Modul Kuliah Mekflud 1

MEKANIKA FLUIDA (TEP201) • Dr. Ir. Erizal, MAgr. • Dr. Ir. Nora Herdiana Panjaitan, DEA. • Dr. Ir. Yuli Suharnoto • Dr. Ir. Roh Santoso

Departemen Teknik Pertanian Fakultas Teknolog Pertanian Institut Pertanian Bogor

TEP201 Fluid Mechanics

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MEKANIKA FLUIDA

@ Mempelajari tentang fluida yang bergerak atau diam dan akibat yang ditimbulkan oleh fluida tersebut pada tempatnya.

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Tujuan Instruksional Umum • Setelah menyelesaikan mata kuliah ini, mahasiswa diharapkan mampu menguraikan karakteristik fluida baik dalam keadaan diam maupun bergerak dalam kaitannya dengan kegiatan perencanaan, pengelolaan dan perancangan

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JADWAL KULIAH Selasa 07.00-08.40 / Rabu 15.00-16.40 No. 1 2-3 4-5 6 7 8-9 10-11 12 13 14-15 16

Pokok Bahasan Pendahuluan Fluida Statik Konsep aliran fluida Aliran fluida ideal Aliran fluida kompresibel

Pengajar Erizal Erizal Yuli Suharnoto Yuli Suharnoto Nora Panjaitan

UTS Aliran fluida nyata di dalam pipa Mesin-mesin fluida Teori lapisan batas Aliran fluida pada saluran terbuka Analisis dimensi dan similitude

Nora Panjaitan Roh Santoso Erizal Roh Santoso Yuli Suharnoto

Sebagian bahan kuliah dapat diambil di: http://web.ipb.ac.id/~erizal/mekflud/ TEP201 Fluid Mechanics

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JADWAL PRAKTIKUM No. 1 2 3 4 5 6 7 8 9 10 11

Topik Pendahuluan Bilangan Reynold Penentuan koefisien Orifice dan Venturi Head loss karena gesekan Head loss karena perubahan diameter pipa Head loss karena belokan dan katup Pengukuran debit aliran udara di pipa Pengukuran debit aliran di saluran terbuka Aliran kritis Lompatan hidrolik Ujian praktikum

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PRAKTIKUM 1. Mahasiswa harap hadir paling lambat 5 menit sebelum praktikum dimulai di Laboratorium Hidrolika dan Hidromekanika Departemen Teknik Pertanian (F-G204). 2. Praktikum dilaksanakan 4 kali dalam 1 minggu (Selasa, Rabu, Kamis, dan Jum’at). 3. Pelaksanaan praktikum secara kelompok/grup yang terdiri atas 6-7 mahasiswa. 4. Pertanyaan sebelum praktikum wajib dijawab dan diserahkan kepada dosen/asisten dosen. 5. Praktikum harus selalu dihadiri. Jika berhalangan harus mendapatkan surat izin dari departemen. 6. Setelah praktikum dilaksanakan, buatlah laporan sementara berisi data hasil pengukuran yang dilengkapi dengan daftar anggota grup/kelompok. 7. Laporan perseorangan dan ditulis dengan tangan pada kertas ukuran A4, kemudian penyerahannya paling lambat sebelum praktikum dimulai pada minggu berikutnya. 8. Laporan berisi : • • • • •

Pendahuluan yang berisi teori singkat dan tujuan praktikum Bahan dan Metode Hasil dan Pembahasan Kesimpulan dan Saran Daftar Pustaka

9. Segala bentuk pelanggaran dapat diberikan sanksi akademik berupa : skorsing praktikum, tidak diperkenankan mengikuti ujian, dan lain sebagainya. 10. Pada akhir semester akan diadakan ujian praktikum oleh dosen.

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PENILAIAN & PUSTAKA • • •

Praktikum : 30% UTS : 30% Ujian Akhir : 40% Streeter, V.L. dan E.B. Wylie. 1999. Mekanika Fluida. Penerbit Erlangga. Jakarta. Giles, Ranald, V. 1994. Fluid Mechanics and Hydraulics. Schaum’s Outline Series. McGraw Hill Book Co. New York Hughes, W.F dan J.A. Brighton. 1967. Theory and Problem of Fluid Dynamic. Schaum’s Outline Series. McGraw Hill Book Co. New York Vennard, J.K dan R.L. Street. 1976. Elementary Fluid Mechanics. John Wiley and Sons. New York Erizal dan Panjaitan, N.H. 2007. Pedoman Praktikum Mekanika Fluida. IPB.

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Introduction to Fluid Mechanics* Fred Stern, Tao Xing, Jun Shao, Surajeet Ghosh AFD

EFD

CFD

(Analytical Fluid Dynamics)

(Experimental Fluid Dynamics)

(Computational Fluid Dynamics)

∇•U = 0 DU 1 2 = −∇p + ∇ U + ∇ • ui u j Re Dt

*Revised version of 4/99 by Fred Stern and Eric Paterson TEP201 Fluid Mechanics

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Fluid Mechanics • Fluids essential to life • Human body 95% water • Earth’s surface is 2/3 water • Atmosphere extends 17km above the earth’s surface

• History shaped by fluid mechanics • • • •

Geomorphology Human migration and civilization Modern scientific and mathematical theories and methods Warfare

• Touches every part of our lives

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History Faces of Fluid Mechanics

Archimedes

(C. 287-212 BC)

Navier (1785-1836)

Newton (1642-1727)

Stokes (1819-1903)

Leibniz (1646-1716)

Reynolds (1842-1912) TEP201 Fluid Mechanics

Bernoulli

Euler

(1667-1748)

(1707-1783)

Prandtl

Taylor

(1875-1953)

(1886-1975) 10

Significance • Fluids omnipresent • Weather & climate • Vehicles: automobiles, trains, ships, and planes, etc. • Environment • Physiology and medicine • Sports & recreation • Many other examples!

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Weather & Climate Tornadoes

Thunderstorm

Global Climate

Hurricanes

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Vehicles Surface ships

Aircraft

High-speed rail

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Submarines

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Environment Air pollution

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River hydraulics

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Physiology and Medicine Blood pump

Ventricular assist device

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Sports & Recreation Water sports

Cycling

Auto racing

Offshore racing

Surfing

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Fluids Engineering • Engineers have different kinds of tools available for solving fluids engineering systems • Analytical Fluid Dynamics (AFD) • Experimental Fluid Dynamics (EFD) • Computational Fluid Dynamics (CFD)

• This class provides an introduction to all three tools: AFD through lecture and CFD and EFD through labs

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Analytical Fluid Dynamics • The theory of mathematical physics problem formulation • Control volume & differential analysis • Exact solutions only exist for simple geometry and conditions • Approximate solutions for practical applications • Linear • Empirical relations using EFD data

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Analytical Fluid Dynamics •

Lecture Part of Fluid Class • • • • • • • •

Definition and fluids properties Fluid statics Fluids in motion Continuity, momentum, and energy principles Dimensional analysis and similitude Surface resistance Flow in conduits Drag and lift

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Analytical Fluid Dynamics • Example: laminar pipe flow

ρUD < 2000 Assumptions: Fully developed, Low Re = μ Approach: Simplify momentum equation, Schematic integrate, apply boundary conditions (noslip wall) to determine integration constants and use energy equation to calculate head loss 0

0 ⎡ ∂ 2u ∂ 2u ⎤ Du 0 ∂ p =− + μ ⎢ 2 + 2 ⎥ + gx ∂x Dt ∂y ⎦ ⎣ ∂x

Exact solution :

u(r) = 1 (− ∂p )(R2 − r 2) 4μ ∂x 8μ du

8τ w = dy w = 64 f = Friction factor: ρV 2 ρV 2 Re p1 p2 L V 2 32 μ LV + z1 = + z2 + h f = hf = f Head loss: γ γ D 2g γ D2 TEP201 Fluid Mechanics

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Analytical Fluid Dynamics • Example: turbulent flow in smooth pipe( Re > 3000) Three layer concept (using dimensional analysis)

y + = yu * ν

u + = u u* 1.

Laminar sub-layer (viscous shear dominates)

u+ = y+ 2.

0 < y+ < 5

Overlap layer (viscous and turbulent shear important) u+ =

3.

u* = τ w ρ

1

κ

ln y + + B

20 < y + < 105

(R=0.41, B=5.5)

Outer layer (turbulent shear dominates)

Assume log-law is valid across entire pipe:

⎛ U −u r⎞ + 5 = f 1 − ⎜ ⎟ y > 10 * u r0 ⎠ ⎝

u (r ) u*

=

1

κ

r0 − r ) u * ( ln +B

ν

Integration for average velocity and using EFD data to adjust constants: 1 = 2log ( Re f 1 2 ) − .8 f TEP201 Fluid Mechanics

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Analytical Fluid Dynamics • Example: turbulent flow in rough pipe Both laminar sublayer and overlap layer are affected by roughness

u+ = u+ ( y k )

Inner layer:

Outer layer: unaffected

u+ =

Overlap layer:

1

κ

ln

y + constant k

Three regimes of flow depending on k+ 1. K+<5, hydraulically smooth (no effect of roughness) 2. 5 < K+< 70, transitional roughness (Re dependent) 3. K+> 70, fully rough (independent Re)

For 3, using EFD data to adjust constants: u+ =

1

κ

ln

y + 8.5 ≠ f ( Re ) k

Friction factor:

TEP201 Fluid Mechanics

1 k D = −2log 3.7 f

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Analytical Fluid Dynamics • Example: Moody diagram for turbulent pipe flow Composite Log-Law for smooth and rough pipes is given by the Moody diagram:

1 f

1

2

⎡k D 2.51 ⎤ = −2log ⎢ + 12⎥ ⎣ 3.7 Re f ⎦

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Experimental Fluid Dynamics (EFD) Definition: Use of experimental methodology and procedures for solving fluids engineering systems, including full and model scales, large and table top facilities, measurement systems (instrumentation, data acquisition and data reduction), uncertainty analysis, and dimensional analysis and similarity. EFD philosophy: • Decisions on conducting experiments are governed by the ability of the expected test outcome, to achieve the test objectives within allowable uncertainties. • Integration of UA into all test phases should be a key part of entire experimental program • test design • determination of error sources • estimation of uncertainty • documentation of the results

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Purpose • Science & Technology: understand and investigate a

phenomenon/process, substantiate and validate a theory (hypothesis)

• Research & Development: document a process/system, provide benchmark data (standard procedures, validations), calibrate instruments, equipment, and facilities • Industry: design optimization and analysis, provide data for direct use, product liability, and acceptance • Teaching: instruction/demonstration

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Applications of EFD

Application in science & technology

Application in research & development

Picture of Karman vortex shedding

Tropic Wind Tunnel has the ability to create temperatures ranging from 0 to 165 degrees Fahrenheit and simulate rain

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Applications of EFD (cont’d)

Example of industrial application NASA's cryogenic wind tunnel simulates flight conditions for scale models--a critical tool in designing airplanes. Application in teaching Fluid dynamics laboratory TEP201 Fluid Mechanics

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Full and model scale

• Scales: model, and full-scale • Selection of the model scale: governed by dimensional analysis and similarity

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Measurement systems • Instrumentation • • • • •

Load cell to measure forces and moments Pressure transducers Pitot tubes Hotwire anemometry PIV, LDV

• Data acquisition • • • •

Serial port devices Desktop PC’s Plug-in data acquisition boards DA software - Labview

• Data analysis and data reduction • Data reduction equations • Fast Fourier Transform

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Instrumentation

Pitot tube

Load cell

3D - PIV

Hotwire TEP201 Fluid Mechanics

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Data acquisition system Hardware

Software - Labview

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Data reduction methods r = F(T ) w w ra = F(Ta ) Q = F(Dz DM ) f = F(r , r , z w

a

SM

, Q) =

2

5

gp D

8LQ

2

rw (z - z ) ra SM i SM j

Example of data reduction equations

Example of FFT application

Fast Fourier Transform FFT: Converts a function from amplitude as function of time to amplitude as function of frequency

Free-surface wave elevation contours 0.15

A(f)

0.1 0.05

Aim: To analyze the natural unsteadiness of the separated flow, around a surface piercing strut, using FFT. TEP201 Fluid Mechanics

0 0

1

2

3 4 f [Hz]

5

6

7

Typical amplitude spectra of the wave elevations

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Uncertainty analysis Rigorous methodology for uncertainty assessment using statistical and engineering concepts ELEMENTAL ERROR SOURCES

1

2

J

INDIVIDUAL MEASUREMENT SYSTEMS

X 1 B ,P

X 2 B ,P

X J B,P

MEASUREMENT OF INDIVIDUAL VARIABLES

1

1

2

2

J

J

r = r (X , X ,......, X ) 1

2

J

r B, P r

r

TEP201 Fluid Mechanics

DATA REDUCTION EQUATION

EXPERIMENTAL RESULT

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Dimensional analysis • Definition : Dimensional analysis is a process of formulating fluid mechanics problems in in terms of non-dimensional variables and parameters.

• Why is it used : • Reduction in variables ( If F(A1, A2, … , An) = 0, then f(Π1, Π2, … Πr < n) = 0,

where, F = functional form, Ai = dimensional variables, Πj = non-dimensional parameters, m = number of important dimensions, n = number of dimensional variables, r = n – m ). Thereby the number of experiments required to determine f vs. F is reduced. • Helps in understanding physics • Useful in data analysis and modeling • Enables scaling of different physical dimensions and fluid properties

Example

Drag = f(V, L, r, m, c, t, e, T, etc.) From dimensional analysis,

Vortex shedding behind cylinder

Examples of dimensionless quantities : Reynolds number, Froude Number, Strouhal number, Euler number, etc. TEP201 Fluid Mechanics

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Similarity and model testing • Definition : Flow conditions for a model test are completely similar if all relevant dimensionless parameters have the same corresponding values for model and prototype. • Πi model = Πi prototype i = 1 • Enables extrapolation from model to full scale • However, complete similarity usually not possible. Therefore, often it is necessary to use Re, or Fr, or Ma scaling, i.e., select most important Π and accommodate others as best possible.

• Types of similarity: • Geometric Similarity : all body dimensions in all three coordinates have the same linear-scale ratios. • Kinematic Similarity : homologous (same relative position) particles lie at homologous points at homologous times. • Dynamic Similarity : in addition to the requirements for kinematic similarity the model and prototype forces must be in a constant ratio.

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EFD process • “EFD process” is the steps to set up an experiment and take data 1. Setup facility 2. Install model 3. Setup equipment 4. Setup Data Acquisition using LabView 5. Perform calibrations 6. Data Analysis and Data Reduction 7. Uncertainty Analysis 8. Comparison with CFD results 9. Documentation and Reporting TEP201 Fluid Mechanics

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EFD – “hands on” experience

Lab1: Measurement of kinematic viscosity of a fluid

Lab2: Measurement of flow rate, friction factor and velocity profiles in smooth and rough pipes.

Lab3: Measurement of surface pressure distribution and lift coefficient for an airfoil

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Computational Fluid Dynamics • CFD is use of computational methods for solving fluid engineering systems, including modeling (mathematical & Physics) and numerical methods (solvers, finite differences, and grid generations, etc.). • Rapid growth in CFD technology since advent of computer

ENIAC 1, 1946

IBM WorkStation

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Purpose • The objective of CFD is to model the continuous fluids with Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem, solve it, validate it and achieve simulation based design instead of “build & test” • Simulation of physical fluid phenomena that are difficult to be measured by experiments: scale simulations (full-scale ships, airplanes), hazards (explosions,radiations,pollution), physics (weather prediction, planetary boundary layer, stellar evolution).

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Modeling • Mathematical physics problem formulation of fluid engineering system • Governing equations: Navier-Stokes equations (momentum), continuity equation, pressure Poisson equation, energy equation, ideal gas law, combustions (chemical reaction equation), multi-phase flows(e.g. Rayleigh equation), and turbulent models (RANS, LES, DES). • Coordinates: Cartesian, cylindrical and spherical coordinates result in different form of governing equations • Initial conditions(initial guess of the solution) and Boundary Conditions (no-slip wall, free-surface, zero-gradient, symmetry, velocity/pressure inlet/outlet) • Flow conditions: Geometry approximation, domain, Reynolds Number, and Mach Number, etc.

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Modeling (examples) Developing flame surface (Bell et al., 2001) Free surface animation for ship in regular waves

Evolution of a 2D mixing layer laden with particles of Stokes Number 0.3 with respect to the vortex time scale (C.Narayanan)

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Modeling (examples, cont’d)

3D vortex shedding behind a circular cylinder (Re=100,DNS,J.Dijkstra)

DES, Re=105, vorticity magnitude of turbulent flow around NACA12 with angle of attack 60.

LES of a turbulent jet. Back wall shows a slice of the dissipation rate and the bottom wall shows a carpet plot of the mixture fraction in a slice through the jet centerline, Re=21,000 (D. Glaze).

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Numerical methods y • Finite difference methods: using numerical scheme to approximate the exact derivatives in the PDEs Pi + 1 − 2 Pi + Pi − 1 ∂2P = ∂x 2 Δx2 P j +1 − 2 P j + P j −1 ∂2P = ∂y 2 Δy2

jmax

Δx

j+1 j j-1

Δy

o

i-1 i i+1

imax

• Grid generation: conformal mapping, algebraic methods and differential equation methods • Solvers: direct methods (Cramer’s rule, Gauss elimination, LU decomposition) and iterative methods (Jacobi, Gauss-Seidel, SOR) Slice of 3D mesh of a fighter aircraft TEP201 Fluid Mechanics

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x

CFD process • “CFD process” is the steps to set up a problem and run the code 1. Geometry: Create the geometry you want 2. Physics: fluid properties, viscous modeling and boundary conditions 3. Mesh: coarse, medium and fine meshes 4. Solve: different solvers and numerical methods 5. Report: time history of convergence of variables 6. Post-Processing: visualizations (contours, vectors), validation and verification TEP201 Fluid Mechanics

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Commercial software •

CFD software 1. FLUENT: http://www.fluent.com 2. CFDRC: http://www.cfdrc.com 3. STAR-CD:http://www.cd-adapco.com 4. CFX/AEA: http://www.software.aeat.com/cfx

•

Grid Generation software 1. Gridgen: http://www.pointwise.com 2. GridPro: http://www.gridpro.com

•

Visualization software 1. Tecplot:

http://www.amtec.com

2. Fieldview: http://www.ilight.com

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“Hands-on” experience using FlowLab 1.1 (pipe template)

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“Hands-on” experience using FlowLab 1.1 (airfoil template)

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57:020 Fluid Mechanics • Lectures cover basic concepts in fluid statics, kinematics, and dynamics, control-volume, and differential-equation analysis methods. Homework assignments, tests, and complementary EFD/CFD labs • EFD/CFD lab materials Lecture

Other Docs

Lab 1: Viscosity

Lab 2: Pipe Flow

Lab 3: Airfoil

EFD Lecture

EFD UA Report Lab Report instructions

Pre EFD Lab1 EFD 1 Lab 1_UA Instructions_UA

Pre EFD Lab2 EFD 2 Lab2_UA Instructions_UA

Pre EFD lab3 EFD 3 Benchmark Data Instructions_UA

CFD Lecture

Lab report instructions

None

Pre CFD lab1 CFD lab1

Pre CFD lab2 CFD lab2

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