Computational Fluid Dynamics Computational Fluid Dynamics (CFD)(CFD)

U7AEA29U7AEA29

Dr. S. Senthil Kumar

Associate Professor

Dept. of Aeronautical Engineering

Vel Tech Dr. RR & Dr. SR Technical University

Avadi, Chennai

.

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OutlineOutline

What is CFD? Why use CFD? Where is CFD used? Physics Modeling Numerics CFD process Resources

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What is CFD?What is CFD?

What is CFD and its objective?

– Computational Fluid Dynamics– Historically Analytical Fluid Dynamics (AFD) and EFD

(Experimental Fluid Dynamics) was used. CFD has become feasible due to the advent of high speed digital computers.

– Computer simulation for prediction of fluid-flow phenomena. – The objective of CFD is to model the continuous fluids with

Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem (Taylor series), solve it, validate it and achieve simulation based design.

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Why use CFD?Why use CFD?

Why use CFD?– Analysis and Design

Simulation-based design instead of “build & test”– More cost effectively and more rapidly than with experiments– CFD solution provides high-fidelity database for interrogation of

flow field Simulation of physical fluid phenomena that are difficult to be

measured by experiments– Scale simulations (e.g., full-scale ships, airplanes)– Hazards (e.g., explosions, radiation, pollution)– Physics (e.g., weather prediction, planetary boundary layer,

stellar evolution)

– Knowledge and exploration of flow physics

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Where is CFD used? (Aerospace)

• Where is CFD used?

– Aerospace– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

F18 Store Separation

Wing-Body Interaction Hypersonic Launch Vehicle

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Where is CFD used? (Appliances)

• Where is CFD used?– Aerospace

– Appliances– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

Surface-heat-flux plots of the No-Frost refrigerator and freezer compartments helped BOSCH-SIEMENS engineers to optimize the location of air inlets.

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Where is CFD used? (Automotive)

• Where is CFD used?– Aerospace

– Appliances

– Automotive– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

External Aerodynamics Undercarriage Aerodynamics

Interior Ventilation Engine Cooling

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Where is CFD used? (Biomedical)• Where is CFD used?

– Aerospace

– Appliances

– Automotive

– Biomedical– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports Temperature and natural convection currents in the eye following laser heating.

Medtronic Blood Pump

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Where is CFD used? (Chemical Processing)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

Polymerization reactor vessel - prediction of flow separation and residence time effects.

Shear rate distribution in twin-screw extruder simulation

Twin-screw extruder modeling

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Where is CFD used? (HVAC&R)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

Particle traces of copier VOC emissions colored by concentration level fall behind the copier and then circulate through the room before exiting the exhaust.

Mean age of air contours indicate location of fresh supply air

Streamlines for workstation ventilation

Flow pathlines colored by pressure quantify head loss in ductwork

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Where is CFD used? (Hydraulics)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics– Marine

– Oil & Gas

– Power Generation

– Sports

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Where is CFD used? (Marine)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine– Oil & Gas

– Power Generation

– Sports

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Where is CFD used? (Oil & Gas)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas– Power Generation

– Sports

Flow vectors and pressure distribution on an offshore oil rig

Flow of lubricating mud over drill bit

Volume fraction of water

Volume fraction of oil

Volume fraction of gas

Analysis of multiphase separator

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Where is CFD used? (Power Generation)

• Where is CFD used?– Aerospace

– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation– Sports

Flow pattern through a water turbine.

Flow in a burner

Flow around cooling towers

Pathlines from the inlet colored by temperature during standard operating conditions

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Where is CFD used? (Sports)

• Where is CFD used?

– Aerospace– Appliances

– Automotive

– Biomedical

– Chemical Processing

– HVAC&R

– Hydraulics

– Marine

– Oil & Gas

– Power Generation

– Sports

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PhysicsPhysics

CFD codes typically designed for representation of specific flow phenomenon– Viscous vs. inviscid (no viscous forces) (Re)– Turbulent vs. laminar (Re)– Incompressible vs. compressible (Ma)– Single- vs. multi-phase (Ca)– Thermal/density effects and energy equation (Pr, , Gr, Ec)– Free-surface flow and surface tension (Fr, We)– Chemical reactions, mass transfer– etc…

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PhysicsPhysics

Fluid Mechanics

Inviscid Viscous

Laminar Turbulence

Internal(pipe,valve)

External(airfoil, ship)Compressibl

e(air, acoustic)

Incompressible(water)

Components of Fluid Mechanics

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Claude-Louis Navier George Gabriel Stokes

gvpvDt

D 2

Navier-Stokes EquationNavier-Stokes Equation

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ModelingModeling Mathematical representation of the physical problem

– Some problems are exact (e.g., laminar pipe flow)– Exact solutions only exist for some simple cases. In these cases nonlinear terms

can be dropped from the N-S equations which allow analytical solution.– Most cases require models for flow behavior [e.g., Reynolds Averaged Navier

Stokes equations (RANS) or Large Eddy Simulation (LES) for turbulent flow] Initial —Boundary Value Problem (IBVP), include: governing Partial Differential

Equations (PDEs), Initial Conditions (ICs) and Boundary Conditions (BCs)

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Governing Equations (B,S,& L)Governing Equations (B,S,& L)

xzxyxxxx

zx

yx

xx g

zyxx

p

z

uu

y

uu

x

uu

t

u

Continuity

x - Equation of motion

0

zyx uz

uy

uxt

v

(Equations based on “average” velocity)(Equations based on “average” velocity)

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Numerics / DiscretizationNumerics / Discretization

Computational solution of the IBVP Method dependent upon the model equations and

physics Several components to formulation

– Discretization and linearization– Assembly of system of algebraic equations– Solve the system and get approximate solutions

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Finite DifferencesFinite Differences

Methods of Solution

Direct methods Iterative methods

Cramer’s Rule, Gauss eliminationLU decomposition

Jacobi method, Gauss-SeidelMethod, SOR method

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2

,

3

3

,

2

2,,1

,

x

x

ux

x

u

x

uu

x

u

jiji

jiji

ji

Finite differencerepresentation

Truncation error

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Numeric SolutionNumeric Solution (Finite Differences) (Finite Differences)

o xi i+1i-1

j+1j

j-1

imax

jmaxx

y

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3

,

3

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,

2

2

,,,1

x

x

ux

x

ux

x

uuu

jijijijiji

Taylor’s Series Expansion u i,j = velocity of fluid

Discrete Grid Points

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CFD processCFD process

Geometry description Specification of flow conditions and properties Selection of models Specification of initial and boundary conditions Grid generation and transformation Specification of numerical parameters Flow solution Post processing: Analysis, and visualization

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Geometry descriptionGeometry description

Typical approaches

– Make assumptions and simplifications

– CAD/CAE integration– Engineering drawings– Coordinates include Cartesian

system (x,y,z), cylindrical system (r, θ, z), and spherical system(r, θ, Φ)

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Selection of models for flow fieldSelection of models for flow field Direct Numerical Simulations (DNS) is to solve the N-S equations

directly without any modeling. Grid must be fine enough to resolve all flow scales. Applied for laminar flow and rare be used in turbulent flow.

Reynolds Averaged Navier-Stokes (NS) equations (RANS) is to perform averaging of NS equations and establishing turbulent models for the eddy viscosity. Too many averaging might damping vortical structures in turbulent flows

Large Eddy Simulation (LES), Smagorinsky’ constant model and dynamic model. Provide more instantaneous information than RANS did. Instability in complex geometries

Detached Eddy Simulation (DES) is to use one single formulation to combine the advantages of RANS and LES.

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Domain for bottle filling problem.

Filling Nozzle

Bottle

CFD - how it worksCFD - how it works Analysis begins with a mathematical

model of a physical problem. Conservation of matter, momentum,

and energy must be satisfied throughout the region of interest.

Fluid properties are modeled empirically.

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

Provide appropriate initial and boundary conditions for the problem.

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Mesh for bottle filling problem.

CFD - how it works (2)CFD - how it works (2) CFD applies numerical methods (called

discretization) to develop approximations of the governing equations of fluid mechanics in the fluid region of interest.– Governing differential equations: algebraic.– The collection of cells is called the grid. – The set of algebraic equations are solved

numerically (on a computer) for the flow field variables at each node or cell.

– System of equations are solved simultaneously to provide solution.

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

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DiscretizationDiscretization Domain is discretized into a finite set of control volumes

or cells. The discretized domain is called the “grid” or the “mesh.” General conservation (transport) equations for mass, momentum,

energy, etc., are discretized into algebraic equations. All equations are solved to render flow field.

VAAV

dVSdddVt AAV

unsteady convection diffusion generation

Eqn.continuity 1x-mom. uy-mom. venergy h

Fluid region of pipe flow discretized into finite set of control volumes (mesh).

control volume

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Design and create the gridDesign and create the grid Should you use a quad/hex grid, a tri/tet grid, a hybrid grid, or a

non-conformal grid? What degree of grid resolution is required in each region 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 meshesTri/tet vs. quad/hex meshes For simple geometries, quad/hex

meshes can provide high-quality solutions with fewer cells than a comparable tri/tet mesh.

For complex geometries, quad/hex meshes show no numerical advantage, and you can save meshing effort by using a tri/tet mesh.

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Hybrid mesh exampleHybrid mesh example Valve port grid. Specific regions can be meshed with

different cell types. Both efficiency and accuracy are

enhanced relative to a hexahedral or tetrahedral mesh alone.

Hybrid mesh for an IC engine valve port

tet mesh

hex mesh

wedge mesh

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Dinosaur mesh exampleDinosaur mesh example

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Set up the numerical modelSet up the numerical model For 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 boundary zones.– Provide an initial solution.– Set up solver controls.– Set up convergence monitors.

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Initial and boundary conditionsInitial and boundary conditions For steady/unsteady flow

IC should not affect final solution, only convergence path, i.e. iteration numbers needed to get the converged solution.

Robust codes should start most problems from very crude IC, . But more reasonable guess can speed up the convergence.

Boundary conditions– No-slip or slip-free on the wall, periodic, inlet (velocity

inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.

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Compute the solutionCompute the solution The discretized conservation equations are solved iteratively. 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 next are negligible.

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

The accuracy of a converged solution is dependent upon:– Appropriateness and accuracy of the physical models.– Grid resolution and independence.– Problem setup.

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Numerical parameters & flow Numerical parameters & flow solution solution

Typical time history of residuals

The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing.

Solution converged, residuals do not change after more iterations

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Post-processingPost-processing Analysis, and visualization

– Calculation of derived variables Vorticity Wall shear stress

– Calculation of integral parameters: forces, moments– Visualization (usually with commercial software)

Simple X-Y plots Simple 2D contours 3D contour carpet plots Vector plots and streamlines (streamlines are the lines

whose tangent direction is the same as the velocity vectors)

Animations (dozens of sample pictures in a series of time were shown continuously)

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Examine the resultsExamine the results Visualization can be used to answer such questions 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 conditions appropriate?– 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 Velocity vectors around a dinosaurdinosaur

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Velocity magnitude (0-6 m/s) Velocity magnitude (0-6 m/s) on a dinosauron a dinosaur

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Pressure field on a dinosaur Pressure field on a dinosaur

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Advantages of CFDAdvantages of CFD Relatively 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 likely to 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 introduced early 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 physical condition.

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Limitations of CFDLimitations of CFD Physical 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 physical models on which they are based.

Numerical errors.– Solving equations on a computer invariably introduces numerical errors.– Round-off error: due to finite word size available on the computer.

Round-off errors will always exist (though they can be small in most cases).

– Truncation error: due to approximations in the numerical models. Truncation errors will go to zero as the grid is refined. Mesh refinement is one way to deal with truncation error.

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poor better

Fully Developed Inlet Profile

Computational Domain

Computational Domain

Uniform Inlet Profile

Limitations of CFD (2)Limitations of CFD (2) Boundary conditions.

– As with physical models, the accuracy of the CFD solution is only as good as the initial/boundary conditions provided to the numerical model.

– Example: flow in a duct with sudden expansion. If flow is supplied to domain by a pipe, you should use a fully-developed profile for velocity rather than assume uniform conditions.

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Software and resourcesSoftware and resources CFD software was built upon physics, modeling, numerics. Two types of available software

– Commercial (e.g., FLUENT, CFX, Star-CD)– Research (e.g., CFDSHIP-IOWA, U2RANS)

More information on CFD can be got on the following website:– CFD Online: http://www.cfd-online.com/– CFD software

FLUENT: http://www.fluent.com/ CFDRC: http://www.cfdrc.com/ Computational Dynamics: http://www.cd.co.uk/ CFX/AEA: http://www.software.aeat.com/cfx/

– Grid generation software Gridgen: http://www.pointwise.com GridPro: http://www.gridpro.com/ Hypermesh

– Visualization software Tecplot: http://www.amtec.com/ Fieldview: http://www.ilight.com/

THANK YOUTHANK YOU

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