fluid mechanics in cfd perspective
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Defense | Nuclear Power | Aerospace | Infrastructure | Industry
Brief introduction on the importance of Fluid Mechanics in CFD
Abhishek [email protected]
Fluid Mechanics in CFD Perspective
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Some initial thoughts
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Fluid Mechanics and its branches
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Analysis tool Year 1600 1700 1800 1900 2000
Experimental
Theoretical
Computational
Theoretical –write eqns.
for flow
Experimental methods
ComputationalFluid dynamics
Validate the prediction
Hypothesis
Predict the flow
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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
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Computing power required to resolve the flow
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MethodScale of turbulence
Resolution required
Surface points
Wake points
Timesteps
Total operations
Direct NavierStokes (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 NavierStokes (RANS)
All scales are modeled
107 107 104 1011
Euler equationScales 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
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Physics of Flows
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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 + uu/x + vu/y + wu/z) + p/x = 0 (2)
( v/t + uv/x + vv/y + wv/z )+ p/y = 0 (3)
(w/t + uw/x + vw/y + ww/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
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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
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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
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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)
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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
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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
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Solving problems using CFD in 6 steps
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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
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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…
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CFD – Computational Tool
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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
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Four important Tools of CFD
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CAD Grids Solution Post_processing
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CAD Grids Solution Post_processing
Source : Catherine M. Maskyumiuk, et. al.
Application of CFD in Aeronautics at NASA AMES 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
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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
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Sponge analogy: Transform a 2D domain in to a rectangle (and 3D domain to a box) by a suitable affine transformation
Grid Generation
Structured GridsOne-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)
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Writing a Two Dimensional problemconstitutes CFD of one year duration
Reactive Flows pose a greater challenge thanviscosity or compressibility aloneModeling turbulence and phase changeare a research fields
Three Dimensional Problemsare very complex to solve
Numerical Algorithms for Differential Eqns.
Normally taught in universities
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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
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How useful is CFD?
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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?
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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
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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
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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
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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
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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
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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
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Thank You!
3 November 2014 31