1/35. Past, present

1
1/35. Past, present future of CFD a limited
review by Brian Spalding

• About the past
• focussing on contributions made by Imperial
  College Mechanical Engineering Department.

• About the present, observations about
• the FVM versus FEM contest,
• computational-grid trends,
• turbulence-model trends.

• About the future
• Population models of turbulence,
• FVM for fluidsolid interactions,
• The APParition,
• Partially-parabolic applications.

2
2/35. The Past Before the digital age
Airplanes appeared years before digital
computers.
Yet designers could even then predict their lift
and drag. They used a combination of
potential-flow theory with boundary-layer theory.
This proceeded by iteration 1. First
source-sink distributions were sought which
caused streamlines to fit the airplane, which led
to
2. distributions of pressure over the surface.
3.They then used boundary-layer theory to
calculate the displacement thickness of the
layer, i.e. the extent to which the airplane
seemed bigger than first assumed.
4. Then they repeated steps 1, 2, 3 until
convergence.
3
3/35. The Past Is the pre-digital method
relevant today?

• Their boundary-layer theory was crude
• two-dimensional,
• integral,
• with assumed velocity profiles.

Therefore wind-tunnel tests were needed in
addition.
But the principle was sound. And it still is
for computers remain too small to allow
adequately fine elliptic grids,
despite the use of many levels of sub-division.
4
4/35. The Past CFD at IC MED How we stumbled
into it
Prior to 1965, IC Mech Eng still used
integral-profile methods for 2D boundary-layer
flows.
Profiles were polynomials, with coefficients
deduced from weighted-integral conservation
equations.
Then the Eureka-insight flash piece-wise-linear
profiles were more flexible with integration
over pieces i.e. with unity weighting factors.
We had invented (our own kind of) finite-volume
CFD.
The rest is history.
A remark aside The finite-element community
still uses non-unity weighting factors to their
great disadvantage. One day theyll learn. More
about this later.
5
5/35. The Past at IC MED Features of the first
computer program
It first appeared in Patankars PhD Thesis of
1967, later published as a book.
It simulated 2D parabolic flows, using axial
distance and dimensionless stream function as
co-ordinates, so minimising false diffusion.
The grid width expanded and contracted to cover
only the region of interest. So it was
self-adaptive.
It handled turbulence via Prandtls mixing-length
model.
Wall functions made their first appearance in it.
It used the TDMA, without iteration, for
cross-stream solution and it marched in the
main-flow direction.
6
6/35. The Past at IC MED More about 2D
parabolic computer programs
A second computer program, GENMIX, applied the
same method to more general 2D parabolic flows,
e.g. wakes, plumes, wall jets for film-cooling,
flames, etc.
A major use was for systematic validation studies
of the then-emerging two-equation turbulence
models.
It too was published as a book, with coding and
therefore used by non-IC researchers.
However the IC group had already developed and
published a stream-functionvorticity program for
simulating 2D elliptic flows.
We sought therefore a method to escape its
restrictions viz. to two dimensions and to
uniform density.
7
7/35. The Past at IC MED SIVA, SIMPLE and 3D
Harlow and Welch (1965) had published 3D methods
for unsteady compressible flows but our 2D
methods handled practically more-important steady
and incompressible ones. We wanted to continue.
Our first success was with SIVA ( Simultaneous
Variable Adjustment) ( Caretto et al 1971). But
it worked point-by-point and converged slowly.
So SIMPLE came into existence, purloining
elements from predecessors, but surpassing them
all (being later surpassed in its turn by
SIMPLER, SIMPLEST, SIMPLEC, etc.)
Later it was extended to two-phase,
free-surface, magneto-hydrodynamics, and much
more.
8
8/35. The Past at IC MED 3D parabolic and
partially parabolic
The first publication of SIMPLE (1972) was for 3D
parabolic flows. This is fact seldom remembered.
Eager to show SIMPLEs elliptic capability, we
too quickly exemplified it. The world followed,
and scarcely noticed its parabolic capability.
Who uses it nowadays?
However, finding our computers too small (they
still are and may be forever), we later created
the partially-parabolic method. This stores 3D
only pressures, but velocities 2D, saving memory
at the expense of time.
There were numerous publication but little
world-wide following.
Our fault, no doubt but the worlds loss (I
believe). More about this below.
9
9/35. The Past at IC MED More about
partially-parabolic
ICs publications concerned flows in curved and
coiled tubes, rotating ducts, 2D turbines, and
around ships hulls. Too few! And with wrong
emphasis.
Their authors (I was one) compared
partially-parabolic with fully-parabolic (and
therefore incorrect) solutions, rather than with
more accurate fully-elliptic ones.
Another distraction was did the turbulence
models used fit the experiments? Beside the
point. What should have been stressed was
Replacing fully-elliptic by partially-parabolic, 1
. scarcely affected accuracy or computer time,
but 2. greatly reduced computer memory
requirement.
When authors forget the point, most readers will
miss it.
10
10/35. The Past at IC MED starting the CFD
software industry
As engineers our aim was to be useful. So we
offered our services to industry with success.
Imperial College was ill-suiteded to industrial
contracts so CHAM Ltd was founded as a
pioneering spin-off.
At first, each task was treated as a start from
scratch and only CHAM personnel could use the
software.
Soon came another Eureka moment Why not create
a general-purpose package, with a closed-off core
and open-to-users outside? Then the customers
own staff could use it.
Hence PHOENICS (1981) followed by many
emulators FLUENT, Star-CD, Flow-3D, CFX, etc.,
etc.
11
11/35. Present some trends FVM versus FEM
Starting with FIDAP, finite-element-based codes
appeared in the CFD-software market and
multplied.
The burgeoning FEM literature implied that
differential equations not multiplied by
non-unity weighting functions (NUWFs) couldt be
solved. Else why do it?
Yet Finite-Volume codes use unity weighting
factors (UWFs), i.e. they use no weighting at all.
Those who never understood the FEM literature can
now take heart FEM-based CFD codes are no more.
The UWFists have at last prevailed .
for CFD.
12
12/35. Present trends FVM for solid stress?
FEM still dominates the solid-stress field but
FVM can solve the problems just as well,
calculating displacements in place of velocities.
So a single FVM computer code can solve
fluid-solid-interaction problems, e.g. thermal
and mechanical stresses in a gas-turbine blade.
Slides extracted from an earlier lecture will now
illustrate this.
The computer code used is PHOENICS which has a
built-in SSFT, i.e. simultaneous-solid-fluid-ther
mal capability.
13
13/35. A typical SSFT problem blade in hot gas,
cooled internally
Hot gas flows outside an internally-cooled
blade-like solid.
The un-structured grid which is used is shown
below.
The picture above shows the whole calculation
domain, with gas inlet on the left and outlet on
the right.
Also visible is the central tube, which
introduces the cooling air. The problem is
illustrative, with idealised geometry.
The smallest cells are placed near the curved
solid-fluid interfaces.
14
14/35. FVM solution for velocities
Velocity vectors in the gas stream. Red is fast
and green slow.
15
15/35. Displacement and thermal strain in solid
Displacement vectors computed at same time and
in the same (SIMPLE) way as velocities.
Thermal-strain distributions here shown as
contours are also computed simultaneously.
Repetition for sake of emphasis The simulation
is performed by a single FVM-based code as part
of a single calculation, with full compatibility
between conditions in solid and fluid?
Can any FEM code do the same?
16
16/35. Pressure distribution in gas
Pressure contours in the flowing gas. Red is
high blue is low.
Pressure is computed by SIMPLE for gas only.
17
17/35. Thermally and mechanically- induced
stresses
X-, y- and z-direction thermally-induced-stress
contours within the blade.
Red is compressive, blue tensile.
Note their strongly three-dimensional variation.
18
18/35. Summary of experiences with FVM applied to
solid-stress problems
Many comparisons with both analytical and
finite-element solutions have been made.
They confirm that FVM for stress-in-solids
problems is practicable, accurate and economical
it is at least as good as FEM.
This is a fertile field for research, still
almost explored.
SIMPLE works well for both fluid flow and solid
stress but surely better SSFT-specific
algorithms can be found.
Other questions remaining to be answered
concern relative advantages of staggered and
collocated structured grids
and of (various kinds of) unstructured grids.
Extensions are also required to time-dependent
phenomena

• to large (enough to influence the flow)
  displacements and

• to non-linear and plastic deformations.

19
19/35. Present trends grids for arbitrary body
shape
First used were body-fitted-coordinate grids
which were topologically Cartesian, i.e. still
structured but sometimes hard to create.
Therefore unstructured grids with tetrahedral
cells (copied from FEM) were popular for many
years. Polyhedral cells followed.
These too present creation difficulties and the
current trend is back to Cartesian, albeit
sub-divided as in just-shown solid-stress
example.
Then surface curvature may be allowed for by use
of the Immersed-Boundary Method (IBM).
20
20/35. Present trends early IBM examples
The PHOENICS IBM viz. PARSOL, simulates, on the
right, flow through a louvred wall. It looks
realistic. But quantitative accuracy is
improbable.
The same is true of the football stadium on the
left. Plausibility is easy to get. Reliable
accuracy - much harder.
The.
21
21/35. Present trends SPARSOL (Structured PARSOL)
Some versions of the IBM perform poorly for
solids which are thin compared with grid cells
careful calculation of the intersection locations
is necessary.
However realism can indeed be procured, with
sufficient care (see below).
22
22/35. Present grid trends Various storage
locations
1. Staggered pressures and scalars at cell
centres velocities on cell boundaries. This is
the natural choice.
2. Collocated all variables at cell centres.
Sometimes (unwisely?) preferred.
3.Other Xcell (various). Seldom used, but having
merit.
In grid on right, scalars , e.g. temperatures
are stored at triangle centroids.
So they are 4 times (8 in 3D) as numerous as
pressures and velocities.
23
23/35. Present grid trends How Xcell reduces
false diffusion
Blue fluid flows in from left, red from below.
Grid is Cartesian staggered.
Interface is blurred, with diagonally- directed
flow, as seen on right.
This is well known false diffusion due to upwind
differencing.
Less well known is that upwind differencing with
Xcell grid causes no blurring at all for flow
angles at 0, 90 or 45 degrees, as shown on right.
False diffusion does exist at other angles, but
less than without Xcell.
24
24/35. Present grid trends More-advanced Xcell
Cartesian sub-divided grids can also be
triangularised see right.
Not all cells need to be triangularised only
those where scalar gradients are large.
In another version of Xcell, velocities are also
stored at triangle centroids. This is
semi-collocated Xcell.
Because pressures and velocities are not stored
at the same points, it is free from the
checker-boarding ailment of conventionally
collocated grids.
What might be termed a smart-grid technology is
emerging which is solution adaptive.
25
25/35. Present turbulence-model trends in terms
of how many population members
Variables of popular turbulence models, e.g. k-e,
LES, are local averages implied population has
1 member.
Eddy-break-up model for combustion (1971) is
most-used 2-member example. Population theory is
not new.
Only 2-(or more)-member-population models can
represent chemical reaction, swirling-flows, and
un-mixing.
The next three slides concern an un-mixing
experiment, first performed in 1978, which no
1-member (i.e. conventional) model has ever been
able to simulate.
Will any one accept the challenge?
26
26/35. Turbulence trends The Stafford experiment
Fill the lower half of a glass-sided vessel with
coloured salty water, and the top half with clear
fresh water. Connect electrodes to a battery.
The salty water heats more rapidly than the
fresh. The consequent Rayleigh-Taylor instability
causes mixing. Soon the vessel appears to be
filled with coloured fluid.
Quickly switch off the current then the two
fluids start to un-mix!
In the end, the original sharp interface is
restored.
27
27/35. Turbulence trends Mixing followed by
unmixing (Sapozhnikov and Mitiakov, 2010)
28
28/35. Turbulence trends A 2-member population
model can do it
Each member has its own vertical- direction
velocity. One is ve the other ve. Values are
calculated from Navier Stokes.
At the start (on the left), the volume fraction
is unity in the bottom half and zero in the top
half. Later (in the middle) fragments of salty
fluid rise, and even begin to concentrate at the
upper surface.
Later still (on the right), the heating has
stopped so the salty fragments, lose heat to the
fresh water and fall down to the bottom again.
Just as the video showed.
Two-member models can simulate both mixing and
un-mixing.
29
29/35. The future perhaps. Models of turbulence
will use multi-member populations
One-member models in effect represent temperature
by one unity ordinate at calculated abscissa.
They know nothing about PDFs.
Multi-member models 1. focus on several
calculated ordinates at arbitrary abscissae. 2.
simulate inter-member-physics 3. calculate PDFs
4. solve more equations 5. generate much more
information.
Computation is cheap ignorance is expensive.
So surely multi-member models must become the
norm.
30
30/35. The future perhaps Use one (FVM) code
for both solid-stress and fluid/heat-flow
problems?
Common sense says Yes! for the world-wide
cost of FEM-for-solid-but-FVM-for-fluid is
enormous
and all because FEM carried needless pre-computer
baggage (the NUWFs) into the computer age
and others have been gulled into using it.
The picture answers.
And why?
31
31/35. The future perhaps Will general-purpose
CFD codes survive?
My answer? Yes, but underground.
Apps will dominate.
Apps, aka SimScenes, apply CFD to special classes
of equipment, i.e. Simulation Scenarios, via
app-specific menus and buttons.
App users may know no more about CFD than apple
eaters about arboriculture.
Apps and apples can be equally healthy if the
tree-roots are well nourished
by the underlying CFD code.
32
32/35. The future perhaps Revival ot the
partially-parabolic method?
The revived method would solve the simple
potential-flow elliptic equation outside
boundary layer, wake and jet.
Inside each of these it would solve 3D parabolic
Navier-Stokes equations on as fine a grid as
needed (easy because only 2D storage is required).
Elliptic and parabolic solutions would alternate,
exchanging domain-boundary information each time.
Why should this not work? Is it perhaps already
used?
33
33/35. The future perhaps Partially parabolic
for automobiles?
Early (1988) PHOENICS needlessly solved elliptic
Navier-Stokes far from the vehicle surface where
the flow is inviscid.
Near much of surface the flow is 3D parabolic.
But elliptic Navier-Stokes must be used for the
wake.
And behind wheels and wing mirrors.
34
34/35. The future perhaps Implementation of
partially- parabolic for automobiles
What is needed, in order to implement such a
hybrid solution procedure, is

• a CFD code with 2D and 3D, elliptic and
  parabolic capabilities (Note that PHOENICS is an
  acronym for
• Parabolic Hyperbolic Or Elliptic Numerical
  Integration Code Series so it will do)

• a flexible module for grid-to-grid transfer and
  interpolation of solved-for variables
• (PHOENICS has an embryonic one) and

• a user-friendly module for problem set-up and
  run-cycle control (coming soon).

Nothing of significant difficulty is involved.
35
35/35. The future perhaps Terrestrial
applications of partially-parabolic
Urban-air-flow and wind-farm simulations have a
predominant flow direction.
Analysis can be parabolic over most of volume,
with embedded elliptic sub-domains of
recirculation.
Grid fineness can be varied according to accuracy
needs of each region.
This and many other possible extensions of the
partially-parabolic method promises a highly
profitable future.
Lets help bring that about.
The End