0D modeling aspects of flame stretch in spark ignition engines and comparison with experimental results
Introduction
Nowadays, due to the increasingly restrictive standards on pollutants and CO2 emissions, the car industry is developing new technologies which require fuel adaptation. Moreover, in order to compensate for the depletion of fossil energy resources, oil companies have introduced biofuels for Spark-Ignition (SI) engines. These fuels can be used either pure or blended with gasoline. As a result, the automotive and oil industries are facing a context of fuel diversification.
However, the use of various fuels in a SI engine can be responsible for a different combustion behavior and could therefore impact the pollutant emissions [1], auto-ignition delays [2] but also the engine efficiency. For SI engines, the heat release rate is linked to the flame propagation speed of the expanding flame kernel. In addition, while aiming at improving efficiency, oil companies have sought to develop fuels that burn faster than typical gasoline. However, in a SI engine, the kernel expansion flame speed depends not only on the fuel but also on several additional phenomena such as turbulence [3], flame stretch [4] and type of ignition system [5]. As a first step to evaluate potential substitutes for gasoline, the fundamental laminar burning speed is mainly investigated [6], [7], [8], [9], [10]. Moreover, it is a key parameter for combustion modeling [11]. This burning speed corresponds to the speed of a one-dimensional planar adiabatic flame in laminar conditions without any instability and it is a function of pressure, temperature, fuel, dilution and fuel/air equivalence ratio. The fundamental laminar burning speed cannot be considered as the consumption speed of an expanding flame, however, since the flame speed of expanding flames is submitted to stretch, which contains two contributions: curvature and strain rate [12]. Flame stretch, which can be defined as the relative growth rate of the flame surface, is related to the thermo-diffusive characteristics of the fuel [13], [14], [15].
Therefore, depending on the fuel used, the different responses to flame stretch will impact the flame propagation differently. While this effect has been fully investigated in laminar conditions [16], [17], [18], only a few recent studies have presented the effect of flame stretch in SI engines [19], [20], [21], [22]. Besides, only a few Computational Fluid Dynamics (CFD) models for spark ignition consider the laminar burning speed dependence on the flame stretch [23], [24], [25] and many models are mainly based on the unstretched laminar burning speed. It is still an open question, however, how to take flame stretch phenomena into account.
In a previous study [19], the impact of the engine speed and of the air/fuel mixture (air with isooctane, propane and methane at different fuel/air equivalence ratios) on the flame stretch rate was studied. It was shown that the flame stretch sensitivities observed in the laminar regime directly impact the combustion process inside the engine. In order to validate the results, an accurate study of flame visualization was performed and the results can be found in [21]. Different lean mixtures presenting almost the same unstretched laminar burning speed were selected. The mixtures also had different Lewis numbers which is a relevant parameter to describe thermo-diffusive instabilities as well as flame stretch interactions. Global flame wrinkling and local flame curvature were also studied.
Recently 0D models have shown great interest for reproducing engine performances with a computational cost that is competitive compared to CFD codes. Even though 0D modeling is less detailed in the description of the physics than the LES technique, it is able to reproduce complex phenomena such as pollutant emissions for SI engines [26], blow-by leakage, fuel injection and engine deformations for direct injection Diesel engines [27]. A 0D model was developed [28] by the authors on the basis of the zero dimensional (0D) Flame Surface Density equation [29] and in the present work, it is enhanced with a sub-model for laminar flame stretch. The mean flame surface is considered to be a sphere, which intersects with the chamber wall. The model calculates a flame radius as well as a flame wrinkling factor and is coupled with a two-zone thermodynamic model. A schematic representation of the model is shown in Fig. 1. This paper focuses on reproducing the previously reported experimental results [21] through 0D modeling, to clarify at which combustion stage flame stretch is important to consider and why the stretched laminar burning speed must be taken into account in SI combustion models.
The main objectives of this paper are:
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To propose a new 0D model that takes into account the effect of stretch on flame propagation for a Spark-Ignition engine.
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To better understand the role of wrinkling and stretch in the flame speed evolution.
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To address new comparisons with experimental results obtained from an optical engine to validate the model. In particular, the calculated burnt mass fraction and in-cylinder pressure, which are key parameters when calibrating a new engine, are compared to experimental data.
This study finally demonstrates the importance of taking stretch into account, especially curvature in the laminar flame speed formulation, to better predict the burnt mass fraction. With such a modification, the overall model is not only able to satisfactorily predict the end of the combustion phase as developed in previous studies [30], [31] but it is also relevant for the early flame propagation phases when flame stretch is high. It is thus a powerful tool for predicting the performances of a new SI engine design with different kinds of fuel and in a wide range of conditions.
Section snippets
Model
In this section the combustion model is briefly presented. Some sub-models were described in a previous study [28] and are briefly covered here. In order to simulate the compression and combustion stages in a SI engine, a two-zone thermodynamic model was used. This kind of modeling takes into account two zones, one for the unburnt (fresh) gases and one for the burnt gases. The equations of this model are the results of the energy conservation inside the combustion chamber. For the heat transfer
Experimental setup
The results obtained from the 0D model were compared to the experimental results obtained in [21]. The experimental set-up has been fully described in several Refs. [19], [21], [46], [55]. The optical engine specifications are summarized in Table 3. In [21], experimental results were deduced from images obtained with Mie-Scattering Tomography. As previously said, no residual burnt gases were present in the cylinder during the experiment since the engine was fired only once every 6 cycles. The
Results and discussion
A basic validation of the simulations consists in calculating the characteristic non-dimensional combustion numbers, checking whether they agree with already published results and exploring their evolution during the engine cycle, during which pressure and temperature evolve. In Fig. 2, the Lewis numbers (calculated with Eq. (8)) for all three fuels are plotted during the combustion cycle. They remain almost constant during combustion and their values match with the ones calculated by CHEMKIN
Conclusion
A 0D Spark Ignition combustion model was developed on the basis of the 0D Flame Surface Density equation, enhanced with a sub-model for laminar flame stretching. Simulation results were compared against previously published experimental results of different lean mixtures (isooctane, propane and methane) presenting almost the same unstretched laminar burning speed during the beginning of combustion.
The Lewis and Markstein numbers remain almost constant during the combustion cycle. Their values
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