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:
- sub-division into types of interaction
- practical examples of the various types
- the associated simulation-technique requirements
- the extent to which PHOENICS already satisfies the requirements
- by what means deficiencies can be most swiftly remedied
See also the
Alferov lecture which considers the same subject from a different point
of view
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Contents
- Solids at rest influence fluid flow
- Solids participate in heat transfer
- Fluids impose forces and moments on solids at rest
- Fluids induce mechanical and thermal stresses in solids at
rest
- Fixed-shape solids, in prescribed motion, influence fluid flow
- Motion of solids depends on forces exerted by fluids
- Stresses in moving solids depend on the heat and momentum
exchange with fluids
- Shapes and sizes of moving objects vary with time
- 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:
- all cells were accorded such 'volume-' and
'area-porosity factors'
as indicated how much of the space was accessible to fluid; or
- '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:
- cooling of electronics assemblies;
- cooling of gas-turbine blades and other power-plant items;
- refrigeration of food;
- manufacturing and processing of metals;
- heat exchangers and other chemical-engineering equipment;
- the natural environment ('heat storage' in soil evens out daily
fluctuations); and
- the thermal comfort afforded to inhabitants of the built environment.
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
- The only interest in CFD of a racing-car designer is the question:
How much can it help me to reduce the drag, and improve the road-holding
performance, of my vehicle?
- Designers of buildings need to be able to predict the forces exerted
on them by the wind.
- Their architects may be more interested in the wind's
tendency to blow babies from balconies.
- Safety specialists need to know whether the momentary pressure peak
occasioned by a postulated bomb will break windows; and, if so, how far
the splinters will fly.
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Current capabilities of PHOENICS
PHOENICS-3.6 has three ways to compute the forces and moments on a body,
namely:
- 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.
- To set PARSOL=T, and thereby automatically activate print-out of
pressure and friction forces on facetted objects.
- 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
- As originally implemented, the method failed to take into account
the effects of bending moments;
- convergence was slow; and
- 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:
- converges rapidly because the u, v and w equations are no longer
linked by (the equivalent of) pressure;
- includes the bending-moment terms [click
here for an
example];
and
- 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:
- the vectors for ix=1 are not identical with those for ix = 23; and
- 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:
- fans blow air;
- piston-cylinder-crankshaft mechanisms compress it;
- inter-meshing-helix and other positive-displacement machines do the
same;
- the Space-Shuttle leaves is launching pad;
- a
ski-jumper 'takes off';
- a rotating paddle stirs liquid in a chemical reactor;
- liquid in a half-filled tank 'sloshes' as a consequence of tank
motion;
- 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:
- Extensive exemplification, and thereby testing, of the all the
currently-existing features, including motion of the computational grid.
- Inclusion of the motion-describing formulae in the .pob (i.e.
PHOENICS object) file, which has come on the scene rather later than it
should have done.
- Extension of the capabilities of the VR-Editor in respect of
defining the motions of both single objects and of 'assemblies'.
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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:
- sport, and
- 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:
- mechanical stress, as when a squash ball is first hit by a racket, and
thereafter bounces from wall to wall;
- chemical action, as when an oil droplet burns as it flies through
the air,
- phase change, as when a soluble material dissolves in the fluid
through which it moves.
Less obvious examples of changing-shape objects are:
- the enlarging and contracting vane of a rotary-vane compressor,
which just fills the space between rotor and casing;
- the free-surface object, which rises and falls so as to ensure that
there is no pressure difference object;
- the air-bag safety device which moves in response to the pressure
difference across its fabric and the tension within it; and
- the human heart.
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No detailed attention has yet been given to any of these. They have been
listed in order to emphasise that:
- much of the territory of fluid-solid interaction remains unexplored;
- 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:
- We have had some good and original ideas.
- We have implemented them quickly, publicised them, and used them
successfully for some time.
- Then deficiencies have appeared, which we have tried to understand
and to repair; but, efforts having failed, we have had to start again,
years being lost meanwhile.
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:
- PARSOL has become reliable;
- a re-worked parallel PHOENICS 3.6 (and 3.5.1 also) will be delivered
to CHAM for testing and (hopefully) transmission to users within a few
weeks;
- the new re-usable PHOENICS-object concept is taking shape and will
be providing better solutions for important problems;
- the VR-environment is being improved so as to help users to profit
from new features like In-Form.
- PARSOL, MOFOR and SFTA are being enabled to work together.
- we may soon even have 'guaranteed convergence' (see next lecture)!
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!
