An Efficient Petrov-Galerkin Chebyshev Spectral Method Coupled with the Taylor-series Expansion Method of Moments for Solving the Coherent Structures Effect on Particle Coagulation in the Exhaust Pipe

Abstract

An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simu- late the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It sat- isfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is much simpler than the method of moment (MOM) and quadrature method of moments (QMOM), and is a promising method to approximate the aerosol general dynamics equation (GDE). The coupled fluid and particle fields were presented with three non-dimensional parameters (i.e., Reynolds number, Re; Schmidt number based on particle moment, ScM, and Damkohler number, Da in the governing equations). The temporal evolutions of the first three moments were discussed for different Damkohler numbers. The particle volume increases at all locations in the flow field, the larger the Damkohler number, the greater generation rate of large-scale particles. Far away from the eddy structure, the effect of the fluid convection on particle coagulation is small; however, the particle coagulation within the eddy core has an obvious wave-like distribution because of the large-scale eddy. The results reveal that the coherent structures play a significant role in the particle coagulation inside an exhaust pipe.