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CFD as applied to combustion: past, present, and future


Brian Spalding, of CHAM Ltd

March, 1999


Computational fluid dynamics has been applied to the prediction of the perfomance of combustion processes since the 1960s.

This lecture briefly:


  1. The past
  2. The present
  3. The future
  4. Conclusions
  5. References

Note: Figures, the titles of which are indicated by underlining, are not provided in the printed paper. They may be inspected, together with the text, on the web-site: www.cham.co.uk

1. The past

  1. Pre-CFD; the combustion analogue
  2. The first CFD computations
  3. The first experimental research
  4. Concluding remarks about the early years

1.1 Pre-CFD; the combustion analogue

Before digital computers were developed, engineers wishing to simulate physical processes employed analogue computers; and, just at the end of the "analogue era" (approx 1955), one of these was created for the simulation of combustion processes [Reference 1].

It may be worth considering, because the concept led naturally to the first digital-computer models.

The concept was this:-

Such an apparatus was created, by the present author; the heater/thermocouple pairs were arrayed on a two-dimensional cartesian grid; and the relation between the heat input and the local temperature was contrived by manual adjustment.

The phenomenon of the extinction of baffle-stabilised flame was indeed predicted; and it could be truly claimed that agreement between the predictions and actual combustion experiments was as satisfactory as could be expected, in view of the crudeness of the rate-versus-temperature expression, and of the fact that the density variations which are present in real combustion chambers were not simulated.

The studies were not confined to uniform-composition gases, but extended also to flows in which the fuel and oxidant entered in separate streams.

Re-reading Reference 1 for the first time in more than forty years, the present author is impressed by:-

It may be interesting to remark that:

In some respects, the combustion-analogue proposal was too far in advance of its time. Thus Stephen Bragg himself had just (1956) published a much-acclaimed paper [Reference 3] on a zero-dimensional model of the extinction of flames; whereas the analogue was already two-dimensional, and was capable of being extended to three dimensions.

However, it was also behind the times; for the digital computer was already beginning to be used for simulating simple combustion processes [Reference 4]; and before long even the present author, whose first (approx 1954) numerical computations had been performed by graphical means [Reference 5], had "gone digital" [Reference 6].

The graphical method, it might be remarked, was very educative; for its user could feel as though he were a part of the flame-development process, which, in a sense, he was.

1.2 The first CFD computations


  1. The 2D parabolic model
  2. The stream-function-vorticity model
  3. The first (but over-looked) 3D model
  4. The 3D model which the world followed

a. The 2D parabolic model

Further advances into the digital-computer age were a consequence of the arrival at Imperial College, as graduate students, of three persons, namely:

Patankar's thesis of 1967 [Reference 7] made no mention of combustion; but the numerical method which was described in it was subsequently incorporated by the present author (approx 1969) into the GENMIX computer code [Reference 8], in the exemplification of which the combustion of methane with air played an important part.

This computer code could simulate laminar and turbulent flame jets; and it was later (1971) used for the prediction of laminar flame propagation [Reference 9]. However, it was not able to simulate combustion phenomena in which "recirculation", ie reverse flow, played a significant part; so something else had to be devised.

GENMIX will be made available for down-loading from CHAM's website, if there is a demand.

b. The stream-function-vorticity model

The "something else" was the "stream-function-vorticity" method (approx 1968) which, after much travail, became for a few years the main means for computing recirculating flows.

So far as the present author recalls, the main ingredients were:-

The computer programming and testing were carried out by Akshai Runchal and Micha Wolfshtein; and the theory and results (including the program) were published as a book in Reference 10 (1969).

Although Runchal and Wolfshtein had been concerned only with non-reacting flows, the present author and WM Pun had been applying the same methodology to flows with chemical reaction.

This work was reported in a separate publication [Reference 11], perhaps the very first (1968) publication in which CFD was applied to a recirculating flow exhibiting combustion. Click here for results. The computer program was included as a final chapter of Reference 10.

Shortly afterwards it was used by British Coal Utilisation Research Association (Morgan and Gibson, 1977) as the basis of the first model of a coal-fired furnace. The size distribution of the particles was one of the features calculated.

Once again it is necessary to remark that the physical modelling was naive, and that the mathematical method (stream-function-vorticity) ultimately proved not to be easily extensible to three dimensions. However, significant forward steps had been taken.

c. The first (but over-looked) 3D model

The Imperial College team was slow in deciding which was the best way to handle three-dimensional problems, at first hoping that stream-function-vorticity methods could be generalised. Reference 12 exemplifies this aspiration.

The best first step in the 3D direction was probably the SIVA (SImultaneous Variable Adjustment) procedure about which a publication [Reference 13] eventually emerged. This contained, incidentally, an application to combustion.

It was however the same paper which explained how the "SIMPLE" procedure, hitherto used only for 3D boundary layers, could also be used for re-circulating flows; and it was finally SIMPLE rather than SIVA which was then preferred.

However, it is proper now to recognise that the first person to devise a method for and publish a paper (1972) on CFD applied to a 3D furnace, was Ingo Zuber, of Czechoslovakia [Reference 14]. His achievement is all the more praiseworthy because, in the circumstances of the country and the times, Zuber's access to Western scientific literature, and his computer resources, were both extremely limited.

d. The 3D model which the world followed

Much more notice was taken of the publication which recorded the techniques finally (or at least for a long time) adopted by the Imperial College group), namely the 1974 publication of Patankar and Spalding [Reference 15].

This employed:

This method was widely disseminated by the authors and their colleagues at Imperial College; and it was extensively adopted by others during the following years.

1.3 The first experimental research

To bring to a close this review of the more remote past, the PhD thesis of Amr Serag-Eldin [Reference 16] will be mentioned. His work at Imperial College between 1973 and 1976 was probably the first ever carried out specifically for testing whether a CFD code was capable of predicting the performance of a steady-flow combustor of gas-turbine type.

The thesis was exemplary in its thoroughness and honesty. Of especial interest, in view of subsequent experiences, are the following extracts from Amr's preface:

Right at the start, therefore, of the researches devoted to testing the validity of CFD-based prediction procedures for combustion, questions arose about how the influences of concentration fluctuations and chemical kinetics, and especially the interactions between them, were to be introduced into the model.

These questions have remained incompletely resolved until the present day!

The improved models referred to, which took account of fluctuations but not (adequately) of chemical kinetics, were those of References 17 and 18 (1971) namely the "eddy-break-up" and "presumed-pdf" methods.

In somewhat modified forms, they are still (regrettably?) in widespread use.

1.4 Concluding remarks about the early years

The foregoing review reveals that, by the mid-1970s, CFD-for-combustion had become a reality.

Adequate means had been discovered and published for solving the relevant equations; and only more computer power would be needed to enable large and geometrically complex problems to be solved.

Moreover, models of turbulence, chemistry and radiation had been devised which, though far from perfect, were enabling predictions to be made, on occasion, of a quality justifying hope that steadily conducted research would soon make them very good.

Although it was to the gas turbine that most attention was given, because of the financial support which could be then obtained from the aerospace industry, attention also began to be paid to the reciprocating engine, to power-station furnaces and to fire hazards.

Thus, the present author has found among his papers a 1969 proposal, made at a meeting of the Institution of Mechanical Engineers in London [Reference 19] for the application of CFD to the Diesel engine; and Patankar and he presented a paper concerned with applications to furnaces in 1972 [Reference 20].

Readers of the remainder of the present paper may well conclude that the optimism of those early years has proved to be sadly falsified by subsequent achievements.

Click here for a historical summary made in 1995.

2. The present

  1. The use of commercial computer codes
  2. The numerical methods
  3. The physical models
  4. The widening of the field of application
  5. The overall degree of success

2.1 The use of commercial computer codes

It could be reasonably argued that it was the needs of the combustion engineers in the aero-space industry which brought the CFD-software business into existence, the reason being that the complexity of the combustion process left expensive experimentation as the only alternative.

Certainly, some of the first computer codes sold by CHAM to UK and US gas-turbine manufacturers were specifically for combustor simulation; for the desigers of the other gas-turbine components, ie the compressor and the turbine, already possessed computer-based methods which they judged (perhaps unwisely) to be satisfactory.

Several of those combustor codes are still in existence and use, having of course also been significantly further developed by their users; and at least one of them entered the public domain by way of the US Army, enabling competing CFD-code vendors to start business; which they did with alacrity.

Maintaining and refining a special-purpose computer code is an expensive and arduous business, which few organizations can afford. It has therefore proved more cost-effective to create and maintain a few general-purpose computer codes, which can be applied to special-purpose problems.

This strategy was first exemplified by CHAM's PHOENICS code, released in 1981, and Creare's FLUENT code released in 1983. Both were capable of simulating either reacting or non-reacting flows. Every few years since then, in one country or another, further general-purpose codes with similar capabilities have made their appearance.

As a consequence, almost all industrial companies using CFD techniques, for designing and improving their equipment or processes, nowadays buy or lease software from one of the CFD-software vendors.

2.2 The numerical methods

The numerical methods which are most commonly employed differ little, in essence, from those of Reference 15. The major novelties are:

The consequence of these developments, coupled with the immense increase in the power of computer hardware, is that it is now possible for CFD models to be set up which fit the geometrical complexities of the equipment very well, yet still provide accurate numerical solutions in an acceptable time.

Whether the numerically accurate solutions provide realistic predictions of how the combustors will actually behave is, of course, quite another matter; for realism depends on the physical models which are employed and on the correctness of the material properties which are supplied to them.

This will be discussed in the next section.

2.3 The physical models

The advances on the numerical side of modelling have not, unfortunately, been matched by corresponding successes on the physical side. Nevertheless, there have been several developments, of which the outcomes most in evidence currently are:

  1. chemical-kinetics models of great complexity, both for hydrocarbon combustion and for the reactions giving rise to oxides of nitrogen;
  2. detailed improvements of turbulence models of the k-epsilon type;
  3. modifications of the "eddy-break-up" model for predicting the influence of the turbulence energy and scale on the time-average reaction rates [Reference 23](1976);
  4. modifications of the "presumed-pdf" approach for the representation of the effects of concentration fluctuations on the rates of production of particular chemical species, for example NOX and "smoke" [Reference 24](1980);
  5. methods of avoiding the arbitrariness of the "presumed-pdf" approach by computing the pdfs (ie probability-density functions) from more-rigorously-based "pdf-transport methods" [Reference 25](1982).

Much valuable work has been done; but, in the present author's opinion, reservations must be expressed about each of the items mentioned, as follows:

  1. There is still no agreement about which "reduced-chemistry" model represents the best compromise in respect of realism and computational economy.
  2. The improvements recommended by various authors differ, with the result that none have been generally accepted.
  3. The "eddy-break-up" model requires not to be improved, but replaced; for it represents (as does the flamelet model) a turbulent reacting mixture as the mingling of just two distinct fluids; and two is too small a number to do justice to reality.
  4. The presumptions about pdf shape lack general validity, and are used more "because one must use something" than for plausible reasons.
  5. The pdf-transport method, although admirable in intention, has been held back by its reliance on the computationally expensive Monte Carlo method, for which reason it is little used in engineering practice.

2.4 The widening of the field of application

Despite the shortcomings just alluded to, the use of CFD for combustion sumulation has become widely accepted as being a valuable aid to the designers and operators of equipment, and to those who are concerned with its environmental and safety impacts.

A short list of active application areas now follows, but without references, because a balanced list would be too large:

At least in this respect, ie the widening of the field, the optimism of the early 1970s has been vindicated.

2.5 The overall degree of success

The success of the CFD-for-combustion campaign could be called complete if nowadays all designs of combustion-related equipment were near-finalized by the use of CFD predictions, and experimental verification were called for only at the end, to ensure that the predictions had been near-enough correct.

This is NOT the situation at the present time, for any of the fields of application; and, as the years go by, its attainability has appeared less rather than more probable.

As computers have increased in power, and mathematical methods improved in efficiency, it has become less and less justifiable to blame the discrepancies between predictions and measurements on the coarseness of the grid or the inability to procure complete convergence.

The deficiencies of the underlying physical models have become, as a consequence, increasingly obvious.

Deficiencies of this kind are much harder to remove than are those of the numerical kind. Computer scientists abound who can improve hardware and software; and mathematicians who can devise more efficient algorithms are also not rare.

An advance in science, however, which is what CFD-for-combustion now requires, depends on rare combinations of circumstance, namely:

In what particular sector of combustion science are "bright ideas" most needed? In the view of the present author it is that concerned with turbulence-chemistry interactions. This opinion will be further developed in part 3.3 of the present paper.

3. The future

  1. The use of Internet-based services
  2. The reduced use of body-fitted coordinates
  3. The models of turbulence and chemistry

3.1 The use of Internet-based services

The future of CFD-for-combustion will be influenced by general developments in the way CFD will be used. It is thefore worth turning for a moment from the particular to the general.

In the view of the present author, the most significant change that will come about will be through the use of the Internet.

The reason is that there exist three deterrents to the wider use of computer-simulation techniques, especially by small and medium-sized enterprises; these 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.

However, techniques are already available, and are being continuously improved, for enabling an engineer with a flow-simulation problem to have it solved by:

In order to illustrate the CAD-to-CFD part of this, a 1997 example will be shown during delivery of the lecture, wherein a domestic gas burner was simulated. This particular calculation was, as it happens, not performed remotely; but it could have been.

The change that seems likely to come into being has been characterised as like that in society when "bucket-and-well" technology was replaced by "piped water".

When low-cost and quality-assured computations are available to all "on-tap", and on payment-according-to-use terms, it seems likely that many combustion engineers will choose that way of working.

3.2 The reduced use of body-fitted coordinates

The user of the remote computing service will not care on what computational grid his or her combustor simulation has been conducted; so he will be able to concentrate his attention only on the physical results.

However, that freedom from worry lies a few years in the future; therefore, until then, the CFD-code user will still need to concern himself with what grid to use in order to fit his geometry.

It is widely believed that the only way to represent curved-wall combustors, and such small but important features as fuel nozzles and air-injection holes, is to use unstructured body-fitted coordinate grids. However, since the creation of such grids is often troublesome and expensive, it seems probable that better ways will be sought and found.

Indeed, one such "better way" has been found quite recently. It has been published on CHAM's website [Reference 26]; and it seems probable that, unless something even better comes along, the techniques described there, namely "PARSOL" and "fine-grid embedding", will be widely used.

If so, body-fitted-coordinate grids will figure less often in the combustor simulations of the future.

3.3 The models of turbulence and chemistry

However, as has been emphasised above, easily-conducted simulations, whether conducted remotely or at home, may be of little use (and even dangerous, when too much trusted) if they are not based upon realistic physical models.

It is therefore appropriate for the present author to disclose his belief that the "multi-fluid model (MFM) of turbulent combustion" [Reference 27] is likely to play a significant role in future applications of CFD to combustion.

It is not possible to provide the justification for this belief in the present paper; but, during the presentation of the lecture, some material from two recent lectures will be shown.

The first [Reference 28] concerns the practicalities of using MFM for predicting smoke generation in a gas-turbine combustor.

The second [Reference 29] is of a more scientific character. It shows how MFM comprehends a wide range of combustion phenomena; and it provides a framework into which "laminar-flamelet models" can be fitted, for those circumstances in which they apply.

Some highlights from the paper in question will be shown during the lecture.

4. Conclusions

The foregoing review, and the arguments presented in References 28 and 29, incline the present author to the following views:

  1. Although the high hopes of the early years of CFD-for-combustion have not yet been realised, the obstacles are being removed or eroded significantly.
  2. The power of computers, and especially those of parallel architecture (which includes clusters of PCs), enables geometries of realistic complexity to be simulated;
  3. The development of Internet-based CFD services will make this power available to everyone, on a convenient pay-by-use basis.
  4. The use of body-fitted and unstructured grids will be increasingly replaced by cartesian grids, enhanced by the "cut-cell" technique, i.e. PARSOL.
  5. It will thus be possible for engineers to export their CAD-geometry files directly into the CFD code, whether this is on their own computer or on the other side of the world.
  6. The multi-fluid model of turbulence will make it possible to investigate, with greater realism than has hitherto been possible, how the main and secondary chemical reactions are influenced by turbulence.

5. References

  1. DB Spalding (1957) "Analogue for high-intensity steady-flow combustion phenomena", Proc. I Mech E London, vol 171, no 10, pp383-411
  2. JH Chesters, RS Howes, IMD Halliday & AR Philip (1949), J Iron & Steel Inst vol 162, no 4, pp 385, 392, 401
  3. SL Bragg, JB Holliday (1956) "Selected Combustion Problems, II", Butterworth's, London, p 270
  4. Spalding DB, Some Fundamentals of Combustion Butterworth's, London, 1955, p 162
  5. JO Hirschfelder, CF Curtiss & DE Campbell (1953), J Phys Chem vol 57 p 403
  6. J Adler & DB Spalding (1961) "One-dimensional laminar flame propagation with an enthalpy gradient", Proc Roy Soc A vol 261, pp 53-78
  7. SV Patankar & DB Spalding (1967) "Heat and mass transfer in boundary layers", Morgan-Grampian, London
  8. SV Patankar & DB Spalding (1970) "Heat and mass transfer in boundary layers; 2nd edition", Morgan-Grampian, London
    See also:
    DB Spalding (1977),"GENMIX; a general computer program for two-dimensional parabolic phenomena" Pergamon Press, Oxford
  9. DB Spalding & PL Stephenson (1971)"Laminar flame propagation in hydrogen & bromine mixtures", Proc Roy Soc A vol 324, pp 315-337
  10. AD Gosman, WM Pun, AK Runchal, DB Spalding and M Wolfshtein (1969), "Heat and mass transfer in recirculating flows", Academic Press, London.
  11. WM Pun and DB Spalding (1968)"A procedure for predicting the velocity and temperature distributions in a confined, steady, turbulent, gaseous diffusion flame", Proceedings of 18th International Aeronautical Congress, Belgrade, 1967, published by Pergamon Press, London.
  12. LS Caretto, RM Curr & DB Spalding (1972), "Two numerical methods for three-dimensional boundary layers", Computer Methods in Applied Maths & Engg, vol 1, no 1, pp 39-57
  13. LS Caretto, AD Gosman, SV Patankar and DB Spalding (1973), "Two calculation procedures for steady, three-dimensional flows with recirculation", Proc, 3rd Int Conf on Numerical Methods in Fluid Mechanics, Springer Verlag
  14. I Zuber (1972),"A mathematical model of the combustion chamber", Staatliches Forschungsinstitut fuer Maschinenbau, Bechovice, Czechoslovakia
  15. SV Patankar and DB Spalding (1974) "Simultaneous predictions of flow patterns and radiation for three-dimensional flames" in Heat Transfer in Flames, NH Afgan and JM Beer (Eds) John Wiley
  16. MA Serag-El-Din (1977),"The nemerical prediction of the flow and combustion processes in a three-dimensional combustion chamber" London University PhD thesis, Imperial College, Mech Eng Dept
  17. DB Spalding (1971) "Mixing and chemical reaction in confined turbulent flames"; 13th International Symposium on Combustion, pp 649-657 The Combustion Institute
  18. DB Spalding (1971) "Concentration fluctuations in a round turbulent free jet"; J Chem Eng Sci, vol 26, p 95
  19. DB Spalding (1969),"Predicting the performance of Diesel Engine Combustion Chambers", Proc I Mech E vol 184 pp241-251
  20. SV Patankar & DB Spalding (1972)"Mathematical models of fluid flow and heat transfer in furnaces", 4th Symposium of Flames & Industry; Predictive Methods for Industrial Flames, pp 1-5
  21. FC Lockwood and NG Shah (1981),"A new radiation solution method for incorporation in general combustion prediction procedures"; 18th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh.
  22. WA Fiveland (1984) "Discrete-ordinates solutions of the radiative-transport equation for rectangular enclosures"; J Heat Transfer, vol 106, pp 699-706
  23. BF Magnussen and BH Hjertager (1976) "On mathematical modelling of turbulent combustion with special emphasis on soot formation and combustion". 16th Int. Symposium on Combustion, pp 719-729 The Combustion Institute
  24. Bray KNC in Topics in Applied Physics, PA Libby and FA Williams, Springer Verlag, New York, 1980, p115
  25. SB Pope (1982) Combustion Science and Technology vol 28, p131
  26. DB Spalding (1999) "The use of CFD in the design and development of gas-turbine combustors"; www.cham.co.uk; shortcuts; CFD
  27. DB Spalding (1995) "Models of turbulent combustion" Proc. 2nd Colloquium on Process Simulation, pp 1-15 Helsinki University of Technology, Espoo, Finland
  28. DB Spalding (1998) The simulation of smoke generation in a 3-D combustor, by means of the multi-fluid model of turbulent chemical reaction: Paper presented at the "Leading-Edge-Technologies Seminar" on "Turbulent combustion of Gases and Liquids", organised by the Energy-Transfer and Thermofluid-Mechanics Groups of the Institution of Mechanical Engineers at Lincoln, England, December 15-16, 1998
  29. Spalding DB (1999) "Connexions between the Multi-Fluid and Flamelet models of turbulent combustion"; www.cham.co.uk; shortcuts; MFM