A paper to be published in PHOENICS Journal, January, 1999

Local heat and mass transfer properties are presented for a turbulent diffusion flame in confined co-axial jet flows.

The calculation procedure employs, a K - epsilon two-equation turbulence model for hydrodynamic part of simulations.

Calculations of mixing and combustion were performed with three models, characterised by instant reaction, instant reaction with scalar fluctuations and multi-fluid instant reaction: comparison with measurements obtained by Razdan and Stevens indicate the superiority of multi-fluid approach.

PLANT feature of PHOENICS 3.1 was used to implant the model formulations.

- Introduction
- Flow details
- Simulation details
- Combustion models
- Implementation
- Comparison with experiment
- Conclusion
- References
- Appendix: Q1 input file

The concentration fluctuations in a turbulent confined jets have been recently analysed by way of Multi-Fluid Model invented by Brian Spalding [1]. The predictions have been found to be in satisfactory quantitative agreement with the measurements [2].

The present work extents the analysis to a more complicated flow, in which the turbulent mixing is followed by chemical reactions forming the steady, confined and physically controlled flame.

The main objective is to validate multi-fluid model performance to predict the features of gaseous combustion by comparison its results with existing models and experimental observations.

The experimental data to be simulated are the results for the turbulent diffusion flame measurements of Razdan and Stevens [3], the main features of which are as follows:

- The geometry comprises a axisymmetric combustion chamber into which carbon monoxide is injected centrally and axially to mix and burn with a coaxial annular air stream.
- Coaxial CO and air streams are admitted separately into the chamber and then burn in a turbulent diffusion flame. The inlet air/CO velocity ratio is 0.035. The Reynolds number based on the nozzle diameter was 1.e4 for all calculations reported here.
- The CO jet enters through a pipe of 5.0 cm diameter at a
temperature of 288 K. The air stream enters through an annulus at
the same temperature. The chamber walls are presumed adiabatic.

### 3 Simulation details

These are as folows:

- The hydrodynamics turbulence is represented via the k-e turbulence model.
- The calculations employ variable specific heats and densities.
- The flame is confined and buoyancy and radiation effects are negligible.
- A cylindrical-polar mesh is used with 30 radial by 40 axial cells.
- Calculations of mixing and combustion were performed with three models, characterised by instant reaction, instant reaction with scalar fluctuations and multi-fluid instant reaction.

### 4 Combustion models

Three combustion models are reffered to in this paper are described and discussed in turn.

#### Model 1

The first model,

**SCRS**- Simple Chemical Reaction System, postulates a physically controled, infinitely fast, one-step reaction, with fuel and oxidant unable to coexist at the same location. The only species equation to be solved is that for the mixture fraction,**f**, [4].#### Model 2

In the second model,

**SCRS plus PDF**-Probability Density Function, the infinitely fast one-step reaction is retained; but fuel and oxidant may exist at the same location, although at different times.Equations for

**f**and for square of concentration fluctuations,**g**, are solved.The maximum and minimum values of f at any point are calculated with presumed PDF, namely, symmetrical square-wave variation for equal times together with proportion of time spent at an upper state in the region where maximum and minimum values exceeds unity or are less than zero.

Temperatures and mass fractions of fuel and oxidant are calculated corresponding to mixture fraction limits and their proportions of time.

Further information is contained in [5].

#### Model 3

In contrast to model 2, an equation for f and g are not used and Multi-Fluid Model,

**MFM**of Spalding [1], is introduced with the essential features being as follows:- The gas flow is represented as a multi-fluid population;
- Each fluid of the population has got its own composition and temperature governed by instant reaction of SCRS mode;
- The mixture fraction, f, is supposed to be uniformly distributed, in the range from zero to unity, between all fluids;
- The fluids are allowed to couple and split; but it can only take place between those parent fluids which would produce the appropriate offsprings inheriting the attributes of either parent in equal proportion;
- The frequency in population is calculated for each fluid by solving its fluid-mass-fraction equation with the source/sink terms are: first-fluid-mass fraction * first-fluid-mass fraction * 5.0 * the energy-dissipation-rate/turbulence-energy.

17 conservation equations for fluid-mass-fractions are solved for all calculations reported here and statistical properties of the fluid population are then deduced.

The above number of fluids was found sufficient for concentration fluctuations to be fluid-population-grid independent [2].

More details of MFM can be found elsewhere [6].

### 5 Implementation

All the results to be displayed below have been created by use of the PLANT feature of PHOENICS 3.1 [7].

The necessary formulae for calculations of source/sinks, physical properties, statistical operations, auxilliary computations and post-processing preparations have been set by way of appropriate statements in Q1 file.

Running SATELLITE then results in the generation of all relevant GROUND codings, compilation and re-linking.

Running private EARTH initiates the calculations and produces the field distributions of all relevant variables.

The basic Q1 file is supplied in Appendix. Further related Q1's can be found in PLANT data-input library.

### 6 Comparison with experiment

It will be shown that neglect of the incompletness of the micro-mixing leads to predictions of heat and mass transfer properties of the flame which can differ significantly, from those predicted by the multi-fluid model (Fig.1) and observed in the experiments (Fig.2 ).

The center-line variation of mean temperature is shown in Fig.2 along with the experimental results from Razdan and Stevens.

There are significant differences both in the magnitude of SCRS results and experimental data. The instant reaction model fails to fit the data reasonable both in location and magnitude of the maximum temperature.

In contrast, the calculations of Multi-Fluid Model and instant reaction with presumed scalar fluctuations are in acceptable agreement with measurements. The former appears to be marginally better than the latter.

In what follows, the results will be presented in a sequence which allows the reader to asses the performance of combustion models employed in more details.

The distribution of the averaged gas composition along the centre-line is plotted in Fig.3 together with experimental data of Razdan and Stevens.

Fig.4 illustrates a comparison between calculations of the radial profiles for the temperature and experimental data. The radial distance is normalized by the diameter of the nozzle.

It can be seen that both SCRS and SCRS plus presumed PDF models overpredict the temperatures in the outer half of the chamber.

The Multi-Fluid Model gives a more accurate predictions in that region and seems to be better in the inner zone as well.

The shapes of the distribution predicted by the models are also different. The location of the minimum temperature is predicted by SCRS and SCRS plus PDF models to be approximately at the third way across the chamber. Neither experiments no Multi-Fluid Model predictions show any indication of the existence of the temperature minimum.

Fig.5 displays the distribution of oxygen mass fraction along the centreline and compares them with the experimental results from Razdan and Stevens.

The SCRS predictions do not fit the measured data. Much better agreement is achieved with the both models using PDF information.

It is rather difficult to state that Multi-Fluid Model is significantly better here than SCRS improved by presumed PDF. Both models indicate correct trends and their results are much closer to the data.

The radial profiles, shown on Fig.6, compare calculated and measured values of oxygen mass fractions. As before, the radial distance is normalized by the diameter of the nozzle.

The degree of agreement is similar to radial temperature profiles of Fig.4:- the Multi-Fluid Model agrees more closely with the measurements in the outer region and can be preffered with respect of overall performance.

SCRS augmented by presumed PDF also allows mass fraction calculations which are in closer agreement with experiment, in inner zone, than SCRS in its standard state. However, neither former no latter seem to fit the experimental data in outer region. They predict different profile shapes and produce underprediction in the magnitudes of the results.

The radial profiles of mixture fraction, at Z/D=40, are shown in Fig.7. They are normalized by their centerline value.

Examination of Fig.7 shows that there are significant differences in the magnitudes of the model results.

It suggests that Multi-Fluid Model is to be preffered. Both others result in incorrect trends and suffer the unreasonable values away from centerline region.

Fig.8 shows two Fluid Population Distributions computed by Multi-Fluid Model for two locations along the radii, progressively farther from the axes. They can not be compared with experiments yet.

The calculated values, however, represent the Probability Density Functions and indicate the fluctuated structure of the flow. They are, indeed, converted in the concentration, temperature and related density fluctuations.

The ordinate of Fig.8 reperesents frequency in the population. The abscissa represents the mixture fractions in the range from zero ( pure oxidant fluid) to unity ( 100% CO fluid).

The PDF at the r/R = 10 is the farthest from the axis; farther from the centerline more oxidant-richer fluids are found.

Fig.9 shows the PDF diagram computed for another location along the axis.

The vertical scale represents the frequency in the population. The horizontal scale represents each of the 17 fluid mixture fractions uniformly distributed in the range from unity (left) to zero (right).

The Multi-Fluid Model predicts the similar distribitions for each cell of the flame and the values at different locations differ radically, in both magnitude and distribution.

It suggests that "two-spike" representation of the fluid population, as presumed PDF, is too crude to represent incompletness of mixing realistically.

### 7 Conclusion

The comparisons presented in this paper show that results obtained with the Multi-Fluid Model are generally in more satisfactory agreement with measurements than the models which are still often used for engineering purposes.

It may be concluded that the multi-fluid approach and the present procedure with its two-equation turbulence model and instant reaction within each member of fluid population is able to represent combusting flows with greater physical realism and quantitative certainty.

### 8 References

- D B Spalding (1995) "Multi-fluid models of turbulent combustion", CTAC95 Conference, Melbourne, Australia.
- S V Zhubrin (1999) "Concentration fluctuations in confined jet: multi-fluid approach", PHOENICS Journal of Computational Fluid Dynamics ( To be published ).
- M K Razdan and J G Stevens (1985) "CO/Air Turbulent Diffusion Flame: Measurements and Modelling", Combustion and Flame, v.59, pp.289-301
- D B Spalding (1979) "Combustion and Mass Transfer", Pergamon Press, 409p.
- M A Serag-Eldin and D B Spalding (1979) "Computations of Three- Dimensional Gas-Turbune Combustion Chamber Flows", Journal of Engineering for Power, v. 101, pp.327-336.
- D B Spalding (1996) "The multi-fluid model of turbulent flow, mixing and combustion", Web-site PHOENICS documentation
- S V Zhubrin (1997) " PLANT - the method of implanting physical-model formulae into the executable solver module", Lecture at the VIIIth International PHOENICS User Conference, Seville, Spain.