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The numerical and analytical study of bifurcation and multicellular flow instability due to natural convection between narrow horizontal isothermal cylindrical annuli at high Rayleigh numbers

机译：高瑞利数水平窄等温圆柱环空自然对流引起的分叉和多细胞流动不稳定性的数值分析研究

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This research effort deals with a numerical and analytical study of multicellular flow instability due to natural convection between narrow horizontal isothermal cylindrical annuli;Buoyancy-induced steady or unsteady flow fields between the annuli are determined using the Boussinesq approximated two-dimensional (2-D) Navier-Stokes (N-S) equations and the viscous-dissipation neglected thermal-energy equation. The vorticity-stream function formulation of the N-S equations is adopted;Both thermal and hydrodynamic instabilities are explored. An asymptotic expansion theory is applied to the N-S equations in the double-limit of Rayleigh number approaching infinity and gap width approaching zero. This double-limiting condition reduces the governing equations to a set of Cartesian-like boundary-layer equations. These equations are further simplified by considering the extreme limits of Pr →[infinity] and Pr → 0. The former limit yields an energy equation which retains the nonlinear convective terms, while the vorticity equation reduces to a Stokes-flow equation, signifying the potential for thermal instability. In the latter limit, the nonlinear terms in the vorticity equation remain, while the energy equation collapses to a one-dimensional conduction equation, signifying the potential for hydrodynamic instability;Thermal instability of air near the top portions of narrow annuli is considered for various size small gap widths. For these narrow gaps, the Rayleigh numbers corresponding to the onset of steady multicellular flow are predicted. Numerical solutions of the 2-D N-S equations also yield hysteresis behavior for the two-to-six and two-to-four cellular states, with respect to diameter ratios of 1.100 and 1.200. In contrast, an unsteady hydrodynamic multicellular instability is experienced near the vertical sections of narrow annuli when the Pr → 0 boundary-layer equations are solved numerically;In addition, analytical steady-state perturbative solutions to the boundary-layer equations are obtained. These results compare favorably to related numerical solutions of both N-S and Pr → 0 simplified equations;In all cases, finite-differenced solutions to the governing equations are obtained using a stable second-order, fully-implicit time-accurate Gauss-Seidel iterative procedure.
机译：这项研究工作是对窄水平等温圆柱环空之间自然对流引起的多细胞流动不稳定性的数值和分析研究;使用Boussinesq近似二维（2-D）确定浮力引起的环空之间的稳态或非稳态流场Navier-Stokes（NS）方程和粘性耗散的热能方程被忽略。采用N-S方程的涡流函数公式;探讨了热和流体动力的不稳定性。在Rayleigh数的双极限接近无穷大且间隙宽度接近零的N-S方程中应用渐近展开理论。这种双重极限条件将控制方程式简化为一组笛卡尔式边界层方程式。通过考虑Pr→无穷大和Pr→0的极限，可以进一步简化这些方程。前一个极限产生一个能量方程，该方程保留了非线性对流项，而涡度方程则简化为斯托克斯流方程，表明了势能对于热不稳定性。在后一个极限中，涡度方程中的非线性项保留下来，而能量方程崩溃为一维传导方程，表明存在水动力不稳定性的可能性；考虑了各种尺寸的窄环形空间顶部附近空气的热不稳定性间隙宽度小。对于这些狭窄的间隙，可以预测与稳定多细胞流动开始相对应的瑞利数。 2-D N-S方程的数值解还产生了相对于直径比1.100和1.200的二元至六元和二元至四元细胞态的磁滞行为。相比之下，数值求解Pr→0边界层方程时，在狭窄环空的垂直截面附近会遇到不稳定的流体动力多细胞不稳定性；此外，还获得了边界层方程的稳态摄动解析解。这些结果优于NS和Pr→0简化方程的相关数值解;在所有情况下，使用稳定的二阶，完全隐式，时间精确的Gauss-Seidel迭代程序可获得控制方程的有限差分解。

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    Fant, Daniel Bartholemew;

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  • 年度 1987
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  • 正文语种 en
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