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Defense | Nuclear Power | Aerospace | Infrastructure | Industry

Brief introduction on the importance of Fluid Mechanics in CFD

Abhishek Jainabhishek@zeusnumerix.com

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