Encyclopaedia Index


in the presence of heat transfer and chemical reaction


Brian Spalding

Keynote lecture at ASME/JSME Joint Pressure Vessels and Piping Conference, July 1998

Summary of main themes

  1. Although fluid-flow, thermal and structural analysis are well handled by modern software packages, certain deficiencies remain, of which the chief are:
  2. Some progress is here reported regarding the CAD-to-CFD difficulty, with the STL format proving to be of key importance.
  3. It will be shown that solid stress and fluid flow can be analysed by a single algorithm, a single code, and therefore a single specialist.
  4. Good compromises between economy and realism for simple circumstances are:
  5. MFM, the "multi-fluid model" of turbulence, promises the same for more complex circumstances, especially those involving chemical reaction.


  1. An overview of computer-aided engineering

  2. CAD to CFD via VR, with a link to Hotbox
  3. SFT: simultaneous Solid-stress, Fluid-flow and Thermal analysis
  4. Modelling turbulence, radiation and chemical reaction

  5. The revival of remote computing
  6. Concluding remarks
  7. References

1. An overview of computer-aided engineering

1.1 An overview of computer-simulation capabilities and difficulties 1.2 Summary of urgent needs 1.3 Outline of the present lecture

1.1 An overview of computer-simulation capabilities and difficulties

(a) CAD-1; computer-aided drawing and display

In the last few decades, the use of software packages by engineers and architects has become commonplace. The intense commercial competition between package vendors, aided by great advances in computer-graphics software has allowed even the poorest to acquire easy-to-use packages for drawing and display.

The term CAD, which is used to describe these packages, is commonly regarded as an acronym for Computer-Aided Design. Yet the D is better regarded as standing for Drawing, or Display; for Design involves more than these, namely Decision-making, based on the systematic evaluation of alternatives.

This is why, in this review of current capabilities, it is useful to distinguish CAD-1 (drawing) from CAD-2 (design). Capabilities are more satisfactory in respect of the former than of the latter.

(b) CASA, ie computer-aided stress analysis

Many fully-sufficient packages also exist for computing the mechanical stresses in solid objects which come into (virtual) existence as a consequence of CAD-1 activities.

Some of the available packages combine both CAD-1 and CASA capabilities, to the great convenience of their users.

The CASA methods, it may be remarked, nearly all make use of the so-called finite-element techniques; and this sets them apart from the so-called finite-volume methods most commonly employed for fluid- flow simulations. This has led to some of the practical difficulties which will be referred to below.

Nevertheless, if calculations of the stresses in solids are all that are required, the availability of the relevant computer software must be regarded as rather satisfactory.

(c) CFD, ie Computational Fluid Dynamics

In many branches of engineering, calculations of fluid-flow phenomena and effects also require to be made. The subject of computational fluid dynamics has come into existence to meet this need.

Software packages have been created, and are in widespread use, which seek to satisfy this requirement. These fall into two categories, namely the general-purpose codes, of which PHOENICS was the first, and the special-purpose codes such as those dealing with the less general phenomena occurring in turbomachinery (eg VISIUN,) electronics cooling (eg FLOTHERM), power engineering, and environmental flows. Several of the general-purpose codes (PHOENICS is one) also have special- purpose manifestations (for example PHOENICS-HOTBOX for electronics- cooling simulations).

The satisfaction given by these codes to their users is lower than that given by CAD-1 and CASA packages to theirs, because:-

  1. the phenomena to be simulated possess inherently greater variety involving, for example: turbulence, chemical reaction, more than one phase, and radiation; so more input data are required;
  2. the grid-fineness requirements are greater; and, since they can rarely be fully satisfied, more skill and experience are needed from the code users, if the simulations are still to be reliable;
  3. most practically-arising problems are three-dimensional in character and often time-dependent as well (turbo-machinery flows, properly considered, are of this kind); and finally
  4. science has not advanced sufficiently to enable all the relevant phenomena to be expressed reliably in tractable mathematical form.
As a consequence, very few CFD calculations deserve to be trusted fully; and the users of the relevant software packages should be constantly on their guard against believing that, because a particular model (eg of turbulence or multi-phase flow) is widely used, it must surely have been adequately validated.

Even when some validating evidence can be provided, the question to be asked is: were the circumstances of the validation sufficiently close to those for which the model is now to be used?

Sceptics say CFD stands for Colourful Fluid Dynamics; stronger critics use the words: Cheats, Frauds and Deceivers.

Press for notes on validation

(d) CAD-2; computer-aided Design

If CAD-2 connotes computer-aided design in the extended sense mentioned in (a) above, it must be stated that it remains as an aspiration rather than a widely-practised activity.

Engineers proceed from design-object description (CAD-1) to analysis (CASA and/or CFD); they then make changes to the shapes, materials, loading, etc, of their to-be-designed objects; then THEY examine and assess the results of the analysis(es); then again THEY repeat the analysis once more.

This human-in-the-loop cycle is repeated until optimal results (ie design-object performance) are attained, or until time, money or patience run out.

CAD-2 happens when the human takes himself out of the loop, having instructed the computer, at the end of one cycle, to change shapes, materials, etc until the conditions for optimum performance have been established. This is the ultimate goal of CAE specialists.

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1.2 Summary of urgent needs

(a) Ease of use of CFD software

In the foregoing overview, it is CFD software which has been pointed out as presenting the greatest ease-of-use difficulties.

Understandably, it is the more powerful CFD codes which present the greatest difficulties; for the user of a code possessing many turbulence models, for example, has more decisions to make than the user of a code possessing only one, or even none.

Adequate documentation, and usually-optimal default settings, can diminish the user's difficulty; but, once again, the more powerful the code, the harder it is to provide documents and defaults.

In all respects, the solution is to be found in "customization", which entails, in effect, making a powerful general-purpose code look, to the user, as though it possesses only those capabilities from which he or she needs to make selections.

A further ease-of-use requirement is the connexion between the widely-available CAD-1 packages and the software which computes the flows around and within the objects which they create.

As already indicated, the CASA packages tend to be better connected with CAD-1 than the CFD packages; but one of the few finite-volume CFD codes, CFDesign, has concentrated its attention on such connexions, with benefits to its users.

That such connexions are not more prevalent is in part due to the gap of understandinq between the finite-element and finite-volume communities. It is a gap which needs urgently to be either bridged or, by using finite-volume methods for CASA, eliminated.

(b) The need for economy

The reason for promoting ease of use is already an economical one. needless difficulties waste the time of intelligent humans; and that, and they, are the most precious resources which we possess.

However, computer-time is also precious; and CFD-package users never have enough of it. What is available should therefore be utilised in a balanced manner, care being taken not to squander time by the use (say) of excessively-fine computational grids when the models of the physical processes are comparatively crude.

The opposite extreme is equally to be avoided. Some turbulence models are rather elaborate and time-consuming; and these are sometimes (ill- advisedly) employed in circumstances in which, because many small solid objects are immersed within the fluid, the number of grid nodes between two adjacent solids is far too small for (say) the velocity gradients to be computed with adequate accuracy.

There is therefore a need for "balanced-accuracy" models, which, by avoiding extremes, make optimal use of limited computer resources.

(c) The need for better physical modelling

(1) Turbulence

CASA specialists may have their own difficulties in repect of the yield properties of plastically-deforming materials; but they are as nothing (or so it seems to the present author) in comparison with those of the CFD specialist in respect of turbulence.

Most practically-occurring flows are turbulent. The methods for simulating derive from ideas put forward by Kolmogorov (1942); but these are inadequate in at least two here-relevant respects, namely:

Kolmogorov's idea (which others conceived later, but independently) was that it might suffice to invent and solve equations for certain statistical properties of the local turbulence. It was partly true.

Because it was partly true, Kolmogorov's followers (whether or not they knew whom they were following) achieved success in predicting the velocity (and sometimes temperature) distributions in:-

Unfortunately, the Kolmogorov concept, which is only one of several possibilities, fails whenever the significant behaviour of a fluid element depends on the differences of its properties, eg temperature, or circumferential velocity, from the local time-mean.

Such circumstances are common; they include:-

Dopazo and O'Brien (1974) recognised that there was another possibility; and Pope (1982) has explored it to same extent, but by means of a computer-time-intensive (Monte-Carlo) method.

What is needed is needed is an economical method of exploration.

(b) Chemical reaction

The scientific study of chemical kinetics is well advanced; and it has revealed, in great detail, how engine fuel (for example) combines with air to produce the desired products (carbon dioxide and water vapour) and others that are undesired (oxides of nitrogen, smoke, carbon monoxide, and unburned hydrocarbons).

The detailed knowledge is however TOO detailed, in the senses that it involves more than designers want to know, and that its computation necessitates enormous computer time. Therefore simplified models have been devised, conveying the important information well enough, while avoiding excessive detail.

That is however not the end of the computer-modeller's difficulties; for chemical reaction rates depend not on time-mean gas properties, which Kolmogorov-type turbulence models predict, but also upon the instantaneous diferences therefrom.

Models of the Dopazo/O'Brien type are needed. (See MFM, below.)

(c) Radiation

Heat transfer by thermal radiation is, like chemical kinetics, one of those phenomena for which it is easy to write down the relevant mathematical equations, and indeed to devise general means of solution. However, these solution means become computationally very intensive, whenever the solid-surface geometry is complex.

Unfortunately, in many practically-important circumstances, the resulting computational task is too great to be executed, at least when the temperature and wave-length dependencies of the radiation properties of gaseous and solid materials are taken into account.

What is commonly done is to neglect the latter dependencies, and also, to at least some extent, the effect of the intervening gases on the transfer from one solid surface to another.

What is therefore needed is the devising of a balanced method, which may allow some geometrical inexactitude if wavelegth and temperature dependences can be accommodated.

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1.3 Outline of the present lecture

The lecture describes how the above-listed needs are being met.

Section 2 describes how the connexion between CAD-1 and CFD can be effected by the use of the STL-file format.

Section 3 explains how the CASA and CFD worlds are being unified.

Section 4 describes some recent physical-modelling developments directed towards:-

Finally, section 5 describes the tendency for remote computing to replace the current practice of software-package purchase.

[Note: In the remainder of the lecture, the "-1" appendage to "CAD" will be dropped, the point having been sufficiently made.] Back to top

Back to start of lecture

2. CAD to CFD via VR and PARSOL

[Chapter 2 of the lecture CAD to SFT.
Click here for the start of the lecture]


2.1 Transferring the geometrical data

2.2 An aeronautical example: the 3-part airfoil

2.3 A test of PARSOL

2.4 Flow around an automobile

2.5 Concluding remarks about CAD to CFD

Further examples of PARSOL, including moving grids

2.1 Transferring the geometrical data

(a) The data-format question

CAD packages are used for defining the shapes and sizes of the objects of which the fluid-flow or solid-stress performance is studied.

The definitions can be expressed in various formats, of which IGES, DXF and STL are examples.

Here the STL (ie STereo-Lithographic) format is considered. It describes solid bodies by defining the locations of their surfaces, these surfaces being made up of an array of approximating triangles, each of which shares its edges with (only) one other.

There exist translator programs which can effect IGES-to-STL, DXF- to-STL and similar conversions. CADfix, from FEGS Ltd, is one.

(b) Import into a "virtual-reality" interface

The STL format is a convenient one for representing objects visually in "virtual-reality"-type data-input interfaces for CFD codes.

Such interfaces can immediately accept and display the objects which the CAD users have created; and they provide their own users with the further abilities:-

  1. to change the sizes, numbers, positions and orientations of those objects;
  2. to specify what materials they are to be made of (if that has not already been done), what their surface roughnesses are, and in what fluids they are immersed;
  3. to add CFD-type boundary conditions such as temperatures, velocities and pressures at various places; and
  4. to provide solution-influencing information regarding the grid-fineness distribution, accuracy tolerances, etc.

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Fig. 2.1-1 a CAD-generated object after transfer into PHOENICS-VR.

Click here for an example of DXF-to-VR conversion

Click here for a description of the DXF-to-VR converter program

Click here for an IGES-to-VR example

(c) Export to the CFD equation-solving package

Once all the data have been inserted, and the user is satisfied that the problem specified is the one which he wants to solve, all that should be necessary is to click on the EXIT button; then the data should be exported to the equation solver; and, after the requisite "number-crunching" time, the results should be returned to the VR Interface.

The "should be" implies the condition "if the user is not a specialist in computational fluid dynamics, but simply wants to get the results of the computations, as quickly as possible, in a form which he can understand".

This condition is frequently satisfied; and it will be almost universally so in the future, as the CAD-to-CFD traffic increases.

Fig. 2.1-2 shows some of the results of the flow simulation corresponding to the data-input specification of Fig. 2.1-1. The VR-viewer is capable of showing vectors, streamlines, contours and iso-surfaces.

Fig. 2.1-2 The same object in the VR-viewer

2.2 An aeronautical example: the 3-part airfoil

(a) Description of the problem

Creating computational grids to fit bodies with curved surfaces is one of the tedious tasks of conventional CFD; and it wastes the time of highly-paid specialists.

In order to show that it is often unnecessary, a two-dimensional example will be shown, in which a three-part airfoil is represented in a cartesian grid possessing three levels of fineness.

The grid-refinement is easily effected by way of mouse-clicks, and keyboard-entered refinement ratios, in the VR-editor operation.

The first of the following two pictures shows the airfoil itself; and the second shows a close-up of part of it, and of the associated grid.

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Fig. 2.2-1 The three-part airfoil

Fig. 2.2-2 The three-part airfoil;close-up

(b) Handling the obliquely-cut cells via PARSOL

There was a time at which inaccuracies of solution were generated in those cells of the cartesian grid which were cut obliquely by the surface of immersed solids.

Taking extra care about the formulation of the equations relating to such cells has however removed the inaccuracies. Relevant references are Yang et al, 1997 a,b,c; and PHOENICS has its own version of the technique, called PARSOL (standing for PARtial SOLid).

When appropriately implemented, computer codes which employ such techniques can provide solutions of the fluid-flow equations of a quality which is equal to those which employ body-fitted grids.

Because of their superior ease of use, such codes make travel along the CAD-to-CFD road especially smooth.

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The next four pictures show results for the three-part airfoil.

Fig. 2.2.3a Contours of velocity.

Fig. 2.2.3b a closer look

Fig. 2.2.3c and another

Fig. 2.2.4 Contours of pressure.

2.3 A test of PARSOL

As a further demonstration of the accuracy which the cut-cell techniqe can provide, the next two pictures show the results of a study of the inviscid flow in a "turn-around" duct.

The first picture shows the grid, which is rather coarse.

Fig. 2.3-1 The cartesian grid

The second shows the computed pressure distribution, albeit first with an early version of the VR-Viewer, which could not do reflect the cut cells properly. How much depends on the Viewer is shown by a supplementary picture.
This distribution should be perfectly symmetrical; and the one shown is very nearly so.

Fig. 2.3-2a The pressure distribution (with early Viewer)

Fig. 2.3-2b The pressure distribution (with improved Viewer)

The present author knows of no code employing a body-fitted grid with a comparable number of cells which can procure superior symmetry.

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2.4 Flow around an automobile

As a final example, a few pictures are shown from a study, which employed the techniques just described, of the flow around the automobile body specified as a benchmark problem for the 1996 WUA Conference.

These pictures illustrate:-

No body-fitted coordinate code presented results at the conference which were better than these.

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Fig. 2.4-1 the automobile in the VR-viewer

Fig. 2.4-2 the automatically-created grid, side view

Fig. 2.4-3 the automatically-created grid, end view

Fig. 2.4-4 comparison with the experimental data

Click here for more examples of PARSOL

2.5 Concluding remarks about CAD to CFD

The foregoing arguments and examples, while not being conclusive, lend plausibility to the following suggestions:

A competent user of CAD packages who also understands fluid and heat flow from a practical viewpoint, can reasonably expect to become a fluid- and heat-flow predictor after very little acquaintance with the relevant software,

The STL format, being common to the CAD, Virtual Reality and CFD packages, is worth bringing into greater prominence. The good accuracy obtained with cartesian grids, combined with fine-grid embedding and the "cut-cell" technique, may render the more expensive body-fitted-coordinate formulation unnecessary.

When combined with simultaneous solid-stress analysis, to be described in the next section, a very considerable advance in the designer's powers will have been achieved.
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Back to start of lecture Click here for the Encyclopaedia article

Simultaneous Solid-stress, Fluid-flow and Thermal analysis

[Chapter 3 of the lecture CAD to SFT.
Click here for the start of the start of the lecture]

  1. The current practice and its disadvantages
  2. A single algorithm for SFT problems
  3. Examples of SFT analysis
  4. Concluding remarks about SFT

3.1. The current practice and its disadvantages

Engineers often need to make both flow and solid-stress calculations for the same system. However, because of the differing methodologies of the CFD and CASA codes, they find it necessary to use one code for the fluid calculations and another for the stress ones.

There are several disadvantages, namely:-

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3.2 A single algorithm for SFT problems

(a) The basic idea

Fortunately, it is possible to devise an algorithm which will solve the solid-stress equations in one part of the field and the fluid- flow ones in another (see, for example, Spalding, 1997); and this can be (and has been) incorporated in a single computer code.

The basic idea is very simple: it rests on the fact that, when the solid-stress equations are formulated with displacements as the dependent variables, their form is almost identical with those governing the velocities in the fluid-flow regions.

Therefore, provided that the detailed programming work is carefully conducted, displacements can be computed for one part of the field while velocities are being computed for the other; and temperatures (which of course influence displacements in the solid regions and the material properties throughout) are computed simultaneously.

Click here for more details of the mathematics

(b) Current status and future prospects

The SFT technique is rather new, and publications making use of it are only now beginning to appear. The work of the present author and his colleagues has indeed been confined to demonstrating the practicability and accuracy of the technique, before applying it to serious practical problems.

It is however now ready for such applications, of which the following spring to mind:-

So far, only elastic strains have been considered; but there appears to be no obstacle to extending the technique to plastic deformations.

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3.3 Examples of SFT analysis

(a) The thick-walled pipe

The first example shows what happens when a thick-walled horizontal pipe carries a hot fluid inside it, while being immersed in a larger-diameter duct carrying a cooler fluid.

Because of gravity, convection occurs within both fluids; this leads to departures of the temperature field from axial symmetry and so to to non-uniform thermally-induced stresses.

Adding the stress calculation increased computer time very little.

Click to return here after viewing Figures The next four pictures show:-

(b) The radiation-heated convection-cooled block

Further calculations have concerned the situation sketched below, which might represent one of many such elements in an electronics- equipment assembly.

Fig 3.3-5 The system considered.

cooling air ----- :-           duct                    -----:-  exit
           H-------------                 -------------H               
Horizontal H// steel ///|____ cavity _____|/// steel //H Horizontal
Constraint H////////////|_________________|////////////H Constraint
           H////////////// aluminium //////////////////H               
The radiating wall and the cooling air combine to produce temperature gradients in the metal blocks, which have different thermal-expansion coefficients. The task is to compute the resulting stresses.

This task has been performed in the manner described above.

The following pictures display:-

In the present case, the assembly is prevented from expanding downward, and to the left or the right.

Once again, it is scarcely more time-consuming to compute the stresses and strains than not to do so.

All that is necessary is to activate a "solve-for-stresses" switch, and then to supply the necessary boundary conditions. The latter supply information concerning mechanical constraints.

Click to return here after viewing Figures

Fig 3.3-6, velocity and displacement vectors

Fig 3.3-7, x-direction strains

Fig 3.3-8, y-direction strains

Fig 3.3-9, x-direction stresses

Fig 3.3-10, y-direction stresses

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3.4 Concluding remarks about SFT

The foregoing arguments and examples, while not being conclusive, lend plausibility to the following suggestions:

(a) It would have been difficult to conduct SFT analyses of either the horizontal-tube or the two-metal-block problems by the currently-common two-program approach, even though the deformations did not influence the flow of fluid.

(b) If the latter influence had to be taken into account, it would have been almost impossible to do so; the single-program method would however encounter no difficulty.

(c) The fact that the same algorithm (SIMPLEST) works for both velocities and displacements is what allows the unification of the CASA and CFD fields; and, since this unification is so advantageous to engineering designers, its widespread use appears to be limited only by the (understandable) conservatism of the profession.

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4. Modelling turbulence, radiation and chemical reaction

[Chapter 5 of the lecture CAD to SFT. Click here for the start of the start of the lecture] Contents

4.1 The requirements: realism; economy; balance

4.2 The wall distance

4.3 The LVEL turbulence model

4.4 The IMMERSOL model for radiation

4.5 The MFM turbulence model, for turbomachines and combustors

Click here for a complete lecture on the Multi-Fluid Model of Turbulence

4.1 The requirements: realism; economy; balance

The just-described two-metal-block problem can also be used to exemplify the practical difficulties of simulating turbulence, and heat transfer by radiation and convection, in practical circumstances; and indeed, fortunately, means of surmounting them.

The difficulties result from the facts that:-

The wise engineer therefore recognises that, if his simulations are to be usefully realistic, within his economic and hardware constraints, it is crucial that his approach must be well-balanced.

Thus, it is pointless to expend large resources on elaborate low- Reynolds number turbulence models if the grid fineness is hopelessly inadequate; or on complex geometrical view-factor calculations if fluid-participation and wave-length dependences are totally ignored.

Considerations of balance led to not-yet-conventional methods being used in the above example. They will now be discussed.

4.2 The wall distance

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Whatever turbulence model is employed, since the Reynolds number is likely to be low, the distance from the nearest wall must be known.

Computing this was not easy until the introduction of the LTLS method (Spalding, 1994), in which the wall-distance (and also the distance between walls) was computed by solving the equation:

div_grad L = - 1

This elliptic linear equation for a single variable is very easy to solve. In PHOENICS, the solution is carried out swiftly at the start of the computation, and the results are stored for subsequent use.

The following pictures show the resulting distributions of wall- distance and the distance-between-walls, for the two-block problem.

The results are exactly correct wherever the quantities in question have precise meanings; and elsewhere they are "plausible". [The quotes imply a need for discussion, for which there is no space here]

Click to return here after viewing Figures

Fig 4.2-1 The distance from the wall

Fig 4.2-2 The gap between walls

4.3 The LVEL turbulence model

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As has been shown by Aganofer, Liao and Spalding (1996), conventional low-Reynolds-number models (eg Lam and Bremhorst, 1981) are computationally expensive and of doubtful realism.

However, there exists a simpler, more economical, and (in these circumstances) equally realistic model, which is described in that paper, and used here. This is the so-called LVEL model, which derives the local effective viscosity from the wall distance, the distance between the walls, and the local velocity.

The following picture shows the effective-viscosity distribution computed for the two-block problem.

Once again, it can be proved that the predicted distribution is precisely correct in simple circumstances, and plausible elsewhere.

Click to return here after viewing Figures

Fig 4.3-1 The effective viscosity

Click here for the PHOENICS Encyclopaedia article on LVEL

4.4 The IMMERSOL model for radiation

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(a) The general idea

If turbulence modelling in domains which are crowded with immersed solids is difficult, no less so is the computation of the radiative heat exchange between the solids and the intervening medium.

In the results presented above, use was made of the IMMERSOL (ie IMMERsed SOLids) method (Spalding, 1996). This represents radiative transport of energy by way of a diffusion equation for radiosity, in which the diffusivity is proportional to:

1 / [ A + S + 1 / WGAP ]

where A and S are the absorption and scattering coefficients of the medium per unit length, and WGAP is the distance between solid walls.

Further formulae represent the radiosity jump at phase boundaries, and so enable the radiosity in the medium and the temperature in the solids to be computed from the solution of one (non-linear) equation.

(b) Results for the two-metal-block problem

In the following pictures, contour diagrams will be presented. These will display, in order:-

All these quantities were of course computed simultaneously with the above-presented velocities which influenced them, and with the displacements and stresses which they caused.

The computations were completed within a few minutes, by the PHOENICS computer code mounted on a Pentium personal computer.

The results are plausible; but experimental verification is needed.

Click to return here after viewing Figures

Fig 4.4-1 Gas and solid temperature

Fig 4.4-2 The radiosity temperature

Fig 4.4-3 y-direction radiation flux

Fig 4.4-4 x-direction radiation flux

(c) Concluding remarks about WDIS, WGAP, LVEL and IMMERSOL

The following points should be recognised in conclusion:

4.5 The MFM turbulence model, for turbomachines and combustors

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Contents of section 4.5

  1. The fundamental ideas
  2. Why turbo-machinery designers need MFM
  3. A two-fluid-model prediction for turbo-machinery
  4. MFM for combustion processes
  5. The significance of the 2D population distribution
  6. An example; smoke production in a 3D gas-turbine-type combustor
  7. Discussion of the MFM smoke calculation
  8. Concluding remarks about MFM and its future

(a) The fundamental ideas

There are currently three approaches to the quantitative prediction of turbulent-flow phenomena, namely:-
  1. use of Kolmogorov-type models which solve equations for quantities such as energy and dissipation, ie k and epsilon;
  2. use of Monte Carlo methods, seeking to compute probability- density functions (ie PDFs) for important variables; and
  3. use of multi-fluid models (ie MFMs), which can be regarded computing DISCRETISED PDFs (Spalding, 1995).
Approach (1) is almost universally followed; but, lacking the necessary physics, it MIS-guides designers of (eg) gas-turbines.

Approach (2), of Dopazo/O'Brien type, is followed by some combustor specialists; but its expense deters all but the wealthiest.

Approach (3), of the same type, has been little publicised; but it is economical, easy to use, and contains the necessary physics.

(b) Why turbo-machinery designers need MFM

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Axial-flow compressors and turbines, as used in aircraft propulsion and in ground- (or sea-) level power production, are characterised by the rapid passing of one blade row behind another.

The slower-moving boundary-layer fluid from the upstream row becomes a "wake" of slower-moving fluid fragments, which are distributed across the entrance plane of the downstream row.

The turbulent mixture which passes from row to row through a turbo- machine is therefore best represented as a population of fluids, with (say) axial velocity as their distinguishing characteristic.

Approach (3), ie use of MFM, is a practicable means of calculating the population distribution and its influence on the mean flow.

Research on the exploitation of this possibility is only now starting; but its promise appears to be very great. Further research on Kolmogorov-type models is now hard to justify.

Click to return here after viewing Figures

(c) A two-fluid-model prediction for turbo-machinery

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The lowest member of the MFM family is the two-fluid model (Spalding, 1987), with which some recent studies have been made.

There follow two pictures which show how the time-mean velocity distribution of a blade row differs according to whether a two- fluid or (as is customary) a single-fluid model is presumed.

The differences are qualitatively similar; but the small quantitative differences are what counts when blade-row losses are to be computed.

If two-fluid calculations can already provide meaningful guidance to turbo-machinery designers, much more can be expected from the full MFM treatment.

Unfortunately, most turbo-machinery researchers still follow each other down the approach-1 tunnel, with no light at the end!

Click to return here after viewing Figures

Fig 4.5-1 Radial-velocity contours at outlet ; 1 fluid

Fig 4.5-2 Radial-velocity contours at outlet ; 2 fluids

(d) MFM for combustion processes

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Combustion-chamber designers need to be concerned that their designs not only burn their fuels efficiently but also reduce to the minimum the production of atmospheric pollutants such as smoke and oxides of nitrogen.

To try one design variant after another is hopelessly expensive of time and money; so computer simulation is their main recourse.

Computer simulation may, of course, be MISleading; and it is likely to be so if the models built into the computer code do not embody the best physical knowledge about the relevant processes.

A realistic MFM model of gas-turbine combustion would supposes that the gases at any location constitute a population distinguished at least two-dimensionally, the dimensions being:

At a particular location, the population distribution might be:

Click to return here after viewing Figures

Fig 4.5-3: a two-dimensional (reactedness/fuel-air ratio) population

(e) The significance of the 2D population distribution

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The random coloured circles on the right illustrate the physical conception underlying MFM; each colour represents a different discrete-fluid state.

The proportions of fluid in each state are represented by the fullnesses of the 2D array of boxes on the left. They are what MFM calculates; and each of the 100 fluids considered here has its own temperature, smoke- and NOX-production rate, velocity, and so on.

A conventional single-fluid model would work out the average fuel- air ratio and the average degree of reactedness, and deduce the smoke- and NOX-production rates from those quantities; but it would be wrong. The reason is that the rate expressions are non-linear.

In mathematical terms:

the average of (A x B) is NOT equal to the average of (A) x the average of (B) .

In human terms, a day-worker wife and a night-worker husband may NEVER meet sufficiently to have offspring.

(f) An example; smoke production in a 3D gas-turbine-type combustor

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This subject is a large one, which cannot be sufficiently discussed in the present context. It must therefore suffice to state that predictions of smoke (or NOX) production are totally different for single- and for multi-fluid models. An example follows.

This concerns smoke production in an imaginary 3D combustor, into which is injected a fuel-rich gaseous mixture at one location and pure air at a succession of other locations.

The following picture shows the distributions of smoke concentrations at the outlet cross-section based on:-

  1. a conventional single-fluid model;
  2. a five-fluid model;
  3. a ten-fluid model; and
  4. a twenty-fluid model.
This example illustrates an important point: "population-grid- refinement" is possible with MFM: one should use only enough fluids.

Click to return here after viewing Figures

Fig 4.5-4 Smoke predicted by a conventional single-fluid model

Fig 4.5-5 Smoke predicted by 5-fluid model

Fig 4.5-6 Smoke predicted by 10-fluid model

Fig 4.5-7 Smoke predicted by 20-fluid model

(g) Discussion of the MFM smoke calculation

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Comparison between the diagrams shows that there is very little difference between the smoke predictions for 10 and for 20 fluids; so it will better to use the smaller number, to save computer time.

Computer times are, in any case, not very large, that for 20 fluids being only three times that for a single fluid.

However, when 100 fluids (say) do prove to be necessary on grounds of accuracy, there are many available means of reducing the computer times.

For example, there is no need to employ the same number in all parts of the field; instead, the number can be varied according to the local behaviour of the solution.

Once, indeed, that it is recognised that MFM entails nothing more than discretizing dependent variables in the same way as is routine for independent ones (space and time), the well-known techniques of grid-adaptation become available.

(h) Concluding remarks about MFM and its future

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New turbulence models need to be tested, by comparison of predictions with experiments, before they can be relied upon as the basis for serious engineering designs.

Performing the tests may be expensive, in man-power at least; so the case for committing the expenditure must be closely argued.

The case for testing MFM rests on three considerations, namely:-

  1. evident need, demonstrated by the failure of Kolmogorov-type models for turbo-machines and combustors;
  2. the inherent plausibility of the basic idea, and its embodiment of sufficient physics to represent (in turbo-machines) the relative motion of the faster- and slower-moving fluids; and (in combustors) their differing reaction rates;
  3. recognition that it does what Monte-Carlo-based methods aim to do, but with much less expense.
In practice, it is the first consideration that many find it hardest to accept; for those who have spent, and are still spending, much money on Kolmogorov-type computations are reluctant to admit the inadequacy of the underlying model.

Consideration (2) is easily understood by scientists, but less easily by those for whom novelty is a synonym for danger. It is, unfortunately (but for good reasons) the latter who are usually put in charge of decisions about money.

It is for them that consideration (3) has been cited; for it implies that MFM is not totally novel, and therefore not extremely dangerous; and it indicates that there is money (currently being spent on Monte-Carlo) which can be saved.

The author's view is that, within ten years, MFM will have become accepted, fashionable and (probably too-credulously) widely used; it certainly needs serious attention from aeronautical engineers right now; and researchers into direct numerical simulation could assist by casting their results in MFM form.

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5. The revival of remote computing

[Chapter 5 of the lecture CAD to SFT.
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5.1 The three deterrents to the wider use of SFT

So far, this review has drawn attention to three promising developments:-
  1. the building of a smooth CAD-to-CFD highway;
  2. the absorption of CFD and CASA into SFT; and
  3. the creation of physical models of improved economy and realism.
However these developments will have only limited impact on engineering practice until three deterrents to the wider use of computer-simulation techniques, especially by small and medium enterprises, can be significantly diminished. These deterrents are:
  1. the cost of the software;
  2. the cost of hardware of sufficient power to run many fine-grid simulations; and
  3. the scarcity and expense of personnel capable of using them.

5.2 The MICA project

(a) Objective and nature

MICA is an EC-funded project designed to show how a "remote- computing" service can diminish the above-mentioned deterrents.

MICA is an acronym for Model for Industrial CFD Applications. It has been conducted by a consortium of companies and universities from nine European countries, namely:

INRIA (France); U Paderborn and U Erlangen (Germany); NTU Athens (Greece); IST-Lisbon (Portugal); Hoogovens and Stork-Comprimo (Holland); CMR (Norway); U Zaragoza (Spain); Vattenfall and SMHI (Sweden); CHAM, BRE and WAT&G (UK).

The general idea is that:-

(b) Customization

Ten application sectors were selected for attention, namely:
  1. Oil-platform explosions
  2. Smoke movement and fire spread in buildings
  3. Heating and ventilating of buildings
  4. Air and pollutant flow around assemblies of buildings
  5. Flow around marine structures
  6. Coal-fired industrial furnaces
  7. Glass-melting and refining furnaces
  8. Annealing furnaces
  9. Industrial ovens
  10. Steam condensers for power stations

(c) Validation

The partners in the project were divided into creators, validators, and end-users; and the aim was to demonstrate that the remote- computing concept could be used cost-effectively and comfortably.

Validation was therefore of several kinds, the questions to be answered being:

It is the first four questions, of course, which relate to the remote-computing service. The last is about CFD, regardless of how it is provided; and the author's views on it have appeared above.

(d) Current status

The two-year MICA project, due for completion at the end of 1997, will over-run by four months; and, since validation is an infinitely extensible activity, its end will inevitably leave some questions still unanswered

It is however safe to assert already:

The advisory aspect is the least-well developed; and its satisfactoriness will in any case take longer to be assessed.

Overall, participants in and observers of MICA regard the project as successful, and have concluded that remote computing, which rose to prominence in the sixties, then (almost) disappeared in the seventies, will soon become prominent again, and will remain so.


So strongly do some of them believe in the above conclusion that they are preparing to launch a world-wide service, of which the current (but not yet final) name is SIMUSERVE.

This will follow the MICA model, and especially the ingredients of:

"On-tap" is an appropriate phrase; for SIMUSERVE has been described as providing, for the CAE-using world, the equivalent of "piped water", in distinction from the "bucket-and-well" technology to which the current own-software-own-hardware practices correspond. SIMUSERVE is due to be launched in the second half of 1998.
It will provide the whole range of services which form CHAM's "solution spectrum" , except for the two traditional extremes, namely consultancy at the one end and stand-alone-software sales at the other.

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6. Concluding remarks

At the end of this review of computer-aided engineering, or rather of that limited part of it with which he has some acquaintance, the present author finds himself optimistic about the future.

There have been disappointments, admittedly; for example:

  1. the turbulence models which came to prominence in the early seventies have proved to be less and less satisfactory the more they are used and studied;
  2. what early CFD-code developers thought were easy to use were found quite otherwise by those to whom they were provided;
  3. even now, scarcely any CFD calculations are carried out with grids which are fine enough for assured accuracy; and
  4. some CFD-code vendors, by claiming too much, have spread disillusionment among practical engineers.
Nevertheless, there are reasons or optimism; and specifically:-
  1. the scarcely-yet-explored multi-fluid turbulence models open vast new vistas;
  2. true ease of use now been made possible by exploiting techniques developed for the general computer-using populace (and especially children), such as virtual reality;
  3. the previously-separate worlds of stress analysis and CFD appear to be amenable to merging into SFT; and
  4. remote parallel computing, with "on-tap" advice, will greatly enlarge the number of engineers who can afford to use the simulation, analysis and design techniques.
Perhaps, when these advances have been made, engineers will soon be enabled to advance from CAD-1 all the way to CAD-2. Back to top

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7. References

Agonafer D, Liao G-Li, Spalding DB (1996) "The LVEL turbulence model for conjugate heat transfer at low Reynolds numbers" EEP6, ASME International Mechanical Congress and Exposition, Atlanta

Dopazo C and O'Brien EE (1974) Acta Astronautica vol 1, p1239

Kolmogorov AN (1942) "Equations of motion of an incompressible turbulent fluid"; Izv Akad Nauk SSSR Ser Phys VI No 1-2, p56

Lam CKG and Bremhorst K (1981) ' A modified form of the k-e model for predicting wall turbulence', ASME J Fluids Engng, Vol 103, p456.

Pope SB (1982) Combustion Science and Technology vol 28, p131

Spalding DB (1987) "A turbulence model for buoyant and combusting flows"; International J for Numerical Methods in Engineering vol 24, pp 1-23

Spalding DB (1994) Poster Session. International Heat Transfer Conference, Institute of Chemical Engineers, London. See also: PHOENICS Encyclopaedia, article on Turbulence Models in PHOENICS, section on LVEL.

Spalding DB (1995) "Models of turbulent combustion" Proc. 2nd Colloquium on Process Simulation, pp 1-15; Helsinki University of Technology, Espoo, Finland

Spalding DB (1996) "PHOENICS Encyclopaedia, article on Radiation Models in PHOENICS, section on IMMERSOL"

Spalding DB 1997, "Simultaneous fluid-flow, heat-transfer and solid- stress computation in a single computer code"; keynote lecture 4th International Colloquium on Process Simulation, Helsinki University of Technology, Espoo, Finland

Yang G, Causon DM, Ingram DM, Saunders R and Batten P, 1997a "A cartesian cut cell method for compressible problems. Part A: static-body problems; part B: moving-body problems" Aero J Roy Aero Soc Feb 1997 pp 47-65

Yang G, Causon DM, Ingram DM, 1997, "Calculation of 3-D compresible flows around moving bodies"; 21st International Symposium on Shock Waves, Australia, July 20-25 Back to top

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