Turbulent mixing is a pivotal phenomenon in fusion research with profound implications for energy gain. A Reynolds-averaged Navier–Stokes model capable of predicting realistic mixing transition processes is of significant importance for fusion applications, yet such a model remains elusive. This work addresses the limitations of prevalent global transition criteria, proposing a new idea to quantify local transition characteristics based on the mixing state, recognizing its direct relevance to fusion reaction rates. We delve into the description and analysis of the spatiotemporal evolution of the mixing state and its interplay with the transition process. Then, a local transition indicator is developed and compared with conventional global criteria using the large-eddy simulation (LES) of Rayleigh–Taylor turbulent mixing. Building upon this foundation, we introduce a novel eddy viscosity model based on the local transition indicator. A posterior assessment using LES data validates that it significantly outperforms standard gradient transport models during the transition stage. Consequently, we integrate this new eddy viscosity model with the Besnard–Harlow–Rauenzahn model to construct a comprehensive transition model, which demonstrates reasonably good performance in comparison with LES results. This work paves the way for future research in developing advanced modelling strategies that can effectively address the complexities of transitional flows in fusion engineering applications.

Convective flows near a cylindrical solid inclusion in a fluid-saturated porous medium heated from above are studied using the Darcy–Boussinesq equations. The impermeability condition is imposed on the inclusion surface. Two-dimensional convective flows uniform in the direction of the cylinder axis are considered. An Oseen-like approximation is implemented, however, different from the conventional Oseen approximation, quasilinearization is applied to the nonlinear terms in the energy equation and not in the momentum equation. It is shown that, when the thermal conductivity of the inclusion is higher than that of the fluid, the convective flow at a distance from the inclusion larger than the inclusion size takes the form of horizontal vortices directed away from the inclusion. In the case of low thermal conductivity of the inclusion, the direction of convective circulation is opposite: in the horizontal plane passing through the cylinder axis, the fluid is leaking to the inclusion.

The presence of dispersed-phase droplets can result in a notable increase in a system's drag. However, our understanding of the mechanism underlying this phenomenon remains limited. In this study, we use three-dimensional direct numerical simulations with a modified multi-marker volume-of-fluid method to investigate liquid–liquid two-phase turbulence in a Taylor–Couette geometry. The dispersed phase has the same density and viscosity as the continuous phase. The Reynolds number $Re\equiv r_i\omega _i d/\nu$ is fixed at 5200, the volume fraction of the dispersed phase is up to $40\,\%$, and the Weber number $We\equiv \rho u^2_\tau d/\sigma$ is approximately 8. It is found that the increase in the system's drag originates from the contribution of interfacial tension. Specifically, droplets experience significant deformation and stretching in the streamwise direction due to shear near the inner cylinder. Consequently, the rear end of the droplets lags behind the fore head. This causes opposing interfacial tension effects on the fore head and rear end of the droplets. For the fore head of the droplets, the effect of interfacial tension appears to act against the flow direction. For the rear end, the effect appears to act in the flow direction. The increase in the system's drag is attributed primarily to the effect of interfacial tension on the fore head of the droplets which leads to the hindering effect of the droplets on the surrounding continuous phase. This hindering effect disrupts the formation of high-speed streaks, favouring the formation of low-speed ones, which are generally associated with higher viscous stress and drag of the system. This study provides new insights into the mechanism of drag enhancement reported in our previous experiments.

Developing large-eddy simulation (LES) wall models for separated flows is challenging. We propose to leverage the significance of separated flow data, for which existing theories are not applicable, and the existing knowledge of wall-bounded flows (such as the law of the wall) along with embedded learning to address this issue. The proposed so-called features-embedded-learning (FEL) wall model comprises two submodels: one for predicting the wall shear stress and another for calculating the eddy viscosity at the first off-wall grid nodes. We train the former using the wall-resolved LES (WRLES) data of the periodic hill flow and the law of the wall. For the latter, we propose a modified mixing length model, with the model coefficient trained using the ensemble Kalman method. The proposed FEL model is assessed using the separated flows with different flow configurations, grid resolutions and Reynolds numbers. Overall good a posteriori performance is observed for predicting the statistics of the recirculation bubble, wall stresses and turbulence characteristics. The statistics of the modelled subgrid-scale (SGS) stresses at the first off-wall grids are compared with those calculated using the WRLES data. The comparison shows that the amplitude and distribution of the SGS stresses and energy transfer obtained using the proposed model agree better with the reference data when compared with the conventional SGS model.

In this paper, aerobreakup in the stagnation region of high-Mach-number flow over a bluff body is studied with experiments and computations. Water drops of diameter 0.51–2.30 mm were acoustically levitated at sea level along the flight path of a rectangular $100\ {\rm mm} \times 150\ {\rm mm}$ rail-gun launched projectile. This enabled the study of aerobreakup at high Mach (3.03–5.12), post-shock Mach (1.5–1.9), Weber $(5 \times 10^4\unicode{x2013}4 \times 10^5)$ and Reynolds $(6 \times 10^4\unicode{x2013}3 \times 10^5)$ numbers. High-speed backlit shadowgraphy is used to record the flow structure. Computations are made for two cases, and it was found that the drop behaviour is not dominated by viscous or surface-tension effects and can be adequately captured by treating the gas as calorically perfect with the ratio of specific heats set to 1.3 to account for thermochemical effects. To assess drop surface stability at early breakup times, results from Newton's inclination method are used to determine the flow along the drop surface and input to a linear-stability analysis; from this, it was found that viscosity and surface tension can be neglected. Moreover, the acceleration term dominates the shear term at the stagnation point, a point accentuated as a drop flattens; this relation inverts closer to the drop equator. Linear-stability analysis was insufficient for modelling late-stage aerobreakup because the predicted wavelengths were too small and the expected aerobreakup times were non-physically short. To address this discrepancy, a nonlinear instability model with constant-rate growth is used that treats the accelerated drop surface as analogous to bubbles rising through a liquid; agreement with computations is good.