The attainable metastability is key to the behaviour of liquids undergoing rapid depressurisation. This tells us how far the liquid can be depressurised, or stretched, before phase change occurs. Previous work on the depressurisation of liquids through nozzles and pipes shows that classical nucleation theory (CNT) can predict the attainable metastability close to the critical point, but fails at lower temperatures. In the latter case, it is common to correct the CNT prediction using a strongly temperature-dependent empirical reduction factor. In the present work, we show that the trend at low temperatures naturally follows if the metastability of the liquid is limited by the growth of pre-existing bubbles. With the new volume balancing method, we calculate the attainable metastability for systems with pre-existing bubbles and attain excellent fit with data for both $\textrm {CO}_2$ and water systems. The method has one tuning parameter related to the number of available bubbles in the flow, which is temperature independent.

The magnetohydrodynamic (MHD) mixed convection in a rectangular cross-section of a long vertical duct is considered. The surrounding walls of the duct can be considered for a wide range of scenarios in this analytical solution, such as arbitrary conductivity, thickness and asymmetry. Analytical solutions are also obtained for various of the governing parameters: Grashof number ($\mathop {\textit{Gr}}\nolimits$), Reynolds number ($Re$), and Hartmann number ($\mathop {\textit{Ha}}\nolimits$). Three convection states under varying ${{\mathop {\textit{Gr}}\nolimits }}/{{\mathop {\textit{Re}}\nolimits }}$ – forced convection, mixed convection and buoyancy-dominated convection – are investigated. When $ {{\mathop {\textit{Gr}}\nolimits }}/{{\mathop {\textit{Re}}\nolimits }}$ increases to a critical value $( {{\mathop {\textit{Gr}}\nolimits }}/{{\mathop {\textit{Re}}\nolimits }})_c$, a reverse flow is observed and $({{\mathop {\textit{Gr}}\nolimits }}/{{\mathop {\textit{Re}}\nolimits }})_c$ is identified for both insulated and electrically conducting ducts. In MHD mixed convection, where $ ({{\mathop {\textit{Gr}}\nolimits }}/{{\mathop {\textit{Re}}\nolimits }}) \sim 1$, the fully developed flow exhibits a steady velocity gradient in the core, scaling as $\sim ({{\mathop {\textit{Gr}}\nolimits }})/({2{\mathop {\textit{Ha}}\nolimits }{\mathop {\textit{Re}}\nolimits }})$ (Tagawa et al. 2002 Eur. J. Mech. B/Fluids 21, 383–398) in the insulated scenario, and this work extends it to the electrically conducting scenario, scaling as $\sim ({{\mathop {\textit{Gr}}\nolimits }})/({2{\mathop {\textit{Re}}\nolimits }{\mathop {\textit{Ha}}\nolimits }(1 + c{\mathop {\textit{Ha}}\nolimits })})$, where $c$ denotes the wall conductance ratio, accompanied by asymmetrical velocity jets. Effects of conductive walls on both pressure drop and flow distribution are thoroughly analysed. The pressure gradient distribution as a function of $\mathop {\textit{Ha}}\nolimits$ is given, in which the combined effect of arbitrary sidewalls and Hartmann walls on the distributions is well illustrated. The wall asymmetry has profound effects on the velocity distribution, especially for the high-velocity jet areas where Hartmann walls exert an opposite effect to that of sidewalls. The velocity magnitude is significantly larger around lower conducting sidewalls and raises questions about new potential instability schemes for high $\mathop {\textit{Re}}\nolimits$, as discussed in previous studies (Krasnov et al. 2016 Numerical simulations of MHD flow transition…; Kinet et al. 2009 Phys. Rev. Lett. 103, 154501).

Accurate prediction of the hydrodynamic forces on particles is central to the fidelity of Euler–Lagrange (EL) simulations of particle-laden flows. Traditional EL methods typically rely on determining the hydrodynamic forces at the positions of the individual particles from the interpolated fluid velocity field, and feed these hydrodynamic forces back to the location of the particles. This approach can introduce significant errors in two-way coupled simulations, especially when the particle diameter is not much smaller than the computational grid spacing. In this study, we propose a novel force correlation framework that circumvents the need for undisturbed velocity estimation by leveraging volume-filtered quantities available directly from EL simulations. Through a rigorous analytical derivation in the Stokes regime and extensive particle-resolved direct numerical simulations (PR-DNS) at finite Reynolds numbers, we formulate force correlations that depend solely on the volume-filtered fluid velocity and local volume fraction, parametrised by the filter width. These correlations are shown to recover known drag laws in the appropriate asymptotic limits and exhibit a good agreement with analytical and high-fidelity numerical benchmarks for single-particle cases, and, compared with existing correlations, an improved agreement for the drag force on particles in particle assemblies. The proposed framework significantly enhances the accuracy of hydrodynamic force predictions for both isolated particles and dense suspensions, without incurring the prohibitive computational costs associated with reconstructing undisturbed flow fields. This advancement lays the foundation for robust, scalable and high-fidelity EL simulations of complex particulate flows across a wide range of industrial and environmental applications.

This paper investigates the flow and density field around a spinning solid spheroid with a given aspect ratio, immersed in a rotating stratified fluid. First, we derive the general system of equations governing such flows around any solid of revolution in the limit of infinite Schmidt number. We then present an exact analytical solution for a spinning spheroid of arbitrary aspect ratio. For the specific case of a sphere, we provide the diffusive spin-up solution obtained via an inverse Laplace integral. To validate the theoretical results, we experimentally reproduce these flows by spinning spheroids in a rotating tank filled with stratified salt water. By varying the stratification intensity, the angular velocities of the spheroid and the rotating table, and the spheroid’s shape, we explore a broad parameter space defined by Froude, Reynolds and Rossby numbers and aspect ratio. Using particle image velocimetry to measure the velocity field, we demonstrate excellent agreement between theory and experiments across all tested regimes.

The problem of a uniform current interacting with bodies submerged beneath a homogeneous ice sheet is considered, based on linearised velocity potential theory for fluid and elastic thin plate theory for ice sheet. This problem is commonly solved by the boundary element method (BEM) with the Green function, which is highly effective except when the Green function becomes singular, and the direct solution of the BEM is no longer possible. However, flow behaviour, body force and ice sheet deflection near the critical Froude numbers are of major practical interest, such as in ice breaking. The present work successfully resolves this challenge. A modified boundary integral equation (BIE) is derived, which converts the singular Green function term to a far-field one and removes the singularity. The BIE is then imposed at infinity for additional unknowns in the far field. It is proved that the solution is finite and continuous at the critical Froude number $F = F_c$, where the body starts generating travelling waves, and finite but discontinuous at depth-based Froude number $F = 1^\pm$. Case studies are conducted for single and double circular cylinders and an elliptical cylinder with various angles of attack. A comprehensive analysis is made on the hydrodynamic forces and the generated flexural gravity wave profiles, and their physical implications are discussed. It is also concluded that the method developed in this paper is not confined to the present case but is also applicable to a variety of related problems when the BEM fails at the critical points.

The extensional rheology of dilute suspensions of spheres in viscoelastic/polymeric liquids is studied computationally. At low polymer concentration $c$ and Deborah number $\textit{De}$ (imposed extension rate times polymer relaxation time), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by $\Delta \textit{De}_{\textit{local}}\gt 0$. This increases the suspension’s extensional viscosity with time and $\textit{De}$ for $De \lt 0.5$. When $\textit{De}$ exceeds 0.5, the coil-stretch transition value, the fully stretched polymers from the far-field collapse in regions with $\Delta \textit{De}_{\textit{local}} \lt 0$ (lower velocity gradient) around the particle’s stagnation points, reducing suspension viscosity relative to the particle-free liquid. The interaction between local flow and polymers intensifies with increasing $c$. Highly stretched polymers impede local flow, reducing $\Delta \textit{De}_{\textit{local}}$, while $\Delta \textit{De}_{\textit{local}}$ increases in regions with collapsed polymers. Initially, increasing $c$ aligns $\Delta \textit{De}_{\textit{local}}$ and local polymer stretch with far-field values, diminishing particle–polymer interaction effects. However, beyond a certain $c$, a new mechanism emerges. At low $c$, fluid three particle radii upstream exhibits $\Delta \textit{De}_{\textit{local}} \gt 0$, stretching polymers beyond their undisturbed state. As $c$ increases, however, $\Delta \textit{De}_{\textit{local}}$ in this region becomes negative, collapsing polymers and resulting in increasingly negative stress from particle–polymer interactions at large $\textit{De}$ and time. At high $c$, this negative interaction stress scales as $c^2$, surpassing the linear increase of particle-free polymer stress, making dilute sphere concentrations more effective at reducing the viscosity of viscoelastic liquids at larger $\textit{De}$ and $c$.

We experimentally and theoretically examine the maximum spreading of viscous droplets impacting ultra-smooth solid surfaces, where viscosity plays a dominant role in governing droplet spreading. For low-viscosity droplets, viscous dissipation occurs mainly in a thin boundary layer near the liquid–solid interface, whereas for high-viscosity droplets, dissipation is expected to extend throughout the droplet bulk. Incorporating these dissipation mechanisms with energy conservation principles, two distinct theoretical scaling laws for the maximum spreading factor ($\beta _m$) are derived: $\beta _m \sim ({\textit{We}}/ {\textit{Oh}})^{1/6}$ for low-viscosity regimes (${\textit{Oh}} \lesssim 0.1$) and $\beta _m \sim \textit{Re}^{1/5}$ for high-viscosity regimes (${\textit{Oh}} \gt 1$), where $\textit{We}$, $\textit{Re}$ and $\textit{Oh}$ are the Weber, Reynolds and Ohnesorge numbers, respectively. Both scaling laws show good agreement with the experimental data for their respective validity ranges of $\textit{Oh}$. Furthermore, to better model experimental data at vanishing $\textit{Re}$, we introduce a semi-empirical scaling law, $\beta _m \sim (A + {\textit{We}}/ {\textit{Oh}})^{1/6}$, where $A$ is a fitting parameter accounting for finite spreading ($\beta _m \approx 1$) at negligible impact velocities. This semi-empirical law provides an effective description of $\beta _m$ for a broad experimental range of $10^{-3} \leqslant {\textit{Oh}} \leqslant 10^0$ and $10^1 \leqslant {\textit{We}} \leqslant 10^3$.

This study investigates the effects of dissipation and the associated self-heating in cone jets of ionic liquids with high electrical conductivities. A numerical model based on the leaky-dielectric formulation that incorporates conservation of energy and temperature-dependent properties (restricted to the viscosity and the electrical conductivity) is developed and compared with isothermal numerical solutions and experimental data for four ionic liquids. The numerical solutions show that self-heating leads to significant temperature increases (up to 446 K) along the cone jet, dramatically enhancing the electrical conductivity and reducing the viscosity. The model reproduces the experimental values of the current for the ionic liquids studied. While isothermal solutions follow established scaling laws, the solutions including self-heating exhibit liquid-specific behaviours due to the unique temperature dependencies of the conductivity and viscosity. Self-heating creates a strong positive feedback between the electric current and the electrical conductivity, resulting in much higher electrospray currents compared with the isothermal solution. Ohmic dissipation dominates over viscous dissipation. Strong self-heating and the opposite effects of temperature on the electrical conductivity and the viscosity, increase the disparity between the two dissipation modes. This work demonstrates the importance of accounting for self-heating in the modelling and analysis of experimental data of cone jets of ionic liquids and other highly conductive liquids. First-principles modelling and case-specific experimental characterisation are necessary to describe these systems, as the traditional scaling laws break down when self-heating is significant.

A mechanical heart valve is a durable device used to replace damaged ones inside a living heart, aiming for regulated blood flow to avoid the risks of cardiac failure or stroke. The modern bileaflet designs, featuring two semicircular leaflets, aim to improve blood flow control and minimise turbulence as compared to the older models. However, these valves require lifelong anticoagulation therapy to prevent blood clots, increasing bleeding risks and necessitating regular monitoring. Turbulence within the valve can lead to complications such as haemolysis (damage to red blood cells), thrombosis, platelet activation and valve dysfunction. It also contributes to energy loss, increased cardiac workload, and endothelial damage, potentially impairing the valve efficiency and increasing the risk of infective endocarditis. To address these challenges, a design-modified St Jude Medical (SJM) valve with streamlined edges was conceptualised and assessed using direct numerical simulations. Results show that the streamlined design minimises abrupt blood flow alterations and reduces turbulence-inducing vortices. Compared to existing SJM valves, the new design ensures smoother flow transitions, reduces flow disturbances, and reduces pressure drop. It significantly decreases shear stress, drag and downstream turbulence, enhancing haemodynamic efficiency. These improvements lower the risk of complications such as haemolysis and thrombosis, offering a safer and more efficient option for valve replacement, establishing the potential of edge streamlining in advancing mechanical heart valve technology, and favouring patient outcomes.

This study connected flow structure and morphological changes in and around a rectangular vegetation patch. The emergent patch was constructed in an 8 cm sand bed. Two patch densities were tested, using a regular configuration of rigid dowels. Near the leading edge of the patch, enhanced turbulence levels produced sediment erosion. Some of the eroded sediment was carried into the patch, forming an interior deposition dune. The denser patch resulted in a smaller dune due to stronger lateral flow diversion and weaker interior streamwise velocity. After the leading-edge dune, in the fully developed region of the patch, vortices formed in the shear layers along the patch lateral edges. Elevated turbulence at the patch edge produced local erosion. For the dense patch, material eroded from the edge was transported into the patch to form a flow-parallel ridge, and there was no net sediment loss/gain by the patch. For the sparse patch, material eroded from the edge was transported away from the patch, resulting in a net loss of sediment from the patch. In the wake of both patches, deposition occurred near the wake edges and not at the wake centreline, which was attributed to the weak lateral transport associated with the weakness of the von Kármán vortex street. Specifically, the lateral transport length scale was less than half the width of the patch. The increasing bedform height within the wake progressively weakened and narrowed the von Kármán vortex street, illustrating an important feedback from morphological evolution to the flow structure. Despite significant local sediment redistribution, the patch did not induce channel-scale sediment transport.

This study investigates the onset of linear instabilities and their later nonlinear interactions in the shear layer of an initially laminar jet using high-fidelity simulations. We present a quantitative analysis of the vortex-pairing phenomenon by computing the spatial growth rates and energy budget of the dominant frequencies. Compared with a turbulent jet, the hydrodynamic instabilities and vortex pairing are enhanced in an initially laminar jet. Using local linear theory, we identify the fundamental as the frequency with the largest spatial growth rate, and its exponential growth causes the shear layer to roll up into vortices. Visualisations and conditional $x$–$t$ plots reveal that fundamental vortices pair to form subharmonic vortices, which then merge to produce second subharmonic vortices. The energy transfer during this process is evaluated using the spectral turbulent kinetic energy equation, focusing on dominant coherent structures identified through spectral proper orthogonal decomposition. Spectral production and nonlinear transfer terms show that the fundamental frequency gains energy solely from the mean flow, while subharmonics gain energy both linearly from the mean flow and nonlinearly through backscatter from the fundamental frequency. Our results confirm Monkewitz’s theoretical model of a resonance mechanism between the fundamental and subharmonic, which supplies energy to the subharmonic. We highlight the energetic versus dynamical importance of tonal frequencies. The second subharmonic corresponds to the largest spectral peak, while the fundamental, though the fourth largest spectral peak, is dynamically dominant, as it determines all other spectral peaks and supplies energy to the subharmonics through a reverse energy cascade.

This work investigates the receptivity mechanisms of a NACA0008 airfoil to a $\textit{Tu}=2.5\,\%$ level of free-stream turbulence (FST) through a direct numerical simulation (DNS) and an associated linearised simulation on the same mesh. By comparing velocity perturbation fields between the two simulations, the study reveals that the streaky structures that degenerate into turbulent spots are predominantly influenced by nonlinear convective terms, rather than the linear amplification of inflow perturbations around the laminar base flow. A power spectral analysis shows differences in the energy distribution between the DNS and linearised simulation, with the DNS containing more energy at higher wavenumbers, for structures located near the airfoil’s leading edge. Representative wavenumbers are identified through modal analysis, revealing a dynamics dominated by streak-like structures. The study employs the Nek5000 numerical solver to distinguish between linear and nonlinear receptivity mechanisms over the NACA0008 airfoil, highlighting their respective contributions to the amplification of perturbations inside the boundary layer. In the high FST case studied, it is observed that the energy of the incoming turbulence is continuously transferred into the boundary layer along the length of the wing. The nonlinear interactions generate streaks with higher spanwise wavenumbers compared with those observed in purely linearised simulations. These thinner streaks align with the spanwise scales identified as susceptible to secondary instabilities. Finally, the procedures presented here generalise the workflow of previous works, allowing for the assessment of receptivity for simulations with arbitrary mesh geometries.

At all scales, porous materials stir interstitial fluids as they are advected, leading to complex (and chaotic) distributions of matter and energy. Of particular interest is whether porous media naturally induce chaotic advection in Darcy flows at the macroscale, as these stirring kinematics profoundly impact basic processes such as solute transport and mixing, colloid transport and deposition and chemical, geochemical and biological reactivity. While the prevalence of pore-scale chaotic advection has been established, and many studies report complex transport phenomena characteristic of chaotic advection in heterogeneous Darcy flow, it has also been shown that chaotic dynamics are prohibited in a large class of Darcy flows. In this study we rigorously establish that chaotic advection is inherent to steady three-dimensional (3-D) Darcy flow with anisotropic and heterogeneous hydraulic conductivity fields. These conductivity fields generate non-trivial braiding of streamlines, leading to both chaotic advection and (purely advective) transverse macro-dispersion. We establish that steady 3-D Darcy flow has the same topology as unsteady 2-D flow and use braid theory to establish a quantitative link between transverse dispersivity and Lyapunov exponent in heterogeneous Darcy flow. Our main results show that chaotic advection and transverse dispersion occur in both anisotropic weakly heterogeneous and in heterogeneous weakly anisotropic conductivity fields, and that the quantitative link between these phenomena persists across a broad range of conductivity fields. As the ubiquity of macroscopic chaotic advection has profound implications for the myriad processes hosted in porous media, these results call for re-evaluation of transport and reaction methods in these systems.

We study convection in a volumetrically heated fluid which is cooled from both plates and is under rotation through the use of direct numerical simulations. The onset of convection matches similar systems and predictions from asymptotic analysis. At low rotation rates, the fluid becomes more organised, enhancing heat transport and increasing boundary layer asymmetry, whereas high rotation rates suppress convection. Velocity and temperature statistics reveal that the top unstably stratified boundary layer exhibits behaviour consistent with other rotating convective systems, while the bottom boundary shows a unique interaction between unstable stratification and Ekman boundary layers. Additional flow statistics such as energy dissipation are analysed to rationalise the flow behaviour.

We study the stationary, intermittent and nonlinear dynamics of nominally ideally expanded, natural and forced supersonic twin-rectangular turbulent jets using spectral modal decomposition. We decompose large-eddy simulation data into four reflectional symmetry components about the major and minor axes. In the natural jet, spectral proper orthogonal decomposition (SPOD) uncovers two resonant instabilities antisymmetric about the major axis. Known as screech tones, the more energetic of the two is a steady flapping instability, while the other is an intermittent double-flapping instability. We test the hypothesis that symmetry breaking can be leveraged for control design. Time-periodic forcing symmetric about the major and minor axes is implemented using a plasma actuation model, and succeeds in removing screech from a different symmetry component. We investigate the spectral peaks of the forced jet using an extension of bispectral mode decomposition (BMD), where the bispectrum is bounded by unity and which conditionally recovers the SPOD. We explain the appearance of harmonic peaks as three sets of triadic interactions between reflectional symmetries, forming an interconnected triad network. BMD modes of active triads distil coherent structures comprising multiple coupled instabilities, including Kelvin–Helmholtz, core and guided-jet modes (G-JM). Downstream-propagating core modes can be symmetric or antisymmetric about the major axis, whereas upstream-propagating G-JM responsible for screech closure (Edgington-Mitchell et al. J. Fluid Mech.945, 2022, p. A8) are antisymmetric only. The dependence of G-JM on symmetry hence translates from the azimuthal symmetry of the round jet to the dihedral group symmetry of the twin-rectangular jet, and explains why the twin jet exhibits antisymmetric but not symmetric screech modes.

Elasto-inertial turbulence (EIT) has been demonstrated to be able to sustain in two-dimensional (2-D) channel flow; however the systematic investigations on 2-D EIT remain scarce. To address this gap, this study conducts direct numerical simulations of 2-D EIT at a modest Reynolds number ($Re=2000$) to examine its statistical characteristics and dynamic mechanisms. Meanwhile, this paper explores the similarities and differences between 2-D EIT with the maximum drag reduction (MDR) state in three-dimensional (3-D) flow. We demonstrate that statistical characteristics of 2-D EIT follow distinct trends compared to those in viscoelastic drag-reducing turbulence as nonlinear elasticity increases. These differences can be attributed to two different underlying dynamical processes: the gradual suppression of inertial turbulence in 3-D flow, and the progressive enhancement of EIT in 2-D flow. Also, we present the role of pressure, energy budget and spectral characteristics of 2-D EIT, which show significant similarities to those in the MDR state, thus providing compelling evidence for the 2-D nature of EIT. More strikingly, we identify an anomalous Reynolds stress in 2-D EIT that contributes negatively to flow resistance, which differs from the extremely small but positive Reynolds stress observed in the MDR state. Although with small values of Reynolds stress, the correlation analysis indicates clearly moderate positive correlation between the streamwise and normalwise velocity fluctuations rather than their being uncorrelated. Moreover, quadrant analysis of velocity fluctuations reveals the predominance of motions in the first and third quadrants, which are closely associated with the typical polymer extension sheet-like structures.