Comparisons of methods for reconstructing particle size distribution from its moments

The reconstruction of particle size distribution (PSD) from a finite number of its moments is extremely important for many industrial operations, especially in dynamic multi-phase flows in chemical engineering where the composition of discrete phases evolves with time and space. For example, control of the fuel droplet PSD in diesel engines has a significant influence on the flame structure. Different reconstruction methods have been proposed in the literature during the last decades. However, most of them have only been tested with particular and simple cases. This paper describes and evaluates three typical reconstruction methods: parameter fitting method with prescribed distributions, extended quadrature method of moments (EQMOM) and maximum entropy (ME). The corresponding mathematical formulations of these methods are described. A number of test cases are devised where different types of PSDs are adopted so that a comprehensive evaluation of these methods (advantages and limitations) can be achieved. In this paper, a new approach for estimating the particle size range is proposed to improve the reconstruction performance of the ME method. Furthermore, a coupled moment projection method (MPM) and the revised ME approach for particle dynamic simulation is introduced and compared with EQMOM for a combined particle process of inception, growth, coagulation and fragmentation. Results suggest that the revised ME method is very efficient with a wide range of applicability. High accuracy can be achieved with this revised ME method as long as sufficient moments are adopted. By contrast, the parameter fitting method has a narrow applicability and EQMOM suffers from the oscillation problem when more than one kernel function are used. The findings observed in this work can be used as a good guide for choosing a proper PSD reconstruction technique.