An initially perturbed interface between two fluids of different densities is usually unstable when driven by an acceleration or a shock wave; it is known as a Rayleigh–Taylor instability or a Richtmyer–Meshkov instability. One of the most significant issues in these instabilities is the spatiotemporal development of fingers generated at the interface, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Accurate theoretical solution of these interfacial fingers remains as an unsolved and challenging problem since Taylor's seminal work more than seven decades ago. This paper reports a unified theory established for such phenomena by combining the classical potential-flow theory and a dual-source model to address the long-standing difficulty highlighted by the initial-value sensitivity and strong nonlinearity. It is the first time for a theory to accurately predict the long-time developments in both growth rate and shape curvature of interfacial fingers at all density ratios in two and three dimensions. Moreover, the new theory clearly reveals the nonlinear coupling mechanism for interfacial evolution, and especially explains the origin of overshot in the growth rate curve.
Hydrodynamic instabilities, including Rayleigh–Taylor, Richtmyer–Meshkov (RM), and Kelvin–Helmholtz, induced turbulent mixing broadly occur in both natural phenomena, such as supernova explosions, and high-energy-density applications, such as inertial confinement fusion. Reshocked RM mixing is the most fundamental physical process that is closely related to practical problems, as it involves three classical instabilities. In complex applications, the Reynolds-averaged Navier–Stokes model analysis continues to play a major role. However, there are very few turbulence models that facilitate unified predictions of the outcome of reshocked RM mixing experiments under different physical conditions. Thus, we aim to achieve this objective using the K-L model based on three considerations: deviatoric shear stress is considered when constructing Reynolds stress tensor; the model coefficients used are derived based on a new systematic procedure; the performance of different numerical schemes are studied to ensure high resolution but basically no numerical oscillation. Consequently, a unified prediction is obtained for the first time for a series of reshocked RM mixing experiments under incident shock Mach numbers Ma = 1.2–1.98, Atwood numbers At = ±0.67, and test section lengths 8 cm ≤ δ ≤ 110 cm. The results reveal the feasibility of demonstrating different reshocked RM processes using a single model, without adjusting the model coefficients, which sheds light on the further application of the present model to practical engineering, such as inertial confinement fusion.
Turbulent mixing induced by interfacial instabilities, such as Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities, widely exist in natural phenomena and engineering applications. On the one hand, the Reynolds-averaged Navier–Stokes (RANS) method, mainly involving physical model and model coefficients, is still the most viable approach in application. On the other hand, predicting different mixing problems with the same physical model and model coefficients—defined as “unified prediction” in this paper—is the basis for practice because (1) different instabilities usually exist simultaneously in a flow system and are coupled to each other; (2) mixing processes involve a wide range of parameters (e.g., time-dependent density ratio and acceleration history, etc.). However, few models can achieve such a unified prediction. Recently, we proposed a RANS route to realize this unified prediction by setting model coefficients to match the given physical model. This study attempts to apply this to the widely used BHR2 model to achieve unified predictions of different turbulent mixing problems, including basic problems (i.e., classical RT, RM, and KH mixing) and complex problems (i.e., re-shocked RM, tilted-RT, and spherical implosion mixing). Good agreement between experiments, large-eddy simulations, and RANS results were obtained. The temporal evolution of mixing width and spatial profiles of important physical quantities are presented. Based on our achievements of the k – L and k−ε models for unified predictions, the success of BHR2 model further confirms that our RANS route is robust for different turbulent mixing models and may be expanded to other fields.
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