Computer simulation of fluid-solid interactions

by

Brian Spalding

PHOENICS User Conference, Melbourne, May, 2004

Abstract

The lecture surveys the title subject from several points of view, namely: See also the Alferov lecture which considers the same subject from a different point of view

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Contents

  1. Solids at rest influence fluid flow
  2. Solids participate in heat transfer
  3. Fluids impose forces and moments on solids at rest
  4. Fluids induce mechanical and thermal stresses in solids at rest
  5. Fixed-shape solids, in prescribed motion, influence fluid flow
  6. Motion of solids depends on forces exerted by fluids
  7. Stresses in moving solids depend on the heat and momentum exchange with fluids
  8. Shapes and sizes of moving objects vary with time
  9. Some reflections on past and future progress

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1. Solids at rest influence fluid flow

Denial of access

From the beginning, computer simulation of fluid flow has had to take account of the presence of solid materials.

At first, the only importance of these solids was that they prevented the fluid from accessing the whole of the space in question.

Therefore their influence was accounted for by one or other of the following methods:

  1. all cells were accorded such 'volume-' and 'area-porosity factors' as indicated how much of the space was accessible to fluid; or

  2. 'body-fitting' coordinate systems (BFCs) were employed, so chosen that the space occupied by the solid lay outside the computational domain.
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Frictional effects

It was quickly recognised that real solids do more than deny space to the fluid: they tend to slow it down, and create on their surfaces 'boundary layers' of often appreciable thickness in which the fluid velocity is lower than in the 'free stream'.

Such effects were first accounted for in PHOENICS by the attachment of 'friction patches' to the sides of cells having zero volume porosities, or to the relevant grid boundaries if BFCs were used.

Later, the PRPS material-index variable, which had been introduced for another purpose, was used to distinguish friction-causing (but otherwise property-less) solids (index = 198) from merely-space-denying ones (index = 199).

This rendered the creation of friction (i.e. 'wall-function') patches unnecessary because the EARTH solver could detect where to generate its own 'wall functions', provided that the PIL variable EGWF had been set TRUE.
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Nowadays, EGWF=T is the default set by the satellite whenever solids are present.

Moreover, if EARTH receives an old-style EARDAT with EGWF=F and a plethora of consequently-needed friction patches, it will change the former and discard the latter.

That this practice has only just been adopted is an indication that 'old habits die hard', especially when they have been embodied in Fortran.

Thus the PHOENICS satellite, working in VR mode, will still create friction patches (which EARTH will ignore) whenever a user positively (albeit perversely) sets EGWF=F.

Users are now advised not to do this.


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2. Solids participate in heat transfer

The PRPS material-index variable

PRPS was introduced so as to enable 'conjugate-heat-transfer' problems to be solved, i.e. those in which the thermal conductivity and specific heat of the solids affect the distribution of temperature.

Such problems arise frequently in practice, for example in:

Often the radiative properties of the surfaces of the solids also play a part.

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How to handle curved-surface objects

If the shapes of the solids were curved, BFC grids would be used inside as well as outside the solids, so that the discontinuity of PRPS value coincided with cell surfaces; but, unless care was taken to ensure that cells on both sides of the discontinuity were parallel-sided, unrealistic temperatures were often generated.

By the time the reason for this was understood, interest had shifted to a different method of handling curved objects, so PHOENICS-BFC's conjugate-heat-transfer feature has still not been upgraded.

[Users who need the upgrade: please inform CHAM]
The 'different method' had its origins in the use of 'facetted shapes' for display purposes when 'virtual-reality' techniques started to be used for data input in the mid 90s.

[Click here to see such a shape in an early version of the VR-Editor,
here to see its facets, and here to see the cells cut by the facets into two parts, one containing fluid, the other solid.]

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PARSOL, the cut-cell technique

Concentration of attention on the 'cut cells', the two parts of which could be treated separately, led in due course to the PARSOL technique, which enables flow past curved surfaces to be handled by cartesian grids quite as well as by BFC ones.

[Click here to see flow through louvres.]

Admittedly, this has not been achieved without much effort, and the first-issued version of PARSOL proved to have many deficiencies, which caused CHAM to re-write all the relevant coding on a sounder basis during 2002 and 2003.

Now, it can be claimed, PARSOL can handle conjugate heat transfer very well; and recent advances allow it to handle solids of thickness smaller than the cell size, as shown here and here.

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From PRPS to properties

An early limitation of the PRPS technique was that it at first allowed only constant properties to be introduced by way of the PROPS file.

The next step was to introduce the possibility of reading from that file pointers to, and constants in, the non-uniform property relationships embodied in certain Fortran subroutines such as GXDENS.HTM. This is still in use; but it is limited in extent and far from easy to understand.

Fortunately, the introduction of In-Form, which makes it possible for properties to be computed from formulae of whatever complexity the situation demands, removes the limitation and is easier to comprehend. See, for example, 089.htm.

In general, it may reasonably be said that PHOENICS is well-equipped to handle conjugate-heat-transfer problems including (by way of IMMERSOL) those in which radiation is important.

The main current deficiency is that the opportunities offered by In-Form are not yet sufficiently made apparent by the VR-Editor.


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3. Fluids impose forces and moments on solids at rest

Applications

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Current capabilities of PHOENICS

PHOENICS-3.6 has three ways to compute the forces and moments on a body, namely:
  1. To place an 'imbalance patch' around the object in question, with appropriate COVAL specifying (only) which velocity (and therefore direction) is in question; this gives print-out of both forces and moments.

  2. To set PARSOL=T, and thereby automatically activate print-out of pressure and friction forces on facetted objects.

  3. To set NAMGRD=F1, and thereby print-out of pressure forces, calculated as though for a 'formula 1' racing car.

The three methods ought to agree; but, at the present moment, they do not always do so, as illustrated by the following extract from data relating to case 805 (flow past a sphere):

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 Method 1: three differently-sized imbalance patches

 Forces on patch IMBL3&2: Z-wise force =  2.508054E+00



 Forces on patch IMBL4&3: Z-wise force =  2.503020E+00

 

 Forces on patch IMBL5&4: Z-wise force =  2.495262E+00

 

 Forces on patch IMBL810: Z-wise force =  2.872604E+00

 

 Forces on patch IMBL815: Z-wise force =  2.300270E+00

 

 Method 2: Integrated force on object: B3

 Total in Z =  3.097499E+00 

       Pressure=  3.097499E+00 Friction=  0.000000E+00 
The differences between the imbalance and integrated-force calculations are rather great. The reason for them is being sought, the coarseness of the grid being the prime suspect.

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Summary of PHOENICS capabilities

It appears wise to conclude that, although PHOENICS does now have easy-to-activate means of calculating forces exerted by fluids on immersed bodies, more research is required into their satisfactoriness for aerodynamic purposes.

On the other hand, if the question is: "Will x kg of dynamite exploded at point A break the windows in building B at a distance y?" PHOENICS will certainly be able to give an answer of accuracy commensurate with that with which window strength is known.

In the modern world, security authorities and insurance companies would be wise to turn engage CFD-savvy consultants for advice before the bomb goes off.


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4. Fluids induce mechanical and thermal stresses on solids at rest

SFTA: Solid-Fluid-Thermal Analysis

To know the total force on a body is often not enough: the distribution of stress (i.e. force per unit area) within the body may be of even more interest; and these may be caused by temperature gradients as well as by pressure and friction.

PHOENICS has long possessed its unique means of computing the internal stresses, whether thermally or mechanically induced.

This method has relied on the supposition that the velocity with which the solid moves is negligible, so that the storage space allocated to the velocity components can be used for the displacements instead.

It has exploited also the fact that the equations governing the displacements are so similar in form to the momentum equations that PHOENICS can solve for both simultaneously. Click here for an early demonstration.

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Three shortcomings and their remedy

  1. As originally implemented, the method failed to take into account the effects of bending moments;
  2. convergence was slow; and
  3. extreme care had to be taken with the coding so as to ensure that velocities and displacements were properly distinguished from one another at all cell faces.

Recently, a new algorithm has been devised which:

  1. converges rapidly because the u, v and w equations are no longer linked by (the equivalent of) pressure;
  2. includes the bending-moment terms [click here for an example]; and
  3. since it no longer depends on calculating the 'dilatation' from a modified 'pressure-correction' equation, no longer requires the velocities and displacements to be stored contiguously.

The last point is fortunate because, as will be argued below, the need can already be foreseen for being able to calculate both velocities and displacements for the same locations.

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Work in progress

Some of the interesting features of SFTA can be explained by reference to the Q1 file of a current project, and by inspecting a PHOTON vector plot: vectors at ix=1 and 23.

The run giving rise to the latter plot was one in which the only influence was the internal pressure of the hydrogen gas; and the question was: do the solutions for displacements in the metal conform to expectations?

The answer is: not quite; for:

  1. the vectors for ix=1 are not identical with those for ix = 23; and
  2. the axial-direction vectors are inexplicably small\near the axis.

Why? Incomplete convergence? Inaccurate display? Incorrect setting of boundary conditions? Imperfections in the internal coding?

The answer will be found, after the proper study. This is work-in-progress.

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Probably the main reaction after inspection of the Q1 file is:

How different is the world of the PHOENICS developer from that of the PHOENICS user!

The later uses the VR-Editor and VR-Viewer; but the developer can not, because he is working in territory that the GUI knows nothing about.

Fortunately he does have the facilities of PIL at his disposal; but he activates them by hand-editing of the Q1.

In due course it will become possible to set up SFTA problems via the GUI, and to display displacements separately from velocities; but only after the developer has finished his work.

Today one can cross Australia from South to North in a comfortable train; but only because the pioneers of 150 years ago made the same journey by foot.


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5. Fixed-shape solids, in prescribed motion, influence fluid flow

Applications

Practically important phenomena pertaining to the above heading are very numerous. They include:
  1. fans blow air;
  2. piston-cylinder-crankshaft mechanisms compress it;
  3. inter-meshing-helix and other positive-displacement machines do the same;
  4. the Space-Shuttle leaves is launching pad;
  5. a ski-jumper 'takes off';
  6. a rotating paddle stirs liquid in a chemical reactor;
  7. liquid in a half-filled tank 'sloshes' as a consequence of tank motion;
  8. and many more.

Current capabilities

The PHOENICS moving-frame-of-reference technique (i.e. MOFOR) has been successful in simulating some of these phenomena; and its 'hierarchical' scheme for describing the motions of articulated objects has proved to be very powerful.

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As at first implemented, MOFOR objects appeared to move in a somewhat 'jerky' manner, the reason being that PARSOL could not then be active simultaneously; but it can be now.

Another early deficiency, namely the inability to handle scalar transport correctly, has also been removed.

Still remaining is a difficulty which arises when the attempt is made to cause one object to 'move through' another, was tried in early simulations of positive displacement motors.

Probably this 'difficulty' will be made an 'impossibility', as of course it is for real rather than virtual objects. The use of 'shape-changing' objects (discussed below) offers a better solution.

Whereas the first implementation of MOFOR required the motion to be defined by way of a .bvh (later called .mof) file, which required a separate program to create it, In-Form has now been extended so as to enable the user to specify motion by way of a formula.

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This formula may even refer to to-be-calculated quantities, as will be required for phenomena discussed in Section 6 below.

Necessary developments

Although much has been done, there is more to do, the most urgent being:

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6. Motion of solids depends on forces exerted by fluids

The need and how to meet it

Library case 360 concerns two spheres which follow predefined paths. An animated display is elicited by clicking here.

The pictures are attractive; but they do not correspond to reality; for the motion of any object projected into a fluid is necessarily influenced by the forces which the fluid exerts upon it.

No demonstration has yet been made of the use of PHOENICS for simulating the mutual influences of fluid and moving solid. However, the elements already exist.

In Section 3, it was shown that forces and moments on objects can be calculated; therefore all that is necessary is link these forces with the acceleration of the object, so as to calculate the latter's position and velocity at each new time step.

In-Form is capable of doing this; then, once this has been successfully demonstrated, it may be economical to embody the formulae in Fortran coding.

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Applications

The two main application areas are:
  1. sport, and
  2. warfare;
insofar, that is to say, as the two activities can be distinguished.

In both areas missiles are projected; and the frequency with which they hit their target depends on the accuracy with which the solid-fluid interactions have been estimated.

Consultants who learn how to use PHOENICS for this purpose can surely find rich sponsors to employ them.


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7. Stresses in moving solids depend on the heat and momentum exchange with fluids

The techniques which are proving successful in computing mechanical and thermal stresses in solids at rest will surely work just as successfully when applied to moving bodies, provided, that is to say, that stresses are not so large as to cause significant changes of shape.

Further thought reveals however a difficulty: even if the displacement field in the solid remains unchanged, in the solid's own coordinate system, the value of the displacement to be assigned to a given grid node will change with time.

No complete strategy for handling the problem has yet been worked out; but it appears probable that displacements,and consequent stresses and strains, will need to be calculated on a grid which moves with the solid object


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8. Shapes of moving solids vary with time

So far, moving objects dealt with by MOFOR have had fixed shapes and sizes. However, there are many phenomena in which shapes and sizes will change. Causes may be:

Less obvious examples of changing-shape objects are:

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No detailed attention has yet been given to any of these. They have been listed in order to emphasise that:

  1. much of the territory of fluid-solid interaction remains unexplored;
  2. applications of interest and importance lie within that territory; in making plans to attain nearer-at hand objectives it is well to keep the more distant ones in mind.

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9. Some reflections on past and future progress

How long it has taken

PHOENICS has now been in active use for 23 years; and other well-known codes are almost as old.

The problems which they address have been recognised from the beginning.

How strange therefore that I have had to report that:

"much of the territory of fluid-solid interaction remains unexplored"!

What can be the reason?

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The development pattern of PHOENICS

The pattern which I see, with hindsight, is this:

This has been true of BFCs, PRPS, SFTA, parallelization, PARSOL, MOFOR, and maybe others.

I do not blame our staff for this; for we have had, and still have, very hard-working, innovative and talented people; so the fault must lie with their, that is to say with my, management!

Or it may be, that continuous forward movement more than mere mortals can achieve; none of us can see very far into the future.
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The brighter side

Despite the setbacks, progress is being made:

In summary, I am hopeful that we shall soon have some new good things to offer to our users.

As I said before: old habits die hard!