In turbulence modeling, model form errors are introduced in the prediction of the Reynolds stresses through the Boussinesq hypothesis and other modeling choices, such as the specific form of the eddy viscosity. These linear eddy viscosity models have known points of failure in flows that feature significant complexity, such as separated flows. In this work, an implied models approach is used to better understand the sources and dynamics of model form error in separated flows through a priori analysis, focusing on the Boussinesq hypothesis using exact inputs for determining the eddy viscosity. In the implied models approach, a transport equation is derived for the model error through the transport equation implied by the model for the quantity of interest; that is, the Reynolds stresses in this work. A boundary layer over a flat plate with a statistically stationary separation bubble is analyzed and shown to have two error modes corresponding to the qualitative behavior of turbulent wall-bounded and turbulent free-shear model form errors. The wall-bounded mode is observed sufficiently upstream of the separation bubble, and the free-shear mode is observed near and within the separation bubble, with a superposition of these two modes observed in the intermediate regions. These results indicate on the one hand a complex picture of model error that changes through the flow but on the other hand a simple picture of model error that comprises elements of canonical flows. Therefore, calibration of turbulence models against simpler canonical flows can capture the main modes of model failure in more complex flows.

A three-dimensional direct numerical simulation database of turbulent boundary layer flashback of a hydrogen-rich premixed flame with an equivalence ratio of 1.5 has been analyzed to investigate flame self-interaction (FSI) events. The nonreacting turbulence characteristics of the channel flow are representative of the friction-velocity-based Reynolds number, ${\text{Re}}_{\tau }=120$. A skeletal chemical mechanism with nine species and twenty reactions is employed for the representation of hydrogen-air combustion. Three definitions of the reaction progress variable, $c$, based on the mass fractions of ${\mathrm{H}}_2, {\mathrm{O}}_2$, and ${\mathrm{H}}_2\mathrm{O}$, have been considered to define the progress variable. It is found that the FSI events predominantly occur close to the burned gas side for all definitions of $c$ at all the wall normal distances. No FSI events adjacent to the wall have been identified for the $c$ definition based on ${\mathrm{O}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ mass fractions, whereas FSI events occur for $c$ based on ${\mathrm{H}}_2$ in the near-wall region. In the regions further away from the wall, all $c$ definitions show that tunnel formation and tunnel closure type FSI events remain predominant, which is consistent with the earlier findings by Griffiths et al. [Proc. Combust. Inst. 35, 1341 (2015)] involving hydrogen-air premixed flame under shear flow conditions. In this work for $c$ based on ${\mathrm{H}}_2$ mass fraction, unburned gas pockets have also been identified at all wall normal distances and are a consequence of the hydrogen-rich nature of the flame. The reason for the variations in topologies with the change in the definition of $c$ based on different species and wall normal distance is a consequence of several factors, including the changes in the level of turbulence within the turbulent boundary layer, heat loss to the isothermal wall in the near-wall region, and the differential diffusion induced by the nonunity Lewis number. The results from the current analysis show that the turbulent boundary layer and heat loss at the wall play important roles in determining the FSI topologies. The differences in the qualitative nature and distributions of the FSI events between different definitions of $c$ have important implications on the possible extension of flame-surface-based modeling methodology for hydrogen-rich flames within turbulent boundary layers.

The accidental implosions of pressure vessels in the deep ocean may cause severe damage to the surrounding structures, and the induced liquid jet and shock wave can even lead to a chain reaction of nearby pressure vessels. Since the whole physical process can be approximately reproduced by the inertial collapse of air bubbles, in this study, the collapse of two adjacent bubbles near a solid wall is considered as an analog to assess the implosions of pressure vessels. An adaptive mesh refinement solver is developed for the high-fidelity simulation of the compressible multiphase flows. First, the implosion of a single bubble and the explosion of two bubbles are simulated for numerical validation. Then the collapsing process of two equal-sized bubbles with a different arrangement is simulated. By the advantage of the present numerical technique, the sharp shock fronts emitted from the collapse are captured with high resolution, and the high wall pressure induced by the shock wave is investigated in detail. Numerical results reveal that the wall-bubble distance and the bubble-bubble distance are crucial for the shock-impacting wall pressure and the jet flow direction. It is found that the maximum wall pressure occurs when the two bubbles are horizontally arranged in relation to the solid wall, while the perpendicular arrangement leads to the lowest wall pressure. The present findings of the two-bubble collapse are significant in determining the arrangement of pressure vessels inside submersible structures.

An experimental investigation has been carried out to study the effect of the low-frequency oscillation of a separated shear layer. A separated shear layer was generated on a flat plate placed horizontally in a low-speed wind tunnel using a contoured wall at the top of the tunnel test section. Two different contoured walls were used to impose a low and high level of adverse pressure gradient in the flow. The time-resolved particle image velocimetry measurements were carried out to study the unsteady characteristics of the separated shear layer. The measured data reveals that the vortex shedding associated with the separating shear layer is regular for the low adverse pressure gradient case, whereas it is found to be irregular or intermittent for the high adverse pressure gradient. We find that the intermittent nature of the vortex shedding for the high adverse pressure gradient case is due to a low-frequency oscillation of the shear layer and the associated movement of the points of inflection in the velocity profiles. The short time-averaged velocity profiles in the intermittent vortex-shedding process are also found to follow the embedded shear layer scaling proposed by Schatzman and Thomas [J. Fluid Mech. 815, 592 (2017)]. We study the effect of this low-frequency oscillation on the stability characteristics of the separated shear layer and the vortex-shedding process. Based on the analyses, a nondimensional parameter (${\delta }_{\mathrm{rms}}^{*}/{\delta }^{*}$) is proposed to quantify the interaction level of the low-frequency oscillation on the vortex shedding. We find that the interaction of the low-frequency oscillation on the vortex shedding vanishes as ${\delta }_{\mathrm{rms}}^{*}/\delta \to 0$. Further, it shows that when the numerical value of this parameter approaches 0.23, the interaction is found to be intensified, leading to the separated shear layer either from a non-vortex-shedding state to vortex-shedding state or a vortex-shedding state to a non-vortex-shedding state.

We phrase boundary-value problems for a dense, steady, fully developed, gravitational flow of identical inelastic spheres and water over an inclined erodible bed in the presence of sidewalls. The mass density and the size of the spheres are that of the particles employed in laboratory experiments by Armanini et al., [J. Fluid Mech. 532, 269 (2005)]. We obtain numerical solutions for the profiles of the solid volume fraction, the strength of the particle velocity fluctuations, and the mean velocities of the particles and fluid. We compare these with those measured in the experiments.

Particle entrainment into a turbulent boundary layer flow is a phenomenon of great importance to many environmental and industrial processes. This paper introduces a generalized dynamic resuspension model for applicability to particles rolling on a surface with fractal-like multiscale roughness elements, which is termed the multiscale asperity model (MSAM). Furthermore, non-Gaussian (log-normal or $\mathrm{\Gamma }$) stochastic models for the flow velocity seen by a particle are introduced and compared with a Gaussian (Ornstein-Uhlenbeck-like) stochastic model. The stochastic flow models are coupled with the MSAM and three complementary studies are performed to test their ability to predict the fraction of particles remaining on the wall after a given exposure time to turbulent flow. First, the predictions using the stochastic flow model and MSAM are compared with the experimental measurements of Reeks and Hall [J. Aerosol Sci. 32, 1 (2001)]. The model predictions using the MSAM show some improvement in matching the experimental data compared with existing models, but challenges remain. Second, in order to evaluate the stochastic flow velocity models, a comparison is performed against a time-resolved direct numerical simulation (DNS) database of a turbulent channel flow coupled with the MSAM. The results show that non-Gaussianity in stochastic flow models improves the agreement with DNS-based resuspension predictions of the fraction of particles remaining on the wall after one flow through time, presumably due to more realistic probabilities of extreme flow events. Third, the prediction of particle resuspension is attempted using coarse-grained simulations (i.e., filtered DNS and large-eddy simulation for resolved flow velocity) in combination with a stochastic model for the subgrid-scale flow velocity. Comparing with (unfiltered) DNS, the simulation results confirm the importance of the inclusion of a particle subgrid-scale model to represent the effect of unresolved fluctuations on resuspension dynamics. Taken together, these three tests highlight both modeling improvements and enduring challenges related to the (multifidelity) prediction of particle resuspension.

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analyzing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong and caustics are induced by large strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique optimal fluctuation that propagates along the Vieillefosse line $27R^2/4+Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.

Wall-bounded turbulence at high-pressure transcritical conditions with intense density fluctuations are encountered in many technical applications. In this study, we analyze the turbulent energy transport in transcritical channel flows specifically focusing on dissipation rate, turbulent kinetic energy budgets, heat fluxes, and momentum-fluctuation statistics; results from this analysis are used to guide the development of turbulent scaling laws. We find that the dissipation rate of turbulent kinetic energy is dominated by the enstrophy in the logarithmic layer, and the fluctuating viscosity results in the reduced tilting of the vortical structures and the attenuation of streamwise vorticity in the near-wall layer; the fluctuating viscosity attenuates the dissipation rate by reducing the shear strain and the enstrophy production. Local equilibrium of the turbulent kinetic energy exists in the logarithmic layer. We show that the real-fluid thermodynamic effects significantly change the turbulent heat flux correlated with the sweep and the ejection events; the density changes alter the turbulent transport and result in noticeable magnitudes of density-fluctuation-related momentum-fluctuation statistics. From these results, scaling laws for the turbulent length scales and turbulent kinetic energy budgets are proposed, thereby contributing to improvement of the wall models in large-eddy simulations and Reynolds-averaged Navier-Stokes (RANS) simulations.

An effect of an angle of attack on the aerodynamic characteristics of a freestream-aligned circular cylinder is investigated and discussed. The experiment without support interference was conducted using a magnetic suspension and balance system (MSBS) which can levitate and support a model. A cylindrical model with a fineness ratio of 1.0 was employed in wind tunnel tests. The Reynolds numbers based on the diameter of the model were $3.3\times {10}^4$ and $6.7\times {10}^4$. The range of the angle of attack is from 0 to ${15}^{\circ }$. Aerodynamic forces and velocity fields were obtained by the MSBS and particle image velocimetry. The results of the time-averaged aerodynamic force and moment coefficients and the time-averaged velocity field illustrate that the flow reattachment occurs at an angle of $9^{\circ }$ or more. The flow reattachment changes the aerodynamic characteristics, especially the lift and pitching moment coefficients and the lift force fluctuations.

Here, we report experimental results on the rupture of flat colloidal films over a large range of volume fractions, 0.00 $\le \varphi \le$ 0.47. The films are formed using a constant fluid volume, ruptured with a needle within a few seconds of formation, and recorded using a high-speed camera. We show that colloidal films rupture in a manner similar to Newtonian fluids, even for high colloidal volume fractions. However, higher-viscosity films made of the same fluid volume show a higher thickness away from the boundary at the time of rupture, possibly due to viscous stresses slowing down the thinning of the film. When allowed to spontaneously rupture instead of manually rupturing right after film formation, the same dense colloidal films show exotic instabilities reminiscent of a wrinkling fabric on the film surface. We hypothesize that these instabilities occur because the film is allowed to thin before rupture, and its thickness may compete with the colloidal particle size. Thus, the film lifetime before rupture has a major role to play in the film rupture dynamics, and the effect of microstructure has dramatic consequences in films that are allowed to spontaneously rupture.

We present an experimental study of a new kind of dual drop-wave entity existing on a localized structure in a water Faraday-wave system. A nonpropagating hydrodynamic soliton can juggle a single drop of $\sim$2–3.5 mm diameter for about ${10}^2$–${10}^4$ rebounds. By analyzing the drop trajectories, several regimes are observed: periodic bouncing, period doubling, period tripling, a sawtooth state, and chaotic/erratic trajectories. We present evidence that the most stable cases result from detuning of the drop self-oscillations and synchronization with the soliton's sloshing motion. This synchronization ensures stability and thus longer lifetimes. We analyzed the lifetime of the drop, concluding that the periodic behavior, which appears for the lowest-amplitude solitons, is the most stable state. Further analysis shows that lifetimes follow a Weibull distribution.

Hypersonic flows are of great interest in a wide range of aerospace applications and are a critical component of many technological advances. Accurate simulations of these flows in thermodynamic (non)equilibrium (accounting for high temperature effects) rely on detailed thermochemical gas models. While accurately capturing the underlying aerothermochemistry, these models dramatically increase the cost of such calculations. In this paper, we present a model-agnostic machine-learning technique to extract a reduced thermochemical model of a gas mixture from a library. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)equilibrium. Then, a surrogate surface from the reduced cluster space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on simulations of a hypersonic flat-plate boundary layer and shock-wave boundary layer interaction with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source $\text{Mutation}++$ library. Substituting $\text{Mutation}++$ with the lightweight, machine-learned alternative improves the performance of the solver by up to 70% while maintaining overall accuracy in both cases.

In a viscoelastic flow over a microfluidic canopy of polymeric pillars, we report the spontaneous emergence of waves in the form of propagating regions of low flow velocity compared to the surrounding flow. The occurrence of the wave is chaotic and shows characteristics of elastic turbulence. We systematically study the coupling between the low-velocity wave and the microfluidic canopy by combining flow velocimetry experiments and high-speed tracking of the pillars. The waves form an angle $\pm \beta$ with the primary flow direction that depends on the geometry of the pillar array. If the canopy is composed of flexible structures, the passage of a wave deflects the structures locally in a manner reminiscent of the emergence of the Monami waves observed in inertial turbulence over canopies of vegetation. Due to the analogies with classical (inertial) canopy turbulence, we name our observed phenomenon canopy elastic turbulence.

We study the temporal linear instability of channel flow subject to a tensorial slip boundary condition that models the slip effect induced by microgroove-type superhydrophobic surfaces. The microgrooves are not necessarily aligned with the driving pressure gradient. Pralits et al. [Phys. Rev. Fluids 2, 013901 (2017)] investigated the same problem and reported that a proper tilt angle of the microgrooves about the driving pressure gradient can reduce the critical Reynolds number and that the flow with a single superhydrophobic wall is much more unstable or less stable than that with two superhydrophobic walls. In contrast, we show that the lowest critical Reynolds number is always realized with two superhydrophobic walls, and we obtain critical Reynolds numbers significantly lower than that reported. Besides, we show that the critical Reynolds number can be further reduced by increasing the anisotropy in the slip length. As the tilt angle changes, there appears to be a strong correlation between the strength of the instability and the magnitude of the cross-flow component of the base flow incurred by the tilt angle. In case the tilt angles of the microgrooves differ on the two walls, the critical Reynolds number increases as the difference in the tilt angles increases, i.e., two superhydrophobic walls with parallel microgrooves give the lowest critical Reynolds number. The results are informative for designing the microgroove-type wall texture to introduce instability at low Reynolds number channel flow, which may be of interest for enhancing mixing or heat transfer in small flow systems where turbulence cannot be triggered.

For some applications involving liquid foams, such as soil remediation for example, the liquid relative permeability of the foam-filled porous medium is a crucial parameter as it sets the liquid flow rate at which active substances or nutrients (for bacteria) can be delivered deep into the medium. We are interested in the liquid relative permeability of foam-filled porous media, within the range of low liquid saturations, i.e., $\lesssim 20\mathrm{vol}\%$. We fill porous media (packed spherical grains) with different foams made from either alkyl polyglucosides (APG) or saponin, in such a manner that we obtain highly controlled samples in terms of the bubble-to-grain size ratio $r$ and the liquid saturation. The liquid relative permeability of saponin samples exhibits an optimal value as a function of $r$, while it increases significantly for APG foams. The ratio of their relative permeability of APG/saponin reveals two regimes as a function of $r$: for $r\lesssim$ 0.25, the permeability ratio is equal to the ratio corresponding to the bulk foams, while for larger $r$ values, the permeability ratio is increased by one order of magnitude. The foam microstructure changes a lot as the bubble-to-grain size ratio increases up to 0.5, so that a new liquid network is activated, made of surface channels and liquid bridges, the former connecting the latter even at low liquid saturation. These new liquid elements may greatly benefit foams with mobile interfaces such as APGs. One such issue would deserve a dedicated study to be elucidated.

Deep reinforcement learning (DRL) was applied to turbulence control for drag reduction in direct numerical simulations of turbulent channel flow. Based on the wall shear stress information only, the DRL is capable of determining the optimal distribution of wall blowing and suction, which can reduce drag by 20%, comparable with previous wall-shear-based controls such as suboptimal control [Lee et al., J. Fluid Mech. 358, 245 (1998)] and neural-network-based control [Lee et al., Phys. Fluids 9, 1740 (1997)]. However, our DRL-based control can determine the optimal amplitude of the wall actuation, which was not possible in previous controls. More importantly, from an analysis of the optimal actuation fields, two distinct types of drag reduction mechanisms are identified: the first cancels the near-wall sweep and ejection events, whereas the second mechanism suppresses the streamwise vortices near the wall, which is similar to that of the suboptimal control. This study demonstrates the successful application of DRL to turbulence control and its physical interpretation.

We report on a systematic numerical exploration of the vesicle dynamics in a channel, which is a model of red blood cells in microcirculation. We find a spontaneous transition, called swirling, from straight motion with axisymmetric shape to a motion along a helix with a stationary deformed shape that rolls on itself and spins around the flow direction. We also report on a planar oscillatory motion of the mass center, called three-dimensional snaking, for which the shape deforms periodically. Both emerge from supercritical pitchfork bifurcation with the same threshold. The universality of these oscillatory dynamics emerges from Hopf bifurcations with two order parameters. These two oscillatory dynamics are put in the context of vesicle shape and dynamics in the parameter space of reduced volume $v$, capillary number, and confinement. Phase diagrams are established for $v=0.95$, $v=0.9$, and $v=0.85$ showing that oscillatory dynamics appears if the vesicle is sufficiently deflated. Stationary shapes (parachute/bullet/peanut, croissant, and slipper) are fixed points, while swirling and snaking are characterized by two limit cycles.

We adopt the reinforcement learning algorithm to train the self-propelling agent migrating long-distance in a thermal turbulent environment. We choose the Rayleigh-Bénard turbulent convection cell with an aspect ratio ($\mathrm{\Gamma }$, which is defined as the ratio between cell length and cell height) of 2 as the training environment. Our results showed that, compared to a naive agent that moves straight from the origin to the destination, the smart agent can learn to utilize the carrier flow currents to save propelling energy. We then apply the optimal policy obtained from the $\mathrm{\Gamma }=2$ cell and test the smart agent migrating in convection cells with $\mathrm{\Gamma }$ up to 32. In a larger $\mathrm{\Gamma }$ cell, the dominant flow modes of horizontally stacked rolls are less stable, and the energy contained in higher-order flow modes increases. We found that the optimized policy can be successfully extended to convection cells with a larger $\mathrm{\Gamma }$. In addition, the ratio of propelling energy consumed by the smart agent to that of the naive agent decreases with the increase of $\mathrm{\Gamma }$, indicating more propelling energy can be saved by the smart agent in a larger $\mathrm{\Gamma }$ cell. We also evaluate the optimized policy when the agents are being released from the randomly chosen origin, which aims to test the robustness of the learning framework, and possible solutions to improve the success rate are suggested. This work has implications for long-distance migration problems, such as unmanned aerial vehicles patrolling in a turbulent convective environment, where planning energy-efficient trajectories can be beneficial to increase their endurance.

Planar particle image velocimetry and volumetric particle tracking velocimetry were used to investigate the flow over isolated and sheltered two-dimensional bar roughness elements immersed within a turbulent boundary layer. Flow measurements were made for bars occupying up to 17% of the boundary layer thickness at a Reynolds number of 68 000, based on the boundary layer thickness and free stream velocity. In addition to an isolated bar case, the flow was investigated over two bars positioned at streamwise spacings of $0.8h_2, 1.6h_2, 2.4h_2$, and $4.8h_2$, where $h_2$ is the height of the downstream bar. By varying the height of the upstream bar $h_1$, three height ratios $h_1/h_2=0.5$, 0.75, and 1 were considered at each spacing. The results highlight the effects of the spacing and height ratio on the mean flow field and turbulence past the downstream bar. Specifically, sheltering by an upstream bar reduces the reattachment length and velocity deficit past the downstream bar. The introduction of an upstream bar with $h_1/h_2<1$ lessens the upwash experienced by the two-bar unit and the overall perturbation to the incoming turbulent boundary layer. The Reynolds shear stress past the downstream bar is also reduced, by up to 45% in some cases, due to sheltering. Overall, the flow organization past the downstream bar is influenced by the flow deflection over the two-bar unit, the upstream bar shear layer, and the structure of flow recirculation between the two bars. Moreover, visualizations of the vortical structures past the isolated bar highlight the growth and evolution of coherent spanwise vortices. Sheltering by an upstream bar enhances the three-dimensionality of the vortical structures in the wake of the downstream bar. The effects of the bar(s) on the boundary layer turbulence structure are investigated through two-point correlations and proper orthogonal decomposition, which suggest a weakening of the large-scale flow structures of the incoming flow.

Homogeneous and isotropic turbulence can be generated by many different mechanisms, from classical passive grids to jet arrays. By using high-speed jets, a jet array becomes a promising way to produce intense turbulence with large energy dissipation rates in water and wind tunnels. In this paper, a systematic experimental investigation was conducted to understand how the turbulence decay scales with the jet velocity, nozzle size, and nozzle spacings. Three-dimensional particle tracking was performed to quantify the spatial distribution of different turbulent characteristics. Combined with several previous experiments focusing on near-field measurements, our results provide a clear picture of the decay of the kinetic energy and the energy dissipation rate as well as the development of the inhomogeneity and anisotropy of turbulence generated by a jet array. Suggestions and design considerations for future wind and water tunnels are also provided.