Thermophoretic Effects on Soot Distribution in a Direct-injection Diesel Engine 960320
A recently developed stochastic particle approach for computing soot particle dynamics is implemented in a three-dimensional model for flows, sprays, combustion and emissions in Diesel engines. The model is applied to study the distribution of soot particles in a direct-injection Diesel engine. In particular, the effect of thermophoresis on soot distribution is examined. It is shown that thermophoresis could be important once the soot particles are brought close to the walls, i.e. within the boundary layer, by turbulent eddy convection or as a result of the orientation of the sprays. Thermophoresis does not appear to result in a change in the distribution of soot in the regions outside the boundary layer as the characteristic time associated with turbulent eddy convection is at least an order of magnitude shorter than that associated with thermophoresis and it and bulk convection are by far the dominant factors in determining the soot distribution.
Particulate emissions from Diesel engines are stringently regulated because of their harmful effects on health and the environment. The limit on particulate matter emissions from heavy-duty Diesel engines is 0.1 g/bhp.hr for 1994 and become tighter in the coming years [1, 2]. The challenge of attaining these goals by faster mixing and faster combustion is confounded by the fact that NO emissions, which are also toxic and therefore regulated, tend to increase as particulate emissions decrease and vice versa . Diesel engine manufacturers have adopted various strategies, such as increased injection pressures and retarded timings, to meet these goals [1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11]. But as the regulations become tighter, and the rather obvious sources of particulate emissions are better controlled, it becomes necessary to understand the physical processes that control particulate formation and oxidation in greater detail and depth so as to design effective strategies of control.
In identifying and understanding these processes, wall deposition mechanisms have been explored as a possible one [12, 13]. It has been suggested that during combustion in the Diesel engine, wall deposition mechanisms result in particulate matter being deposited on walls where they are shielded from oxidation. During the exhaust blowdown process, these particulates that are on the wall would be vigorously stirred and stripped off the walls by the shear forces induced by the high velocity gas stream and they would then be reentrained and exhausted. The lack of oxidation of particulate matter trapped on walls results in the particulate concentration in the chamber being higher than it should be otherwise during exhaust .
Several of these wall deposition mechanisms that might be relevant in Diesel engines have been reviewed in the literature by Suhre and Foster . They considered thermophoresis, inertial deposition, electrophoresis and gravitational sedimentation. Characteristic times associated with these processes were estimated and the authors concluded that thermophoresis was likely to be the most important of these mechanisms. Inertial deposition, though less important, was also likely to be a minor contributor. In thermophoresis, particles move down a temperature gradient because of the differential forces acting on them due to differences in molecular collisions on the hot and cold sides . Experimental measurements made by Kittelson et.al  suggests that the thermophoretic effect is likely to be an important mechanism affecting soot deposition on walls and emission from Diesel engines. They carried out measurements of deposition rates on a probe in an indirect-injection Diesel engine and concluded that wall deposition rates were significant and caused by thermophoresis. They support their results by using simple analysis. Similar measurements and analysis were also carried out by Suhre and Foster who arrived at similar conclusions .
Theoretical expressions for the thermophoretic force have been derived in the limit of high Knudsen number  and low Knudsen number . The Knudsen number is the ratio of the gas mean free path to the soot particle radius. For soot particles, Knudsen numbers may vary by as much as three orders of magnitude and so using one expression or the other is not always rigorously justified . However, the likely error in using one expression over the other is only a few percent even in the limit and so theoretical expressions for thermophoretic velocities may be derived by equating the thermophoretic force to the drag force on the particle which are approximately valid over the range of particle sizes that are encountered in a Diesel engine . Then, characteristic times associated with the thermophoretic process may be estimated. These estimates would typically lie in the order of milliseconds, which in an engine running at 1500rpm would correspond to about 100°CA. Such estimates have been presented in the work of Kittelson et.al  and Suhre and Foster . However, these estimates do not consider the details of the spatial and temporal variations in the flowfield, such as in the spatial distribution of temperature, the gas velocity and the details of the boundary layer. The anaylsis presented have been essentially zero-dimensional.
In this work, a three dimensional model for flows, sprays, combustion and emissions in Diesel engines is used to evaluate the possible effects of thermophoresis on soot distribution in a Diesel engine. The accuracy of the model has been assessed previously in comparisons with experimental data . These comparisons were of cylinder pressure, soot and NO as a function of crank angle. Adequate quantitative agreement and also agreement in trends with changes in engine conditions were obtained. Such models are being used increasingly to provide guidance in identifying strategies for engine design to improve efficiency and reduce emissions [17, 18, 19 and 20]. Also, in this work, we use a recently developed method to compute soot particle dynamics. This approach, based on a stochastic particle technique which is described in detail elsewhere , is briefly summarized below. The approach allows the calculation of the effects of various forces on the soot particles with relative ease and hence is appropriate for computing thermophoretic effects in multidimensional computations.
In the next section, we describe the three-dimensional model that we use in our work. The stochastic particle approach is briefly described in this section. Following this, we present and discuss the results of our work. We end the paper with summary and conclusions.