computational fluid mechanics intro
TRANSCRIPT
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FUNDAMENTS OF CFD1.
33:45 PM
Introduction
2.3:45 AM 5 PM
ComputationalHeat TransferDevelopment
Series of Invited Lecture onCFD:
Developments, Appl ications & Analysis
NIT Hamirpur
To pic I : In tr o d uc tio n1.
CFD:What is it?
3.
CFD:Why?
2.
CFD:How it is ?
Series of Invited Lecture onCFD:
Developments, Appl ications & Analysis
NIT Hamirpur
Contents
01.
CFD: What is it?
Definition
Role
Major Aspects
03.
CFD: Why
02.
CFD: How is it?
Grid Generation
Finite Volume Method
Solution Methodology
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01. CFD: What is it
?
Definition
Role
Major Aspects
1
CFD: Defination
Computational Fluid Dynamics (CFD) is a theoretical
method of scientific and engineering investigation,concerned with the development and
application of avideo-camera like tool - a software - which is used toanalyze a fluid dynamics as well as heat and masstransfer problem in a unified
way.
Here, the software is like a virtual video-camera andresults in a movie where each picture gives a fluid-dynamics information, i.e., flow-properties.
Vortex Shedding Fluid Flow
across a Circular Cylinder at Re=100
Vortex Shedding Fluid Flow
across a Circular Cylinder at Re=100
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Vorticity Contours at Re=100 Group of Fish Like Locomotion
Dam Break Simulation 2D Film-Boiling Over a Superheated Plate
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Granular Flow CFD: Role
Analogy between a video-camera and a CFD
software.Analytical (CFD) solution are like a virtual video
camera of infinite (finite) spatial as well as temporalresolution.
The role of CFD software is not limited to creatingscientifically excitin
g fluid dynamic movie of flowproperties but also to create engineering relevantmovie of engineering parameters, for a unifiedcause-and-effect study of various heat and fluidflow situations.
CFD: Major Aspects
There are three major aspects of CFD
Development
Application Analysis
With a continuous development and a wider
application of CFD, the definition of Navier-
Stokes equations and CFD has broaden.
02. CFD: How is it?
Grid Generation
Finite Volume Method
Solution Methodology
2
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CFD: How is it?
SolutionMethodology
It consists of
1. Solution Method: Amethod to solve theset of algebraicequations
Explicit and Implicit Methodfor unsteady state formulation
Iterative method for steadystate formulation.
2. Implementation Details
3. Solution Algorithm
Grid-Generation
A method to convert the completedomaininto certain fixed numbero f Control Vo lumes (CVs). Thepoints located at the centroid ofthe CVsare calledas grid points.They areof twotypes:
Cartesian, Cylindrical and SphericalGrid: used for simple geometry.
Curvilinear-Structured andUnstructured Grid: used for complexgeometry.
Finite Volume Method
A method to obtain a systemof algebraic equations, withunknowns as flow propertiesat thegridpoints,obtainedby
Physics based Approach:Applying conservation laws to the CVsand using certain approximations.
Mathematics based Approach:Applying volume integral to thegoverning partial differential equations,using gauss divergence theorem forcertain terms and using certainapproximations.
L 2
L 1
i
j
1 imax1
jmax
Boundary CVs:
i=1 & imax;
j=2 to jmax-1
j=1 & jmax;
i=2 to imax-1
P
N
S
EW
InteriorCVs:
i=2 & imax-1;
j=2 to jmax-1
j=2 & jmax-1;
i=2 to imax-1
Outer Square Boundary
Plate
Inner Square Boundary
Square Hole
Both the Boundaries are
aligned along direction of
Cartesian Coordinates
Heat Transfer in a Square
Plate with a Square Hole
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Heat Transfer in a Squareplate with a Circular Hole
The Outer SquareDomain Boundary is
aligned along the
direction of Cartesian
Coordinates
Inner Circular Domain
Boundary is aligned
along the direction of
cylindrical coordinates
Complex Domain & Unstructured Grids
x
y
PressureForce
Pressure
Force inX-direction
PressureForce in
Y-direction
ZERO
Body Forceor Heat
Generation
Body Force
inX-direction
Body Forcein
Y-direction
HeatGained by
HeatGeneration
ViscousForce or
HeatConduction
Viscous
Force inX-direction
ViscousForce in
Y-direction
HeatGained by
Conduction
ACROSSthe CV
X-Momentum
Y-Momentum
Energy
Conservation Laws: Mass, Momentum & Energy
INSIDE theCV
Mass
X-Momentum
Y-Momentum
Energy
Rate of Change
Unsteady Advection Diffusion S o u r c e
Mass Zero
X-Mom.
Energy
Y-Mom.
Mass
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CFD: How is it?Fi ni te Vol um e M et ho d for Computational Fluid Dynamics
A Novel
Physics
based
Control
Volume
The
Traditional
Mathematics
based
Two Levels ofApproximations
Governing
PDEs
Gauss Div. Theorem
Approximations
V
Discretized LAEs
(Linear Algebraic Equations)
FluidMechanics
& Heat
TransferCourse
limV 0
Navier-Stokes
Equations
Mass
Momentum
Energy
Conservation
Laws Continuity
Momentum
Energy
Tnb=4000C Ti,jmax=400
0C Grid Points
Internal:
at 2500C
Boundary:
at 100/200/
300/4000C
Twb=1000C
T1,j=1000C
jmax=7
6
5
4
3
2
j=1 xy
Teb=3000C
Timax,j=3000C
Tsb=2000C Ti,1=200
0C
i=1 2 3 4 5 6 imax=7
n+1
n
E x p l i c i t M e t h o d
Unsteady State Heat Conduction: Computational Stencil
1
, , ,
n nP P nb nb
n b E W N S
a T a T b
CFD: How is it?
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S o l u t i o n M e t h o d o l o g y f o r
U n s t e a d y C o m p u t a t i o n a l h e a t C o n d u c t i o n
A Novel Physics basedThe Traditional
Mathematics
basedS i n g l e S t e p
( )
( ) ( )
( ) ( )
P P
E E W W
N N S S
a T t t
a T t a T t
a T t a T t
b
( )P
T t t
x xq y
y yq x
xi r s t S t e p :( ) ( ) ( ); ( ) ( ) ( )
( ) ( ) ( ); ( ) ( ) ( )
x x E E P P x P P W W
y y N N P P y P P S W
q t c T t c T t q t d T t d T t
q t e T t e T t q t f T t f T t
S e c o n d S t e p :
( ) ( ) ( ) ( )
( ) ( )
conducti on x x x y y y
P P P conducti on
Q t q t q t y q t q t x
T t t T t g Q t
xq y
yq x
N
P EW
S
y
03. CFD: Why 3
CFD: Why?
Now a days, a computer simulation and analysis have
become an integral part of a design and optimization study.
CFD is more commonly used as a powerful analysis, than adesign and optimization, tool by scientists as well as
engineers - dealing with fluid dynamics and heat-transfer
problems; in various industry such as aerospace,
automobile, turbo-machinery, chemical, electronics
cooling, biomedical, etc.
CFD: Why?
In academics, CFD is taught as an under-graduate
elective and post-graduate course, in different
branches of engineering. The increasing importance of CFD development,
application and analysis, in the industry as well as
research organizations, along with the lack of trained
manpower in this area has greatly increased the
importance of this course.
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Brief History Modern Trends2
Brief History of Developments of CFD Difficulties in Solving for Pressure
Discretization Method, Geometry and Grid
Modern Trends in CFD Cartesian Grid Method
Multilevel Cartesian Grid Method
Parallel Computing
Industrial Applications
Difficulties in Solving for Pressure
Three conservation laws based equations (mass,
momentum and energy) and three dependent variables
(pressure, velocity and temperature).
Law of conservation of momentum and energy have a
term as rate of change of momentum and energy
No rate of change of pressure term in the massconservation law
No explicit equation for pressure and continuity equation
needs to be converted into an equation for pressure.
Difficulties in Solving for Pressure
This resulted in a stream-function vorticity method and was one
of the first popular method in CFD - limited to 2D and steady-
state problems.
To circumvent these limitations, a pressure-velocity formulationcalled as pressure correction approach was proposed where thecontinuity equation was employed as a constraint to derivecorrect pressure field - through a detailed iterative solutionprocedure.
However, there was an issue of pressure velocity decouplingand the first remedy suggested was solution on a staggeredgrid.
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Discretization Method, Geometry & Grid
Early development of CFD started with FDM for problems - called as
simple geometry problem. The Cartesian/Cylindrical/Spherical geometry problems were solved in
a uniform or nonuniformgrid, where one of the grid line fits to the
boundary of the computational domain -called as body fitted grid.
With advances in CFD and more application to industrial problems,
there was a need to develop method for computing flows in complex
geometry.
Initially, this was attempted with FDM on a body-fitted (a) Cartesian
and (b) curvilinear grid
Discretization Method, Geometry & Grid
This led to development of FVM where the governing PDEs
are solved directly in the physical complex/curved domain, onbody-fitted curvilinear structured grid.
However, implementation of staggered grid was found almost
impossible for complex geometry and another remedy to
obtain physical solution in co-located grid was proposed as
usage of momentum interpolation.
This continued for quite some time with further development
from the FVM based solution in structured to multi-block
structured to unstructured body-fitted grid system.
Thank You for Your attention
Welcome for any Questions,
Comments, and Suggestions