Ventilated cavitating flows are investigated via direct numerical simulations, using a coupled level set and volume of fluid method to capture the interface between the air and water phases. A ventilated disk cavitator is used to create the cavity and is modelled by a sharp-interface immersed boundary method. The simulation data provide a comprehensive description of the two-phase flow and the air leakage and vortex shedding processes in the cavitating flow. The mean velocity of the air phase suggests the existence of three characteristic flow structures, namely the shear layer (SL), recirculating area (RA) and jet layer (JL). The turbulent kinetic energy (TKE) is concentrated in the JL in the closure region, and streamwise turbulent fluctuations dominate transverse fluctuations in both SL and JL. Budget analyses of the TKE show that the production term causes the TKE to increase in the SL due to the high velocity gradients, and decrease in the JL due to streamwise stretching effects. Air leakage and vortex shedding occur periodically in the closure region, and the one-to-one correspondence between these two processes is confirmed by the velocity and volume fluid spectra results, and the autocorrelation function of the air volume fraction. Moreover, the coherent flow structures are analysed using the spectral proper orthogonal decomposition method. We identify several fine coherent structures, including $SL_{KH}$ induced by the Kelvin–Helmholtz instability, $SL_{out}$ associated with large-scale vortex shedding, $SL_{in}$ associated with small-scale vortex shedding, and $SL_{r}$ associated with upstream turbulent convection. The present study complements previous research by providing detailed descriptions of the turbulent motions associated with the violent mixing of air and water, and the complex interactions between different characteristic structures in cavitating flows.

One of the most significant issues in hydrodynamic interfacial instabilities is the growth rate of the interfacial perturbations, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Yet the underlying mechanisms of such flow phenomena remain unclear or controversial. In this paper the decoupled mechanisms of two effects are found to dominate the interface growth of the single-mode Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) via Layzer's potential-flow model. One is the inertial effect induced by the interfacial density gradient and the acceleration, and the other is the frontal distortion effect stemming from interface shape evolution. The former determines the dominant features of interface evolution, while the latter influences the local concavity and convexity of growth rate such as the overshoot phenomenon. These two effects can be approximated as a linearly decoupled analytical solution if their nonlinear interaction term is neglected. With the decoupled solution, the theoretical growth rates agree well with high-fidelity numerical simulation results. The present result indicates that the long-time evolution of fluid interface in both RTI and RMI at all density ratios can be accurately predicted if both inertia and frontal distortion effects are taken into account. Furthermore, the strong dependence of instability evolution on initial amplitude is quantified based on the effects of decoupling, which sheds light on the physical origin of the overshoot phenomenon.

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.

A transition-predictive Reynolds-averaged Navier–Stokes (RANS) model is introduced as the Reynolds controlling condition to constrained large-eddy simulation (TrCLES) to improve the ability of this method to predict wall-bounded laminar–turbulent transition flows. In the TrCLES method, the constraint conditions for total Reynolds stress and heat flux are only imposed to the near-wall region in transitional and turbulent boundary layer. The newly proposed method recovers direct numerical simulation in the laminar boundary region, and retrieves the traditional large-eddy simulation method in the far-wall regions. The TrCLES method is validated in simulations of external flow around the Eppler 387 (E387) airfoil and internal flow past the ultrahigh-lift low-pressure turbine T106C cascade. The improved delayed detached-eddy simulation (IDDES) method, CLES method based on full-turbulence shear stress transport model and RANS method with a three-equation transition model are also evaluated in comparison with the available experimental and numerical data. As expected, the TrCLES method can predict laminar separation bubble and separation-induced transition process in both the E387 and T106C flows pretty well. In contrast, neither IDDES nor the original CLES can provide reasonable prediction for the laminar separation-induced transition phenomenon. The validity and fidelity of the TrCLES method are further verified by simulations of the T106C cascade flows in a wider range of exit Reynolds and Mach numbers. It is shown that the TrCLES method can not only predict the time-averaged aerodynamic quantities such as isentropic Mach number and exit kinetic energy loss very well, but also capture the laminar separation bubble and unsteady flow structures with satisfactory accuracy.

We investigate the effect of the secondary baroclinic vorticity (SBV) on the energy cascade in the mixing induced by the multi-mode Richtmyer–Meshkov instability (RMI). With the aid of vorticity-based simplified models and the vortex-surface field, we find that the effect of the SBV peaks at a critical time when the vortex reconnection widely occurs in the mixing zone. Before the critical time, spikes and bubbles evolve almost independently, and we demonstrate that the variation of the kinetic energy spectrum induced by the SBV has the $-1$ scaling law at intermediate wavenumbers using the model of vortex rings. This SBV effect causes the slope of the total energy spectrum at intermediate wavenumbers to evolve towards $-3/2$ at the critical time. Subsequently, the SBV effect diminishes and the energy spectrum decays to the $-5/3$ law. Inspired by the vortex dynamics, we develop a model for estimating the mixing width and validate the model using numerical simulations of the multi-mode RMI with various modes of initial perturbations. This model captures the nonlinear growth of the mixing width before the self-similar growth stage.

We elucidate the effect of the secondary baroclinic vorticity (SBV) on the Richtmyer–Meshkov instability (RMI) accelerated by a weak incident shock and develop a vortex-based model for spike and bubble growth rates. Two major mechanisms of the single-mode RMI, the primary baroclinic vorticity (PBV) and the pressure perturbation, are distinguished by simplified models with the vortex-surface field. We find that the effect of the pressure perturbation can be neglected in the present RMI, and the growth of the interface or vortex surface is first driven by the PBV. Subsequently, the SBV, generated by the misalignment between the density gradient across the interface and the pressure gradient produced by the PBV-induced velocity, leads to the nonlinear growth of the interface with the generation of spikes and bubbles. Inspired by this mechanism, we develop a predictive model of spike and bubble growth rates using the motion of viscous vortex rings. The circulation of the vortex ring is modelled with the SBV effect. This model is validated by five data sets of direct numerical simulations and experiments of the single-mode RMI with various initial conditions.

Evolution of the two-dimensional single-mode Richtmyer–Meshkov (RM) instability in a cylindrical geometry is numerically investigated through direct numerical simulation. A proper decomposition of the measured initial perturbation amplitude is found to be crucial for a comparative study between the numerical simulation and benchmark experiment. A refined compressible model is proposed based on the Bell equation by taking the premixed width of the initial interface into consideration. The modified model can accurately reproduce the development history of a single-mode perturbed gaseous interface between the first shock-interface interaction and reshock based on the evolution data of the unperturbed interface under the same premixing condition. The detailed effects of the RM instability, Rayleigh–Taylor stabilization and compressibility coupled with the Bell–Plesset effect are also specified with the aid of this model. It turns out that the refined Bell model can be further applied to the post-reshock stage of the RM instability before the appearance of strong nonlinearity.

We investigate how compressibility affects the turbulent statistics from a Lagrangian point of view, particularly in the parameter range where the flow transits from the incompressible type to a state dominated by shocklets. A series of three-dimensional simulations were conducted for different types of driving and several Mach numbers. For purely solenoidal driving, as the Mach number increases a new self-similar region first emerges in the Lagrangian structure functions at sub-Kolmogorov time scale and gradually extends to larger time scale. In this region the relative scaling exponent saturates and the saturated value decreases as the compressibility becomes stronger, which can be attributed to the shocklets. The scaling exponent for the inertial range is still very close to that of incompressible turbulence for small Mach number, and discrepancy becomes visible when the Mach number is high enough. When the driving force is dominated by the compressive component the shocklet-induced self-similar region occupies a much wider range of time scales than that in the purely solenoidal driving case. Regardless of the type of driving force, the probability density functions of the velocity increment collapse onto one another for the time scales in the new self-similar region after proper normalization.

Compressible flow past a circular cylinder at an inflow Reynolds number of 2 x 105 is numerically investigated by using a constrained large-eddy simulation (CLES) technique. Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows. Some typical and characteristic physical quantities, such as the drag coefficient, the root-mean-square lift fluctuations, the Strouhal number, the pressure and skin friction distributions around the cylinder, etc. are calculated and compared with previously reported experimental data, finer-grid large-eddy simulation (LES) data and those obtained in the present LES and detached-eddy simulation (DES) on coarse grids. It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well. Then, the effects of Mach number on the flow patterns and parameters such as the pressure, skin friction and drag coefficients, and the cylinder surface temperature are studied, with Mach number varying from 0.1 to 0.95. Non-monotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5. Additionally, the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures. It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature. Moreover, the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point. Moreover, the influences of different thermal wall boundary conditions on the flow field are graduallymagnified from the front stagnation point to the rear stagnation point. It is inferred that the CLES approach in its current version is a useful and effective tool for simulating wall-bounded compressible turbulent flows with massive separations.

Using a simulated highly compressible isotropic turbulence field with turbulent Mach number around 1.0, we studied the effects of local compressibility on the statistical properties and structures of velocity gradients in order to assess salient small-scale features pertaining to highly compressible turbulence against existing theories for incompressible turbulence. A variety of statistics and local flow structures conditioned on the local dilatation – a measure of local flow compressibility – are studied. The overall enstrophy production is found to be enhanced by compression motions and suppressed by expansion motions. It is further revealed that most of the enstrophy production is generated along the directions tangential to the local density isosurface in both compression and expansion regions. The dilatational contribution to enstrophy production is isotropic and dominant in highly compressible regions. The emphasis is then directed to the complicated properties of the enstrophy production by the deviatoric strain rate at various dilatation levels. In the overall flow field, the most probable eigenvalue ratio for the strain rate tensor is found to be −3:1:2.5, quantitatively different from the preferred eigenvalue ratio of −4:1:3 reported in incompressible turbulence. Furthermore, the strain rate eigenvalue ratio tends to be −1:0:0 in high compression regions, implying the dominance of sheet-like structures. The joint probability distribution function of the invariants for the deviatoric velocity gradient tensor is used to characterize local flow structures conditioned on the local dilatation as well as the distribution of enstrophy production within these flow structures. We demonstrate that strong local compression motions enhance the enstrophy production by vortex stretching, while strong local expansion motions suppress enstrophy production by vortex stretching. Despite these complications, most statistical properties associated with the solenoidal component of the velocity field are found to be very similar to those in incompressible turbulence, and are insensitive to the change of local dilatation. Therefore, a good understanding of dynamics of the compressive component of the velocity field is key to an overall accurate description of highly compressible turbulence.

In the traditional hybrid RANS/LES approaches for the simulation of wall-bounded fluid turbulence, such as detached-eddy simulation (DES), the whole flow domain is divided into an inner layer and an outer layer. Typically the Reynolds-averaged Navier–Stokes (RANS) equations are used for the inner layer, while large-eddy simulation (LES) is used for the outer layer. The transition from the inner-layer solution to the outer-layer solution is often problematic due to the lack of small-scale dynamics in the RANS region. In this paper, we propose to simulate the whole flow domain by large-eddy simulation while enforcing a Reynolds-stress constraint on the subgrid-scale (SGS) stress model in the inner layer. Both the algebraic eddy-viscosity model and the one-equation Spalart–Allmaras (SA) model have been used to constrain the Reynolds stress in the inner layer. In this way, we improve the LES methodology by allowing the mean flow of the inner layer to satisfy the RANS solution while small-scale dynamics is included. We validate the Reynolds-stress-constrained large-eddy simulation (RSC-LES) model by simulating three-dimensional turbulent channel flow and flow past a circular cylinder. Our model is able to predict mean velocity, turbulent stress and skin-friction coefficients more accurately in turbulent channel flow and to estimate the pressure coefficient after separation more precisely in flow past a circular cylinder compared with the pure dynamic Smagorinsky model (DSM) and DES using the same grid resolution. Furthermore, the computational cost of the RSC-LES is almost the same as that of DES.