Similarity solutions of vertical plane wall plume based on finite analytic method

• Published in: Applied mathematics and mechanics 2007-04, Vol.28 (4), p.447-454, Article 447
• Main Author: 槐文信 曾玉红
• Format: Article
• Language: English
• Subjects: Buoyancy; Computational fluid dynamics; Energy; Energy dissipation; Fluid flow; Kinetic energy; Mathematical analysis; Mathematical models; Plumes; Schmidt number; Similarity solutions; Turbulence; Turbulent flow; Vertical distribution; 垂直平面壁; 有限解析法; 浮力效应; 相似解
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-007-0404-z

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.