Similarity Solutions of Vertical Plane Wall Plume Based on Finite Analytic Method
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摘要: 应用计及浮力对湍动能及其耗散率的影响的k-epsilon湍流模式，结合有限分析法对密度差引起的平面铅垂紊动壁羽流进行了数值分析．在均匀环境条件下控制该类流动的连续性方程、流动方向的动量方程、浓度扩散方程、湍动能及其耗散率方程存在相似解．考虑到浮力通量守恒条件，应用有限分析法给出了铅直壁羽流的速度、相对密度差、湍动能及耗散率的分布，进而给出了各物理量最大值沿主流方向变化的关系式．湍流Schmidt数为1.0时的计算结果与实验资料吻合较好，表明应用有限分析法分析铅垂平面羽流是有效的，即在分析壁羽流时浮力对湍动能及其耗散率的影响应该予以考虑．Abstract: 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 with numerical method is good, i. e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account. The finite analytic method is effective.
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Key words:
- wall plume /
- similarity /
- turbulence model /
- finite analytic method /
- buoyancy effect
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