The thermal conductivity of a molecular gas consists of the translational and internal parts. Although in continuum flows the total thermal conductivity itself is adequate to describe the heat transfer, in rarefied gas flows they need to be modelled separately, according to the relaxation rates of translational and internal heat fluxes in an homogeneous system. This paper is dedicated to quantifying how these relaxation rates affect rarefied gas dynamics. The kinetic model of Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) is adapted to recover the relaxation of heat fluxes, which is validated by the direct simulation Monte Carlo method. Then the model of Wu et al., which has the freedom to adjust the relaxation rates, is used to investigate the rate effects of thermal relaxation in problems such as the normal shock wave, creep flow driven by Maxwell's demon and thermal transpiration. It is found that the relaxation rates of heat flux affect rarefied gas flows significantly, even when the total thermal conductivity is fixed.

Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.

Gust/turbulence–leading edge interaction is a significant source of airfoil broadband noise. An approach often used to predict the sound is based on Amiet’s flat-plate solution. Analytical studies have been conducted to investigate the influences of airfoil geometries, non-uniform mean flows and turbulence statistics, which, however, were often too convoluted. In this work, the problem is revisited by proposing simple corrections to the standard flat-plate solution to account for the effect of non-uniform mean flows of real airfoils. A key step in the method is to use a new space–time transformation that is analogous to the Prandtl–Glauert transformation to simplify the sound governing equation with spatially varying coefficients to a classical wave equation, which is then solved using the Schwarzschild technique as in Amiet’s solution. The impacts of Mach number, wavenumber and airfoil geometry on the prediction accuracy are investigated for both single-frequency and broadband cases, and the results are compared against high-fidelity simulations. It predicts the sound reduction by the airfoil thickness, and reveals that the reduction is caused by the non-uniform streamwise velocity. The limitations of the model are discussed and the approximation errors are estimated. In general, the prediction error increases with the airfoil thickness, the sound frequency and the flow Mach number. Nevertheless, in all cases studied in this work, the proposed correction can effectively improve the prediction accuracy of the flat-plate solution much more efficiently compared to numerical solutions of the Euler equations using computational aeroacoustics.

Flow past a circular cylinder and a downstream sphere is simulated numerically for Reynolds numbers between 100 and 300 for cylinder-to-sphere gap ratios between 0 and 3. The aim of this study is to investigate the influence of the sphere on the vortex shedding of the cylinder, and the wake-induced forces on the sphere. If vortices are shed from the cylinder upstream of the sphere, vortices are disconnected after they pass the sphere. This type of vortex disconnection is defined as sphere-induced vortex disconnection. The key finding is the so-called sphere-induced vortex dislocation (SIVDL) which occurs within the vortex formation region. The main characteristics of SIVDL include the adhesion of vortices to the cylinder at dislocation positions, and periodical occurrences of SIVDL. The periodic occurrence of SIVDL makes the frequency of vortex shedding change over time. Another interesting phenomenon is the reattachment of the separated shear layers from the cylinder to the sphere, which occurs when the sphere–cylinder gap is small. This leads to the formation of vortices without disconnection downstream of the sphere that it is similar to the case of tandem cylinders. In all cases, vortices are inclined, and their angle of inclination increases when SIVDL occurs. SIVDL reduces the frequency of the lift coefficient and increases the standard deviation of the drag coefficient of the sphere. The periodic occurrence of SIVDL causes the beating of the lift coefficient along with large-amplitude, low-frequency oscillations of the sphere's drag coefficient.

Modelling of fluid–particle interactions is a major area of research in many fields of science and engineering. There are several techniques that allow modelling of such interactions, among which the coupling of computational fluid dynamics (CFD) and the discrete element method (DEM) is one of the most convenient solutions due to the balance between accuracy and computational costs. However, the accuracy of this method is largely dependent upon mesh size, where obtaining realistic results always comes with the necessity of using a small mesh and thereby increasing computational intensity. To compensate for the inaccuracies of using a large mesh in such modelling, and still take advantage of rapid computations, we extended the classical modelling by combining it with a machine learning model. We have conducted seven simulations where the first one is a numerical model with a fine mesh (i.e. ground truth) with a very high computational time and accuracy, the next three models are constructed on coarse meshes with considerably less accuracy and computational burden and the last three models are assisted by machine learning, where we can obtain large improvements in terms of observing fine-scale features yet based on a coarse mesh. The results of this study show that there is a great opportunity in machine learning towards improving classical fluid–particle modelling approaches by producing highly accurate models for large-scale systems in a reasonable time.

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.

We study experimentally the motion and deformation of individual capsules transported by a constant volume-flux flow of low Reynolds number, through the T-junction of a channel with rectangular cross-section. We use millimetric ovalbumin-alginate capsules which we characterise independently of the flow experiment. Centred capsules travel at constant velocity down the straight channel leading to the T-junction, where they decelerate and expand in the spanwise direction before turning into one of the two identical daughter channels. There, non-inertial lift forces act to re-centre them and relax their shape until they reach a steady state of propagation. We find that the dynamics of fixed-size capsules within our channel geometry is governed by a capillary number $Ca$ defined as the ratio of viscous shear forces to elastic restoring forces, which we quantify by statically compressing the capsule between parallel plates to 50 % of its initial diameter, in order to account for different membrane thickness, pre-inflation and nonlinear elastic deformation. We show that the maximum extension in the T-junction of capsules of different stiffness collapses onto a master curve in $Ca$. This provides a sensitive measure of the relative stiffness of capsules at constant flow rate, particularly for softer capsules. We also find that the T-junction can sort fixed-size capsules according to their stiffness because the position in the T-junction from which capsules are entrained into the daughter channel depends uniquely on $Ca$. We demonstrate that a T-junction can be used as a sorting device by enhancing this initial capsule separation through a diffuser.

The unsteady forces acting on a body depend strongly on the local flow structures such as vortices. A quantitative understanding of the contribution of these structures to the instantaneous overall force is of fundamental significance. In the present study, a three-dimensional (3-D) vortex force map (VFM) method, extended from a two-dimensional (2-D) one, is used to provide better insight into the complex 3-D flow dynamics. The VFM vectors are obtained from solutions of potential equations and used to build the 3-D VFMs where the critical regions and directions associated with significant positive or negative contributions to the forces are identified. Using the existing velocity/vorticity field near the body, these VFMs can be used to obtain the body forces. A decomposed form of the force formula is also derived to separate the correction term contributed from the uncaptured vortices (close to or far away from the body). The present method is applied to the starting flow of a delta wing at high angle of attack, where LEVs are enhanced and stabilized by an axial flow effect. The analogy between the normal force of a slender delta wing and that of a 2-D flat plate with a steadily growing span is demonstrated via the VFM analysis. We find, for this application, that the force evolution exhibits some similar behaviour to a 2-D airfoil starting flow and, surprisingly, the force contribution mainly comes from the conical vortex sheet rather than the central core. Moreover, a quantitative understanding of the influence of LEVs in different evolution regimes on the body force is demonstrated.

In this work, theoretical modelling, quasi-three-dimensional (quasi-3D) simulations and micromodel experiments are conducted to study spontaneous imbibition with gravity in porous media micromodels. By establishing the force balance governing the spontaneous imbibition process, we develop a theoretical model for predicting the imbibition length against time in a rectangular capillary. The theoretical model is then extended to the prediction of a compact displacement process in a micromodel by using an equivalent width, which is derived by analogising the micromodel to a rectangular capillary. By simulating spontaneous imbibition in a rectangular capillary with various aspect ratios ($\varepsilon$), we show that the application condition of the quasi-3D method is $\varepsilon \leqslant 1/3$. Next, we simulate spontaneous imbibition in micromodels with various geometries and flow conditions. Fingering and compact displacement are identified for varying viscosity ratios and gravitational accelerations. At low (high) viscosity ratio of wetting to non-wetting fluids, an upward (downward) gravity can promote the stability of the wetting front, favouring the transition from fingering to compact displacement. In addition, we find that the depth-oriented interface curvature dominates the capillary effect during the imbibition, and such a mechanism is considered by introducing an equivalent contact angle into the theoretical model. With the help of equivalent width and contact angle, the theoretical model is shown to provide satisfactory prediction of the compact displacement process. Finally, a micromodel experiment is presented to further verify the developed theoretical model and the quasi-3D simulation.

We study the topology and the temporal dynamics of turbulent Rayleigh–Bénard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of $\varGamma = 5$. Experiments and numerical simulations are focused on the Rayleigh number range $6.7 \times 10^{4} \leqslant Ra \leqslant 3.5 \times 10^{5}$, where a new cellular flow regime has been reported previously (Akashi et al., Phys. Rev. Fluids, vol. 4, 2019, 033501). This flow structure shows symmetries with respect to the vertical planes crossing at the centre of the container. The dynamic behaviour is dominated by strong three-dimensional oscillations with a period length that corresponds to the turnover time. Our analysis reveals that the flow structure in the $\varGamma = 5$ box corresponds in key features to the jump rope vortex structure, which has recently been discovered in a $\varGamma = 2$ cylinder (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). While in the $\varGamma = 2$ cylinder a single jump rope vortex occurs, the coexistence of four recirculating swirls is detected in this study. Their approach to the lid or the bottom of the convection box causes a temporal deceleration of both the horizontal velocity at the respective boundary and the vertical velocity in the bulk, which in turn is reflected in Nusselt number oscillations. The cellular flow regime shows remarkable similarities to properties commonly attributed to turbulent superstructures.

Fish typically swim by periodic bending of their bodies. Bending seems to follow a universal rule; it occurs at about one-third from the posterior end of the fish body with a maximum bending angle of about $30^{\circ }$. However, the hydrodynamic mechanisms that shaped this convergent design and its potential benefit to fish in terms of swimming speed and efficiency are not well understood. It is also unclear to what extent this bending is active or follows passively from the interaction of a flexible posterior with the fluid environment. Here, we use a self-propelled two-link model, with fluid–structure interactions described in the context of the vortex sheet method, to analyse the effects of both active and passive body bending on the swimming performance. We find that passive bending is more efficient but could reduce swimming speed compared with rigid flapping, but the addition of active bending could enhance both speed and efficiency. Importantly, we find that the phase difference between the posterior and anterior sections of the body is an important kinematic factor that influences performance, and that active antiphase flexion, consistent with the passive flexion phase, can simultaneously enhance speed and efficiency in a region of the design space that overlaps with biological observations. Our results are consistent with the hypothesis that fish that actively bend their bodies in a fashion that exploits passive hydrodynamics can at once improve speed and efficiency.