pendahuluan.pdf

48
MEKANIKA FLUIDA (TEP201) Dr. Ir. Erizal, MAgr. Dr Ir Nora Herdiana Panjaitan DEA 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 1

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Page 1: pendahuluan.pdf

MEKANIKA FLUIDA(TEP201)( )

• Dr. Ir. Erizal, MAgr.• Dr Ir Nora Herdiana Panjaitan DEA• Dr. Ir. Nora Herdiana Panjaitan, DEA.

• Dr. Ir. Yuli Suharnoto• Dr. Ir. Roh Santoso

Departemen Teknik PertanianFakultas Teknolog Pertanian

Institut Pertanian Bogor

TEP201 Fluid Mechanics 1

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MEKANIKA FLUIDAMEKANIKA FLUIDA

Mempelajari tentang fluida yang bergerak atau diam dan akibat yangbergerak atau diam dan akibat yang ditimbulkan oleh fluida tersebut pada tempatnyatempatnya.

TEP201 Fluid Mechanics 2

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T j I t k i l UTujuan Instruksional Umum

• Setelah menyelesaikan mata kuliah ini, mahasiswa diharapkan mampu menguraikan karakteristik fluida baik gdalam keadaan diam maupun bergerak dalam kaitannya dengan kegiatandalam kaitannya dengan kegiatan perencanaan, pengelolaan dan perancanganperancangan

TEP201 Fluid Mechanics 3

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JADWAL KULIAH

Selasa 07.00-08.40 / Rabu 07.00-08.40

No. Pokok Bahasan Pengajar 1 Pendahuluan Erizal

2-3 Fluida Statik Erizal4-5 Konsep aliran fluida Roh Santoso 6 Aliran fluida ideal Yuli Suharnoto 7 Aliran fluida kompresibel Nora Panjaitan

8-9 UTS 10-11 Aliran fluida nyata di dalam pipa Nora Panjaitan

12 Mesin-mesin fluida Roh Santoso 13 Teori lapisan batas Erizal

14-15 Aliran fluida pada saluran terbuka Yuli Suharnoto 16 Analisis dimensi dan similitude Yuli Suharnoto

Sebagian bahan kuliah dapat diambil di:~

TEP201 Fluid Mechanics 4

http://web.ipb.ac.id/~erizal/mekflud/

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JADWAL PRAKTIKUMJADWAL PRAKTIKUM

No. Topik 1 Pendahuluan, Pengenalan alat 2 Bilangan Reynold2 Bilangan Reynold3 Penentuan koefisien Orifice dan Venturi 4 Head loss karena gesekan dan perubahan diameter pipa 5 Latihan soal 16 Latihan soal 2 7 Head loss karena belokan dan katup 8 Pengukuran debit aliran udara di pipa 9 Pengukuran debit aliran di saluran terbuka 10 Lompatan hidrolik 11 Latihan soal 3 12 Latihan soal 413 Ujian praktikum

TEP201 Fluid Mechanics 5

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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)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 P ktik h l l dih di i Jik b h l h d tk t i i d i5. 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 L d dit li d t d k t k A4 k di7. 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.

TEP201 Fluid Mechanics 6

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PENILAIAN & PUSTAKAPENILAIAN & PUSTAKA• Praktikum : 30%• 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 HydraulicsGiles, Ranald, V. 1994. Fluid Mechanics and Hydraulics. Schaum’s Outline Series. McGraw Hill Book Co. New YorkHughes, W.F dan J.A. Brighton. 1967. Theory and Problem of Fluid Dynamic Schaum’s Outline Series McGraw Hill Book CoFluid Dynamic. Schaum s Outline Series. McGraw Hill Book Co. New YorkVennard, J.K dan R.L. Street. 1976. Elementary Fluid Mechanics. John Wiley and Sons. New YorkMechanics. John Wiley and Sons. New YorkErizal dan Panjaitan, N.H. 2007. Pedoman Praktikum Mekanika Fluida. IPB.

TEP201 Fluid Mechanics 7

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Introduction to Fluid MechanicsIntroduction to Fluid MechanicsFred Stern Tao Xing Jun Shao Surajeet Ghosh

CFDEFDAFD

Fred Stern, Tao Xing, Jun Shao, Surajeet Ghosh

CFD(Computational Fluid Dynamics)

EFD(Experimental Fluid Dynamics)

AFD(Analytical Fluid Dynamics)

2

01

Re i jD p u uDt

∇ • =

= −∇ + ∇ + ∇ •

UU U

TEP201 Fluid Mechanics 8

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Fluid Mechanicsu d a

• Fluids essential to lifeFluids 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 mechanicsy p y• Geomorphology• Human migration and civilization• Modern scientific and mathematical theories and methods• Warfare

• Touches every part of our lives

TEP201 Fluid Mechanics 9

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HistoryHistoryFaces of Fluid Mechanics

Archimedes(C. 287-212 BC)

Newton(1642-1727)

Leibniz(1646-1716)

Euler(1707-1783)

Bernoulli(1667-1748)

Navier Stokes Reynolds Prandtl Taylor

TEP201 Fluid Mechanics 10

Navier(1785-1836)

Stokes(1819-1903)

Reynolds(1842-1912)

Prandtl(1875-1953)

Taylor(1886-1975)

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SignificanceSignificance

• Fluids omnipresentp• Weather & climate• Vehicles: automobiles trains ships and• Vehicles: automobiles, trains, ships, and

planes, etc.E i t• Environment

• Physiology and medicine• Sports & recreation• Many other examples!Many other examples!

TEP201 Fluid Mechanics 11

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Weather & ClimateWeather & Climate

Tornadoes Thunderstorm

HurricanesGlobal Climate

TEP201 Fluid Mechanics 12

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VehiclesVehicles

Aircraft Surface ships

SubmarinesHigh-speed rail

TEP201 Fluid Mechanics 13

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EnvironmentEnvironment

Ri h d liAir pollution River hydraulics

TEP201 Fluid Mechanics 14

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Physiology and MedicinePhysiology and Medicine

Blood pump Ventricular assist deviceBlood pump Ventricular assist device

TEP201 Fluid Mechanics 15

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Sports & RecreationSports & Recreation

Water sports Offshore racingCycling

Auto racing Surfing

TEP201 Fluid Mechanics 16

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Fluids EngineeringFluids Engineering

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

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

TEP201 Fluid Mechanics 17

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Analytical Fluid DynamicsAnalytical Fluid Dynamics

• The theory of mathematical physicsThe theory of mathematical physics problem formulation

• Control volume & differential analysis• Control volume & differential analysis• Exact solutions only exist for simple

d di igeometry and conditions• Approximate solutions for practical pp p

applications• LinearLinear• Empirical relations using EFD data

TEP201 Fluid Mechanics 18

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Analytical Fluid DynamicsAnalytical Fluid Dynamics

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

TEP201 Fluid Mechanics 19

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Analytical Fluid Dynamicsa y a u d y a• Example: laminar pipe flow

A i F ll d l d L UDρ

Schematic

Assumptions: Fully developed, Low Approach: Simplify momentum equation, integrate, apply boundary conditions (no-

UD 2000Re ρ <μ

=

slip wall) to determine integration constants and use energy equation to calculate head loss 0

Exact solution :

xgyu

xu

xp

DtDu

+⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

+∂∂

−= 2

2

2

2

μ0 0 0

Exact solution :2 21( ) ( )( )4

pu r R rxμ∂= − −∂

8 duμFriction factor:

88 64Re2 2

wdywfV V

μτρ ρ

= = =

1 2p p h2 32L V LVμ

TEP201 Fluid Mechanics 20

Head loss:1 2

1 2 fp pz z hγ γ

+ = + +2

322f

L V LVh fD g D

μγ

= =

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Analytical Fluid Dynamicsy y• Example: turbulent flow in smooth pipe( )Re 3000>

Three layer concept (using dimensional analysis)*y yu ν+ =*u u u+ =

*wu τ ρ=

y p ( g y )

1. Laminar sub-layer (viscous shear dominates)

0 5y+< <u y+ +=

2. Overlap layer (viscous and turbulent shear important)1 lnu y Bκ

+ += + 520 10y+< <

U u r⎛ ⎞− 5+3 O t l (t b l t h d i t )

( =0.41, B=5.5)

*0

1U u rfu r

⎛ ⎞= −⎜ ⎟

⎝ ⎠

510y + >

( ) ( ) *0

*

1 lnu r r r u

Bu κ ν

−= +

3. Outer layer (turbulent shear dominates)

Assume log-law is valid across entire pipe:u κ ν

Integration for average velocity and using EFD data to adjust constants:

( )1 21 2l R 8f

TEP201 Fluid Mechanics 21

( )1 22log Re .8ff

= −

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Analytical Fluid DynamicsAnalytical Fluid Dynamics• Example: turbulent flow in rough pipe

Both laminar sublayer and overlap layer

( )u u y k+ +=

Both laminar sublayer and overlap layerare affected by roughnessInner layer:

1 ln yu+ = +

Outer layer: unaffected

Overlap layer: constantkκ

Three regimes of flow depending on k+

1. K+<5, hydraulically smooth (no effect of roughness)

O e ap aye constant

, y y ( g )2. 5 < K+< 70, transitional roughness (Re dependent)3. K+> 70, fully rough (independent Re)For 3, using EFD data to adjust constants:

1 2log3.7k D

f= −( )1 ln 8.5 Reyu f

kκ+ = + ≠ Friction factor:

For 3, using EFD data to adjust constants:

TEP201 Fluid Mechanics 22

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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 1 2

2

1 2.512log3.7 Rek D

ff

⎡ ⎤= − +⎢ ⎥

⎣ ⎦

TEP201 Fluid Mechanics 23

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Experimental Fluid Dynamics (EFD)p y ( )Definition:

Use of experimental methodology and procedures for solving fluidsUse 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 similaritysimilarity.

EFD philosophy:• Decisions on conducting experiments are governed by the ability of theDecisions 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

TEP201 Fluid Mechanics 24

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PurposePurpose

•Science & Technology: understand and investigate a phenomenon/process, substantiate and validate a theory (hypothesis)theory (hypothesis)

• Research & Development: document a process/system, provide benchmark data (standard proceduresprovide 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

TEP201 Fluid Mechanics 25

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Applications of EFDApplications of EFD

Application in research & development

T i Wi d T l h th bilit t t

Application in science & technology

Pi t f K t h ddi Tropic Wind Tunnel has the ability to create temperatures ranging from 0 to 165 degreesFahrenheit and simulate rain

Picture of Karman vortex shedding

TEP201 Fluid Mechanics 26

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Applications of EFD (cont’d)pp ( )

Example of industrial applicationExample of industrial application

NASA's cryogenic wind tunnel simulates flight conditions for scale models--a critical tool indesigning airplanes.

Application in teaching

TEP201 Fluid Mechanics 27

pp g

Fluid dynamics laboratory

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Full and model scaleu a d od a

• Scales: model, and full-scale

• Selection of the model scale: governed by dimensional analysis and similarity

TEP201 Fluid Mechanics 28

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Measurement systemsMeasurement systems• Instrumentation

• Load cell to measure forces and momentsLoad cell to measure forces and moments• Pressure transducers• Pitot tubes

H t i t• Hotwire anemometry• PIV, LDV

• Data acquisitionData acquisition• Serial port devices• Desktop PC’s

l d b d• Plug-in data acquisition boards• DA software - Labview

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

TEP201 Fluid Mechanics 29

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Instrumentationu a o

Pitot tube

Load cellLoad cell

TEP201 Fluid Mechanics 30

Hotwire 3D - PIV

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Data acquisition systema a a qu o y

Hardware

Software LabviewSoftware - Labview

TEP201 Fluid Mechanics 31

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Data reduction methods

)g D� �

Q = F( z )�DM 2 5

= F(T )�

�w

= F(T )a

w

a

f = F( , , z , Q =� � )a

a

wg D�

8LQ

�w SM 2( )z

SMi

- zSM

j

Example of data reduction equations

Fast Fourier Transform

FFT: Converts a function from amplitude as function of time to amplitude as function of frequencyequations

Example of FFT li ti F f l ti tapplication

0.1

0.15

Free-surface wave elevation contours

Ai T l th t l t di fA(

f)0

0.05

TEP201 Fluid Mechanics 32

Aim: To analyze the natural unsteadiness of the separated flow, around a surface piercing

strut, using FFT.f [Hz]

0 1 2 3 4 5 6 7

Typical amplitude spectraof the wave elevations

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Uncertainty analysisUncertainty analysisRigorous methodology for uncertainty assessment

using statistical and engineering concepts

ELEMENTALERROR SOURCES

using statistical and engineering concepts

1 2 JINDIVIDUALMEASUREMENTSYSTEMS

MEASUREMENTOF INDIVIDUALVARIABLES

XB , P

1

1 1

XB , P

2

2 2

XB , P

J

J J

r = r (X , X ,......, X )1 2 J

DATA REDUCTIONEQUATION1 2 J EQUATION

EXPERIMENTALRESULT

rB P

TEP201 Fluid Mechanics 33

RESULTB , Pr r

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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 : y

• 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-dimensionalparameters, 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 propertiesEnables scaling of different physical dimensions and fluid properties

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

From dimensional analysis,

TEP201 Fluid Mechanics 34

Vortex shedding behind cylinder Examples of dimensionless quantities : Reynolds number, FroudeNumber, Strouhal number, Euler number, etc.

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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 = 1E bl l i f d l f ll l• Enables extrapolation from model to full scale

• However, complete similarity usually not possible. Therefore, often it is necessary touse Re, or Fr, or Ma scaling, i.e., select most important Π and accommodate othersas best possible.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 ratioand prototype forces must be in a constant ratio.

TEP201 Fluid Mechanics 35

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EFD processp• “EFD process” is the steps to set up an experiment and

take datatake data

1. Setup facility

2 I t ll d l2. Install model

3. Setup equipment

4. Setup Data Acquisition using LabView

5. Perform calibrations5. Perform calibrations

6. Data Analysis and Data Reduction

7 U t i t A l i7. Uncertainty Analysis

8. Comparison with CFD results

TEP201 Fluid Mechanics 36

9. Documentation and Reporting

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EFD – “hands on” experiencea d o p

Lab1: Measurement of ki ti i it f fl id Lab2: Measurement ofkinematic viscosity of a fluid Lab2: Measurement of

flow rate, friction factor andvelocity profiles in smooth andrough pipes.

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

TEP201 Fluid Mechanics 37

distribution and lift coefficient for an airfoil

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Computational Fluid DynamicsComputational Fluid Dynamics• CFD is use of computational methods for

solving fluid engineering systems includingsolving fluid engineering systems, including modeling (mathematical & Physics) and numerical methods (solvers finite differencesnumerical methods (solvers, finite differences, and grid generations, etc.).R id h i CFD h l i d• Rapid growth in CFD technology since advent of computer

ENIAC 1, 1946 IBM WorkStation

TEP201 Fluid Mechanics 38

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PurposePurpose• The objective of CFD is to model the continuous fluids

with Partial Differential Equations (PDEs) andwith Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem, solve it, validate it and achieve simulation based designginstead of “build & test”

• Simulation of physical fluid phenomena that are difficult to be measured by experiments: scale i l ti (f ll l hi i l ) h dsimulations (full-scale ships, airplanes), hazards

(explosions,radiations,pollution), physics (weather prediction planetary boundary layer stellar evolution)prediction, planetary boundary layer, stellar evolution).

TEP201 Fluid Mechanics 39

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Modelingg• Mathematical physics problem formulation of fluid

engineering systemg g y• Governing equations: Navier-Stokes equations (momentum),

continuity equation, pressure Poisson equation, energy equation ideal gas law combustions (chemical reactionequation, ideal gas law, combustions (chemical reaction equation), multi-phase flows(e.g. Rayleigh equation), and turbulent models (RANS, LES, DES).C di t C t i li d i l d h i l di t• Coordinates: Cartesian, cylindrical and spherical coordinates result in different form of governing equations

• Initial conditions(initial guess of the solution) and Boundary ( g ) yConditions (no-slip wall, free-surface, zero-gradient, symmetry, velocity/pressure inlet/outlet)

• Flow conditions: Geometry approximation domain Reynolds• Flow conditions: Geometry approximation, domain, Reynolds Number, and Mach Number, etc.

TEP201 Fluid Mechanics 40

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Modeling (examples)Free surface animation for ship in regular waves

Developing flame surface (Bell et al., 2001)

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

TEP201 Fluid Mechanics 41

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Modeling (examples, cont’d)

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

DES,Re=105, vorticity magnitude of turbulent flow around NACA12 withNACA12 with angle of attack 60.

TEP201 Fluid Mechanics 42

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

• Finite difference methods: using numerical scheme to

y

j+1jmax

using numerical scheme to approximate the exact derivatives in the PDEs

j+1j

j-1 yΔ2

1 12P P PP − +∂

o xi i+1i-1 imax

1 12 2

2i i iP P PPx x

+ −+∂=

∂ Δ2

1 12 2

2j j jP P PPy y

+ −− +∂=

∂ Δ• Grid generation: conformal

mapping, algebraic methods and differential equation methods

y y∂ Δ

differential equation methods• Solvers: direct methods (Cramer’s

rule, Gauss elimination, LU decomposition) and iterativedecomposition) and iterative methods (Jacobi, Gauss-Seidel, SOR)

TEP201 Fluid Mechanics 43

Slice of 3D mesh of a fighter aircraft

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CFD processCFD process• “CFD process” is the steps to set up a problem

and run the codeand run the code1. Geometry: Create the geometry you want2 Physics: fluid properties viscous modeling and2. Physics: fluid properties, viscous modeling and

boundary conditions3. Mesh: coarse, medium and fine meshes3. Mesh: coarse, medium and fine meshes4. Solve: different solvers and numerical

methods5. Report: time history of convergence of

variables6. Post-Processing: visualizations (contours,

vectors), validation and verification

TEP201 Fluid Mechanics 44

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Commercial softwareCommercial software• CFD software

h // fl1. FLUENT: http://www.fluent.com2. CFDRC: http://www.cfdrc.com3 STAR-CD:http://www cd-adapco com3. STAR-CD:http://www.cd-adapco.com4. CFX/AEA: http://www.software.aeat.com/cfx

• Grid Generation software• Grid Generation software1. Gridgen: http://www.pointwise.com2 GridPro: http://www gridpro com2. GridPro: http://www.gridpro.com

• Visualization software1. Tecplot: http://www.amtec.com2. Fieldview: http://www.ilight.com

TEP201 Fluid Mechanics 45

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

TEP201 Fluid Mechanics 46

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“Hands-on” experience using FlowLab 1.1 ( i f il t l t )(airfoil template)

TEP201 Fluid Mechanics 47

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57:020 Fluid Mechanics• Lectures cover basic concepts in fluid statics, kinematics,

and dynamics control-volume and differential-equationand dynamics, control volume, and differential equation analysis methods. Homework assignments, tests, and complementary EFD/CFD labsp y

• EFD/CFD lab materials

Lecture Other Docs Lab 1: Viscosity

Lab 2: Pipe Flow

Lab 3: Airfoil

EFD EFD UA Report Pre EFD Lab1 Pre EFD Lab2 Pre EFD lab3Lecture Lab Report instructions EFD 1

Lab 1_UAInstructions_UA

EFD 2Lab2_UA

Instructions_UA

EFD 3Benchmark DataInstructions_UA

CFDLecture

Lab report instructions None Pre CFD lab1CFD lab1

Pre CFD lab2CFD lab2

TEP201 Fluid Mechanics 48