Direct numerical simulations are employed to investigate a shock wave impinging on a turbulent boundary layer at free-stream Mach number $M_{\infty }=2.28$ with different wall thermal conditions, including adiabatic, cooled, and heated, for a wide range of deflection angles. It is found that the thermal boundary condition at the wall has a large effect on the size of the interaction region and on the level of pressure fluctuations. The distribution of the Stanton number shows a good agreement with prior experimental studies and confirms the strong heat transfer and complex pattern within the interaction region. An effort was also made to describe the unsteady features of the flow by means of wall pressure and heat flux spectra. Numerical results indicate that the changes in the interaction length due to the wall thermal condition are mainly linked to the incoming boundary layer, which is in agreement with previous experimental studies.

High-Peclet-number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of convective simulations, and we test the validity of this method. This accelerated evolution (AE) method involves measuring the dynamics of convection early in a simulation and using its characteristics to adjust the mean thermodynamic profile within the domain toward its evolved state. We study Rayleigh-Bénard convection as a test case for AE. Evolved flow properties of AE solutions are measured to be within a few percent of solutions which are reached through standard evolution (SE) over a full thermal diffusion timescale. At the highest values of the Rayleigh number at which we compare SE and AE, we find that AE solutions require roughly an order of magnitude fewer computing hours to evolve than SE solutions.

When a solid body rises from a bath, a liquid column is formed and stretched until pinch-off occurs at different locations and times. In the present paper, we study the temporal and spatial evolution of a less viscous liquid column extracted by an accelerating sphere from a bath. At high acceleration, the observed liquid column has the shape of an up-pointing cone, which implies that the column near the sphere is stretched so quickly that the liquid cannot keep up with it. This causes the liquid column to pinch off at the upper location. At low accelerations, a liquid column pinches off at a lower location near the free surface. The shift in the pinch-off location is explained by the axial velocity-gradient profile in the liquid column. The numerical results show that the gradient of the axial velocity near the sphere increases when the solid sphere has a higher acceleration. As a result, at high accelerations, the axial velocity gradient is responsible for the necking and pinching off at the upper location of the liquid column. At low sphere accelerations, the column pinches off at the lower location by the strong Laplace pressure due to the higher gradient of the interfacial curvature between the column and the bath. Next the pinch-off time is observed to decrease as the acceleration increases regardless of the pinch-off location. We use a linear stability analysis to predict the pinch-off time as the inverse of the growth rate in the dispersion relation.

Previous research has shown that using fractal-like blades instead of regular ones can result in a significant decrease in the power consumption of an unbaffled stirred vessel with a four-bladed radial impeller. In order to fully assess the mixing efficiency of a fractal-like or just irregular impeller with respect to a regular impeller, the mixing time required to homogenize an injected passive scalar was evaluated for both impeller types at $\text{Re}=320$ and 1600 using direct numerical simulations. It was observed that the irregular impeller can lead to a considerably shorter mixing time. This result was explained by the differences in characteristics of flow and scalar fields generated by the two impellers. We also assess the effect of Re in the transitional regime. Moreover, a simple mathematical model is proposed which can approximate the decay rate of the passive scalar fluctuations integrated over the tank volume.

The combined effect of wall pulsed jets and roughness in a laminar channel flow is investigated to determine whether or not turbulence can be triggered and maintained at low Reynolds numbers. The study is carried out through a direct numerical simulation based on the lattice Boltzmann method. The roughness, mounted on both walls of the channel, consists of transverse square bars spanning the whole width of the channel. Rectangular orifice(s) at the bottom wall act as pulsed jets. The jets are pulsed only once with the second jet activated at the end of the cycle of the first jet. Without activating the jets, the flow in the rough wall channel consists mainly in steady secondary motions in the canopies (spaces between bars) and a skimming two-dimensional laminar flow with some oscillations above the canopies. When the jets are activated, a localized three-dimensional turbulence develops and grows in the channel. Not only it is found that this localized turbulence bears strong similarity to that of a fully rough wall turbulent channel flow, but it appears to be in a “pseudo-” fully rough regime, as observed by the relatively negligible (averaged) viscous drag as compared to the form drag generated by the roughness elements. The physical mechanism which allows this to occur is discussed.

Two liquid pumps are investigated theoretically and numerically: a single thin liquid layer actuated by a periodic force at an elastic beam and a two-layer geometry actuated by an elastic beam. For the second geometry, the beam actuates the liquid from both sides. For both pumps, the liquid film thickness is small compared to the lateral characteristic length of the system. A lubrication theory is developed. The Euler-Bernoulli equation for transverse deformations of an elastic beam is coupled to the fundamental hydrodynamic equations: the Navier-Stokes equation and a continuity equation in the long-wave approximation. In this way, one connects the transverse displacement of the beam with the hydrodynamic quantities (pressure, velocity fields, and flow rates). Appropriate boundary conditions incorporate the function of the valves. The derivation of the theoretical model is followed by numerical simulations. We estimate flow rates (in two and three spatial dimensions) for different system parameters and we compute the efficiency of a well-designed liquid pump.

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry produced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady-state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach applies the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cutoff length beyond which the bending forces become subdominant to an external body force.

Increasing the printing resolution of drop-on-demand printing and deposition techniques is important for many industrial applications. In this Rapid Communication, we present a technique to minimize the jet size and reduce the laser threshold energy of a variant of the laser-induced forward transfer (LIFT) process called blister-actuated LIFT. We fabricate micrometer-sized holes onto the solid polyimide thin-film substrate which hosts the donor liquid ink film to be printed. Due to the micrometer size of the holes, surface tension effects are enhanced, a meniscus is formed at the air-ink interface, and the resulting focused jets are thinner and faster than regular jets.

In this study both the small- and large-scale flow properties of turbulent Rayleigh-Bénard convection are investigated. Experiments are carried out using the $\mathrm{\Pi }$ chamber (aspect ratio $\mathrm{\Gamma }=2$) for Rayleigh number range $\mathrm{Ra}\sim {10}^8–{10}^9$ and Prandtl number $\mathrm{Pr}\approx 0.7$. Furthermore, experiments are run for dry and wet conditions, i.e., top and bottom surfaces of the chamber are dry and wet, respectively. For wet conditions we further distinguish between conditions with and without the presence of sodium chloride aerosol particles which, if supersaturated conditions are achieved, lead to cloud droplet formation. We therefore refer to these conditions as moist and cloudy, respectively. We see that the addition of water vapor influences the turbulent flow. In all cases, the turbulent kinetic energy dissipation rates increase with increasing temperature difference, but the slopes are different for wet and dry convection. We do not observe a clear difference between moist and cloudy convection due to low liquid water content. A similar lack of collapse with Ra is observed for the characteristic oscillations of the large-scale circulation. We observe that the first normalized characteristic oscillation frequency increased with increasing temperature difference, i.e., increasing Ra, for all conditions considered, but the slopes are different for wet and dry convection with again no clear difference between moist and cloudy convection. It turns out that the sloshing or torsional mode of the large-scale circulation and the turbulent flow or energy dissipation rate seem to be influenced by the same mechanism additional to the effect of buoyancy alone. These observational results provide supporting evidence that the large-scale circulation is insensitive to phase composition or interfacial physics and rather depends only on the strength of the turbulence.

We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational velocity is shown to depend on the direction of the magnetic field. In a strong-field regime (i.e., above the critical strength), the particles are impeded at steady angles and the stability of these angles is examined. Under a uniform field, paramagnetic and ferromagnetic particles behave differently, in terms of the critical strength, symmetry property of the rotational velocity, and steady angles. In the second part, we use two-dimensional numerical simulations to study the implications of rotational dynamics for lateral migration of the particles in wall-bound shear flows. In the weak-field regime, the paramagnetic prolate particles migrate away when the field is applied perpendicular to the flow and towards the bounded wall when the field is applied parallel to the flow. Ferromagnetic particles exhibit negligible migration under fields that are parallel or perpendicular to the flow. The different lateral migration behaviors are due to the difference in the symmetry property of particle rotational velocity. In the strong-field regime, the particles are impeded at different stable steady angles, which result in different lateral migration behaviors as well. The fundamental insights from our work demonstrate various feasible strategies for manipulating paramagnetic and ferromagnetic particles.

We investigate the effective friction encountered by an intruder moving through a sedimented medium, which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction ${\mu }_e$ on a spherical intruder is captured by the inertial number $I$ given by the ratio of the timescale over which the intruder moves and the inertial timescale of the granular medium set by the overburden pressure. Further, ${\mu }_e$ is described by the function ${\mu }_e\left(I\right)={\mu }_s+\alpha I^{\beta }$, where ${\mu }_s$ is the static friction, and $\alpha$ and $\beta$ are material-dependent constants which are independent of intruder depth and size. By measuring the mean flow of the granular component around the intruder, we find significant slip between the intruder and the granular medium. The motion of the medium is strongly confined near the intruder compared with a viscous Newtonian fluid and is of the order of the intruder size. The return flow of the medium occurs closer to the intruder as its depth is increased. Further, we study the reversible and irreversible displacement of the medium by not only following the medium as the intruder moves down but also while returning the intruder back up to its original depth. We find that the flow remains largely reversible in the quasistatic regime, as well as when ${\mu }_e$ increases rapidly over the range of $I$ probed.

The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed toward the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward manner due to the loss of axial symmetry. We experimentally investigate the bubble collapse and jet formation in corners formed of two flat solid boundaries with different opening angles. Using potential flow analysis, we accurately predict the direction of the jet and bubble displacement. We further show that for a corner with an opening angle $\alpha$, there exist analytic solutions that predict the jet direction for all the cases $\alpha =\pi /n$, where $n$ is a natural number. These solutions cover, in discrete steps, the full range of corners from the limiting case of a bubble near a single wall $\left(n=1\right)$ up to a bubble in between parallel walls $\left(n\to \infty \right)$.

It has long been thought that small amounts of polymer additives can alter the balance between strain and rotation in turbulent flow. Quantitative evidence for this idea, however, is scant, in part because measuring the velocity gradient in intense turbulence is very difficult. Here, we take a different approach to investigating this question, using the well-known preferential concentration effect of inertial particles in turbulence as a probe of the strain-rotation balance. By measuring the pair correlation function of weakly inertial particles in a turbulent water flow with varying concentrations of a high-molecular-weight polyacrylamide, we show that particle clustering is monotonically enhanced as the polymer concentration increases. Our results are consistent with the recently developed energy flux balance model for polymer turbulence, which demonstrates that the balance between strain and rotation is indeed modified by polymers and that this effect increases with the polymer concentration. Our results provide further support for the energy flux balance model as the proper description of polymer turbulence, and highlight the utility of inertial particle clustering as a probe for characterizing the small-scale dynamics of turbulence.

We study the dissipation range of the turbulent energy spectrum in homogeneous and isotropic turbulence via highly resolved direct numerical simulations for microscale Reynolds numbers $R_{\lambda }$ between 1 and 100. The simulations resolve scales as small as a tenth of the Kolmogorov scale. We find that the spectrum in this range is essentially exponential for $R_{\lambda }$ up to about 20, but assumes a more complex form for higher $R_{\lambda }$. This shape can be regarded roughly as a superposition of two exponentials where the second exponential, which becomes stronger with increasing $R_{\lambda }$, appears to be the result of intermittent interactions with the lower wave-number part of the spectrum; it disappears when these interactive parts are filtered out before computing the spectrum, essentially recovering the initial exponential shape. The multifractal theory accounts for better collapse in a limited range of wave numbers up to Reynolds numbers of 1000 observed with additional simulations at lower resolutions.

The combination of high-resolution visualization techniques and pore-scale flow modeling is a powerful tool used to understand multiphase flow mechanisms in porous media and their impact on reservoir-scale processes. One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse-interface, or phase-field, theories particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play important roles. Here we present a diffuse-interface model of single-component two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization-condensation fronts and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the breakup of wetting films.

Asymmetric liquid sheet fragmentation is ubiquitous in nature and potentially shapes critical phenomena such as rain-induced propagation of foliar diseases. In this experimental study, we investigate the formation and fragmentation of a liquid sheet upon impact of a drop close to the edge of a solid substrate. Both the impact Weber number and the offset, the distance from the impact point to the edge, are systematically varied. Their influence on the kinematics of the liquid sheet and the subsequent statistics of droplet ejection are rationalized. Three major asymmetry scenarios are identified and linked to distinct droplet ejection patterns. Scaling laws are proposed to rationalize these scenarios based on impact parameters.

The response of initially isotropic turbulence to a strong magnetic field in the low magnetic Reynolds number regime has been studied using direct numerical simulations on elongated solution domains that are necessary for reliable results at long evolution times. Most results are obtained using a $16384\times 2{048}^2$ periodic domain of aspect ratio 8, without numerical forcing, after a presimulation that creates the desired initial conditions before the magnetic field is applied. At early times, velocity fluctuations parallel to the magnetic field becomes dominant as a result of Joule dissipation being weaker in this direction. However, this anisotropy is reversed after several large-eddy timescales. Statistics of the velocity gradients indicate a strong trend toward local axisymmetry and quasi-two-dimensionality, with reduced intermittency. Scale-dependent anisotropy is studied in spectral space in terms of a wave number $\left(k_1\right)$ along the magnetic field and a radial wave number $\left(k_r\right)$ in the orthogonal plane. Axisymmetric spectra show that the Joule dissipation plays a dominant role in causing kinetic energy to be concentrated in a narrow spectral region at very low values of $k_1$, which would not be captured if the domain were cubic. Simulations spanning over two orders of magnitude variation in the magnetic interaction parameter $\left(N\right)$ show that Reynolds stress anisotropy scales with the Joule time only for a short initial period. At large $N$, accelerated development of anisotropy leads to an even greater need for elongated domains which have not been employed frequently in the literature. Overall the results in this work provide both a confirmation of trends seen in simulations on cubic domains at earlier times and new observations at later times where the benefits of an elongated domain are clearly evident. A clear parametrization of Reynolds number effects still awaits larger simulations at inevitably higher cost.

The effect of different definitions of the momentum flux on the properties of the coherent structures of the logarithmic region of wall-bounded turbulence is investigated by comparing the structures of intense tangential Reynolds stress with those of the alternative flux proposed in [Jiménez, J. Fluid Mech. 809, 585 (2016)]. Despite the fairly different statistical properties of the two flux definitions, it is found that their intense structures show many similarities, such as the dominance of “wall-attached” objects, and geometric self-similarity. The new structures are wider, but not taller, than the classical ones, and include both high- and low-momentum regions within the same object. It is concluded that they represent the same phenomenon as the classical groups of a sweep, an ejection, and a roller, suggesting that these groups should be considered the fundamental coherent structures of the momentum flux. The present results show that the properties of these composite momentum structures are robust with respect to the definition of the fluxes.

Steady unidirectional gravity-driven flow of a uniform thin rivulet (i.e., a rivulet with small transverse aspect ratio) of a generalized Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the shear rate and the explicit solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behavior of these two fluids. In addition, the general behavior of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux as well as the behavior of rivulets of strongly shear-thinning Carreau and Ellis fluids are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three nondimensional parameters and of an Ellis fluid on two of its three nondimensional parameters leads to the expected dependence of the behavior of the rivulet on these parameters (namely, that increasing the viscosity of the fluid leads to a larger rivulet), the nonmonotonic dependence of the viscosity of an Ellis fluid on the nondimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behavior of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shear-thinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of nonzero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a nonconstant power-law viscosity, leading to a pluglike velocity profile with large magnitude in the narrow central region of the rivulet.

Three-dimensional turbulent magnetohydrodynamic flow in a duct with a square cross section and insulating walls is investigated by direct numerical simulations. The flow evolves in the presence of a uniform vertical magnetic field and is driven by an applied mean pressure gradient. A boundary element technique is applied to treat the magnetic field boundary conditions at the walls consistently. Our primary focus is on the large- and small-scale characteristics of turbulence in the regime of moderate magnetic Reynolds numbers up to $\text{Rm}\sim {10}^2$ and a comparison of the simulations with the quasistatic limit at $\text{Rm}=0$. The present simulations demonstrate that differences to the quasistatic case arise for the accessible magnetic Prandtl number $\text{Pm}\sim {10}^{-2}$ and different Hartmann numbers up to $\text{Ha}=43.5$. Hartmann and Shercliff layers at the duct walls are affected differently when a dynamical coupling to secondary magnetic fields is present. This becomes manifest by the comparison of the mean streamwise velocity profiles as well as the skin friction coefficients. While large-scale properties change only moderately, the impact on small-scale statistics is much stronger as quantified by an analysis of local anisotropy based on velocity derivatives. The small-scale anisotropy is found to increase at moderate $\text{Rm}$. These differences can be attributed to the additional physical phenomena which are present when secondary magnetic fields evolve, such as the expulsion of magnetic flux in the bulk of the duct or the presence of turbulent electromotive forces.