination criterion is

Transient Thermal Analysis 199 Perform Transient Analysis

N

Δt

N ≤ DT ⋅ NDT  Δtn + -------2

n=1

where DT ⋅ NDT is the user-specified time duration for the current subcase. The adjusted time step remains effective across the subcases.

Integration and Iteration Control The incremental and iterative solution processes are controlled by the parameters specified on the TSTEPNL Bulk Data entry with the data format and default values described as follows: 1

2

3

4

5

6

7

8

9

TSTEPNL

ID

NDT

DT

NO

METHOD

KSTEP

MAXITER

CONV

1

ADAPT

2

10

PW

FSTRESS

TSTEPNL

+TNL1

+TNL2

EPSU

EPSP

EPSW

MAXDIV

MAXQN

MAXLS

1.0E-2

1.0E-3

1.0E-6

2

10

2

MAXBIS

ADJUST

MSTEP

RB

MAXR

UTOL

5

5

0

0.75

16.0

0.1

10 +TNL1

+TNL2

RTOLB

In thermal analysis, the options AUTO and TSTEP (specified in METHOD field) are disabled. The FSTRESS and RTOLB fields are also ignored and should be left blank for heat transfer. The ID field specifies an integer selected by the Case Control command TSTEPNL. The initial time increment and the number of time steps are specified by DT and NDT. Since the time increment is adjusted during the analysis, the actual number of time steps may not be equal to NDT. However, the total time duration is close to

NDT ⋅ D, pT .

For printing and plotting purposes, data recovery is performed at time steps O, NO, 2 • NO, ..., and the last converged step. The Case Control command OTIME may also be used to control the output times. Since both linear and nonlinear problems are solved by the same solution sequence, only the ADAPT option can be selected in the METHOD field for heat transfer. The ADAPT method automatically adjusts the incremental time and uses bisection. During the bisection process, the heat capacitance matrix and the tangential stiffness matrix are updated every KSTEP-th converged bisection solution. The number of iterations for a time step is limited to MAXITER. If MAXITER is negative, the analysis is terminated on the second divergence condition during the same time step or when the solution diverges for five consecutive time steps. If MAXITER is positive, the program computes the best solution and continues the analysis until divergence occurs again. If the solution does not converge in MAXITER iterations, the process is considered divergent. Either bisection or matrix update is activated when the process diverges.

200 Perform Transient Analysis

The convergence criteria are defined through the test flags in the CONV field and the tolerances in the EPSU, EPSP, and EPSW fields. The requested criteria (combination of temperature error U, load error P, and work error W) are satisfied upon convergence. Note that at least two iterations are required to check the temperature convergence criterion. MAXDIV limits the divergence conditions allowed for each iteration. Depending on the divergence rate, the number of diverging iteration NDIV is incremental as follows:

NDIV = NDIV + 2 if

E 1i ≥ 1

or E 1i < – 10 12

NDIV = NDIV + 1 if

– 10 12 < E 1i ≥ –1

or E 2i > 1

where: T

i { Δu i } { R i } E1 = --------------------------------{ Δu i } { R i – 1 } i E2

E pi = ----------E pi – 1

The solution is assumed to diverge when NDIV reaches MAXDIV. If the bisection option is used, the time step is bisected upon divergence. Otherwise, the left-hand side matrices are updated, and the computation for the current time step is repeated. If NDIV reaches MAXDIV again within the same time step, the analysis is terminated. The BFGS update and the line search process are performed in the same way as in steady state analysis. Nonzero values of MAXQN and MAXLS activate the quasi-Newton update and the line search process, respectively. The number of bisections for a load increment is limited to |MAXBIS|. Different actions are taken when the solution diverges, depending on the sign of MAXBIS. If MAXBIS is positive and the solution does not converge after MAXBIS bisections, the best solution is computed and the analysis is continued to the next time step. If MAXBIS is negative and the solution does not converge in |MAXBIS| bisections, the analysis is terminated. ADJUST controls the automatic time stepping in the following ways: If ADJUST = 0, the automatic adjustment is deactivated. If ADJUST > 0, the time increment is continually adjusted for the first few steps until a good value of

Δt is obtained. After this initial adjustment, the time increment is adjusted every ADJUST-th time step only. If ADJUST is one order greater than NDT, the automatic adjustment is deactivated after the initial adjustment.

Transient Thermal Analysis 201 Perform Transient Analysis

Parameters MSTEP and RB are used to adjust the time increment. The upper and lower bounds of time step size are defined with MAXR. If the solution approaches steady state (checked by tolerance UTOL), the time step size is doubled. Detailed computations involving these parameters are described in the previous section.

Iteration Output At each iteration or time step, the related output data are printed under the following heading:

TIME

Cumulative time for the duration of the analysis.

ITER

Iteration count for each time step.

DISP

Relative error in terms of temperatures defined as

λi ui – ui – 1E ui = -----------------------------( 1 – λ i )u max where

u max = max ( u 1 , u 2 , …, u n ) and λ i = E pi ⁄ E pi – 1 LOAD

Relative error in terms of loads defined as

R i E pi = -----------------------------------------max ( F n , P tn ) where:

{ F n } and { Ptn } In thermal analysis,

are internal heat flows and external applied heat loads, respectively.

{ Fn } is a heat flow vector defined in the Automatic Time

Stepping section, and

{ P t n } is the total heat flow associated with conduction, convection, radiation, and applied loads, i.e.,

.

202 Perform Transient Analysis

{ P t n } = { P n } + { N n } ld – { F n }

where WORK

{ N n } ld = { N n } QBDY3 + { N n } QVECT + { N n } QVOL

Relative error in terms of work defined as

{ ui – ui – 1 }T{ R }i E wi = --------------------------------------------------------------------------max ( { u n } T { F n }, { u n } T { P tn } ) LAMDBA(I) DLMAG

λ i ( = E pi ⁄ E pi – 1 ) . Absolute norm of the residual vector ( R ) . The absolute convergence is defined Rate of convergence

using DLMAG by R < 10 –12 . FACTOR

Final value of the line search parameter.

E-FIRST

Divergence rate, initial error before line search.

E-FINAL

Error at the end of line search.

NQNV

Number of quasi-Newton vectors appended.

NLS

Number of line searches performed during the iteration.

ITR DIV

Number of occurrences of divergence detected during the adaptive iteration.

MAT DIV

Number of occurrences of bisection conditions during the iteration.

NO. BIS

Number of bisections executed for the current time interval.

ADJUST

Ratio of time step adjustment relative to DT.

Diagnostic messages are requested by DIAG 50 or 51 in the Executive Control Section. DIAG 50 only prints subcase status, TSTEPNL data, and iteration summary, while DIAG 51 prints all data at each iteration. In general, the user should be cautioned against using DIAG 51, because it is used for debugging purposes only and the volume of output is significant. It is recommended that DIAG 51 be used only for small test problems. The diagnostic output is summarized as follows: For each entry into NLTRD2, the following is produced: • Subcase status data. • TSTEPNL data. • Core statistics (ICORE, etc). • Problem statistics (g-size, etc.). • File control block. • Input file status.

Transient Thermal Analysis 203 Perform Transient Analysis

For each time step, the following is produced: • NOLINi vector:

{ Nd }

• External load vector:

{ Pd }

• Load vector including follower forces and NOLINs: • Constant portion of residual vector: • Total internal force:

{ P td }

{ R' d }

{ Fd }

• Initial residual vector:

{ Rd }

For each iteration, the following is produced: • Initial energy for line search: • Nonlinear internal force: •

{ Δud } T { Rd }

{ F g } , which is

{ F g } = { K g } nl { u g } – { N g } CONV – { N g } CONVM – { N g } RADBC

• Temperature vector:

{ ud }

• Nonlinear internal force:

{ F d } nl , which is 4

• { F d } nl = [ K d ]nl { u d } + [ ℜ d ] { u d + T abs } – { N d } CONV – { N d } CONVM – { N d } RADBC • Total internal force: •

{ F d } , which is

{ F d } = [ K d ] l { ud } + { F d } nl

• NOLINi vector:

{ Nd }

• Enthalpy vector:

{ Hd }

• Load vector including follower forces and NOLINs: •

{ P td } , which is

{ P td } = { P d } + { N d } ld – { F d }

• where

{ N d }ld = { N d } QBDY3 + { N d } QVECT + { N d } QVOL

• Residual vector:

{ Rd }

• Iteration summary (convergence factors, line search data, etc.)

204 Perform Transient Analysis

For each quasi-Newton vector set, the following is produced: • Condition number:

λ

2

• quasi-Newton vector:

δ

• quasi-Newton vector:

γ

1 • Energy error: z = --------T δj γ j

For each line search; the following is produced: • Previous line search factor: • Previous error:

αk

Ek

• New line search factor:

αk + 1

For each converged time step, the following is produced: Time derivative of temperature:

{ u· d }

For each time step adjustment, the following is produced: • Magnitude of the time derivative of temperature:

{ u· n }

• Magnitude of the new time derivative of temperature: • General conductance: DENOM1 =

• General enthalpy: DENOM2 = • Work:

{ u· n + 1 }

T

{ Δu n } [ KT ] { Δu n } n

T

{ Δu n } { ΔH n }

T

{ Δu n } { ΔF n }

• Inverse of Characteristic time: • Conductance ratio:

ωn

λ

• Number of steps for the period of dominant frequency: MSTEP • Controlling ratio for time step adjustment: r

Transient Thermal Analysis 205 Perform Transient Analysis

Recommendations The following are recommendations designed to aid the user. • Time step size

To avoid inaccurate or unstable results, a proper initial time step associated with spatial mesh size is suggested. The selection criterion is

1 2 ρc p Δt = --- Δx -------n k Δt is the time step, n is the modification number of the time scale, Δx is the mesh size (smallest element dimension), ρ is the material density, c p is the specific heat, and k is the where

thermal conductivity. A suggested value of n is 10. For highly nonlinear problems, a small step size is recommended. • Numerical stability

Numerical stability is controlled by the parameter

η (specified on the PARAM,NDAMP Bulk

η = 0 (i.e., no numerical damping) is adequate, but for nonlinear problems a larger value of η may be advisable. Increasing the value of η improves Data entry). For linear problems,

numerical stability; however, the solution accuracy is reduced. The recommended range of values is from 0.0 to 0.1 (default value is 0.01). • Initial temperatures and boundary temperatures

The specification of initial temperatures and boundary condition temperatures should be consistent. For a given point, the initial temperature should be equal to the boundary condition temperature at t = 0. • Convergence criteria

At the beginning stages of a new analysis, it is recommended that the defaults be used on all options. However, the UPW option may be selected to improve the efficiency of convergence. For nonlinear problems with time-varying boundary conditions, the U option must be selected, because the large conductance (internally generated) affects the calculations of the PW error functions. For problems with poor convergence, the tolerances EPSU, EPSP, and EPSW can be increased within the limits of reasonable accuracy. • Fixed time step

If a fixed time step is desired, the adaptive time stepping can be deactivated by setting ADJUST = 0 on the TSTEPNL Bulk Data.

206 Results

Results The results menu (set of forms) allows the user to process any results that have been accessed (imported or attached) by MSC SimXpert. The basic things that can be done under Result in MSC SimXpert are • Display in the computer screen • Deformation • Fringe • Vector • Write out from MSC SimXpert • Results report file

The Result dropdown menu that allows the user access to all the forms is

As can be seen there are two choices • Chart • This is for creating X-Y plots • State Plot • This is for creating on model result plots in the MSC SimXpert screen/viewport

Transient Thermal Analysis 207 Results

State Plot Look at creating a State Plot type plot first. The form to do this with is shown as follows:

The first thing to select is an item under Plot type, e.g. Fringe Two possible choices will be looked at • Fringe • Vector

Fringe Now, set to creating a Fringe plot.

Expand the result case SC1 by clicking “+”.

208 Results

Select a Result Case corresponding to a value of Time.

Select a Result Type.

Click Update Plot button to obtain a state plot for Time = 2.5.

To clear the display of the fringe plot click Clear Plot button.

Transient Thermal Analysis 209 Results

Another temperature fringe plot is shown below.

If necessary, select a layer. A form appears for picking a layer.

If needed, an Option can be used.

210 Results

To select only certain finite element entities (a subset of the results) to display the Fringe results on use the following part of the form:

Now, change to selecting Display attributes for the Fringe plot. There are four parts of this. • Fringe attributes • Element Edge display • Spectrum Range • Labels (Font, Title, Model, Legend)

Transient Thermal Analysis 211 Results

Sometimes it is necessary to apply a coordinate transformation to the Fringe data. This can be done using the next part of the Fringe form, Data transforms.

The Coordinate transformations are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system • Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems

212 Results

It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Fringe form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged • All entities -- all element results at the common node are averaged

Transient Thermal Analysis 213 Results

• Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

214 Results

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Fringe / Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value Vector Change to creating a Vector plot.

Transient Thermal Analysis 215 Results

Expand the result case SC1 by clicking “+”.

Select a Result Case corresponding to a value of Time.

Select a Result Type.

Click Update Plot button to obtain a vector plot.

216 Results

To clear the display of the vector plot click Clear Plot button.

This can be done for different values of Time. If necessary, select a layer. A form appears for picking a layer.

If needed, an Option can be used.

Transient Thermal Analysis 217 Results

To select only certain finite element entities (a subset of the results) to display the Vector results on use the following part of the form:

Change to selecting Display attributes for the Vector plot. There are five parts of this. • Vector attributes • Display on • Spectrum Range • Vector component colors

218 Results

• Labels (Font, Title, Model, Legend)

Sometimes it is necessary to apply a coordinate transformation to the Vector data. This can be done using the next part of the Vector form, Data transforms.

The Coordinate transformations are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system

Transient Thermal Analysis 219 Results

• Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Vector form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

220 Results

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged • All entities -- all element results at the common node are averaged • Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

Transient Thermal Analysis 221 Results

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Result averaging / Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value

222 Results

Chart Plot Next, look at creating a Chart (X-Y) plot. The form to do this with is shown as follows:

Expand the result case SC1 by clicking “+”.

Select a set of result cases for different values of Time.

Transient Thermal Analysis 223 Results

Select a Result Type.

Screen pick a node, e.g. Node 8140. Click Add Curves button.

If necessary, select a layer. A form appears for picking a layer.

224 Results

If needed, an Option can be used.

To specify a type of finite element entity to display the X-Y plot data results for use the following part of the form:

Now, change to specifying the Transforms for the Chart data.

There are five types of Transforms. • Coordinate transforms • Scale factor • Filter • Result averaging • Result extrapolation

Transient Thermal Analysis 225 Results

Sometimes it is necessary to apply a coordinate transformation to the Chart (X-Y) data. This can be done using the following form:

The Coordinate transforms are defined as follows: • No transform -- no transformation; the results are in the MD Nastran coordinate systems • Local CS -- local coordinate system • Projected Local CS -- coordinate system from the projection of a local coordinate system’s axes

onto an element • Global -- MSC SimXpert Thermal global coordinate system • Default -- coordinate system from the projection of the MSC SimXpert Thermal global

coordinate system axes onto an element • Material -- element coordinate systems based on a material definition and angle. Only for Quad

and Tri topology. • Element IJK --MSC SimXpert defined element coordinate systems. These can be different from

the MD Nastran element coordinate systems The data can be filtered as follows:

226 Results

It is necessary to decide how to average data for elements that have a common node, to obtain results at that common node.

For this example Element 6, 7, 10, and 11 all use Node 13. It is necessary to obtain element results at Node 13 from the results of Element 6, 7, 10, and 11. This is done using the Result averaging part of the Chart / Transforms form.

There are two choices that must be made. • Domain • Method

Making a selection for Domain will direct MSC SimXpert how to average between elements.

The choices for Result averaging / Domain are • Property -- all element results, for elements that have the same property set, at the common node

are averaged • Material -- all element results, for elements that have the same material set, at the common node

are averaged

Transient Thermal Analysis 227 Results

• All entities -- all element results at the common node are averaged • Target entities -- all element results, for elements that have been selected under Plot Data/Plot

type: Fringe/Target Entities, at the common node are averaged • Element type -- all element results, for elements that are of the same type (e.g. Quad4), at the

common node are averaged • None -- no averaging at the common node is done

Making a selection for Method will direct MSC SimXpert how to obtain invariant results at nodes, to obtain the difference between results at nodes, or to obtain the sum of results at nodes.

The choices for Result averaging / Method are • Derive/Average -- calculate (Derive) a result invariant at element integration points, extrapolate

the calculated results to element nodes, then average (Average) the results at the element nodes • Average/Derive -- extrapolate result component values, e.g.

σ xx , to element nodes, average

(Average) the result component values at the nodes, then calculate (Derive) the result invariant values at the nodes • Difference -- obtain the difference between results at nodes • Sum -- obtain the sum of results at nodes

228 Results

It is necessary to decide how to extrapolate the data for an element to its nodes. The extrapolation is from the element’s integration points to its nodes.

For this example Element 1 uses Node 1, 2, 3, 4. The results are at the element integration points; the integration points are labeled with ip j; j = 1, 2, 3, 4; inside the element. The arrows point from the integration points to the element nodes. The extrapolation is done using the Chart / Result extrapolation form.

The choices for Result extrapolation are • Shape function -- result value at element’s nodes is determined from fitting an extrapolating

surface through the known element result values • Average -- result is averaged within the element, then the average value is assigned to the

element’s nodes • Centroid -- the centroidal value from the extrapolating surface is used at the element’s nodes • Minimum -- the smallest of the integration point values is used; if the only result is at the

centroid, the minimum value is set equal to the centroidal value • Maximum -- the largest of the integration point values is used; if the only result is at the centroid,

the maximum value is set equal to the centroidal value