This paper considers the stability of an unsteady, two-phase flow with heat and mass transfer. The model problem is motivated by loss of coolant accidents in nuclear power plants. For the example problem, two flow geometries are considered: inverted annular flow boiling and an annular mist flow. The model is comprised of coupled Mathieu equations so that stability can be determined using a Floquet analysis. The flow is found to be mathematically unstable to all perturbative wavenumbers, but for practical purposes there are regions of stability. Using the solution's growth behavior and doubling-time, the notion of practical stability, which is termed herein as "engineering stability," is quantified and a method is provided for application to other engineering stability problems.

本文考虑了具有传热传质的非定常两相流的稳定性。该模型问题的动机是核电厂冷却剂损失事故。对于示例问题，考虑了两种流动几何结构：反向环形流动沸腾和环形雾状流动。该模型由耦合的 Mathieu 方程组成，因此可以使用 Floquet 分析来确定稳定性。发现流动对于所有微扰波数在数学上都是不稳定的，但出于实际目的，存在稳定区域。使用解决方案的增长行为和倍增时间，实际稳定性的概念（在此称为“工程稳定性”）被量化，并提供了一种应用于其他工程稳定性问题的方法。