Presentation shows insight into the basic of fluid mechanics involved in CFD.

1. ©ZeusNumerix
Defense | Nuclear Power | Aerospace | Infrastructure | Industry
Brief introduction on the importance of
Fluid Mechanics in CFD
Abhishek Jain
abhishek@zeusnumerix.com
Fluid Mechanics in CFD
Perspective

2. ©ZeusNumerix
Some initial thoughts
2

3. ©ZeusNumerix
Fluid Mechanics and its branches
3
Analysis tool Year 1600 1700 1800 1900 2000
Experimental
Theoretical
Computational
Theoretical –
write eqns.
for flow
Experimental
methods
Computational
Fluid dynamics
Validate the
prediction
Hypothesis
Predict the flow

4. ©ZeusNumerix
Theoretical Fluid Dynamics
 Most important branch of fluid dynamics
 Crucial in understanding concepts (Example: Lift =
ρUxΓ)
 Compressible flow in a converging diverging nozzles
 Usually good in predicting trends (Example: δ ~ Re-1/2)
 Can generate a lot of information using simple
assumptions (SR-71 Blackbird was designed completely
using theoretical Fluid Dynamics)
 However, theoretical fluid dynamics requires insight
which requires extensive training and several years of
experience
 The idea is to incorporate as much fluid dynamics as
possible in tools and only manual work is carried out by
some one with some very essential background in fluid
dynamics

5. ©ZeusNumerix
Computing power required to
resolve the flow
6
Method
Scale of
turbulence
Resolution required
Surface
points
Wake
points
Time
steps
Total
operations
Direct Navier
Stokes (DNS)
No modeling 1016 1017 108 1025
Large Eddy
Simulation (LES)
Sub-grid
modeling
1012 109 108 1020
LES with wall
layer
Near wall &
sub-grid
modeling
1010 109 107 1017
Reynolds Navier
Stokes (RANS)
All scales are
modeled
107 107 104 1011
Euler equation
Scales are
absent
107 107 103 1010
Inviscid vortex
based methods
Scales are
absent
102 102 103 105
Computational cost of analysis of a wing of AR=10, Re=5 x 106

6. ©ZeusNumerix
Physics of Flows
7

7. ©ZeusNumerix
8
Physics of Incompressible flow
 Incompressible flow is governed by:
 Conservation of mass (continuity equation)
u/x + v/y + w/z = 0 (1)
 Conservation of momentum (Euler equation)
(u/t + uu/x + vu/y + wu/z) + p/x = 0 (2)
( v/t + uv/x + vv/y + wv/z )+ p/y = 0 (3)
 (w/t + uw/x + vw/y + ww/z) + p/z = 0 (4)
 Density is a constant. Temperature does not take part in the
motion of the flow
 Heat energy of an element, e or temperature, T (if Cp is constant)
is convected as if ‘T’ is an independent attribute of fluid not
related to its motion

8. ©ZeusNumerix
9
 In incompressible flows, the kinetic energy may get converted
in to internal energy (heat), but not vice versa.
 Due to large value of specific heat capacity of liquids
temperature changes due to loss of kinetic energy is not
appreciable
 Thus only four equations (accounting for viscosity) are
adequate for solution of incompressible fluid motion . The
energy equation is required to be coupled with eqn of motion.
It would be in fact wrong to simultaneously solve for them.
Physics of Incompressible flow

9. ©ZeusNumerix
10
Peculiarity of Partial Differential
Equations
 In principle eqns. (2) to (4) ( slide 7)can be used to correct u, v
and w from their guesses (initial condition)
 What can be done so that pressure can be corrected from its
initial condition ? Note that a term p/t does not exist.
 Mathematically, treatment for p must be different from the
treatment to be given to u, v and w
 Interestingly, p/x, p/y and p/z appear in the equations,
but pressure, p does not appear in any of the equations. Thus
the solution does not change if p = p + constant

10. ©ZeusNumerix
11
Physics of Compressible flow
 Compressible flow is governed by:
 Conservation of mass (continuity equation)
/t + (u)/x + (v)/y + (w)/z = 0 (1)
 Conservation of momentum (Euler equation)
(u)/t + (u2)/x + (uv)/y + (uw)/z + p/x = 0 (2)
(v)/t + (uv)/x + (v2)/y + (vw)/z + p/y =
0 (3)
(w)/t + (uw)/x + (vw)/y + (w2)/z + p/z =
0 (4)
 Conservation of energy equation
(E)/t + (u(E+p))/x + (v(E+p))/y + (w(E+p))/z = 0
(5)

11. ©ZeusNumerix
12
E =  (e + ½ u2)
E = internal energy (e) + kinetic energy (½ u2)
 In principle eqns. (1) to (5) can be used to correct , u, v, w and
E (or e) from their guesses (initial condition)
 What can be done so that pressure can be corrected from its
initial condition ? Note that there is no equation for p. This is
where equation of state (EoS) can be used
p = (-1)(E- ½ u2)
 Note that equations do have p as well as p/x, p/y and
p/z. Hence solution depends on pressure, p.
Physics of Compressible flow

12. ©ZeusNumerix
13
 There 6 unknown (, u, v, w, e and p) and 5 partial differential
equations + one algebraic equations; i.e. the problem is well
posed.
 Interestingly, compressible CFD prefers to choose internal
energy, e as a variable and hence equation of state is p = (-
1)(E- ½ u2) and not the conventional p = RT
 In compressible flows, internal energy can be converted to
mechanical and kinetic energy and vice versa. Thus
momentum equation can not be considered as conservation of
momentum equation.
 Though not stated explicitly, the second law of
thermodynamics must be obeyed.
Peculiarity of Partial Differential
Equations

13. ©ZeusNumerix
Solving problems using CFD in 6 steps
3
2
Build Computational
Domain
Create suitable
Mesh
Boundary Conditions &
Initial conditions
Solution of discrete
equationsPlot flow FieldInterpret solution
These steps will be discussed in detail in this workshop

14. ©ZeusNumerix
 Identify the computational domain
 Generate the correct type of mesh
 Structured or Unstructured mesh or hybrid mesh
 Set up Simulation
 Assign boundary conditions, initial conditions, etc
 Execute the solver
 Choose accuracy, Viscous/In-viscid, Laminar /
Turbulent, Incompressible / compressible, etc
 Post-process the data
 Organize data and understand results
 Understand the fluid dynamics
 Do the results make any sense? Is the design
correct?
 Note that at every step, good understanding of
theoretical fluid dynamics is essential!
In brief the steps are…

15. ©ZeusNumerix
CFD – Computational Tool

16. ©ZeusNumerix
CFD – The Computational Tools
 CFD tools are required for solving industrial problems
 Emphasis is on economy of solution without sacrificing the
required accuracy
 Advances are in tools is linked to other branches of
technology; e.g. storage devices
 Tools are for getting rid of manual work
 Tools must capture as much physics as possible from first
principle
 They must a part of larger suite of simulation technologies
such as FEM, CEM, etc. being used by the engineering
fraternity
 Measure of success – the ease with which diverse problems
can be solved

17. ©ZeusNumerix
Four important Tools of CFD
0
10
20
30
40
50
60
70
80
Days
CAD Grids Solution Post_processing
0
1
2
3
4
5
6
7
Days
CAD Grids Solution Post_processing
0
20
40
60
80
100
120
140
160
180
Minutes
CAD Grids Solution Post_processing
Source : Catherine M. Maskyumiuk, et. al.
Application of CFD in Aeronautics at NASAAMES Research Centre,
pp 57-67, NASA CP 3291, 1995
 Importance of the tools in
Calendar time spent in a
CFD cycle
 Creating / Repairing Geometry
 Discretising Domain
 Numerical Simulation
 Post-processing the Data
Case #2
Case #3
Case #1

18. ©ZeusNumerix
CAD Geometry
 Importance of Geometry in CFD
 CFD tools can become a commodity in CAE only if CAD data can be read
 Geometry fidelity is an essential element in CFD, Retain the details that matter for
simulation
 Errors in CAD data in the form of gaps, overlaps, non-physical protrusions is expensive
CAD data with gaps, overlaps, etc. geometry ready for meshing

19. ©ZeusNumerix
Sponge analogy: Transform a 2D
domain in to a rectangle (and 3D
domain to a box) by a suitable affine
transformation
Grid Generation
Structured Grids
One-to-one mapping
How to divide the domain into
collection of rectangular blocks?
Assembly of simple shapes : Fill a
given domain with simple shapes such
as triangles so that the given domain is
fully covered
Emphasis is on cells there are grid points
but no continuous lines or what can be
called as grid lines.
Un-structured Grids
A good mesh is half the solution – Kordulla (Frontiers of CFD 2002)

20. ©ZeusNumerix
0
10
20
30
40
50
60
70
80
0thdimension
1D
Axisymmetric
2DSingleBody
2DUnsteady
2DMulti-Body
3DSingleBody
3DMulti-Body
0
10
20
30
40
50
60
70
80
90
100
Viscosity
HeatTransfer
Compressibility
Non-Newtonian
Conjugateheattransfer
ReactiveFlows
PhaseChangemodelling
Turbulencemodelling
Writing a Two Dimensional problem
constitutes CFD of one year duration
Reactive Flows pose a greater challenge than
viscosity or compressibility alone
Modeling turbulence and phase change
are a research fields
Three Dimensional Problems
are very complex to solve
Numerical Algorithms for
Differential Eqns.
Normally taught in
universities

21. ©ZeusNumerix
Advection of massless particle from one point to another obeys two
differential equation
Position = Position |t =0 + (t) velocity
D(colour)/Dt = C 2(color concentration)
Post-processing
The purpose of computing is insight, not numbers

22. ©ZeusNumerix
How useful is CFD?

23. ©ZeusNumerix
Universal Challenge-Reduce Development
Cost
Where We Need to be
Current design methods: more than 70 % of project cost goes for Test-Fail-Fix cycle
Can we carry out “Test-Fail-Fix cycle” with virtual parts, sub-systems, systems?

24. ©ZeusNumerix
CFD is one of the Key Enabling
Technologies
 The Technology Readiness Level (TRL) of
CFD has moved from TRL 1 to TRL 7
 The current Requirements
• CFD now works for “real” problems
• CFD is an engineering tool for designers and NOT ONLY for
CFD scientist
• Turnaround times is compatible with the design cycle (say)
o Conceptual design (1-2 months)
o Preliminary design (4-6 months)
o Detail design (6-9 months)
• It must produce required accuracy
• The cost must be reasonable

25. ©ZeusNumerix
CFD as a process for engineering design
 CFD needs provide
 Flow field analysis
 Structural and thermal loads
 Approach - Use best tool available
 Use Multiple customized
 Get solutions from many software developed strategic partners, in-house,
commercial of-the-shelf, or government laboratories
 Always use hierarchical physical models (e.g. laminar flames first then
turbulent flames
 Validate and calibrate periodically
 Emphasize getting engineering solutions and not very
accurate solution
 CFD results must make sense
•
•

26. ©ZeusNumerix
CFD Validation
 Validation is essential
 Ensure that analysis results are sufficiently reliable and accurate for intended
purposes
 Must Provide necessary confidence to the designer
 It should offer to quantify
 Code accuracy
 Code sensitivities
 Validation is a learning process for application engineers
 It is important to know what not to do
 Validation process depend on end application and the
intended use of CFD

27. ©ZeusNumerix
Current status
 Now CFD is defined as a process of understanding flow field
 Most time consuming process are (a) CAD repair and (b)
mesh generation. Lots of benefit are possible from
automating the CAD repair and mesh generation
 Current problems size is around 20 to 30 million cells.
Complete aircraft, missile, rocket, etc can be analysed
 Turn around time for a drag polar on high performance
computers could be 24 hours

28. ©ZeusNumerix
Technology Needs
 Extensive use of CFD requires quality data for validation.
The quality data sources are:
 Analytical solutions
 Very high fidelity simulations (e.g. DNS)
 Benchmark experiments
 Subcomponent Component tests and system tests
 Validation is industry specific. Validation
for aerospace applications can not be
derived form automobile industry
 Validation is continuous process

29. ©ZeusNumerix
Recommended texts
 Introduction to Computational Fluid Dynamics, A.W. Date, Cambridge
 Computational Fluid Dynamics, Anderson, JD
 An introduction to Computational Fluid Dynamics, W. Malasekara, H. K.
Versteeg
 Computational Methods for Fluid Dynamics, J. H. Ferziger & M. Peric,
Spinger
 Computational Gas Dynamics, Cubert B. Laney, Cambridge university Press
 Handbook of Computational Fluid Mechanics, Roger Peyret
 Numerical Computation of Internal and External Flows (2 volumes), C.
Hirsch, John Wiley & Sons
 Numerical Simulation in Fluid Dynamics – A practical Introduction, Michael
Griebel, et.al., Siam
 Numerical Methods for Conservation Laws, RJ Le Veque, Birkhauser Verlag
 Principles of Computational Fluid Dynamics, Pieter Wesseling, Spinger
 Riemann Solvers and Numerical Methods for Fluid Dynamics, Toro, E.F.,
Springer

30. ©ZeusNumerix
Thank You!
3 November 2014 31