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This study resolves a long-standing controversy in two-phase flow physics regarding how buoyancy forces should be calculated when modeling flows containing dispersed particles (like bubbles or droplets in a fluid). The authors demonstrate that existing mathematical models for buoyancy are inconsistent with simulations and physical experiments, and derive a unique correct closure that includes all fluid stresses except Reynolds stress in the buoyancy calculation. This new closure naturally prevents mathematical instabilities that have plagued two-fluid models for decades, providing a first-principles solution to their ill-posedness problem.
Why it matters
This work could significantly improve the reliability of computational models used in industrial applications involving two-phase flows, such as chemical reactors, oil and gas pipelines, nuclear reactor cooling systems, and environmental flows. By solving fundamental mathematical stability problems, it enables more accurate predictions of multiphase flow behavior without requiring ad-hoc fixes.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: The Maxey–Riley–Gatignol equation for the flow around a sphere at low particle Reynolds number tells us that the fluid-particle interaction force decomposes into a contribution from the local flow disturbance caused by the particle’s boundary—consisting of the drag, virtual-mass, and history forces, and their Fax’en corrections—and another contribution from the stress of the background flow, termed generalized-buoyancy force. There is also a consensus that, for general disperse two-phase flow, the interfacial force density, coupling the average fluid phase and dispersed-phase momentum balances, decomposes in a like manner. However, there has been a long-standing controversy about the physical closure separating the generalized-buoyancy from the interfacial force density, especially whether or not pseudo-stresses, such as the Reynolds stress, should be attributed to the background flow. Furthermore, most existing propositions for this closure involve small-particle approximations. Here, we show that all existing buoyancy closures are inconsistent with particle-resolving numerical simulations and/or at least one of two simple thought experiments designed to determine the roles of pseudo-stresses and small-particle approximations. We then derive the unique consistent closure. It requires no approximation and implies that all stresses and pseudo-stresses in the average fluid phase momentum balance, except the Reynolds stress, fully contribute to the background flow responsible for buoyancy. Remarkably, it exhibits a low-pass filter property, attenuating buoyancy at short wavelengths, that prevents it from causing Hadamard instabilities, constituting a first-principles-based solution to the long-standing ill-posedness problem of two-fluid models. When employing the derived closure, even simplistic two-fluid models are linearly well-posed.
Source: On buoyancy in disperse two-phase flow and its impact on the well-posedness of two-fluid models