ASME - Cfd Fundamentals

8/14/2019 ASME - Cfd Fundamentals

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ASME-SCVS Professional Development Series CFD Fundamentals & Applications 1

CFD Fundamentals and Applications

Metin Ozen, Ph.D., CFD Research Corpo rat ion

Ashok Das, Ph.D., Appl ied Mater ials

K im Parnel l, Ph .D ., Parnel l Engineer ing and Consu l t ing




AGENDA

n 9:00-9:05 Introductions by Scott Burr

n 9:05-10:30 CFD Fundamentals by Metin Ozen

n 10:30-10:45 Break

n 10:45-12:00 Applications in Semiconductor Industryby Ashok Das

n 12:00-1:00 LUNCH

n 1:00-2:15 Applications in Biomedical Industry by KimParnell

n 2:15-2:30 Breakn 2:30:3:45 CFD Applications by Metin Ozen

n 3:45-4:00 Q&A




Some CFD Books

n Computational Fluid Dynamics: TheBasics with ApplicationsJohn David Anderson

n Computational Methods for FluidDynamics Joel H. Ferziger

n Turbulence Modeling for CFD David C.Wilcox

n http://www.sali.freeservers.com/engineering/cfd/cfd_books.html




Definitions of CFD on the WEB

n Computational Fluid Dynamics (CFD); the simulation

or prediction of fluid flow using computers

n Computer modeling of fluid behaviour, for example

the flow of fuel/air mixture into a combustionchamber.

n Computational Fluid Dynamics refers to

computational solutions of differential equations,

such as the Navier Stokes set, describing fluid

motion.

n …




What is CFD?1

n CFD has grown from a mathematical curiosity to

become an essential tool in almost every branch of

fluid dynamics, from aerospace propulsion to

weather prediction. CFD is commonly accepted asreferring to the broad topic encompassing the

numerical solution, by computational methods, of the

governing equations which describe fluid flow, the

set of the Navier-Stokes equations, continuity and

any additional conservation equations, for exampleenergy or species concentrations.

1 - http://www.cranfield.ac.uk/sme/cfd/




Biochips

BioMedical

MEMS

Semiconductor

Equipment & Processes

Environmental

CBW Protection

Fuel Cells

Power Conversion

Plasmas

Non-Equilibrium

Thermal

Combustion

PropulsionMicroelectronics

Photonics

Aerodynamics

Aerostructures

CFD RESEARCH CORPORATIONCFD RESEARCH CORPORATION -- Major Major Application Application Areas of CFD Areas of CFD




What is CFD?

n As a developing science, Computational FluidDynamics has received extensive attentionthroughout the international community since theadvent of the digital computer. The attraction of the

subject is twofold. Firstly, the desire to be able tomodel physical fluid phenomena that cannot be easilysimulated or measured with a physical experiment,for example weather systems or hypersonicaerospace vehicles. Secondly, the desire to be able to

investigate physical fluid systems more costeffectively and more rapidly than with experimentalprocedures.




What is CFD?

n There has been considerable growth in the

development and application of Computational Fluid

Dynamics to all aspects of fluid dynamics. In design

and development, CFD programs are now consideredto be standard numerical tools, widely utilised within

industry. As a consequence there is a considerable

demand for specialists in the subject, to apply and

develop CFD methods throughout engineering

companies and research organisations.




Commercial CFD Codes - 1

n ACRi

n ARSoftware (TEP: a combustion analysis tool for windows)

n COSMIC NASA

n Fluent Inc. (FLUENT, FIDAP, POLYFLOW, GAMBIT, TGrid, Icepak, Airpak, MixSim)

n Flowtech Int. AB (SHIPFLOW: analysis of flow around ships)

n Fluid Dynamics International, Inc. (FIDAP)

n ANSYS-CFX (CFX: 3D fluid flow/heat transfer code)

n ICEM CFD (ICEM CFD, Icepak)

n KIVA (reactive flows)

n CFD Research Corporation (ACE: reactive flows)

n Computational Dynamics Ltd. (STAR-CD)

n Analytical Methods, Inc. (VSAERO, USAERO, OMNI3D, INCA)

n AeroSoft, Inc. (GASP and GUST)

n Ithaca Combustion Enterprises (PDF2DS)

n Flow Science, Inc. (FLOW3D)

n

ALGOR, Inc. (ALGOR)n Engineering Mechanics Research Corp. (NISA)

n Reaction Engineering International (BANFF/GLACIER)

n Combustion Dynamics Ltd. (SuperSTATE)

n AVL List Gmbh. (FIRE)

n IBM Corp. catalogue (30 positions)

n Sun Microsystems catalogue (70 positions)




Commercial CFD Codes – 2

n Cray Research catalogue (100 positions)

n Silicon Graphics, Inc. catalogue (75 positions)

n Pointwise, Inc. (Gridgen - structured grids)

n Simulog (N3S Finite Element code, MUSCL)

n Directory of CFD codes on IBM supercomputer environment

n ANSYS, Inc. (FLOTRAN)

n Flomercis Inc. (FLOTHERM)

n Computational Mechanics Corporation

n Computational Mechanics Company, Inc. (COMCO)

n KASIMIR (shock tube simulation program)

n Livermore Software Technology Corporation (LS-DYNA3D)

n Advanced Combustion Eng. Research Center (PCGC, FBED)

n NUMECA International s.a. (FINE, FINE/Turbo, FINE/Aero, IGG, IGG/Autogrid)

n Computational Engineering International., Inc. (EnSight, ...)

n Blocon Software Agency (HEAT2, HEAT3)

n Adaptive Research Corp. (CFD2000)

n Unicom Technology Systems (VORSTAB-PC)

n Incinerator Consultants Incorporated (ICI)

n PHOENICS/CHAM (multi-phase flow, N-S, combustion)

n Innovative Aerodynamic Technologies (LAMDA)

n XYZ Scientific Applications, Inc. (TrueGrid)

n South Bay Simulations, Inc. (SPLASH)





n PHASES Engineering Solutions

n Engineering Sciences, Inc. (UNIC)

n Catalpa Research, Inc. (TIGER)

n Swansea NS codes (LAM2D, TURB)

n Engineering Systems International S.A. (PAM-FLOW, PAM-FLUID)

n Daat Research Corp. (COOLIT)

n Flomerics Inc. (FLOVENT)

n Innovative Research, Inc.

n Centric Engineering Systems, Inc. (SPECTRUM)

n Blue Ridge Numerics, Inc.

n WinPipeD

n Exa Corporation (PowerFLOW)

n Polyflow s.a.

n Flow Pro

n Computational Aerodynamics Systems Co.

n Tahoe Design Software

n ADINA-F

n YFLOW

n PSW

n Advanced Visual Systems

n Flo++

n KSNIS





n Flowcode

n Concert

n SMARTFIRE

n VISCOUS

n Polydynamics

n Cullimore and Ring Technologies, Inc. (SINDA/FLUINT, SINAPS)

n Linflow (ANKER - ZEMER ENGINEERING)

n PFDReaction

n Airfoil Analysis

n Institute of Computational Continuum Mechanics GmbH

n CFD++

n RADIOSS-CFD

n VECTIS

n MAYA Simulation

n Compass

n Arena Flow

n Newmerical Technologies International

n CFDpc

n NIKA EFDLab

n SC/Tetra

n TES International

n ACUITIV




Computational Fluid Dynamics2

n Computational Fluid Dynamics is concerned with

obtaining numerical solution to fluid flow problems

by using computers. The advent of high-speed and

large-memory computers has enabled CFD to obtainsolutions to many flow problems including those that

are compressible or incompressible, laminar or

turbulent, chemically reacting or non-reacting.

2 - http://www.sali.freeservers.com/engineering/cfd/#gotop




Computational Fluid Dynamics

n The equations governing the fluid flow problem are

the continuity (conservation of mass), the Navier-

Stokes (conservation of momentum), and the energy

equations. These equations form a system of couplednon-linear partial differential equations (PDEs).

Because of the non-linear terms in these PDEs,

analytical methods can yield very few solutions.




Governing (Navier-Stokes) Equations(in Cartesian Tensor form)

n Continuity - Conservation of mass

??/?t + ?(?ui)/?xi = 0

n Navier-Stokes - Conservation of Momentum

?(?vi)/?t + ?(?viv j)/?x j = ?Bi - ?p/?xi - ?/?xi [2/3µ(?v j /?x j)]

+ ?/?x j [µ(?vi /?x j + ?v j /?xi)]

(For compressible and viscous flows)





n In general, closed form analytical solutions are

possible only if these PDEs can be made linear, either

because non-linear terms naturally drop out (eg., fully

developed flows in ducts and flows that are inviscid

and irrotational everywhere) or because nonlinear

terms are small compared to other terms so that they

can be neglected (eg., creeping flows, small

amplitude sloshing of liquid etc.). If the non-linearities

in the governing PDEs cannot be neglected, which isthe situation for most engineering flows, then

numerical methods are needed to obtain solutions.




Governing (Navier-Stokes) Equations

n Continuity - Conservation of mass

??/?t + ?(?u)/?x + ?(?v)/?y + ?(?w)/?z = 0





Governing (Navier-Stokes) Equations

n Conservation of Momentum

?[?u/?t + u?u/?x + v?u/?y + w?u/?z] = ?Bx - ?p/?x -(2/3)?/?x[µ(?u/?x+?v/?y + ?w/?z)] + 2?/?x(µ?u/?x) + ?/?y[µ(?u/?y +?v/?x)]+?/?z[µ(?u/?z+?w/?x)]

?[?v/?t + u?v/?x + v?v/?y + w?v/?z] = ?By - ?p/?y -(2/3)?/?y[µ(?u/?x+?v/?y + ?w/?z)] + 2?/?y(µ?v/?y) + ?/?z[µ(?v/?z +?w/?y)]+?/?x[µ(?v/?x+?u/?y)]

?[?w/?t + u?w/?x + v?w/?y + w?w/?z] = ?Bz - ?p/?z -(2/3)?/?z[µ(?u/?x+?v/?y + ?w/?z)] + 2?/?z(µ?w/?z) + ?/?x[µ(?w/?x +?u/?z)] + ?/?y[µ(?w/?y + ?v/?z)]






n CFD is the art of replacing the differential equation

governing the Fluid Flow, with a set of algebraic

equations (the process is called discretization), which

in turn can be solved with the aid of a digital

computer to get an approx imate solution. The well

known discretization methods used in CFD are Finite

Difference Method (FDM), Finite Volume Method

(FVM), Finite Element Method (FEM), and Boundary

Element Method (BEM).




CFD – SOLUTION METHODS

n FDM – Resistance Network

n FEM – [K] {u} = {F}

n FVM – [A] {Φ} = {Q}

n BEM – [B] {d} = {P}




Computational Fluid Dynamics2

n Computational Fluid Dynamics (CFD) provides a good

example of the many areas that a scientific

computing project can touch on, and its relationship

to Computer Science. Fluid flows are modeled by a

set of partial differential equations, the Navier-Stokes

equations. Except for special cases no closed-form

solutions exist to the Navier-Stokes equations.

2 - http://www.sali.freeservers.com/engineering/cfd/#gotop






CFD – PROBLEM SIZE

n On the discretized mesh the Navier-Stokes equations take the

form of a large system of nonlinear equations; going from the

continuum to the discrete set of equations is a problem thatcombines both physics and numerical analysis; for example, it

is important to maintain conservation of mass in the discreteequations. At each node in the mesh, between 3 and 20 variablesare associated: the pressure, the three velocity components,

density, temperature, etc. Furthermore, capturing physically

important phenomena such as turbulence requires extremelyfine meshes in parts of the physical domain. Currently meshes

with 20 000 to 2 000 000 nodes are common, leading to systemswith up to 40 000 000 unknowns.




CFD - SOLVERS

n That system of nonlinear equations is typically solved by aNewton-like method, which in turn requires solving a large,sparse system of equations on each step.

n Methods for solving large sparse systems of equations are a hottopic right now, since that is often the most time-consuming partof the program, and because the ability to solve them is thelimiting factor in the size of problem and complexity of thephysics that can be handled

n Direct methods, which factor the matrices, require morecomputer storage than is permissible for all but the smallestproblems.

n Iterative methods use less storage but suffer from a lack ofrobustness: they often fail to converge.

n The solution is to use preconditioning; that is, to premultiply thelinear system by some matrix that makes it easier for theiterative method to converge.




CFD – PARALLEL PROCESSING

n CFD problems are at the limits of computational

power, so parallel programming methods are used.

That brings in the research problem of how to

partition the data to assign parts of it to different

processors; usually domain decomposition methods

are applied. Domain decomposition is often

expressed as a graph partitioning problem, namely

finding a minimum edge cut partitioning of the

discrete mesh, with roughly the same number ofnodes in each partition set.






TYPICAL PROCEDUREn CONCEPT/DESIGN

n GEOMETRY

n DISCRETIZATION/MESHING

n ENVIRONMENT – VOLUME CONDITIONS

– BOUNDARY CONDITIONS

– INITIAL CONDITIONS

n SOLUTION

n VISUALIZATION

n (OPTIMIZATION)




CFD – PROBLEM SIZE3

n In CFD, the flow region or calculation domain is divided into a

large number of finite volumes or cells. The governing partial

differential equations are discretized using a wide range oftechniques: finite difference, finite volume or finite element. This

provides a set of algebraic equations (corresponding to therespective partial differential equations) for each dependentvariable in each cell volume or cell. A two dimensional

isothermal incompressible flow is governed by three equations,

namely, the continuity equation (conservation of mass), and twomomentum equations (Newton's Second Law), one for each

coordinate. For example consider the flow between the twoparallel plates shown in the figure.

3 - http://www.cfdnet.com




CFD – PROBLEM SIZE3

n For example consider the flow between the two parallel plates

shown in the figure.

n If the calculation domain is divided into 100 rectangular cells,

then there will be 100 algebraic equations for each velocitycomponent and 100 equations for the pressure, giving a total of

300 simultaneous algebraic equations.

3 - http://www.cfdnet.com






CFD – FLUID PROPERTIES

n Fluid is defined as a substance that cannot resist

stress by static deformation.

n Both gases and liquids are fluids.

n Density : defined as the mass of a small fluid element

divided by its volume (units in kg/m3)

volume

mass=ρ




CFD – FLUID PROPERTIES

n Viscosity: is defined in terms of the force needed to

pull a flat plate at constant speed across a layer of

fluid (Units in N.s/m2 or Poise)

n Kinematic viscosity is defined as

Layer of fluid

vF

dy

duµτ =

Shear strain

Shear stress

ρ

µν =




CFD – NEWTONIAN/NON-NEWTONIAN

•Newtonian FluidFluids for which the shear stress-shear

rate relation is a straight line passing

through the origin.

•Common Newtonian FluidsWater and air

•Non-Newtonian FluidFluids that have a viscosity which

may be a function of not only the fluid

velocity, but also the velocity gradient

•Common Non-Newtonian FluidsBlood and alcohol




CFD – EFFECT OF VISCOSITY

n Viscosity is a kind of internal friction.

n Viscosity prevents neighboring layers of fluid

from sliding freely past one another.

n Fluid in contact with the wall is stationary (no-s l ip

condi t ion ).

Velocity of fluid varies from zero to a maximum along the axis




CFD – REYNOLDS NUMBER

n Reynolds number is a dimensionless number.

n Reynolds number is the ratio of the inertial toviscous forces. It is defined as:

n Flow is characterized as LAMINAR orTURBULENT based on the Reynolds number

(>2100 turbulent)

µρvL=Re




CFD – LAMINAR/TURBULENT

Re=1.54

Re=9.6

Re=13

Re=105

Re=150




CFD – LAW OF CONTINUITY

Mass Conservation: the rate of change of the conserved

quantity within a control volume minus the rate at which theconserved quantity leaves the control volume

A1V 1

A2V 2

2211 AV AV Adz

dt

d ><−>=<><∫ ρρρ




CFD – CONSERVATION OF MOMENTUM

Newton’s second law states that the time rate of change ofthe momentum of a fluid element is equal to the sum of the

forces on the element.

g pvvvt

ρτρρ +∇−∇−⋅∇−=∂∂ ].[][

Rate of change

of momentum

Convection Pressure Viscous Gravitational

Surface forces Body forces

Navier-Stokes Equation






CFD – COMPRESSIBLE FLUIDSn When density varies appreciably as a result of pressure

and temperature. The static temperature becomes afunction of velocity and stagnation temperature.

n Compressibility becomes important when the MachNumber becomes greater than about 0.3.

n Mach Number is defined as the ratio of an object’s speedto the speed of sound in the medium through which theobject is traveling:

n when M is less than 1 the flow is subsonic, whilesupersonic flows are with Mach numbers greater thanone.

a

v M =




CFD – BOUNDARY LAYER

The no-slip boundary condition at the wall leads to the formation a

Boundary Layer .

A boundary layer is a thin fluid layer near the wall which experiences

velocity variations.

Inside the boundary layer the fluid velocity goes from some finite value

at the boundary layer edge to zero at the wall in a very short distance.

dyv

u)1(*

0

∫ ∞

−=δ




CFD – BOUNDARY LAYER

x

y

u

δ

U=0.99u

Flow

Boundary layer thickness

u

U

δ*

Flow

Displacement thickness

δ is defined as the

distance from the wall

where the velocity has

increased to 99 percent

of the freestreamvelocity.

δ* is defined as the

distance to which

streamlines outside the boundary layer are

displaced away from the

wall.




CFD – SOME PLANNING

n Is the flow laminar or turbulent?

n Is the fluid Newtonian or Non-Newtonian?

n Is the fluid compressible or incompressible?

n Is boundary layer and near wall solution of importance?

n What are the fluid properties and are they dependent on statevariables (T, P,..)?

n What are the dominant physics?




CFD-ACE(U) Introduction and Overview

CFD – APPLICATIONS




n CFD-ACE+ System

– CFD-ACE(U) Modules

– Unique Attributes

n Theory

– General Transport Equation

– Discrete Methods

– Solution Procedure

– Linear Equation Solvers – Under-Relaxation

n Graphical User Interface

CFD – CFD-ACE+ OVERVIEW




(1) Geometry and Grid Generation

(2) Problem Setup

(4) Post Processing

(3) Solution Generation

CFD-GEOM CFD-GUI CFD-VIEW

Input Files Graphical Results

Batch Solver

CFD-ACE(U)

Text Results

Computational Gridand BC / VC Locations

CFD – CFD-ACE+ SYSTEM




Optional Modules Optional Modules

FLOW

HEAT TRANSFER

TURBULENCE

M IXING

USER SCALAR

RADIATION

CAVITATION

GRID DEFORMATION

STRESS

PLASMA

ELECTRIC

MAGNETIC

ELECTROPLATING

ELECTROKINETICS

BIO-CHEMISTRY

FREE SURFACES

SPRAY

TWO-FLUID

MONTE-CARLO RAD

Your Building Blocks for a Multi-Disciplinary Simulation

Core Modules

CFD – CFD-ACE+ MODULES




n Structured or Unstructured Grid Systems

– quadrilateral ( ), hexahedral ( )

– triangle ( ), tetrahedral ( ), prism ( ), polyhedral ( )

+ =n Arbitrary Interfaces

– mix and match grid systems

– parametric part studies

– fully conservative

Velocity Vectors

on Second Design

Stream Traces on

First Design

Close-Up of Interface

CFD – UNIQUE ATTRIBUTES




n User Subroutines

– ability to customize the solver for special needs

• boundary conditions

• properties

• source terms

• output• initial conditions

• time step

• grid deformation

• much more...

11.6

3.4 2.6

1.8

1.0

6.4

0

4

8

12

16

0 4 8 12 16

S p e e d u p F

a c t o r

Number of Processors

Ideal Speedup

Actual Speedup

n

Parallel Processing – optional feature

– automatic domain decomposition

CFD – UNIQUE ATTRIBUTES




Control Volume

t ∂∂ρφ

φφφρρφ

S t

+∇Γ •∇=•∇+∂

∂)()( V

r

transient convection diffusion source

diffusion

convection convection

diffusion

source

CFD – TRANSPORT EQUATION






n Calculation Domain Sub-divided into

Discrete Control Volumes (Cells)

– grid generation process

n Variables Calculated at Centers of Cells

– assumed constant over entire cell

6 equally spaced cells 8 cells with stretching

n Build Equation for Each Variable at Each Cell

φφφφφφφφ S aaaaaaa L L H H S S N N W W E E P P ++++++=S

N L

H

W EP

CFD – DISCRETE METHODS




S

PW

N

E

n Each anb Represents Effects of Convection and

Diffusion

w

w

wwwW Aua ∆

Γ +−= ρ

W www Au φρ

w

w

P W w A

∆−

Γ )( φφ

– e.g., at the west face

• convection =

• diffusion =

– rearrange and assemble link coefficients

∑= nb P aa

uw

φφφ S aa nbnb P P += ∑





u

x

n Spatial Differencing Scheme Determines Face Values

– 1st-order upwind, central, 2nd-order upwind, etc.

x

x

x PW

<≥

=0if

0if

w P

wW

wu

u

φ

φφ1st-upwind

2 P W

w

φφφ

+=central

<

≥=

0if

2

1-

2

3

0if 2

1-

2

3

wW P

wWW W

w

u

u

φφ

φφφ2nd-upwind

n Upwind Blending Used to Maintain Stability

order higher upwind1st) 1(

−− −+= www φφφ α α

(α is a user input)





n Source Term ( S ) Contains Terms Other Than Convection and

Diffusion

– transient term, boundary conditions, under-relaxation, etc.

– linearized P P U S S S φ+=

P P U nbnb P P S S aa φφφ ++=

∑ U nbnb P P P S aS a +=− ∑ φφ)(

n Final Equation





At t=tf Prescribe Initial Flow FieldAt t=tf Prescribe Initial Flow Field

t = t + ∆tt = t + ∆t

Evaluate Link Coefficients (a’s)Evaluate Link Coefficients (a’s)

Solve VelocitiesSolve Velocities

Evaluate Mass ImbalancesEvaluate Mass Imbalances

Solve Pressure CorrectionSolve Pressure Correction

Correct p, u, v, wCorrect p, u, v, w

Solve EnthalpySolve Enthalpy

Solve Mixture/Species FractionsSolve Mixture/Species Fractions

StopStop

Repeat For EachSolution Iteration

(until solution stops changing)

Repeat For EachSolution Iteration

(until solution stops changing)

Repeat For Each Time Step

(transient simulations only)

Repeat For Each Time Step

(transient simulations only)

Solve Turbulence / Scalar / Etc.Solve Turbulence / Scalar / Etc.

SIMPLEC

CFD – SOLUTION PROCEDURE




n Need to Solve Sparse Matrix of Equations

=

RφA

=

21

1

12

231

123

321

nn

n

nn

nnn

nnn

nnn

aa

aaa

aaa

aaa

aaa

A

n Use an Iterative Linear Equation Solver

– conjugate gradient squared (CGS) – conjugate gradient squared + preconditioning (CGS+Pre)

– algebraic multigrid (AMG)

# cells

# cells

CFD – LINEAR EQUATION SOLVERS




n Anywhere in Solution Procedure where SOLVE is

Found

Solve φSolve φ

Attempt to Solve Attempt to SolveR A =φ

DONEDONE

STOP with WARNINGSTOP with WARNING

sweep = sweep + 1sweep = sweep + 1

yes

no

sweep > maxsweeps

<−∑ *φφyes

no

criteria

(criteria and maxsweeps are user inputs)

CFD – LINEAR EQUATION SOLVERS






n Linear Under-Relaxation (Auxiliary Variables)

– auxiliary variables are not directly solved for but arecomputed during the solution procedure

• density, pressure, temperature, viscosity, etc. – specifies the amount of “correction” to be applied

φφφ ′+= oldnew α (α is a user input)

α is bounded from 0.0 to 1.0 with 1.0 the

default

– decreasing the value of α adds constraint

(stability)

– decreasing the value of α slows convergence

CFD – UNDER RELAXATION




(1) Geometry and Grid Generation

(2) Problem Setup

(4) Post Processing

(3) Solution Generation

CFD-GEOM CFD-GUI CFD-VIEW

Input Files Graphical Results

Batch Solver

CFD-ACE(U)

Text Results

Computational Gridand BC / VC Locations

CFD – GRAPHICAL USER INTERFACE




n What CFD-GUI Is:

– graphical front end to the CFD-ACE(U) solver

– expert system for setting up multi-disciplinary

simulations• guides user through the setup process

• protects user from inappropriate inputs

• provides reasonable default inputs

– solver controller (submit / save / stop)

– solver monitor (residuals / output)

n What CFD-GUI Is Not:

– CFD-GUI is not a solver




Graphics Area

Title Bar Menu Bar

Tool Bar

Control Panel

Model Explorer

Status Line


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ASME - Cfd Fundamentals