Cfd 0

Computational Fluid Dynamics
22nd May- 27th May, 2017
@
ICT, Mumbai
Part-0 Introduction to CFD
Dr. Sachin L. Borse
Professor,
Rajarshi Shahu College of Engineering , Pune, Maharashtra
(Formerly Hydraulic Design Engineer,
Klein Schanzline Becker Pumps, India)

i) Definition of CFD
ii)How CFD helps in design?
iii ) CFD Analysis- steps
iv) CFD-Aim of analysis
v) CFD-equations to solve
vi)CFD-Input needed from user
vii)CFD-Boundary conditions
viii) CFD-Initial conditions
ix)CFD-Turbulence modelling
x)Numerical Solutions steps
Content

i)Definition of CFD:-
CFD is the simulation of fluid flow and heat transfer
associated phenomenon(chemical reaction) using
modeling (mathematical physical problem
formulation) and numerical methods (discretization
methods, solvers, numerical parameters, and grid
generations, etc.)
What is CFD?

ii) How CFD helps in design?
1)It helps to predict performance of hydraulic and
thermal design
2) Plenty alternate options can be tried, which
otherwise difficult in experimental work
3) CFD gives detail insight of flow which otherwise
is difficult
4) Can be used to validate experimental and
analytical results.
5) This helps to make design process more scientific.

iii) CFD Analysis :- steps
0)Decide your goal:- accuracy, time,
1)Identification of domain(geometry):-
Determine the domain size and shape.
Decide on possibility of geometry simplifications to
save time eg. 2D, symmetry, periodicity
2)Identification of right approximation
Viscous/Inviscid,
Laminar/Turbulent,
Incompressible / compressible,
Single-phase/multi-phase)
3)Identification of right solution method
Finite Element / Difference/Volume,
Structured/Unstructured mesh, Order of accuracy

CFD Analysis :- steps
4)Pre-processing:- Generate computational grid, assign
boundary conditions, set initial conditions, compile code,
prepare input parameters
Meshing
Mesh generation consist in dividing the physical domain into a finite
number of discrete regions, called control volumes or cells in which
equations are solved to obtain solution.

Solution:-Run the code, monitor the solution
Post-processing:-Collect and organize data, analyze results
Verification:-Do the results make sense? Are the trends right? Does
it agree with previous calculations on similar configurations?
Validation:- Does the result agree with theory/ experiment?
CFD Analysis :- steps
At every step, good understanding of theoretical fluid dynamics and
heat transfer is essential.

iv) CFD-Aim of analysis
what we look from Engineering analysis:
 forces (pressure , viscous stress etc.) acting on
surfaces (Example:1) In an airplane, we are interested in the lift, drag,
power, pressure distribution etc

CFD-Aim of analysis
2)forces and torque acting on impeller blade)
 velocity field (Example: 1)In a race car, we are
interested in the local flow streamlines, so that we can design for less
drag. 2)we look for flow separation in turbomachinery which can be
corrected in future design)

CFD-Aim of analysis
 temperature distribution (Example: 1)Heat transfer in the
vicinity of a computer chip 2)hot spot in gas turbine blade)
Ultimate aim is to predict the behaviour of systems, to design more
efficient systems.

Unknowns: Density (ρ), Velocity (u,v,w), Pressure (p)
Dynamics of fluids is then given by
 Conservation of Mass (Continuity equation)
Algebraic summation of Rate of mass flow rate in
= Algebraic summation of rate of mass flow rate out
 Conservation of Momentum (Navier-Stokes
equations) [Newton’s second law]
Mass*acceleration in i direction =sum of forces in i direction
Total three equations in x, y and z direction.
 Conservation of Energy (Energy equation) [First law
of thermodynamics]
Heat added = change in internal energy + work done
CFD-equations to solve

 Conservation of Mass (Continuity equation)
 Conservation of Momentum (Navier-Stokes
equations) [Newton’s second law]
      0











z
w
y
v
x
u
t


Unknowns: Density (ρ), Velocity (u,v,w), Pressure (p)
5 equations to determine 5 unknowns.
All of fluid dynamics is contained in these equations.
If turbulence is considered additional one or two or six equations are
solved based on type of turbulence model.
Mixing length-
k-epsilon model 2-equation
K-omega model 2-equation
For k-epsilon turbulence model total 7 equations will be
solved.

vi)CFD-Input needed from user
1)Model/s selection:-
Laminar/turbulent
Single phase/multi phase
Isothermal/heat transfer
Pressure based/density based
2)Material properties:- material properties
Fluid flow only
Density, viscosity
Fluid flow with heat transfer
Density, viscosity, specific heat, thermal conductivity,
If properties of particular material are not available, please visit
http://www.matweb.com
3)Cell zone specification:-rotating or non rotating
4) Boundary conditions:-set by selecting patch and assigning required
boundary condition with values.

CFD-Input needed from user
5)Initial conditions:- initial conditions are only enforced at the
beginning of analysis
6)Stopping criteria:-input to decide stopping of calculations
Steady state problem
a)Number of iterations
b)Maximum residual value permitted
Unsteady state problem
a)End time
b)Maximum residual value permitted per time step
7)Solution control:-to control solution to get converged solution
Steady state problem
Relaxation parameters
Unsteady state problem
Time step

vii)CFD-Boundary conditions
Boundary conditions, are enforced through out calculations. They
are must. The boundary settings have strong effect on the
convergence rate and on the accuracy of the results.
Types of boundary conditions
1)Wall:-translational and rotational velocity can be assigned to wall.
for fluid flow
a)No slip
b)free slip
c)wall roughness
for heat transfer
a)constant heat flux
b)zero gradient(adiabatic wall)
c)constant wall temperature

CFD-Boundary conditions
2)Symmetry:- used to reduce computational effort
Assumption-zero normal velocity and zero normal gradient .
In above diagram only half domain divided by redline will be
considered.

3)Periodic:- used when physical geometry and expected pattern of
flow /thermal solutions have periodically repeating nature
Benefit-reduces computational
efforts

4)inlet:-
Pressure inlet
or
Incompressible
Velocity inlet
Compressible flow
Mass flow inlet

5)Outlet:-
Pressure outlet
Or
Velocity outlet
Outflow

Recommended boundary condition configurations:-
Most robust:-
velocity /mass flow at an inlet;
static pressure at outlet
Robust:-
Total pressure at inlet
velocity /mass flow at an inlet;
Sensitive to initial guess:-
Total pressure at inlet
Very unreliable:-
static pressure at inlet

Convergence is major issue in CFD.
Ways to improve convergence
1)Extend the location of inlets and outlets so that outlet is far from
recirculation area.
2)Use laminar solution to as initial condition.

viii) CFD-Initial conditions
Unlike boundary conditions, initial conditions are only enforced at
the beginning of analysis. They are primarily used for transient
analyses, but sometimes they are useful for steady state analysis.
Convergence problem can be improved by giving better initial
condition.

IX)CFD-Turbulence modelling
In real life most of fluid flow problem fall under turbulent category.
Turbulent flow has fluctuations in field which small in magnitude but
large frequency. Solving turbulent Navier stokes takes huge
computation resource. Hence turbulence modeling is required.
Flow becomes turbulent with following condition,
Re>2300 for internal flow eg flow inside duct or pipe line
Re>1*105 for external flow eg flow over aeroplane
Ra>109 for natural convection heat transfer eg hot surface in stand
still air

CFD-Turbulence modelling
Reynolds Averaged Navier stokes equation(RANS or RAS):- solves
time averaged Navier stokes Equation. All length scale are modeled.
Most widely used for calculating industrial flows. Faster and requires
less computer resources.
Eg.
Spalart Allmaras model (one equation )
k-epsilon model (two equation)
K-omega(two equation)
RSM( Six equation )
Large Eddy Simulation(LES):- Large eddies are solved, small eddies
are modeled. More expensive than RANS. Less expensive than DNS
Direct Numerical Simulation(DNS):-Turbulent NS is directly solved
without modeling.

CFD-Turbulence modelling
Reynolds Averaged Navier stokes equation(RANS or RAS):-
RANS may use wall function (eg k-epsilon model) to avoid large
number of elements at wall and thus reduces computation effort. In
such case y+ of boundary element should be in 30 to 100. More
preferred for industrial application.
When not using wall function eg (k-omega model) near wall element
should have y+ <2. Thus requires more number of elements. More
computation effort needed.

X)Numerical Solutions steps
Monitoring Solution:- It
involves observation of
residual and certain
parameter like drag etc

xi)Components of Numerical Solution
a)mathematical model:-set of partial differential equations or integro-
differential equations. Choose appropriate model for given application.
b)Discretization method:- method of approximation of differential
equation by set of algebraic equations
i) finite difference method:-
• oldest method.
• Taylor series expansion(TSE) is used to approximate partial
derivative.
• Commonly applied to structured grid as it requires a mesh having
high
• degree of regularity.
• This method is simple to apply.
• Main disadvantage of this method is conservation is not enforced
unless care is taken.

• Taylor series expansion(TSE) is used to approximate partial
derivative.

Field variable at point (i, j) with forward difference can be given by TSE
Field variable at point (i, j) with backward can be given by TSE

Field variable at point (i, j) with central difference can be given by TSE
Second order derivative at point (i, j) can be given by TSE

ii) finite volume method:-
•It discretize the integral form of conservation equations in space.
•The domain is divided into a finite number of connected control
volumes.
•At centroid of each of control volumes, variable values are
calculated.
•Interpolation is used to express variable values at control volume
surface.
•An algebraic equation for each of control volumes can be obtained,
in which a number of neighbouring nodal values appear.
•As it works with control volumes and not grid intersection points, it
has the capacity to accommodate any type of grid.
• Thus here unstructured grid can be used, thus complicated shape can
be mapped.
•This method ensures conservation.

iii) Finite element method: -
•it was developed for determining stress-strain displacement solution in
structural analysis.
•Both FEM and FVM can handle complex computation domain.
•Governing equations are first approximated by multiplying with shape
functions before they are integrated over entire computational domain.
•Each method gives same solution if mesh is very fine.
c)Numerical grid:- discrete locations at which variables are to be
calculated are defined by numerical grid. It divides domain into finite
number of subdomains(element, control volume).

d) Solution method:-
i)direct method:-
•Gauss elimination method. –convert matrix to upper triangular matrix.
Use backward substitution to obtain values of variables.
•Thomas Algorithm used for 1-D steady state conduction.
ii)Iterative method
In iterative method, solution is guessed and uses equation to
systematically improve the solution until it reaches some level of
convergence.
Cost of using direct method is quite high if large number of elements.
Two methods Jacobi and Gauss Siedal Method.
Gauss Siedal method twice faster than Jacobi method. Jacobi method
requires more memory space.
e)Convergence criteria:- It value of residual at which software should
stop to calculate.

e) Few terms:-
i)consitency:-
•With decrease in cell size or time step truncation error should tend to
zero this is called consistency.
ii)stability
Numerical method is said to be stable if it does not magnify errors
occuring during solution process.
Stability criteria for unsteady problem
Co Courant No< 1
Co= u*Δt/Δx
This is also called CFL criteria.

Cfd 0

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