Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.

Online in situ prediction of 3-D flame evolution has been long desired and is considered to be the Holy Grail for the combustion community. Recent advances in computational power have facilitated the development of computational fluid dynamics (CFD), which can be used to predict flame behaviours. However, the most advanced CFD techniques are still incapable of realizing online in situ prediction of practical flames due to the enormous computational costs involved. In this work, we aim to combine the state-of-the-art experimental technique (that is, time-resolved volumetric tomography) with deep learning algorithms for rapid prediction of 3-D flame evolution. Proof-of-concept experiments conducted suggest that the evolution of both a laminar diffusion flame and a typical non-premixed turbulent swirl-stabilized flame can be predicted faithfully in a time scale on the order of milliseconds, which can be further reduced by simply using a few more GPUs. We believe this is the first time that online in situ prediction of 3-D flame evolution has become feasible, and we expect this method to be extremely useful, as for most application scenarios the online in situ prediction of even the large-scale flame features are already useful for an effective flame control.

The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $\unicode[STIX]{x1D719}\approx 35\,\%$, the particle dynamics seems to be hindered by the increase in the magnitude of excluded volume interactions with concentration. However, a non-trivial suspension behaviour is observed in concentrated regimes, where the hydrodynamic diffusivity starts to increase with the volume fraction at $\unicode[STIX]{x1D719}\approx 35\,\%$, before reaching a local maximum, and then drastically decreases on approaching random close packing. Similar non-trivial behaviours are observed in the particle velocity and number-density fluctuations around volume fractions at which the non-trivial behaviour of the hydrodynamic diffusion is observed. We explain these non-trivial behaviours as a consequence of particle contacts, which are related to the dominant mechanism of particle pairings. The particle contacts are classified into attractive and repulsive classes by the nature of contacts, and in particular, the strong repulsive contact becomes predominant at $\unicode[STIX]{x1D719}>20\,\%$. Moreover, this transition is visible in the pair distribution functions, which also reveal the change in the suspension microstructure in concentrated regimes. It appears that strong and massive repulsive contacts along the direction perpendicular to an electric field promote the non-trivial suspension behaviours observed in concentrated regimes.

We develop a novel ‘moving-capacitor’ dynamic network model to simulate immiscible fluid–fluid displacement in porous media. Traditional network models approximate the pore geometry as a network of fixed resistors, directly analogous to an electrical circuit. Our model additionally captures the motion of individual fluid–fluid interfaces through the pore geometry by completing this analogy, representing interfaces as a set of moving capacitors. By incorporating pore-scale invasion events, the model reproduces, for the first time, both the displacement pattern and the injection-pressure signal under a wide range of capillary numbers and substrate wettabilities. We show that at high capillary numbers the invading patterns advance symmetrically through viscous fingers. In contrast, at low capillary numbers the flow is governed by the wettability-dependent fluid–fluid interactions with the pore structure. The signature of the transition between the two regimes manifests itself in the fluctuations of the injection-pressure signal.

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

Recent evidence from both oceanic observations and global-scale ocean model simulations indicate the existence of regions where low-mode internal tidal energy dominates over that of the geostrophic balanced flow. Inspired by these findings, we examine the effect of the first vertical mode inertia–gravity waves on the dynamics of balanced flow using an idealized model obtained by truncating the hydrostatic Boussinesq equations on to the barotropic and the first baroclinic mode. On investigating the wave–balance turbulence phenomenology using freely evolving numerical simulations, we find that the waves continuously transfer energy to the balanced flow in regimes where the balanced-to-wave energy ratio is small, thereby generating small-scale features in the balanced fields. We examine the detailed energy transfer pathways in wave-dominated flows and thereby develop a generalized small Rossby number geophysical turbulence phenomenology, with the two-mode (barotropic and one baroclinic mode) quasi-geostrophic turbulence phenomenology being a subset of it. The present work therefore shows that inertia–gravity waves would form an integral part of the geophysical turbulence phenomenology in regions where balanced flow is weaker than gravity waves.

The mean skin-friction drag in a wall-bounded turbulent flow can be decomposed into different physics-informed contributions based on the mean and statistical turbulence quantities across the wall layer. Following Renard & Deck’s study (J. Fluid Mech., vol. 790, 2016, pp. 339–367) on the skin-friction drag decomposition of incompressible wall-bounded turbulence, we extend their method to a compressible form and use it to investigate the effect of density and viscosity variations on skin-friction drag generation, using direct numerical simulation data of compressible turbulent channel flows. We use this novel decomposition to study the skin-friction contributions associated with the molecular viscous dissipation and the turbulent kinetic energy production and we investigate their dependence on Reynolds and Mach number. We show that, upon application of the compressibility transformation of Trettel & Larsson (Phys. Fluids, vol. 28, 2016, 026102), the skin-friction drag contributions can be only partially transformed into the equivalent incompressible ones, as additional terms appear representing deviations from the incompressible counterpart. Nevertheless, these additional contributions are found to be negligible at sufficiently large equivalent Reynolds number and low Mach number. Moreover, we derive an exact relationship between the wall heat flux coefficient and the skin-friction drag coefficient, which allows us to relate the wall heat flux to the skin-friction generation process.

We explore the ability of anisotropic permeable substrates to reduce turbulent skin friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform direct numerical simulations of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performance begins to degrade. We observe that the degradation is associated with the appearance of spanwise-coherent structures, attributed to a Kelvin–Helmholtz-like instability of the mean flow. This feature is common to a variety of obstructed flows, and linear stability analysis can be used to predict it. For large permeabilities, these structures become prevalent in the flow, outweighing the drag-reducing effect of slip and eventually leading to an increase of drag. For the substrate configurations considered, the largest drag reduction observed is ${\approx}$20–25 % at a friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}=180$.

The effects of a water surface wave on the vorticity in the turbulence underneath are studied for Langmuir turbulence using wave-phase-resolved large-eddy simulation. The simulations are performed on a dynamically evolving wave-surface-fitted grid such that the phase-resolved wave motions and their effects on the turbulence are explicitly captured. This study focuses on the vorticity structures and dynamics in Langmuir turbulence driven by a steady and co-aligned progressive wave and surface shear stress. For the first time, the detailed vorticity dynamics of the wave–turbulence interaction in Langmuir turbulence in a wave-phase-resolved frame is revealed. The wave-phase-resolved simulation provides detailed descriptions of many characteristic features of Langmuir turbulence, such as elongated quasi-streamwise vortices. The simulation also reveals the variation of the strength and the inclination angles of the vortices with the wave phase. The variation is found to be caused by the periodic stretching and tilting of the wave orbital straining motions. The cumulative effect of the wave on the wave-phase-averaged vorticity is analysed using the Lagrangian average. It is discovered that, in addition to the tilting effect induced by the Lagrangian mean shear gradient of the wave, the phase correlation between the vorticity fluctuations and the wave orbital straining is also important to the cumulative vorticity evolution. Both the fluctuation correlation effect and the mean tilting effect are found to amplify the streamwise vorticity. On the other hand, for the vertical vorticity, the fluctuation correlation effect cancels the mean tilting effect, and the net change of the vertical vorticity by the wave straining is negligible. As a result, the wave straining enhances only the streamwise vorticity and cumulatively tilts vertical vortices towards the streamwise direction. The above processes are further quantified analytically. The role of the fluctuation correlation effect in the wave-phase-averaged vorticity dynamics provides a deeper understanding of the physical processes underlying the wave–turbulence interaction in Langmuir turbulence.

We consider two-dimensional quasi-geostrophic annular flows around a circular island with a radial offshore bottom slope. Since the conical bottom topography causes a certain beta effect, by analogy with the conventional beta plane we term our model a beta cone. Our focus is on the flows with zero total circulation, which are composed of two concentric rings of uniform potential vorticity (PV) attached to the island. The linear stability of such flows on a beta cone was investigated in a previous publication of ours. In the present paper, we study numerically the nonlinear evolution of weakly viscous flows, whose parameters are fitted so as to guarantee the highest instability of the azimuthal mode $m=1,\ldots ,6$. We study the production of vortices and Rossby waves due to the instability, consider the effect of waves on the emerging vortices and the interaction between the vortices. As in the flat-bottom case, at $m\geqslant 2$, the instability at weak bottom slopes normally leads to the emission of $m$ dipoles. However, a fundamental difference between the flat-bottom and beta-cone cases is observed in the trajectories of the dipoles as the latter recede from the island. When the flow is initially counterclockwise, the conical beta effect may force the dipoles to make a complete turn, come back to the island and rearrange in new couples that again leave the island and return. This quasi-periodic process gradually fades due to filamentation, wave radiation and viscous dissipation. Another possible outcome is symmetrical settling of $m$ dipoles in a circular orbit around the island, in which they move counterclockwise. This behaviour is reminiscent of the adaptation of strongly tilted beta-plane modons (dipoles) to the eastward movement. If the initial flow is clockwise, the emerged dipoles usually disintegrate, but sometimes, the orbital arrangement is possible. At a moderate slope, the evolution of an unstable flow, which is initially clockwise, may end up in the formation of a counterclockwise flow. At steeper slopes, a clockwise flow may transform into a quasi-stationary vortex multipole. When the slope is sufficiently steep, the topographic Rossby waves developing outside of the PV rings can smooth away the instability crests and troughs at the outer edge of the main flow, thus preventing the vortex production but allowing the formation of a new quasi-stationary pattern, a doubly connected coherent PV structure possessing $m$-fold symmetry. Such an $m$-fold pattern can be steady only if it rotates counterclockwise, otherwise it radiates Rossby waves and transforms eventually into a circularly symmetric flow.

High-speed free-shear-flow turbulence, laden with droplets or particles, can radiate weaker pressure fluctuations than its unladen counterpart. In this study, Eulerian–Lagrangian simulations of high-speed temporally evolving shear layers laden with monodisperse, adiabatic, inertial particles are used to examine particle–turbulence interactions and their effect on radiated pressure fluctuations. An evolution equation for gas-phase pressure intensity is formulated for particle-laden flows, and local mechanisms of pressure changes are quantified over a range of Mach numbers and particle mass loadings. Particle–turbulence interactions alter the local pressure intensity directly via volume displacement (due to the flow of finite-size particles) and drag coupling (due to local slip velocity between phases), and indirectly through significant turbulence changes. The sound radiation intensity near subsonic mixing layers increases with mass loading, consistent with existing low Mach number theory. For supersonic flows, sound levels decrease with mass loading, consistent with trends observed in previous experiments. Particle-laden cases exhibit reduced turbulent kinetic energy compared to single-phase flow, providing one source of their sound changes; however, the subsonic flow does not support such an obvious source-to-sound decomposition to explain its sound intensity increase. Despite its decrease in turbulence intensity, the louder particle-laden subsonic flows show an increase in the magnitude and time-rate-of-change of fluid dilatation, providing a mechanism for its increased sound radiation. Contrasting this, the quieter supersonic particle-laden flows exhibit decreased gas-phase dilatation yet its time-rate-of-change is relatively insensitive to mass loading, supporting such a connection.

Direct numerical simulations of viscoelastic turbulent channel flow laden with neutrally buoyant spherical particles are performed. Two FENE-P viscoelastic and one Newtonian fluid are examined, and for each the particle-laden configuration is contrasted to a reference condition without seeding. The size of the particles is larger than the dissipation length scale, and their presence enhances drag in a manner that is intrinsically different in the viscoelastic and Newtonian flows. While the particles effectively suppress the turbulence activity, they significantly enhance the polymer stresses. The polymer chains are markedly stretched in the vicinity of the particles, altering the correlation between the turbulence and polymer work that is commonly observed in single-phase viscoelastic turbulence. At the lower elasticity, the particles enhance the cycle of hibernating and active turbulence and, in turn, their migration and volume-fraction profiles are qualitatively altered by the intermittency of the turbulence. Particle–fluid momentum transfer is investigated by estimating the local fluid field on a trimmed spherical shell around the individual particles. And by comparing the particle microstructures, a lower probability of particle alignment in the streamwise direction is observed in the viscoelastic configuration. This effect is attributed to a qualitative difference in the conditionally averaged velocity fields in the vicinity of the particles in the Newtonian and viscoelastic flows.

The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

We propose a cluster-based control strategy for feedback control of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law (using blowing/suction actuation) is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in aerodynamic flight. The optimized control laws re-route the flow trajectories to the aerodynamically favourable regions in the feature space in a model-free manner. Utilizing a limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present approach is applied to the control of two- and three-dimensional separated flows over a NACA 0012 airfoil in large-eddy simulations at an angle of attack of $9^{\circ }$, Reynolds number $Re=23\,000$ and free-stream Mach number $M_{\infty }=0.3$. The optimized control laws avoid the intermittent occurrence of long-period shedding associated with high-drag clusters, thus lowering the mean drag. The present work aims to address some of the challenges associated with feedback control design for turbulent separated flows at moderate Reynolds number.

We present a method for predicting forces on a plough – modelled as a flat, rigid plate inclined in the direction of motion – as it moves through a granular bed. Our method combines coarse, but representative, discrete element (DE) simulations with continuum mechanics. We first homogenize the kinematic information obtained from DE simulations to obtain a continuum strain field. The strain field is then combined with an appropriate continuum constitutive law for the granular material being ploughed and linear momentum balance to obtain forces acting on the plough. Our method has the advantage that it does not require (i) detailed DE simulations nor (ii) extensive calibration of grain parameters to match experiments which, in turn, requires significant effort and may be system dependent. Both (i) and (ii) are necessary if forces are to be estimated directly from simulations. We confirm the effectiveness of our approach by comparing our predictions with results from calibrated DE simulations and experiments.

A method for studying weakly nonlinear acoustic propagation in two-dimensional ducts of general shape – including curvature and variable width – is presented. The method is based on a local modal decomposition of the pressure and velocity in the duct. A pair of nonlinear ordinary differential equations for the modal amplitudes of the pressure and velocity modes is derived. To overcome the inherent instability of these equations, a nonlinear admittance relation between the pressure and velocity modes is presented, introducing a novel ‘nonlinear admittance’ term. Appropriate equations for the admittance are derived which are to be solved through the duct, with a radiation condition applied at the duct exit. The pressure and velocity are subsequently found by integrating an equation involving the admittance through the duct. The method is compared, both analytically and numerically, against published results and the importance of nonlinearity is demonstrated in ducts of complex geometry. Comparisons between ducts of differing geometry are also performed to illustrate the effect of geometry on nonlinear sound propagation. A new ‘nonlinear reflectance’ term is introduced, providing a more complete description of acoustic reflection that also takes into account the amplitude of the incident wave.

Immiscible displacement in porous media is common in many practical applications. Under quasi-static conditions, the process is significantly affected by disorder of the porous media and the wettability of the pore surface. Previous studies have focused on wettability effects, but the impact of the interplay between disorder and contact angle is not well understood. Here, we combine microfluidic experiments and pore-scale simulations with theoretical analysis to study the impact of disorder on the quasi-static displacement from weak imbibition to strong drainage. We define the probability of overlap to link the menisci advancements to displacement patterns, and derive a theoretical model to describe the lower and upper bounds of the cross-over zone between compact displacement and capillary fingering for porous media with arbitrary flow geometry at a given disorder. The phase diagram predicted by the theoretical model shows that the cross-over zone, in terms of contact angle range, expands as the disorder increases. The diagram further identifies four zones to elucidate that the impact of disorder depends on wettability. In zone I, increasing disorder destabilizes the patterns, and in zone II, a stabilizing effect plays a role, which is less significant than that in zone I. In the other two zones, invasion morphologies are compact and fingering, respectively, independent of both contact angle and disorder. We evaluate the proposed diagram using pore-scale simulations, experiments in this work and in the literature, confirming that the diagram can capture the effect of disorder on displacement under different wetting conditions. Our work extends the classical phase diagrams and is also of practical significance for engineering applications.

We employ lattice Boltzmann simulation to numerically investigate the two-dimensional incompressible flow inside a right-angled isosceles triangular enclosure driven by the tangential motion of its hypotenuse. While the base flow, directly evolved from creeping flow at vanishing Reynolds number, remains stationary and stable for flow regimes beyond $Re\gtrsim 13\,400$, chaotic motion is nevertheless observed from as low as $Re\simeq 10\,600$. Chaotic dynamics is shown to arise from the destabilisation, following a variant of the classic Ruelle–Takens route, of a secondary solution branch that emerges at a relatively low $Re\simeq 4908$ and appears to bear no connection to the base state. We analyse the bifurcation sequence that takes the flow from steady to periodic and then quasi-periodic and show that the invariant torus is finally destroyed in a period-doubling cascade of a phase-locked limit cycle. As a result, a strange attractor arises that induces chaotic dynamics.

Direct particle–fluid simulations of heavy spheres and ellipsoids interacting with decaying isotropic turbulence are conducted. This is the rigorous extension of the spherical particle analysis in Schneiders et al. (J. Fluid Mech., vol. 819, 2017, pp. 188–227) to $O(10^{4})$ non-spherical particles. To the best of the authors’ knowledge, this represents the first particle-resolved study on turbulence modulation by non-spherical particles of near-Kolmogorov-scale size. The modulation of the turbulent flow is precisely captured by explicitly resolving the stresses acting on the fluid–particle interfaces. The decay rates of the fluid and particle kinetic energy are found to increase with the particle aspect ratio. This is due to the particle-induced dissipation rate and the direct transfer of kinetic energy, both of which can be substantially larger than for spherical particles depending on the particle orientation. The extra dissipation rate resulting from the translational and rotational particle motion is quantified to detail the impact of the particles on the fluid kinetic energy budget and the influence of the particle shape. It is demonstrated that the previously derived analytical model for the particle-induced dissipation rate of smaller particles is valid for the present cases albeit these involve significant finite-size effects. This generic expression allows us to assess the impact of individual inertial particles on the local energy balance independent of the particle shape and to quantify the share of the rotational particle motion in the kinetic energy budget. To enable the examination of this mechanistic model in particle-resolved simulations, a method is proposed to reconstruct the so-called undisturbed fluid velocity and fluid rotation rate close to a particle. The accuracy and robustness of the scheme are corroborated via a parameter study. The subsequent discussion emphasizes the necessity to account for the orientation-dependent drag and torque in Lagrangian point-particle models, including corrections for finite particle Reynolds numbers, to reproduce the local and global energy balance of the multiphase system.