Calculation of the power cycle of hydrogen IC engines

Transcription

1 Calculation of the power cycle of hydrogen IC engines S. Verhelst a*, S. Verstraeten b, R. Sierens a a Ghent University; Department of Flow, Heat and Combustion Mechanics; Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium b Karel de Grote-Hogeschool; Industrial Sciences and Technology Department; Salesianenlaan 30, B-2660 Hoboken, Belgium * Corresponding author, Sebastian.Verhelst@UGent.be ABSTRACT: Hydrogen is an attractive alternative energy carrier, which could make harmful emissions, global warming and the energy insecurity a thing of the past. Hydrogen internal combustion engines can be introduced relatively easily. This paper discusses the development of a model for the combustion of hydrogen in spark ignition engines, which has lead to a simulation program that can assist the optimization of these engines. A laminar burning velocity correlation published previously by two of the authors is combined with a number of turbulent burning velocity models in a quasi-dimensional two-zone combustion model framework. Simulation results are compared with experimental cylinder pressure data recorded on a single cylinder hydrogen engine. Correspondence between simulation and measurement is shown for varying equivalence ratio, ignition timing and compression ratio. All models performed well for varying ignition timings and compression ratios; the real test proved to be the ability of the models to predict the effects of a varying equivalence ratio, this lead to a clear distinction in the models. KEYWORDS : hydrogen, internal combustion engines, simulation, power cycle. 1. Introduction Hydrogen is an interesting fuel for internal combustion engines (ICEs). Hydrogen fueled ICEs have the potential for an increased engine efficiency, with a demonstrated indicated efficiency of 52% for a hydrogen fueled spark-ignition engine [1] and a power generation efficiency of 49% for a hydrogen fueled compression-ignition engine [2]. Furthermore, hydrogen is a very versatile fuel, allowing several load control strategies [3] for optimization of the efficiency and emissions (NOx) throughout the load range. The practical consequence is widely varying ranges for the equivalence ratio and recycled exhaust gas fraction (EGR), which is an important distinction between hydrogen engines and other homogeneous charge, spark ignition engines. Ghent University has been working on hydrogen fueled ICEs since This research started off purely experimental, recently there was a wish to support this work with simulation. This has resulted in a PhD [4] and a quasi-dimensional code for the power cycle of SI engines fueled with hydrogen. Some elements of this work are presented here. 2. Literature review of numerical work The literature on hydrogen engine simulation is quite limited. Fagelson et al. [5] use a two-zone quasidimensional model to calculate power output and NOx emissions from a hydrogen SI engine. They use a semi-empirical turbulent combustion model of the form u t = ARe B u l, where A and B are constants, Re is the Reynolds number based on piston diameter, mean piston speed and burned gas properties; u t and u l are the turbulent and laminar burning velocities, respectively. Spherical flame propagation is assumed, heat transfer is neglected, and the laminar burning velocity is calculated from an overall second order reaction with an estimated activation energy. The model is validated against measurements with varying equivalence ratio and ignition timing only. Prabhu-Kumar et al. [6] use this model to predict the performance of a supercharged hydrogen engine. They report an overestimation of the rate of pressure rise (and thus of the burning velocity). 1/9

2 Keck [7] reports measurements in an optically accessible engine, operated on propane as well as hydrogen, and uses a turbulent entrainment model to compare predicted trends with experimentally observed trends. Johnson [8] uses the Kiva-3V engine simulation code developed at Los Alamos National Laboratory with the standard eddy-turnover model to simulate a hydrogen engine at a fixed equivalence ratio and volumetric efficiency. The standard model contains one free parameter that is adapted for hydrogen and held constant for varying ignition timing and engine speed. Future work is hinted at, with the aim of including the dependence of the model constant on the equivalence ratio, pressure and temperature through the dependence of the laminar burning velocity on these variables. Zero- and multi-dimensional models have been used for hydrogen engine simulation at the Czech Technical University [9]. A zero-dimensional model based on the GT-Power code is used with a Wiebe law fitted to measured rates of heat release. An Advanced Multizone Eulerian Model is developed for multi-dimensional simulation. This model is a combination of zero-dimensional and multi-dimensional elements: the combustion chamber seems to be limited to simple geometries because of limitations to grid generation, and the heat transfer is modeled for the cylinder contents as a bulk volume. The combustion model is a semi-empirical PDF-like model that relies on a measured rate of heat release and the assumption of a hemispherical flame front to track flame propagation. Finally, Ma et al. [10] use a zero-dimensional model using Wiebe s law. It is not clear to what data this law is fitted. The model is used to calculate the effects of varying compression ratio and ignition timing and to determine an optimum cylinder diameter, for a fixed equivalence ratio. No validation against experimental data or any justification of extrapolation outside conditions for which the fit is valid is given, so the quality of the reported results is doubtful. 3. Simulation program: framework and assumptions The objective of developing a simulation program for hydrogen fueled SI engines was to enable the evaluation of existing engines, performing parameter studies and predicting optimum engine settings. A reasonable accuracy and fast computation on a PC system was desirable. These conditions are satisfied by quasi-dimensional models. Multi-dimensional models are ruled out as they are computationally too demanding. Their best use is for detailed studies, or to support theory and model development. A simulation code for the complete cycle of SI engines was developed at Ghent, with emphasis on the gas dynamic part of the cycle [11]. The present study looks at the power cycle and more specifically at the turbulent combustion in hydrogen fueled engines. The following, standard, assumptions were made in the derivation of a two-zone quasi-dimensional model. During compression and expansion the pressure, temperature and gas composition are assumed uniform throughout the cylinder, with the gas composition fixed during compression and following chemical equilibrium during expansion. During combustion, the assumptions of a uniform temperature and gas composition are made for the unburned and burned zone separately, with a fixed gas composition in the unburned gas and chemical equilibrium in the burned gas. The pressure is assumed uniform throughout the cylinder, equal in burned and unburned zones. The burned and unburned zones are assumed separated by an infinitely thin, spherically propagating flame front, with no heat exchange between the two zones. All cylinder gases are treated as ideal gases. The equations for the rate of change of the cylinder pressure, dp/dθ, and unburned and burned temperatures, dt u /dθ and dt b /dθ (θ being the crank angle), are then derived from conservation of energy. A number of additional models and assumptions are necessary to close these equations: Heat exchange is calculated from Annand s model [12]. As the engine used for validation of the simulations (see later) has a simple disc shaped combustion chamber, turbulence quantities were calculated using a very simple turbulence model, in which the integral length scale is kept constant at one-fifth the minimum clearance height, and the rms turbulent velocity u linearly decreases according to u' = u TDC [1-0.5(θ-360)/45]; where u TDC is the rms turbulent velocity at TDC, taken to be 0.75 times the mean piston speed, θ is the crank angle (360 at TDC of compression); the decay rate of u was taken from ref. [13]. The mass burning rate is an unknown in the equations for dp/dθ, dt u /dθ and dt b /dθ. In quasidimensional models it is derived from a turbulent combustion model. The turbulent combustion model used in this work is based on the entrainment framework, where the rate of entrainment of unburned gas into the flame front is given by: dm e /dθ = ρ u A f u te (1) 2/9

3 here, m e is the entrained mass, A f is a mean flame front surface and u te is the turbulent entrainment velocity (see later). The mass entrained into the flame front is then supposed to burn with a rate proportional to the amount of entrained unburned gas, with a time constant τ b : dm b /dθ = (m e m b ) / τ b (2) with τ b = l / u l (3) where l is a turbulent length scale and u l is the laminar burning velocity. In the present work, the ideas of Blizard and Keck [14] and Tabaczynski et al. [15] concerning turbulent eddies being entrained and subsequently burned with the laminar burning velocity are abandoned, and Eqs. (1) and (2) are used as a mathematical representation of the effects of a finite flame thickness δ t. The entrained mass m e is seen as the mass behind a mean entrainment flame surface (comparable to a mean Schlieren surface). When this entrainment flame front reaches the cylinder walls, combustion still proceeds due to the finite flame thickness: there are still parcels of unburned gas. Experimental data of engine combustion indicates an initial increase in turbulent flame thickness [16] and a final mass burning rate after all the cylinder charge has been entrained in the flame (Schlieren front) well approximated by an exponential decay [7]. Both observations are reproduced by Eqs. (1) and (2). Equation (3) requires a turbulent length scale. The integral length scale Λ [14] as well as the Taylor length scale λ T [15] have been used in literature. In the present study, the integral length scale will be used, as the parameter τ b expresses the finite flame thickness which is primarily determined by the large scales of turbulence [17]. A flame propagating after spark ignition is at first only wrinkled by the smallest scales of turbulence. Several methods or models have been proposed to account for turbulent flame development [4] and were implemented in the code. Curiously, the best correspondence of simulation with measurement was obtained without any flame development model. A possible explanation is the form of Eqs. (1) and (2): in this form, the mass burning rate initially develops during a few time constants τ b. For the single speed measurements (600 rpm) used here (see later), the ignition delay will not vary much, and simulation results were satisfactory. 4. Turbulent burning velocity models A turbulent entrainment velocity u te is needed for closure of Eq. (1). A number of turbulent burning velocity models were selected to procure values for u te. These models were adapted to include (where necessary) a laminar term to satisfy u te u n when u 0, where u n is the stretched laminar burning velocity; and a calibration constant C 2 (see later). The form in which the models are used in the simulations is summarized below (for a full description see the original references or [4]): Damköhler [14,15]: u te = C 2 u + u n (4) Gülder [18]: u te = 0.62 C 2 u 0.5 u n 0.5 Re t u n (5) Bradley ( Leeds KLe ) [19]: u te = 0.88 C 2 u (KaLe) u n (6) with Ka the Karlovitz stretch factor. Fractals [20]: u te = u n (Re t ) 0.75 (D3-2) (7) with D 3 = 2.35 C 2 u /(u + u n ) u n /(u + u n ) (8) 3/9

4 where the constant C 2 was placed as shown to account for the uncertainty in the fractal dimension of a developed turbulent flame front surface. Lipatnikov [17,21]: u te = C 2 u 0.75 u n 0.5 Λ 0.25 D T u n (9) Peters [22]: u te = C 2 u Da [( /Da) 0.5-1] + u n (10) where Da is the Damköhler number. Names between quotation marks are collective names given by the current authors, for models that cannot be attributed to a single author or reference. These models will be compared in simulations using the framework constituted by Eqs. (1) and (2). This also means that in the present implementation, the distinction between the Lipatnikov model and the other models, of a growing mean flame brush thickness [17], disappears: the behavior of δ t is now expressed by the form of Eq. (2), yielding (conceptually) a turbulent flame thickness that first increases and then decreases again, which is probably a better representation of the combustion process inside engines. More detailed information on the evolution of δ t inside engines is difficult to measure or estimate because of the complication of end-gas compression and corresponding changes in pressure and temperature which could increase as well as decrease δ t [16]. This viewpoint does not follow the historical distinction in (quasi-dimensional) engine modeling literature between eddy-burning (entrainment) models and flamelet models (as in e.g. ref. [23]). Flamelet models not using the above framework and directly modeling dm b /dθ ~ ρ u A f u t have been reported to need special measures for a correct simulation of the end of combustion [20], further strengthening the argument of using Eqs. (1) and (2) as a model for a finite δ t and using the turbulent burning velocity models to provide u te. 5. Laminar burning velocity correlation The turbulent burning velocity models need laminar burning velocity data of the air/fuel/residuals mixture at the instantaneous pressure and temperature. As most models use the laminar burning velocity as the local burning velocity, the stretched laminar burning velocity should be used. This implies the need for either a library of stretched flamelets or a model for the effect of stretch. A number of stretch models for use in turbulent combustion modeling have been suggested, most of which embody the effects of stretch in a factor I 0, with u n = I 0 u l [17]. Most of these models assume a linear relation between flame speed and stretch, valid for weakly perturbed laminar flames. Models for I 0 have been proposed, tailored for use in spark ignition engine modeling (e.g. in ref. [20]). However, calculating the local flame speed from stretch-free data and a stretch model requires stretch-free data, naturally. As of today, there is insufficient data on stretch-free burning velocities at engine conditions, for any fuel. Stretch and instabilities hamper the experimental determination of stretch-free data at higher (engine-like) pressures [24]. Because of the very high mass diffusivity of hydrogen (the highest of all fuels), a lean to stoichiometric hydrogen/air mixture (i.e. for equivalence ratios such as used in hydrogen engines) will be diffusionally unstable, both from the Lewis number (D T << D M,H2 ) as from the preferential diffusion (D M,H2 >> D M,O2 ) point of view [25]. Experimental data [24,26] shows hydrogen/air flames at atmospheric conditions to have positive Markstein numbers close to stoichiometric, but all mixture ratios lean of stoichiometric have negative Markstein numbers as soon as the pressure exceeds about 4 bar. Thus, all flames at engine-like conditions are unstable and will be cellular from inception. Two of the present authors have worked on the laminar burning velocity of hydrogen mixtures, compiling data from the literature [27], and looking at numerical [27] as well as experimental [24] means to determine a suitable correlation. A laminar burning velocity correlation has been determined, based on measurements of cellular flames [4,24], as the best (intermediate) solution available at present. This correlation will be used for the simulations, without any stretch model as the effects of stretch are embodied in the data. The correlation by Iijima and Takeno [28] will also be tested, being the only one from literature that incorporates the effect of equivalence ratio, pressure and temperature. The term expressing the effect of residual gas fraction, reported in refs. [4,24] and determined by two of the present authors, is added to this correlation to describe the effects of residuals. For completeness, the un correlation constructed by two of the present authors [4,24] is given here: u n (φ, p, T, f) = u n0 (φ)(t/t 0 ) αt (p/p 0 ) βp (1-γf) (11) 4/9

5 Here, the reference conditions T 0 and p 0 are 365K and 5 bar respectively. The influence of the equivalence ratio at these reference conditions is embodied in u n0 and was estimated at: u n0 = -4.77φ φ φ (12) The values for α T, β p and γ are the following: The temperature exponent α T has a mean value of The pressure exponent β p is dependent on the equivalence ratio, φ < 0.6 : β p = 2.90 φ φ φ (13) φ > 0.6 : β p = φ (14) The parameter γ expressing the effect of residual gases, is given by γ = φ 6. Calibration The calibration sets the coefficients in the heat transfer model, the flame development model and the turbulent burning velocity model. Once the code has been calibrated for a single measurement, the calibration coefficients are kept constant and the models predictive capability (simulations at other operating conditions) can be evaluated. The constants to calibrate are: heat transfer model: the coefficient a in Annand s model, with separate values during compression, combustion and expansion turbulent burning velocity model: a coefficient C 2 has been added to the turbulent burning velocity models, as shown above; increasing C 2 increases the mass entrainment rate. A coefficient C 3 has been added to the burn-up time constant τ b in eq. (3), τ b = C 3 Λ/u n. Increasing C 3 decreases the mass burning rate (or, alternatively, increases the flame thickness) The calibration is done by matching a simulated cylinder pressure trace to a measured pressure trace. The compression heat transfer coefficient can be calibrated to a motored pressure trace. The other coefficients need to be set more or less simultaneously. A series of measurements on a carbureted hydrogen fueled CFR engine reported in ref. [29] was selected to evaluate the turbulent burning velocity models. These measurements comprise variable fuel/air equivalence ratios φ, ignition timings IT and compression ratios CR, as shown in Table 1. Two parameters remained constant while a third was varied. A measurement with interlying values for φ, IT and CR was chosen for the calibrations, with φ = 0.59, IT = 15 ca and CR = 9. As mentioned above, the laminar burning velocity correlations by Iijima and Takeno [28] and by the present authors were used in the engine code. However, the calibrations failed with the correlation of Iijima and Takeno, with the rate of pressure rise too high even when programming laminar flame propagation (i.e., setting u te = u n ). This is probably caused by the pressure exponent that is too high; all calibrations and further simulations were therefore done with the correlation derived in the present work. The calibration coefficients C 2 tuning the turbulent burning velocity for best correspondence with the measured pressure trace were as follows: Damköhler : C 2 = 1.7 Gülder: C 2 = 0.52 Bradley : C 2 = 0.32 Fractals : C 2 = 1.013, corresponding with a maximum fractal dimension D 3 of 2.38 Lipatnikov : C 2 = 0.37, somewhat lower than the values found in the literature, that vary between 0.5 and 1.0 Peters: C 2 = 0.87 All values are of order unity, as would be expected for model tuning constants. The best value for the coefficient C 3 in the burn-up time constant was found to be 0.01, this value was used for all turbulent burning velocity models. The low value perhaps indicates a different choice for the length scale in Eq. (3) would be more physical, it is noteworthy that using the Taylor length scale would result in a calibration coefficient of order unity. The pressure trace obtained with the Damköhler model using the calibration coefficients as given above is compared with the measured pressure trace in Fig. 1. The agreement is not perfect but is considered very good. The calibrations using the other models with the coefficients given above are very similar. All simulated pressure traces deviate from the measured pressure trace around the maximum pressure, predicting pressures that are too high. This is probably explained by the neglect of blowby. 5/9

6 φ IT ( ca) CR Table 1. Measurements on CFR carburetted set up cylinder pressure (Pa) 5x10 6 4x10 6 3x10 6 2x10 6 1x ca 'Damköhler' measurement Figure 1. Calibrated pressure trace using the Damköhler model, compared to measurement, pressure versus crank angle, combustion close-up; CFR, 600 rpm, IT = 15 ca, CR = 9, φ = Comparison of model predictions to measurements (validation) For ease of comparison, the simulation results are synthesized into graphs showing the peak pressure p max, the position of peak pressure θ pmax and the gross indicated work W i,g (the indicated work from compression to expansion, or from inlet valve closing to exhaust valve opening [30]). Figure 2 compares these quantities with the measured ones, for variable ignition timing. Trends are well reproduced by all models. Results for W i,g are within 3%, which is very good. W i,g (J) measurement 'Damköhler' 'Lipatnikov' Gülder 'Bradley' Peters 'Fractals' θ pmax ( ca) W i,g (J) θ pmax ( ca) p max (bar) p max (bar) measurement 'Damköhler' 'Lipatnikov' Gülder 'Bradley' Peters 'Fractals' IT ( ca) Figure 2. Peak pressure, peak pressure position and gross indicated work: simulations compared to measurement, 600 rpm, φ = 0.6, CR = 9, variable ignition timing CR Figure 3. Peak pressure, peak pressure position and gross indicated work: simulations compared to measurement, 600 rpm, φ = 0.6, IT = 15 ca BTDC, variable compression ratio 6/9

7 Figure 3 compares p max, θ pmax and W i,g with measured values for variable compression ratio. Trends are reasonably well reproduced by all models and gross indicated work is predicted within 3%. However, the experimentally observed increase in W i,g when going from a compression ratio of 7 to 8 is not reproduced by the simulations. This could be due to experimental uncertainty (the uncertainty on W i,g is about 3 J [4]). Figure 4 plots results for variable equivalence ratio. The ability to predict the effects of mixture richness is clearly the criterion to distinguish between models: the models of Gülder, Bradley, Lipatnikov and the Fractals model follow the trends observed in the measurements, whereas the models of Damköhler and Peters predict quasi linear dependencies on equivalence ratio. The peaking of the position of peak pressure with equivalence ratio is not recovered; maximum pressures for the lean mixtures are more than 50% higher than measured; and the bending of gross indicated work with equivalence ratio is also not predicted W i,g (J) measurement 'Damköhler' 'Lipatnikov' Gülder 'Bradley' Peters 'Fractals' θ pmax ( ca) p max (bar) ,36 0,42 0,48 0,54 0,60 0,66 0,72 φ Figure 4. Peak pressure, peak pressure position and gross indicated work: simulations compared to measurement, 600 rpm, IT = 15 ca BTDC, CR = 9, variable fuel/air equivalence ratio The appearance of three model groups, Gülder- Bradley - Lipatnikov, Damköhler -Peters and Fractals is easily understandable when the model equations are rewritten using the definitions of turbulent Reynolds number, Damköhler, Karlovitz and Lewis numbers, and using (1 + x) 1/2 1 + x/2 to obtain a first order approximation of Peters model, which is valid for small x, or in this case: for a large Damköhler number (which is the case for stoichiometric to moderately lean hydrogen/air mixtures [31]). The fully developed value of 2.35 is used for the fractal dimension in the Fractals model. This yields the following model equations: Damköhler /Peters: u te ~ Cu + u n (15) Gülder/ Bradley / Lipatnikov (with D a diffusivity: hydrodynamic, thermal or molecular): u te ~ Cu a u n b Λ c D d + u n (16) Fractals : u te ~ Cu 0.26 u n Λ 0.26 υ u u n (17) 7/9

8 In the present case of constant engine speed and thus constant rms turbulent velocity u at ignition time, the models of Gülder, Bradley and Lipatnikov are very similar to each other. The model of Lipatnikov would actually be identical to Gülder s model if the diffusivity chosen by Lipatnikov and Chomiak [15] to evaluate the laminar flame thickness would have been the kinematic viscosity instead of the thermal diffusivity. For large Damköhler numbers, Peters model reduces to the simple Damköhler model. Only for the leanest condition of φ = 0.38, the results obtained with Peters model can be seen to start deviating from the results obtained with the Damköhler model. Although the Fractals model uses similar terms in its u te equation as the Gülder group, the exponents are quite different, so this model is placed in a third group, although the results are quite close to the results obtained by the models in the Gülder group. 8. Conclusions and future work A simulation code for the power cycle of hydrogen fueled engines has been described, using a quasidimensional model with standard modeling assumptions. A combustion model consisting of two differential equations was used, one for the entrainment mass burning rate and one for the fully burned mass burning rate, to account for the finite turbulent flame thickness (affecting the end of combustion). A number of turbulent burning velocity models were evaluated in this framework, comparing simulation results with an experimental cylinder pressure database. It was described how the use of an existing correlation for the laminar burning velocity of hydrogen/air mixtures resulted in a faulty pressure development, whereas the use of the correlation constructed by the authors gave consistent results. After calibration to a single reference condition, simulations were run for different conditions, where ignition timing, compression ratio and equivalence ratio were varied compared to the reference condition. All turbulent burning velocity models considered were able to qualitatively as well as quantitatively predict the effects of changes in ignition timing and compression ratio. The ability to recover the effects of changes in equivalence ratio clearly is the benchmark to distinguish between models, with the Gülder, Bradley, Fractals and Lipatnikov model predictions corresponding well with experiments and the Damköhler and Peters models failing. Hydrogen is the ideal fuel to assess models ability to recover equivalence ratio effects due to its wide flammability limits. Measurements at variable engine speeds are now planned, so evaluation of the models at variable engine speeds will be the next step. Thus, the models have not been tested for their ability to recover the correct behavior with the rms turbulent velocity (being the prime quantity affected by engine speed). The variations in ignition timing, compression ratio and equivalence ratio on the other hand, result in changing pressures, temperatures and mixture compositions. This enabled the evaluation of the correspondence between simulation and experiment over a fairly wide range of conditions. It would be interesting to look at results for leaner mixtures, e.g. up to φ = 0.25, as used in hydrogen engines, as these conditions are the most challenging for the combustion models. This will be the subject of future work. References [1] Tang X. et al., Ford P2000 hydrogen engine dynamometer development. SAE paper , [2] Akagawa H. et al., Development of hydrogen injection clean engine. 15th World Hydrogen Energy Conference, paper 28J-05, [3] Verhelst S., Verstraeten S. and Sierens R. A Critical Review of Experimental Research on Hydrogen Fuelled SI Engines, SAE paper nr , Detroit, USA, [4] Verhelst S., A study of the combustion in hydrogen-fuelled internal combustion engines. PhD thesis, Ghent University, Gent, Belgium, [5] Fagelson J.J., McLean W.J., and de Boer P.C.T., Combust. Sci. Technol. 18: 47 57, [6] Prabhu-Kumar G.P., Nagalingam B., and Gopalakrishnan K.V., Int J Hydrogen Energ 10: , [7] Keck J.C., Proc. Combust. Inst. 19: , [8] Johnson N.L., Hydrogen as a zero-emission, high-efficiency fuel: uniqueness, experiments and simulation. 3rd Int. Conf. ICE97, Internal combustion engines: experiments and modeling, [9] Polášek M., Macek J., Takáts M., and Vítek O., Application of advanced simulation methods and their combination with experiments to modeling of hydrogen fueled engine emission potentials. SAE paper , [10] Ma J., Su Y., Zhou Y., and Zhang Z.,Int J Hydrogen Energ 28: 77 83, [11] Vandevoorde M., Sierens R., and Dick E., ASME J. Eng. Gas Turbines Power 122: , [12] Borman G. and Nishiwaki K., Prog. Energy Combust. Sci. 13: 1 46, /9

9 [13] Hall M.J. and Bracco F.V., A study of velocities and turbulence intensities measured in firing and motored engines. SAE paper , [14] Blizard N. C. and Keck J. C., Experimental and theoretical investigation of turbulent burning model for internal combustion engines. SAE paper , [15] Tabaczynski R. J., Trinker F.H., and Shannon B.A.S., Combust. Flame 39: , [16] Hicks R.A., Lawes M., Sheppard C.G.W., and Whitaker B.J., Multiple laser sheet imaging investigation of turbulent flame structure in a spark ignition engine. SAE paper , [17] Lipatnikov A.N. and Chomiak J., Prog. Energy Combust. Sci. 28: 1 74, [18] Gülder Ö.L., Proc. Combust. Inst. 23: , [19] Bradley D., Lau A.K.C., and Lawes M., Phil. Trans. R. Soc. of Lond. A-338: , [20] Wu C. M., Roberts C. E., Matthews R. D., and Hall M. J., Effects of engine speed on combustion in SI engines: Comparison of predictions of a fractal burning model with experimental data. SAE paper , [21] Zimont V.L., Exp. Therm. Fluid Sci. 21: , [22] Peters N., Turbulent combustion. Cambridge University Press, [23] Heywood J.B., Combustion and its modeling in spark-ignition engines. In Int. Symposium COMODIA 94, [24] Verhelst S., Woolley R., Lawes M., Sierens R., Proc. Combust. Inst. 30: , [25] Clavin P., Prog. Energy Combust. Sci. 11: 1 59, [26] Aung K. T., Hassan M. I., and Faeth G. M., Combust. Flame, 112:1 15, [27] Verhelst S., Sierens R., A laminar burning velocity correlation for hydrogen/air mixtures valid at sparkignition engine conditions. ASME Spring Engine Technology Conference, paper ICES , [28] Iijima T. and Takeno T., Combust. Flame, 65:35 43, [29] Sierens R., Verhelst S., Comparison between a carburetted and a port injected hydrogen fuelled single cylinder engine. 8th EAEC European Automotive Congress, paper SAITS01009, [30] Heywood J.B., Internal Combustion Engine Fundamentals. McGraw-Hill, [31] Verhelst S., Sierens R., Simulation of hydrogen combustion in spark-ignition engines. 14th World Hydrogen Energy Conference, /9