Oct 2123

1
Enlarging the Frontiers of Computational Fluid
Dynamics
A lecture at the International Symposium HMTH
in Swirling Flow

• by
• Brian Spalding
• of CHAM Ltd

2
This lecture is a shortened version of my
presentation at the 2008 International
Computational Heat Transfer Conference in
Marrakech.
A lecture at the Third International
Symposium HMTH in Swirling Flow
I have added some new material about swirling
flows for the present conference.
In the earlier lecture, I proposed three
directions of CFD enlargement 1, stresses in
solids 2. multi-phase flow, and 3. The
population dimension, especially for combustion
studies..
Today I add that it is only by way of
fluid-population studies that swirling-flow
hydrodynamics and heat transfer will ever truly
become part of Computational Fluid Dynamics
3
1. INTRODUCTION1.1 Background

• In my J P Hartnett lecture at the Sydney
  International Heat Transfer Conference, I
  explained why I thought it possible and desirable
  to enlarge the frontiers of computational heat
  transfer.

At the Xian Computational Heat Transfer
Conference, I argued for a shift of emphasis
towards the 'population dimension'.
Today I present little new but until the ideas
become accepted, I judge it not improper to
repeat them and to suggest some worthwhile
research opportunities..
4
1. INTRODUCTION1.1 Outline of the lecture

• In section 2, I argue that what I called in
  Sydney the 'finite-element Tsunami' has
  devastated solid-stress analysis but extension
  of Computational Heat Transfer in that direction
  will aid recovery.
• In section 3, about extensions to multi-phase
  flow, I summarise the state of the art and point
  out opportunities for Computational Heat Transfer
  to assist engineers.
• Here I first mention the 'population
  dimension, which is highly relevant to
  multi-phase phenomena.
• In section 4, the population idea enables CHT
  to be extended so as to explain
  turbulent-combustion phenomena.

5
2. EXTENSION TO STRESS ANALYSIS2.1 History
Before the electronic computer, analysts of
fluid- and heat-flow phenomena on one hand, and
stresses in solids on the other, used similar
mathematical methods.
Analytical methods sufficed for only the simplest
problems. Therefore numerical methods were used,
of two kinds

• 1. 'presumed-profile, also called
  shape-function, using
• parameterized expressions for the distributions
  of the solved-for variables (displacement,
  velocity, temperature, etc), together with
• approximate integral equations to determine
  their parameters, and

2. 'finite-difference', using algebraic equations
connecting the values at a finite number of
locations.
6
2. EXTENSION TO STRESS ANALYSIS2.1 History
(contd)
Equations of both kinds were derived from
differential equations, embodying the underlying
physical laws, by

• for 1, multiplying the differential equations by
  a series of 'weighting functions' and then
  integrating them analytically over the whole or
  parts of the domain of interest and
• for 2, truncating a Taylor-series expansion.

The presumed-profile method (1) was often
preferred because the finite-difference (2)
method required too much expensive human labour.
7
2. EXTENSION TO STRESS ANALYSIS2.1 History
(contd)
The advent of the electronic computer set human
computers free. Yet the finite-difference
method (2) triumphed immediately only for heat
conduction.

• Why?
• Because a single differential equation was
  involved, whereas
• fluid-dynamicists must solve coupled momentum
  and mass-conservation equations and,
• stress-analysts must solve equations for
  displacements in several directions, coupled by
  Poisson's ratio.

8
2. EXTENSION TO STRESS ANALYSIS2.1 History
(contd)
Fluid-dynamicists faced the more severe problem
for their equations have first-order
derivatives, representing convection fluxes and
varied source terms and turbulent transport.
Therefore they soon agreed that it was best to
solve 'finite-volume' equations. These involved
very simple 'presumed profiles of histogram
type and they were derived by integration over
contiguous 'control volumes, with a 'weighting
function' of unity, i.e. no weighting at all.
The stress-analysts also limited their
integrations to contiguous control volumes, which
they called finite elements but they retained
non-unity weighting functions.
This was the crucial parting of the ways between
UWFists and N-UWFists.
9
Some founders of N-UWFism
Before computers
B.G. Galerkin
After computers
10
Some early UWFists
Before computers
L.F. Richardson
After computers
Graham de Vahl Davis
Francis Harlow
Patankar Spalding Runchal Wolfshtein
Larry Caretto
11
2.2 Finite-volume finite-element methods
comparedUWF versus NUWF

• Concession 1 All fluid-dynamics problems could
  be (and many have been) solved with non-unity
  weighting functions, i.e. with finite-element
  methods.

Concession 2 Whatever weighting-function
policy one adopts, the same solution should be
arrived at to any particular problem, just as
Moscow is the same city whether reached by UWFist
(finite-volume) or N-UWFist finite-element
vehicles.
12
2.2 Finite-volume and finite-element methods
compared (contd)

• Nevertheless I assert

• The finite-volume method (henceforth FVM) has
  been used for solving solid-stress problems by
  many authors Beale, Elias 1991 Spalding, 1993
  Demirdzic, Muzaferija 1994 Bailey, Cross, Lai
  1995 and more recently Artemov ,
  whether or not they interact with fluid- or
  heat-flow ones.

• Therefore the widely-held belief that the
  finite-element (henceforth FEM) must be used for
  solid-stress problems is demonstrably false.

• This belief has wrongly dissuaded the majority
  of stress-analysis researchers from paying any
  attention at all to FVM.

• Yet FVM is inherently superior, requiring only
  one function (that of the variable-distribution
  shape) to be guessed, not two (i.e. the weighting
  function in addition).

13
2.2 Finite-volume and finite-element methods
compared (contd)

• Fluid structure interaction

A wing twisting under the influence of
aerodynamic forces, computed using FVM, by
Greenwich University group under Professor Mark
Cross. Original animation provided by Professor
Koulis Pericleous.
14
2.2 Finite-volume and finite-element methods
compared (contd)

• The use of two functions by NUWFists has
  needlessly complicated the language and
  literature of FEM. It represent needless baggage
  carried in from pre-computer years, with no
  advantage whatever..

• The enormous and expensive effort devoted to
  creating the finite-element literature represents
  a profligate and still-continuing waste of
  resources.

• Because solid-stress and fluid-flow analysts
  use different methods, engineers still lack
  economical software tools for solving
  fluid-structure-interaction problems.

• It is not too late to change course and
  specialists in Computational Heat Transfer are
  well placed, by reason of their experience of
  FVM, to take the lead.

15
2.2 Finite-volume and finite-element methods
compared Some FVM-based results

• I now show a few results by way of
  substantiation. First a comparison between
  numerical (FVM) (left) and analytical (right)
  calculations of the x- and y-direction stresses
  in a rectangular plate in tension when the plate
  was perforated by a circular hole. Only the
  top-right-hand quarter of the plate is shown.

16
2.2 Finite-volume and finite-element methods
compared Some FVM-based results (contd)
Next I show some several-years-old results for a
'multi-physics' problem, in which stresses are
computed simultaneously with turbulent fluid flow
and with conductive, radiative and convective
heat transfer.
Blocks of differing materials, radiation-heated
and convection-cooled
17
2.2 Finite-volume and finite-element methods
compared Some FVM-based results (contd)
The task is to calculate the temperature
distribution and the resulting stresses and
strains, using a single software package, in this
case PHOENICS.
Above are shown, from left to right, the
distributions of true temperature, radiation
temperature, x-direction stress, and y-direction
stress.
18
2.2 Finite-volume and finite-element methods
compared Some FVM-based results (contd)
The dependent variables solved in the solid
regions were the displacement vectors the
stresses and strains were then obtained by
post-processing. Computer times were only a few
seconds.
Here are displayed the vectors of solid
displacement and of air
velocity.
19
2.2 Finite-volume and finite-element methods
compared Some FVM-based results (end)

• A final example deformation of an under-water
  structure by periodic wave motion.

20
2.3 Some research opportunities regarding use of
UWF for solid-stress problems
So stress-in-solids and fluid-structure-interactio
n problems can be solved by a single computer
code embodying FVM.
But that does not mean that the available
solution methods are optimal in respect of

• universality of application,

• economy of computer-time and storage,

• literature making them accessible to all.

The printed text contains some discussion and
suggestions regarding worthwhile research
opportunities in this area. Many more will spring
from the recognition that decades of CFD research
has yet to be applied to the equally important
field of stresses in solids.
21
3. EXTENSION TO MULTI-PHASE FLOW 3.1 Overview
The phenomena in question. Multi-phase-flow
phenomena to which I urge CHT specialists to pay
more attention are of two kinds free-surface and
dispersed.

• Examples of the free-surface phenomena include
• film condensation of water from a steam-air
  mixture
• film boiling at the surface of a hot solid
  immersed in a liquid
• vaporisation and burning of a pool of oil
• melting of an icicle in a warm wind
• motion of large vapour bubbles, when slug-flow
  motion occurs in a tube.

22
3.3 Research opportunities in respect of
free-surface flows

• Research opportunities in respect of free-surface
  flows are also explained in the printed text. I
  merely summarise here

• Fitting the grid to the surface is rarely
  practical surface shapes are too convoluted.
  The motion must be defined by reference to a
  pre-determined grid.

• A two-phase model may be used but numerical
  diffusion makes the surface fuzzy.

• Particle tracking is useful (seen on right)
  but algorithms vary greatly in efficiency.

• The volume-of-fluid scalar-equation method has
  many advocates, and variants. Improvements are
  still needed, e.g. for multiple layers.

• Another scalar-equation method, called
  level-set, can produce spectacular results seen
  on the next slide.

23
3.3 Research opportunities in respect of
free-surface flows (end)
Level-set calculations by J.Hernandez et al at
the International PHOENICS Conference in Moscow
2002
24
3. EXTENSION TO MULTI-PHASE FLOW 3.1 Overview
(end)

• Examples of dispersed-flow phenomena include
• vaporisation of water droplets injected into an
  air stream in order to cool and humidify it
• pool boiling in a kettle
• dissolution of granulated sugar in a stirred cup
  of tea
• flow of liquid and vapour in the shell of a
  nuclear-plant steam-generator
• cooling of a fluidised-bed reactor by a
  cold-water-containing tube bundle immersed within
  it
• vaporisation, ignition and combustion of oil
  droplets sprayed into a Diesel engine and
• burning of, and radiation from, pulverised coal
  in a power-station furnace.

25
3.2 Research opportunities in respect of
dispersed flows
The two-phase idealisation. Computer simulation
of dispersed-flow phenomena is always based on
the neglect of some of the features of the real
situation. For example

• although in fact bubbles of many different
  sizes exist at a particular location in a boiler,
  they are usually supposed all to have the same
  size there

• although some coal particles have greater
  velocities than others at a particular place in a
  furnace, the differences are disregarded.

• These presumptions make it possible to regard the
  true multi-phase mixture as being a two-phase one.

26
3.2 Research opportunities in respect of
dispersed flows(contd)

• . The two-phase model entails that
• At any point of space and any instant of time,
  there are
• six velocity components (i.e. three for each
  phase
• viz u1, u2, v1, v2, w1 and w2)
• two temperatures (i.e. one for each phase, viz T1
  and T2)
• one pressure, p and
• two volume fractions (viz r1 and r2), summing to
  zero.
• There are therefore eleven variables to compute
  for each point.
• These are coupled, but in a slightly non-linear
  fashion.
• The finite-volume equations (of mass momentum and
  energy) are similar to the single-phase ones
• but there are differences too, namely

27
3.2 Research opportunities in respect of
dispersed flows(contd)

• they possess additional terms representing the
  rates of interchange of mass, momentum and energy
  between phases
• formulae are used for these terms, which must
  usually be obtained from interpolated
  experimental data
• these terms cause further coupling between the
  equations, which may cause slow convergence of
  the solution process
• whatever is the reliability of the formulae (e.g.
  k-epsilon turbulence model) for the transport
  properties of a single-phase fluid, it will be
  much less when they are used for two-phase
  mixtures for there has been little research on
  the subject.

28
3.2 Research opportunities in respect of
dispersed flows(contd)

• Dispersed two-phase flows are familiar to us all
  yet traditional CFD ignores them.

An example of two-phase flow computation. Consider
the steady flow of a two-phase mixture in a
'turn-around duct.
The two fluids may be thought of as air and
water, with a density ratio of 11000.
Centrifugal force flings the water to the outside
of the bend pushing the air to the inside. This
is what I call the sifting phenomenon, wherein
intermingled fluids move relative to one another
under the influence of body forces.
29
3.2 Research opportunities in respect of
dispersed flows(contd)
Here are the computed velocity vectors.
Air velocity vectors
Water velocity vectors
Their angles differ near the inner wall of the
bend.
30
3.2 Research opportunities in respect of
dispersed flows(contd)
Water Air

• Their volume-fraction contours, shown here,
  confirm the relative movements of the two
• Phases they have been 'cyclonically separated'.

Yellow high light blue low
The computations should be studied even by those
interested only in single-phase flow for a
similar 'sifting' motion would be observed if the
two fluids had equal densities but differing
velocities. This is how the turbulent flows in
curved ducts are to be understood. I shall
return to this in connection with population
analysis.
31
3.2 Research opportunities in respect of
dispersed flows(contd)
Here is another scarcely-explored field of
two-phase study the collapse of buildings
The penetration of armour by explosive devices
has long been simulated by recognising that
metals under very high pressure can flow like
fluids
So can other solids fragmented concrete for
example.
Why did the World Trade Center Twin Towers
collapse so quickly on September 11?
The pressure generated as the higher floors fell
on the next below fluidised that one too and
so on to Ground Zero.
On the right is a two-phase-flow simulation of
the process. Blue is air, red is concrete
etcetera.
32
3.2 Research opportunities in respect of
dispersed flows(end)

• Research opportunities in respect of dispersed
  two-phase flows are explained in the printed
  text. I merely summarise here
• Numerical All commercial CFD codes appear to
  use a form of the IPSA algorithm of the mid
  1970s. This is a two-phase version of SIMPLE.
  Just as the latter has been refined and
  surpassed, so could the former be.
• Experimental All code vendors would introduce
  more reliable interphase-transport formulae if
  they existed and their users would rejoice. But
  the research to produce them is unglamorous, and
  so neglected. Should not that change?
• Extension to true multi-phase flow This is
  possible, desirable and neglected. See printed
  text for suggestions.
• Applications Designers of steam condensers,
  cooling towers, furnaces seek numerical two-phase
  models in vain.
• The population dimension This is virgin
  territory. See below.

33
4. EXTENSION TO THE POPULATION DIMENSION

• 4.1 Introduction by reference to turbulent
  combustion
• Highlights of my personal exploration of the
  population dimension have been
• Scurlocks unaccountable turbulent-flame findings
  (1948)
• The Eddy-Break-Up model (1971), which explained
  some of them
• The Four-Fluid model (1995), which explained more
  
• The Multi-Fluid model with a one-dimensional
  population
• The Multi-Fluid model with a two-dimensional
  population
• Here I merely summarise.

34
4.1 Introduction by reference to turbulent
combustion (contd)

• Scurlock (1948) discovered that the speed of
  turbulent flame propagation in a plane-walled
  duct was approximately
• proportional to the velocity of the incoming gas
  stream,
• independent of the turbulence intensity of this
  stream, and
• independent of its fuel-air ratio and indeed of
• the choice of fuel, all of which however did
  affect the incoming velocity which caused sudden
  extinction. Why? Why? Why?

35
4.1 Introduction by reference to turbulent
combustion (contd)

• The Eddy-Break-Up model of 1971 explained the
  flame-speed finding by presuming the burning
  gases to comprise a two-component population,
  consisting of
• wholly un-reacted gas fragments, too cold to
  burn, and
• hot fully-reacted gas fragments, which also could
  not burn.

These collided at a rate proportional to their
volume-fraction product and to the turbulence
intensity, producing intermediate gas which could
burn instantly. The EBU became popular and is
still (too!) widely used.
36
4.1 Introduction by reference to turbulent
combustion (contd)

The four-fluid model (1995) refined the
population grid, as shown here. All four fluids
could collide but only one could react, at a
chemical-kinetically limited rate. Unlike EBU,
this model could explain Scurlocks
sudden-extinction findings. The next step was
obvious, viz. the (one-dimensional) multi-fluid
model.
The four-fluid extension to EBU
37
4.1 Introduction by reference to turbulent
combustion (contd)
The multi-fluid extension of EBU Why not refine
the population grid further, as shown here? Each
histogram ordinate is now the dependent variable
of its own standard conservation equation plus
source/sink terms for reaction (i.e. convection
in reactedness space) and collision.
The equations, solved by any sufficiently-flexible
CFD code, result in computed (i.e. not
presumed) population profiles. Just so did
finite-volumes replace presumed profiles in
CFD. Here FVM has been extended to the population
dimension.
38
4.1 Introduction by reference to turbulent
combustion (contd)

• Calculations have shown why EBU has worked so
  well with fast chemical kinetics the
  distribution does show high spikes at
  zero and unity reactedness.
• Calculations also allow determination of how
  many fluids are needed for accuracy.
• The analogy with spatial-grid-refinement tests
  is very close.

• Of course, the computer time increases, as
  expected, with the number of fluids (i.e.
  population components, histogram ordinates)
• Interestingly, no case of divergence has ever
  arisen

Examples shown so far (for EBU, 4-fluid and MFM)
have all had one population dimension,
reactedness. The fuel/air ratio can also be used
for MFM as the second dimension.
39
4.1 Introduction by reference to turbulent
combustion (contd)

• Computations for a 2D population of burning fuel
  and air are shown below. Each square represents a
  population component. The extent to which it is
  filled represents its prevalence in the
  population.

40
4.1 Introduction by reference to turbulent
combustion (end)

• MFM predictions of total smoke-generation rate in
  a gas-turbine combustor
• Each component in the gas-fragment population
  generates smoke at a different rate. Only when
  their prevalences at each point in space are
  known can the total rate be predicted.

Above are smoke-concentration distributions for
single-fluid (left) and eleven-fluid (right)
models. Both distributions and maximum values
differ by amounts of practical significance to
engineers.
41
4.2 Multi-fluid models of reactive mixtures in
general

• Applications of population approach in chemical
  industry
• Gas-turbine industry has not yet availed itself
  of MFM.
• Chemical industry ought to be more receptive for
  stirred reactors generate many of its products.
• It does use CFD for their design but, without
  the population dimension, the CFD-based
  predictions are of doubtful value.

On the right is a sketch of a paddle-stirred
reactor for mixing the A and B streams so that
they can react chemically. Can CFD predict the
effect of the stirring on the yield?
42
4.2 Multi-fluid models of reactive mixtures in
general(contd)

• .

The 1997 WUA benchmark simulation CFD-code-vendors
were invited to predict velocity fields in a
specified reactor shown below but not chemical
yields.
Geometry and grid for 3-dimensional transient
stirred-reactor simulation
43
4.2 Multi-fluid models of reactive mixtures in
general(contd)

• .

Slava Semin and I used the opportunity to
demonstrate that reaction depends on mixing, and
specifically on micro-mixing rather than
macro-mixing, as the pictures below reveal. They
show, as examples, the distributions of
mixture-average reaction- product distributions
after ten revolutions of the paddle, The
reactants A and B are initially entirely
separate.
Left-hand contours pertain to the conventional
single-fluid presumption. Right-hand ones
resulted from using an eleven-fluid model. They
differ. Why? Because rate depends non-linearly on
mixture ratio.
44
4.2 Multi-fluid models of reactive mixtures in
general(end)

• .

Calculated histograms
These histograms represent the distributions
in reactant-ratio space at one instant of time,
at one vertical position and at six radial
positions in the reactor. Calculating such
histograms for all positions and all times
allows the total yield of the reactor to be
computed. Ignoring the population dimension
amounts to replacing the histograms by single
spikes at particular abscissas. (mixture
ratios) That is what conventional CFD does, with
worthless results.
45
4.3 Research opportunities

• .

• The printed text describes some opportunities.
  Here I summarise them under the headings
• Conceptual
• Computational
• Experimental
• Physical Hydrodynamics
• Physical Heat and Mass Transfer
• However, what is suggested is a tiny fraction of
  what comprehensive consideration would reveal.
  How can such studies be made popular?
• Should we speak of nano-populations?

46
4.3 Research opportunities(contd)

• Desirable conceptual advances
• The Prandtls mixing-length concept is an
  inspired guess about how colliding fragments of
  fluid might interact.
• It concerns interactions between neighbouring
  locations in geometrical space.

• .

• In population space, there are some interactions
  between neighbouring locations thus reacting
  material passes from a lower- to a
  higher-reactedness component.
• But there are also interactions between remote
  components, namely collisions between gases of
  very different reactedness.

If Ludwig Prandtl had asked himself How
collisions affect population, would he have
thought about Gregor Mendel?
47
4.3 Research opportunities(contd)
The first MFM employs the Promiscuous-Mendelian'
hypothesis this implies that any pair can
procreate and their offspring share their
parents attributes, uniformly graded.

• .

Who can provide a better one? See printed paper
for some ideas.
48
4.3 Research opportunities(contd)

• .

Experimental opportunities scientific and
industrial Would someone please measure the
population distributions, so that the hypotheses
can be checked and then improved? And how about
testing experimentally what has been predicted
about gas-turbine combustors and stirred reactors?
Computational opportunities I have used fixed,
uniform and structured population grids.. Who
will extend to them our knowledge of moving,
non-uniform, unstructured, problem-adaptive and
other sophisticated geometric grids?
Pure-hydrodynamics opportunities A
round-the-bend idea I believe that allowing
high-velocity population members to sift
through lower-velocity ones will explain
swirling-flow observations. Is it not at least
worth a try?
49
4.3 Research opportunitiesThe round-the-bend
idea explored. 1
How try?

• .

• Take a general-purpose CFD code having
  population-dimension capability.
• Envisage a turbulent swirling flow, between
  cylinders rotating at
  different speeds.
• Select a multi-fluid turbulence model, with
  circumferential velocity as the
  population-defining attribute.
• Choose a high Reynolds Number for which
  turbulent-diffusion and inter-fluid-collision
  processes are of the same order of magnitude.
• Postulate that radial sifting velocity depends
  on the radial body forces being different for
  each fluid. This needs new thinking.
• Vary this force systematically, by changing
  curvature then observe the effects on
  velocity-population distribution, shear stress,
  etc.

I have done this, as anyone could have done. A
few results now follow.
50
4.3 Research opportunities The round-the-bend
idea explored. 2

• The general-purpose CFD code which I used was
  PHOENICS.
• A steady, rotating, turbulent flow between two
  cylinders was set up in a switch-on manner.
• The 17-fluid model of Zhubrin and
  Pavistkiy was selected.
• Turbulent-diffusion/collision-rate ratios were
  chosen, based on experimental data for channel
  flow.
• A body force proportional to fluid velocity was
  postulated (velocity-squared might have been
  more realistic).
• A new slip-velocity-proportional-to-body-force-dif
  ference hypothesis was formulated. This
  hypothesis was conveyed to PHOENICS by way of the
  In-Form feature no new programming or
  executable-building was needed.

The computations, of which the results will be
displayed, employed only standard features of
PHOENICS.
51
4.3 Research opportunities The round-the-bend
idea explored, 3

• .

Here are results for zero curvature, i.e. no
swirl.They are contours of computed mass
fractions of individual population components.
Flow is from left to right.
First, the
highest-velocity fluid, which is clearly
concentrated near the upper, higher-velocity
wall.
Next, contours for the 9th fluid with velocity
equal to the mean wall velocity. They spread as a
consequence of turbulent diffusion opposed by
collision. Downstream cessation of spread implies
that the two processes are in balance.
Here are contours of the lowest-velocity fluid.
Its concentrations are high near the low-velocity
wall, ts spread also ceases downstream.
Diagrams for all 17 fluids have been computed
but to display them all would be tedious.
52
4.3 Research opportunities The round-the-bend
idea explored, 4

• .

The fluid-population distributions (FPDs) have
also been computed. Here is that for the central
plane, when the duct is not curved. Fluid-9 has
the highest mass fraction, viz 0.187. Results for
curved ducts will now be shown.

Here is the corresponding FPD for radius
increasing with average velocity the
distribution becomes narrower . The
fluid-9 mass fraction has risen to 0.21.
Faster fluids sift towards the
faster-moving outer wall.
Now the direction of curvature is changed.
Faster-moving fluids now sift away from the
faster-moving, now inner wall. The
shape of the FPD broadens dramatically. Fluid-9
mass fraction has fallen to 0.81, and the shear
stress increases.
These results explain why flows near convex and
concave walls are so different. Only population
models can begin to simulate swirling- flow
behaviour.
They should be vigorously
developed and used..
53
4.3 Research opportunities The round-the-bend
idea, 5. Conclusion

• .

What I have shown is the result of a few days
work by an 85-year-old. Perhaps interesting but
hardly conclusive.
Why can I not report on, and praise, what the
younger generation is doing to explore the
fluid-population dimension of CFD? Because such
work does not exist.
Why does it not exist? Because the younger
generation does little but copy Kolmogorov and
Harlow and Spalding and Launder and Rodi and
other old men, whose ideas they seem reluctant to
challenge! They should be less in awe of them.
Perhaps also they suppose it would be difficult
to get started. That is incorrect as I hope to
have shown. Let it now be understood that the
door is wide open.
54
4.3 Research opportunities(contd)

• .

Heat- and mass-transfer opportunities. The
near-earth atmosphere. The first two-fluid-model
simulations were made twenty years ago. These
pictures show how different are the temperature
distributions in the upward-and downward-moving
air components. Is it not time for a further
research step forward?
wind
height
distance
wind
height
distance
55
4.3 Research opportunities(contd)

• .

Turbulent buoyant heat and mass transfer a
return to the Stafford experiment of 1978 Fill
the lower half of a glass-sided vessel with
coloured salty water, and the top half with clear
fresh water. Connect electrodes at each end to a
battery.
The salty water heats more rapidly than the
fresh. The consequent Rayleigh-Taylor
instability causes complete(?) mixing. Within a
second, the vessel appears to be filled with
coloured fluid. Quickly switch off the
current. If conditions and timing are just right,
the two fluids start to un-mix! Then the original
sharp interface is restored. Sapozhnikov and
Mitiakov recently repeated this, as the video
shows. No Prandtl-Kolmogorov-type turbulence
model can simulate this. A two-fluid model can.
It understands sifting.
56
Experiment - video
57
4.3 Research opportunities(end)

• .

The heated-salt-water experiment
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. The video showed that. Is not this
also an opportunity for further research?
58
5. CONCLUDING REMARKS
My message is that It is our duty to enlarge the
frontiers of Computational Heat Transfer and
Fluid Dynamics.

• Neighbouring territories which especially deserve
  our liberating attentions include
• Solid-stress-land, which needs a complete change
  of regime,
• Multi-phase-flow-land, which is insufficiently
  cultivated,
• Chemical-reaction-land where the ruling
  intelligentsia care too little about the workers
  needs.

But let us make sure that the forces which occupy
territories 2 and 3 are well-trained in
distinguishing the significant attributes of the
populations.
They will then be ready to invade and rule over
swirling-flow-land too.
59
5. CONCLUDING REMARKS(concluded)

• In this lecture room, a two-dimensional
  population exists, with the significant
  attributes
• Understanding (0baffled 1enlightened)
• Pleasure (0disgusted 1 delighted)
• What, I ask myself, would its histogram look like?

I shall be not displeased if it is something like
the one I showed earlier for a reactor. This
would show that the majority understood about
half but more than half enjoyed it.
But whichever box each of you is placed in, I
thank you for your attention.
60
5. CONCLUDING REMARKS(end, nearly)

• my further thanks go to
• Valeriy Artemov for his work on FVM for Solid
  Stress
• Julio Hernandez for his level-set contribution
• Koulis Pericleous for the flexing wing
• Sergey Sapozhnikov for the salty-water video
• Elena Pankova for the Power Point presentation.
• I applaud all of them!
• And at last, it is

61
A final overview