CFD Lecture 01

7/29/2019 CFD Lecture 01

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Introduction to Computational

Fluid Dynamics (CFD)


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Computational fluid dynamicsFluid dynamics is the science of fluid motion.

Fluid flow is commonly studied in one of three ways:Experimental fluid dynamics.

Theoretical fluid dynamics.

Numerically: computational fluid dynamics (CFD).

Computational fluid dynamics (CFD) is the science of predicting

fluid flow, heat transfer, mass transfer, chemical reactions, andrelated phenomena by solving the mathematical equationswhich govern these processes using a numerical process.

The result of CFD analyses is relevant engineering data used in:

Conceptual studies of new designs.

Detailed product development.

Troubleshooting.

Redesign.


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CFD analysis complements testing and experimentation.

Reduces the total effort required in the laboratoryHistorically only Analytical Fluid Dynamics (AFD) and Experimental FluidDynamics (EFD).

CFD made possible by the advent of digital computer and advancingwith improvements of computer resources


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Why use CFD?

Analysis and Design1. Simulation-based design instead of build & testMore cost effective and more rapid than EFD

CFD provides high-fidelity database for diagnosing flowfield

2. Simulation of physical fluid phenomena that aredifficult for experimentsFull scale simulations (e.g., ships and airplanes)

Environmental effects (wind, weather, etc.)

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

Physics (e.g., planetary boundary layer, stellar

evolution)

Knowledge and exploration of flow physics


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Where is CFD used?

Where is CFD used?

Aerospace

Automotive

Biomedical

ChemicalProcessing

HVAC

Hydraulics

Marine

Oil & Gas Power Generation

Sports

F18 Store Separation

Temperature and naturalconvection currents in the eyefollowing laser heating.

Aerospace

Automotive

Biomedical


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Where is CFD used?

Polymerization reactor vessel - predictionof flow separation and residence timeeffects.

Streamlines for workstationventilation

Where is CFD used? Aerospacee

Automotive

Biomedical

ChemicalProcessing

HVAC

Hydraulics

Marine

Oil & Gas

Power Generation

Sports

HVAC

Chemical Processing

Hydraulics


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Where is CFD used?

Where is CFD used? Aerospace

Automotive

Biomedical

Chemical Processing HVAC

Hydraulics

Marine

Oil & Gas

Power Generation Sports

Flow of lubricating

mud over drill bit Flow around coolingtowers

Marine (movie)

Oil & Gas

Sports

Power Generation


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Domain for bottle filling

problem.

Filling

Nozzle

Bottle

CFD - how it works

Analysis begins with a mathematicalmodel of a physical problem.

Conservation of matter, momentum, andenergy must be satisfied throughout theregion of interest.

Fluid properties are modeled empirically.

Simplifying assumptions are made inorder to make the problem tractable(e.g., steady-state, incompressible,inviscid, two-dimensional).

Provide appropriate initial and boundaryconditions for the problem.


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Mesh for bottle filling

problem.

CFD - how it works (2)CFD applies numerical methods (calleddiscretization) to develop approximations

of the governing equations of fluidmechanics in the fluid region of interest.

Governing differential equations: algebraic.

The collection of cells is called the grid.

The set of algebraic equations are solvednumerically (on a computer) for the flow fieldvariables at each node or cell.

System of equations are solved simultaneouslyto provide solution.

The solution is post-processed to extractquantities of interest (e.g. lift, drag,torque, heat transfer, separation,pressure loss, etc.).


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CFD process

Purposesof CFD codes will be different for different

applications: investigation of bubble-fluid interactions for bubblyflows, study of wave induced massively separated flows forfree-surface, etc.

Depend on the specific purpose and flow conditions of theproblem, different CFD codescan be chosen for differentapplications (aerospace, marines, combustion, multi-phaseflows, etc.)

Once purposes and CFD codes chosen, CFD process is thesteps to set up the IBVP problem and run the code:

1. Geometry

2. Physics3. Mesh

4. Solve

5. Reports

6. Post processing


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CFD Process

Viscous

Model

Boundary

Conditions

Initial

Conditions

Convergent

Limit

Contours

Precisions

(single/

double)

Numerical

Scheme

Vectors

StreamlinesVerification

Geometry

Select

Geometry

Geometry

Parameters

Physics Mesh Solve Post-

Processing

Compressible

ON/OFF

Flow

properties

Unstructured

(automatic/

manual)

Steady/

Unsteady

Forces Report(lift/drag, shear

stress, etc)

XY Plot

Domain

Shape and

Size

Heat Transfer

ON/OFF

Structured

(automatic/

manual)

Iterations/

Steps

Validation

Reports


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Geometry

Selection of an appropriate coordinate

Determine the domain size and shape

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 createdusing commercial software (either separated from thecommercial code itself, like Gambit, or combinedtogether, like FlowLab)

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


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Physics Flow conditions and fluid properties

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

2. Fluid properties: density, viscosity, and

thermal conductivity, etc.

3. Flow conditions and properties usually presented indimensional form in industrial commercial CFDsoftware, whereas in non-dimensional variables forresearch codes.

Selection of models: different models usually fixed bycodes, options for user to choose

Initial and Boundary Conditions: not fixed by codes,user needs specify them for different applications.


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Mesh

Meshes should be well designed to resolveimportant flow features which are dependent uponflow condition parameters (e.g., Re), such as thegrid refinement inside the wall boundary layer

Mesh can be generated by either commercial codes(Gridgen, Gambit, etc.) or research code (usingalgebraic vs. PDE based, conformal mapping, etc.)

The mesh, together with the boundary conditionsneed to be exported from commercial software in a

certain format that can be recognized by theresearch CFD code or other commercial CFDsoftware.


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Reports Reports saved the time history of the residuals of

the velocity, pressure and temperature, etc.

Report the integral quantities, such as total pressuredrop, friction factor (pipe flow), lift and dragcoefficients (airfoil flow), etc.

XY plots could present the centerlinevelocity/pressure distribution, friction factordistribution (pipe flow), pressure coefficientdistribution (airfoil flow).

AFD or EFD data can be imported and put on top ofthe XY plots for validation


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Post-processing Analysis and visualization

Calculation of derived variablesVorticity

Wall shear stress

Calculation of integral parameters: forces,moments

Visualization (usually with commercialsoftware) Simple 2D contours

3D contour isosurface plots

Vector plots and streamlines(streamlines are the lines whose

tangent direction is the same as thevelocity vectors)

Animations

Post-processing usually through usingcommercial software


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DiscretizationDomain is discretized into a finite set of control volumesor cells. The discretized domain is called the grid or the

mesh.

General conservation (transport) equations for mass,momentum, energy, etc., are discretized into algebraicequations.

All equations are solved to render flow field.

VAAV

dVSdddVt

AAV

unsteady convection diffusion generation

Eqn.

continuity 1

x-mom. u

y-mom. v

energy h

Fluid region of

pipe flow

discretized intofinite set of

control volumes

(mesh).

control

volume

D i d h id


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Design and create the gridShould you use a quad/hex grid, a tri/tet grid, a hybridgrid, or a non-conformal grid?

What degree of grid resolution is required in eachregion of the domain?

How many cells are required for the problem?

Will you use adaption to add resolution?Do you have sufficient computer memory?

triangle

quadrilateral

tetrahedron pyramid

prism or wedgehexahedronarbitrary polyhedron


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Tri/tet vs. quad/hex meshes

For simple geometries, quad/hex

meshes can provide high-qualitysolutions with fewer cells than acomparable tri/tet mesh.

For complex geometries,quad/hex meshes show nonumerical advantage, and youcan save meshing effort by usinga tri/tet mesh.


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Hybrid mesh example

Valve port grid.

Specific regions can be meshedwith different cell types.

Both efficiency and accuracy areenhanced relative to ahexahedral or tetrahedral meshalone.

Hybrid mesh for an

IC engine valve port

tet mesh

hex mesh

wedge mesh


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Grids can either be structured(hexahedral) or unstructured(tetrahedral). Depends upon type ofdiscretization scheme and application

Scheme Finite differences: structured

Finite volume or finite element:

structured or unstructured Application

Thin boundary layers bestresolved with highly-stretchedstructured grids

Unstructured grids useful forcomplex geometries

Unstructured grids permitautomatic adaptive refinementbased on the pressure gradient,or regions interested (FLUENT)

structured

unstructured


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Example of CFD Process (Mesh)

Grid need to be refined near the

foil surface to resolve the boundary

layer

N i l th d ( id


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Numerical methods (gridtransformation)

y

xo o

Physical domain Computational domain

x x

f f f f f

x x x

y y

f f f f f

y y y

Transformation between physical (x,y,z)

and computational (,,z) domains,important for body-fitted grids. The partial

derivatives at these two domains have the

relationship (2D as an example)

Transform


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Solvers and numerical parameters Solversinclude: tridiagonal, pentadiagonal solvers,,

solution-adaptive solver, multi-grid solvers, etc. Solvers can be either direct (Cramers rule, Gauss

elimination, LU decomposition) or iterative (Jacobimethod, Gauss-Seidel method, SOR method)

Numerical parameters need to be specified to control

the calculation. Under relaxation factor, convergence limit, etc. Different numerical schemes Monitor residuals (change of results between

iterations)

Number of iterations for steady flow or number oftime steps for unsteady flow

Single/double precisions


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Example of CFD Process (Solve)

Residuals vs. iteration


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Example of CFD Process (Reports)

E l f CFD P (P t i )


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Example of CFD Process (Post-processing)

Di h l


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Dinosaur mesh example

S t th i l d l


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Set up the numerical modelFor a given problem, you will need to:

Select appropriate physical models.Turbulence, combustion, multiphase, etc.

Define material properties.Fluid.

Solid.

Mixture.

Prescribe operating conditions.

Prescribe boundary conditions at all boundaryzones.

Provide an initial solution.

Set up solver controls.

Set up convergence monitors.

Compute the solution


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Compute the solutionThe discretized conservation equations are solvediteratively. A number of iterations are usually

required to reach a converged solution.

Convergence is reached when:

Changes in solution variables from one iteration to the nextare negligible.

Residuals provide a mechanism to help monitor this trend.Overall property conservation is achieved.

The accuracy of a converged solution is dependentupon:

Appropriateness and accuracy of the physical models.Grid resolution and independence.

Problem setup.

Examine the results


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Examine the resultsVisualization can be used to answer suchquestions as:

What is the overall flow pattern?

Is there separation?

Where do shocks, shear layers, etc. form?

Are key flow features being resolved?Are physical models and boundary conditionsappropriate?

Numerical reporting tools can be used to calculate

quantitative results, e.g:Lift, drag, and torque.

Average heat transfer coefficients.

Surface-averaged quantities.


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Velocity vectors around a dinosaur


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Velocity magnitude (0-6 m/s) on adinosaur


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Pressure field on a dinosaur

Forces on the dinosaur


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Forces on the dinosaurDrag force: 17.4 N.

Lift force: 5.5 N.

Wind velocity: 5 m/s.

Air density: 1.225 kg/m3.

The dinosaur is 3.2 m tall.

It has a projected frontal area of A = 2.91 m2

.The drag coefficient is:

11.091.2*25*225.1*5.0

4.17

2

2

1

Av

FC D

D

Consider revisions to the model


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Consider revisions to the model

Are physical models appropriate?Is flow turbulent?

Is flow unsteady?Are there compressibility effects?

Are there 3D effects?

Are boundary conditions correct?

Is the computational domain large enough?Are boundary conditions appropriate?

Are boundary values reasonable?

Is grid adequate?Can grid be adapted to improve results?

Does solution change significantly with adaption, or is the solutiongrid independent?

Does boundary resolution need to be improved?

Advantages of CFD


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Advantages of CFDRelatively low cost.

Using physical experiments and tests to get essential

engineering data for design can be expensive.CFD simulations are relatively inexpensive, and costs are likelyto decrease as computers become more powerful.

Speed.

CFD simulations can be executed in a short period of time.Quick turnaround means engineering data can be introducedearly in the design process.

Ability to simulate real conditions.

Many flow and heat transfer processes can not be (easily)

tested, e.g. hypersonic flow.

CFD provides the ability to theoretically simulate any physicalcondition.

Advantages of CFD (2)


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Advantages of CFD (2)

Ability to simulate ideal conditions.

CFD allows great control over the physical process, andprovides the ability to isolate specific phenomena for study.

Example: a heat transfer process can be idealized withadiabatic, constant heat flux, or constant temperatureboundaries.

Comprehensive information.Experiments only permit data to be extracted at a limitednumber of locations in the system (e.g. pressure andtemperature probes, heat flux gauges, LDV, etc.).

CFD allows the analyst to examine a large number of locationsin the region of interest, and yields a comprehensive set offlow parameters for examination.

Limitations of CFD


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Limitations of CFDPhysical models.

CFD solutions rely upon physical models of real world

processes (e.g. turbulence, compressibility, chemistry,multiphase flow, etc.).

The CFD solutions can only be as accurate as the physicalmodels on which they are based.

Numerical errors.

Solving equations on a computer invariably introducesnumerical errors.

Round-off error: due to finite word size available on thecomputer. Round-off errors will always exist (though they can

be small in most cases).Truncation error: due to approximations in the numericalmodels. Truncation errors will go to zero as the grid is refined.Mesh refinement is one way to deal with truncation error.

Limitations of CFD (2)


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poor better

Fully Developed Inlet

Profile

Computational

Domain

Computational

Domain

Uniform Inlet

Profile

Limitations of CFD (2)

Boundary conditions.

As with physical models, the accuracy of the CFDsolution is only as good as the initial/boundaryconditions provided to the numerical model.

Example: flow in a duct with sudden expansion. If

flow is supplied to domain by a pipe, you shoulduse a fully-developed profile for velocity ratherthan assume uniform conditions.

Summary


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Summary

CFD is a method to numerically calculate heattransfer and fluid flow.

Currently, its main application is as an engineeringmethod, to provide data that is complementary totheoretical and experimental data. This is mainly thedomain of commercially available codes and in-house

codes at large companies.CFD can also be used for purely scientific studies,e.g. into the fundamentals of turbulence. This ismore common in academic institutions and

government research laboratories. Codes are usuallydeveloped to specifically study a certain problem.

CFD Lecture 01

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