Introduction to Computational Fluid Dynamics

stickshrivelMechanics

Oct 24, 2013 (3 years and 10 months ago)

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©

Ram Ramanan
10/24/2013

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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


Use of spreadsheets (and vb
-
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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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/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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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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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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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.


Adjust solver
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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Advantages of CFD


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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Advantages of CFD (2)


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

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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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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

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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