Goshayeshi B, Di Staso G, Toschi F, Clercx H J H
Fluid Dynamics Laboratory and J.M. Burgers Center for Fluid Dynamics, Department of Applied Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
Centre of Analysis, Scientific Computing, and Applications W&I, Department of Mathematics and Computer Science, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
Phys Rev E. 2020 Jul;102(1-1):013102. doi: 10.1103/PhysRevE.102.013102.
The focus of this research is to delineate the thermal behavior of a rarefied monatomic gas confined between horizontal hot and cold walls, physically known as rarefied Rayleigh-Bénard (RB) convection. Convection in a rarefied gas appears only for high temperature differences between the horizontal boundaries, where nonlinear distributions of temperature and density make it different from the classical RB problem. Numerical simulations adopting the direct simulation Monte Carlo approach are performed to study the rarefied RB problem for a cold to hot wall temperature ratio equal to r=0.1 and different rarefaction conditions. Rarefaction is quantified by the Knudsen number, Kn. To investigate the long-time thermal behavior of the system two ways are followed to measure the heat transfer: (i) measurements of macroscopic hydrodynamic variables in the bulk of the flow and (ii) measurements at the microscopic scale based on the molecular evaluation of the energy exchange between the isothermal wall and the fluid. The measurements based on the bulk and molecular scales agreed well. Hence, both approaches are considered in evaluations of the heat transfer in terms of the Nusselt number, Nu. To characterize the flow properly, a modified Rayleigh number (Ra_{m}) is defined to take into account the nonlinear temperature and density distributions at the pure conduction state. Then the limits of instability, indicating the transition of the conduction state into a convection state, at the low and large Froude asymptotes are determined based on Ra_{m}. At the large Froude asymptote, simulations following the onset of convection showed a relatively small range for the critical Rayleigh (Ra_{m}=1770±15) that flow instability occurs at each investigated rarefaction degree. Moreover, we measured the maximum Nusselt values Nu_{max} at each investigated Kn. It was observed that for Kn≥0.02, Nu_{max} decreases linearly until the transition to conduction at Kn≈0.03, known as the rarefaction limit for r=0.1, occurs. At the low Froude (parametric) asymptote, the emergence of a highly stratified flow is the prime suspect of the transition to conduction. The critical Ra_{m} in which this transition occurs is then determined at each Kn. The comparison of this critical Rayleigh versus Kn also shows a linear decrease from Ra_{m}≈7400 at Kn=0.02 to Ra_{m}≈1770 at Kn≈0.03.
本研究的重点是描绘限制在水平热壁和冷壁之间的稀薄单原子气体的热行为，从物理角度来看这被称为稀薄瑞利 - 贝纳德（RB）对流。稀薄气体中的对流仅在水平边界之间存在较大温差时才会出现，此时温度和密度的非线性分布使其有别于经典的RB问题。采用直接模拟蒙特卡罗方法进行数值模拟，以研究冷壁与热壁温度比(r = 0.1)且处于不同稀薄条件下的稀薄RB问题。稀薄程度由克努森数(Kn)来量化。为了研究系统的长期热行为，采用了两种方法来测量热传递：（i）测量流体主体中的宏观流体动力学变量；（ii）基于等温壁与流体之间能量交换的分子评估在微观尺度上进行测量。基于流体主体和分子尺度的测量结果吻合良好。因此，在根据努塞尔数(Nu)评估热传递时，两种方法都予以考虑。为了恰当地描述流动，定义了一个修正瑞利数((Ra_{m}))，以考虑纯传导状态下的非线性温度和密度分布。然后，基于(Ra_{m})确定在低弗劳德渐近线和大弗劳德渐近线处表示传导状态向对流状态转变的不稳定性极限。在大弗劳德渐近线处，对流开始后的模拟显示临界瑞利数（(Ra_{m}=1770\pm15)）的范围相对较小，即在每个研究的稀薄程度下都会发生流动不稳定性。此外，我们测量了每个研究的(Kn)下的最大努塞尔值(Nu_{max})。观察到对于(Kn\geq0.02)，(Nu_{max})呈线性下降，直到在(Kn\approx0.03)时转变为传导状态，这被称为(r = 0.1)时的稀薄极限。在低弗劳德（参数）渐近线处，高度分层流动的出现是转变为传导状态的主要可疑因素。然后在每个(Kn)下确定发生这种转变的临界(Ra_{m})。这种临界瑞利数与(Kn)的比较也显示出从(Kn = 0.02)时的(Ra_{m}\approx7400)到(Kn\approx0.03)时的(Ra_{m}\approx1770)呈线性下降。
