Concentric Spheres With Radiation

Chapter 44: Concentric Spheres with Radiation

44

Concentric Spheres with Radiation 

Summary



Introduction



Modeling Details



Material Modeling



Solution Procedure



Results



Modeling Tips



Pre- and Postprocess with SimXpert



Input File(s)



Video

799 800 800 807 807

808

854

809

853

810

CHAPTER 44 799 Concentric Spheres with Radiation

Summary Title

Chapter 44: Concentric Spheres with Radiation

Features

Hemi-cube versus Gaussian Integration Methods

Geometry

T∞ = 0

t = 0.05

i 2

2

ε = 0.7 R = 1.5 T=?

o 2

ε = 1.0

o 1

ε = 0.9 t = 0.01

R=1 T = 1000

1

Units: inch, watt, K

Material properties

k 1 = 4.0W   in – K 

Analysis characteristics

• Nonlinear steady state thermal analysis

Boundary conditions

Inside sphere temperature fixed at 1000 K. The heat sink is ambient temperature at zero K where the radiation to space boundary condition is applied on the outer sphere. Stefan-Boltzmann constant is  (above).

Element type

4-node QUAD4

FE results

Outer sphere temperature using different radiation schemes and compared to an analytic solution

k 2 = 6.0W   in – K 

2

Temperature K (Grid 367) Analytic Gaussian integration Hemi-cube

710.5 710.0 709.5 709.0 708.5 708.0

Analytic

Gaussian integration

4

 = 3.66x10 – 11 W   in – K 

Hemi-cube

710.30 709.85 708.91

800 MD Demonstration Problems CHAPTER 44

Introduction This problem demonstrates the ability of the Nastran SOL 400 thermal nonlinear solution sequence to perform thermal radiation view factor calculations using the Hemi-cube and Gaussian integration methods. The Gaussian adaptive integration view factor calculation method has been with Nastran for many years. The view factor computed by the Gaussian method is extremely accurate. However, as the problems get big, computation time is roughly proportional to the number of surfaces squared. The introduction of Hemi-cube method in MD Nastran permits the solution of very large scale view factor problems where previously the use of the Gaussian method was overly time intensive. As compared to the adaptive Gaussian method, we have seen an improvement in CPU speed of 33 times in some problems. The CPU time increases linearly with the number of radiation surfaces because in Hemi-cube, the computation time is linearly proportional to the number of surfaces. In this problem, we have an analytical solution in which we compare both Hemi-cube and the Adaptive Gaussian integration methods to see which method offers the most accuracy.

Modeling Details

Figure 44-1

Concentric Spheres (top sector of outer sphere removed)

As shown in (Figure 44-1), the inner sphere with radius equal to 1 inch is subjected to a constant temperature of 1000°K (red). There is radiation exchange between the inner and the outer sphere (orange). The outer sphere radiates to space at an ambient temperature of zero K with view factors equal to 1.0.

Reference Solution For these two diffuse isothermal concentric spheres, the view factors need to be determined. Since all of the energy leaving the inner sphere (1) will arrive at the outer sphere (2), F 1 – 2 = 1.0 . The reciprocity relation for view factors

CHAPTER 44 801 Concentric Spheres with Radiation

gives A 1 F 1 – 2 = A 2 F 2 – 1 , or F 2 – 1 =  R 1  R 2  2 . Since the inner sphere cannot see itself, F 1 – 1 = 0 . Finally since energy must be conserved, the sum of all view factors of a closed cavity must be unity, which yields, F 2 – 2 = 1 –  R 1  R 2  2 . Notice how the number of view factors grow as the square of the number of surfaces, i.e. two surfaces yield 4 view factors. Given the geometry of the spheres as R 1 = 1 and R 2 = 1.5 , the four view factors become: F1 – 1 = 0 F1 – 2 = 1 4 5 F 2 – 1 = --- F 2 – 2 = --9 9

. Below is an equation for calculation of outer sphere temperature where the outer sphere is

radiating to space at absolute zero and a view factor of 1. (Holman, Jack P. Holman Heat Transfer. McGraw-Hill, 2001).  1 = 0.9

2

= 1

ou t

2

= 0.7

inner

T 1 = 1000 2

2

A1 = 4    R1

A2 = 4    R2

A 1 = 12.566

A 2 = 28.274

 1 A1  1 C = ----- + ------  ---------------- – 1 1 A2  2  inner

C = 1.302

4

A1  T1 D 2 = -------------------------------------------A1 + C  2  A2 out

D 2 = 2.545  10 11

0.25

T2 = D2

T 2 = 710.299

This solution assumes perfect conduction (no resistance to heat flow) in the outer sphere. While, in general, the view factors cannot be obtained from analytical solutions, in this simple problem, the view factors can be found analytically and we can use these view factors in a simple three grid model to check our analytic solution above. One grid represents the inner sphere, another represents the outer sphere, and the last grid represents the ambient temperature of the outer sphere. Nastran test file: user1_point.dat $Model concentric sphere with two nodes $ Length in Inches $! NASTRAN Control Section NASTRAN SYSTEM(316)=19 $! File Management Section $! Executive Control Section SOL 400 CEND ECHO = NONE $! Case Control Section TEMPERATURE(INITIAL) = 21 TITLE=MSC.Nastran job created on 05-Dec-03 at 13:33:05

802 MD Demonstration Problems CHAPTER 44

SUBCASE 1 $! Subcase name : subcase_1 $LBCSET SUBCASE1 lbcset_1 SUBTITLE=Default SPCFORCES(SORT1,PRINT,REAL)=ALL OLOAD(SORT1,PRINT,REAL)=ALL THERMAL(SORT1,PRINT)=ALL FLUX(PRINT)=ALL ANALYSIS = HSTAT SPC = 23 NLSTEP = 1 BEGIN BULK $! Bulk Data Pre Section PARAM SNORM 20. PARAM K6ROT 100. PARAM WTMASS 1. PARAM* SIGMA 3.6580E-11 PARAM POST 1 PARAM TABS 0.0 $! Bulk Data Model Section RADM 11 0.0 0.9 RADM 12 0.0 0.7 RADM 13 0.0 1. PHBDY 1 12.566 PHBDY 2 28.274 GRID 101 0.0 0.0 GRID 102 1. 0.0 $! SPOINT 777 CHBDYP 1 1 point 10 + 11 CHBDYP 2 2 point 10 + 12 CHBDYP 3 2 point + 13 SPC 23 101 1 1000. SPC 23 777 1 0.0 RADBC 777 1. 3 RADCAV + VIEW VIEW3D RADSET RADMTX RADMTX RADLST TEMPD TEMP TEMP NLSTEP + + +

RadMat_1 RadMat_1 RadMat_1 PHBDY_1_ PHBDY_2_ 0.0 0.0

1. -1. -1.

101 0.0 102 0.0 102 0.0

+ 0.0 + 0.0 + 0.0

1 10 10 1 10 10 1 21 21 21 1 GENERAL 25 FIXED 1 HEAT PW

+ 1 1 0.012.56637 215.70922 1 1 2 900. 777 0.0 101 1000. 1.

+ + +

1 0.001

1.E-7AUTO

5

CHAPTER 44 803 Concentric Spheres with Radiation

ENDDATA b1272084 Notice that the Stefan-Boltzmann constant (sigma) is 3.66e-11 W/in2/K4 and, the radiation matrix is define above by A1 F1 – 1 = 0

the RADLST and RADMTX, RADMTX =

A2 F2 – 1

A 1 F 1 – 2 =  12.566   1

4 5 =  28.274   --- A 2 F 2 – 2 =  12.566   --9 9

=

0 12.56637 sym 15.70796

The radiation matrix must be symmetric to conserve energy (reciprocity relation A 1 F 1 – 2 = A 2 F 2 – 1 ), and the symmetric terms are not entered. Running this three node problem yields the output below with the temperature of the outer sphere of 710.31, agreeing to within 4-digits of our analytic solution of 710.3. T E M P E R A T U R E

POINT ID.

TYPE

V E C T O R

ID

VALUE

101

S

1.000000E+03

777

S

0.0

ID+1 VALUE

ID+2 VALUE

ID+3 VALUE

ID+4 VALUE

ID+5 VALUE

7.103098E+02

Solution Highlights The following are highlights of the Nastran input file necessary to model this problem using 700 elements to represent the inner and outer spheres with 1268 radiating surfaces: $! NASTRAN Control Section NASTRAN SYSTEM(316)=19 $! File Management Section $! Executive Control Section SOL 400 CEND ECHO = SORT $! Case Control Section TEMPERATURE(INITIAL) = 33 SUBCASE 1 $! Subcase name : NewLoadcase $LBCSET SUBCASE1 DefaultLbcSet THERMAL(SORT1,PRINT)=ALL FLUX(PRINT)=ALL ANALYSIS = HSTAT SPC = 35 NLSTEP = 1 BEGIN BULK $! Bulk Data Pre Section PARAM WTMASS 1. PARAM GRDPNT 0 NLMOPTS HEMICUBE1 PARAM* SIGMA 3.6580E-11 PARAM POST 1 $! Bulk Data Model Section PARAM OGEOM NO PARAM MAXRATIO 1e+8

804 MD Demonstration Problems CHAPTER 44

The use of a steady-state thermal analysis is indicated by ANALY=HSTAT. The NLMOPTS parameters indicate that we are using the Hemi-cube method as the view factor calculation method. If one desires to run the Gaussian integration method, then you do not need the NLMOPTS bulk data entry. The inner sphere is composed of CHBDYG elements (see command details below) numbered from 6987 through 7214, and the outer sphere is from 7215 to 7734. The set1 ID option is used on the RADCAV bulk data entry to sum up all the view factors between the inner and outer spheres for comparisons against theory.

Loading and Boundary Conditions

Radiation- View Factor Calculation (CHBDYG Element) The CHBDYG element is used in Nastran thermal analysis for any surface heat transfer phenomenon such as radiation or convection or imposing heat flux on these elements. CHBDYG CHBDYG RADM RADM RADM RADSET RADCAV VIEW3D $! VIEW

6987 3390 6988 3404

3403

AREA4 3397 AREA4 3389

3 4 5 4 4 4

0.9 0.7 1.

0.9 0.7 1.

0

YES 0

0

4 0.0

2

4

KSHD

1

1

3389

2 3398 2 3390

3 3 Radm_3 Radm_4 Radm_5 0.0

0.1 0.0

CHAPTER 44 805 Concentric Spheres with Radiation

In this case, we have CHBDYG element 6987 with TYPE='AREA4' bounded by grid 3390, 3389, 3397, 3398. The normal vector is defined by the grid connectivity and is directed from the inner sphere to the outer sphere (Figure 44-2 and Figure 44-3). The internal sphere has KSHD defined on the 4th field of the VIEW data entry, which means that this group of elements can shade the view of other elements. The external sphere has KBSHD defined which means that these elements can also be shaded by other elements. The reason that we have specified the shading flag is to speed up the sorting for these potential blockers in the view factor calculations. In general when the surface is very complex, the use of the flag called BOTH is recommended. The RADSET option tells us there is only 1 cavity in the model, and the 2nd field on the VIEW points to the IVIEWF or IVIEWB on the CHBDYG field 5th or 6th, respectively. For a plate element, there is top and the bottom surface for view factor calculations. For a solid element, only the front side IVIEWF should be used. The inner sphere here is represented by number as 1 on the field 5 (IVIEWF) on the CHBDYG. The 7th and 8th represent the ID for the RADM option where 7th field is the top surface RADM ID and the 8th field is the bottom surface RADM ID. The RADM specified the emissivity used for the sphere and, in this case, the emissivity for the inner sphere is equal to 0.7. The RADCAV bulk data entry indicates that we will print the summary of view factor calculations. In this case, we have a complete enclosure and, therefore, the view factor summation should equal 1.0. The surface numbers 703, 704 are the ID numbers for the CHBDYG that has the radiation exchange. *** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = SURF-I 6987 6988 6989 6990 6991

SURF-J -SUM -SUM -SUM -SUM -SUM

4 ***

ELEMENT TO ELEMENT VIEW FACTORS AREA-I AI*FIJ FIJ

OF OF OF OF OF

5.19803E-02 6.14400E-02 4.30822E-02 4.36718E-02 5.08568E-02

SCALE

9.99998E-01 9.99997E-01 9.99988E-01 1.00000E+00 1.00000E+00

The continuation field on the RADCAV is optional. Radiation - RADBC (radiation to space) On the outer sphere, we have a radiation to space using the view factor supplied on the 3rd field on the RADBC. (see Example below) The 2nd field on the RADBC points to the ambient grid ID 100001 and, in this case, we have the grid fixed at 0° K. SPOINT SPC TEMP RADBC CHBDYG RADBC CHBDYG RADBC CHBDYG

6497 5 33 6497 6467 5987 6497 6468 5989 6497 6469 5997

6497 6497 1. 5975 1. 5976 1. 5996

1 0.0 0 AREA4 5976 0 AREA4 5975 0 AREA4 5975

0.0 -6467 5 5986 -6468 5 5988 -6469 5 5987

806 MD Demonstration Problems CHAPTER 44

Please note the negative EID represents that the radiation to space is effected from the back surface (opposite to the direction of normal) of the element. Also, we have the temperature boundary conditions applied to all grids on the inner sphere at 1000 K via the SPC option. SPC

1

RADBC

1

1

1000.

Space Radiation Specification

Specifies an CHBDYi element face for application of radiation boundary conditions. Format 1

2

3

4

5

6

7

8

RADBC

NODAMB

FAMB

CNTRLND

EID1

EID2

EID3

-etc.-

6

7

8

9

10

9

10

Example 1

2

3

4

5

RADBC

5

1.0

101

10

Field

Contents

Type

NODAMB

Ambient point for radiation exchange.

I>0

FAMB

Radiation view factor between the face and the ambient point.

R>0

CNTRLND

Control point for radiation boundary condition. (Integer > 0; Default = 0)

I>0

EIDi

CHBDYi element identification number. ( Integer  0 or “THRU” or “BY”)

Remarks: 1. The basic exchange relationship is: • if CNTRLND = 0, then q =   FAMB   e   T 4e – T 4amb  • if CNTRLND > 0, then 4

4

q =   FAMB  u CNTRLND   e   T e – T amb 

Default

0

CHAPTER 44 807 Concentric Spheres with Radiation

Figure 44-2

Normal Vectors Point Outward from the Inner Sphere

Figure 44-3

Normal Vectors Point Inward for the Outer Sphere

Material Modeling Thermal conductivity value is supplied on the MAT4 bulk data entry. MAT4 MAT4

1 2

4. 6.

Iso_1 Iso_2

Solution Procedure The nonlinear procedure used is defined using the following NLPARM entry: NLSTEP + +

FIXED HEAT

1 1 UPW

1.

+ + 0.001

0.001

1.E-7PFNT

808 MD Demonstration Problems CHAPTER 44

In thermal analysis, the TEMPD bulk data entry specifies the initial temperature for the nonlinear radiation analysis. In this case, an initial guessed temperature of 800° was used. A casual selection of initial guessed temperature is not so important in a nonlinear conduction and convection thermal analysis. However, for nonlinear radiation analysis where the thermal radiation transfer is given by Q = A  T 14 – T 24  , an initial guess is very helpful. The error (residual) is proportional to the temperature to the 4th power. It is. therefore, recommended to specify a higher estimated temperature in a radiation dominant problem. The default method for the NLPARM is the AUTO method in SOL 400 analyses. The convergence criterion is based on UPW. In this problem, you can achieve convergence by either the PFNT method (as above) or the AUTO method: NLSTEP + +

FIXED HEAT

1 1 UPW

1.

+ + 0.001

0.001

1.E-7AUTO

The U convergence criterion measures the error tolerance for the temperature. It has a recommended value of 1.0e-3 or smaller for thermal problem. The P and W convergence criteria measure the error tolerances for the load and work, respectively. The number of increments is specified on the 3rd field of the NLPARM data entry (NINC). This should be set to 1 for steady-state thermal analyses since convergence can be achieved in one step only. This, typically, is not the case for structural analyses, where NINC is set to 10 by default. Generally, the PFNT or FNT methods are used for highly nonlinear mechanical analyses.

Results Temperature K (Grid 367) Analytic Gaussian integration Hemi-cube

710.5

710.30 709.85 708.91

710.0 709.5 709.0 708.5 708.0

Analytic

Gaussian integration

Hemi-cube

Both methods yield temperatures very close to the analytical solution.

CHAPTER 44 809 Concentric Spheres with Radiation

Figure 44-4

Hemi-cube Results

Modeling Tips The current model uses 1268 surfaces to define the radiating surfaces of both spheres. The CPU run times for the Gaussian and Hemi-cube methods are nearly the same, at 27 seconds. Figure 44-5, however, shows the dramatic increase in run time for the Gaussian model and the clear benefits of the Hemi-cube method as the number of surfaces increases. At 20,000 surfaces, the Gaussian model takes 33 time longer to complete. CPU Time (s) 12000 10000

Gaussian

8000

Hemi-cube

6000 4000 2000 0

0

5000

10000

15000

20000

Number of Surfaces

Figure 44-5

CPU Run Times

810 MD Demonstration Problems CHAPTER 44

Pre- and Postprocess with SimXpert The same physical model will now be built, run and postprocessed with SimXpert. The Gaussian integration scheme will be used to compute the viewfactors. While the dimensions of length in the summary and nug*.dat files is inches, the model built here with SimXpert will use the same geometry but with units of meters. The only other change will be in the selection of the correct units of the Stefan-Boltzmann constant (p. 844).

Units a. Tools: Options b. Observe the User Options window c. Select Units Manager d. For Basic Units, specify the model units: e. Length = m, Mass = kg, Time = s, Temperature = Kelvin, and Force = N

b d c

a

e

CHAPTER 44 811 Concentric Spheres with Radiation

Create First Hemispherical Surface a. Geometry tab: Curve/Arc b. Select Arc c. Select 3 Points d. For X,Y,Z, Coordinate, enter 0.0245, 0, 0; input, click OK e. For X,Y,Z, Coordinate, enter 0, 0.0245, 0; input, click OK (not shown) f. For X,Y,Z, Coordinate, enter -0.0245, 0, 0; click OK (not shown) g. Click OK h. Observe in the Model Browser tree: Part 1 l. Observe the curve arc

b c

a

d

g

h i

812 MD Demonstration Problems CHAPTER 44

Create First Hemispherical Surface (continued) a. Geometry tab: Surface/Revolve b. Select Vector c. For X,Y,Z Coordinate, enter 0 0 0; click OK d. Click OK e. For Axis, select X; click OK f. For Entities screen select the Curve arc g. For Angel Of Spin (Degrees), enter 180; click OK h. Observe the first hemispherical surface

a

b c

e d

f g j h -

CHAPTER 44 813 Concentric Spheres with Radiation

Create Part for Second Hemispherical Surface a. Assemble tab: Parts/Create Part b. Use defaults of form c. Click OK d. Observe Part_2 in the Model Browser Tree

a

b

c

d

814 MD Demonstration Problems CHAPTER 44

Create Second Hemispherical Surface a. Geometry tab: Curve/Arc b. Select Arc c. Select 3 Points d. For X,Y,Z, Coordinate, enter 0.0381, 0, 0; input, click OK e. For X,Y,Z, Coordinate, enter 0, 0.0381, 0; input, click OK (not shown) f. For X,Y,Z, Coordinate, enter -0.0381, 0, 0; click OK (not shown) g. Click OK h. Observe the curve arc

a b c

d

g

h -

CHAPTER 44 815 Concentric Spheres with Radiation

Create Second Hemispherical Surface (continued) a. Geometry tab: Surface/Revolve b. Select Vector c. For X,Y,Z Coordinate, enter 0 0 0; click OK d. Click OK e. For Axis, select X; click OK f. For Entities screen select the Curve arc g. For Angel Of Spin (Degrees), enter 180; h. Click OK i. Observe the second hemispherical surface

a

b

c

e d

f g h ik

816 MD Demonstration Problems CHAPTER 44

Create Third Hemispherical Surface a. Tools: Transform/Reflect b. Select X-Y Plane c. Select Make Copy d. Select Inner (smaller) hemispherical surface e. Click Done; then click Exit f. A third hemispherical surface is created that is the same color as the copied surface g. Observe that there is another Part in the Model Browser tree

b c

a e

f

g

CHAPTER 44 817 Concentric Spheres with Radiation

Create Third Hemispherical Surface (continued) a. In the Model Browser tree, right click on PART_1.COPY; select Change Color b. Select a different color c. Observe that the third hemispherical surface is now a different color

b

a

c

818 MD Demonstration Problems CHAPTER 44

Create Fourth Hemispherical Surface a. Tools: Transform/Reflect b. Select X-Y Plane c. Select Make Copy d. Select outer (larger) hemispherical surface e. Click Done; then click Exit f. A fourth hemispherical surface is created that is the same color as the copied surface g. Observe that there is another Part in the Model Browser tree

b c

e

a

f

g

CHAPTER 44 819 Concentric Spheres with Radiation

Create Fourth Hemispherical Surface (continued) a. In the Model Browser tree, right click on PART_2.COPY; select Change Color b. Select a different color c. Observe that the fourth hemispherical surface is now a different color

b

c

a

820 MD Demonstration Problems CHAPTER 44

Create Material Properties a. Materials and Properties tab: Material/Isotropic b. For Name enter Inner_sphere c. For Description enter a description d. For Young’s Modulus enter 10e9 (needed for the software to run) e. For Poisson’s Ratio enter 0.28 (needed for the software to run) f. For Thermal Conductivity enter 157.48 g. Click OK

a

b c d e

f

gf

h

CHAPTER 44 821 Concentric Spheres with Radiation

Create Material Properties (continued) a. Materials and Properties tab: Material/Isotropic b. For Name enter Outer_sphere c. For Description enter a description d. For Young’s Modulus enter 10e9 (needed for the software to run) e. For Poisson’s Ratio enter 0.28 (needed for the software to run) f. For Thermal Conductivity enter 236.22 g. Click OK

a

b c d e

f

g

h

822 MD Demonstration Problems CHAPTER 44

Create Inner Sphere Element Property a. Create the element property for the inner sphere b. Right click on PART_2; select HIDE to hide the outer hemispherical surfaces c. Repeat Step b. for PART_2.COPY d. Create the element property for the inner sphere

a

b

d

c

CHAPTER 44 823 Concentric Spheres with Radiation

Create Inner Sphere Element Property (continued) a. Materials and Properties tab: 2D Properties/Shell b. For Name, enter Inner_sphere c. For Entities screen, select the two inner hemispherical surfaces d. For Material, select Inner_sphere from the Model Browser tree e. For Part thickness, enter 2.54e-4 f. Click OK

a

b c d e

f

c

824 MD Demonstration Problems CHAPTER 44

Create Outer Sphere Element Property a. Create the element property for the outer sphere b. Right click on PART_1; select HIDE to hide the outer hemispherical surfaces c. Repeat Step b. for PART_1.COPY d. Right click on PART_2; select SHOW to show the outer hemispherical surfaces e. Repeat Step d. for PART_2.COPY f. Create the element property for the outer sphere

a

f

CHAPTER 44 825 Concentric Spheres with Radiation

Create Outer Sphere Element Property (continued) a. Materials and Properties tab: 2D Properties/Shell b. For Name, enter Outer_sphere c. For Entities screen, select the two outer hemispherical surfaces d. For Material, select Outer_sphere from the Model Browser tree e. For Part thickness, enter 1.27e-3 f. Click OK

a

b c d e

c f

826 MD Demonstration Problems CHAPTER 44

Create Surface Mesh for Outer Sphere a. Meshing tab: Automesh/Surface b. For Surface to mesh screen, select both surfaces c. For Element Size, enter 0.35 d. For Mesh type, select Quad Dominant e. For Element property, select Outer_sphere from the Model Browser tree f. Click OK

a

b

b

c

d e

f

CHAPTER 44 827 Concentric Spheres with Radiation

Create Surface Mesh for Outer Sphere (continued) a. Display the geometric surfaces in wireframe b. Display the elements as shaded c. Observe resulting mesh for the outer sphere d. Notice the elements at the geometric interface are congruent e. Verify that the elements at the interface are connected

a

b

c

d

e

e

828 MD Demonstration Problems CHAPTER 44

Create Surface Mesh for Inner Sphere a. Display only the inner sphere using the picks in the Model Browser tree and those of the Render toolbar for Geometry and FE.

a

CHAPTER 44 829 Concentric Spheres with Radiation

Create Surface Mesh for Inner Sphere (continued) a. Meshing tab: Automesh/Surface b. For Surface to mesh screen, select both surfaces c. For Element Size, enter 0.35 d. For Mesh type, select Quad Dominant e. For Element property, select Inner_sphere from the Model Browser tree f. Click OK

a

b

b

c

d e

f

830 MD Demonstration Problems CHAPTER 44

Create Surface Mesh for Inner Sphere (continued) a. Display the geometric surfaces in wireframe b. Display the elements as shaded c. Observe resulting mesh for the inner sphere d. The elements at the geometric interface are congruent e. Verify that the elements ar the interface are connected

a

b

c

d

e

e

CHAPTER 44 831 Concentric Spheres with Radiation

Equivalence All Nodes a. Right Click Part_1 Show All b. Nodes/Elements Modify/Equivalence c. Select All d. Observe Highlighted Nodes e. OK f. Observe 52 merged unreferenced nodes deleted

d

a b

c

e

f

832 MD Demonstration Problems CHAPTER 44

Create Fixed Temperature LBC for Inner Sphere a. LBCs tab: Heat Transfer/Temperature BC b. For Name, enter Temperature_inner c. For Entities screen, select the two inner hemispherical surfaces; best to have only the Pick Surfaces icon active and pick near the center of an element away from the nodes. d. For Temperature, enter 1000 e. Click OK

a

b c

c

d

e

CHAPTER 44 833 Concentric Spheres with Radiation

Create Fixed Temperature LBC for Inner Sphere (continued) a. Observe the applied temperatures as values b. Display temperature values; turn Detailed Rendering On/Off c. Set Geometry and FE to Wireframe d. Double click on Temperature_Inner under LBC in the Model Browser e. Click on Visualization tab f. Select Short under LBC Type and Value Labels g. Select Associated Geometry under Display on Geometry / FEM h. Click OK

a b

e f

g

h

834 MD Demonstration Problems CHAPTER 44

Create Fixed Temperature LBC for Inner Sphere (continued) a. Observe the applied temperatures (red dots) b. Select FE Shaded

a

CHAPTER 44 835 Concentric Spheres with Radiation

Create Radiation Enclosure LBC Between Spheres a. Create two radiation enclosure faces (inner and outer spheres) b. LBCs tab: Heat Transfer/Encl Rad Face c. For Name, enter Encl Rad Face_Inner d. For Entities screen, select both the inner hemispherical surfaces e. Click on Advanced f. For Shell surface option select, Front; direction of the element normals is found by Quality tab: edit/fix Elements/Fix Elements/Normals g. For Shell surface option, select Front h. For Absorptivity, enter 0.9 i. For Emissivity, enter 0.9 j. Click OK

b

c d e f

g

h i

j

836 MD Demonstration Problems CHAPTER 44

Create Radiation Enclosure LBC Between Spheres (continued) a. Create two radiation enclosure faces (inner and outer spheres) b. Display only the outer sphere surfaces c. Using the Model Browser tree, hide the inner surfaces and show the outer surfaces d. Observe the outer surfaces

d

CHAPTER 44 837 Concentric Spheres with Radiation

Create Radiation Enclosure LBC Between Spheres (continued)

a. Create two radiation enclosure faces (inner and outer spheres) b. LBCs tab: Heat Transfer/Encl Rad Face c. For Name, enter Encl Rad Face_outer d. For Entities screen, select both the outer hemispherical surfaces e. Click on Advanced f. For Shell surface option select, Front; direction of the element normals is found by Quality tab: edit/fix Elements/Fix Elements/Normals g. For Shell surface option, select Back h. For Absorptivity, enter 0.7 i. For Emissivity, enter 0.7 j. Click OK

b

c d

e g

h i

j

f

838 MD Demonstration Problems CHAPTER 44

Create Radiation Enclosure LBC Between Spheres (continued) a. Create a single radiation enclosure b. LBCs tab: Heat Transfer/Radiation Enclosure c. For Name, enter Rad Enclosure d. For Shadowing Option, select NO e. For Unused Enclosure Faces, select Encl Rad Face_outer f. Click the > icon g. For Unused Enclosure Faces, select Encl Rad Face_inner h. Click the > icon i. Click OK

b

c d

g e

f

i

h

CHAPTER 44 839 Concentric Spheres with Radiation

Radiation Enclosure LBC Between Spheres (continued) a. Create a single radiation enclosure; display created Radiation Enclosure LBS form b. In the Model Browser tree under LBC, double click Radiation Enclosure c. Observe the form for Rad Enclosure

c

b

840 MD Demonstration Problems CHAPTER 44

Create Radiation to Space From Outer Sphere a. Create radiation to space (ambient) b. LBCs tab: Heat Transfer/Rad to Space c. For Name, enter Rad to Space d. For Entities screen, select the two outer surfaces e. For Ambient temperature, enter 0.0 f. For View Factor, enter 1.0 g. For Absorptivity, enter 1.0 h. For Emissivity, enter 1.0 i. For Shell surface option, enter Front j. Click OK

b

c

d

d e f

g

h i

j

CHAPTER 44 841 Concentric Spheres with Radiation

Create SimXpert Analysis File a. Specify parameter values for SOL 400 analysis b. Right click on FileSet c. Select Create new Nastran job d. For Job Name, enter a title e. For Solution Type, select SOL 400 f. For Solver Input File, specify the fine name and its path g. Unselect Create Default Layout h. Click OK

b c

d

e f g h

842 MD Demonstration Problems CHAPTER 44

Create SimXpert Analysis File (continued) a. Specify parameter values for SOL 400 analysis b. Right click on Load Cases c. Select Create Loadcase d. For Name (Title), enter NewLoadcase e. For Analysis Type, select Nonlinear Steady Heat Trans f. Click OK

b c

d

e f

CHAPTER 44 843 Concentric Spheres with Radiation

Create SimXpert Analysis File (continued) a. Specify parameter values for SOL 400 analysis b. Right click on Load/Boundaries c. Select Select Lbc Set d. For Selected Lbc Set, select DefaultLbcSet in the Model Browser tree e. Click OK f. To see the contents of DefaultLbcSet, click on it in the Model Browser tree

b c

d

e

d

844 MD Demonstration Problems CHAPTER 44

Create SimXpert Analysis File (continued) Remember that our length unit is meter, so the correct Stefan-Boltzmann constant to pick will have units of W/M2/K4. a. Specify parameter values for SOL 400 analysis b. Select Solution 400 Nonlinear Parameters c. For Default Init Temp, enter 750.0 d. For Absolute Temp Scale, select 0.0 e. For Stefan-Boltzmann, select 5.6696e-8 W/M2/K4 (Expert) f. Click Apply

b

c

d e

CHAPTER 44 845 Concentric Spheres with Radiation

Create SimXpert Analysis File (continued) Finally let’s pick the hemicube viewfactor algorithm a. Right Click Solver Control b. Select Direct Input (BULK) c.Enter nlmopts,hemicube,1 d. Check box Export this Section e. Click Apply and Close

c nlmopts,hemicube,1 b

a d e

846 MD Demonstration Problems CHAPTER 44

Create SimXpert Analysis File (continued) a. Specify parameter values for SOL 400 analysis b. Select Output File Properties c. For Text Output, select Print d. Click Apply

c b

d

CHAPTER 44 847 Concentric Spheres with Radiation

Create SimXpert Analysis File (continued) a. Specify parameter values for Sol 400 analysis b. Double click on Loadcase Control c. Select Subcase Steady State Heat d. Click Temp Error e. For Temperature Tolerance, enter 0.01 f. Click Load Error g. For Load Tolerance, enter 1e-5 h. Click Apply i. Click Close

c

d e f g b

848 MD Demonstration Problems CHAPTER 44

Create SimXpert Analysis File (continued) a. Specify parameter values for Sol 400 analysis b. Right click on Output Requests c. Select Nodal Output Requests d. Select Create Temperature Output e. Click OK

c

d

b

e

CHAPTER 44 849 Concentric Spheres with Radiation

Perform SimXpert SOL 400 Thermal Analysis a. Perform steady state heat transfer analysis Sol 400 b. Right click on rad_between_concentric_spheres c. Select Run d. After the analysis is complete, the shown files are created

d b

c

850 MD Demonstration Problems CHAPTER 44

Attach the Analysis Results File a. Analysis complete, attach the .xdb results file b. File: Attach Results c. Select Results d. Click OK

b

c

d

CHAPTER 44 851 Concentric Spheres with Radiation

Display the Temperature Results a. Create a fringe plot for the temperature results b. Display just the two original surfaces (PART_1 and PART_2) c. Results tab: Results/Fringe d. For Result Cases, select Non-linear: 100. % of Load e. For Result type, select Temperatures f. Click Target entities g. Screen select the elements for the two surfaces

c

f e d

g

852 MD Demonstration Problems CHAPTER 44

Display the Temperature Results (continued) a. Create a fringe plot for the temperature results b. Click Label attributes c. Set color to black d. Set format to Fixed e. Click Update

b

c d

e

CHAPTER 44 853 Concentric Spheres with Radiation

Display the Temperature Results (continued) a. Create a fringe plot for the temperature results b. Observe the fringe plot

b 709.3

1000

Input File(s) File

Description

nug_44a.dat

MD Nastran input using Hemi-cube method

nug_44b.dat

MD Nastran input using Gaussian integration method

nug_44c.dat

MD Nastran input with simple three grid model with user-defined radiation matrix

Ch_44b.SimXpert

SimXpert model file

Ch_44c.SimXpert

SimXpert model file

854 MD Demonstration Problems CHAPTER 44

Video Click on the image or caption below to view a streaming video of this problem; it lasts approximately 24 minutes and explains how the steps are performed.

Temperature K (Grid 367) Analytic Gaussian integration Hemi-cube

710.5 710.0 709.5 709.0 708.5 708.0

Analytic

Figure 44-6

Gaussian integration

Hemi-cube

Video of the Above Steps

710.30 709.85 708.91