# New Papers in Fluid Mechanics

### Faraday waves over a permeable rough substrate

Author(s): Diego Barba Maggi, Alejandro Boschan, Roman Martino, Marcelo Piva, and Jean-Christophe Géminard

We report on an experimental study of the Faraday instability in a vibrated fluid layer situated over a permeable and rough substrate, consisting either of a flat solid plate or of woven meshes having different openings and wire diameters, open or closed (by a sealing paint). We measure the critical...

[Phys. Rev. E 99, 053110] Published Wed May 15, 2019

### Predicting the maximum spreading of a liquid drop impacting on a solid surface: Effect of surface tension and entrapped air layer

Author(s): Thijs C. de Goede, Karla G. de Bruin, Noushine Shahidzadeh, and Daniel Bonn

At low impact velocities, a droplet does not immediately make contact with a surface because of an entrapped air layer, leading to delayed surface wetting. High-speed images are used to investigate the influence of this entrapped air layer and the surface wettability on droplet spreading.

[Phys. Rev. Fluids 4, 053602] Published Wed May 15, 2019

### Why capillary flows in slender triangular grooves are so stable against disturbances

Author(s): Nicholas C. White and Sandra M. Troian

Lyapunov and non-modal stability analysis reveal why stationary and self-similar capillary flows in slender open triangular channels are so stable to disturbances. This robust feature allows superior flow management for applications ranging from space micropropulsion to microfluidic diagnostics.

[Phys. Rev. Fluids 4, 054003] Published Wed May 15, 2019

### Reynolds-average Navier-Stokes study of steady and pulsed gaseous jets with different periods for the shock-induced combustion ramjet engine

The mixing process is very important for the shock-induced combustion ramjet engine. In the current study, the steady jet, as well as pulsed jets with different periods, is investigated in order to achieve adequate fuel/air mixing in the supersonic flow. Flow field properties are studied numerically based on grid independency analysis and code validation. The influence of the hydrogen distribution, as well as the flow field parameters such as mixing efficiency, total pressure recovery coefficient, and fuel penetration depth, is deeply analyzed for different jet-to-crossflow pressure ratios, namely, 10.29 and 25.15. The obtained results predicted by the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with the two equation shear stress transport k-ω turbulence model show that the grid scale makes only a slight difference to wall pressure profiles. The pulsed jets with different periods are beneficial for the mixing process, especially when the jet-to-crossflow pressure ratio is high, and it has special advantages on reducing the total pressure loss and improving the fuel penetration depth. Among the pulsed jets considered in the current study, the T1 pulsed jet with higher frequency has the best performance, and its mixing augmentation mechanism is predicted. Its mixing enhancement mechanism is focusing on merging a mass of air around into the fuel core by the intermittent injection.

### Hysteresis behavior in spanwise rotating plane Couette flow with varying rotation rates

Author(s): Yuhan Huang, Zhenhua Xia, Minping Wan, Yipeng Shi, and Shiyi Chen

In direct numerical simulations of spanwise rotating plane Couette flow, hysteresis is found between a 2-pair-roll-cell as the rotation increases to a 3-pair-roll-cell when the rotation decreases.

[Phys. Rev. Fluids 4, 052401(R)] Published Tue May 14, 2019

### On the optimal morphology and performance of a modeled dragonfly airfoil in gliding mode

Numerical investigation on the effect of wing morphology of the dragonfly Aeshna cyanea is carried out to understand its influence on the aerodynamic performance. The two-dimensional wing section has corrugation all over the surface along the chord length on both upper (suction side) and lower (pressure side) surfaces. By considering each corrugation separately on different airfoils at their different positions, 10 single corrugated airfoils were generated. Simulations are performed on these different airfoils to determine the effect of each corrugation on aerodynamic performance. The flow is modeled as incompressible, Newtonian, homogeneous, and unsteady. The angle of attack was varied from 0° to 20°, and the Reynolds number (Re) was varied from 150 to 10 000. The optimum morphology and angle of attack were predicted by using the surrogate-based optimization technique for a maximum gliding ratio at different Re. A fully corrugated pressure side gives the best performance at angles of attack of 9.79° and 14.83° at low Re. At high Re, corrugations on the pressure side which are in the middle and those near the trailing edge give a maximum gliding ratio at angles of attack 9.22° and 5.276°. The spatiotemporal dynamics indicate that corrugations near the leading edge on the upper surface and corrugations near the trailing edge for the lower surface and which are in the middle are beneficial. It is also found that shear drag due to corrugation decreases but pressure drag increases; therefore, the overall drag coefficient for a fully corrugated airfoil increases. Corrugations on the suction side have little influence, while those on the pressure side causes lift enhancement.

### Numerical study of natural convection in a differentially heated square cavity filled with nanofluid in the presence of fins attached to walls in different locations

The phenomenon of natural convection in a square cavity filled with a copper-water nanofluid is investigated numerically. The studied domain is a square cavity with hot and cold isothermal walls at x = 0 and x = L, respectively, while the other walls are adiabatic. The fins are considered perfectly conductive with different lengths (Lf) and positioned at different locations. We examined the situation for Rayleigh numbers ranging between 104 and 106. The governing equations are expressed in the vorticity, stream function, and temperature formulation. The system of equations was solved by the finite difference method, using the upwind scheme. The computation code thus developed was used to analyze the effect of the different locations of the fins on the thermal performances. The obtained results were validated by comparing with those of a previously published work and with those obtained using COMSOL Multiphysics. It has been found that adding fins on the cold and adiabatic walls results in an increase in the average Nusselt number, while it decreases when the fin is located on the hot wall. That is to say, placing the fins on the cold and adiabatic walls increases the thermal performances of the transfer.

### Propulsion by stiff elastic filaments in viscous fluids

Author(s): Panayiota Katsamba and Eric Lauga

Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world. For example, the swimming of bacteria and spermatozoa as well as important physiological functions at organ level, such as the cilia-induced motion of mucus in the lungs, or individual cell level, such as ac...

[Phys. Rev. E 99, 053107] Published Mon May 13, 2019

### Normal and oblique droplet impingement dynamics on moving dry walls

Author(s): K. Ashoke Raman

Industrial applications that depend on jetting-based technology, such as painting or additive layered manufacturing, involve sequential deposition of droplets onto a moving surface. Spreading and receding dynamics of these impinging drops depend on the momentum transferred by the moving wall to the ...

[Phys. Rev. E 99, 053108] Published Mon May 13, 2019

### Characterization of blood velocity in arteries using a combined analytical and Doppler imaging approach

Author(s): Bchara Sidnawi, Zhen Chen, Chandra Sehgal, Sridhar Santhanam, and Qianhong Wu

Using ultrasound Doppler imaging we experimentally and analytically reconstruct the blood flow field in arteries and provide an in−vivo-validated, noninvasive, and reliable Wall Shear Stress (WSS) estimation. WSS is a major mechanical modulator of many functions of the cardiovascular system.

[Phys. Rev. Fluids 4, 053101] Published Mon May 13, 2019

### Maximum entropy modeling of oxygen vibrational excitation and dissociation

Author(s): Jiaao Hao and Chih-Yung Wen

An accurate and efficient model based on the maximum entropy principle is established for the vibrational excitation and dissociation of oxygen. Good agreement with state-specific calculations and recent experimental data is obtained.

[Phys. Rev. Fluids 4, 053401] Published Mon May 13, 2019

### Flow field around a confined active droplet

Author(s): Charlotte de Blois, Mathilde Reyssat, Sébastien Michelin, and Olivier Dauchot

Experimental measurements of the velocity field around a droplet swimming close to a wall demonstrate the critical impact of confinement.

[Phys. Rev. Fluids 4, 054001] Published Mon May 13, 2019

### Mannheimer and Schechter model revisited: Viscosimetry of a (non-)Newtonian and curved interface

Author(s): Kévin Patouillet, Laurent Davoust, Olivier Doche, and Jules Delacroix

Channel viscosimetry makes it possible to estimate surface viscosity of a layer of surfactants or metal oxides. A new model is presented with surface curvature effects accounted for, regardless of whether or not the supporting liquid is wetting or if the contaminated surface is Newtonian.

[Phys. Rev. Fluids 4, 054002] Published Mon May 13, 2019

### Probability of noise-induced separatrix crossing for inertial particles in flows

Author(s): Jean-Régis Angilella

When approaching a recirculation cell, Brownian aerosols can enter the cell or slip along its border or drift away. Determining which particles do what is very challenging. A general analytical expression for the probability of capture of aerosols in such cells is derived.

[Phys. Rev. Fluids 4, 054304] Published Mon May 13, 2019

### Formation of a thin circulation layer in a two-fluid rotating flow

Author(s): Igor V. Naumov, Vladimir G. Glavny, Bulat R. Sharifullin, and Vladimir N. Shtern

An experimental study reveals the formation of a thin circulation layer (TCL) adjacent to the entire interface of a two-fluid swirling flow in a sealed, vertical cylindrical container. The TCL scenario differs from that predicted numerically.

[Phys. Rev. Fluids 4, 054702] Published Mon May 13, 2019

### On the circulation prediction of shock-accelerated elliptical heavy gas cylinders

A theoretical model is presented to predict the circulation generation in the interaction of a shock wave with elliptical heavy gas cylinders with various elongations. The focus is to introduce the interface geometrical relation into circulation modeling. This high-speed multifluid flow is simulated by solving the Navier-Stokes (NS) equations in a finite difference frame. The second-order Strang time-splitting scheme is used to decouple the NS equations into the hyperbolic and parabolic steps. The fifth-order weighted essentially nonoscillatory scheme and the three-order total variation diminishing Runge-Kutta scheme are applied in the hyperbolic step. The fourth-order central difference scheme and the second-order explicit Runge-Kutta-Chebyshev scheme are applied to handle the viscosity term in the parabolic step. Nine elliptical heavy gas interfaces filled with SF6/air mixture are examined under the impact of incident shock with Mach number 1.2. The evolutions of the wave system are presented, and the interfaces are correspondingly classified based on a shock wave competition between the incident shock and the transmitted shock. The distributions of vorticity and generations of circulations on different interfaces are computed. Based on the present numerical results, a unified circulation model is proposed for the elliptical interfaces considering both the interface classification and the geometrical relation between the incident shock and the initial interface. This model is found to provide an accurate prediction of the circulation generation. For the cases being studied, the maximum prediction error is 8%, and the minimum error reaches 1.6%. It highlights the geometric role as an independent factor that played in the interaction of shock with gas inhomogeneities.

### Separation induced low-frequency unsteadiness in a supersonic combustor with single-side expansion

Systematic studies on separation induced low-frequency unsteadiness in a canonical supersonic combustor are implemented through wind tunnel experiment and numerical simulation. With an inflow Mach number of 3, cold flow analysis has been carried out to focus on the key impact factor of flow instability. Dynamic flow features are captured by high-frequency pressure signals, and three-dimensional Reynolds-Averaged Navier-Stokes simulation is performed to represent the typical unsteady movement of the shock train. The separated flowfield shows an intrinsic instability, whose feature is the large-amplitude and low-frequency streamwise movement of the oblique shock train. The oscillation of shock train is in a broadband frequency range, and pressure signals obtained from different streamwise regions behave various features. The intermittent region and the backpressure-affected region are two major resources of oscillation energy. Numerical results represent variable-speed shock train motions with multiple amplitudes, and broadband behaviors in experiments are captured. The autocorrelation analysis shows that the broadband behavior of the unsteadiness is not caused by the white noise. From the coherence analysis, it is found that two kinds of oscillation modes (independent and synchronous) exist in the flowfield. The independent mode exists extensively in the unstable flow, while the synchronous mode only appears occasionally and is always suppressed in the very-low-frequency band (below 80 Hz). Repeated experiments indicate that signals from these two oscillation modes superpose randomly. The phase analysis reveals that the backpressure is the original source of this complicated unstable separated flow.

### Fast flow field prediction over airfoils using deep learning approach

In this paper, a data driven approach is presented for the prediction of incompressible laminar steady flow field over airfoils based on the combination of deep Convolutional Neural Network (CNN) and deep Multilayer Perceptron (MLP). The flow field over an airfoil depends on the airfoil geometry, Reynolds number, and angle of attack. In conventional approaches, Navier-Stokes (NS) equations are solved on a computational mesh with corresponding boundary conditions to obtain the flow solutions, which is a time consuming task. In the present approach, the flow field over an airfoil is approximated as a function of airfoil geometry, Reynolds number, and angle of attack using deep neural networks without solving the NS equations. The present approach consists of two steps. First, CNN is employed to extract the geometrical parameters from airfoil shapes. Then, the extracted geometrical parameters along with Reynolds number and angle of attack are fed as input to the MLP network to obtain an approximate model to predict the flow field. The required database for the network training is generated using the OpenFOAM solver by solving NS equations. Once the training is done, the flow field around an airfoil can be obtained in seconds. From the prediction results, it is evident that the approach is efficient and accurate.

### Resolving vortex-induced pressure fluctuations on a cylinder in rotor wake using fast-responding pressure-sensitive paint

The interaction between rotor wake and a cylinder has been studied experimentally in the current work. The cylinder was placed in close proximity to the rotor plane, and the pressure fluctuations induced by the rotor wake on the cylinder surface were measured by microphones and fast-responding pressure-sensitive paint. Based on the developed data processing methods, challenges such as the low signal-to-noise ratio were resolved and small pressure fluctuations (less than 100 Pa) during the interaction were successfully extracted. The high-resolution vortex-induced pressure field under different blade-cylinder separation distances and rotor collective pitches were compared and analyzed, which clearly showed the effects of tip vortex strength and its evolution. More importantly, for cylinders with different cross section shapes, the pressure footprints left on the surface showed significant distinction in both pressure patterns and overall fluctuation levels. The flat surface would break the structure of the tip vortex and lead to both pressure rise and drop on the surface, while wedge-shaped obstacles would cut the vortex in half and result in two strong pressure drops on both sides. The square cylinder with a 0° installation angle (parallel to the blade) generated the least amount of pressure fluctuation due to its capability of fully breaking the vortex structure during the interaction.

### Suspended particle motion close to the surface of rotating cylindrical filtering membrane

The rotational filtration principle is known as an effective approach to slow the plugging of pores in a cylindrical filtering membrane. The existing applications are based on the study of the Taylor-Couette cell with a weak imposed radial inflow through a rotating inner cylinder. They are mostly related to thin filtration with a high transmembrane pressure. We consider a possible flow mode characterized by a high through-flow rate providing the subcritical liquid rotation within the inner cylinder boundary layer. An interphase interaction model is substantiated for the typical conditions considered and equations of a suspended solid particle motion are obtained in a dimensionless form giving similarity criteria of the problem. A number of benefits can be achieved with using this proposed flow mode when the particle size is one order of magnitude less than the boundary layer thickness. The influence of centrifugal force on the phase slip is the most notable when the particles are of the above size. It is possible, in particular, to exclude the contact of such particles with the membrane surface. The results obtained allow extending the application area of the high performance rotational filtration.