An engineering stability technique for unsteady, two-phase flows with heat and mass transfer. (September 2021) - Beck, Faith R.; Mohanta, Lokanath; Henderson, Diane M.; Cheung, Fan-Bill; Talmage, Gita
Highlights: Stability of an unsteady, two-phase flow with heat and mass transfer considered. Work motivated by loss of coolant accidents in nuclear power plants. Flow is mathematically unstable, regions of ǣengineering stabilityǥ identified. Engineering stability quantified using solution growth behavior and doubling time. Framework provided for application to other types of problems. Abstract: 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.