高转速转静盘腔流动换热相似性数值研究

Numerical Study on Similarity of Flow and Heat Transfer in a High-Speed Rotor-Stator Cavity

关键词:  高转速  转静盘腔  热边界  马赫数准则  相似性

Key words:  High speed rotating  Rotor-stator cavity  Thermal bondary  Mach number criterion  Similarity

摘要:

为了得到高转速转静盘腔流动换热实验中的相似准则，在定几何、变物性、可压缩和有耗散的情况下，对转静盘腔中的控制方程进行无量纲化，得到了除无量纲位置外的8个无量纲准则数。并以高转速转静盘腔模型为基础，采用数值方法对影响发动机工况（高温）和实验工况（常温）换热相似性的主要无量纲准则数进行了研究。研究表明：流动雷诺数、旋转雷诺数、流动马赫数、旋转马赫数和转子表面温度与来流气流温度之比是影响换热相似性的主要因素。计算结果显示：在热边界条件相似时，仅需保证发动机状态与实验状态的雷诺数相等就可保证局部努塞尔数相同；仅需保证发动机状态与实验状态的马赫数相等就可保证绝热壁温分布相同；但只有保证实验状态和发动机状态的雷诺数和马赫数都相等时，无量纲换热量才保持一致。

Abstract:

In order to gain the similarity criterion in the experiment of flow and heat transfer in high-speed rotor-stator cavity， the governing equations in the rotor-stator cavity were nondimensionalized under the condition of fixed geometry， variable properties， compressibility and dissipation considered. And eight dimensionless criterion numbers are obtained except for the dimensionless position. Based on a high-speed rotor-stator cavity model，numerical simulations were carried out under the engine typical operating conditions （high temperature） and experimental conditions （normal temperature） in order to study the main dimensionless numbers related to similarity criterion. The research shows that the flowing Reynolds number， rotating Reynolds number， flowing Mach number， rotating Mach number and temperature ratio between the rotor wall and inlet airflow are the main factors affecting the similarity of heat transfer in rotating disk cavity. The numerical results suggest when thermal boundary is similar，the local Nusselt number at experimental conditions equal to that of engine condition is only caused by the same Reynolds number. The adiabatic disc temperature at experimental conditions equal to that of engine condition is only caused by the same Mach number. When the Reynolds number and the Mach number are the same， the dimensionless heat flux at the experimental conditions equals to that of the engine condition.