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Solutions of the twin plane jets HF chemical laser flow based on a turbulent kinetic theory, due to a modified Green’s function method, are presented. The calculated results of probability density function (PDF) of various chemical species in velocity space, and mass fraction concentration distributions of various reactants and products in the flow field, are revealed and discussed in this analysis. The transport phenomena of different pumping rate, collisional deactivation rate, and radiative deactivation rate in the interaction between the twin plane jets HF chemical laser show that the properties of species mass fraction concentrations, collisional reaction rate, and radiative incident intensity are the dominant factors. The present study provides the fundamentals for theoretical understanding of twin plane jets HF chemical laser and further application to multiple‐jet HF chemical laser analysis.

A transport equation for the one‐point velocity probability density function (pdf) of turbulence is derived, modelled and solved. The new pdf equation is obtained by two modeling steps. In the first step, a dynamic equation for the fluid elements is proposed in terms of the fluctuating part of Navier‐Stokes equation. A transition probability density function (tpdf) is extracted from the modelled dynamic equation. Then the pdf equation of Fokker‐Planck type is obtained from the tpdf. In the second step, the Fokker‐Planck type pdf equation is modified by Lundgren’s formal pdf equation to ensure it can properly describe the turbulence intrinsic mechanism. With the new pdf equation, the turbulent plane Couette flow is solved by the direct finite difference method coupled with dimensionality reduction and QUICKER scheme. A simple boundary treatment is proposed such that the near‐wall solution is tractable and then no refined grid is required. The calculated mean velocity, friction coefficient, and turbulence structure are in good agreement with available experimental data. In the region departed from the center of flow field, the contours of isojoint pdf of V₁ and V₂ is very similar to that of experimental result of channel flow. These agreements show the validity of the new pdf model and the availability of the boundary treatment and QUICKER scheme for solving the turbulent plane Couette flow.

A turbulent kinetic theory due to Chung and a Green’s function method by Hong were employed to solve a reacting turbulent plane jet problem. An instantaneous mixing concept was used to simulate the steady state of turbulent plane jet with combustion. The probability density function description of the fluid elements in a turbulent reacting flow could properly explain the turbulent flame zone structure and the turbulent transport of heat, momentum and chemical species even under the infinitely fast reaction rate assumption. The calculated distributions of the various moments of the turbulent combustion field were found in good agreement with the available experimental data. The dynamic behaviour of combustion in the turbulent field could be better understood via the probability density function description of the present turbulent kinetic theory approach.