Choked Flow and Heat Transfer of Low Density Gas in a Narrow Parallel-Plate Channel

本文首先采用有限差分数值计算、实验和解析解相结合的方法，研究了低密度空气通过绝热壁面平行平板窄缝通道的连续流动和滑移阻塞流动。在基于二维可压缩粘性边界层方程的数值计算中，通过将压力项与动量方程解耦，改进了以往的计算方法，提高了阻塞状态的计算精度。流量系数、压力分布和表面温度分布的数值计算结果与实验数据吻合较好。随着上游槽道压力的降低，摩擦系数和恢复因子的数值计算结果接近不可压缩发展流的渐近值。其次，采用实验、数值模拟和解析近似解相结合的方法，研究了均匀热流壁面平行平板窄缝通道内连续和滑移阻塞气体流动的排放和换热特性。流量系数和壁面温度分布的数值计算结果与实验结果吻合较好。壁面传热对流量系数的影响与壁面无因次热输入有关。提出了以绝热壁温、体平均温度和总温度为参考温度的三种Nusselt数，并阐明了粘性加热对Nusselt数的影响。

In the first place, the continuum and slip choked flows of low-density air through a narrow parallel-plate channel with adiabatic walls are investigated by means of finite-difference numerical calculation, experiment and analytical solution. In the numerical calculation based on two-dimensional compressible viscous boundary layer equations, the previous method is improved to achieve a higher precision of the choked state by decoupling the pressure term from momentum equation. The numerical results of discharge coefficient, pressure distribution and surface temperature distribution agree well with the experimental data. As the upstream tank pressure drops, the numerical results of friction coefficient and recovery factor approach the asymptotic values for the incompressible developed flow.Secondly, the discharge and heat transfer characteristics of the continuum and slip choked gas flows through a narrow parallel-plate channel with uniform heat flux walls are studied by experimental means, numerical simulation, and analytical approximate solution. The numerical results of the discharge coefficient and the wall surface temperature distributions agree relatively well with the experimental results. The effects of the heat transfer at the walls on the discharge coefficient can be correlated with the dimensionless heat input at the walls. Three kinds of Nusselt numbers which are defined by adiabatic wall, bulk mean, and total temperatures as a reference temperature, respectively, are proposed and the effects of the viscous heating on these Nusselt numbers are clarified.