# Marc ZELLAT, Driss ABOURI and Stefano DURANTI CD-adapco

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2 2 THE NEW COMBUSTION MODEL: The ECFM-CLEH The ECFM-3Z model is a combustion model based on a flame surface density transport equation and a mixing model that can describe inhomogeneous turbulent premixed and diffusion combustion. The idea is to divide the computational domain taking into account the local stratification. The probability Density Function (PDF) of the mixture fraction is defined by three Dirac functions. The evolution of the mass included in the 3 mixing zones (Figure 1) is computed and modified with the help of a mixing model base on local turbulent time-scale. Figure 1: Principle of ECFM-3Z Model New ECFM-CLEH model inherit some concepts from the ECFM-3Z described above. In ECFM- CLEH, a new treatment of propagation and diffusion flame effects is introduced by accommodating the details of equilibrium chemistry. In addition a dynamic lookup table is introduced for turbulent mixing time scale [3]. The principle of ECFM-CLEH is described in figure 2. The computational cell is divided into three zones in term of mixing: Unmixed fuel (Y F UM ), Premixed fuel (Y F PM ) and fuel into the Diffusion zone (Y F DIF ). A Zeldovich variable (passive mixture fraction) is defined for fuel, transported and solved in the premixed (PM) and the combustion un-premixed or diffusion zone (diff). UM means for fresh un-premixed quantities. According to mass conservation for the total fuel (Y F ) in the cell and its corresponding Zeldovich variable Z F, the system is completely described and closed: Y F = Y F UM + Y F PM + Y F DIF Z F = Z F UM + Z F PM + Z F DIF Finally, a transport equation for mixture fraction variance is added to the system to have access to the turbulent fluctuations. A linear relaxation method is introduced to close the scalar dissipation rate term, using a dynamic constant as a function of local turbulent Reynolds number [3]. Figure 2: The principle of ECFM-CLEH Model 2

3 In premixed combustion (PM) zone and the diffusion combustion zone (diff), an equilibrium fuel mass fraction is calculated by an approach to make the temperature resulting from single-step combustion chemistry equals to the equilibrium temperature calculated using fully detailed chemistry. Therefore, the model will take into account for two equilibriums fuel: One for the premixed zone and one for the diffusion zone. For more details, see G. Subramanian and al. SAE [4]. This makes fundamental difference between ECFM-3Z and ECFM-CLEH, one can now represent two different progress variables for combustion. A first one called (c) is defined for auto-ignition and propagation, a second called (alpha) one for diffusion. This will obviously strongly affect the pollutants formation depending on which combustion mode is dominating the combustion process. 3 FUNDAMENATAL VALIDATION: ACADEMIC TEST CASES Before the evaluation of the new model under engine conditions, we have decided to establish a range of over twenty fundamental test cases to demonstrate its new functionality. We have chosen to present a significant one in this section. The test case is described in figure 3. Figure 3: Test case for premixed and un-premixed reactive terms This test case described the mixing and combustion processes in a mixing layer created by two different streams. The fuel entering zone 1 and zone 2 is fully premixed, however the concentration is different between the two zones. The combustion is ignited by spark located downstream the mixing layer. Because of the difference in fuel concentration entering each zone, one can expect as an asymptotic (or steady state) solution to this problem a flame composed with a mixture of propagation and diffusion. This can be illustrated by plotting the progress variables for these two modes of combustion. The results are shown in figure 4-1 and demonstrate clearly the presence of propagation and diffusion taking place simultaneously in to the combustion zone. Figure 4-1: Test case for premixed and un-premixed reactive terms Left: Progress variable for propagation Right: Progress variable for diffusion 3

4 Figure 4-2: NOx level 4 DI ENGINE: MODEL VERIFICATION The combustion in DI engine and especially under full load conditions exhibits the three mode of combustion: Auto-ignition, propagation and diffusion. Therefore, the emissions history will strongly depend on the combustion mode depending on the different progress of the combustion. The objective is to test and validate the model in a DI engine under full load operating conditions for combustion understanding as well as conditions under which emissions are produced. 4.1 THE ENGINE CONFIGURATION The computed configuration is a typical 2 liters DI Engine, under production. The symmetry of the geometry, the relative position if the injector into the combustion chamber and the nature of the swirling flow at Intake Valve Closing make the choice of a sector mesh good enough for this evaluation. The geometry and the mesh are shown in figure 5. Figure 5: View of computational grid: Complete geometry (left) and sector mesh (right) 4.2 MODEL VALIDATION 4000 RPM Full load The computed and measured in-cylinder pressures and corresponding rate of heat release are represented on figure 6 and 7 for the full load 4000 RPM. 4

5 The overall agreement is rather good including the combustion speed for this two operating conditions. Figure 6: Comparison between calculated and measured in-cylinder pressure: full load-4000 rpm Figure 7: Comparison between calculated and measured Rate Of Heat Release: full load-4000 rpm 4.3 MODEL VALIDATION FULL LOAD 4000 RPM: COMBUSTION ANALYSIS Figure 8 shows the time history of the progress variable associated to combustion by flame propagation (ctilde) and the progress variable associated to the combustion by diffusion. This demonstrates clearly the competition between these two modes of combustion. Figure 8: Progress variable history- ctilde : flame propagation (premixed) alpha : Diffusion 5

6 An illustration in space of the two progress variables is shown in figure 9 around the maximum peak pressure location. Obviously, depending on local oxygen concentration, field s fluctuations and local temperature, this will play an important role on NO formation during the combustion process. Figure 9: Progress variable contours - Left: Premixed Right: Diffusion 4.4 NO Emissions As it was indicated earlier, the major development in ECFM-CLEH is related to refined description of the simultaneous premixed and diffusion combustion. Two different progress variables are derived for each mode of combustion. These variables are c for the premixed combustion and alpha for the diffusion. Therefore, all species and especially the emissions will contain two different sources terms. The first is from premixed part and second from the diffusion. Formally, the equation below is an example for NO formation. ~ ~ ~ & ω = c & ω + cα & ω NO NO PM NO DIFF The results of NO history from the previous engine case are shown in figure 11. Figure 11: NO History Comparison between ECFM-3Z, ECFM-CLEH predictions and measurement at Exhaust 6

7 Figure 11 is showing clearly, that despite the same mechanism used in ECFM-3Z and ECFM- CLEH, the latter is doing a much better job in NO prediction, this is due to the mixture and temperature fluctuations effects and the combined rate of formation in both premixed and diffusion phase. 5 CONCLUSIONS A new combustion model for DI combustion, the ECFM-CLEH is presented. ECFM-CLEH is roughly belonging to Flame Surface Density family, which inherits some, but not all concepts from ECFM-3Z as far as the mixing process modeling and the chemistry are concerned. A dynamic mixing constant is developed and implemented in ECFM-CLEH. In ECFM-CLEH, each computational cell is divided into unmixed, premixed and diffusion zones. To track information on the reaction progress and the amount of fuel consumed by premixed and diffusion flames, two more conservative transport equations for the Zeldovich variables of fuel present in each zone are solved. The chemical source terms in the reactive zones are modeled by introducing an equilibrium limiting approach. The equilibrium functions are weighted using a Presumed Probability Density Function using a detailed reaction mechanism for fuel. Predictions have been compared with extensive data from a DI Engine in production at full load. The results show that the models give realistic Heat Release History, Indicated Power, as well as NO prediction. 6 REFRENCES [1] Colin,O. And Benkenida,A. The 3-Zones Extended Coherent Flame Model (ECFM-3Z) for computing Premixed/Diffusion Combustion. Oil & Gas Science Technology, Vol. 59 (2004) [2] STAR-CD V3.26 PROSTAR & es-ice are Trademarks of CD-adapco Group [3] Fox,R., O., Computational models for turbulent reacting flows. Cambridge University Press (2000) [4] Subramanian,G., Vervish,L. and Ravet,F. New Developments in Turbulent Combustion Modeling for Engine Design: ECFM-CLEH Combustion Submodel. SAE paper

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