introduction cfd

8/8/2019 Introduction Cfd

http://slidepdf.com/reader/full/introduction-cfd 1/52

n ro uc on o ompu a ona



lin

1. What, why and where of CFD?

. o e ng

3. Numerical methods

5. CFD Educational Interface

6. CFD Process7. Example of CFD Process

8. 58:160 CFD Labs

2



Wh i FD?

• CFD is the simulation of fluids engineering systems usingmodeling (mathematical physical problem formulation) andnumer ca me o s scre za on me o s, so vers, numer ca

parameters, and grid generations, etc.)

• Historically only Analytical Fluid Dynamics (AFD) andxper men a u ynam cs .

• CFD made possible by the advent of digital computer and

advancing with improvements of computer resources(500 flops, 194720 teraflops, 2003)

3



Wh use CFD?• Analysis and Design

1. Simulation-based desi n instead of “build & test”

More cost effective and more rapid than EFDCFD provides high-fidelity database for diagnosing flowfield

2. Simu ation o p ysica ui p enomena t at aredifficult for experiments

Full scale simulations (e.g., ships and airplanes), , .

Hazards (e.g., explosions, radiation, pollution)

Physics (e.g., planetary boundary layer, stellarevolution)

• Knowledge and exploration of flow physics

4



Where is CFD used?• Where is CFD used? Aerospace

• Aerospace

• Automotive

• Biomedical Biomedical

• ChemicalProcessing

• HVAC

F18 Store Separation

• Hydraulics

• Marine

• Oil & Gas

• Power Generation

• Sports

Temperature and natural Automotive

5

convect on currents n t e eye following laser heating.



Where is CFD used?• Where is CFD used?

Chemical Processing

• Aerospacee

• Automotive

• Biomedical

Polymerization reactor vessel - prediction of flow separation and residence time

effects.

• Chemical

Processing

• HVAC

H d liHydraulics

• Hydraulics

• Marine

• Oil & Gas

• Power Generation• Sports

HVAC

6

Streamlines for workstation ventilation



Where is CFD used?• Where is CFD used?

Marine (movie) Sports

• Aerospace

• Automotive

• Biomedical

• Chemical Processing

• HVAC

• Hydraulics

• Marine

• Oil & Gas

• Power Generation

• Sports

7

Flow of lubricating mud over drill bit Flow around cooling

towers



Modeling• Modeling is the mathematical physics problemformulation in terms of a continuous initial

• IBVP is in the form of Partial DifferentialEquations (PDEs) with appropriate boundaryconditions and initial conditions.

• Modeling includes:

1. Geometry and domain.3. Governing equations4. Flow conditions

5. Initial and boundary conditions6. Selection of models for different applications

8



Modelin eometr and domain• Simple geometries can be easily created by few geometricparameters (e.g. circular pipe)

• Com lex eometries must be created b the artialdifferential equations or importing the database of thegeometry(e.g. airfoil) into commercial software

• Domain: size and shape

• Typical approaches

• Geometry approximation• CAD/CAE integration: use of industry standards such as

Parasolid, ACIS, STEP, or IGES, etc.

• The three coordinates: Cartesian system (x,y,z), cylindrical, , , , ,

appropriately chosen for a better resolution of the geometry(e.g. cylindrical for circular pipe).

9



Modeling (coordinates)z z z

(r,θ,z) (r,θ,φ)(x,y,z)

Cartesian Cylindrical Spherical

z

x x xr θ r

10

Coordinates



Modeling (governing equations)• av er- o es equa ons n ar es an coor na es

⎥⎦

⎤⎢⎣

⎡

∂

∂+

∂

∂+

∂

∂+

∂

∂−=

∂

∂+

∂

∂+

∂

∂+

∂

∂2

2

2

2

2

2ˆ

z

u

y

u

x

u

x

p

z

uw

y

uv

x

uu

t

u μ ρ ρ ρ ρ

⎥⎦

⎤⎢⎣

⎡

∂∂+∂∂+∂∂+∂∂−=∂∂+∂∂+∂∂+∂∂ 2

2

2

2

2

2

ˆ z

v y

v x

v y p

zvw

yvv

xvu

t v μ ρ ρ ρ ρ

ˆ⎥⎦

⎢⎣ ∂

+∂

+∂

+∂

−=∂

+∂

+∂

+∂ 222

z

w

y

w

x

w

z

p

z

ww

y

wv

x

wu

t

w μ ρ ρ ρ ρ

( ) ( ) ( )0=

∂+

∂+

∂+

∂ wvu ρ ρ ρ ρ

Convection Piezometric pressure gradient Viscous termsLocal

acceleration

∂∂∂∂ z y xt

RT p ρ =

2

Equation of state

11

L

v p p

Dt Dt R

ρ

−=+ 2

2)(

2Rayleigh Equation



Modeling (flow conditions)• Based on the physics of the fluids phenomena, CFDcan be distinguished into different categories using

• Viscous vs. inviscid (Re)

• External flow or internal flow wall bounded or not

• Turbulent vs. laminar (Re)

• Incompressible vs. compressible (Ma)• Single- vs. multi-phase (Ca)

• Thermal/density effects (Pr, γ , Gr, Ec)

• Free-surface flow Fr and surface tension We

• Chemical reactions and combustion (Pe, Da)

• etc…

12



Modeling (initial conditions)

• Initial conditions (ICS, steady/unsteady flows)

• ICs should not affect final results and onl

affect convergence path, i.e. number of iterations (steady) or time steps (unsteady).

• More reasonable guess can speed up the

convergence• For complicated unsteady flow problems,

CFD codes are usually run in the steady

initial conditions

13



Modelin boundar conditions•Boundary conditions: No-slip or slip-free on walls,periodic, inlet (velocity inlet, mass flow rate, constant

, . , ,

convective, numerical beach, zero-gradient), and non-reflecting (for compressible flows, such as acoustics), etc.

No-slip walls: u=0,v=0

v=0, dp/dr=0,du/dr=0

Inlet ,u=c,v=0 Outlet, p=c

Periodic boundary condition in

spanwise direction of an airfoil

r

14

Axisymmetric



Modeling (selection of models)• CFD codes typically designed for solving certain fluid

phenomenon by applying different models

scous vs. nv sc e

• Turbulent vs. laminar (Re, Turbulent models)

• Incom ressible vs. com ressible Ma e uation of state

• Single- vs. multi-phase (Ca, cavitation model, two-fluid

model)• erma ensity e ects an energy equation

(Pr, γ , Gr, Ec, conservation of energy)

• Free-surface flow Fr level-set & surface trackin model and

surface tension (We, bubble dynamic model)

• Chemical reactions and combustion (Chemical reaction

15

model)

• etc…



Modeling (Turbulence and free surface models)

Turbulent models

• Turbulent flows at high Re usually involve both large and small scale

vortical structures and very thin turbulent boundary layer (BL) near the wall

Turbulent models

• DNS: most accurately solve NS equations, but too expensivefor turbulent flows

• RANS: predict mean flow structures, efficient inside BL but excessive

diffusion in the separated region.

• LES: accurate in separation region and unaffordable for resolving BL

• DES: RANS inside BL, LES in separated regions.

• Free-surface models:

• -

limited to small and medium wave slopes

• Single/two phase level-set method: mesh fixed and level-set

16

,

studying steep or breaking waves.



Examples of modeling (Turbulence and free

surface modelsURANS, Re=105, contour of vorticity for turbulent

flow around NACA12 with angle of attack 60 degrees

DES, Re=105, Iso-surface of Q criterion (0.4) for

turbulent flow around NACA12 with angle of attack 60

degrees

17

URANS, Wigley Hull pitching and heaving



Numerical methods• The continuous Initial Boundary Value Problems

using numerical methods. Assemble the system of algebraic equations and solve the system to get

• Numerical methods include:

1. Discretization methods. o vers an numer ca parame ers

3. Grid generation and transformation

4. High Performance Computation (HPC) and post-

processing

18



Discretization methods• Finite difference methods (straightforward to apply,

usually for regular grid) and finite volumes and finitee emen me o s usua y or rregu ar mes es

• Each type of methods above yields the same solution if the grid is fine enough. However, some methods aremore suitable to some cases than others

• Finite difference methods for spatial derivatives withdifferent order of accuracies can be derived using

Taylor expansions, such as 2nd

order upwind scheme,central differences schemes etc. • Higher order numerical methods usually predict higher

order of accuracy for CFD, but more likely unstable dueto less numerical dissipation

explicit method (Euler, Runge-Kutta, etc.) or implicitmethod (e.g. Beam-Warming method)

19



Discretization methods Cont’d• Explicit methods can be easily applied but yield

conditionally stable Finite Different Equations (FDEs),w c are res r c e y e me s ep; mp c me o s

are unconditionally stable, but need efforts onefficiency.• Usually, higher-order temporal discretization is used

when the spatial discretization is also of higher order.• Stability: A discretization method is said to be stable if

it does not magnify the errors that appear in the courseof numerical solution rocess. • Pre-conditioning method is used when the matrix of the

linear algebraic system is ill-posed, such as multi-phaseflows, flows with a broad range of Mach numbers, etc.

efficiency, accuracy and special requirements, such asshock wave tracking.

20



Discretization methods (example)• 2D incompressible laminar flow boundary layer

(L,m+1)

0=∂∂+

∂∂

yv

xu

=

y

m=MMm=MM+1(L,m)(L-1,m)

2 y

u

e

p

x y

uv

x

uu

∂+⎟

⎠⎜⎝ ∂

−=∂

+∂

μ m=0

L-1 Lx

(L,m-1)

l1l lm

m m

uuu u u

x x

−⎡ ⎤= −⎣ ⎦∂ Δ2

1 12 22l l l

m m m

uu u u

y y

μ μ + −

∂⎡ ⎤= − +⎣ ⎦∂ Δ

1l lmm m

vuv u u y y

+∂ ⎡ ⎤= −⎣ ⎦∂ Δl

l lv

FD Sign( )<0l

mv 2nd order central difference

i.e., theoretical order of accuracy

P = 2.

21

1m mu u y

−= −Δ

l

mvBD Sign( )>0es

1st order upwind scheme, i.e., theoretical order of accuracy Pkest= 1



Discretization methods (example)

1

2l l ll l l lm m m

FDu v v y

v u FD u BD u μ μ μ

⎡ ⎤−⎢ ⎥ ⎡ ⎤ ⎡ ⎤Δ

+ − + + + −⎢ ⎥

B2B3 B1

x y y y y y BD

y

−Δ Δ Δ Δ Δ Δ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

⎢ ⎥Δ⎣ ⎦1 /

ll lmu

u e− ∂= −m m

x xΔ ∂B4( )1

1 1 2 3 1 4 /ll l l l

m m m m m B u B u B u B u p e

x

−− +

∂+ + = −

∂ l

1

4 1

12 3 1

1 2 3

0 0 0 0 0 0

0 0 0 0 0

l

lB u

B B x eu

B B B

− −⎢ ⎥⎜ ⎟∂⎡ ⎤⎡ ⎤ ⎝ ⎠⎢ ⎥

⎢ ⎥⎢ ⎥ ⎢ ⎥••⎢ ⎥⎢ ⎥ ⎢ ⎥

o ve us ng

Thomas algorithm

1 2 3

1 2 1

0 0 0 0 0

0 0 0 0 0 0 l lmm l

B B B

B B u p−

=• • • • ••⎢ ⎥⎢ ⎥ ⎢ ⎥••⎢ ⎥⎢ ⎥ ⎢ ⎥

⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ∂⎣ ⎦ ⎛ ⎞−

22

4 mm

mm x e−

∂⎢ ⎥⎝ ⎠⎣ ⎦To be stable, Matrix has to be

Diagonally dominant.



Solvers and numerical arameters• Solvers include: tridiagonal, pentadiagonal solvers,PETSC solver, solution-adaptive solver, multi-grid

, .

• Solvers can be either direct (Cramer’s rule, Gausselimination, LU decomposition) or iterative (Jacobi

-, ,

• Numerical parameters need to be specified to control

the calculation. , , .

• Different numerical schemes

• Monitor residuals (change of results between

terat ons• Number of iterations for steady flow or number of

time steps for unsteady flow

23

• Single/double precisions



Numerical methods (grid generation)• Grids can either be structured

(hexahedral) or unstructured(tetrahedral). Depends upon type of

structured

• Scheme Finite differences: structured

n e vo ume or n e e emen :structured or unstructured

• Application

resolved with highly-stretchedstructured grids

unstructured

complex geometries Unstructured grids permit

automatic adaptive refinement

24

based on the pressure gradient,or regions interested (FLUENT)



Numerical methods (grid

y η

Transform

x

o o ξ

x x

f f f f f ξ η ξ η

∂ ∂ ∂ ∂ ∂ ∂ ∂= + = +

•Transformation between physical (x,y,z)

x x xη η

y y

f f f f f

y y y

ξ η ξ η

ξ η ξ η

∂ ∂ ∂ ∂ ∂ ∂ ∂= + = +

∂ ∂ ∂ ∂ ∂ ∂ ∂

, , ,

important for body-fitted grids. The partialderivatives at these two domains have the

relationshi 2D as an exam le

25



High performance computing and post-processing

• compu a ons e.g. uns ea y ows are usua yvery expensive which requires parallel high performancesupercomputers (e.g. IBM 690) with the use of multi-block technique.

• As required by the multi-block technique, CFD codes need

to be developed using the Massage Passing Interface (MPI)Standard to transfer data between different blocks.

• - . ,velocity vectors, streamlines, pathlines, streak lines, andiso-surface in 3D, etc.), and 2. CFD UA: verification and

validation using EFD data (more details later)-

26



es of CFD codes• Commercial CFD code: FLUENT, Star-CD, CFDRC, CFX/AEA, etc.

• -

• Public domain software (PHI3D,HYDRO, and WinpipeD, etc.)

• Other CFD software includes the Grid generation software (e.g. Gridgen,Gambit) and flow visualization software

(e.g. Tecplot, FieldView)

27

CFDSHIPIOWA



CFD Educational Interface

Lab1: Pipe Flow Lab 2: Airfoil Flow Lab3: Diffuser Lab4: Ahmed car

1. Definition of “CFD Process”

2. Boundary conditions

1. Boundary conditions

2. Effect of order of accuracy

1. Meshing and iterative

convergence

1. Meshing and iterative

convergence

3. Iterative error

4. Grid error

5. Developing length of

laminar and turbulent pipe

flows.

on verification results

3. Effect of grid generation

topology, “C” and “O”

Meshes

4. Effect of angle of

2. Boundary layer

separation

3. Axial velocity profile

4. Streamlines

5. Effect of turbulence

2. Boundary layer separation

3. Axial velocity profile

4. Streamlines

5. Effect of slant angle and

comparison with LES,

28

. er ca on us ng

7. Validation using EFD

a ac ur u en mo e s on

flow field

5. Verification and Validation

using EFD

mo e s

6. Effect of expansion

angle and comparison

with LES, EFD, andRANS.

, an .



CFD rocess• Purposes of CFD codes will be different for differentapplications: investigation of bubble-fluid interactions for bubblyflows stud of wave induced massivel se arated flows for free-surface, etc.

• Depend on the specific purpose and flow conditions of theproblem, different CFD codes can be chosen for differentapp ications aerospace, marines, com ustion, mu ti-p aseflows, etc.)

• Once purposes and CFD codes chosen, “CFD process” is the

1. Geometry

2. Physics

3. Mesh4. Solve

5. Reports

29

6. Post processing



CFD Process

Contours

Geometry

Select

Physics Mesh Solve Post-

Processing

Unstructured Steady/ Forces ReportHeat Transfer

Reports

Vectors

Geometry

GeometryCompressible

ON/OFF

(automatic/

manual)

Unsteady (lift/drag, shear

stress, etc)

XY Plot

ON/OFF

Structured

(automatic/

Iterations/

Steps

Convergent

Limit

StreamlinesVerification

arame ers

Flow

properties

Domain

Shape and

Size

manual)

Viscous

Model

Precisions

(single/

double)

Validation

BoundaryConditions

NumericalScheme

30

Conditions



Geometr• Selection of an appropriate coordinate

• Determine the domain size and sha e

• Any simplifications needed?• What kinds of shapes needed to be used to best

resolve the geometry? (lines, circular, ovals, etc.)

• For commercial code, geometry is usually created

commercial code itself, like Gambit, or combinedtogether, like FlowLab)

• For research code, commercial software (e.g.Gridgen) is used.

31



Physics• Flow conditions and fluid properties

1. Flow conditions: inviscid, viscous, laminar, orturbulent, etc.

2. Fluid properties: density, viscosity, andthermal conductivit etc.

3. Flow conditions and properties usuallypresented in dimensional form in industrial

commercial CFD software whereas in non-dimensional variables for research codes.

• Selection of models: different models usuallyfixed b codes o tions for user to choose

• Initial and Boundary Conditions: not fixedby codes, user needs specify them for different

32



Mesh• Meshes should be well designed to resolveim ortant flow features which are de endent u onflow condition parameters (e.g., Re), such as thegrid refinement inside the wall boundary layer

• es can e genera e y e er commerc a co es(Gridgen, Gambit, etc.) or research code (using

algebraic vs. PDE based, conformal mapping, etc.)• The mesh, together with the boundary conditions

need to be exported from commercial software in a

research CFD code or other commercial CFDsoftware.

33



Solve

• Setup appropriate numerical parameters

• oose appropr a e o vers

• Solution procedure (e.g. incompressible flows)

,equations and get flow field quantities, such as

velocit , turbulence intensit , ressure andintegral quantities (lift, drag forces)

34



Re orts• Reports saved the time history of the residualsof the velocity, pressure and temperature, etc.

• Report the integral quantities, such as totalpressure drop, friction factor (pipe flow), liftand dra coefficients airfoil flow etc.

• XY plots could present the centerlinevelocity/pressure distribution, friction factor

,distribution (airfoil flow).

• AFD or EFD data can be imported and put on

35



Post-processing

• Analysis and visualization• Calculation of derived variables

Vorticity

Wall shear stress• Calculation of integral parameters: forces,

moments

• Visualization (usually with commercial

software) mp e con ours

3D contour isosurface plots

Vector plots and streamlines

tangent direction is the same as thevelocity vectors)

36



Post-processing (Uncertainty Assessment)

• imu ation error: the difference between a simulation resultS and the truth T (objective reality), assumed composed of additive modeling δSM and numerical δSN errors:

• Verification: process for assessing simulation numerical

SN SM S T S δ δ δ +=−=

222

SN SM S

U U U +=

uncer a n es SN an , w en con ons perm , es ma ng esign and magnitude Delta δ*

SN of the simulation numerical erroritself and the uncertainties in that error estimate UScN

J

• Validation: process for assessing simulation modelinguncertainty U SM by using benchmark experimental data and,

=

== j

j I PT G I SN

1PT G I SN U U U U U +++=

when conditions permit, estimating the sign and magnitude of the modeling error δ SM itself.

)( SN SM DS D E δ δ δ +−=−=222

SN DV U U U +=

37

V U E < Validation achieved



Post-processing (UA, Verification)

• onvergence s u es: onvergence s u es requ re aminimum of m=3 solutions to evaluate convergence withrespective to input parameters. Consider the solutions

∧ ∧∧

, ,1k 2k

3k

21 2 1k k k S Sε ∧ ∧

= − 32 3 2k k k S Sε ∧ ∧

= −

(i). Monotonic convergence: 0<R k <1

ii . Oscillator Conver ence: R <0 R <1

21 32k k k R ε ε =

(iii). Monotonic divergence: R k >1

(iv). Oscillatory divergence: R k <0; | R k |>1

• .

12312 −ΔΔ=ΔΔ=ΔΔ=

mm k k k k k k k x x x x x xr

38



Post-processing (Verification: Iterative

•Typical CFD solution techniques for obtaining steady state solutions

involve be innin with an initial uess and erformin time marchin or

iteration until a steady state solution is achieved.

•The number of order magnitude drop and final level of solution residual

can be used to determine stopping criteria for iterative solution techniques

(1) Oscillatory (2) Convergent (3) Mixed oscillatory/convergent

(b)(a)

)(1

LU I SSU −=

39

Iteration history for series 60: (a). Solution change (b) magnified view of total

resistance over last two periods of oscillation (Oscillatory iterative convergence)



Post- rocessin Verification RE

• Generalized Richardson Extrapolation (RE): Formonotonic convergence, generalized RE is used toestimate the error δ*

k and order of accuracy p k due

to the selection of the kth input parameter.

with integer powers of Δxk as a finite sum.

• The accuracy of the estimates depends on howmany terms are retained in the expansion, themagnitude (importance) of the higher-order terms,

theory

40

Post processing (Verification RE)



Post-processing (Verification, RE)*

Finite sum for the k th

SN SN SN

*

SN C SS δ −=SN

SC is the numerical benchmark

( )( )

( )i

k

pn

i

k k g x

i

k

mm ∑=

Δ=1

*δ ∑≠=++=−=

J

k j j

jmk C I k k mmk mmSSS

,1

***ˆ δ δ δ

parameter an mt so ut on

)(i

k p( ) ∑∑≠==

+Δ+= J

k

jm

i

k

pn

i

k C k g xSS

ik

mm 1

*)(

1

)(

ˆ δ order of accuracy for the ith term

( ) ∑≠=

+Δ+= J

k j j

jk

p

k C k g xSS k

,1

*

1

)1()1(

11

ˆ δ ( ) ∑≠=

+Δ+= J

k j j

jk

p

k k C k g xr SS k

,1

*

2

)1()1(

12

ˆ δ

Three equations with three unknowns( ) ∑≠=

+Δ+= J

k j j

jk p

k k C k g xr SS k

,1

*3

)1(2

)1(

13ˆ δ

411

21

11

**

−

==k k p

k

k

RE k

r

ε δ δ

( )k

k k

k

r

p

ln

ln2132

ε ε =



Post-processing (UA, Verification, cont’d)

• Monotonic Convergence: Generalized RichardsonExtrapolation

p

1. Correction

( )

( )

32 21ln

ln

k k

k

k

p

r

ε ε =

1

k est

k k p

k

C

r

−=

−

( )1

1

*

*

9.6 1 1.1

2 1 1

k

k

k RE

k

k RE

C

U C

δ

δ

− +⎪⎣ ⎦

= ⎨ ⎡ − + ⎤⎪ ⎣ ⎦⎩

1 0.125k C − <

1 0.125k C − ≥

[ ]

( )

⎩⎨⎧=

+−

+−

*

1

2

*

1

1.014.2

11

k RE k

k RE k

C

C kcU δ

δ

factors 1

21

1k k

k RE p

k r δ =

−1 0.25k C − <

25.0|1| ≥− k C |||]1[| *

1k RE k C δ −est k p is the theoretical order of accuracy, 2 for 2nd

order and 1 for 1st order schemes U is the uncertainties based on fine mesh

2. GCI approach *

1k RE sk F U δ = ( ) *

11

k RE skc F U δ −=

solution, is the uncertainties based on

numerical benchmark SC

kcU is the correction factor

k C

• Oscillatory Convergence: Uncertainties can be estimated, but withoutsigns and magnitudes of the errors.

• Divergence( ) LU k SSU −=

2

1

42

• In this course, only grid uncertainties studied. So, all the variables with

subscribe symbol k will be replaced by g, such as “Uk ” will be “Ug”

Post processing (Verification



Post-processing (Verification,

• Asymptotic Range: For sufficiently small Δxk , the

higher-order terms are negligible and theassumption that and are independent of Δxk

( )i

k p( )i

k g

is valid.

• When Asymptotic Range reached, will be close tok p

,

will be close to 1.

• o achieve the as m totic ran e for ractical

est

k C

geometry and conditions is usually not possible andm>3 is undesirable from a resources point of view

43



Post-processing (UA, Verification, cont’d)

• Verification for velocity profile using AFD: To avoid ill-

defined ratios, L2 norm of the εG21 and εG32 are used to define R Gand PG ln ε ε

22 3221 GGG =( )G

Gr

pln

22 2132

=

Where <> and || ||2 are used to denote a profile-averaged quantity (with ratio of

NOTE: For verification using AFD for axial velocity profile in laminar pipe flow (CFD

Lab1), there is no modeling error, only grid errors. So, the difference between CFD and

+ – + –

, .

, , ,

verified.

44



Post-processing (UA, Validation)

• Validation procedure: simulation modeling uncertainties

was presented where for successful validation, the comparison

error, , s ess t an t e va at on uncerta nty, v.

• Interpretation of the results of a validation effort

−−V

E U V <

Validation not achieved22

DSN V U U U +=

SN SM D

• Validation example

and validation of wave profile for

series 60

45

Example of CFD Process using CFD



p geducational interface (Geometry)

• Turbulent flows (Re=143K) around Clarky airfoil with.

• “C” shape domain is applied• The radius of the domain Rc and downstream length

Lo should be s ecified in such a wa that the

46

domain size will not affect the simulation results

Example of CFD Process (Physics)



Example of CFD Process (Physics) No heat transfer

47

Example of CFD Process (Mesh)



Example of CFD Process (Mesh)

Grid need to be refined near the

48

foil surface to resolve the boundary

layer

Example of CFD Process (Solve)



Example of CFD Process (Solve)

Residuals vs. iteration

49

Example of CFD Process (Reports)



Example of CFD Process (Reports)

50

Example of CFD Process (Post-processing)



p ( p g)

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58 160 CFD L b



58:160 CFD Labs

Schedule

CFD Lab Lab1:

Pipe Flow

Lab 2:

Airfoil Flow

Lab3:

Diffuser

Lab4:

Ahmed car

Date Sept. 5 Sept. 22 Oct. 13 Nov. 10

• Use the CFD educational interface — FlowLab 1.2.10

http://www.flowlab.fluent.com/

http://css.engineering.uiowa.edu/~me_160

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introduction cfd

Documents