# Introduction to Computational Fluid Dynamics

Mechanics

Oct 24, 2013 (4 years and 8 months ago)

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Ram Ramanan
10/24/2013

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2005
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Introduction to Computational Fluid
Dynamics

Lecture 2: CFD Introduction

Ram Ramanan
10/24/2013

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Numerical Simulations

System
-
level CFD problems

Includes all components in the product

Component or detail
-
level problems

Identifies the issues in a specific component or a sub
-
component

Different tools for the level of analysis

Coupled physics (fluid
-
structure interactions)

Ram Ramanan
10/24/2013

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CFD Codes

Available commercial codes

fluent, star
-
cd, Exa, cfd
-
ace, cfx etc.

Other structures codes with fluids capability

ansys, algor, cosmos
etc.

Supporting grid generation and post
-
processing codes

NASA and other government lab codes

Netlib, Linpack routines for new code development

Mathematica or Maple for difference equation generation

-
based macros) for simple solutions

Ram Ramanan
10/24/2013

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What is Computational Fluid Dynamics?

Computational Fluid Dynamics

(CFD) is the science of predicting
fluid flow, heat transfer, mass transfer, chemical reactions, and related
phenomena by solving the
mathematical equations

which govern these
processes using a
numerical process

(that is, on a computer).

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

conceptual studies of new designs

detailed product development

troubleshooting

redesign

CFD analysis complements testing and experimentation.

Reduces the total effort required in the laboratory.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Applications

Applications of CFD are numerous!

flow and heat transfer in industrial processes (boilers, heat exchangers,
combustion equipment, pumps, blowers, piping, etc.)

aerodynamics of ground vehicles, aircraft, missiles

film coating, thermoforming in material processing applications

flow and heat transfer in propulsion and power generation systems

ventilation, heating, and cooling flows in buildings

chemical vapor deposition (CVD) for integrated circuit manufacturing

heat transfer for electronics packaging applications

and many, many more...

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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CFD
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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

to make the problem tractable (e.g., steady
-
state, incompressible, inviscid, two
-
dimensional).

Provide appropriate initial and/or boundary
conditions for the problem.

Domain for bottle filling
problem.

Filling
Nozzle

Bottle

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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ME 5337/7337

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2005
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CFD
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How It Works (2)

CFD applies numerical methods (called
discretization
) to develop approximations of the
governing equations of fluid mechanics and the fluid
region to be studied.

Governing differential equations

algebraic

The collection of cells is called the
grid
or
mesh
.

The set of approximating 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, heat transfer, separation points,
pressure loss, etc.).

Mesh for bottle filling
problem.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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ME 5337/7337

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2005
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An Example: Water flow over a tube bank

Goal

compute average pressure drop, heat
transfer per tube row

Assumptions

flow is two
-
dimensional, laminar,
incompressible

flow approaching tube bank is steady with
a known velocity

body forces due to gravity are negligible

flow is translationally periodic (i.e.
geometry repeats itself)

Physical System can be modeled
with repeating geometry.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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2005
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Mesh Generation

Geometry created or imported into
preprocessor for meshing.

Mesh is generated for the fluid region
(and/or solid region for conduction).

A fine structured mesh is placed
around cylinders to help resolve
boundary layer flow.

Unstructured mesh is used for
remaining fluid areas.

Identify interfaces to which boundary
conditions will be applied.

cylindrical walls

inlet and outlets

symmetry and periodic faces

Section of mesh for tube bank problem

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Using the Solver

Import mesh.

Select solver
methodology.

Define operating and
boundary conditions.

e.g., no
-
slip, q
w

or
T
w

at walls.

Initialize field and
iterate for solution.

parameters and/or
mesh for convergence
problems.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Post
-
processing

Extract relevant engineering
data from solution in the
form of:

x
-
y plots

contour plots

vector plots

surface/volume integration

forces

fluxes

particle trajectories

Temperature contours within the fluid region.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Low Cost

Using physical experiments and tests to get essential engineering data for
design can be expensive.

Computational 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 at Mach 20

CFD provides the ability to theoretically simulate any physical condition

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Ability to Simulate Ideal Conditions

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

Example: a heat transfer process can be idealized with adiabatic, constant heat
flux, or constant temperature boundaries.

Comprehensive Information

Experiments only permit data to be
extracted at a limited number of
locations in the system (e.g. pressure
and temperature probes, heat flux
gauges, LDV, etc.)

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

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Limitations of CFD

Physical Models

CFD solutions rely upon physical models of real world processes (e.g.
turbulence, compressibility, chemistry, multiphase flow, etc.).

The solutions that are obtained through CFD 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

-

errors due to finite word size available on the computer

Truncation error

-

error due to approximations in the numerical models

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

Truncation errors will go to zero as the grid is refined
-

so
mesh

refinement

is one way to deal with truncation error.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

CFD
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ME 5337/7337

Notes
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2005
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002

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.

poor

better

Fully Developed
Inlet Profile

Computational
Domain

Computational
Domain

Uniform Inlet
Profile

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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Summary

Computational Fluid Dynamics is a powerful way of modeling fluid
flow, heat transfer, and related processes for a wide range of important
scientific and engineering problems.

The cost of doing CFD has decreased dramatically in recent years, and
will continue to do so as computers become more and more powerful.

Courtesy: Fluent, Inc
.

Ram Ramanan
10/24/2013

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ME 5337/7337

Notes
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2005
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Numerical solution methods

Consistency and truncation errors

As h
-
> 0, error
-
> 0 (h
n
, t
n
)

Stability

Converging methodology

Convergence

Gets close to exact solution

Conservation

Physical quantities are conserved

Boundedness (Lies within physical bounds)

Higher order schemes can have overshoots and undershoots

Realizability (Be able to model the physics)

Accuracy (Modeling, Discretization and Iterative solver errors)

Ram Ramanan
10/24/2013

CFD
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ME 5337/7337

Notes
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2005
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002

CFD Methodologies

Finite difference method

Simple grids (rectangular)

Complex geometries
-
> Transform to simple geometry (coordinate
transformation)

Finite volume method

Complex geometries (conserve across faces)

Finite element method

Complex geometries (element level transformation)

Spectral element method

Higher order interpolations in elements

Lattice
-
gas methods

Basic momentum principle
-
based