Cryogenic carbon capture (CCC) is an innovative technology to desublimate $\text {CO}_2$ out of industrial flue gases. A comprehensive understanding of $\text {CO}_2$ desublimation and sublimation is essential for widespread application of CCC, which is highly challenging due to the complex physics behind. In this work, a lattice Boltzmann (LB) model is proposed to study $\text {CO}_2$ desublimation and sublimation for different operating conditions, including the bed temperature (subcooling degree $\Delta T_s$), gas feed rate (Péclet number $Pe $) and bed porosity ($\psi$). The $\text {CO}_2$ desublimation and sublimation properties are reproduced. Interactions between convective $\text {CO}_2$ supply and desublimation/sublimation intensity are analysed. In the single-grain case, $Pe $ is suggested to exceed a critical value $Pe _c$ at each $\Delta T_s$ to avoid the convection-limited regime. Beyond $Pe _c$, the $\text {CO}_2$ capture rate ($v_c$) grows monotonically with $\Delta T_s$, indicating a desublimation-limited regime. In the packed bed case, multiple grains render the convective $\text {CO}_2$ supply insufficient and make CCC operate under the convection-limited mechanism. Besides, in small-$\Delta T_s$ and high-$Pe $ tests, $\text {CO}_2$ desublimation becomes insufficient compared with convective $\text {CO}_2$ supply, thus introducing the desublimation-limited regime with severe $\text {CO}_2$ capture capacity loss ($\eta _d$). Moreover, large $\psi$ enhances gas mobility while decreasing cold grain volume. A moderate porosity $\psi _c$ is recommended for improving the $\text {CO}_2$ capture performance. By analysing $v_c$ and $\eta _d$, regime diagrams are proposed in $\Delta T_s$–$Pe $ space to show distributions of convection-limited and desublimation-limited regimes, thus suggesting optimal conditions for efficient $\text {CO}_2$ capture. This work develops a viable LB model to examine CCC under extensive operating conditions, contributing to facilitating its application.

The flow field of a bluff body, a circular disk, that moves horizontally in a stratified environment is studied using large-eddy simulations. Five levels of stratification (body Froude numbers of ${{Fr}} = 0.5, 1, 1.5, 2$ and $5$) are simulated at Reynolds number of ${{Re}} = 5000$ and Prandtl number of $Pr =1$. A higher ${{Re}} = 50\,000$ database at ${{Fr}} = 2, 10$ and $Pr =1$ is also examined for comparison. The wavelengths and amplitudes of steady lee waves are compared with a linear-theory analysis. Excellent agreement is found over the entire range of ${{Fr}}$ if an ‘equivalent body’ that includes the separation region is employed for the linear theory. For asymptotically large distances, the velocity amplitude varies theoretically as ${{Fr}}^{-1}$ but a correction owing to the dependence of the separation zone on ${{Fr}}$ is needed. The wake waves propagate in a narrow band of angles with the vertical, and have a wavelength that increases with increasing ${{Fr}}$. The envelope of wake waves, demarcated using buoyancy variance, exhibits self-similar behaviour. The higher ${{Re}}$ results are consistent with the buoyancy effects exhibited at the lower ${{Re}}$. The wake wave energy is larger at ${{Re}} = 50\,000$. Nevertheless, independent of ${{Fr}}$ and ${{Re}}$, the ratio of the wake wave potential energy to the wake turbulent energy increases to approximately 0.6–0.7 in the non-equilibrium stage showing their energetic importance besides suggesting universality in this statistic. There is a crossover of energetic dominance of lee waves at ${{Fr}} <2$ to wake-wave dominance at ${{Fr}} \approx 5$.

The motion of small non-spherical particles is often studied using the unsteady Stokes equations. Zhang & Stone (J. Fluid Mech., vol. 367, 1998, pp. 329–358) reported an asymptotic treatment for nearly spherical particles, to first order in particle non-sphericity, i.e. $O(\epsilon )$, where $\epsilon$ quantifies the shape deviation from a sphere. Importantly, key physical phenomena are absent at $O(\epsilon )$, including (1) coupling between the torque experienced by the particle and its linear translation, (2) coupling between the force the particle experiences and its rotation and (3) the effect of non-sphericity on the orientation averages of these forces and torques. We present an explicit asymptotic theory to second order in particle non-sphericity, i.e. $O(\epsilon ^2)$, for the force and torque acting on a particle in a general unsteady Stokes flow. The derived analytical formulae apply to particles of arbitrary shape, providing the leading-order asymptotic theory for the three above-mentioned phenomena. The theory is demonstrated for several example nearly spherical particles including a spheroid, a ‘pear-shaped’ particle and a simple model for a SARS-CoV-2 virion. This includes formulae for force and torque as a function of particle orientation and their corresponding orientation averages. Our study reveals that the orientation-averaged forces and torques experienced by a nearly spherical particle cannot be generally represented by a perfect sphere. The reported formulae are validated using finite-amplitude three-dimensional direct numerical simulations of the Navier–Stokes equations. A Mathematica notebook is also provided, facilitating implementation of the theory for particle shapes of the user's choosing.

A theoretical analysis is presented of peristaltic pumping down a narrow conduit with permeable walls, motivated by the flushing action of lugworms and other marine organisms in sandy burrows. Flow in the conduit is dealt with using lubrication theory; the leakage into the surrounding medium is taken into account by exploiting slender-body theory to solve the associated Darcy problem. By adopting a model for the local force balance on the pumping surface, we bridge between the limits in which the pump operates with either fixed load or displacement. In the latter limit we characterize peristaltic waves with either fixed form or ones that partially collapse the conduit. We construct pump characteristics (the relation between the mean flux and net pressure drop) when the burrow wall is impermeable and pressures are fixed at each end, and compare the results with existing laboratory experiments performed on lugworms. We then consider how the peristaltic dynamics is changed when the wall is made permeable. Last, we consider pumping along an impermeable burrow into a leaky head shaft. The results reveal that the permeability of the conduit wall or end can greatly impact the direction and strength of the recirculating flow.

While the problem governing Stokes flow about a single particle that is subject to an external force is ill posed in two dimensions (the ‘Stokes paradox’), the related problem of two mutually repellent particles is well posed. Motivated by self-assembly phenomena in thin viscous membranes, we consider this problem in the limit of remote particles. Such limits are typically handled in the literature using reflection techniques, which provide successive approximations to the mutual hydrodynamic interactions. Since their starting point is a single particle in an unbounded fluid domain, these techniques are futile in the present two-dimensional problem. We show how this apparent contradiction is resolved via use of singular perturbations. We obtain a two-term approximation for the velocity acquired by circular disks, considering both rigid and free particle surfaces. We also illustrate our perturbation scheme for elliptic disks, deriving a renormalised single-particle velocity. The utility of our asymptotic scheme is illustrated in the general problem of hydrodynamic interaction between a cluster of remote disks.

This experimental study investigates the fluid–structure–surface interactions of a flexibly mounted rigid plate in axial flow, focusing on flow-induced vibration (FIV) response and vortex dynamics of the system within a reduced velocity range of $U^*=0.29\unicode{x2013}8.73$, corresponding to a Reynolds number range of $Re=518\unicode{x2013}15\,331$. The plate, with one and two degrees of freedom (DoFs) for pitching and plunging oscillations, is examined at various submerged heights near the free surface. Results show that the plate exhibits divergence instability at low reduced velocities in both 1DoF and 2DoF systems. As the flow velocity surpasses a critical reduced velocity, periodic limit-cycle oscillations (LCOs) occur, increasing in amplitude until a second critical reduced velocity is reached. Beyond this point, LCOs are suppressed, and the plate experiences an increased static divergence angle with further flow velocity increase. The proximity to the free surface significantly influences the FIV response, with decreasing submerged heights leading to reduced LCO amplitudes and a shift of instabilities to higher reduced velocities. Vortex dynamics are analysed using time-resolved volumetric particle tracking velocimetry and hydrogen bubble flow visualisation. The analysis reveals disruptions in the symmetric flow field near the free surface, causing elongation and fragmentation of vortices in the wake of the plate, as well as vortex coupling. Proper orthogonal decomposition (POD) identifies dominant coherent structures, including leading-edge and trailing-edge vortices, captured in the first and second paired modes. On the other hand, higher POD modes capture the interaction of vortices in the wake and near the free surface.

When a cylinder is free to move along a transverse rectilinear path within a current, the vibrations developing with and without structural restoring force (SRF) noticeably deviate: if the elastic support is removed, their onset is delayed from a Reynolds number ($Re$, based on the body diameter and inflow velocity) value of approximately 20 to 30, and their peak amplitudes and frequency bandwidths are substantially reduced. The present study examines the influence of a curved path on this deviation by considering that the cylinder, mounted on an elastic support or not, is free to translate along a circular path whose radius is varied. The investigation is carried out numerically at $Re=25$ and $100$, i.e. subcritical and postcritical values relative to the threshold of $47$ that marks the onset of flow unsteadiness for a fixed body. The principal result of this work is that the behaviours of the flow–structure systems with and without SRF tend to converge under the effect of path curvature. Beyond a certain curvature magnitude, both systems explore the same vibration ranges and the presence or absence of SRF becomes indiscernible. This convergence is accompanied by an enhancement of the responses appearing without SRF. It is analysed in light of the evolution of the effective added mass which determines the subset of responses reached with SRF that remain accessible without SRF. The apparent continuity of the physical mechanisms between the subcritical- and postcritical-$Re$ values suggests that the convergence phenomenon uncovered here could persist at higher $Re$.

This paper investigates the linear and nonlinear evolution of radiating modes in supersonic boundary layers under the influence of impinging sound waves. It is found that the ensuing boundary-layer response is extraordinarily large for a subset of the sound frequency and incident angle, and the resonant over-reflection, corresponding to the reflection coefficient becoming infinite, occurs at a particular pairing of frequency and incident angle. At this point, the reflected wave coincides with a locally neutral radiating mode, which emits spontaneously sound in the form of Mach waves. A fundamental resonance takes place between the incident wave and the radiating mode. Viewed in a developing boundary layer, the response is rendered finite by introducing non-parallelism and nonlinear effects near the neutral location of the radiating mode, where the sound wave directly excites the radiating mode and/or acts on the pre-existing radiating mode. Inhomogeneous amplitude equations are derived to describe the excitation as well as the nonlinear development of the radiating mode in the two regimes where non-equilibrium and non-parallelism play a leading-order role, respectively. A composite amplitude equation is then constructed to take into account both non-parallelism and non-equilibrium effects. This amplitude equation is, with an appropriate initial condition, solved to quantify the impact of the impinging sound wave on the linear and nonlinear instability characteristics of the radiating mode. The far-field analysis shows that the Mach wave field of the radiating mode is changed significantly due to the incident sound.

The motion of a sphere freely rising or falling in a 5d (d is the diameter of the sphere) square tube was numerically studied for the sphere-to-fluid density ratio ranging from 0.1 to 2.3 (0.1 ≤ ρs/ρ ≤ 2.3, ρs is the density of spheres and ρ the fluid density) and Galileo number from 140 to 230 (140 ≤ Ga ≤ 230). We report that Hopf bifurcation occurs at Gacrit ≈ 157, where both the heavy and light spheres lose stability. The helical motion is widely seen for all spheres at Ga > 160 resulting from a double-threaded vortex interacting with the tube walls, which becomes irregular at Ga ≥ 190 where heavy spheres act differently from their counterparts; that is, heavy spheres change their helical directions alternately while light spheres exhibit helical trajectories with jaggedness in connection with the shedding of the double-threaded vortices. This is because of the difference in inertia between the heavy and light spheres. We also checked the oscillation periods for the helical motion of the spheres. They show opposite variations with ρs/ρ for the two types of spheres. Light spheres (ρs/ρ ≤ 0.7) reach a zigzagging regime at Ga ≥ 200 where a vortex loop (hairpin-like vortical structure) is formed which may develop into a vortex ring downstream at small ρs/ρ. This might be the first time a transition from the helical motion to the zigzagging motion for heavy spheres (ρs/ρ ≥ 1.8) has been reported. Finally, we examined the dependence of both the terminal Reynolds number and the drag coefficient of the spheres on the Galileo number.

The linear stability of plane Couette–Poiseuille flow (CPF) is studied with the physical effects of stratification, rotation and viscosity all included for the first time together. With no stratification, two instability mechanisms are present due to the shear and rotation which, for the most part, do not interact as they favour different forms of two-dimensionality. However, there are some small parts of parameter space where new three-dimensional instability appears indicating that Rayleigh's criterion is also violated in parameter space beyond where shear instability is expected. No fully localised centrifugal instabilities can be found for CPF, but they are shown to exist if the base flow shear has a maximum in the domain (the base flow needs to be at least cubic in the cross-stream variable rather than just quadratic as in CPF). With stable stratification present, new instabilities are found due to the combined effects of stratification and rotation, but only some appear to be of the resonance-type associated with the strato-rotational instability. The other unstable branches are more accurately interpreted as a stratification-modified centrifugal instability. Three-dimensional versions of this violate Rayleigh's criterion even when this is extended to include stratification. When stratification is stronger than rotation, the resonance-type instabilities are only dominant for cyclonic flows.