# Latest papers in fluid mechanics

### Viscous reflection of internal waves from a slope

Author(s): T. Kataoka and T. R. Akylas

A weakly nonlinear model is developed that accounts for viscous dissipation in the reflection of an internal wave beam from a uniform slope. The theoretical predictions compare favorably with Navier-Stokes simulations and also explain the poor quantitative agreement of earlier inviscid models with laboratory experiments.

[Phys. Rev. Fluids 5, 014803] Published Mon Jan 13, 2020

### Shockwave effects on supersonic combustion using hypermixer struts

This study describes combustion features due to streamwise vorticity when using hypermixer struts at Mach numbers of 2.5 and 3.5. Two types of struts are used with hydrogen fuel (at an equivalence ratio of 0.4) injected at sonic speed from the trailing edges of the struts. To study the effects of shockwaves on streamwise vorticity formation and supersonic combustion for an alternating-wedge strut, the intersection point at which the shockwaves cross the central axis is varied by changing the length of the strut. When the incident shock is near the trailing edge of the strut, boundary-layer separation occurs on the ramp of the strut due to pressure increase near the strut and subsonic combustion occurs on the basis of this separation. Conversely, when the incident shock is far from the trailing edge of the strut, a streamwise vortex is generated by the strut and supersonic combustion caused by this vortex makes it effective at entraining fuel into itself. Each flame structure obtained here unquestionably differs in its combustion mode. For a separation-resistant strut, the results show that a streamwise vortex with the required circulation can be induced behind the strut without separation. Moreover, the combustion depends strongly on the incident shockwaves in that the combustion efficiency is not subject to the mixing efficiency because the moderate combustion originates near the point at which the formed streamwise vortex interacts with the shockwaves. Therefore, because an ignition point with moderate combustion can detach from its trailing edge, with a separation-resistant strut, it is possible to control the combustion and avoid an excessive heat load.

### The effect of a synthetic input on small-scale intermittent bursting events in near-wall turbulence

This study reports the effect of a synthetic input on the arrangements of near-wall small-scale intermittent bursting events. The hot-wire data were decomposed into small scales by wavelet transform, and the local energy bursts relevant to anomalous scaling were extracted and examined. The premultiplied spectral analysis revealed that the synthetic input reorganizes the intermittency distribution of the small-scale local energy bursts. The reorganization was confirmed by the cross spectra of the small-scale bursting events and the rest scales, which indicated that the synthetic input has a dominant interaction on the near-wall small-scale bursts by means of frequency coupling. The phase difference relationship demonstrated that the small-scale energy bursts are in phase with the synthetic input in the near wall region and then gradually phase-lagged to be out of phase further away from the wall. Moreover, conditional average provided a more direct configuration of the phase-switching phenomenon. The current study manifested that the synthetic input could have the ability to reorganize the near-wall small-scale intermittent bursting events in a deterministic way.

### Flow of wormlike micellar solutions through a long micropore with step expansion and contraction

In this study, an extensive numerical investigation has been carried out in order to understand the flow characteristics of a wormlike micellar (WLM) solution through a long micropore with step expansion and contraction. The VCM (Vasquez-Cook-McKinley) [P. A. Vasquez, G. H. McKinley, and P. L. Cook, “A network scission model for wormlike micellar solutions: I. Model formulation and viscometric flow predictions,” J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)] constitutive model has been used for the present WLM solution for predicting its rheological behavior and the governing equations, namely, mass and momentum equations along with the VCM constitutive model equations have been solved using the finite-volume method based open source code OpenFOAM. Within the range of conditions encompassed in this study, different flow regimes have been observed in the pore geometry, for instance, Newtonian like regime, lip vortex formation regime, unsteady and vortex merging regime, etc. In particular, an elastic instability regime has been observed in the pore geometry, and the onset of this regime is accentuated with the increasing values of the Weissenberg number and decreasing values of the nonlinear VCM model parameter ξ. Apart from the flow pattern, a detailed discussion on the distribution of the wormlike micellar concentration, principal stress difference, apparent relative viscosity, etc., is also presented. Finally, a good qualitative agreement (in terms of the flow pattern) has been found between the present simulations and the corresponding experiments.

### Comparison of turbulent drag reduction mechanisms of viscoelastic fluids based on the Fukagata-Iwamoto-Kasagi identity and the Renard-Deck identity

The friction coefficient decomposition was investigated in viscoelastic incompressible fluid turbulent channel flows based on two methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14(11), L73–L76 (2002)] and the Renard-Deck (RD) identity [N. Renard and S. Deck, “A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer,” J. Fluid Mech. 790, 339–367 (2016)]. Direct numerical simulations of viscoelastic fluid turbulent and Newtonian fluid turbulent channel flows were carried out to provide a database for comparative investigations. By comparing the friction coefficient decomposition results based on the two identities, different understandings about the turbulent drag reduction (TDR) mechanism were comparatively analyzed. It was found that the reduction of the viscous contribution to the friction coefficient is also an important cause for TDR under the RD identity, and that the TDR effect in the near-wall region is more intense than that under the FIK identity. In addition, if the weight coefficient for the shear-stress contribution to the friction coefficient in the FIK identity is interpreted as the laminar shear strain rate, the TDR mechanisms obtained by the two identities can be unified; the difference in the understandings can be attributed to the difference in base flow selected to determine the weight coefficient.

### Interaction between shock wave and a movable sphere with cavitation effects in shallow water

In this paper, we establish a fluid-structure interaction (FSI) model to investigate the dynamic interactions between the underwater explosion (UNDEX) shock wave and a movable sphere near the free surface. We utilize the local discontinuous Galerkin (LDG) method to capture the propagation of the shock wave in the fluid domain and employ the pressure cutoff model to calculate cavitation effects. The fluid elements at the fluid-structure interface are directly coupled to the structural dynamic model, and the structural transient dynamic responses are coupled with fluid acoustic pressure at the fluid-structure interface in the governing equation. The validity of the present FSI model is verified by comparing with the continuous Galerkin method. Due to the advantage of the LDG method in capturing the discontinuous wave, the present model shows better properties than the traditional coupled acoustic-structural model. With the present FSI model, we investigate the interaction between the UNDEX shock wave and a submerged and floated sphere. Under the combined effects of the free surface and structure, the UNDEX shock and cavitation loading characteristics are analyzed, and the influences of complicated cavitation effects on dynamic responses of the sphere are discussed.

### Mode-locked rotating detonation waves: Experiments and a model equation

Author(s): James Koch, Mitsuru Kurosaka, Carl Knowlen, and J. Nathan Kutz

Direct observation of a rotating detonation engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave fronts and global gain dynamics. We develop a m...

[Phys. Rev. E 101, 013106] Published Fri Jan 10, 2020

### Multifidelity kinematic parameter optimization of a flapping airfoil

Author(s): Hongyu Zheng, Fangfang Xie, Tingwei Ji, Zaoxu Zhu, and Yao Zheng

We construct a multifidelity framework for the kinematic parameter optimization of flapping airfoil. We employ multifidelity Gaussian process regression and Bayesian optimization to effectively synthesize the aerodynamic performance of the flapping airfoil with the kinematic parameters under multire...

[Phys. Rev. E 101, 013107] Published Fri Jan 10, 2020

### Experimental study of hypersonic boundary layer transition on a permeable wall of a flared cone

The effects of an alternative permeable material on the hypersonic boundary layer transition are investigated. The new permeable material is shown to be effective in delaying the transition, although the second mode grows faster on the material surface. Experiments are conducted on a flared cone using Rayleigh-scattering flow visualization, fast-response pressure sensors, and infrared thermography. On the permeable wall, the second mode appears earlier and persists over a longer distance along the flow direction. By applying bicoherence analysis, it is determined that the second mode decays more slowly on the permeable wall due to weaker nonlinear interactions.

### Machine learning strategies applied to the control of a fluidic pinball

The wake stabilization of a triangular cluster of three rotating cylinders is investigated. Experiments are performed at Reynolds number Re ∼ 2200. Flow control is realized using rotating cylinders spanning the wind-tunnel height. The cylinders are individually connected to identical brushless DC motors. Two-component planar particle image velocimetry measurements and constant temperature hot-wire anemometry were used to characterize the flow without and with actuation. Main open-loop configurations are studied and different controlled flow topologies are identified. Machine learning control is then implemented for the optimization of the flow control performance. Linear genetic algorithms are used here as the optimization technique for the open-loop constant speed-actuators. Two different cost functions [math] are considered targeting either drag reduction or wake symmetrization. The functions are estimated based on the velocity from three hot-wire sensors in the wake. It is shown that the machine learning approach is an effective strategy for controlling the wake characteristics. More significantly, the results show that machine learning strategies can reveal unanticipated solutions or parameter relations, in addition to being a tool for optimizing searches in large parameter spaces.

### Modelling of the laminar dispersion force in bubbly flows from direct numerical simulations

In a previous study, we have shown that the momentum transfer between phases, which requires modeling in two-fluid models, is partly comprised of a laminar dispersion force connected to surface tension and pressure effects. This dispersion force, which is obtained by stepping away from the particle hypothesis, is important for the prediction of the void fraction distribution and therefore requires modeling. In this article, based on five direct numerical simulations of turbulent bubbly flows in a vertical channel, a model is proposed by using, inter alia, the structure of the pressure field in the vicinity of bubbles. The resulting model shows very positive results. It is expected to be valid through a wide range of flow regimes for spherical and deformable bubbles as long as the drag force closure is accurate. It is ready for use and can be integrated into an Euler-Euler calculation code.

### Absolute instability of free-falling viscoelastic liquid jets with surfactants

The effect of surfactants on the absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. In general, the inclusion of surfactants to the interface of a viscoelastic liquid jet allows for the possibility of further processing droplet sizes and breakup lengths. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of the jet. An asymptotic approach, based on the slenderness of the jet, is used to render the problem more tractable and obtain steady-state solutions and then perform a linear analysis of the convective and absolute instability on these base solutions. By considering travelling wave modes, we derive a dispersion relationship, which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the initial surfactant concentration, on convective and absolute instability. In this work, we use a mapping technique known as the cusp map method to explore absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

### Passive control of the onset of vortex shedding in flow past a circular cylinder using slit

This study investigates the passive flow control phenomena over a two-dimensional circular cylinder using numerical simulations in the laminar regime. The aim is to explore one of the passive control techniques, which involves the introduction of a slit to the geometry of the cylinder. The two parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured with respect to the incoming flow direction), play an essential role in determining the trend of critical Reynolds number (Rec). Most of the analysis invokes flow visualization and saturation amplitude methods to obtain the critical Reynolds number (indicative of the onset of vortex shedding) for different cases. Furthermore, Hopf bifurcation analysis using the Stuart-Landau equation and global stability analysis confirm the accuracy and consistency in the predicted solutions. The additional amount of flow through the slit increases the pressure downstream of the cylinder, which consequently leads to an increase in Rec of the modified cylinder. The critical Reynolds number increases with S/D of the modified cylinder at 0° slit angle (as an additional amount of flow grows with S/D). The critical Reynolds number shows an increasing trend with the slit angle in the range of S/D = 0.05–0.15 as the fluctuation intensity reduces with the slit angle in this range. For S/D = 0.15–0.25, the extra amount of flow through the slit induces instability in the wake, which causes a decrease in Rec with the slit angle. A correlation is obtained, which estimates the critical Reynolds number for a given S/D and slit angle.

### Evaporation-driven liquid flow through nanochannels

Evaporation-driven liquid flow through nanochannels has attracted extensive attention over recent years due to its applications in mass and heat transfer as well as energy harvesting. A more comprehensive understanding is still expected to reveal the underlying mechanisms and quantitatively elucidate the transport characteristics of this phenomenon. In this study, we investigated evaporation-driven liquid flow through nanochannels using molecular dynamics simulations. The evaporation flux from the solid-liquid interface was higher than that from the middle region of the channel or the liquid-vapor interface. This finding may explain why experimental observations of evaporation flux through nanochannels exceed the limits predicted by the classical Hertz–Knudsen equation. Upon increasing the interaction strength between liquid atoms, the liquid exhibited enhanced solid-liquid interfacial evaporation and higher surface tension, albeit with reduced total flux. We also found that lyophilic channels exhibited higher evaporation fluxes than lyophobic channels, which can be interpreted by a Gibbs free energy analysis. The energy conversion analysis indicated that the effective pressure gradient exerted on a liquid flow by evaporation depends on the channel length. This was consistent with our simulations. Evaporation-driven liquid flow through nanochannels could be modeled quantitatively using this knowledge.

### Numerical evaluation of novel kinetic models for binary gas mixture flows

Most flows of practical interest consist of a mixture of gases. Therefore, the ability to model a gas mixture flow is important. Kinetic models for multicomponent gases have been considered since the original Bhatnagar–Gross–Krook (BGK) model was formulated. BGK-derived models pose a number of difficulties, e.g., avoiding negative density and temperature(s). A distinct challenge of the BGK approximation lies in recovering correct transport coefficients in the continuum limit. Two new kinetic models for gas mixtures, a Shakhov-based model and an ellipsoidal-statistical-based model, were recently introduced. Both models are capable of modeling a binary mixture of monoatomic gases and account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The main advantage is the recovery of three correct transport coefficients in the hydrodynamic limit and, as a result, having a correct Prandtl number for the mixture. The goal of this paper is to numerically validate the two new kinetic models for a range of high-speed flows and demonstrate their capabilities and limitations. The models are first validated against the known results for normal shocks, showing good agreement for species density and temperature profiles. Moreover, the importance of the Prandtl number correction is demonstrated with the evaluation of the heat flux. A parametric study demonstrates the variation in flow properties for different mass ratios between species and for different Mach numbers. Finally, the models are evaluated for the flow around a circular cylinder. A detailed comparison with the Monte Carlo results demonstrates promising results from both kinetic models.

### Evolution of a thin film down an incline: A new perspective

A new model which accounts for energy balance while describing the evolution of a thin viscous, Newtonian film down an incline at high Reynolds numbers and moderate Weber numbers has been derived. With a goal to improve the predictions by the model in inertia dominated regimes, the study employs the Energy Integral Method with ellipse profile EIM(E) as a weight function and is motivated by the success of EIM in effectively and accurately predicting the squeeze film force in squeeze flow problems and in predicting the inertial effects on the performance of squeeze film dampers [Y. Han and R. J. Rogers, “Squeeze film force modeling for large amplitude motion using an elliptical velocity profile,” J. Tribol. 118(3), 687–697 (1996)]. The focus in the present study is to assess the performance of the model in predicting the instability threshold, the model successfully predicts the linear instability threshold accurately, and it agrees well with the classical result [T. Benjamin, “Wave formation in laminar flow down an inclined plane,” J. Fluid Mech. 2, 554–573 (1957)] and the experiments by Liu et al. [“Measurements of the primary instabilities of film flows,” J. Fluid Mech. 250, 69–101 (1993)]. The choice of the ellipse profile allows us to have a free parameter that is related to the eccentricity of the ellipse, which helps in refining the velocity profile, and the results indicate that as this parameter is increased, there is a significant improvement in the inertia dominated regimes. Furthermore, the full numerical solutions to the coupled nonlinear evolution equations are computed through approximations using the finite element method. Based on a measure {used by Tiwari and Davis [“Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface,” Phys. Fluids 21, 102101 (2009)]} of the temporal growth rate of perturbations, a comparison of the slope of the nonlinear growth rate with the linear growth rate is obtained and the results show an excellent agreement. This confirms that the present model’s performance is as good as the other existing models, weighted residual integral boundary layer (WRIBL) by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J: B 15, 357–369 (2000)] and energy integral method with parabolic profile [EIM(P)] by Usha and Uma [“Modeling of stationary waves on a thin viscous film down an inclined plane at high Reynolds numbers and moderate Weber numbers using energy integral method,” Phys. Fluids 16, 2679–2696 (2004)]. Furthermore, for any fixed inclination θ of the substrate, 0 < θ < π/2, there is no significant difference between the EIM(E) and EIM(P) results for weaker inertial effects, but when the inertial effects become stronger, the EIM(E) results for energy contribution from inertial terms to the perturbation at any streamwise location is enhanced. More detailed investigation on the model’s performance due to this enhancement in energy contribution and the assessment of the model as compared to the other existing theoretical models, experimental observations, and numerical simulations, in the inertia dominated regimes, will be reported in a future study.

### Measurements of fluctuating lift forces on rectangular cylinders in turbulent flow

The fluctuating lift on a rectangular cylinder induced by turbulent flow is investigated by force measurement experiments. A square uniform grid is installed downstream of the entrance of the working section of the wind tunnel to generate approximately homogeneous and isotropic turbulence. The rectangular cylinder models of two different cross sections (width to depth ratio B/D = 5, 10) are tested in the experiments. Each rectangular cross section has two aspect ratios (length to width ratio θ = 1, 7) and a fixed width (B = 0.15 m). The measurements include the spectra of fluctuating lift force and vertical turbulent velocity component. From these measurements, the experimental values of generalized transfer functions of these rectangular cylinder models are obtained, which are compared with the calculated values based on three aerodynamic force theories. The one-wavenumber transfer functions and the spanwise influence terms of these rectangular cylinders are used in the calculations, which were determined by the pressure measurement experiments in the previous work. Comparisons of the measured and calculated values of generalized transfer functions demonstrate that the three-dimensional theory is satisfactory and confirm that the one-wavenumber transfer functions and spanwise influence terms determined by the pressure measurements are valid. The results also show that both the two-dimensional theory and the strip theory would overestimate the generalized transfer function, but for the rectangular cylinder with the larger aspect ratio, the strip theory is very close to the three-dimensional theory. The one-wavenumber transfer functions of these rectangular cylinders are therefore determined based on the strip theory. This indicates that the approximate approach to determination of the one-wavenumber transfer function, which was proposed for an airfoil in the previous work, could also be applicable to bluff bodies.

### Hydrodynamics of median-fin interactions in fish-like locomotion: Effects of fin shape and movement

Recent studies have shown that by utilizing the interactions among median fins (the dorsal, anal, and caudal fins), fishes can achieve higher propulsion performance at the caudal fin. This work aims at a systematic study of the effects of dorsal/anal fin shape and flapping phase on the hydrodynamic performance due to median-fin interactions (MFI) in underwater propulsion using a three-dimensional bluegill sunfish model. Flow simulations were conducted on stationary Cartesian grids using an immersed-boundary-method-based incompressible Navier-Stokes flow solver. The results showed that, due to the collision between the posterior body vortices (PBVs) and caudal fin leading edge vortices (LEVs), the latter is strengthened. As a result, the thrust and efficiency of the caudal fin are improved simultaneously, by 25.6% and 29.2%, respectively. Increases in the dorsal/anal fin area result in stronger caudal fin LEVs, and thus further caudal fin performance enhancement. On the other hand, changing the dorsal/anal fin flapping phase affects the collision time between the PBVs and the LEVs, and results in caudal fin performance changes. Phase-leading dorsal and anal fins are found to improve caudal fin efficiency, whereas phase-lag dorsal and anal fins maintain caudal fin thrust at a higher level. Compared to trunk-synchronized dorsal and anal fins, 60° phase-leading dorsal and anal fins increase the propulsive efficiency of the caudal fin from 77.9% to 90.1%. In addition, it is found that the presence of the dorsal and anal fins greatly reduces drag on the fish body by preventing the PBVs from crossing the body midline and debilitating interactions between the left- and right-stroke PBVs. Results of this work improve our understanding of MFI in fishlike swimming and demonstrate the benefits of optimal MFI for the design of high-performance bioinspired underwater vehicles.

### Influence of the viscosity and charge mobility on the shape deformation of critically charged droplets

Author(s): E. Giglio, J. Rangama, S. Guillous, and T. Le Cornu

In this work, we model and simulate the shape evolution of critically charged droplets, from the initial spherical shape to the charge emission and back to the spherical shape. The shape deformation is described using the viscous correction for viscous potential flow model, which is a potential flow...

[Phys. Rev. E 101, 013105] Published Thu Jan 09, 2020

### Flow structures and kinetic-potential exchange in forced rotating stratified turbulence

Author(s): Tianyi Li, Minping Wan, Jianchun Wang, and Shiyi Chen

Flow structures and the kinetic-potential energy exchange in rotating stratified turbulence are studied by simulations. Differences of cyclonic and anticyclonic vortices are shown. The intense kinetic-potential energy exchange is found to be associated with the cyclonic structures.

[Phys. Rev. Fluids 5, 014802] Published Thu Jan 09, 2020