A mathematical model that uses an adaptive mesh for predicting scalar transport in a transient incompressible jet

摘要

This paper describes a mathematical model for fluid flow and scalar transport in the impulsively started jet. The motivation of the work is the goal of developing a model for a diffusion flame found in the compression-ignited, direct injection (CIDI) engine. The mathematical model in this paper describes the transient jet's hydraulic structure using a combination of closed-form equations for two flow structures, a quasi steady state jet and a steady state spherical vortex. Numerical methods are employed to couple the two flow structures as well as to extend them to transient. The resulting hydrodynamic model is used in a numerically-based model for predicting the entrainment and transport of a scalar (either mass or heat) in the transient jet. Fluid flow in the jet is assumed quasi-steady and taken from closed-form analytical results. The jet's scalar transport is calculated on a time-adaptive mesh. The fluid flow in the spherical vortex is also based on closed-form mathematics, which are made transient as a result of an adaptive mesh. The scalar quantity is transferred from the jet to the vortex by means of a source term distributed within the vortex's growing domain. Results derived from the model illustrate the distribution of the scalar quantity in the transient jet as a function of time from the start of injection. The results can be calculated on a PC in a matter of minutes. These results are compared to results from a FIDAP simulation and seem reasonable, but experimental data are needed for more reliable validation as well as for a better understanding of the interaction of the two structures.