非定常湍流浮力羽流
Unsteady turbulent buoyant plumes
摘要：
我们模拟了湍流浮力羽流随时间变化的源条件的非定常演变。积分模型是从径向积分的控制方程表达的质量，轴向动量和浮力守恒。在羽流中的轴向速度和密度赤字的非均匀的径向配置文件中明确描述的形状因子的积分方程;通常假设的顶帽配置文件导致的形状因子等于1。所得模型是双曲线的动量形状因子时，确定从径向分布的平均轴向速度，不同于统一。当源条件保持在恒定值时，模型的解保持了公认的稳定羽流解的形式。我们证明，包含一个动量形状因子，不同于统一导致一个适定的积分模型。因此，我们的模型没有表现出出现在以前提出的湍流羽流的非定常积分模型的数学病理。确定的形状因子的值的稳定性阈值，导致在其值的范围内，小扰动的振幅的稳定的解决方案衰减与距离的来源。该系统的双曲线特征允许在非定常演化过程中描述羽流特性的字段中形成不连续性。我们计算数值解来说明源条件突变后的瞬态发展。通过羽流传播流体脉冲，可对新的源条件进行调整。这个脉冲的动力学描述的相似性解决方案，并通过构建这个新的相似性解决方案，我们确定三个制度，在其中的瞬态脉冲的演变以下调整的源质的不同。
英文摘要：
We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed integral model. Therefore, our model does not exhibit the mathematical pathologies that appear in previously proposed unsteady integral models of turbulent plumes. A stability threshold for the value of the shape factor is identified, resulting in a range of its values where the amplitude of small perturbations to the steady solutions decay with distance from the source. The hyperbolic character of the system allows the formation of discontinuities in the fields describing the plume properties during the unsteady evolution. We compute numerical solutions to illustrate the transient development following an abrupt change in the source conditions. The adjustment to the new source conditions occurs through the propagation of a pulse of fluid through the plume. The dynamics of this pulse are described by a similarity solution and, by constructing this new similarity solution, we identify three regimes in which the evolution of the transient pulse following adjustment of the source qualitatively differ.
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