We present an experimental and numerical study of turbulent thermal convection in the presence of an effective horizontal buoyancy that generates extra shear at the boundary. Geometrical confinements are also applied by varying the streamwise and spanwise aspect ratios of the convection cell to condense the plumes. With these, we systematically explore the effects of plume and shear on heat transfer. It is found that a streamwise confinement results in increased plume coverage but decreased shear compared with spanwise confinement. The fact that streamwise confinement leads to a higher vertical heat transfer efficiency than the spanwise confined case suggests that the increase of plume coverage is the dominant effect responsible for the enhanced heat transfer. Our results highlight the potential applications of coherent structure manipulation in efficient passive heat transfer control and thermal engineering. We also analyse the energetics of the present system and derive the expression of mixing efficiency accordingly. The mixing efficiency is found to increase with both the buoyancy ratio and streamwise dimension.

We consider the effect of droplet geometry on the early-stages of coffee-ring formation during the evaporation of a thin droplet with an arbitrary simple, smooth, pinned contact line. We perform a systematic matched asymptotic analysis of the small capillary number, large solutal Péclet number limit for two different evaporative models: a kinetic model, in which the evaporative flux is effectively constant across the droplet, and a diffusive model, in which the flux is singular at the contact line. For both evaporative models, solute is transported to the contact line by a capillary flow in the droplet bulk, while local to the contact line, solute diffusion counters advection. The resulting interplay leads to the formation of the nascent coffee-ring profile. By exploiting a coordinate system embedded in the contact line, we solve explicitly the local leading-order problem, deriving a similarity profile (in the form of a gamma distribution) that describes the nascent coffee ring. Notably, for an arbitrary contact line geometry, the ring characteristics change due to the concomitant asymmetry in the shape of the droplet free surface, the evaporative flux (for diffusive evaporation) and the mass flux into the contact line. We utilize the asymptotic model to determine the effects of contact line geometry on the growth of the coffee ring for a droplet with an elliptical contact set. Our results offer mechanistic insight into the effect of contact line curvature on the development of the coffee ring from deposition up to jamming of the solute; moreover, our model predicts when finite concentration effects become relevant.

By adapting the triple decomposition of an instantaneous turbulent flow into a time-averaged mean field, large-scale coherent motion and fine-scale random fluctuations, and treating the coherent motion as instability modes on the mean flow, a mathematical theory is developed to describe the nonlinear spatial–temporal modulation and acoustic radiation of a coherent structure (CS) on a circular jet in the form of a wavepacket consisting of an axisymmetric (ring) mode and its sideband components. The effect of fine-scale turbulence on the CS is characterised via a gradient closure model, and the non-parallelism due to the axial variation and radial velocity of the mean flow is taken into account. By employing the matched asymptotic expansion and multi-scale techniques, a strongly nonlinear system is derived, which governs the envelope of the CS and its vorticity and temperature in the critical layer. Numerical solutions to the evolution system show that the theory captures the nonlinear amplitude attenuation and vorticity roll-up as observed in experiments. The large-distance asymptotic properties of the CS allow us to describe and predict its acoustic radiation on the basis of first principles. The CS is trapped within the jet, but its self-interaction generates a temporally and axially modulated mean-flow distortion, which acts as the emitter to radiate low-frequency sound waves, with the Reynolds stresses driving this mean-flow distortion being identified unambiguously to be the physical source in the present context. An equivalent source in the Lighthill type of acoustic analogy is also identified. For the present ring-mode CS in the fully developed region of a circular jet, the equivalent source can be determined before the acoustic field is, and the intensity of the radiated sound waves is found to be $O(\epsilon ^3)$, where $\epsilon$ measures the magnitude of the CS. The directivity and spectrum of the acoustic far field are calculated for representative parameters, and the predicted features resemble experimental measurements.

The Enskog–Vlasov equation is a phenomenological kinetic equation that extends the Enskog equation for the dense (non-ideal) hard-sphere fluid by adding an attractive soft potential tail to the purely repulsive hard-sphere contribution. Simplifying assumptions about pair correlations lead to a Vlasov-like self-consistent force field that adds to the Enskog non-local hard-sphere collision integral. Within the limitations imposed by the underlying assumptions, the extension gives the Enskog–Vlasov equation the ability to give a unified description of ideal and non-ideal fluid flows as well as of those fluid states in which liquid and vapour regions coexist, being separated by a resolved interface. Furthermore, the Enskog–Vlasov fluid can be arbitrarily far from equilibrium. Thus the Enskog–Vlasov model equation provides an excellent, although approximate, tool for modelling processes with liquid–vapour interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective. Here, a set of 26 moment equations is derived from the Enskog–Vlasov equation by means of the Grad moment method. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of Knudsen layers. This work focuses on the – rather involved – derivation of the moment equations, with only a few applications shown.

The linear instability of the flow in a pipe subjected to a wavelike transpiration velocity at the walls is considered. The fully nonlinear problem is formulated at high Reynolds numbers and small transpiration velocities. Solutions of the nonlinear system describing the bifurcation of disturbances caused by the transpiration are calculated and a complex bifurcation structure is uncovered with several nonlinear states possible at some transpiration amplitudes. The symmetries and structure of the nonlinear solutions are discussed.

We study the injection flow of a heavy viscoplastic fluid into a light Newtonian fluid, via modelling and experiments. The injection is carried out downward, via an eccentric inner pipe inside a vertical closed-end outer pipe. This configuration results in a core viscoplastic fluid surrounded by an annular Newtonian fluid. The flow is structured and mixing is negligible. As the injection rate increases in a typical experiment, we observe three distinct flow regimes, associated with the core fluid behaviour, namely the breakup, coiling and buckling (bulging) regimes. In the breakup regime, the core fluid is yielded due to the extension caused by buoyancy, while in the buckling regime the yielding occurs due to the compression promoted by the pressure and the interfacial shear stress applied by the upward flow of the annular fluid. For the coiling regime, the core fluid remains largely unyielded until it exhibits a coiling behaviour. We develop a lubrication approximation model, using the Herschel–Bulkley constitutive equation, with dimensionless flow parameters including the Bingham number, the power-law index, the buoyancy number, the viscosity ratio, the diameter ratio, the eccentricity and the aspect ratio. Based on a reasonable prediction to the yielding onset, the model allows us to classify the flow regimes versus an elegant combination of the dimensionless numbers.

Flow through mechanical aortic valves (MAVs) has been constantly associated to higher haemolysis and platelet activation levels with respect to native valves, due to non-physiologic haemodynamic features. Both computational and experimental investigations have correlated the blood damage to augmented levels of turbulent stress downstream of MAVs. This study provides a computational estimation, drawn from high-resolution direct numerical simulations, of turbulent and fluctuating viscous stresses in three different MAV configurations, at subsequent stages of the cardiac cycle. The configurations comprise a St. Judes Medical Regent valve (SJMV), a Lapeyre-Triflo FURTIVA valve (LTFV) with three leaflets, and a SJMV with vortex generators (VGs). Non-standard configurations are expected to mitigate the mean stress level on blood constituents reducing the turbulent production. Computations are carried out by means of a finite-difference flow solver with a direct-forcing immersed boundary technique to handle fixed and moving bodies. The VGs are found to provide instabilities which corrupt the Kármán-like vortex shedding downstream of the leaflets, reducing the intensity of turbulent kinetic energy at the peak flow rate, thus lowering the local Reynolds shear stress. Conversely, the LTFV configuration provides comparable haemodynamic performance at peak flow rate but further reduced stress level in the deceleration phase. These interpretations are supported by probability density distributions from three-dimensional fields, and further corroborated by a pointwise mapping of the Taylor length scale and local energy spectra. The outcomes of this study might potentially be exploited to improve the design of new-generation MAVs, with the aim of decreasing the risk of thromboembolic complications.

The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and surface vortices. While near-bed vortices are generated by the flow separation occurring at the bed discontinuity, surface vortices are induced by the wave breaking in conjunction with a breaking-induced jet. A ‘backward breaking’ (previously observed in the case of solitary waves) occurs at the air–water interface downstream of the discontinuity and generates a surface anticlockwise vortex that interacts with the near-bed clockwise vortex. With the vortex–vortex interaction influenced by many physical mechanisms, a point-vortex model, by which vortices evolve under both self-advection (in relation to both free surface and seabed) and mutual interaction, has been implemented to separately investigate the vortex- and wave-induced dynamics. The available data indicate that both self-advection and mutual interaction are the governing mechanisms for the downward motion of the surface vortex, with the effect of the breaking-induced jet being negligible. The same two mechanisms, combined with the mean flow, are responsible for the almost horizontal and oscillating path of the near-bed vortex. The investigation of the vortex paths allow us to group the performed tests into three distinct classes, each characterized by a specific range of wave nonlinearity. The time evolution of the main variables characterizing the vortices (e.g. circulation, kinetic energy, enstrophy, radius) and their maximum values increase with the wave nonlinearity, such dependences being described by synthetic best-fit formulas.

We study the statistics of passive scalars at $Pr=1$, for turbulent flow within a smooth straight pipe of circular cross section up to $Re_{\tau } \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. While featuring a general organisation similar to the axial velocity field, passive scalar fields show additional energy at small wavenumbers, resulting in a higher degree of mixing and in a $k^{-4/3}$ spectral inertial range. The DNS results highlight logarithmic growth of the inner-scaled bulk and mean centreline scalar values with the friction Reynolds number, implying an estimated scalar von Kármán constant $k_{\theta } \approx 0.459$, which also nicely fits the mean scalar profiles. The DNS data are used to synthesise a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15 (12), 1972, pp. 2329–2351), which points to some shortcomings of the original formulation. Universality of the mean core scalar profile in defect form is recovered, with very nearly parabolic shape. Logarithmic growth of the buffer-layer peak of the scalar variance is found in the Reynolds number range under scrutiny, which well conforms with Townsend's attached-eddy hypothesis, whose validity is also supported by the spectral maps. The behaviour of the turbulent Prandtl number shows good universality in the outer wall layer, with values $Pr_t \approx 0.84$, as also found in previous studies, but closer to unity near the wall, where existing correlations do not reproduce the observed trends.

The surface thermodynamics and wetting condition are investigated for the recent multiphase lattice Boltzmann model with a self-tuning equation of state (EOS), where the multiphase EOS is specified in advance and the reduced temperature is set to a relatively low value. The surface thermodynamics is first explored starting from the free-energy functional of a multiphase system and a theoretical expression for the contact angle is derived for the general multiphase EOS. The conventional free-energy density for the solid surface, which is in linear form, is analysed, and it is found that the fluid density on the solid surface significantly deviates from that in the bulk phase when the reduced temperature is relatively low. A new free-energy density for the solid surface, which is in hyperbolic tangent form, is then proposed. Two independent parameters are introduced, which can dramatically reduce the density deviation and effectively adjust the contact angle, respectively. Meanwhile, the contact angle, surface tension and interface thickness can be independently adjusted in the present theoretical framework. Based on the analysed surface thermodynamics, a thermodynamically consistent treatment for the wetting condition is proposed for both straight and curved walls. Numerical tests of droplets on straight and curved walls validate the theoretical analysis of the surface thermodynamics and the present wetting condition treatment. As further applications, a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, and the evaporation of a droplet on an adiabatic substrate are simulated, and satisfying results consistent with previous studies are obtained.