(a) CAD-1; computer-aided 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.
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.
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:-
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.
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.
(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.
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.
(1) 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.
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.)
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.
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
[Chapter 2 of the lecture CAD to SFT.
Click here for the start of the lecture]
2.2 An aeronautical example: the 3-part airfoil
2.5 Concluding remarks about CAD to CFD
Further examples of PARSOL, including moving grids
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.
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:-
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
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
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.
Fig. 2.2-1 The three-part airfoil
Fig. 2.2-2 The three-part airfoil;close-up
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.
The next four pictures show results for the three-part airfoil.
Fig. 2.2.3a Contours of velocity.
Fig. 2.2.4 Contours of pressure.
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.
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.
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:-
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
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
[Chapter 3 of the lecture CAD to SFT.
Click here for the start of the start of the lecture]
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:-
(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.
(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:-
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.
RRRRRRRRRRRRRRRRRRR radiating wall RRRRRRRRRRRRRRRRRRRRR cooling air ----- :- duct -----:- exit H------------- -------------H Horizontal H// steel ///|____ cavity _____|/// steel //H Horizontal Constraint H////////////|_________________|////////////H Constraint H////////////// aluminium //////////////////H H///////////////////////////////////////////H IIIIIIIIIIIIIIIIIIII insulated wall IIIIIIIIIIIIIIIIIIIIThe 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
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.
[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
4.4 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
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:-
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.
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
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
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.
In the following pictures, contour diagrams will be presented. These will display, in order:-
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
Contents of section 4.5
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.
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
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
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:
Click to return here after viewing Figures
Fig 4.5-3: a two-dimensional (reactedness/fuel-air ratio) population
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.
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:-
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
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.
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:-
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.
[Chapter 5 of the lecture CAD to SFT.
Click here for the start of the start of the lecture]
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:-
Validation was therefore of several kinds, the questions to be answered being:
It is however safe to assert already:
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.
This will follow the MICA model, and especially the ingredients of:
There have been disappointments, admittedly; for example:
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