倾斜热平板上自然对流气体流动的非Boussinesq稳定性分析
Non-Boussinesq stability analysis of natural-convection gaseous flow on inclined hot plates
AI总结：
本文通过非Boussinesq稳定性分析，研究了倾斜热平板上气体自然对流边界层中倾角和温度比对临界格拉晓夫数及不稳定模态的影响，发现非Boussinesq效应显著拓宽了展向行波占主导的倾角范围。
摘要：
在半无限倾斜热平板上发展的浮力驱动边界层流动已知会在距前缘有限距离处变得不稳定，其特征是由基于当地边界层厚度的格拉晓夫数Gr的临界值来界定。所产生不稳定性的性质取决于从竖直方向测量的倾角$ϕ$。当$ϕ$低于临界值$ϕ_c$时，不稳定性表现为展向行波的出现；而当$ϕ>ϕ_c$时，分叉后的流动呈现类似Görtler的流向涡。先前线性稳定性分析中采用的Boussinesq近似在壁面与环境温度比$Θ_w$不接近1时对气体流动不再有效。本文给出了相应的非Boussinesq分析，并考虑了不同输运性质随温度的变化。采用包含基本流非平行效应的时域稳定性分析来确定中性稳定曲线，进而利用这些曲线刻画两种不稳定模态下临界格拉晓夫数及其相关波长对倾角$ϕ$和温度比$Θ_w$的依赖关系，为$Θ_w-1\sim 1$的构型提供了有意义的定量信息。该分析特别给出了交叉倾角$ϕ_c$对$Θ_w$的预测依赖关系，表明对于$Θ_w-1\sim 1$的气体流动，展向行波在$0 \le ϕ\le ϕ_c$的倾角范围内占主导地位，该范围显著宽于Boussinesq近似所预测的范围。
英文摘要：
The buoyancy-driven boundary-layer flow that develops over a semi-infinite inclined hot plate is known to become unstable at a finite distance from the leading edge, characterized by a critical value of the Grashof number Gr based on the local boundary-layer thickness. The nature of the resulting instability depends on the inclination angle $ϕ$, measured from the vertical direction. For values of $ϕ$ below a critical value $ϕ_c$ the instability is characterized by the appearance of spanwise traveling waves, whereas for $ϕ>ϕ_c$ the bifurcated flow displays Görtler-like streamwise vortices. The Boussinesq approximation, employed in previous linear stability analyses, ceases to be valid for gaseous flow when the wall-to-ambient temperature ratio $Θ_w$ is not close to unity. The corresponding non-Boussinesq analysis is presented here, accounting also for the variation with temperature of the different transport properties. A temporal stability analysis including nonparallel effects of the base flow is used to determine curves of neutral stability, which are then employed to delineate the dependences of the critical Grashof number and of its associated wave length on the inclination angle $ϕ$ and on the temperature ratio $Θ_w$ for the two instability modes, giving quantitative information of interest for configurations with $Θ_w-1\sim 1$. The analysis provides in particular the predicted dependence of the crossover inclination angle $ϕ_c$ on $Θ_w$, indicating that for gaseous flow with $Θ_w-1\sim 1$ spanwise traveling waves are predominant over a range of inclination angles $0 \le ϕ\le ϕ_c$ that is significantly wider than that predicted in the Boussinesq approximation.
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