Instabilities of boundary layers along a tilt plate dissipating uniform heat flux

对恒热流条件下的斜板自然对流边界层的稳定性进行了分析及数值模拟.研究发现在一定的倾角和Prandtl数范围内,三维波可存在两种不稳定模态,其临界频率分别接近于重力内波和二维T-S(Tol-mien-Schlichting)波的频率.更为特殊的是,在适当条件下该三维波模态可比二维T-S波更不稳定.这一看似违反Squire定理的结果是由于控制方程中的浮力项造成的.数值模拟初步验证了三维波的临界特性.由于稳定性总是同层流至湍流的转捩过程密切相关,计算结果可为高效换热翅片的设计提供理论依据.The stabilities of natural convection boundary layers along a tilt uniform-heat-flux plate were studied theoretically and numerically. For some Prandtl numbers, three-dimensional instability may have two critical modes, whose critical frequencies are close to the internal wave frequency and the value of two-dimensional T-S (Tolmien-Schlichting) wave, respectively. Specially, at proper tilt angles the three-dimensional wave mode is more unstable than the two-dimensional T-S wave. This result that seems contradict with the Squire Theorem is caused by the additional buoyancy terms in the governing equations. Direct numerical simulations confirmed the critical properties of the three-dimensional waves. Since hydrodynamic instability always exists at the first stage of turbulence transition process, current results may provide theoretical basis for optimal design of fins with high heat transfer efficiency.国家自然科学基金中文核心期刊要目总览(PKU)中国科技核心期刊(ISTIC)中国科学引文数据库(CSCD)0112397-24022