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BASICS OF COMPUTATIONAL FLUID DYNAMICS BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSISANALYSIS
MEEN 5330MEEN 5330Presented Presented
ByBy
Chaitanya VuduthaChaitanya VuduthaParimal NilangekarParimal NilangekarRavindranath GouniRavindranath Gouni
Satish Kumar BoppanaSatish Kumar BoppanaAlbert KoetherAlbert Koether
Pages-28
OverviewOverview
IntroductionIntroduction History of CFD History of CFD Basic conceptsBasic concepts CFD ProcessCFD Process Derivation of Navier-Stokes Duhem Derivation of Navier-Stokes Duhem
EquationEquation Example ProblemExample Problem ApplicationsApplications ConclusionConclusion ReferencesReferences
Introduction Introduction
Since 1940s analytical solution to most fluid dynamics problems was Since 1940s analytical solution to most fluid dynamics problems was available for idealized solutions. Methods for solution of ODEs or PDEs available for idealized solutions. Methods for solution of ODEs or PDEs were conceived only on paper due to absence of personal computer. were conceived only on paper due to absence of personal computer.
Daimler Chrysler was the first company to use CFD in Automotive Daimler Chrysler was the first company to use CFD in Automotive sector.sector.
Speedo was the first swimwear company to use CFD.Speedo was the first swimwear company to use CFD. There are number of companies and software's in CFD field in the There are number of companies and software's in CFD field in the
world. Some software's by American companies are FLUENT, TIDAL, world. Some software's by American companies are FLUENT, TIDAL, C-MOLD, GASP, FLOTRAN, SPLASH, Tetrex, ViGPLOT, VGRID, etc.C-MOLD, GASP, FLOTRAN, SPLASH, Tetrex, ViGPLOT, VGRID, etc.
History ofHistory of CFDCFD
What is CFD?What is CFD?Prediction fluid flow with the complications of Prediction fluid flow with the complications of simultaneous flow of heat, mass transfer, phase simultaneous flow of heat, mass transfer, phase change, chemical reaction, etc using computerschange, chemical reaction, etc using computers
Components of Fluid Mechanics
Fluid Mechanics
Fluid Statics Fluid Dynamics
Laminar Turbulent
Newtonian Fluid Non-Newtonian Fluid
Ideal Fluids Viscous Fluids
Compressible
Flow
Incompressible Flow
BASIC CONCEPTSBASIC CONCEPTS
CFD Solutions for specific Regimes
Rheology
Molecular Particles of Fluid
Basic fluid motion can be described as some combination of 1) Translation: [ motion of the center of mass ]
2) Dilatation: [ volume change ]
3) Rotation: [About one, two or 3 axes ].
4) Shear Strain
volumes no smaller than say (1*10 6m3)
Compressible and Incompressible flowCompressible and Incompressible flowA 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
jjiiii qpfdt
dq,,
~1
In a viscous flow the fluid friction has significant effects on the solution where the viscous forces are more significant than inertial forces
0)()(
vy
ux
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
Initial or Boundary ConditionsInitial or Boundary Conditions
Initial condition involves knowing the state of Initial condition involves knowing the state of pressure (p) and initial velocity (u) at all points in pressure (p) and initial velocity (u) at all points in the flow.the flow.
Boundary conditions such as walls, inlets and Boundary conditions such as walls, inlets and outlets largely specify what the solution will be.outlets largely specify what the solution will be.
Discretization MethodsDiscretization Methods Finite volume Finite volume
methodmethod
Finite Element Finite Element methodmethod
0
FdAQdvt
eii QdvWR
• Where Q - vector of conserved variables • F - vector of
fluxes • V - cell volume
• A –Cell surface area
Ri=Equation residual at an element vertexQ- Conservation equation expressed on
element basis
Wi= Weight Factor
Finite difference methodFinite difference method
Boundary element methodBoundary element method
0
z
H
y
G
x
F
t
Q
The boundary occupied by the fluid is divided into surface mesh
Q – Vector of conserved variables
F,G,H – Fluxes in the x ,y, z directions
CFD PROCESSCFD PROCESS
Geometry of Geometry of problem is problem is defined .defined .
Volume occupied Volume occupied by fluid is divided by fluid is divided into discrete cells.into discrete cells.
CFD PROCESS cont..CFD PROCESS cont..
Physical modeling is defined.Physical modeling is defined.
Boundary conditions are Boundary conditions are defined which involves defined which involves specifying of fluid behavior specifying of fluid behavior and properties at the and properties at the boundaries.boundaries.
Equations are solved Equations are solved iteratively as steady state or iteratively as steady state or transient state.transient state.
Analysis and visualization of Analysis and visualization of resulting solution.resulting solution.
post processing
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:
jjiijjii fqqt
q,,
)(
.1
,, jjiijijii fqqt
q
dt
dq
(1)
(2)
DERIVATION OF NAVIER-STOKES-DUHEM EQUATION
If we assume that the fluid is isotropic ,
homogeneous , and Newtonian, then :
.~2)~
( ijijkkij p (3)
DERIVATION (Cont’d)
Substituting Equ(3) into Equ(2), and utilizing the Eulerian
relationship for linear stress tensor we get :
,,,,
~~~1jjijijii
i qqpfdt
dq
(4)
( for compressible fluids )
For incompressible fluid flow the Navier-Stokes-
Duhem equation is:
jjiiii qpfdt
dq,,
~1
DERIVATION (Cont’d)
If the fluid medium is a monatomic ideal gas, then :
~3
2~
Navier stokes equation for compressible flow of
monatomic ideal gas is :
,,,,
~~
3
11jjijijii
i qqpfdt
dq
DERIVATION (Cont’d)
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.
The Navier – stokes equations for incompressible flow is:
jjiiijiji qpfqqdt
dq,,,
~1
Since the flow is steady and the body forces are
neglected, the Navier-stokes equation becomes:
jjiijij qpqq ,,,
~1
SOLUTION (Cont’d)
The no slip boundary conditions for viscous flow are:
0iq at ay 2
Using the boundary conditions ( q2= 0 at y2=+/- a )
Thus, the first Navier-stokes equations becomes
122
12
dy
dp
dy
qd
SOLUTION (Cont’d)
Integrating twice, we obtain
222
11 2
1ay
dy
dpq
The results, assumptions and boundary conditions of this problem in terms of, mathematical symbols are as follows:
Constant 0if 0
t
0
3
y
222
11 2
1ay
dy
dpq
SOLUTION (Cont’d)
HOMEWORK PROBLEM
Using the Navier-Stokes equations investigate the flow (qUsing the Navier-Stokes equations investigate the flow (qii) ) between two stationary, infinite, parallel plates a distance h between two stationary, infinite, parallel plates a distance h apart. Assuming that you have laminar flow of a constant-apart. Assuming that you have laminar flow of a constant-density, Newtonian fluid and the pressure gradient is density, Newtonian fluid and the pressure gradient is constant (partial derivative of P with respect to 1).constant (partial derivative of P with respect to 1).
Types of Errors and ProblemsTypes of Errors and ProblemsTypes of Errors:
Modeling Error.
Discretization Error.
Convergence Error.
Reasons due to which Errors occur:
Stability.
Consistency.
Conservedness and Boundedness.
Applications of CFDApplications of CFD1. Industrial Applications:1. Industrial Applications:
CFD is used in wide variety of disciplines and industries, CFD is used in wide variety of disciplines and industries, including aerospace, automotive, power generation, chemical including aerospace, automotive, power generation, chemical manufacturing, polymer processing, petroleum exploration, manufacturing, polymer processing, petroleum exploration, pulp and paper operation, medical research, meteorology, and pulp and paper operation, medical research, meteorology, and astrophysics.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.
Application (Contd..)Application (Contd..)
2. 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.
3. 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
Application (Contd..)Application (Contd..)
4. Blast Interaction with a Generic Ship Hull
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
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
Application (Contd..)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.
ConclusionConclusion Nearer the conditions of the experiment to those which concern Nearer the conditions of the experiment to those which concern
the user, more closely the predictions agree with those data, the the user, more closely the predictions agree with those data, the greater is the reliance which can be prudently placed on the greater is the reliance which can be prudently placed on the predictions.predictions.
CFD iterative Methods like Jacobi and Gauss-Seidel Method are CFD iterative Methods like Jacobi and Gauss-Seidel Method are used because the cost of direct methods is too high and used because the cost of direct methods is too high and discretization error is larger than the accuracy of the computer discretization error is larger than the accuracy of the computer arithmetic.arithmetic.
Many software’s offer the possibility of solving fully nonlinear Many software’s offer the possibility of solving fully nonlinear coupled equations in a production environment.coupled equations in a production environment.
In the future we can have a multidisciplinary, database linked In the future we can have a multidisciplinary, database linked framework accessed from anywhere on demand simulations with framework accessed from anywhere on demand simulations with unprecedented detail and realism carried out in fast succession so unprecedented detail and realism carried out in fast succession so that designers and engineers anywhere in the world can discuss that designers and engineers anywhere in the world can discuss and analyze new ideas and first principles driven virtual realityand analyze new ideas and first principles driven virtual reality
ReferencesReferences1.1. Hoffmann, Klaus A, and Chiang, Steve.T “Computational fluid Hoffmann, Klaus A, and Chiang, Steve.T “Computational fluid
dynamics for engineer’s” vol. I and vol. IIdynamics for engineer’s” vol. I and vol. II2.2. Rajesh Bhaskaran, Lance Collins “Introduction to CFD Basics” Rajesh Bhaskaran, Lance Collins “Introduction to CFD Basics” 3.3. http://www.cham.co.uk/website/new/cfdintro.htm accessed on http://www.cham.co.uk/website/new/cfdintro.htm accessed on
11/10/06.11/10/06.4.4. Adapted from notes by: Tao Xing and Fred Stern, The University of Adapted from notes by: Tao Xing and Fred Stern, The University of
Iowa.Iowa.5.5. http://www.cfd-online.com/Wiki/Historical_perspective accessed on http://www.cfd-online.com/Wiki/Historical_perspective accessed on
11/12/06.11/12/06.6.6. Frederick and Chang,T.S.,”Continuum Mechanics”Frederick and Chang,T.S.,”Continuum Mechanics”7.7. http://navier-stokes-equations.search.ipupdate.com/http://navier-stokes-equations.search.ipupdate.com/8.8. http://en.wikipedia.org/wiki/http://en.wikipedia.org/wiki/
Computational_fluid_dynamics#Discretization_method s, Computational_fluid_dynamics#Discretization_method s, ”Discretization Methods””Discretization Methods”
9.9. McIlvenna P and Mossad R “Two Dimensional Transfer Chute Analysis McIlvenna P and Mossad R “Two Dimensional Transfer Chute Analysis Using a Continuum Method”, Third International Conference on CFD Using a Continuum Method”, Third International Conference on CFD in the Minerals and Process Industries, Dec 2003.in the Minerals and Process Industries, Dec 2003.
10.10. Subramanian R.S. “Non-Newtonian Flows”.Subramanian R.S. “Non-Newtonian Flows”.11.11. Lohner R., Cebral J., Yand C., “Large Scale Fluid Structure Interaction Lohner R., Cebral J., Yand C., “Large Scale Fluid Structure Interaction
Simulations, IEEE June 2004”.Simulations, IEEE June 2004”.12.12. http://www.cd-adapco.com/press_room/dynamics/23/http://www.cd-adapco.com/press_room/dynamics/23/
behr.html,“Predicting Passenger Comfortbehr.html,“Predicting Passenger Comfort13.13. http://www.adl.gatech.edu/classes/lowspdaero/lospd2/lospd2.html, http://www.adl.gatech.edu/classes/lowspdaero/lospd2/lospd2.html,
“Types of Fluid Motion”“Types of Fluid Motion”
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