# Latest papers in fluid mechanics

### Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

Author(s): Pedro Stefanin Volpiani, Morten Meyer, Lucas Franceschini, Julien Dandois, Florent Renac, Emeric Martin, Olivier Marquet, and Denis Sipp

We combine data assimilation and machine learning to correct the RANS Spalart-Allmaras turbulence model. The final neural-network contribution is a Boussinesq-correction, rather than a turbulent eddy-viscosity adjustment. Flows over periodic hills at distinct Reynolds numbers and geometries were selected to demonstrate the potential gain of machine learning-augmented turbulence models.

[Phys. Rev. Fluids 6, 064607] Published Wed Jun 16, 2021

### The nature of bubble entrapment in a Lamb–Oseen vortex

Bubble trajectories in the presence of a decaying Lamb–Oseen vortex are calculated using a modified Maxey–Riley equation. Some bubbles are shown to get trapped within the vortex in quasi-equilibrium states. All the trapped bubbles exit the vortex at a time that is only a function of the Galilei number and the vortex Reynolds number. The set of initial bubble locations that lead to entrapment is numerically determined to show the capturing potential of a single vortex. The results provide insight into the likelihood of bubble entrapment within vortical structures in turbulent flows.

### Sessile liquid drops damp vibrating structures

In this study, we explore the vibration damping characteristics of singular liquid drops of varying viscosity and surface tension resting on a millimetric cantilever. Cantilevers are displaced 0.6 mm at their free end, 6% their length, and allowed to vibrate freely. Such ringdown vibration causes drops to deform, or slosh, which dissipates kinetic energy via viscous dissipation within the drop and through contact line friction. Damping by drop sloshing is dependent on viscosity, surface tension, drop size, and drop location. A solid weight with the same mass as experimental drops is used to compare against the damping imposed by liquids, thereby accounting for other damping sources. Neither the most viscous nor least viscous drops studied imposed the greatest damping on cantilever motion. Instead, drops of intermediate viscosity strike the most effective balance of sloshing and internal dissipative capacity. Very thin cantilevers with sloshing drops express more than one dominant frequency and vibrate erratically, often shifting phase, presenting a challenge for quantification of damping. Finally, we introduce a new dimensionless group aimed at incorporating all salient variables of our cantilever-drop system.

### Sound absorption of petal shaped micro-channel porous materials

Experiments demonstrated that surface roughness could significantly improve the sound absorption performance of porous materials. In this study, to quantitatively explore the underlying physical mechanisms, porous materials with roughened pore surfaces are modeled as a bundle of parallel petal shaped tubes, so that relevant acoustic transport parameters, namely, viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length, can be theoretically predicted. Multi-scale numerical simulations are implemented to validate the theoretical predictions, with good agreement achieved. Compared with smooth tubes, petal shaped tubes reduce the viscous and thermal characteristic lengths as well as the viscous and thermal permeabilities, resulting in enhanced sound absorption over a wide frequency band.

### Maximum spreading of an impacting air-in-liquid compound drop

We study numerically the dynamics of an air-in-liquid compound drop impacting onto a solid surface. We demonstrate that the addition of a bubble in the drop decreases its maximum spreading. This decrease is explained by the lower kinetic energy of the drop, but also amplified by the formation of a vertical jet emerging from its center, and a relative increase in the viscous dissipation. We propose a new theory describing the maximum spreading of an air-in-liquid compound drop by including these effects into modified Weber and Reynolds numbers. Finally, we demonstrate that the eventual bursting of the bubble does not significantly affect the maximum spreading diameter, by characterizing the bubble bursting and performing additional simulations where the bursting of the bubble is prevented.

### Vertical force generation of a vectorial thruster that employs a rigid flapping panel

The vertical force generation and flow features of a flapping panel that employs combined motion of horizontal oscillation, longitudinal rotation, and leading-edge-based pitching motion were investigated numerically. The sole vertical force generation is realized by combining the horizontal oscillation and longitudinal rotation, while the vertical force and forward thrust are obtained simultaneously by employing the combined motion of the horizontal oscillation, longitudinal rotation, and pitching motion about the leading edge of the panel. The effects of the phase shift ([math]) of the longitudinal rotation and the amplitudes of the longitudinal rotation and pitching motion are investigated and discussed, respectively. Results show that the phase shift determines the instantaneous attitude of the panel and influences the directions of the instantaneous generated forces and thus plays an important role in the vertical force generation. The panel could generate stable forward thrust while maintaining the pitching motion constant and adjusting the longitudinal rotation amplitude, and in the meantime, the vertical force increases linearly with the rotation amplitude. On the other hand, the vertical force may change to the opposite direction when the longitudinal rotation is kept constant and the pitching amplitude is adjusted. The results of the current research show the potential of employing these kinds of combined motions to fish-tail-mimic propulsors of robotic fishes that pursue high maneuverability.

### Multiphase lattice Boltzmann modeling of dielectrophoresis fractionation of soft particles

Dielectrophoresis-field flow fractionation (DEP-FFF) is a promising method of fractionating particles from a continuous flow and has considerable application potential in the fields of biomedical, chemical, and environmental engineering. Particle deformation is an important issue in DEP-FFF, having a critical influence on the fractionation accuracy and viability of bioparticles. However, this problem has been largely ignored in both theoretical and numerical investigations. In the present work, a hybrid lattice Boltzmann scheme is introduced to study the deformation of soft particles subjected to the coupled effects of hydrodynamics and electrokinetics in a DEP-FFF process. The interaction of the particles with the fluid medium is calculated using a multiphase lattice Boltzmann model. The dielectrophoretic effect on the flow is introduced through a DEP force, which is obtained from a finite-element solution of the electric field. The hybrid scheme avoids the need to solve a coupled multiphysics problem, making it very efficient. The proposed simulation framework is validated through a well-known model, and the particle deformation and its influence on DEP-based fractionation are discussed.

### Drag reduction and transient growth of a streak in a spanwise wall-oscillatory turbulent channel flow

The drag-reduction mechanism of spanwise wall oscillation in a turbulent channel was investigated as an extension of the work of Yakeno et al. [“Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation,” Phys. Fluids 26, 085109 (2014)] at a low Reynolds number. Flow instability was evaluated by computing the transient energy growth under an oscillating base flow which governed the generation of a near-wall streak structure. Oscillation affected the optimal energy growth of the streak mode, whose characteristics were reasonably consistent with those in a direct numerical simulation. The optimal growth of the tilted-streak mode was enhanced with a thicker Stokes layer under longer oscillation periods, while that of the original streak mode was weakened. The transition of the optimal perturbation under oscillation showed that the spanwise Stokes layer shear contributed considerably more to modification than the spanwise velocity did. A new drag-reduction performance estimation model was suggested using the acceleration of the spanwise velocity shear based on streak formation modification under oscillation, which restrains energy transfer to streamwise vortices via a tilting delay due to oscillation. This simple model worked well even under long oscillation periods and was theoretically consistent with that of Yakeno et al. based on the change in the Reynolds shear stress due to a streamwise vortex at a low Reynolds number.

### Capillary and viscous fracturing during drainage in porous media

Author(s): Francisco J. Carrillo and Ian C. Bourg

Detailed understanding of the couplings between fluid flow and solid deformation in porous media is crucial for the development of novel technologies relating to a wide range of geological and biological processes. A particularly challenging phenomenon that emerges from these couplings is the transi...

[Phys. Rev. E 103, 063106] Published Tue Jun 15, 2021

### Extraction of invariant manifolds and application to turbulence with a passive scalar

Author(s): N. E. Sujovolsky and P. D. Mininni

The reduction of dimensionality of physical systems, especially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant physical information on the original system. We present a meth...

[Phys. Rev. E 103, 063107] Published Tue Jun 15, 2021

### Toward modeling of turbulent flow over surfaces of arbitrary roughness

The problem of Reynolds-averaged modeling of turbulent boundary-layer flow over surfaces of arbitrary roughness is studied using the results of direct numerical simulations of turbulent flow over many different rough surfaces. The complexity of flow in the roughness sublayer is such that the most effective general strategy appears to be to model it as a prescribed velocity profile, either at a coarse level as a conventional roughness-specific log-linear wall function, or at a fine level as a modeled roughness-specific velocity profile across the roughness sublayer, together with a standard Reynolds-averaged closure in the outer flow. Calculations made with sandgrain roughness wall functions and velocity-profile models were in excellent agreement with channel-flow simulation data and, after correction for effects of Reynolds number and roughness height, were in good agreement with friction coefficients for a wide range of reference pipe-flow data. Equally good predictions of friction coefficients were made of flows over wavy walls, walls with spaced arrays of semi-ellipsoids, and walls with roughness elements of random size and orientation, when either sublayer velocity profiles or wall functions for the corresponding roughnesses were used. This modeling approach is made possible by the availability of relevant data from a library of roughness-sublayer velocity profiles from simulations of flow over many different kinds of rough surfaces.

### Simulation of high pressure, direct injection processes of gaseous fuels by a density-based OpenFOAM solver

The direct injection of a gaseous fuel in internal combustion engines involves under-expanded supersonic jets and complex air/fuel fluid-dynamics. Furthermore, with the high pressure ratios between the injector and the cylinder, the gaseous flow usually becomes choked even inside the injector. Knowledge of all these phenomena is essential to achieve a deeper understanding of the air–fuel mixing process that follows, influencing combustion and pollutant formation. In this framework, this study deals with the development and validation of a fully explicit, density-based solver for supersonic compressible flows, using the OpenFOAM library and featuring Runge–kutta fourth order time discretization and the Kurganov central flux splitting scheme. This methodology was applied to analyze the inner and the external flow of an innovative, multi-hole, high pressure injector for heavy-duty vehicle applications. The adoption of multi-hole patterned injectors in gaseous fuel combustion systems is believed to be an efficient way of achieving a better air/fuel mixture and, therefore, improving the combustion reaction. The present work aims to evaluate the reliability of the aforementioned mathematical approach for such kinds of complex flows and, especially, provide a comprehensive characterization of the multi-jet spray. It was found that shock waves in the internal-nozzle deeply modify the flow development and the external Mach disk as shock cells move the mixing activity on a lateral shear layer. It was also observed that a methane cloud grows downstream and, although flammable conditions are present, it later inhibits air recirculation toward the near nozzle zone.

### Bridge expansion after coalescence of two droplets in air: Inertial regime

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane, or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number (Oh), the dynamics of the bridge differs a lot. For Oh [math]1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge center. The expansion is thus caused by the capillary pressure that drives the fluid toward the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of nondispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result in the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow rate that enters the bridge and thus determines its radial expansion.

### An extended model for orifice starting jets

Starting jets emanating from a straight nozzle and orifices of different orifice-to-tube diameter ratios are investigated using time-resolved particle image velocimetry. The invariants of the motion, namely, the circulation, the hydrodynamic impulse, and the kinetic energy, are measured and compared to the classic slug-flow model, and this for both fixed exhaust speed and fixed diameter-based Reynolds numbers. An extension to the slug-flow model is proposed to account for the contraction the fluid is experiencing when being pushed out through orifice geometries. The contraction coefficients obtained for two-dimensional jets formed through a slit in a channel are applied to the axisymmetric problem. This modified slug-flow model is shown to better predict the invariants of the motion with discrepancies of the order of 10% compared to underpredictions of 130%, 50%, and 120% for the circulation, the hydrodynamic impulse, and the kinetic energy, respectively, using the classic slug-flow model. Moreover, for a fixed target exhaust speed, the model suggests the existence of a maximum in the production of impulse and energy at an orifice-to-tube diameter ratio of about 0.9, which was also observed experimentally for the kinetic energy. Practically speaking, this suggests that the most efficient way of producing a starting jet is using an orifice plate of ratio close to 1, but different from a straight nozzle. Finally, the overpressure correction of Krueger [“The significance of vortex ring formation and nozzle exit overpressure to pulsatile jet propulsion,” Ph.D. thesis (California Institute of Technology, 2001)] is applied and revisited to account for the orifice-to-tube diameter ratio. Overall, good agreement with the present experimental data is found.

### Withdrawal and dip coating of an object from a yield-stress reservoir

Author(s): Wilbert J. Smit, Christophe Kusina, Annie Colin, and Jean-François Joanny

How much fluid adheres to an object pulled out from a liquid reservoir? We re-examine this dip-coating problem for yield-stress fluids. We propose a complete description that links the yield-stress fluid case with the Newtonian case. For extreme cases, asymptotic scaling laws are provided.

[Phys. Rev. Fluids 6, 063302] Published Mon Jun 14, 2021

### Experimental study of shock wave modulation caused by velocity and temperature fluctuations in cylinder wakes

Author(s): Kento Inokuma, Tomoaki Watanabe, Koji Nagata, and Yasuhiko Sakai

We perform wind tunnel experiments of a spherical shock wave propagating across an unheated- or a heated-cylinder wake to investigate statistical properties of a shock wave interacting with turbulence with velocity and temperature fluctuations. We find that the ovepressure fluctuations behind the shock wave are negatively correlated with the temperature fluctuations of the heated-cylinder wake. We also propose the shock deformation model, where the overpressure modulation of the shock wave is derived by considering the surface deformation of the shock wave due to the propagation in a locally turbulent region. The model explains well shock wave statistics obtained in experiments.

[Phys. Rev. Fluids 6, 063401] Published Mon Jun 14, 2021

### Influence of freestream turbulence on the flow over a wall roughness

Author(s): M. A. Bucci, S. Cherubini, J.-Ch. Loiseau, and J.-Ch. Robinet

We demonstrate that free-stream turbulence has a strong impact on the dynamics of flow past a cylindrical roughness element. Previous works have shown that, depending on operating conditions, the leading flow instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures, even though optimal response analysis predicts strong amplification of sinuous disturbances with frequency near the marginally stable sinuous eigenmode. We show that this is due to the flow essentially being an amplifier of varicose perturbations rather than a resonator.

[Phys. Rev. Fluids 6, 063903] Published Mon Jun 14, 2021

### Rayleigh-Taylor instability of viscous liquid films under a temperature-controlled inclined substrate

Author(s): Youchuang Chao, Lailai Zhu, and Hao Yuan

A liquid film flowing under an inclined substrate exhibits the well-known Rayleigh-Taylor instability. Here we show, using long-wave theory and stability analysis, that this instability can be modulated by adjusting the substrate temperature. In particular, we derive analytically two critical (composite) Marangoni numbers delineating stable, convectively unstable, and absolutely unstable regions, which is also verified by numerical solutions of the full evolution equation.

[Phys. Rev. Fluids 6, 064001] Published Mon Jun 14, 2021

### Faraday instability of binary miscible/immiscible fluids with phase field approach

Author(s): M. Bestehorn, D. Sharma, R. Borcia, and S. Amiroudine

The objective of the present work is to model the continuous passage of a binary fluid mixture from its immiscible state into a miscible one. This is achieved with a phase field model using an extended Cahn-Hilliard equation which permits us to move from the immiscible to the miscible states. The phase field is coupled to the Navier-Stokes equations via Korteweg stress and buoyancy. A thorough analysis of the Faraday instability is then demonstrated by means of a Floquet analysis and by direct numerical simulations.

[Phys. Rev. Fluids 6, 064002] Published Mon Jun 14, 2021

### Learned discretizations for passive scalar advection in a two-dimensional turbulent flow

Author(s): Jiawei Zhuang, Dmitrii Kochkov, Yohai Bar-Sinai, Michael P. Brenner, and Stephan Hoyer

Calculating the evolution of a passive scalar in a turbulent flow requires resolving the intricate stretching and folding of the scalar field. Traditionally, this requires that the computational mesh is much smaller than the smallest scale of the concentration field. Here we demonstrate the use of machine learning to learn discretizations of the governing equation that give accurate computations with a coarser mesh. The model learns the universal small scale structures of the concentration field stretching, allowing it to accurately interpolate with less information.

[Phys. Rev. Fluids 6, 064605] Published Mon Jun 14, 2021