# Latest papers in fluid mechanics

### Effects of inner bubble on liquid jet breakup

In this study, the effects of the bubble on the liquid jet breakup process were investigated using a high-speed camera. The liquid jet containing bubbles revealed a considerable decrease in the breakup length when compared with the water jet without bubbles, which promoted the atomization performance significantly. Theoretical analysis was based on the classical linear stability theory and the equivalence of the initial jet diameter and velocity disturbance amplitude. We deduced a correlation between the breakup length ratio and the diameter of the bubbles, and the theoretical results showed good agreement with our experimental results. Our results also showed that the property of gas affected the breakup process of the liquid jet containing bubbles. The experimental findings indicated that lighter gases could realize a more significant decrease in the breakup length, which could then be attributed to the conservation of momentum of the fluid.

### The control of flow separation: Study of optimal open loop parameters

Effective parameters in active flow control (AFC) have been studied to clarify a perspective of AFC. In particular, NACA0015 airfoil has been chosen for this study. Fluidic devices such as a synthetic jet actuator (SJA) have been considered because these can enforce two main control parameters of AFC, frequency and momentum ratio, but fluidic excitation with complete blowing and suction cycle was applied with the harmonic excitation as the boundary condition. Flows around the NACA0015 airfoil were simulated for a range of operating conditions. Attention was paid to the active open loop control for the flow separation of the airfoil with SJA at different angles of attack and flap angles. A large number of simulations using unsteady Reynolds averaged Navier-Stokes and large eddy simulation models were performed to study the effects of momentum ratio (Cμ) in the range of 0% to 11% and non-dimensional frequency, F+, in the range of 0–2 for the control of flow separation at the various angles of attack. The optimum value of Cμ as well as F+ was evaluated and discussed. The computational model predictions showed good agreement with several experimental data available such as NASA Langley, Texas A&M, and Clarkson University. It was observed that different angles of attack and flap angles have different requirements for the minimum value of the momentum coefficient, Cμ, for the SJA to be effective for control of separation. It was also found that the variation of F+ noticeably affects the lift and drag forces acting on the airfoil. An intuitive analogy was introduced to evaluate the optimum momentum ratio in AFC, and the results of the optimum momentum ratio have been presented in comparison with available literature data.

### Unlikely existence of [math] spectral law in wall turbulence: An observation of the atmospheric surface layer

For wall turbulence, a range of streamwise wavenumbers kx has been predicted such that the spectral density of streamwise velocity fluctuations is proportional to [math]. The existence or nonexistence of this [math] law is examined here. We observe the atmospheric surface layer over several months, select suitable data, and use them to synthesize the energy spectrum that would represent wall turbulence at a very high Reynolds number. The result is not consistent with the [math] law. It is, rather, consistent with a recent correction to the prediction of a model of energy-containing eddies that are attached to the wall. The reason for these findings is discussed mathematically.

### Transport dynamics of an ellipsoidal particle in free molecular gas flow regime

Translational and rotational dynamics of a transporting particle in the free molecular gas flow regime are investigated using an in-house, multi-species, three dimensional Direct Simulation Monte Carlo (DSMC) solver. The DSMC algorithm is modified to study free molecular gas flows and validated against the analytical results for the dynamics of a spherical particle. A particular focus of this work is on estimating the effects of particle size, shape, and orientation on the dynamics of an ellipsoidal particle in free molecular gas and comparing them with that of a spherical particle. Properties such as particle speed, temperature, drag, and heat transfer coefficients are considered for comparison. The effect of particle shape on the aforesaid properties is qualitatively discussed and quantified through a comprehensive analysis taking care of lift, pitching moment, particle rotation, and the associated resistive torque. The relaxation of an ellipsoidal particle to surrounding gas conditions is simulated at zero and non-zero angles of attack to demonstrate the effect of particle orientation. Furthermore, the particle size effect on its translational and rotational dynamics is discussed. Finally, the trajectory of a spherical particle is compared with that of an ellipsoidal particle at different eccentricities.

### Red blood cell and platelet diffusivity and margination in the presence of cross-stream gradients in blood flows

The radial distribution of cells in blood flow inside vessels is highly non-homogeneous. This leads to numerous important properties of blood, yet the mechanisms shaping these distributions are not fully understood. The motion of cells is governed by a variety of hydrodynamic interactions and cell-deformation mechanics. Properties, such as the effective cell diffusivity, are therefore difficult to investigate in flows other than pure shear flows. In this work, several single-cell, cell-pair, and large-scale many-cell simulations are performed using a validated numerical model. Apart from the single-cell mechanical validations, the arising flow profile, cell free layer widths, and cell drift velocities are compared to previous experimental findings. The motion of the cells at various radial positions and under different flow conditions is extracted, and evaluated through a statistical approach. An extended diffusive flux-type model is introduced which describes the cell diffusivities under a wide range of flow conditions and incorporates the effects of cell deformability through a shear dependent description of the cell collision cross sections. This model is applicable for both red blood cells and platelets. Further evaluation of particle trajectories shows that the margination of platelets cannot be the net result of gradients in diffusivity. However, the margination mechanism is strongly linked to the gradient of the hematocrit level. Finally, it shows that platelets marginate only until the edge of the red blood cell distribution and they do not fill the cell free layer.

### Smoothed particle hydrodynamics (SPH) model for coupled analysis of a damaged ship with internal sloshing in beam seas

The flooding of a damaged ship in waves is a complex process, often coupled with the internal and external liquid motion together with the ship hull motion. Paramount to the operation safety, in order to improve the prediction accuracy of ship motion during the flooding process, the strip theory is applied to study the dynamic response of the damaged ship in beam seas; a smoothed particle hydrodynamics (SPH) model is developed to consider the coupling effects of various factors including internal sloshing of intact cabins and damaged cabins and external waves. The numerical wave tank with a perfectly matched layer absorbing boundary condition is established and validated by the experimental results. The detailed sensitivity study is carried out focusing on the effects of damaged opening sizes, the relative position of opening, and the incident wave and the liquid loading conditions on the dynamic response of the damaged ship in regular beam waves. It is observed that the flooding process was slowed down and interrupted by the water exchanges at the damaged opening due to the dynamic motion. Compared with the opening facing the incident wave, the back one endangered the ship pronouncedly with large amplitude and frequency roll motion. It is also revealed that the liquid tank in the damaged ship imposes a significant influence on its rolling response. It is further demonstrated that the present SPH model is capable of handling the nonlinear phenomenon in a flooding process of a damaged ship.

### Numerical modeling of the acoustically driven growth and collapse of a cavitation bubble near a wall

This paper describes the first high-order accurate, fully compressible, multiphase model to simulate the expansion and collapse of a near-wall cavitation bubble in a low-frequency ultrasound field. The model captures the compressibility of the fluids, subsequent shocks, and a physically correct representation of the acoustic input through an immersed moving boundary that represents the active face of the ultrasound transducer face. The model’s predictions of bubble dynamics are compared to existing models that are able to capture the collapse of a near wall bubble, (1) the Rayleigh growth and collapse model and (2) the Rayleigh-Plesset growth initialized collapse model, highlighting the limitations of the previously developed models.

### Why do wet-particles adhere to a high-speed roll in a three-roll mill?

A three-roll mill is used in various engineering fields to manufacture high-value-added products. This mill has three horizontally positioned rolls with different rotational velocities. In the mill, viscous materials (or pastes) pass through the narrow gap between the rolls to be mixed, refined, dispersed, and/or homogenized. The viscous materials tend to consist of wet-particles connected by liquid bridges. Although viscous materials always adhere to a faster roll in the three-roll mill, the mechanism has not yet been clarified. Herein, the adhesion mechanism is clarified scientifically by numerical simulation. In the calculations, a Lagrangian method, such as the discrete element method, is used to analyze the specific phenomena in the particle–particle and the particle–wall interaction. A latest liquid bridge force model is used in this study to examine the effect of a wide range of liquid volumes on the adhesion phenomena. In the calculation, a lump of wet-particles is fed into the gap between the two rolls and the roll speed is changed to investigate its influence on the adhesion phenomena. Through numerical examples, it is proven that wet-particles always adhere to a fast roll because the liquid bridge force that acts on the faster roll is larger than that on the slower roll after the compression force is released. This is because the extension of the wet-particles is larger on the faster roll because of the speed difference between the two rolls. Consequently, the adhesion mechanism of the wet-particles in the three-roll mill is proven scientifically to be the force balance due to the liquid bridge force.

### Stability analysis of a thin film on a rotating cylinder with low airflow

This paper studies the operating conditions of a novel pesticide applicator, by analyzing the stability of a thin film on a rotating horizontal cylinder in the presence of low airflow. The analysis shows that the film is destabilized by the airflow, with a few notable further findings. First, when the airflow coincides with the angular velocity at the underside of the cylinder, the film becomes unstable at smaller wind speeds compared to airflow anti-parallel to the angular velocity. Second, in the absence of surface tension, the thin film model does not have a stable stationary state. The solution settles into an oscillatory state instead. Finally, an analytical solution is presented for the special case where the initial condition is a uniform film thickness. When surface tension is included in this analysis, the temporal terms decay when the stability condition is satisfied. Some of the modes decay very slowly, as confirmed by the multiple time scale analysis.

### Mechanism study of coupled aerodynamic and thermal effects using plasma actuation for anti-icing

Anti-icing performance using the surface dielectric barrier discharge plasma actuator is studied using detailed visualization and surface thermal measurements. To reveal the physical mechanism of coupled aerodynamic and thermal effects on anti-icing, three types of actuators are designed and mounted on a NACA 0012 airfoil. The coupled aerodynamic and thermal effects are confirmed in still air. The results show that the plasma actuation is effective for in-flight anti-icing, and the anti-icing performance is directly related to the design of the plasma actuators based on the coupled aerodynamic and thermal effects. When the direction of plasma induced flow is consistent with the incoming flow, the heat generated by plasma discharge is concentrated in the region of the actuator and the ability of the actuator for heat transfer downstream is relatively weak during the anti-icing. When the induced flow is opposite to the incoming flow, there is less heat accumulation in the actuator region, while the ability of heat transfer downstream becomes stronger. With the consistent and opposite direction of induced flow, the plasma actuation can ensure that 57% and 81% chord of the lower surface of the airfoil are free of the ice accumulation, respectively. Another actuator is designed to induce the air jets approximately perpendicular to the airfoil surface. This exhibits both a stronger ability of heat accumulation locally and heat transfer downstream and hence ensures that there is no ice on the entire lower surface of the airfoil.

### Generation of a magnetic field by a double vortex in a rotating cylinder

Author(s): M. C. Navarro, D. Castaño, and H. Herrero

In this paper we use simulations of the magnetohydrodynamic equations coupled with heat to show the generation of magnetic field by the dynamical interaction of a pair of vortices in a fluid electrically conducting within a cylindrical domain nonhomogeneously heated from below, setting in a rotation...

[Phys. Rev. E 99, 033109] Published Mon Mar 11, 2019

### Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration

Author(s): G. Boffetta, M. Magnani, and S. Musacchio

The dynamics of Rayleigh-Taylor turbulence convection in the presence of an alternating, time-periodic acceleration is studied by means of extensive direct numerical simulations of the Boussinesq equations. Within this framework, we discover a mechanism of relaminarization of turbulence: the alterna...

[Phys. Rev. E 99, 033110] Published Mon Mar 11, 2019

### Wall slip regimes in jammed suspensions of soft microgels

Author(s): Justin Péméja, Baudouin Géraud, Catherine Barentin, and Marie Le Merrer

The slip velocity of jammed polymer microgels is measured as the wall stress is increased by 4 orders of magnitude. The friction law exhibits a transition in slip regimes, from a nonlinear to a linear scaling, linked to two distinct dissipation mechanisms at the scale of the soft elements.

[Phys. Rev. Fluids 4, 033301] Published Mon Mar 11, 2019

### Enhanced and suppressed multiscale dispersion of bidisperse inertial particles due to gravity

Author(s): Rohit Dhariwal and Andrew D. Bragg

Direct numerical simulations are used to study the relative dispersion of settling, bidisperse inertial particles in isotropic turbulence. It is found that gravity can significantly enhance the relative dispersion, not only in the direction parallel, but even in the direction normal to gravity.

[Phys. Rev. Fluids 4, 034302] Published Mon Mar 11, 2019

### Experimental study of the parameters for stable drop-on-demand inkjet performance

We present an experimental study of drop-on-demand inkjet behavior, with particular emphasis on the thresholds for drop generation and formation of satellite drops, using inks covering a range of fluid properties. Drop behavior can be represented as a “phase diagram” in a parameter space bound by the dimensionless number Z (the inverse of the Ohnesorge number) and the Weber number of the fluid jet prior to drop formation, Wej. Stable drop generation is found to be bounded by a parallelogram with minimum and maximum values of 2 < Wej < 25. The lower bound indicates where capillary forces prevent drop ejection, and the upper bound indicates the onset of satellite drop formation. For Z < 50, the critical Wej for drop ejection increases with decreasing Z because of the contribution of viscous dissipation during drop formation. This requires an increase in the voltage required to drive the piezoelectric actuator until at Z ≈ 0.3 no drop ejection is possible. With Z > 4, the value of Wej at which satellite drops form decreases with increasing Z until at very large values of Z single drops can no longer form at any Wej. However, despite the large range of fluid properties over which stable drops can form, the need for a large range of both Z and Wej limits the region of practical ink design to the approximate range of 2 < Z < 20. These results are shown to be compatible with current models of the drop formation process reported in the literature.

### Transition from convection rolls to large-scale cellular structures in turbulent Rayleigh-Bénard convection in a liquid metal layer

Author(s): Megumi Akashi, Takatoshi Yanagisawa, Yuji Tasaka, Tobias Vogt, Yuichi Murai, and Sven Eckert

A new coherent structure appears on turbulent Rayleigh-Bénard convection in a liquid metal layer; transitions to large-scale cellular structures from oscillatory roll structures occur with Rayleigh numbers. A scaling law describing characteristic length of the structures is suggested.

[Phys. Rev. Fluids 4, 033501] Published Fri Mar 08, 2019

### Evaluation of potential flow models for unsteady separated flow with respect to experimental data

Author(s): Field Manar and Anya R. Jones

Wake characteristics and force production of a flat plate wing starting from rest at high incidence are examined. Circulation production at the wing leading edge is shown to be coupled to wing kinematics and the wake state. Several potential flow models are compared to experiments.

[Phys. Rev. Fluids 4, 034702] Published Fri Mar 08, 2019

### Erratum: “Experimental investigation of shock oscillations on V-shaped blunt leading edges” [Phys. Fluids 31, 026110 (2019)]

### Boundary integral simulations of a red blood cell squeezing through a submicron slit under prescribed inlet and outlet pressures

We developed a boundary integral formulation to simulate a red blood cell (RBC) squeezing through a submicron slit under prescribed inlet and outlet pressures. The main application of this computational study is to investigate splenic filtrations of RBCs and the corresponding in vitro mimicking microfluidic devices, during which RBCs regularly pass through inter-endothelial slits with a width less than 1.0 µm. The diseased and old RBCs are damaged or destroyed in this mechanical filtration process. We first derived the boundary integral equations of a RBC immersed in a confined domain with prescribed inlet and outlet pressures. We applied a unified self-adaptive quadrature to accurately evaluate singular and nearly singular integrals, which are especially important in this fluid-structure interaction problem with strong lubrication. A multiscale model is applied to calculate forces from the RBC membrane, and it is coupled to boundary integral equations to simulate the fluid-structure interaction. After multi-step verifications and validations against analytical and experimental results, we systematically investigated the effects of pressure drop, volume-to-surface-area ratio, internal viscosity, and membrane stiffness on RBC deformation and internal stress. We found that spectrins of RBCs could be stretched by more than 2.5 times under high hydrodynamic pressure and that the bilayer tension could be more than 500 pN/μm, which might be large enough to open mechanosensitive channels but too small to rupture the bilayer. On the other hand, we found that the bilayer-cytoskeletal dissociation stress is too low to induce bilayer vesiculation.

### Viscoelastic planar elongational flow past an infinitely long cylinder

Following our previous work [K. D. Housiadas and R. I. Tanner, “Viscoelastic shear flow past an infinitely long and freely rotating cylinder,” Phys. Fluids 30, 073101 (2018)], we study analytically the effect of steady planar elongational flow past an infinitely long circular cylinder using asymptotic methods. The ambient fluid is assumed viscoelastic and modelled with the Upper Convected Maxwell, Oldroyd-B, exponential Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic model with the Peterlin approximation constitutive equations under isothermal and creeping flow conditions. The solution for all the dependent variables is expanded as an asymptotic power series with the small parameter being the Weissenberg number, Wi, which is defined as the product of the single relaxation time of the fluid times the constant rate of elongation. The resulting sequence of equations is solved analytically up to fourth order in the Weissenberg number. The solution derived here is the first analytical result in the literature for the planar elongational flow of viscoelastic fluids past a cylinder. It reveals the effect of viscoelasticity and all the relevant rheological parameters on the flow variables and the extensional viscosity of the fluid.