A mesoscopic lattice Boltzmann model is implemented for modelling isothermal two-component evaporation in porous media. The model is based on the pseudopotential multiphase model with two components to mimic the phase-change component (e.g. water and its vapour) and the non-condensible component (e.g. dry air), and the cascaded collision operator is used to enhance the numerical performance. The model is first analysed based on Chapman–Enskog expansion and then validated by the theoretical solution of an isothermal diffusive evaporation problem. We then discuss in detail the implementation of wettability based on a geometric function scheme and further validate the model with microfluidic evaporation experiments. We apply the method to simulate the convective evaporation of a dual-porosity medium and investigate the effects of inflow vapour concentration (${Y_{vapour,in}}$) and contact angle ($\theta$) on the evaporation. Simulation results reproduce the typical transition from the constant evaporation regime (CRP) at large liquid saturation (S) to the receding front period (RFP) at small S, with an intermediate falling rate period in between. The dependence of the average evaporation rates on ${Y_{vapour,in}}$ and $\theta$ during CRP and RFP is investigated. A universal scaling formulation for the evaporation rate during CRP is found with respect to the concentration-related mass transfer number $B_Y$, contact angle $\theta$ and inflow Reynolds number Re, i.e. $E{R_{CRP}} = {k_3}\ln \left ( {1 + {B_Y}} \right ) {\cdot } \left [ {\ln \left ( {1 + {Re}} \right ) + {k_2}} \right ]\left [ {\cos (\theta ) + {k_1}} \right ]$, where ${k_1}$, ${k_2}$ and ${k_3}$ are fitting parameters.

Large-eddy simulations of the unsteady flows around rectangular prisms with chord-to-depth ratios (B/D) ranging from 3 to 12 are carried out at a Reynolds number of 1000. A particular focus of the study is the physical mechanisms governing the global instability of the flow. The coherent structures and velocity spectra reveal that large-scale leading-edge vortices (L vortices) are formed by the coalescence of Kelvin–Helmholtz rollers. Based on dynamic mode decomposition, the interactions between the L vortex and the trailing-edge vortex (T vortex) at different B/D values are revealed. It is found that the phase difference between the L and T vortices is the critical factor promoting a stepwise increase in the Strouhal number with increasing B/D. According to the phase analysis, there are two types of pressure feedback-loop mechanisms maintaining the self-sustained oscillations. When B/D = 4–5, the feedback loop covers the separation region, and the global instability is controlled by the impinging shear-layer instability. When B/D = 3 and 6–12, the feedback loop covers the entire chord, and the global instability is controlled by the impinging leading-edge vortex shedding instability. Self-sustained oscillations of the shear layer still exist after a splitter plate is placed in the near wake, indicating that the T vortex shedding is not essential in triggering the global instability. Nevertheless, with the participation of the T vortex, the primary instability mode may be reselected due to the upper and lower limits of the shedding frequency imposed by the T vortex.

We stabilize an open cavity flow experiment to 1 % of its original fluctuation level. For the first time, a multi-modal feedback control is automatically learned for this configuration. The key enabler is automatic in situ optimization of control laws with machine learning augmented by a gradient descent algorithm, named gradient-enriched machine learning control (Cornejo Maceda et al., J. Fluid Mech., vol. 917, 2021, A42, gMLC). The physical interpretation of the feedback mechanism is assisted by a novel cluster-based control law visualization for the flow dynamics and corresponding actuation commands. Starting points of the control experiment are two unforced open cavity benchmark configurations: a narrow-bandwidth regime with a single dominant frequency and a mode-switching regime where two frequencies compete. The flow is forced by a dielectric barrier discharge actuator located at the leading edge and is monitored by a downstream hot-wire sensor over the trailing edge. The feedback law is optimized with respect to the monitored fluctuation level. As reference, the self-oscillations of the mixing layer are mitigated with steady actuation. Then, a feedback controller is optimized with gMLC. As expected, feedback control outperforms steady actuation by achieving a better amplitude reduction with approximately 1 % of the actuation energy required for similarly effective steady forcing. Intriguingly, optimized laws learned for one regime perform well for the other untested regime as well. The proposed control strategy can be expected to be applicable for many other shear flow experiments.

Dynamic mode decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman operators. However, verifying the decomposition, equivalently the computed spectral features of Koopman operators, remains a significant challenge due to the infinite-dimensional nature of Koopman operators. Challenges include spurious (unphysical) modes and dealing with continuous spectra, which both occur regularly in turbulent flows. Residual dynamic mode decomposition (ResDMD), introduced by Colbrook & Townsend (Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems. 2021. arXiv:2111.14889), overcomes such challenges through the data-driven computation of residuals associated with the full infinite-dimensional Koopman operator. ResDMD computes spectra and pseudospectra of general Koopman operators with error control and computes smoothed approximations of spectral measures (including continuous spectra) with explicit high-order convergence theorems. ResDMD thus provides robust and verified Koopmanism. We implement ResDMD and demonstrate its application in various fluid dynamic situations at varying Reynolds numbers from both numerical and experimental data. Examples include vortex shedding behind a cylinder, hot-wire data acquired in a turbulent boundary layer, particle image velocimetry data focusing on a wall-jet flow and laser-induced plasma acoustic pressure signals. We present some advantages of ResDMD: the ability to resolve nonlinear and transient modes verifiably; the verification of learnt dictionaries; the verification of Koopman mode decompositions; and spectral calculations with reduced broadening effects. We also discuss how a new ordering of modes via residuals enables greater accuracy than the traditional modulus ordering (e.g. when forecasting) with a smaller dictionary. This result paves the way for more significant dynamic compression of large datasets without sacrificing accuracy.

This paper is dedicated to the development of particle charge and velocity second-order moment transport equations for monodisperse particles in gas flow with a tribocharging effect. The full transport equations for the particle charge–velocity covariance and the charge variance are derived in the framework of the kinetic theory of granular flow assuming that the electrostatic interaction does not modify the collision dynamics. The collision integrals are solved without presuming the form of the electric part for the particle probability density function. The full second-order transport equation model is tested in a one-dimensional periodic domain. The results show that this model is able to capture more important physical mechanisms that are neglected by simple algebraic models proposed in the past. An in-depth analysis of the transport equations is also performed. This study reveals that, for sufficiently small covariance characteristic destruction time scales, the transient and third-order moments terms can be safely neglected. In addition, two different reduced-order models are proposed: a more general algebraic model that takes into account the variance effect and a semi-algebraic model that only resolves a transport equation for the charge variance coupled with an algebraic model for the covariance. The former could, however, lead to non-physical predictions in many cases, while the latter can be a suitable alternative only for a sufficiently small interparticle collision time. Finally, a simple chart based on test case simulations is proposed to show under which conditions a semi-algebraic model could be considered as a suitable alternative.

In detonation engines and accidental explosions, a detonation may propagate in an inhomogeneous mixture with non-uniform reactant concentration. In this study, one- and two-dimensional simulations are conducted for detonation propagation in hydrogen/oxygen/nitrogen mixtures with periodic sinusoidal or square wave distribution of the reactant concentration. The objective is to assess the properties of detonation propagation in such inhomogeneous mixtures. Specifically, detonation quenching and reinitiation, cellular structure, cell size and detonation speed deficit are investigated. It is found that there exists a critical amplitude of the periodic mixture composition distribution, above which the detonation quenches. When the amplitude is below the critical value, detonation quenching and reinitiation occur alternately. A double cellular structure consisting of substructures and a large-scale structure is found for a two-dimensional detonation propagating in inhomogeneous mixtures with a periodic reactant concentration gradient. The detonation reinitiation process and the formation of the double cellular structure are interpreted. To quantify the properties of detonation propagation in different inhomogeneous mixtures, the large cell size, critical amplitude, transition distance and detonation speed deficit are compared for hydrogen/air without and with nitrogen dilution and for periodic sine wave and square wave distributions of the reactant concentration. The large-scale cell size is found to be linearly proportional to the wavelength, and both the critical amplitude and the transition distance decrease with the wavelength. The small detonation speed deficit is shown to be due to the incomplete combustion of the reactant. This work provides helpful understanding of the features of detonation propagation in inhomogeneous mixtures.

The linear and nonlinear dynamics of two-phase swirling flows produced by the Grabowski–Berger profile under the influence of a viscosity stratification are investigated. We perform axisymmetric nonlinear simulations and fully three-dimensional linear global stability analysis of the flow for several swirl numbers $S$ and viscosity ratios $\tilde {\mu }$. They are accompanied by nonlinear three-dimensional simulations and subsequent modal analysis using the bispectral mode decomposition, recently introduced by Schmidt (Nonlinear Dyn., vol. 102, issue 4, 2020, pp. 2479–2501). We find a pronounced destabilising effect of the viscosity stratification on both the onset of axisymmetric vortex breakdown and helical instability that is linked to the required shear stress continuity across the interface. Consequently, destabilisation is shifted to lower $S$ as compared with an equivalent flow with uniform viscosity. Further, the stability analysis reveals the simultaneous destabilisation of two global modes with wavenumbers $m=1$ and $m=2$ that have harmonic frequencies. The analysis of the nonlinear flow reveals a strong triadic resonance between these modes that governs the nonlinear dynamics and leads to a rapid departure from the linear dynamics. At larger swirl, the bifurcation of additional modes initiates an interaction cascade by means of triadic resonance which is elucidated by the bispectral analysis. It leads to the emergence of a variety of additional modes in the nonlinear flow. This study contributes to an improved understanding of the influence of viscosity stratification on the onset of vortex breakdown and the destabilisation of global modes. Further, it provides a clear picture of the dynamics of swirling flows with a codimension-two point and related triadic interaction of two global modes at harmonic frequencies and wavenumbers.

Elastocapillarity has attracted increasing interest in recent years due to its important roles in many industrial applications. In this work, we derive a thermodynamically consistent continuum model for the dynamics of two immiscible fluids on a thin and inextensible elastic sheet in two dimensions. With the sheet being modelled by a deformable curve with the Wilmore energy and local inextensibility constraint, we derive a two-phase hydrodynamics model with the interfacial and boundary conditions consistent with the second law of thermodynamics. In particular, the boundary conditions on the sheet and at the moving contact line take the form of force balances involving the fluid stress, surface tensions, the sheet bending force and sheet tension, as well as friction forces arising from the slip of fluids on the sheet. The resulting model obeys an energy dissipation law. To demonstrate its capability of modelling complex elastocapillary interactions, we consider two applications: (1) the relaxation dynamics of a droplet on an elastic sheet and (2) the transport of a droplet driven by bendotaxis in a channel bounded by elastic sheets. Numerical solutions for the coupled fluid–sheet dynamics are obtained using the finite element method. The detailed information provided by the full hydrodynamics model allows us to better understand the dynamical processes as compared to other simplified models that were used in previous work.

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a periodic pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are unstable to perturbations of sufficiently small wavenumber regardless of parameter values, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

We study drop impacts on an immiscible viscous liquid pool and investigate the formation of droplet surface craters using experimental and theoretical analyses. We attribute the formation of air craters to the rapid deceleration of the droplet due to viscous drag force. The droplet response to the external impulsive decelerating force induces oscillatory modes on the surface exposed to the air forming capillary waves that superimpose to form air craters of various shapes and sizes. We introduce a non-dimensional parameter (${\varGamma }$), that is, the ratio of the drag force to the capillary force acting on the droplet. We show that ${\varGamma }$ is directly proportional to the capillary number. We show that droplets forming air craters of significant depths have ${\varGamma }>1$. Further, we demonstrate that Legendre polynomials can locally approximate the central air crater jet profile. We also decipher that the air crater response time scale ($T$) varies as the square root of impact Weber number ($T\sim We^{1/2}$). Further, we generalize the local droplet response with a global response model for low impact energies based on an eigenvalue problem. We represent the penetrating drop as a constrained Rayleigh drop problem with a dynamic contact line. The air–water interface dynamics is analysed using an inviscid droplet deformation model for small deformation amplitudes. The local and global droplet response theories conform with each other and depict that the deformation profiles could be represented as a linear superposition of eigenmodes in Legendre polynomial basis. We unearth that the droplet response in an immiscible impact system differs from the miscible impact systems due to the presence of such a dynamic contact line.

An impulsively starting motion of a cylindrical body submerged below a calm water surface in an open container of arbitrary shape is considered. This work generalizes the case of an infinite-depth liquid studied by Semenov et al. (J. Fluid Mech., vol. 919, 2021, R4). Particular attention is paid to the interaction between the body, the free surface and the container. The integral hodograph method is employed to derive the complex velocity potential in a parameter plane. The boundary-value problem is reduced to a system of integral equations, which is solved numerically. The velocity field, the pressure impulse on the body and the container wall and the added mass just after the impact are determined for a wide range of depths of submergence and container geometries and for various cross-sectional shapes of the body, such as a flat plate, a circle and a rectangle.

The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid–solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities.

We consider suspensions of finite-size neutrally buoyant rigid spherical particles in channel flow and investigate the relevance of different momentum transfer mechanisms and the relation between the local particle dynamics and the bulk flow properties in the highly inertial regime. Interface-resolved simulations are performed in the range of Reynolds numbers $3000 \leq Re \leq 15\ 000$ and solid volume fractions $0 \leq \phi \leq 0.3$. The Lagrangian particle statistics show that pair interactions are highly inhomogeneous and dependent on the distance from the wall: in their vicinity, the underlying mean shear drives the pair interactions, while a high degree of isotropy, dictated by more frequent collisions, characterizes the core region. Analysis of the momentum balance reveals that while the particle-induced stresses govern the dynamics in dense conditions, $\phi =0.3$, and moderate Reynolds numbers, $Re <10\ 000$, the turbulent stresses take over at higher Reynolds numbers. This behaviour is associated with a reduced particle migration toward the channel core, which decreases the importance of the particle-induced stress and increases the turbulent activity. Our results indicate that Reynolds stresses and the associated velocity fluctuations, characteristics of near-wall turbulence, prevail at high inertia over the resistance to deformation presented by the particles for volume fractions lower than 30 %.

In this paper, we conduct a systematic study of the instability of a boundary layer over a rotating cone that is inserting into a supersonic stream with zero angle of attack. The base flow is obtained by solving the compressible boundary-layer equations using a marching scheme, whose accuracy is confirmed by comparing with the full Navier–Stokes solution. Setting the oncoming Mach number and the semi-apex angle to be 3 and 7$^\circ$, respectively, the instability characteristics for different rotating rates ($\bar \varOmega$, defined as the ratio of the rotating speed of the cone to the axial velocity) and Reynolds numbers ($R$) are revealed. For a rather weak rotation, $\bar \varOmega \ll 1$, only the modified Mack mode (MMM) exists, which is an extension of the supersonic Mack mode in a quasi-two-dimensional boundary layer to a rotation configuration. Further increase of $\bar \varOmega$ leads to the appearance of a cross-flow mode (CFM), coexisting with the MMM but in the quasi-zero frequency band. The unstable zones of the MMM and CFM merge together, and so they are referred to as the type-I instability. When $\bar \varOmega$ is increased to an $O(1)$ level, an additional unstable zone emerges, which is referred to as the type-II instability to be distinguished from the aforementioned type-I instability. The type-II instability appears as a centrifugal mode (CM) when $R$ is less than a certain value, but appears as a new CFM for higher Reynolds numbers. The unstable zone of the type-II CM enlarges as $\bar \varOmega$ increases. The vortex structures of these types of instability modes are compared, and their large-$R$ behaviours are also discussed.

The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.

The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall is investigated using laser-Doppler anemometry measurements of velocities in a large oscillatory flow tunnel and direct numerical simulation (DNS) of the Navier–Stokes equations. The same periodic irregular roughness was used for both experiments and DNS. Four flow shapes are investigated: sinusoidal, skewed, asymmetric and combined skewed–asymmetric. The experiments were conducted for target Reynolds numbers (based on the Stokes length and standard deviation of free-stream velocity) of $R_{\delta,\sigma }=800$ and $R_{\delta,\sigma }=1549$; DNS was conducted for flows with target $R_{\delta,\sigma }=800$. Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtl's secondary flows of the second kind in oscillatory flow is presented. Turbulence structure is visualised using isosurfaces of $\lambda _{2}$ (Jeong & Hussain J. Fluid Mech., vol. 285, 1995, pp. 69–94), revealing densely packed structures that grow stronger and weaker in correspondence with the free-stream velocity. Reynolds and dispersive stresses peak just below the highest roughness crest, with dispersive stress vanishing a short distance above the roughness. Bursts of turbulence kinetic energy and wake kinetic energy are generated each flow half-cycle, with variable behaviour depending on flow shape. Non-Gaussian turbulence statistics are observed that originate near the wall, becoming increasingly non-Gaussian far from the wall. Probability density functions of turbulence statistics can be closely approximated by a fourth-order Gram–Charlier distribution at most phases and elevations, though when statistics deviate more strongly from Gaussian, streamwise and wall-normal (spanwise) statistics are better described by a Pearson type IV (VII) distribution.

We propose a novel nonlinear manifold learning from snapshot data and demonstrate its superiority over proper orthogonal decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap, as encoder and, $K$-nearest neighbours ($K$NN) algorithm as decoder. The proposed technique is applied to numerical and experimental datasets including the fluidic pinball, a swirling jet and the wake behind a couple of tandem cylinders. Analysing the fluidic pinball, the manifold is able to describe the pitchfork bifurcation and the chaotic regime with only three feature coordinates. These coordinates are linked to the vortex-shedding phases and the force coefficients. The manifold coordinates of the swirling jet are comparable to the POD mode amplitudes, yet allow for a more distinct and less noise-sensitive manifold identification. A similar observation is made for the wake of two tandem cylinders. The tandem cylinders are aligned and located at a streamwise distance which corresponds to the transition between the single bluff body and the reattachment regimes of vortex shedding. Isomap unveils these two shedding regimes while the Lissajous plot of the first two POD mode amplitudes features a single circle. The reconstruction error of the manifold model is small compared with the fluctuation level, indicating that the low embedding dimensions contain the coherent structure dynamics. The proposed Isomap–$K$NN manifold learner is expected to be of great importance in estimation, dynamic modelling and control for a large range of configurations with dominant coherent structures.

The fluid–structure interactions between flexible fibres and viscous flows play an essential role in various biological phenomena, medical problems and industrial processes. Of particular interest is the case of particles transported freely in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations and theoretical modelling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behaviour through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler–Bernoulli rods whose hydrodynamics is described by local slender-body theory.

We show that a vertical viscosity stratification at a localized region caused by a chemical reaction yields an inconspicuous shear layer. A chemo-hydrodynamic Kelvin–Helmholtz instability or cat-eye-shaped morphology develops at one reaction front, while the other front diffuses steadily over time. Through linear stability and nonlinear simulations, the existence of such instabilities is established if the log-mobility ratio exceeds a critical value. We find unique scalings between the stable and unstable zones that demonstrate how the influence of variations in solute diffusion on instability can be eliminated. The observed unstable patterns agree with existing experimental results.

Reliable prediction of the erosion rate of sediment beds is important for many applications in coastal and river engineering. Theoretical understanding of empirically derived scaling relations is still lacking. This applies in particular for the scaling anomaly between low and high Shields number conditions. In this work, the erosion process is studied from the perspective of the phase-averaged turbulent kinetic energy (TKE) equations. The multi-phase TKE equations are written in a form that allows for a direct comparison with the TKE equation that appears for a stratified single-phase flow under the Boussinesq approximation. This reveals that next to buoyancy destruction, several other TKE modulation mechanisms become important at high Shields numbers and concentrations. Two scaling laws are derived for both moderate and high Shields numbers, and are tested against a wide range of experimental data.