标题： 非定常湍流浮力射流 显示英文标题

标题： Unsteady turbulent buoyant plumes

摘要： 我们模拟了湍流浮力射流在源条件随时间变化时的非定常演变过程。 积分模型是从描述质量、轴向动量和浮力守恒的控制方程的径向积分中推导出来的。 射流中轴向速度和密度缺陷的非均匀径向分布通过积分方程中的形状因子进行显式描述；通常假设的平顶型分布会导致形状因子等于1。 当从平均轴向速度的径向分布确定的动量形状因子不同于1时，所得模型是双曲型的。 当源条件保持为常数值时，模型的解保留了已建立的稳定射流解的形式。 我们证明，包含一个不同于1的动量形状因子会导致一个适定的积分模型。 因此，我们的模型不会表现出先前提出的湍流射流非定常积分模型中出现的数学病态。 确定了形状因子值的稳定性阈值，导致一个形状因子值范围，在该范围内，对稳定解的小扰动振幅随着远离源的距离而衰减。 系统的双曲特性允许在非定常演变过程中形成描述射流特性的场中的不连续性。 我们计算数值解以说明源条件突然变化后的瞬态发展。 对新源条件的调整是通过射流中流体脉冲的传播来实现的。 这个脉冲的动力学由相似解描述，通过构建这个新的相似解，我们识别出三种演化区域，在这些区域中，源调整后瞬态脉冲的演化在定性上有所不同。 显示英文摘要

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.