BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS

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BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS

• MEEN 5330
• Presented
• By
• Chaitanya Vudutha
• Parimal Nilangekar
• Ravindranath Gouni
• Satish Kumar Boppana
• Albert Koether

Pages-28
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Overview

• Introduction
• History of CFD
• Basic concepts
• CFD Process
• Derivation of Navier-Stokes Duhem Equation
• Example Problem
• Applications
• Conclusion
• References

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Introduction
What is CFD? Prediction fluid flow with the
complications of simultaneous flow of heat, mass
transfer, phase change, chemical reaction, etc
using computers
History of CFD

• Since 1940s analytical solution to most fluid
  dynamics problems was available for idealized
  solutions. Methods for solution of ODEs or PDEs
  were conceived only on paper due to absence of
  personal computer.
• Daimler Chrysler was the first company to use CFD
  in Automotive sector.
• Speedo was the first swimwear company to use CFD.
• There are number of companies and software's in
  CFD field in the world. Some software's by
  American companies are FLUENT, TIDAL, C-MOLD,
  GASP, FLOTRAN, SPLASH, Tetrex, ViGPLOT, VGRID,
  etc.

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BASIC CONCEPTS
Fluid Mechanics
Fluid Statics
Fluid Dynamics
Laminar
Turbulent
Newtonian Fluid
Non-Newtonian Fluid
Rheology
Ideal Fluids
Viscous Fluids
Compressible Flow
Incompressible Flow
CFD
Solutions for specific Regimes
Components of Fluid Mechanics
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volumes no smaller than say (110
m3)
Molecular Particles of Fluid
Basic fluid motion can be described as some
combination of

• Translation motion of the center of mass

2) Dilatation volume change
3) Rotation About one, two or 3 axes .
4) Shear Strain
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Compressible and Incompressible flow
A fluid flow is said to be compressible when the
pressure variation in the flow field is large
enough to cause substantial changes in the
density of fluid.
Viscous and Inviscid Flow
In a viscous flow the fluid friction has
significant effects on the solution where the
viscous forces are more significant than inertial
forces
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Steady and Unsteady Flow
Whether a problem is steady or unsteady depends
on the frame of reference
Laminar and Turbulent Flow
Newtonian Fluids and Non-Newtonian Fluids
In Newtonian Fluids such as water, ethanol,
benzene and air, the plot of shear stress versus
shear rate at a given temperature is a straight
line
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Initial or Boundary Conditions

• Initial condition involves knowing the state of
  pressure (p) and initial velocity (u) at all
  points in the flow.
• Boundary conditions such as walls, inlets and
  outlets largely specify what the solution will be.

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Discretization Methods

• Finite volume method
• Finite Element method

• Where Q - vector of conserved variables

• F - vector of fluxes

• V - cell volume

• A Cell surface area

RiEquation residual at an element vertex
Q- Conservation equation expressed on element
basis
Wi Weight Factor
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• Finite difference method
• Boundary element method

Q Vector of conserved variables
F,G,H Fluxes in the x ,y, z directions
The boundary occupied by the fluid is divided
into surface mesh
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CFD PROCESS

• Geometry of problem is defined .
• Volume occupied by fluid is divided into discrete
  cells.

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• CFD PROCESS cont..
• Physical modeling is defined.
• Boundary conditions are defined which involves
  specifying of fluid behavior and properties at
  the boundaries.
• Equations are solved iteratively as steady state
  or transient state.
• Analysis and visualization of resulting solution.

post processing
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DERIVATION OF NAVIER-STOKES-DUHEM
EQUATION
The Navier-Stokes equations are the
fundamental partial differentials equations that
describe the flow of incompressible fluids.
Two of the alternative forms of equations of
motion, using the Eulerian description, were
given as Equation (1) and Equation (2)
respectively
(1)
(2)
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DERIVATION
(Contd)
If we assume that the fluid is isotropic ,
homogeneous , and Newtonian, then
(3)
Substituting Equ(3) into Equ(2), and utilizing
the Eulerian relationship for linear stress
tensor we get
(4)
( for compressible fluids )
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DERIVATION
(Contd)
For incompressible fluid flow the
Navier-Stokes- Duhem equation is
If the fluid medium is a monatomic ideal gas,
then
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DERIVATION
(Contd)
Navier stokes equation for compressible flow of
monatomic ideal gas is
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EXAMPLE PROBLEM
Neglecting the gravity field, describe the steady
two- dimensional flow of an isotropic ,
homogeneous, Newtonian fluid due to a constant
pressure gradient between two infinite, flat,
parallel, plates. State the necessary
assumptions. Assume that the fluid has a uniform
density.
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SOLUTION
(Contd)
The Navier stokes equations for incompressible
flow is
Since the flow is steady and the body forces are
neglected, the Navier-stokes equation becomes
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SOLUTION
(Contd)
The no slip boundary conditions for viscous flow
are
at
Using the boundary conditions ( q2 0 at y2/- a
) Thus, the first Navier-stokes equations becomes
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SOLUTION
(Contd)
Integrating twice, we obtain
The results, assumptions and boundary conditions
of this problem in terms of, mathematical symbols
are as follows
Constant
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HOMEWORK PROBLEM

• Using the Navier-Stokes equations investigate the
  flow (qi) between two stationary, infinite,
  parallel plates a distance h apart. Assuming that
  you have laminar flow of a constant-density,
  Newtonian fluid and the pressure gradient is
  constant (partial derivative of P with respect to
  1).

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Types of Errors and Problems

• Types of Errors
• Modeling Error.
• Discretization Error.
• Convergence Error.

• Reasons due to which Errors occur
• Stability.
• Consistency.
• Conservedness and Boundedness.

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Applications of CFD
1. Industrial Applications CFD is used in wide
variety of disciplines and industries, including
aerospace, automotive, power generation, chemical
manufacturing, polymer processing, petroleum
exploration, pulp and paper operation, medical
research, meteorology, and astrophysics.
Example Analysis of Airplane CFD allows one to
simulate the reactor without making any
assumptions about the macroscopic flow pattern
and thus to design the vessel properly the first
time.
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Application (Contd..)

• Two Dimensional Transfer Chute Analyses Using a
  Continuum Method
• Fluent is used in chute designing tasks like
  predicting flow shape, stream velocity, wear
  index and location of flow recirculation zones.
• Bio-Medical Engineering

The following figure shows pressure contours and
a cutaway view that reveals velocity vectors in a
blood pump that assumes the role of heart in
open-heart surgery.
Pressure Contours in Blood Pump
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Application (Contd..)
4. Blast Interaction with a Generic Ship Hull
The figure shows the interaction of an explosion
with a generic ship hull. The structure was
modeled with quadrilateral shell elements and the
fluid as a mixture of high explosives and air.
The structural elements were assumed to fail once
the average strain in an element exceeded 60
percent
Results in a cut plane for the interaction of an
explosion with a generic ship hull (a) Surface
at 20msec (b) Pressure at 20msec (c) Surface at
50msec and (d) Pressure at 50msec
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Application (Contd..)
5. Automotive Applications
Streamlines in a vehicle without (left) and
with rear center and B-pillar ventilation (right)
In above figure, influence of the rear center and
B-pillar ventilation on the rear passenger
comfort is assessed. The streamlines marking the
rear center and B-pillar ventilation jets are
colored in red. With the rear center and B-pillar
ventilation, the rear passengers are passed by
more cool air. In the system without rear center
and B-pillar ventilation, the upper part of the
body, in particular chest and belly is too warm.
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Conclusion

• Nearer the conditions of the experiment to those
  which concern the user, more closely the
  predictions agree with those data, the greater is
  the reliance which can be prudently placed on the
  predictions.
• CFD iterative Methods like Jacobi and
  Gauss-Seidel Method are used because the cost of
  direct methods is too high and discretization
  error is larger than the accuracy of the computer
  arithmetic.
• Many softwares offer the possibility of solving
  fully nonlinear coupled equations in a production
  environment.
• In the future we can have a multidisciplinary,
  database linked framework accessed from anywhere
  on demand simulations with unprecedented detail
  and realism carried out in fast succession so
  that designers and engineers anywhere in the
  world can discuss and analyze new ideas and first
  principles driven virtual reality

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References

• Hoffmann, Klaus A, and Chiang, Steve.T
  Computational fluid dynamics for engineers
  vol. I and vol. II
• Rajesh Bhaskaran, Lance Collins Introduction to
  CFD Basics
• http//www.cham.co.uk/website/new/cfdintro.htm
  accessed on 11/10/06.
• Adapted from notes by Tao Xing and Fred Stern,
  The University of Iowa.
• http//www.cfd-online.com/Wiki/Historical_perspect
  ive accessed on 11/12/06.
• Frederick and Chang,T.S.,Continuum Mechanics
• http//navier-stokes-equations.search.ipupdate.com
  /
• http//en.wikipedia.org/wiki/Computational_fluid_d
  ynamicsDiscretization_method s,
  Discretization Methods
• McIlvenna P and Mossad R Two Dimensional
  Transfer Chute Analysis Using a Continuum
  Method, Third International Conference on CFD in
  the Minerals and Process Industries, Dec 2003.
• Subramanian R.S. Non-Newtonian Flows.
• Lohner R., Cebral J., Yand C., Large Scale Fluid
  Structure Interaction Simulations, IEEE June
  2004.
• http//www.cd-adapco.com/press_room/dynamics/23/be
  hr.html,Predicting Passenger Comfort
• http//www.adl.gatech.edu/classes/lowspdaero/lospd
  2/lospd2.html, Types of Fluid Motion

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Thank You Questions are Welcome