The paper presents results for the resolved numerical simulation of a turbulent flow past a homogeneous sphere and a spherical shell of equal mass and radius (and, therefore, with a larger moment of inertia) free to rotate around a fixed center. This situation approximates the behavior of a particle whose relative motion with respect to the fluid is driven by external forces, such as a density difference in a gravitational field. Holding the center fixed makes it possible to have precise information on the turbulent flow incident on the particle by repeating the same simulations without the particle. Two particle Reynolds numbers based on the mean velocity, ${\text{Re}}_p=80$ and 150, are investigated; the incident turbulence has ${\text{Re}}_{\lambda }=36$ and 31, respectively. The particle diameter is an order of magnitude larger than the Kolmogorov length scale and close to the integral length scale. The turbulent eddies that interact most strongly with the particle are characterized. Their size is found to increase with ${\text{Re}}_p$ due to the interplay of the convection timescale, the particle timescale, and the eddy timescale, but it remains of the order of the particle diameter. The sign of the hydrodynamic torque is likely to persist much less than the convection time, although longer durations are also found, revealing the effect of occasional interactions with larger eddies. The autocorrelation of the torque changes sign at shorter and shorter fractions of the convection time as the Reynolds number increases. Significant cross-stream forces are found. An analysis of their magnitude shows that they are mostly due to induced vortex shedding combined with a weaker Magnus-like mechanism.

Harnessing fluidic instabilities to produce structures with robust and regular properties has recently emerged as a new fabrication paradigm. This approach is exemplified in the work of Gumennik et al. [Nat. Commun. 4, 2216 (2013)], in which the authors fabricated silicon spheres by feeding a silicon-in-silica coaxial fiber into a flame. Following the localized melting of the silicon, a capillary instability of the silicon-silica interface induced the formation of uniform silicon spheres. Here we investigate the physical mechanisms at play in selecting the size of these particles, which was notably observed by Gumennik et al. to vary monotonically with the speed at which the fiber is fed into the flame. Using a simplified model derived from standard long-wavelength approximations, we show that linear stability analysis strikingly fails at predicting the selected particle size. Nonetheless, nonlinear simulations of the simplified model do recover the particle size observed in experiments, without any adjustable parameters. This result demonstrates that the formation of the silicon spheres in this system is an intrinsically nonlinear process that has little in common with the loss of stability of the underlying base flow solution.

Fish combine a wide variety of passive and active control mechanisms to generate thrust. Muscle actuation is used by fish in order to dynamically alter the shape or the stiffness of different parts of the body, to ultimately control propulsion. We uncover the effects of locally altering the tip region of a flapping fin system, by using a low-order robotic model. We show how the actuation of this region can largely modify propulsion. Detailed forces and torque measurements and a low-order eigenmode reconstruction of the flow around the flapping fin show the effects of varying the phase difference between the tip region and the body of the fin on the propulsive performance. Kinematics that force the trailing edge to move behind the main body of the fin are beneficial in terms of efficiency and thrust generation. For a very small range of phase differences, large thrusts can be combined with large side forces that could be used by fish to increase maneuverability.

Large eddy simulations are performed to investigate the possibility of bypass transition delay in spatially developing boundary layers. An open loop wall control mechanism is employed which consists of either spatial or temporal oscillations of the spanwise wall velocity. Both spatial and temporal oscillations show a delay in the sharp rise in skin friction coefficient which is characteristic of laminar-turbulent transition. An insight into the mechanism is offered based on a secondary filtering of the continuous Orr-Sommerfeld-Squire (OSQ) modes provided by the Stokes layer, and it is shown that the control mechanism selectively affects the low-frequency penetrating modes of the OSQ spectrum. This perspective clarifies the limitations of the mechanism's capability to create transition delay. Furthermore, we extend the two-mode model of bypass transition proposed by T. Zaki and P. Durbin [J. Fluid Mech. 531, 85 (2005)] to cases with wall control and illustrate the selective action of the wall oscillations on the penetrating mode in this simplified case.

We study the chaotic mixing of non-Newtonian fluids in a static mixing device based upon ideas from topological mixing. The kinematic and topological basis of this device means that fluid mixing and deformation is independent of the flow dynamics, facilitating rapid, global mixing of continuous media regardless of rheology and flow rate. Via experiments and computational studies, we demonstrate the efficacy of this device for a range of viscoplastic non-Newtonian materials, which are traditionally difficult to mix. We elucidate the governing principles upon which this device operates and gauge the scope for applications to a broad class of rheological materials.

The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations. The invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors are computed in the carrier phase. The joint probability density functions of the invariants are calculated and conditioned on different distances from the droplet surface. The results show that outside the viscous region near the interface, the flow topologies favor stable focus/stretching and unstable node/saddle/saddle structures, which is in agreement with those found in canonical homogeneous isotropic turbulence. Inside the viscous layer at the droplet surface, the flow topologies shift from a preference for high-enstrophy/low-dissipation motions to favoring low-enstrophy/high-dissipation. At the droplet surface, there is a strong tendency for boundary-layer-like and vortex-sheet flow topologies in which the strain and rotation rates are positively correlated. An interesting observation is that the shapes of the invariant distributions at the droplet surface are remarkably similar to those reported in the viscous sublayer of turbulent wall-bounded flows. Also, the results show that the smallest hydrodynamic length scale of the carrier fluid turbulence is located at the droplet interface and that this length scale is two to three times smaller than that of the surrounding bulk flow. From a computational viewpoint, this suggests a more stringent spatial resolution requirement for the direct numerical simulation of finite-size droplets in isotropic turbulence than its single-phase counterpart.

Strong time-periodic accelerations applied tangentially to an infinite horizontal plane layer between two miscible fluids trigger a parametric instability leading to remarkable sawtooth patterns known as frozen waves. The resulting turbulent mixing zones grow in time and then saturate when the resonance conditions of internal gravity waves are no longer fulfilled. The Floquet analysis of a model equation and direct numerical simulations reveal that the final mixing zone sizes evolve as the square of the forcing amplitude while, by contrast, the horizontal wavelengths grow nearly linearly. This explains why frozen waves sharpen with increasingly intense horizontal oscillations. It also suggests that a horizontal forcing mixes more efficiently fluids than a vertical one at large forcing accelerations.

In fluid turbulence, energy is transferred from one scale to another by an energy cascade that depends only on the energy-dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Here we show that the normal modes of vibrations in elastic plates also manifest an energy cascade with the same K41 spectrum in the fully nonlinear regime. In particular, we observe different patterns in the elastic deformations such as folds, developable cones, and even more complex stretching structures, in analogy with spots, swirls, vortices, and other structures in hydrodynamic turbulence. We show that the energy cascade is dominated by the kinetic contribution and that the stretching energy is at thermodynamical equilibrium. We characterize this energy cascade, the validity of the constant energy-dissipation rate over the scales. Finally, we discuss the role of intermittency using the correlation functions that exhibit anomalous exponents.

The turbulent premixed flame-wall interaction (FWI) has been numerically analyzed in a head-on quenching configuration at statistically stationary state under different boundary conditions. When the wall temperature is not high enough, the near wall flame isosurfaces become broken because of local flame extinction within the quenching and influence zones of FWI. According to the relative orientation of the flame normal and the wall normal, the flame can be either head-on or entrained. Outside of the influence zone the head-on flame elements are predominant, while inside the quenching zone flames are more likely to be entrained. The alignment relations among important vectors, including the principal axes of the strain rate tensor, the flame normal vector and vorticity have been investigated. Outside of the influence zone the normal vector of the progress variable isosurfaces aligns with the most extensive principle axis in the reaction zone and with the most compressive axis in the unburned and burned gas regions. Within the quenching zone, the preferential orientation with the most extensive principal axis disappears, once the flame dilatation and flame-normal strain rate decrease. Conditional alignment statistics demonstrate the distinctly different properties between the entrained flame and the head-on flame parts. In summary, the alignment relations are primarily determined by the relative strengths of chemical heat release, turbulent staining, and wall heat flux.

We use three-dimensional computer simulations to examine turning strategies for a biomimetic oscillating elastic rectangular plate propulsor submerged in a viscous fluid. The elastic plate is actuated near the first natural frequency at the leading edge. Two kinematic actuation patterns are probed to produce both pitching and yaw moments: (1) periodic plunging with asymmetric velocities on the upstroke and downstroke and (2) combined sinusoidal plunging and twisting motion. Both strategies lead to net lateral forces and turning moments. For the first case, we find that the magnitudes of the force and turning moment increase with the degree of asymmetry in the stroke. For the second case, our simulations reveal a range of optimal phase angles and twisting amplitudes that lead to the maximum yaw moment.

While fiber-turbulence interactions are common in industrial and environmental applications, little is known about inertial fiber dynamics in isotropic turbulence. Here, rotational and translational dynamics of rigid, heavy fibers in air isotropic turbulence were measured using two-orthogonal-view, holographic cinematography. Measurements were conducted in a turbulence chamber (${\mathrm{Re}}_{\lambda }$ = 115). Several batches of nylon fibers with different diameters and lengths were investigated, resulting in Stokes numbers ranging between 1.0 $\le$ St $\le$ 32.5, and fiber length to Kolmogorov length scale ratios ranging between 3.6 $\le \overline{L}/{\eta }_k\le$ 17.3. Ratios between fiber settling velocities in turbulence and quiescent conditions, ${\overline{V}}_2/V_s$, scaled with the ratio of the rms of air fluctuating velocities, $u^{\prime }$, and $V_s$, similar as for spherical particles. Fiber inertia (as indicated by St) decreased the response of the fibers to the fluctuating air velocities, and ratios of the rms values of fluctuating fiber centroid velocities and air velocities dropped from 0.96 to $\sim 0.77$ for the highest St and were well predicted by the model of Wang and Stock [J. Atmos. Sci. 50, 1897 (1993)]. Furthermore, with increasing St, probability density functions (PDFs) of fiber centroid velocities that were well described by a normal distribution narrowed in comparison to the those of the air velocity. PDFs of in-plane fiber rotation rates could not be described by a normal distribution. In the absence of significant length effects, fiber rotation rates were governed by St. Our results indicate that the fiber “tumbling” rate peaks at around St $\approx$ 4, most likely as a result of reduced fiber alignment with the vorticity vector compared to fibers having lower St. At the highest investigated St, decreasing “tumbling” rates are the result of increasingly limited response to the fluctuating flow field, well predicted by the slightly modified model proposed by Bounoua et al. [Phys. Rev. Lett. 121, 124502 (2018)].

The rheology of dense suspensions is studied by discrete-element method simulation, focusing on the interplay of the solid fraction, confining pressure, shear rate, and viscosity. Using a minimal model based on lubrication and contact forces, we are able to recover experimental results available in the literature, in a very large range of solid fractions. We show that bulk friction is only weakly dependent on contact friction when a normalized shear rate, the so-called viscous number $I_v$, is kept constant. In contrast, contact friction has a strong influence on the jamming solid fraction ${\varphi }_m$. We provide empirical proof that all the rheology could be accounted for using $I_v$ and $\varphi /{\varphi }_m$. By separating the contributions of lubrication and contact forces on the total shear stress, it is shown that contacts dominate at a solid fraction above 0.77 of jamming solid fraction. Universal expressions of macroscopic friction and solid fraction as functions of the viscous number are finally offered.

A distributed vortex in a stratified fluid is treated using numerical simulations in two dimensions. The distributed vortex allows the density field and velocity field to evolve together, as happens in real flows behind lifting surfaces. The numerical simulations treat the anelastic equations using a spectral method in space with periodic horizontal directions and a projection method in time using the third-order Adams-Bashforth method. The primary parameter is the Froude number. For large Froude number, the distributed vorticity quickly rolls up and forms a vortex pair, approximately matching cases initiated as a fully developed vortex pair. For small Froude number, the vortices disintegrate into internal waves. The results indicate that the transition Froude number with a distributed vortex is larger than cases initiated with a vortex pair.

The impact of the Lewis number, $\mathrm{Le}$, on the dynamics and morphology of a premixed flame front, spreading through a toothbrushlike array of obstacles in a semiopen channel, is studied by means of the computational simulations of the reacting flow equations including fully compressible hydrodynamics and one-step Arrhenius chemical kinetics. The channels of blockage ratios $\alpha =1/3,1/2,2/3$ are considered, with the Lewis numbers in the range $0.2\le \mathrm{Le}\le 2$ employed. It is shown that the Lewis number influences flame evolution substantially. Specifically, flame acceleration weakens for $\mathrm{Le}>1$, inherent to fuel-rich hydrogen or fuel-lean propane burning. In contrast, $\mathrm{Le}<1$ flames, corresponding to lean hydrogen-air or rich propane-air mixtures, acquire strong folding of the front and thereby accelerate even faster. The latter effect can be devoted to the onset of the diffusional-thermal combustion instability.

The unresolved stress tensor in large-eddy simulations is an important unclosed term which affects the evolution of the resolved kinetic energy and consequently the evolution of large-scale motions. The literature on modeling this term for nonreacting flows is substantial but very scarce for turbulent flames and reacting flows with nonuniform density in general. The modeling assumptions in classic models are often strong even for nonreacting flows, which limits their range of applicability. In this study, a method using an iterative reconstruction algorithm is used in order to model the unresolved stress tensor for a highly demanding flow configuration which involves reaction, modeled using detailed chemistry, and mean shear. The evaluation of the method is conducted a priori using direct numerical simulation data, which are filtered and then sampled onto a coarser mesh. The performance of the method is compared against eight different classic models in the literature which include both static and dynamic formulations.

In this paper, the influence of a small amount of noncondensable gas on shock wave generation inside a collapsing vapor bubble is examined by combining numerical analysis of a bubble dynamics equation and of the Boltzmann equation for gas flow inside a bubble. We show the importance of the high Knudsen number in the flow, i.e., the nonequilibrium gas flow, to the temperature field inside the collapsing bubble. We also show that the maximum mean Knudsen number inside the collapsing bubble can be evaluated from the initial Knudsen number and the initial number density ratio of noncondensable gas and vapor molecules. As a result, we conclude that a small amount of noncondensable gas strongly affects the temperature field inside the collapsing bubble, preventing shock wave generation inside the bubble in the final stage of collapse.

Vortex merging in a laminar separation bubble (LSB) is studied experimentally. The bubble is formed on the suction side of a NACA 0018 airfoil at an angle of attack of $4^{\circ }$ and a Reynolds number of 125 000. The merging process in the bubble is manipulated through acoustic forcing applied as a tone at either the fundamental vortex shedding frequency or at the first subharmonic of this frequency. The flow field is assessed using time-resolved, two-component particle image velocimetry. A method for detecting merged structures using wavelet analysis is introduced, allowing for reliable quantification of merging events. The results show that vortex merging occurs naturally in the separation bubble, while forcing at the subharmonic and fundamental frequencies promotes and inhibits merging, respectively. While these trends are similar to those observed for free shear layers, the subharmonic forcing of an LSB is found to directly promote disturbance development at the subharmonic frequency. For all cases, the majority of merging events take place in the aft portion of the bubble, i.e., downstream from the maximum bubble height location and upstream of mean reattachment, with subharmonic forcing causing merging to shift upstream. The merged structures are found to be the most energetic flow features; however, promoting vortex merging through subharmonic forcing does not lead to significant changes in the mean bubble topology. The spanwise behavior of the vortex merging process is studied, revealing that structures merge in a spanwise nonuniform manner, with localized merging occurring away from where forward or rearward streamwise bugles develop in the vortex filaments. Statistical characterization reveals that merging tends to occur more often over some specific spanwise segments, with the number of primary structures that merge varying by as much as 50% between spanwise locations. These findings offer insight into vortex merging in laminar separation bubbles and the attendant influence of forcing, while also highlighting the need to consider spanwise aspects of flow development.

This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation, with a gravity force whose magnitude and direction depend on the time-dependent orientation of the surface. Solidification is modeled with a temperature-dependent viscosity. Because the flow eventually ceases as the liquid film becomes very viscous, the key question this study aims to address is: what is the optimal surface kinematics for spreading the liquid layer uniformly? Two methods are proposed to tackle this problem. In the first one, the surface kinematics is assumed a priori to be harmonic and parameterized. The optimal parameters are inferred using the Monte Carlo method. This “brute-force” approach leads to a moderate improvement of the film uniformity compared to the reference case when no motion is imposed to the surface. The second method is formulated as an optimal control problem, constrained by the governing partial differential equation, and solved with an adjoint equation. Key benefits of this method are that no assumption is made on the form of the control, and that significant improvement in thickness uniformity are achieved with a comparatively smaller number of evaluations of the objective function.

We present experimental Lagrangian measurements of tracer particle acceleration autocorrelation functions in an anisotropic and inhomogeneous flow spanning the typical range of experimentally accessible Reynolds numbers. The large-scale forcing of the flow creates a stagnation point topology where straining motion governs the anisotropic velocity and acceleration fluctuations. We show that the timescales of the acceleration components remain anisotropic at high Reynolds numbers and that they are related to the dissipative timescale by the Lagrangian structure function scaling constants $C_0$ and $a_0$, as well as $C_0^{{}^{★}}$, which is shown to be kinematically related to the velocity increments. The proposed scaling relation is supported by observations using experimental Lagrangian trajectory data sets and analytical calculations using a jointly Gaussian two-time stochastic model. Examination of acceleration power spectra show that acceleration fluctuations become isotropic in the dissipative range, which suggests that the acceleration timescale is determined not only by small scales, but also by large and anisotropic scales whose contributions are substantial, even in the high Reynolds number limit.

So-called very-large-scale motions (VLSM) have been observed in turbulent pipe flows recently. It was discovered that they carry a substantial fraction of turbulent kinetic energy. However, the question how they gain and loose their energy from other scales has not been rigorously studied yet. Hence, the present study is intended to investigate how energy is transferred toward and away from the very-large scales. The inter- and intrascale energy flux in turbulent pipe flow is analyzed by means of the $\langle {\overline{u^{\prime }}}_z\overline{u_z^{\prime }}\rangle$-budget equation of the two-dimensionally filtered streamwise fluctuating velocity field $\overline{u_z^{\prime }}$ obtained from a direct numerical simulation at ${\text{Re}}_{\tau }=1500$. We show that the largest scales of motion gain their energy in the logarithmic layer through the production term of the low-pass filtered budget equation. In contrast to the small-scale energy transfer near the wall, no mean backscattering of energy is observed toward VLSM. Instantaneous flow field realizations as well as conditional averages, on the contrary, show backscattering into negative ejecting VLSM up to $y^{+}=200$, which is overcompensated by even stronger forward scattering from positive sweeping VLSM. This behavior opposes the small-scale energy transfer near the wall, where backscattering is associated with high-speed sweeping motions.