Latest papers in fluid mechanics
Severe wave run-ups on a surface-piercing column leading to strong uprush water jets may cause unexpected impact loads on offshore structures. To reveal the underlying mechanism related to the complicated wave–column interaction, this paper investigates the occurrence and evolution of wave run-ups on a fixed surface-piercing square column under focused waves experimentally and numerically by comparing the wave run-up profiles, wave loads on the column, and velocity and pressure fields in the cases of different peak periods and steepnesses. The results manifested that the wave run-up under a very steep focused wave is significantly influenced by the localized nonlinear interaction between the wave crest and the uplifted water mound in front of the column and experiences a different regime from those primarily due to nonlinear wave diffraction. In the cases of breaking or nearly breaking focused waves, the sudden change in the fluid velocity on the wave crest when impacting on the uplifted water mound dramatically increases the peak value and gradient of dynamic pressure in the adjacent region and hence results in critical impact load on the column and strong accelerating effect of the uprush flow. Additionally, a larger peak period can further increase the thickness (or volume) of the uprush flow, potentially increasing the damage risk of offshore structures.
This paper describes an experimental investigation of the cavity evolution and shedding wake behind a hydrophobic sphere during the water-entry process. Two distinct shedding phenomena are confirmed by varying the impact velocity and sphere size: regular air-bubble shedding and unstable air-cloud shedding. Both of these modes are highly dependent on the Weber and Bond numbers. Under the air-bubble shedding mode, approximately periodic big bubble shedding and low-frequency oscillation signals are observed. The relationship between big bubble shedding events and the corresponding acoustic signals is derived, and an empirical method for predicting the shedding period is proposed. The in-phase relationship between small bubble shedding and cavity rippling is confirmed, and we refer to the cavity shedding phenomenon as “acoustic” shedding. Unlike the observations of air-bubble shedding, the air-cloud shedding mode produces a group of disordered small bubbles from the rear of the cavity. Moreover, the cavity seal type has a significant effect on the cavity shedding mode. A deep seal always promotes the onset of air-cloud shedding, whereas surface seals with relatively low Bond numbers result in the air-bubble shedding mode. A surface seal suppresses resonance in the cavity volume. By observing the cavity motion, we find that air-cloud shedding is always accompanied by severe cavity resonance and a rapid decrease in cavity length. Under the air-bubble shedding mode, the cavity motion exhibits relatively weak oscillations.
The abnormality of small overshoot in the temperature profile of strong normal shock waves has been resolved, and the bulk viscosity of dilute monatomic gases cannot be ignored. By introducing the total energy conservation equation rather than the internal energy equation, an equation for the non-equilibrium temperature has been suggested. The postulated temperature equation gives a monotonically increasing profile of Monte Carlo data. The Navier–Stokes approximation derives shock equations in one differential equation and one algebraic equation and gives that the ratio of the bulk viscosity to the shear viscosity is equal to 1/15 for dilute monatomic gases.
The impact of droplets on low-adhesion solid surfaces vibrating in the vertical direction was numerically investigated. An axisymmetric multiphase lattice Boltzmann model capable of handling high density and viscosity ratios was implemented to simulate the impact. The effects of vibration parameters on the spreading, contact time, and droplet rebound velocity were addressed. According to the results, the phase angle of the surface vibration is the most dominant factor in determining the dynamics of the droplet upon impact. The contact time generally increases when the surface is vibrated. However, for a certain range of phase angles, the contact time can decrease, as compared to the stationary surface. The rebound velocity also shows a strong dependence on the vibration frequency and phase angle. For droplets with higher impact velocities, the surface vibration becomes a less important factor, whereas on surfaces with lower contact angles, the impact dynamics are much more heavily affected by the surface vibration. The rebound velocity is also heavily affected by surface vibration and varies depending on the frequency and phase angle. This study offers insights into the physics of droplet impact upon vibrating surfaces, which can be utilized to improve surface wettability control in applications where vibration is present.
The effect of acoustic excitation on a low Reynolds number jet with constant centerline velocity u0 but varying velocity profile u(y) is investigated experimentally by particle imaging velocimetry. Different initial conditions at the nozzle orifice are here used with the intent to characterize the relation between the jet preferred mode fp and the natural shear layer mode fn. The jet response to acoustic excitation is described in terms of the centerline velocity decay and the downstream increase in momentum thickness. This study intends to shed some light onto the duality of the two most fundamental flow instabilities and their controversial dependency on each other.
Flows induced by Coriolis-influenced vertically propagating two-dimensional internal gravity wave packets
Author(s): Bruce R. Sutherland, Wyatt Reeves, and Ton S. van den Bremer
In the absence of background rotation, the Eulerian flow induced by two-dimensional internal wave packets is well known to have the structure of long trailing internal waves. We show that rotation makes these waves evanescent and the structure of the flow over the waves in the wave packet qualitatively changes, with implications for the modulational stability of the waves.
[Phys. Rev. Fluids 5, 064805] Published Thu Jun 25, 2020
The flow of viscous fluid injected from a point source into the space between two horizontal plates initially filled with a second fluid of lesser density and different viscosity is studied theoretically and numerically. The volume of the dense input fluid increases with time in proportion to tα. When the fluid has spread far from the source, lubrication theory is used to derive the governing equations for the axisymmetric evolution of the interface between the fluids. The flow is driven by the combination of pressure gradients associated with buoyancy and pressure gradients associated with the input flux. The governing equation is integrated numerically, and we identify that with a constant input flux, the flow is self-similar at all times with the radius growing in proportion to t1/2. In the regimes of injection-dominated and gravity-dominated currents, we obtain asymptotic approximations for the interface shape, which are found to agree well with the numerical computations. For a decreasing input flux (0 < α < 1), at short times, the flow is controlled by injection; the current fills the depth of the channel spreading with radius r ∼ tα/2. At long times, buoyancy dominates and the current becomes unconfined with the radius growing in proportion to t(3α+1)/8. The sequence of regimes is reversed in the case of an increasing input flux (α > 1) with buoyancy dominating initially while the pressure associated with the injection dominates at late times. Finally, we consider the release of a fixed volume of fluid (α = 0). The current slumps under gravity and transitions from confined to unconfined, and we obtain asymptotic predictions for the interface shape in both regimes.
This paper quantitatively investigates the role of flexibility of blade-like stems and, in particular, the occurrence of stem resonance on lateral dispersion in emergent aquatic canopies. Two sets of experiments are presented: single-stem and canopy tests. In the first set, the flow around single blade-like flexible model stems and the proximity to a resonant state are studied. Wake areas behind four model stems with distinct flexibilities are measured by particle image velocimetry for stem Reynolds numbers between 350 and 850. A single flexible emergent stem bends and oscillates in in-line and cross-flow directions due to periodic forcing associated with the vortex shedding. The plant motion, especially at resonance, affects the width of the wake area and, hence, the extent to which a tracer is dispersed laterally around a stem. The results show that the oscillation amplitude of a stem increases significantly as the vortex shedding frequency approaches the natural frequency of the stem in the corresponding direction. As a result, the size of the wake area is greater for the resonated stems. In the second set of the experiments, lateral dispersion in two different flexible model canopies was measured. The results show that the proximity to a resonant state is the major factor describing the variation of the lateral dispersion coefficient in the experiments for the tested Reynolds numbers and canopies. The dispersion coefficient increases as the vortex shedding frequency approaches the natural frequency of stems in either direction.
Author(s): Hamid Daryan, Fazle Hussain, and Jean-Pierre Hickey
Compressible direct numerical simulation of vortex reconnection uncovers the source and far-field pattern of aeroacoustic noise.
[Phys. Rev. Fluids 5, 062702(R)] Published Wed Jun 24, 2020
Author(s): A. J. Archer, H. A. Wolgamot, J. Orszaghova, L. G. Bennetts, M. A. Peter, and R. V. Craster
An experimental demonstration is presented that a chirped array of cylinders can be designed to control the spatial distribution of water wave energy and substantially amplify target frequencies at specified locations, over a broad range of frequencies, consistent with linear band-gap theory.
[Phys. Rev. Fluids 5, 062801(R)] Published Wed Jun 24, 2020
Author(s): Patrick S. Eastham and Kourosh Shoele
Numerical techniques are employed to study the locomotion of a spheroidal squirmer in a complex fluid with a nutrient-dependent viscosity. It is found that the nonuniform viscosity significantly affects the pressure field around the swimmer rather than the velocity field. Results obtained here will be helpful in interpreting experimental observation where a microswimmer significantly affects a fluid’s local rheology.
[Phys. Rev. Fluids 5, 063102] Published Wed Jun 24, 2020
Author(s): Thomas Dombrowski and Daphne Klotsa
A study of the kinematics, power and recovery strokes, fluid flows, and efficiency of a reciprocal dumbbell swimmer with finite inertia finds that the swimmer’s average flow field is dominated by the flow during its power stroke, and it switches from pullerlike to pusherlike depending on the (finite) Reynolds number.
[Phys. Rev. Fluids 5, 063103] Published Wed Jun 24, 2020
Author(s): Muhammad Saif Ullah Khalid, Junshi Wang, Haibo Dong, and Moubin Liu
Unfolding the connection between kinematics and physiology of natural swimming species is of much value for bioinspired designs of autonomous underwater vehicles. Extensive numerical investigations find which wavelength of the undulating motion of carangiform and anguilliform swimmers is suitable to maximize their swimming performance in terms of thrust production and efficiency under different flow conditions. It is also explained how jet switching in the wake of a swimmer deteriorates the hydrodynamic efficiency of anguilliform and carangiform swimmers.
[Phys. Rev. Fluids 5, 063104] Published Wed Jun 24, 2020
Author(s): Thomas D. Nevins, Daniel E. Troyetsky, and Douglas H. Kelley
Chemical reactors often need to generate products quickly, with minimal stirring energy. What flow is best? By studying two-dimensional laminar flows via advection-diffusion simulations and via simulations of moving chemical reaction fronts, analytic predictions of converged front shape and reaction rate are devised. In the regime studied, concentrating kinetic energy in small regions causes the fastest reactions.
[Phys. Rev. Fluids 5, 063201] Published Wed Jun 24, 2020
Author(s): Yadong Ruan, Ali Nadim, and Marina Chugunova
If a thin liquid film is generated from a source region on a vertical surface, it may flow down the wall as a result of gravity or, if there is a strong upward air current, get carried up by the resulting shear stress. An analysis of the dynamics of such a system both with and without surface tension finds that at low source strengths, the film is carried entirely upward, whereas for stronger source strengths, the bulk of the film falls down while some is still carried upward by the air flow. Surface tension strongly affects the film profiles and the speeds of the fronts.
[Phys. Rev. Fluids 5, 064004] Published Wed Jun 24, 2020
Similarities in the free-surface elevations and horizontal velocities of undular bores propagating over a horizontal bed
This paper presents experimental results regarding the existence of similarities and/or Froude number similitudes in the time series of the free-surface elevation (FSE) and horizontal velocity of undular bores (UBs) propagating over a horizontal bed. Two wave gauges and high-speed particle image velocimetry are employed to measure the FSEs and velocity fields. A complete evolution of the FSE (or horizontal velocity) of UBs is divided into four temporal stages, named stages I–IV. The surge-wave amplitudes, constant characteristic horizontal velocities, and specified time differences are then identified as the characteristic length scale, velocity scale, and timescale of UBs. Data for the dimensionless FSE and free-stream velocity vs the dimensionless shifted time are found to collapse onto two unique similarity trends. This demonstrates the existence of Froude number similitudes for the entire evolution of UBs with geometric similarity. Under the same water-depth ratio and length ratio, but distinct values of the relative basin and travel length for different UBs, larger values of the relative basin length produce greater end times for the final occurrence of the constant FSE and characteristic horizontal velocity. This demonstrates that the end time is not influenced by the relative travel length. Under identical values of the water-depth ratio and relative basin length, a smaller relative travel length results in a greater rate of decrease in the unit discharge during stage IV. Correspondingly, this results in earlier bifurcation of the time series of FSE (or free-stream velocity), which has a smaller (or larger) rate of decrease, from their counterparts with larger relative travel lengths.
Peristaltic transport of inelastic circular droplets immersed in an immiscible viscous fluid is numerically studied in a planar two-dimensional channel using the finite-volume method. Numerical results could be obtained for a wide range of droplet’s material properties at large deformations. Based on the results obtained in this work, for a particle that is initially placed at the centerline, an increase in the droplet’s viscosity is predicted to increase its transport velocity, but the effect can saturate at viscosity ratios as small as two. The transport velocity is shown to linearly increase with the droplet’s density, but the effect turns out to be quite weak. An increase in the interfacial tension is found to lower the transport velocity although the effect appears to approach an asymptote. Depending on their size and the Weber number, droplets are predicted to move faster or slower than rigid particles. The transport velocity of droplets is found to increase with an increase in the wave speed or, equivalently, the Reynolds number. Off-center droplets are predicted to migrate toward the wall or toward the centerline. Droplets that migrate toward the centerline remain a short distance away from it under steady conditions. Distribution of surface forces is used to explain some of these results with viscous normal stress predicted to play a key role in controlling the dynamics of droplets in peristaltic flow.
Compound droplets are excellent analogs of complex biological entities such as vesicles or cells. Despite significant advancements toward understanding the morphological evolution of a compound droplet in an incipient flow, the specific role of interfacial rheology toward dictating the same remains unaddressed. Here, we bring out non-trivial implications of interfacial rheology on the deformation of a compound drop subject to an imposed flow. The interfacial viscosity, in effect, interacts with the flow-induced non-uniform surfactant distribution to alter the droplet morpho-dynamics in a rather engaging manner. We employ a closed-form analytical approach to delineate the relative roles of advective and diffusive transport. In the paradigm of diffusion-dominated interfacial transport, viscous interfacial stress arrests the droplet deformation, thus enhancing its stability. However, for large values of the interfacial dilatational viscosity, the drop deformation increases with the interfacial shear viscosity. On the contrary, in the paradigm of surface convection-dominated surfactant transport, the interfacial rheology does not have any significant effect on either the shape deformation or the emulsion rheology. These results may pave a way toward explaining several unique features of complex fluid–fluid interfaces encountered in nature and biology.
In this work, we propose an approach for Temporal Large-Eddy Simulation (TLES) with direct deconvolution. In contrast to previous approaches such as the Temporal Approximate Deconvolution Model (TADM) by Pruett et al. [“A temporal approximate deconvolution model for large-eddy simulation,” Phys. Fluids 18, 028104 (2006)], the non-filtered velocity field is recovered using the differential form of the filter operation rather than from a truncated series expansion of the inverse filter operator. This direct deconvolution is used to obtain formal closure of an analytic evolution equation of the temporal residual-stress tensor. Thus, the Temporal Direct Deconvolution Model (TDDM) has advantages relative to the TADM in being both more accurate and requiring less computational effort. As for the TADM, a secondary regularization term based on selective frequency damping is employed. The TDDM was implemented in the spectral element code Nek5000 (Argonne National Laboratory, NEK5000 Version 17.0, 2019, https://nek5000.mcs.anl.gov) to simulate two canonical incompressible flows as three test cases: an a priori test case of Homogeneous Isotropic Turbulence (HIT) at Reλ = 50, a greatly coarsened a posteriori HIT case at Reλ = 190, and an a posteriori highly anisotropic turbulent channel flow at Reτ = 180. Analyses of the energy spectrum, the mean flow, the root-mean-square of the velocity fluctuations, and the Reynolds stresses are presented. The results demonstrate a significant improvement compared to no-model solutions regarding the mean flow in the turbulent channel and the energy spectrum in the HIT case, while the computational cost is reduced dramatically compared to the direct numerical simulation.
A new pressure-based lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest-neighbor lattices (e.g., D3Q19), the model consists of a predictor step comparable to classical athermal lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation—for which the Hermitian quadrature is not accurate enough on such a lattice—is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, entropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions with very limited dissipation. Last, the robustness of the method is tested in a one-dimensional shock tube and a two-dimensional shock–vortex interaction.