bmcf 3233 chap 2 - cfd intro

8/10/2019 Bmcf 3233 Chap 2 - Cfd Intro

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Introduction to

Computational Fluid Dynamics


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Experimental Vs CFD Measure the real world

May required complicatedinstrumentations & rigs

Provides limited flow infor

Approximated solutions ofdifferential equations

Everything are done on acomputer

Provides details of flow

kiel probes

Wind tunnel

Motion manipulation device


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Motivation

Modern engineers apply both experimental and CFDanalyses

the two complement each other For example, engineers may obtain global properties , such

as lift, drag, pressure drop, or power, experimentally, butuse CFD to obtain details about the flow field, such as shearstresses, velocity and pressure profiles, and flowstreamlines.

In addition, experimental data are often used to validateCFD solutions by matching the computationally andexperimentally determined global quantities.

CFD is then employed to shorten the design cycle throughcarefully controlled parametric studies, thereby reducingthe required amount of experimental testing.


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The equations of motion to be solved byCFD for the case of steady,

incompressible, laminar flow of a

Newtonian fluid with constant propertiesand without free-surface effects.A Cartesian coordinate system is used.

There are four equations and fourunknowns: , , , and .

Equations of Motion

Continuity equation

Navier Stokes equation

= 0

= 1

+


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Equations of Motion

Continuity equation

Navier Stokes equation

The equations of motion to be solved byCFD for the case of steady,

incompressible, laminar flow of a

Newtonian fluid with constant propertiesand without free-surface effects.A Cartesian coordinate system is used.

There are four equations and fourunknowns: , , , and .

= 0

= 1

+

first-order approximation


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kiel probes


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Geometry& Domain Meshing

Boundaryconditions

& Fluidproperties

Initial values,discretization

methods,& solutionalgorithms

SolvedIteratively

Postprocessing

FD Process

=

= 0

= 0 =


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Grid Generation

Structured grid Unstructured grid

Node9 nodes and 8 intervals onthe top & bottom edges5 nodes and 4 intervals onthe left & right edges

Note: Same node distribution in the structured and unstructured grids


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A quality grid is essential to

a quality CFD simulation


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EAS = MAXmax equal

180 equal,

equal min

equal

Equiangle skewness:


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Hybrid grid with the sharpcorner chopped off

EAS max = 0.53


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Grid Independent

CFD solution is grid independent? To test:

Repeat the simulation using finer grid

(a factor of 2 in all directions if feasible) If the results do not change

appreciably, the original grid isprobably adequate

If it does change significantly, theoriginal grid resolution is inadequate

Use even finer grid(s) until the grid isadequately resolved 2 = 8

Twice finer

e.g.1 million cells 8 million cells 64 million cells


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Boundary Conditions

Appropriate boundary conditionsare required to obtain an accurateCFD solution


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Wall Boundary Conditions

Fluid cannot pass through a wall The normal component of velocity is set

to zero relative to the wall along a faceon which the wall boundary condition isprescribed

Because of the no-slip condition, weusually set the tangential component of

velocity at a stationary wall to zero aswell

Wall BC

= 0

= 0 (no-slip wall) = (Free-slip wall)


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Free-slip wall BC

Vehicle surface:Log-law BC

Ground:Log-law Velocity BC or Log-law BC

Boundary conditions

21

Side walls and ceiling:Free slip


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Inflow/Outflow Boundary Conditions

There are several options at theboundaries through which fluid entersthe computational domain (inflow) orleaves the domain (outflow).

They are generally categorized as either: Velocity-specified conditions

Pressure-specified conditions At a velocity inlet , we specify the velocity

of the incoming flow along the inlet face If energy and/or turbulence equations

are being solved, the temperature and/orturbulence properties of the incomingflow need to be specified as well


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With pressure inlet and pressure outlet ,we specify the pressure, not the velocity

As the CFD solution converges, thevelocity adjusts itself such that theprescribed pressure BC are satisfied

With Outflow BC , the gradient or slope of

velocity normal to the outflow face iszero Neither pressure nor velocity are

specified at the outflow boundary


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Miscellaneous Boundary Conditions

Some boundaries are neither walls nor

inlets or outlets, but rather enforce somekind of symmetry or periodicity

For example, the periodic boundarycondition is useful when the geometryinvolves repetition

Periodic boundary conditions must bespecified as either translational (periodicity applied to two parallel faces,or rotational (periodicity applied to tworadially oriented faces).


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The symmetry BC is imposed on a face sothat the flow across that face is a mirror

image of the calculated flow


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Internal Boundary Conditions

The final classification of boundary conditions isimposed on faces or edges that do not define aboundary of the computational domain, butrather exist inside the domain.

When an interior boundary condition isspecified on a face, flow crosses through theface without any user-forced changes, just as itwould cross from one interior cell to another.

This boundary condition is necessary forsituations in which the computational domain isdivided into separate blocks or zones, andenables communication between blocks.


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Pipe Flow EntranceRegion at Re = 500

Case 1:LAMINAR CFD CALCULATIONS


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Case 2: Flow around a Circular Cylinder at Re = 150


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CdCoarse 120 1.00

Medium 110 0.982

Fine 109 0.977

Exp. 82 1.1 to 1.4


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TURBULENT CFD CALCULATIONS

CFD simulations of turbulent flow aremuch more difficult than those of laminarflow, even for cases in which the flow fieldis steady in the mean

The reason is that the finer features of theturbulent flow field are always unsteadyand 3-D random, swirling, vorticalstructures called turbulent eddies of allorientations arise in a turbulent flow

Laser-induced fluorescence image of an incompressible turbulent boundary layer, by C.Delo . Flow is from left to right, the flow was visualized with disodium fluorescein dye in

water. Reynolds number based on momentum thickness is 700.
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Direct numerical simulation (DNS)

Attempt is made to resolve the unsteadymotion of all the scales of the turbulent flow

Large eddy simulation (LES)

Only large eddies are resolved Small eddies are modeled

Significantly reducing computer requirements

Reynolds-averaged Navier-Stokes (RANS) All turbulent eddies are modeled

Only Reynolds-averaged flow properties arecalculated

Computer requirements are minimum

Types of CFD Method based on theextend to which the turbulent eddies are being resolved


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In Reynolds-averaged Navier Stokes (RANS) method, turbulence model isneeded due to the additional parameters introduced in the RANS equation

Specific Reynolds

stress tensor


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Case 3: Flow around a Circular Cylinder at Re = 10,000

l d l l d 7


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Flow around a Circular Cylinder at Re = 10 7

C 4 D i f


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Case 4: Design ofthe Stator for aVane-Axial Flow Fan


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Finer grid near walls


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Targets:

avg > 45 deg.No significant flow separation


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15 4 CFD WITH HEAT TRANSFER


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15 4 CFD WITH HEAT TRANSFERBy coupling the differential form of theenergy equation with the equations of fluidmotion, we can use a computational fluid

dynamics code to calculate propertiesassociated with heat transfer (e.g.,temperature distributions or rate of heattransfer from a solid surface to a fluid).

Since the energy equation is a scalarequation, only one extra transport equation(typically for either temperature orenthalpy) is required, and thecomputational expense (CPU time andRAM requirements) is not increasedsignificantly.

Heat transfer capability is built into mostcommercially available CFD codes, sincemany practical problems in engineeringinvolve both fluid flow and heat transfer. Asmentioned previously, additional boundaryconditions related to heat transfer need to

be specified.

C 5 T Ri h h C Fl H E h


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Case 5: Temperature Rise through a Cross-Flow Heat Exchanger

Hot tube

i h h C l h


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Temperature Rise through a Cross-Flow Heat Exchanger

= 0 T increase = 5.51 K

= 10 T increase = 5.65 KImproved by 2.5%

T Ri h h C Fl H E h


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Temperature Rise through a Cross-Flow Heat Exchanger

= 0 Turbulent intensity = 10%

T increase = 5.51 K

Turbulent intensity = 25%T increase = 5.87 KImproved by 6.5%

= 10 T increase = 5.65 KImproved by 2.5%


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Case 6: Cooling of an Array of Integrated Circuit Chips


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Case 6: Cooling of an Array of Integrated Circuit Chips


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15 5 COMPRESSIBLE FLOW CFD CALCULATIONS


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15 5 COMPRESSIBLE FLOW CFD CALCULATIONS

When the flow is compressible , density is no longer a constant, butbecomes an additional variable in the equation set.

We limit our discussion here to ideal gases .

When we apply the ideal-gas law , we introduce yet another unknown,namely, temperature T .

Hence, the energy equation must be solved along with the

compressible forms of the equations of conservation of mass andconservation of momentum.

In addition, fluid properties, such as viscosity and thermal conductivity,are no longer necessarily treated as constants, since they are functionsof temperature; thus, they appear inside the derivative operators in thedifferential equations of Fig. 15 74.

While the equation set looks ominous, many commercially availableCFD codes are able to handle compressible flow problems, includingshock waves.


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Compressible Flow through a Converging Diverging


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Compressible Flow through a Converging DivergingNozzle


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Obli Sh k W dg


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Oblique Shocks over a Wedge


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Two-phase Flow Simulation


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Two phase Flow Simulation

Flow over a Bump on the Bottom of a Channel

Fr = 1.81

Fr = 0.452


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How to ensure good quality CFD results?

Grid quality (skewness of cells)? Errors, converged results Grid adequately fine? Grid independent test Domain large enough? Verify domain Appropriate flow assumptions? Verify flow types Suitable boundary conditions? Verify BCs Suitable turbulence model? Verify turbulence models Simulation results are physically correct? Validation

(compare to experimental or analytical results)

bmcf 3233 chap 2 - cfd intro

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