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The use of CFD in the design and development of gas-turbine combustors


Brian Spalding, of CHAM Ltd

January, 1999


Computational fluid dynamics has been used for predicting the perfomance of gas-turbine combustors since the early 1970s; but its more extensive use is hampered by two main factors, namely:-

  1. the difficulty of creating computational grids which will adequately represent the complex geometries of actual combustion chambers; and

  2. the uncertain reliability of its predictions in respect of the production of undesired secondary products of combustion.

This lecture concerns the first of these; and it explains how a newly-developed "cut-cell" technique, called PARSOL, enables curved-surface geometries to be adequately handled by easy-to-create cartesian or polar grids.

For a lecture on the second topic, click here.

Coupled with another available technique, namely fine-grid-embedding, PARSOL may provide an acceptable solution to the grid-generation difficulty.

PARSOL has already been incorporated into PHOENICS, as has fine-grid-emedding; and some applications to combustion-chamber flows are described in the lecture.

PARSOL is however still being developed further. Some of the started and planned further features are described.


  1. Problems associated with the computer simulation of gas-turbine combustion
  2. The PARSOL solution of the grid-generation problem
  3. PARSOL applied to a 3D combustor
  4. Future developments of PARSOL
  5. Conclusions
  6. 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. Problems associated with the computer simulation of gas-turbine combustion

(a) The historical perspective

Computational fluid dynamics has been used for predicting the perfomance of gas-turbine combustors since the 1970s, the earliest paper known to the author being Reference 1, in which a 7*7*7 (!) grid was used to solve the equations for:

The SIMPLE algorithm was used for solving the coupled hydrodynamic equations; and the mixed-is-burned hypothesis was employed.

At around the same time, the first papers were being published on how the influences of the turbulence on the chemical reaction might be taken into account, by way of the "eddy-break-up" [Reference 2] and "presumed-PDF" [Reference 3] concepts.

(b) The current situation

Current uses of CFD by combustor developers employ essentially the same quarter-century-old ideas, but with the following differences:-

Despite the advances just alluded to, the use of CFD is far from enabling extensive experimental testing to be dispensed with. The reasons are:-

The present author has addressed the latter difficulty in a two recent papers [References 10 & 11]. The present paper is therefore directed towards the first problem, i.e. that of grid generation.

(c) The main grid-generation alternatives

Adjectives distinguishing computational grids are:-

Of these, and of their advantages and disadvantages, there is much that can be said, but little that will procure agreement among the specialists.

The present author's views are:-

Recently, two developments have made the latter preference realisable. They are:-

The next section will be devoted to describing FGEM and PARSOL in general terms; thereafter applications to gas-turbine combustors will be presented.

2. The FGEM/PARSOL solution to the grid-generation problem

To present the topic of this section, it is necessary to introduce several ideas in quick succession, namely:-

  1. Engineers designing equipment commonly employ computer-aided-design (CAD) software packages for defining the equipment shapes.

  2. The output of their endeavours is embodied in the form of computer files, having one of several standard formats, for example:-

  3. PHOENICS is able to read such files, and to import the so-defined geometries directly into its own "virtual-reality" data-input software module; whereafter boundary conditions of a CFD character (e.g. flow rates and heat inputs) can be supplied.

  4. The format employed for describing objects in PHOENICS VR, ie by way of "facets", is very close to the STL format; and translators for IGES and DXF have also been created; so the CAD-to-CFD transition can be very speedily effected.

  5. In the most straightforward implementation, PHOENICS first sets up a cartesian grid which fits exactly the "bounding boxes" of all the objects in the space, and has a fineness which the user determines by specifying the number of grid intervals in each direction.
    PHOENICS then examines the facets defining the objects, and having determined on which side of the facet the cell-centre lies, fills the whole of the cell with solid or fluid.

  6. The PHOENICS solver is additionally able to respond to user's specifications of regions in which grid-refinement is thought to be necessary, by means of what is called the FGEM (fine-grid embedding) technique.
    All that is necessary in order to use this is to:

  7. The PHOENICS solver has also been equipped with the PARSOL feature which, whenever an object-defining facet intersects a computational cell obliquely, calculates the intersections of the facets with the cell edges and then does what is necessary to ensure that the terms in the algebraic representations of the conservation equations are properly modified.

  8. FGEM and PARSOL can be used in combination to such effect that, it may be argued, the case for using body-fitted coordinates is much diminished.

How the CAD-to-CFD path can be quickly traversed by CAD-literate engineers, by the use of PHOENICS, can be seen by clicking here.

The capabilities of the FGEM and PARSOL techniques can be best be displayed by a tour of the relevant parts of the PHOENICS Applications Album, which can be entered by clicking here.

Legitimate conclusions from detailed inspection of the just-mentioned material appear to be:-

3. PARSOL applied to a 3D combustor

(a) The problem considered

In order to illustrate how PHOENICS can be used for simulating flows within combustors having curved walls without use of body-fitted coordinate grids, an idealized combustor model has been created which exhibits all the main geometrical features, namely:-

The geometry has not in fact been created by means of a standard CAD package, but rather by a stand-alone Fortran-program utility which can make simple shapes very fast. However, that is not relevant to the present demonstration of the ability of PHOENICS to handle objects defined by facets, whatever their origin.

Click here to go direct to PARSOL results. The geometry is shown in the following screen dumps from the VR editor.

Figure 2, which is a view of the interior of the chamber, seen from the outlet end;

Figure 3, which is a similar view, but with more of the intervening solid "cut away";

Figure 4, in which still more sight-obstructing material has been removed; and

Figure 5 which, because the "viewing eye" has drawn nearer, and slightly changed the line of sight, reveals more clearly:

The flow is steady and turbulent, with use of the so-called LVEL model for simplicity; heat transfer results from the fact that the various streams enter at different temperature; but chemical reaction has not been activated.

The same problem has been simulated in three different ways, namely:-

  1. with a mono-block cartesian grid;
  2. with additionally an embedded fine grid; and
  3. with PARSOL activated.

(b) The grid-generation problem

On this topic it perhaps suffices to say that there is no grid-generation problem, for the user, because:

(c) Results of the stage 1 (mono-block-grid) calculation

The following Figures represent various aspects of the first-stage solution, by way of "screen dumps" from the PHOENICS "Virtual-Reality" Viewer.

Noteworthy features are:

[In parenthesis, it may remarked that these inaccuracies may not be as great as those arising when badly-skewed body-fitted grids are employed. The appearance of the steps is probably worse than their effect.]

stage 1 pressures, which shows the above-mentioned "step" effect.
It should be noted that chamber-wall-defining objects are shown only in "wire-frame" view; and several have been hidden so that the contour plots can be seen more clearly.

stage 1: temperatures, from the same viewpoint.

stage 1: velocities , likewise.

stage 1: wall distances , likewise.
The values of distance to the wall are of couse needed by the LVEL model of turbulence.

stage 1: vectors of velocity, coloured, incidentally, according to wall distance.

stage 1: wall distances at the cross-section where the secondary air enters.
What is interesting is to note the near-circularity of all contours, apart from the expected distortions near the apertures.

stage 1: vectors of velocity at the same cross-section, where the influence is shown of the swirl imparted by the secondary air.

Such results, it should be mentioned, are produced by PHOENICS on a Pentium 200 MHz PC in less than half an hour.

(d) Results of the stage-2 (FGEM) calculation

The following Figures represent various aspects of the second-stage solution, by way of "screen dumps" from the PHOENICS "Virtual-Reality" Viewer.

They focus attention on the conical area enlargement, where the fine grid has been located.

stage 2: pressures ;

stage 2: temperatures ;

stage 2: vectors

Qualitatively, the results are similar to the previous ones; but the fitting of the conical-divergence shape is obvously better because of the fine grid is embedded there.

[Refinenment of this simple kind could, indeed, have been effected more easily in mono-block mode. However, the purpose here has been only to show how easily grid-refinement is effected, and how it reduces the "step" effect.]

The following further results relate to another Stage-2 calculation in which the fine-grid region is moved to the air and fuel inlet region.

Figure 6 :

Figure 7 :

Figure 8 :

Figure 9 :

Figure 10 :

Figure 11

They will be left to speak for themselves.

(e) Results of the stage-3 (PARSOL) calculation

Finally a few results are shown for the case in which FGEM and PARSOL are both active.

Comparison of the contour and vector plots for the outlet cone show that the cone surface shows no significant "step effect", even though the z-direction step is still large.

Two figures which show the difference between the without-PARSOL and with-PARSOL treatments in the conical outlet region:

without PARSOL ; and


It is the latter which can be expected to be, as well as look, the more realistic.

4. Future developments of PARSOL

It needs now to be stated that, although PHOENICS, FGEM and PARSOL can already enable flow and combustion to be simulated, with a cartesian grid, for the space within the main combustor, or for that matter outside, handling both spaces simultaneously presents more difficulty.

The reasons are that:-

Fortunately, the PARSOL coding has been constructed in a modular fashion, which allows for expansion of its capabilities. Extension of its capabilities to the handling of the "thin-sloping-wall" problem is therefore now being planned by CHAM, and will be carried out during the next months.

This is not the only desirable extension. Others, for which plans are now being drawn up include:-

5. Conclusions

To the conclusions drawn at the end of section 2, it is now suggested, the following might be reasonably added:-

6. References

  1. 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 and Sons
  2. DB Spalding (1971) "Mixing and chemical reaction in confined turbulent flames"; 13th International Symposium on Combustion, pp 649-657 The Combustion Institute
  3. DB Spalding (1971) "Concentration fluctuations in a round turbulent free jet"; J Chem Eng Sci, vol 26, p 95
  4. 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
  5. Bray KNC in Topics in Applied Physics, PA Libby and FA Williams, Springer Verlag, New York, 1980, p115
  6. SB Pope (1982) Combustion Science and Technology vol 28, p131
  7. DB Spalding (1995) "Models of turbulent combustion" Proc. 2nd Colloquium on Process Simulation, pp 1-15 Helsinki University of Technology, Espoo, Finland
  8. 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.
  9. WA Fiveland (1984) "Discrete-ordinates solutions of the radiative-transport equation for rectangular enclosures"; J Heat Transfer, vol 106, pp 699-706
  10. Spalding DB (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
  11. Spalding DB (1999) "Connexions between the Multi-Fluid and Flamelet models of turbulent combustion"; www.cham.co.uk; shortcuts; MFM