Krishnan Mahesh

ABSTRACT We develop a three‐dimensional Eulerian framework to simulate fluid‐structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume‐of‐fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF‐based one‐continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface‐capturing (IC) approach, the piecewise linear interface calculation (PLIC) method is used to reconstruct the interface, and the Lagrangian explicit (LE) method is used in the directionally split advection procedure. To model the hyperelastic behavior of the solid, we consider linear and nonlinear Mooney–Rivlin material models, where we use the left Cauchy–Green deformation tensor () to account for the solid deformation on an Eulerian grid and the fifth‐order weighted essentially non‐oscillatory (WENO‐Z) finite difference reconstruction method is utilized to treat the advection terms involved in the transport equation of . Multiple benchmark problems and reversibility tests are considered to verify the accuracy of the approach. Furthermore, to demonstrate the capability of the solver to handle turbulent interactions, we perform direct numerical simulation (DNS) of turbulent channel flow with a deformable compliant bottom wall and a rigid top wall; our observations align well with previous experimental and numerical works. The detailed numerical experiments show that: (i) despite the discontinuity of the interface across the cell boundaries and stress discontinuity across the interface, a VOF/PLIC‐based FSI framework can provide stable and accurate solutions that significantly minimizes numerical artifacts (e.g., flotsam and spurious currents) while maintaining a sharp interface. (ii) The accuracy of a VOF/PLIC‐based FSI approach on coarse grids is comparable to the accuracy of a diffusive IC method‐based FSI approach on much finer grids.

Cavitation inception in the wake of propulsor systems often arises from the interaction between multiple vortices. We use large-eddy simulation (LES) to study cavitation during the canonical interaction of a pair of unequal strength counter-rotating vortices generated in the wake of a hydrofoil pair at a chord-based Reynolds number ( $ \textit{Re}$ ) of $1.7 \times 10^6$ . The simulations reproduce the experimental observations by Knister et al. (In 33rd Symposium on Naval Hydrodynamics, Osaka, Japan, 2020) of spatially and temporally intermittent inception events occurring in the weaker vortex. Sinusoidal instabilities representing the Crow instability develop on the weaker vortex beyond one chord length downstream of the hydrofoils, causing it to bend and wrap around the stronger vortex. The inviscid stretching causes a significant reduction of the weaker core pressure and inception occurs as it approaches close to the stronger core. These intermittent inception events correspond to $3{-}4$ fold pressure reduction from the unperturbed value, with the instantaneous pressures reaching $40\,\%{-}60\,\%$ lower than the mean minimum pressure. However, the loss of circulation ( ${\gt} 20\,\%$ ) in both cores during the later stages of interaction reduces the possibility of further inception events. Statistical analysis reveals that inception occurs once per Crow cycle and is most likely to occur near the central regions of the Crow wavelength. Conditional averages show that the axial stretching is non-uniform along the weaker vortex axis, with the stretching intensities in the central regions being four times larger than the wavelength-averaged value. Probability distribution analysis shows that only a small portion of the weaker core experiences inception pressures and these regions have relatively lower axial stretching intensities compared with the bulk of the core.

Direct numerical simulation is performed to study the effects of spanwise curvature on transitioning and turbulent boundary layers. Turbulent transition is induced with an array of resolved cuboids. Spanwise curvature is prescribed using a novel approach with a body force that is applied orthogonally to the bulk flow to curve the mean free-stream streamlines at a set radius. The flows are analysed in a streamline-aligned coordinate system. Although the radius of curvature is large compared with the size of the boundary layer, its effects on the development of the boundary layer are appreciable. The results indicate that spanwise curvature induces a non-uniform mean secondary flow and alters the structure of turbulence within the boundary layer. Analytical expressions for the crossflow are derived in the viscous sublayer and log layer. These alterations are visible as changes in the distribution of the turbulent stresses and alignment of the vortical structures with the mean flow. These modifications are responsible for a misalignment between the Reynolds stress tensor and the velocity gradient tensor, which has important consequences for the validity of the widely used Boussinesq turbulent viscosity hypothesis in Reynolds-averaged Navier–Stokes models. Spanwise curvature was observed to decrease turbulent kinetic energy. These results have important implications on the development of turbulence in general applications, such as the flow over a prolate spheroid.

A large-scale parametric study of the flow over the prolate spheroid is presented to understand the effect of Reynolds number and angle of attack on the separation, the wake formation and the loads. Large-eddy simulation is performed for six Reynolds numbers ranging from ${\textit{Re}} = 0.15\times 10^6$ to $4 \times 10^6$ and for eight angles of attack ranging from $\alpha = 10^\circ$ to $\alpha = 90^\circ$ . For all the cases considered, the boundary layer separates symmetrically and forms a recirculation region. Several distinct flow topologies are observed that can be grouped into three categories: proto-vortex, coherent vortex and recirculating wake. In the proto-vortex state, the recirculation does not have a distinct centre of rotation, instead, a two-layer detached flow structure is formed. In the coherent vortex state, the separated shear layer rolls into a three-dimensional vortex that is aligned with the axis of the spheroid. This vortex has a clear centre of rotation corresponding to a minimum of pressure and transforms the transverse momentum from the separated shear layer into axial momentum. In the recirculating wake regime, the recirculation is incoherent and the primary separation forms a dissipative shear layer that is convected in the direction of the free stream. This symmetric pair of shear layers bounds a low-momentum recirculating cavity on the leeward side of the spheroid. The properties of these states are not constant, but evolve along the axis of the spheroid and are dictated by the characteristics of the boundary layer at separation. The variation of the flow with Reynolds number and angle of attack is described, and its connection to the loads on the spheroid are discussed.

Wall-resolved large-eddy simulation (LES) of a non-equilibrium turbulent boundary layer (TBL) is performed. The simulations are based on the experiments of Volino (2020 a J. Fluid Mech. 897 , A2), who reported profile measurements at several streamwise stations in a spatially developing zero pressure gradient TBL evolving through a region of favourable pressure gradient (FPG), a zero pressure gradient recovery and subsequently an adverse pressure gradient (APG) region. The pressure gradient quantified by the acceleration parameter $K$ was held constant in each of these three regions. Here, $K = -(\nu /\rho U_e^{3}) {\textrm d}P_e/{\textrm d}x$ , where $\nu$ is the kinematic viscosity, $\rho$ is density, $U_e$ is the free stream velocity and ${\textrm d}P_e/{\textrm d}x$ is the streamwise pressure gradient at the edge (denoted by the subscript ‘ $e$ ’) of the TBL. The simulation set-up is carefully designed to mimic the experimental conditions while keeping the computational cost tractable. The computational grid appropriately resolves the increasingly thinning and thickening of the TBL in the FPG and APG regions, respectively. The results are thoroughly compared with the available experimental data at several stations in the domain, showing good agreement. The results show that the computational set-up accurately reproduces the experimental conditions and the results demonstrate the accuracy of LES in predicting the complex flow field of the non-equilibrium TBL. The scaling laws and models proposed in the literature are evaluated and the response of the TBL to non-equilibrium conditions is discussed.

A large scale parametric study of the flow over the prolate spheroid is presented to understand the effect of Reynolds number and angle of attack on the separation, the wake formation and the loads. Large-Eddy Simulation is performed for six Reynolds numbers ranging from Re = 0.15M to Re = 4M and for eight angles of attack ranging from 10 degrees to 90 degrees. For all the cases considered, the boundary layer separates symmetrically and forms a recirculation region. Several distinct flow topologies are observed that can be grouped into three categories: proto-vortex, coherent vortex and recirculating wake. In the proto-vortex state, the recirculation does not have a distinct center of rotation, instead, a two-layer detached flow structure is formed. In the coherent vortex state, the separated shear layer rolls into a three-dimensional vortex that is aligned with the axis of the spheroid. This vortex has a clear center of rotation corresponding to a minimum of pressure and transforms the azimuthal momentum from the separated shear layer into axial momentum. In the recirculating wake regime, the recirculation is incoherent and the primary separation forms a dissipative shear layer that is convected in the direction of the free-stream. This symmetric pair of shear layers bounds a low-momentum recirculating cavity on the leeward side of the spheroid. The properties of these states are not constant, but evolve along the axis of the spheroid and are dictated by the characteristics of the boundary layer at separation. The variation of the flow with Reynolds number and angle of attack is described, and its connection to the loads on the spheroid are discussed.

Large-eddy simulation (LES) is performed to study the tip vortex flow in a ducted propulsor geometry replicating the experiments of Chesnakas & Jessup (2003, pp. 257–267), Oweis et al. (2006 a J. Fluids Engng 128 , 751–764) and Oweis et al. (2006 b J. Fluids Engng 128 , 751–764). Inception of cavitation in these marine propulsion systems is closely tied to the unsteady interactions between multiple vortices in the tip region. Here LES is used to shed insight into the structure of the tip vortex flow. Simulation results are able to predict experimental propeller loads and show agreement with laser Doppler velocimetry measurements in the blade wake at design advance ratio, $J=0.98$ . Results show the pressure differential across the blade produces a leakage vortex which separates off the suction side blade tip upstream of the trailing edge. The separation sheet aft of the primary vortex separation point is shown to take the form of a skewed shear layer which produces a complex arrangement of unsteady vortices corotating and counter-rotating with the primary vortex. Blade tip boundary layer vortices are reoriented to align with the leakage flow and produce instantaneous low-pressure regions wrapping helically around the primary vortex core. Such low-pressure regions are seen both upstream and downstream of the propeller blade trailing edge. The trailing edge wake is found to only rarely have a low-pressure vortex core. Statistics of instantaneous low pressures below the minimum mean pressure are found to be concentrated downstream of the blade’s trailing edge wake crossing over the primary vortex core and continue in excess of 40 % chord length behind the trailing edge. The rollup of the leakage flow duct boundary layer behind the trailing edge is also seen to produce counter-rotating vortices which interact with the primary leakage vortex and contribute to strong stretching events.

Marine propellers are studied in design and off-design modes of operation like crashback, where the propeller rotates in reverse while the vehicle is in forward motion. Past experiments (Jessup et al. , Proceedings of the 25th Symposium on Naval Hydrodynamics, St John's, Canada , 2004; Proceedings of the 26th Symposium on Naval Hydrodynamics, Rome, Italy , 2006) studied the marine propeller David Taylor Model Basin 4381 in the open-jet test section of the 36-inch variable pressure water tunnel (VPWT). In crashback, a significant discrepancy with unclear sources exists between the mean propeller loads from the VPWT and open-water towing tank (OW) experiments (Ebert et al. , 2007 ONR Propulsor S & T Program Review, October , 2007). We perform large-eddy simulation at $Re=561\,000$ and advance ratios $J=-0.50$ and $-0.82$ with the VPWT geometry included, contrasting to the unconfined (OW) case at those same $J$ and $Re=480\,000$ . We identify and delineate the water tunnel interference effects responsible, and demonstrate that these effects resemble those of a symmetric solid model or bluff body. Solid blockage due to jet expansion and nozzle blockage due to proximity to the tunnel nozzle are identified as the primary interference effects. Their impact varies with the advance ratio $J$ and strengthens for higher magnitudes of $J$ . The effective length scale to assess the severity of interference effects is found to be larger than the vortex ring diameter.

ABSTRACT In the inviscid limit, the energy of a velocity field satisfying the incompressible Navier–Stokes equations is conserved. Non‐dissipative numerical methods that discretely mimic this energy conservation feature have been demonstrated in the literature to be extremely valuable for robust and accurate large‐eddy simulations of high Reynolds number incompressible turbulent flows. For complex geometries, such numerical methods have been traditionally developed using the finite volume framework and they have been at best second‐order accurate. This paper proposes a non‐dissipative and energy‐conserving numerical method that is arbitrary high‐order accurate for triangle/tetrahedral meshes along with its efficient implementation. The proposed method is a Hybridizable Discontinuous Galerkin (HDG) method. The crucial ingredients of the numerical method that lead to the discretely non‐dissipative and energy‐conserving features are: (i) The tangential velocity on the interior faces, just for the convective term, is set using the non‐dissipative central scheme and the normal velocity is enforced to be continuous, that is, (div)‐conforming. (ii) An exactly (pointwise) divergence‐free basis is used in each element of the mesh for the stability of the convective discretization. (iii) The combination of velocity, pressure, and velocity gradient spaces is carefully chosen to avoid using stabilization which would introduce numerical dissipation. The implementation description details our choice of the orthonormal and degree‐ordered basis for each quantity and the efficient local and global problem solution using them. Numerical experiments demonstrating the various features of the proposed method are presented. The features of this HDG method make it ideal for high‐order LES of incompressible flows in complex geometries.

The speed of sound in bubbly water is an important parameter in the wave equations governing pressure-density relations for turbulent multi-phase flow simulations. Recent molecular simulation results indicate that, for bubbles that are thermodynamically stable at finite volume conditions, the derivative of total pressure P with density ρ has a negative sign, complicating the interpretation of the speed of sound. We show that such a negative compressibility is thermodynamically consistent in a single-component two-phase model at finite volume, and identify an empirically derived equation of state to illustrate that this observation is not an artifact of small simulation length scales. To reconcile this thermodynamic relation with measurements of sound propagation, we decompose the derivative ∂P/∂ρ for bubbly water into its constituent phases to identify absorptive and transmissive contributors, both with an equation of state and using molecular simulations. We find that the speed of sound in the liquid phase remains real-valued while the bubble attenuates sound, giving a negative system compressibility. The inclusion of N2 molecules in molecular simulations illustrates that these observations are robust and hold also for mixtures. From these simulations, we also compute scattering functions for bubbly systems to identify oscillations associated with the speed of sound. Finally, the spherical harmonic modes of bubble oscillations are analyzed in the context of resonance with propagating waves.

Secondary streamlines (left half) and stagnation pressure isolines (right half) colored by stagnation pressure, in a transverse view of the 6:1 prolate spheroid for a Reynolds number based on length of 10,000 and an angle of attack of 70 degrees. A high degree of correlation is observed between the streamlines and the stagnation pressure isolines, which are able to capture the complexity of the vortical flow. Thus, the current study proposes to use the largest closed isolines of stagnation pressure as a boundary for a vortex.

This paper introduces a groundbreaking approach to Load Frequency Control (LFC) in two-area interconnected power systems through the development of a Lyrebird-Optimized Proportional-Integral (PI) controller. The crux of this research lies in the innovative application of a novel optimization algorithm inspired by the lyrebird's exceptional mimicry capabilities, aimed at auto-tuning the PI controller parameters for improved system response to load variations. Traditional PI controllers, while prevalent for their simplicity, often fall short in dynamic environments due to the criticality of parameter tuning. The proposed Lyrebird-Optimized Algorithm (LOA) addresses this limitation by iteratively adjusting the PI parameters to find an optimal balance, significantly enhancing the system's stability and response characteristics. The proposed controller demonstrate superior performance in minimizing frequency deviations, reducing settling times, and maintaining system stability under varying load conditions. This study not only paves the way for more efficient and resilient power system operations but also opens new avenues for applying bio-inspired algorithms in complex engineering optimization problems.

Abstract A directionally‐split volume‐of‐fluid (VOF) methodology for evolving interfaces under curvature‐dependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interface‐advecting velocity. The numerical details of the volume‐of‐fluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS.

A novel method is proposed to identify vortex boundary and center of rotation based on tubular surfaces of constant stagnation pressure and minimum of the stagnation pressure gradient. The method is derived from Crocco's theorem, which ensures that the gradient of stagnation pressure is orthogonal to both the velocity and vorticity vectors. The method is Galilean invariant, requires little processing and is robust. It enables visualization of complex turbulent flows and provides a physically consistent definition of vortex boundaries for quantitative analyses. This vortex boundary is a material surface that is representative of the kinematics of the flow by construction, constitutes a vortex tube, ensures conservation of circulation in the inviscid limit and provides a unique relation to the conservation of momentum equations and vortex loads.

Large-eddy simulation (LES) is used to simulate flow over a three-dimensional elliptical hydrofoil at 12 degrees angle of attack and Reynolds numbers ( 𝑅𝑒 ) of 9×10 5 and 1 . 4×10 6 based on root chord length and freestream velocity. The simulations are performed at the cavitation number ( 𝜎 ) of 2.1 and are based on the experiments of Boulon et al. (1999), who studied the tip vortex cavitation behavior under the confinement of side and bottom walls. The present simulations correspond to their case where the confinement due to the bottom wall is negligible. The computational model of Brandao and Mahesh (2022) that treats vapor as a passive scalar in an incompressible liquid is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The simulations include two different freestream nuclei distributions that are taken from the water tunnel data of Khoo et al. (2020c). It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a location very close to the hydrofoil tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions revealed that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow depleted of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Lagrangian statistics showed that as 𝑅𝑒 is increased, nuclei have higher likelihood of experiencing very low pressure fields. However, the amount of time they are subject to very low pressures is also shorter with increasing 𝑅𝑒 .

Cavitation inception originates from nuclei in a liquid. This paper proposes a Gibbs free energy approach that provides a smooth transition from homogeneous to heterogeneous nucleation when gas is present. The impact of gas content on nucleation is explored. It is found that the gas content stabilises nuclei, a phenomenon not present in pure liquid–vapour systems. This reduces the energy barrier over that required to nucleate a vapour bubble. Different gas saturation levels are studied. Gas content can significantly reduce the energy barrier required for nucleation, and under certain circumstances eliminate it. An analytic solution for the critical radius and activation energy is obtained that accounts for gas content. The classical Blake radius is recovered as a limiting case. The hysteresis between incipience and desinence is explained using the asymmetry observed in the critical radii. The solution is used to obtain the initial bubble radius, given a critical pressure condition in cavitation susceptibility meter experiments. The relationship between initial bubble diameter and critical pressure is described by an analytic solution that accounts for gas content. A model for the derivative of the cumulative nuclei histogram with respect to bubble diameter is proposed. An analytic expression is obtained that shows good agreement with decades worth of experimental data compiled by Khoo et al. ( Exp. Fluids , vol. 61, issue 2, 2020, pp. 1–20) from ocean to water tunnels. The expression recovers the $-4$ power law that is observed experimentally.

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared with isolated roughness elements at the same Reynolds number $Re_h=U_eh/\nu$ ( $U_e$ is the boundary layer edge velocity, h is roughness height and $\nu$ is the kinetic viscosity of the fluid). Small spanwise spacing ( $\lambda _z=2.5h$ ) inhibits the formation of counter-rotating vortex pairs (CVP) and, as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda _z=5h$ , the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical roughness Reynolds number for instability to occur and a more significant breakdown of the boundary layer compared with isolated roughness. When the streamwise spacing is $\lambda _x=5h$ , the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ( $\lambda _x=10h$ ), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interact with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 106 and 4.5 × 109 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L-1. Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models' differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh-Plesset equation when using the models' thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. We also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

We use direct numerical simulation to study the vibroacoustic response of an elastic plate in a turbulent channel at $Re_\tau$ of 180 and 400 for three plate boundary conditions and two materials – synthetic rubber and stainless steel. The fluid–structure–acoustic coupling is assumed to be one-way coupled, i.e. the fluid affects the solid and not vice versa, and the solid affects the acoustic medium and not vice versa. The wall pressure consists of intermittent large-amplitude fluctuations associated with the near-wall, burst-sweep cycle of events. For stainless steel plates, displacement has similar large-amplitude peak events due to comparable time scales of plate vibration and near-wall eddies. For synthetic rubber plates, large-amplitude displacement fluctuations are observed only near clamped or simply supported boundaries. Away from boundaries, plate displacement resembles an amplitude-modulated wave, and no large-amplitude events are observed. We discuss displacement and acoustic pressure spectra over different frequency ranges. For frequencies much smaller than the first natural frequency, the product of plate-averaged displacement spectrum and bending stiffness squared collapses with Reynolds number and plate material in outer units. At high frequencies, displacement and acoustic pressure spectra scale better in inner units, and the scaling depends on the type of damping. For synthetic rubber plates, the spectra display an overlap region that collapses in both outer and inner units. Soft plate deformation displays a range of length scales. However, stiff plate deformation does not exhibit a similar range of scales and resembles plate mode shapes. The soft plate has two distinct deformation structures. Low-speed, large deformation structures with slow formation/break-up time scales are found away from boundaries. High-speed, small deformation structures with fast formation/break-up time scales formed due to boundary reflections exist near the boundaries.

Trip-resolved large-eddy simulations of the DARPA SUBOFF are performed to investigate the development of turbulent boundary layers (TBLs) in model-scale studies. The primary consideration of the study is the extent to which the details of tripping affect statistics in large-eddy simulations of complex geometries, which are presently limited to moderate Reynolds number TBLs. Two trip wire configurations are considered, along with a simple numerical trip (wall-normal blowing), which serves as an exemplar of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip wire also induces a large jump in the boundary layer thickness, which affects the way in which the TBL responds to the pressure gradients and streamwise curvature of the hull. The trip-induced turbulence decays along the edge of the TBL as a wake component that sits on top of the underlying TBL structure, which dictates the evolution of the momentum and displacement thicknesses. In contrast, for a trip wire height shorter than the laminar boundary layer thickness, transition is initiated at the reattachment point of the trip-induced recirculation bubble, and the artificial trip reasonably replicates the resolved trip wire behaviour relatively shortly downstream of the trip location. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses and mean momentum balance, which is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, and finally against the 99 % thickness. By this point, the lasting impact of the trip is the offset in boundary layer thickness due to the trip itself, which becomes a diminishing fraction of the total boundary layer thickness as the TBL grows. The importance of tripping the model appendages is also highlighted due to their lower Reynolds numbers and susceptibility to laminar separations.

We propose a compressible multi-scale model that (i) captures the dynamics of both large vapour cavities (resolved vapour) and micro-bubbles (unresolved vapour), and (ii) accounts for medium compressibility. The vapour mass, momentum and energy in the compressible homogeneous mixture equations are explicitly decomposed into constituent resolved and unresolved components that are independently treated. The homogeneous mixture of liquid and resolved vapour is tracked as a continuum in an Eulerian sense. The unresolved vapour terms are expressed in terms of subgrid bubble velocities and radii that are tracked in a Lagrangian sense using a novel ‘ $kR$ - $RP$ equation’ ( k , constant multiple; R , bubble size; RP , Rayleigh-Plesset). The $kR$ - $RP$ equation is formally derived in terms of the pressure at a finite distance ( $kR$ ) from the bubble while accounting for the effects of neighbouring bubbles; $p(kR)$ may therefore be either a near-field or far-field pressure. The equation exactly recovers the classical Rayleigh–Plesset and Keller–Miksis equations in the limits that $k$ and $c$ (speed of sound) become very large. Also, the results are independent of $k$ for a single bubble for all $k$ , and for multiple bubbles when $kR < d$ (where $d$ denotes separation distance). Numerical results show this robustness of the model to the choice of $k$ , which can be different for each bubble. The multi-scale model is validated for the collapse of a single resolved/unresolved bubble. Its ability to capture inter-bubble interactions is demonstrated for multiple bubbles exposed to an acoustic pulse. The model is then applied to a problem where resolved and unresolved bubbles co-exist. Finally, it is validated using a cluster of $1200$ bubbles exposed to a strong acoustic pulse. The results show the impact of the bubble cluster on the transmitted and reflected waves and the shielding effect where bubbles at the edge of the cluster shield the interior bubbles by dampening the incident acoustic wave.

Large-eddy simulation is used to simulate the flow around a 6 : 1 prolate spheroid at $10^\circ$ and $20^\circ$ angles of attack, and Reynolds number $4.2 \times 10^6$ . Flows with and without trip are compared to understand the relative effect of the trip on the state of the boundary layer and separation. For the tripped case, the geometry of the trip is resolved to better predict its effect on the downstream flow. The simulations employ overset grids that allow adequate resolution of the trips without significant increase in the overall computational cost. Results suggest that while the trip accelerates transition to turbulence at $10^\circ$ , it does not induce a fully developed turbulent boundary layer as intended at $20^\circ$ . Rather, the influence of the trip is localized, and the near-wall flow converges towards a solution similar to that of the non-tripped case upstream of separation. This is due to two distinct phenomena: directly downstream of the trip, favourable pressure gradient and streamline curvature effects suppress the disturbance on the windward side. Further along the spheroid, the boundary layer receives a small fraction of the initial perturbation due to spanwise and wall-normal streamline curvatures inducing a secondary flow that advects the low-momentum trip wake to the leeward side. The locations of transition and separation are insensitive to the presence of the trip. The simulation results are used to construct a regime map that identifies different regions characterized by distinct boundary layer properties and flow features. The present results underscore the difficulty associated with tripping smooth bodies at angle of attack, and the importance of accounting for transition in simulations of such flows, even on tripped geometries.

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation (DNS) and global stability analysis, and compared to isolated roughness elements at the same Reh. Small spanwise spacing ($λ_z = 2.5h$) inhibits the formation of counter-rotating vortices (CVP) and as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $λ_z = 5h$, the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical Reh for instability to occur and a more significant breakdown of the boundary layer compared to isolated roughness. When the streamwise spacing is comparable to the region of flow separation ($λ_x = 5h$), the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ($λ_x = 10h$), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interacting with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

Direct numerical simulations (DNS) of a jet in cross-flow (JICF) with a triangular tab at two positions are performed at jet-to-cross-flow velocity ratios of $R = 2$ and $4$ with a jet Reynolds number of 2000 based on the jet's bulk velocity and exit diameter. The DNS and dynamic mode decomposition show the sensitivity of the tab's effect on the jet upstream shear layer (USL) structure and cross-section to $R$ , echoing the experimental discoveries of Harris et al. ( J. Fluid Mech. , vol. 918, 2021). Furthermore, DNS reveals that the presence of a tab placed on the upstream side of the nozzle significantly modifies the USL through production of streamwise vortices that curl around the spanwise vortex tubes originating from the primary instability of the USL. This provides an explanation for the improvement in mixing that has been associated with an upstream tab. The streamwise vortex structure shows remarkable similarities to the ‘strain-oriented vortex tubes’ observed for disturbed plane shear layers by Lasheras & Choi ( J. Fluid Mech. , vol. 189, 1988, pp. 53–86). For both $R$ cases, the USL instability is delayed, the jet penetration is reduced, and the jet cross-section is flattened, although the tab has a less pronounced effect on the USL structure at higher velocity ratios, where the formation of the streamwise vortices is delayed. In contrast, a tab placed 45 $^\circ$ from the upstream position produces significantly different effects compared with the upstream tab. At $R = 4$ , the jet cross-section is significantly skewed away from the tab and a tertiary vortex is formed, as observed in past studies of round JICFs at relatively high $R$ and low Reynolds numbers. The ability of the tab to produce a controllable steady-state tertiary vortex has implications for a variety of applications. The 45 $^\circ$ tab produces asymmetric effects in the wake of the jet at $R = 2$ , but the effect on the jet cross-section is much smaller, highlighting the sensitivity of jets at high $R$ to asymmetric perturbations.

A variational volume-of-fluid (VVOF) methodology is devised for evolving interfaces under curvature-dependent speed. The interface is reconstructed geometrically using the analytic relations of Scardovelli and Zaleski [1] and the advection of the volume fraction is performed using the algorithm of Weymouth and Yue (WY) [2] with a technique to incorporate a volume conservation constraint. The proposed approach has the advantage of simple implementation and straightforward extension to more complex systems. Canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the VVOF approach and results are compared with existing work in LS.