# Latest papers in fluid mechanics

### 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.

### Numerical simulation of self-propelled non-equal sized droplets

In general, external energy is needed to remove a liquid from a solid wall during cooling by dropwise condensation. However, experiments have shown that in some cases, droplets can propel themselves from the wall, without any external energy, due to the coalescence-induced conversion of surface energy to kinetic energy. Several authors have reported scaling analysis combined with an energy balance of kinetic energy, surface energy, and viscous dissipation to estimate whether the droplets can be self-propelled or not. Here, we use numerical simulation to describe the coalescence and self-propelling for nonequal sized droplets based on a finite-volume/front-tracking method and the generalized Navier boundary condition to model the moving contact lines. We find that a slightly smaller contact angle (165°) will give a larger out-of-plane jumping velocity than a superhydrophobic surface (with a contact angle of 180°). Further decreasing the contact angles results in “immobile coalescence.” The speed of the moving contact line does not influence the spontaneous removal process as long as it is large enough to let the contact areas detach. Nonequal sized drops are much more difficult to be spontaneously removed from a wall compared to equal-sized ones. Two spherical drops with a diameter ratio of 2.0 have 60% total usable energy compared to equal-sized ones, and only 0.5% of the total released energy can be effectively used for out-of-plane jumping.

### Effect of heat transfer coefficient, draw ratio, and die exit temperature on the production of flat polypropylene membranes

In this work, a stable numerical scheme has been developed for the 1.5-dimensional film casting model of Silagy et al. [Polym. Eng. Sci. 36, “Study of the stability of the film casting process,” 2614–2625 (1996)] utilizing the viscoelastic modified Leonov model as the constitutive equation and energy equation coupled with the crystallization kinetics of semicrystalline polymers taking into account actual temperature as well as cooling rate. The model has been successfully validated on the experimental data for linear isotactic polypropylene taken from the open literature. Drawing distance, draw ratio, heat transfer coefficient, and die exit melt temperature were systematically varied in the utilized model in order to understand the role of process conditions in the neck-in phenomenon (unwanted film width shrinkage during stretching in the post die area) and crystalline phase development during flat film production. It is believed that the utilized numerical model together with the suggested stable numerical scheme as well as obtained research results can help to understand a processing window for the production of flat porous membranes from linear polypropylene considerably.

### Experimental investigation of drag characteristics of ventilated supercavitating vehicles with different body shapes

This paper presents an experimental investigation on drag characteristics and flow physics of ventilated supercavitating objects with different body shapes. The test model consists of a disk-type cavitator with two different forebodies (slender and blunt shape) and three different rear bodies (flat, shrinkage, and expanded shape). Experiments are conducted in a cavitation tunnel of the Chungnam National University. First, the drag forces acting on different body-combinations in fully wetted conditions are measured. The results show that the drag coefficients strongly depend on the body shapes. It explains in detail through particle image velocimetry measurements. Second, the drag characteristics are systematically examined over a broad range of ventilation rates. The formation and the drag characteristics of the foamy and clear supercavity flow are investigated for different Froude number conditions. The results reveal that the drag of the blunt forebody is smaller than that of the slender fore body in foamy cavity conditions. In ventilated supercavity conditions, supercavity shapes according to Froude numbers are examined and corresponding effects on drag characteristics are analyzed. The results show that the drag coefficients of the models with the expanded rear body are larger than that of models with the flat and shrinkage rear bodies until the cavity covers the body.

### Stokes-layer formation under absence of moving parts—A novel oscillatory plasma actuator design for turbulent drag reduction

A novel plasma actuator concept is proposed to mimic the effect of spanwise wall oscillations without mechanically moving parts, where four groups of electrodes and three independently operated high-voltage power supplies maintain a pulsatile dielectric barrier discharge (DBD) array. Time-resolved planar velocity fields are obtained with high-speed particle image velocimetry (PIV) in proximity of the discharge zones for quiescent ambient conditions. Resulting flow topologies and wall-normal velocity profiles indicate the Stokes-layer-like flow formation, which is elevated above the wall due to the no-slip condition. The underlying body forces are derived from the PIV data to provide further insight into cause-effect relations between pulsatile discharge and oscillatory flow. The momentum transfer domain is found to be only interrupted with the width of the exposed electrode, which is an important step toward homogeneous virtual wall oscillations. A comparison with earlier studies by Gatti et al. [“Experimental assessment of spanwise-oscillating dielectric electroactive surfaces for turbulent drag reduction in an air channel flow,” Exp. Fluids 56, 110 (2015)] leads to the hypothesis that DBD-based turbulent drag reduction might be a competing alternative to conventional active and passive shear-layer formation strategies, where the adjustability of both oscillation frequency and velocity amplitude might cover a wide range of Reynolds numbers.

### Hypersonic aerodynamic heating over a flared cone with wavy wall

The influence of a wavy wall on the hypersonic boundary layer transition and the related aerodynamic heating is investigated on a flared cone at a range of unit Reynolds numbers. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, and infrared thermography. The results show that compared to the smooth-wall cone, the wavy-wall one can suppress the second-mode instability to a certain degree and eliminate the local heating spot before transition is completed (denoted as HS). These verify our recent work on aerodynamic heating that HS is caused by the second-mode instability.

### Three-dimensional simulation of oblique detonation waves attached to cone

Author(s): Wenhu Han, Cheng Wang, and Chung K. Law

A numerical simulation finds that a three-dimensional conical oblique wave takes on a cellular structure on the front, presenting a fish-scale shape. The cell shape becomes relatively irregular as the heat release is increased.

[Phys. Rev. Fluids 4, 053201] Published Fri May 10, 2019

### Capillary filtering of particles during dip coating

Author(s): Alban Sauret, Adrien Gans, Bénédicte Colnet, Guillaume Saingier, Martin Z. Bazant, and Emilie Dressaire

We develop a passive method of soft filtration which leverages interfacial forces to prevent the contamination of substrates withdrawn from a liquid polluted by microparticles and micro-organisms.

[Phys. Rev. Fluids 4, 054303] Published Fri May 10, 2019

### Passive directors in turbulence

Author(s): L. Zhao, K. Gustavsson, R. Ni, S. Kramel, G. A. Voth, H. I. Andersson, and B. Mehlig

With experiments and direct numerical simulations we study the angular distribution of symmetry axes of nearby small spheroids in a turbulent flow when inertial effects are negligible. We find the angles to be unexpectedly large with a fractal attractor and a distribution with power law tails.

[Phys. Rev. Fluids 4, 054602] Published Fri May 10, 2019

### Predictions of turbulent shear flows using deep neural networks

Author(s): P. A. Srinivasan, L. Guastoni, H. Azizpour, P. Schlatter, and R. Vinuesa

The long short-term memory (LSTM) neural network is used to predict the temporal evolution of a low-order representation of near-wall turbulence. This network leads to excellent predictions of turbulence statistics and of the system dynamics, characterized by Poincaré maps and Lyapunov exponents.

[Phys. Rev. Fluids 4, 054603] Published Fri May 10, 2019

### An experimental study on the effect of swirl number on pollutant formation in propane bluff-body stabilized swirl diffusion flames

The combustion characteristics of propane/air bluff-body stabilized swirl diffusion flames within the turbulent regime are studied experimentally to determine the effect of the swirl number on the flame dynamics and pollutant emissions. The investigated burner consists of a central bluff body with an annulus to introduce the tangential and axial air flows. Results show that in low annulus Reynolds numbers (ReS), the temperature distribution is more affected by the overall equivalence ratio (φo), which is calculated based on the flow rates of the air supplies and the fuel jet. However, by increasing ReS, the impact of swirl number becomes more apparent. Analysis of the combustion products demonstrates a reduction in CO concentration with increasing the geometric swirl number which becomes more evident in higher annulus Reynolds numbers. In addition, the trend of NO emission is strongly analogous to the temperature distribution which is an indication of thermal NO formation. Measurements demonstrate that in lower annulus Reynolds numbers, the dominant factor is the overall equivalence ratio, while with increasing the annulus Reynolds number, the swirl number represents more significance.

### On the suppression and distortion of non-equilibrium fluctuations by transpiration

A fluid in a nonequilibrium state exhibits long-ranged correlations of its hydrodynamic fluctuations. In this article, we examine the effect of a transpiration interface on these correlations—specifically, we consider a dilute gas in a domain bisected by the interface. The system is held in a nonequilibrium steady state by using isothermal walls to impose a temperature gradient. The gas is simulated using both direct simulation Monte Carlo (DSMC) and fluctuating hydrodynamics (FHD). For the FHD simulations, two models are developed for the interface based on master equation and Langevin approaches. For appropriate simulation parameters, good agreement is observed between DSMC and FHD results with the latter showing a significant advantage in computational speed. For each approach, we quantify the effects of transpiration on long-ranged correlations in the hydrodynamic variables. The principal effect of transpiration is a suppression of the correlations, an outcome largely explained by a reduction in the temperature gradient due to the interface. We also observe a distortion of the temperature correlations, specifically the appearance of a new peak located near the interface.

### Orthogonal wavelet multiresolution analysis of the turbulent boundary layer measured with two-dimensional time-resolved particle image velocimetry

Author(s): Guosheng He, Jinjun Wang, and Akira Rinoshika

The turbulent boundary layer flow measured by two-dimensional time-resolved particle image velocimetry is analyzed using the discrete orthogonal wavelet method. The Reynolds number of the turbulent boundary layer based on the friction velocity is Reτ=235. The flow field is decomposed into a number o...

[Phys. Rev. E 99, 053105] Published Thu May 09, 2019