# Computer code for combustion modelling in diesel engines.

1. INTRODUCTION

During the past decades research studies in the field of internal combustion engines have been dedicated to the issue of pollutant emissions, starting with the necessity to model the combustion process accurately.

The purpose of this work is to achieve an open structure computing programme. This will enable us to model the combustion process accurately enough, so that it may be used as a instrument to study the pollutant formation in the models to be created and other models of various phenomena involved in combustion process.

2. MODEL FORMULATION

The model is two-dimensional and it takes advantage of the symmetry, being it used only two of the three spatial coordinates. If axial symmetry approach of the combustion chamber is considered, which is common in most of the practical cases, it is appropriate to take into account the swirl movement. In this way the spatial resolution is enhanced and the third dimension is partially implemented. The governing equations are written in a two-dimensional form, the plane of calculation being the xy-plane. Vector notation is employed in order to have a compact set of relations.

2.1 The Fluid Phase

For fluid phase, approximated as Newtonian fluid, we can use the known set of equations for fluid flow with additional terms which take into account the effect of chemical reactions and interaction between fluid mixture and spray droplets. The set of equations (Chung, 2006) is: continuity equation (1) for species k and fluid (2), momentum equation (3) for the mixture, angular momentum (4), the internal energy equation (5), and the state relation assumed for ideal gas mixture:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

where: [[rho].sub.k] is the partial density of the k species, [rho] is the total density of the fluid mixture, [[??].sub.s], is the rate of change of fuel (k = 1) density due to spray evaporation or condensation, [??] is the viscous tensor, [[sigma].sub.o] is the cylindrical viscous stress, [??] is the momentum transferred from spray droplets to the fluid, [??] is the external force, [??] is the swirl stress vector, N is the angular momentum transferred from spray, I is specific internal energy (exclusive chemical), [??] is the heat flux vector, [[??].sub.c] is the rate of chemical heat release, [[??].sub.s] is a source term associated with the interaction between the spray droplet and the fluid.

The mean values in the equations are mass weighted (Favre procedure). The fluctuation terms are ordinarily modeled by the gradient-flux approximation. In this approximation the averaged turbulent equations become identical in form to the laminar ones; the transport coefficients are simply replaced by the appropriate turbulent values (6), which are much larger:

[mu] = [rho][[upsilon].sub.0] + [[mu].sub.air] + [[mu].sub.t], K = [mu][c.sub.v] / Pr', D = [mu] / [rho]Sc', (6)

where: [mu] is the viscosity, [[upsilon].sub.0] is the constant uniform turbulent diffusivity, [[mu].sub.air] is air viscosity, [[mu].sub.t] is turbulent viscosity computed using SGS (SubGrid Scale turbulent viscosity) model (Sabau, 2007).

2.2 Chemical Reactions

The consequent chemical reactions used may be included in two categories:

* one kinetic equation, fuel stoichiometric in air combustion;

* four equilibrium equation, dissociation equations of combustion products;

The chemical source term (1) and the chemical heat release term (5) is given by equation 8,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (8)

where [a.sub.kr] and [b.sub.kr] are the dimensionless stoichiometric coefficients for the r-th reaction, [W.sub.k] is the molecular weight of specie k, [[??].sub.r] is reaction speed of r-th reaction, [q.sub.r] is the negative of the heat of reaction for r-th reaction at 0[degrees]K .

Reaction speed [[??].sub.r] is computed for the kinetic reaction and is implicitly determined by the constrain condition imposed for the equilibrium reaction (Poinsot & Veynante, 2005).

2.3 The Spray Droplets

The equation of motion for the spray will be given in Lagrangian form for discrete computational particle (Sabau & Buzbuchi, 2006). The flow of liquid jet is computed using the general equation of jet simplified in stochastic approach and the evaporation using the equation deducted by O'Rouke.

The equations for fluid--particle interaction are:

[[??].sub.s] = - [summation over (k)] [dm.sub.k] / dt[delta](r - [r.sub.k]), (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (10)

N = [summation over (k)] [[D.sub.k]([w.sub.k] - w) - [w.sub.k] [dm.sub.k] / dt][delta](r - [r.sub.k]), (11)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)

where: [dm.sub.k] is the mass of droplet k, [H.sub.k] is the specific enthalpy of liquid fuel, r position vector and [delta] is the Dirac function.

2.4 Numerical Technique

The temporal differentiate is based on ICE (Implicit Continuous-fluid Eulerian) algorithm which is a partial implicit scheme. This iterative technique joins the continuity and moment equations and solves them simultaneously by using the state equation; the energy equation is solved in an explicit way. To move forward in time each cycle is achieved in three temporal sub-steps or phases. This approach is in direct connection to the spatial discretization based on ALE (Alternate Lagrangian Eulerian) method. Interaction of spay with the gas is treating based on the ideas of Monte Carlo method (Oanta, 2007). The spray is considered to be composed of discrete computational particles. Each of them represents a group of droplets of similar size, velocity, temperature (Stiesch, 2003).

The grid is adjustable and is consists of generalised quadrangle, whose corners are specified by co-ordinates dependent on time. This offers additional flexibility, the problem being solved in an Eulerian or Lagrangian way, as required.

The code is written in MATLAB language.

3. NUMERICAL SIMULATION

The model was used for the numerical simulation on two engines: T684 made by "Tractorul" Plant of Brasov, a four stroke automotive engine, and L90 B&W two strokes marine engine. Experimental data are available for these engines.

For the studies and calibration it was used the in-cylinder pressure variation at full power for T684, measured and calculated with the Wave 5 cod (figure 1) and at exploitation speed and power for the marine engine (figure 2) (Sabau, 2007).

Figure 2 and 3 present spray and O2 concentration, very important information for the combustion process analysis. Unfortunately we not have data for validation these values.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

4. CONCLUSION

The original software created meets the requirements (combustion modelling), i.e. to estimate the in-cylinder pressure with a 2-8 % error from the measured data.

Results are in good compliance with experiment for the full speed and load state of the engine.

Results closely depend on the constants of the models and for this reason they have to be carefully analysed.

Accurate data is need for the calibration of model constants.

The performances of the program are limited by the models used, few of them requiring improvements, such as:

* the third dimension is need;

* a more accurate turbulence model is necessary (k-e model);

* more chemical reactions are need (Zeldovich mechanism);

* evaporation and boiling mechanisms for fuel droplets should be also improved;

* numerical algorithms should be redesigned in order to have an increased accuracy and lower run times.

5. ACKNOWLEDGEMENT

Several ideas presented in this paper use the accomplishments of the "Computer Aided Advanced Studies in Applied Elasticity from an Interdisciplinary Perspective" ID1223 scientific research project (Oanta et al., 2007).

6. REFERENCES

Chung, K. L. (2006). Combustion Physics, Cambridge University Press, ISBN 0521870526, New York

Oanta, E. (2007), Numerical methods and models applied in economy, PhD Thesis, Academy of Economical Studies of Bucharest, Promoter Prof. Mat. Ec. Ioan Odagescu

Oanta, E.; Panait, C.; et al. (2007-2010). Computer Aided Advanced Studies in Applied Elasticity from an Interdisciplinary Perspective, ID1223 Scientific Research Project, under the supervision (CNCSIS), Romania

Poinsot, T. & Veynante D. (2005). Theoretical and Numerical Combustion, R.T. Edwards Inc., ISBN 1930217102, Paris

Sabau, A. (2007). Studies regarding the combustion process in marine diesel engines in order to reduce the pollutant emissions, PhD Thesis, 'Transilvania' University of Brasov

Sabau, A. & Buzbuchi, N. (2006). Model of spray in Diesel engine, Annals of Maritime University of Constanta, Vol. 9, No. 9 (June, 2006), pp. 82-89, ISSN 1582-3601

Stiesch, G. (2003). Modeling Engine Spray and Combustion Processes, Springer; ISBN 3540006826, Berlin