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Computational Fluid Dynamics (CFD) U7AEA29

- Dr. S. Senthil Kumar
- Associate Professor
- Dept. of Aeronautical Engineering
- Vel Tech Dr. RR Dr. SR Technical University
- Avadi, Chennai
- .

Outline

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

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.

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

Where is CFD used? (Aerospace)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- 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
- HVACR
- 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.

Where is CFD used? (Automotive)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

External Aerodynamics

Undercarriage Aerodynamics

Interior Ventilation

Engine Cooling

Where is CFD used? (Biomedical)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Medtronic Blood Pump

Temperature and natural convection currents in

the eye following laser heating.

Where is CFD used? (Chemical Processing)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Polymerization reactor vessel - prediction of

flow separation and residence time effects.

Twin-screw extruder modeling

Shear rate distribution in twin-screw extruder

simulation

Where is CFD used? (HVACR)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Flow pathlines colored by pressure quantify head

loss in ductwork

Where is CFD used? (Hydraulics)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Where is CFD used? (Marine)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Where is CFD used? (Oil Gas)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Volume fraction of gas

Flow vectors and pressure distribution on an

offshore oil rig

Volume fraction of oil

Volume fraction of water

Analysis of multiphase separator

Flow of lubricating mud over drill bit

Where is CFD used? (Power Generation)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Flow around cooling towers

Pathlines from the inlet colored by temperature

during standard operating conditions

Flow pattern through a water turbine.

Where is CFD used? (Sports)

- Where is CFD used?
- Aerospace
- Appliances
- Automotive
- Biomedical
- Chemical Processing
- HVACR
- Hydraulics
- Marine
- Oil Gas
- Power Generation
- Sports

Physics

- 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,

g, Gr, Ec) - Free-surface flow and surface tension (Fr, We)
- Chemical reactions, mass transfer
- etc

Physics

Fluid Mechanics

Inviscid

Viscous

Laminar

Turbulence

External (airfoil, ship)

Internal (pipe,valve)

Incompressible (water)

Compressible (air, acoustic)

Components of Fluid Mechanics

Navier-Stokes Equation

Claude-Louis Navier

George Gabriel Stokes

Modeling

- 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)

Governing Equations (B,S, L)

(Equations based on average velocity)

Continuity

x - Equation of motion

Numerics / 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

Finite Differences

Finite difference representation

Truncation error

Methods of Solution

Direct methods

Iterative methods

Jacobi method, Gauss-Seidel Method, SOR method

Cramers Rule, Gauss elimination LU decomposition

Numeric Solution (Finite Differences)

jmax

j1

j

Taylors Series Expansion u i,j velocity of

fluid

j-1

o

x

i

i1

i-1

imax

Discrete Grid Points

CFD 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

Geometry description

- Typical approaches
- Make assumptions and simplifications
- CAD/CAE integration
- Engineering drawings
- Coordinates include Cartesian system (x,y,z),

cylindrical system (r, ?, z), and spherical

system(r, ?, F)

Selection 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.

CFD - 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.

Filling Nozzle

Bottle

Domain for bottle filling problem.

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.).

Mesh for bottle filling problem.

Discretization

- 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.

control volume

Design 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?

arbitrary polyhedron

Tri/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.

Hybrid 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.

Dinosaur mesh example

Set 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.

Initial 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.

Compute 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.

Numerical parameters flow 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

Post-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)

Examine 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.

Velocity vectors around a dinosaur

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

Pressure field on a dinosaur

Advantages 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.

Limitations 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.

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.

Software 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 YOU