Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching modelling framework is absent. This paper provides a unified framework for N-phase incompressible Navier–Stokes Cahn–Hilliard Allen–Cahn mixture models with a single momentum equation. The framework emerges naturally from continuum mixture theory, exhibits an energy-dissipative structure, and is invariant to the choice of fundamental variables. This opens the door to exploring connections between existing N-phase models and facilitates the computation of N-phase flow models rooted in continuum mixture theory.

The interaction between the dynamics of a flame front and the acoustic field within a combustion chamber represents an aerothermochemical problem with the potential to generate hazardous instabilities, which limit burner performance by constraining design and operational parameters. The experimental configuration described here involves a laminar premixed flame burning in an open–closed slender tube, which can also be studied through simplified modelling. The constructive coupling of the chamber acoustic modes with the flame front can be affected via strategic placement of porous plugs, which serve to dissipate thermoacoustic instabilities. These plugs are lattice-based, 3-D-printed using low-force stereolithography, allowing for complex geometries and optimal material properties. A series of porous plugs was tested, with variations in their porous density and location, in order to assess the effects of these variables on viscous dissipation and acoustic eigenmode variation. Pressure transducers and high-speed cameras are used to measure oscillations of a stoichiometric methane–air flame ignited at the tube’s open end. The findings indicate that the porous medium is effective in dissipating both pressure amplitude and flame-front oscillations, contingent on the position of the plug. Specifically, the theoretical fluid mechanics model is developed to calculate frequency shifts and energy dissipation as a function of plug properties and positioning. The theoretical predictions show a high degree of agreement with the experimental results, thereby indicating the potential of the model for the design of dissipators of this nature and highlighting the first-order interactions of acoustics, viscous flow in porous media and heat transfer processes.

We investigate the dynamics of a cavitation bubble near rigid surfaces decorated with a single gas-entrapping hole to understand the competition between the attraction of the rigid and the repulsion of the free boundary. The dynamics of laser-induced bubbles near this gas-entrapping hole is studied as a function of the stand-off distance and diameter of the hole. Two kinds of toroidal collapses are observed that are the result of the collision of a wide microjet with the bubble wall. The bubble centroid displacement and the strength of the microjet are compared with the anisotropy parameter $\zeta$, which is derived from a Kelvin impulse analysis. We find that the non-dimensional displacement $\delta$ scales with $\zeta$.

The fate of deformable buoyancy-driven bubbles rising near a vertical wall under highly inertial conditions is investigated numerically. In the absence of path instability, simulations reveal that, when the Galilei number, $Ga$, which represents the buoyancy-to-viscous force ratio, exceeds a critical value, bubbles escape from the near-wall region after one to two bounces, while at smaller $Ga$ they perform periodic bounces without escaping. The escape mechanism is rooted in the vigorous rotational flow that forms around a bubble during its bounce at high enough $Ga$, resulting in a Magnus-like repulsive force capable of driving it away from the wall. Path instability takes place with bubbles whose Bond number, the buoyancy-to-capillary force ratio, exceeds a critical $Ga$-dependent value. Such bubbles may or may not escape from the wall region, depending on the competition between the classical repulsive wake–wall interaction mechanism and a specific wall-ward trapping mechanism. The latter results from the reduction of the bubble oblateness caused by the abrupt drop of the rise speed when the bubble–wall gap becomes very thin. Owing to this transient shape variation, bubbles exhibiting zigzagging motions with a large enough amplitude experience larger transverse drag and virtual mass forces when departing from the wall than when returning to it. With moderately oblate bubbles, i.e. in an intermediate Bond number range, this effect is large enough to counteract the repulsive interaction force, forcing such bubbles to perform a periodic zigzagging-like motion at a constant distance from the wall.

The dynamics of ice basal melting in seawater is one of the key factors in understanding and modelling the ice–seawater interaction in the polar oceans. In this work we study the basal melting of solid ice in seawater, and focus on the interaction between the melting process and the double diffusive convection developed in the seawater layer. Different temperatures and salinity differences are systematically simulated, and two different flow regimes are identified. For a relatively weak salinity difference, the convection layer occupies most of the liquid layer and grows in height as the ice melts. When the salinity difference is strong enough, the convection layer shrinks with time and a stably stratified layer grows between the ice layer and convection layer. When the dynamics is dominated by the convection layer, the global heat and salinity transfer rates follow a power-law scaling. Theoretical models are developed for the local mean salinity at the ice–water interface and the melting rates, and the critical density ratio corresponding to the transition between the two regimes, which all agree with the numerical results. Density inversion happens consistently adjacent to the ice–seawater interface, which has a profound influence on the ice surface shape. All these findings provide useful insights into the detailed dynamics of ice basal melting in oceans.

Many hypersonic flows of interest feature high free-stream stagnation enthalpies, which lead to high flow-field temperatures and thermochemical non-equilibrium (TCNE) effects, such as finite-rate chemistry and vibrational excitation. However, very few studies have considered receptivity for high-enthalpy flows. In this paper, we investigate the receptivity of a high-enthalpy Mach 5 straight-cone boundary layer to slow and fast acoustic free-stream waves using direct numerical simulation alongside linear stability theory and the linear parabolised stability equations. In addition, we investigate the TCNE effect on receptivity by comparing results between the TCNE gas model and a thermochemically frozen gas model. The dominant instability mechanism for this flow configuration is found to be Mack’s second mode, with the unstable mode being the fast mode. Second-mode receptivity coefficients are obtained for a number of frequencies. For free-stream slow acoustic waves, these receptivity coefficients are found to generally increase with frequency. For a small subset of the considered frequency range, the receptivity coefficients corresponding to free-stream fast acoustic waves are found to be several times larger than for free-stream slow acoustic waves. The TCNE effects are found to lead to higher peak $N$-factors while also reducing second-mode receptivity coefficients, indicating that TCNE effects have competing impacts on receptivity versus stability for the considered frequencies.

The phenomenon of bulge evolution under the action of gravity on shallow water is prevalent both in natural occurrences and engineering industries. However, despite its ubiquity, its physical process remains largely unexplored. The evolution of bulge contains two fundamental physical processes: collapse and propagation. The collapse process can be further divided into two sub-processes: squeezing process and diffusion process. Based on the weakly nonlinear shallow water assumption with the classical perturbation method, the governing equations controlling the surface elevations in the diffusion process and the propagation process have been theoretically derived, where a bulge-induced surface pressure is modeled for the propagation process. Moreover, their scaling laws for the decay of wave height are also established, which have been validated by direct numerical simulation results. The derived scaling laws for wave height attenuation of bulge evolution provide profound insights, which hold the potential to applications in the engineering industry.

This paper presents a method to stabilise oscillations occurring in a mixed convective flow in a nearly hemispherical cavity, using actuation based on the receptivity map of the unstable mode. This configuration models the continuous casting of metallic alloys, where hot liquid metal is poured at the top of a hot sump with cold walls pulled in a solid phase at the bottom. The model focuses on the underlying fundamental thermohydrodynamic processes without dealing with the complexity inherent to the real configuration. This flow exhibits three branches of instability. The solution of the adjoint eigenvalue problem for the convective flow equations reveals that the regions of highest receptivity for unstable modes of each branch concentrate near the inflow upper surface. Simulations of the linearised governing equations show that a thermomechanical actuation modelled on the adjoint eigenmode asymptotically suppresses the unstable mode. If the actuation’s amplitude is kept constant in time, which is easier to implement in an industrial environment, the suppression is still effective but only over a finite time, after which it becomes destabilising. Based on this phenomenology, we apply the same actuation during the stabilising phase only in the nonlinear evolution of the unstable mode. It turns out stabilisation persists, even when the unstable mode is left to evolve freely after the actuation period. These results not only demonstrate the effectiveness of receptivity-informed actuation in stabilising convective oscillations but also suggest a simple strategy for their long-term control.