# Latest papers in fluid mechanics

### A lattice Boltzmann study of rarefied gaseous flow with convective heat transfer in backward facing micro-step

Rarefied pressure-driven gaseous flow with heat transfer in a microchannel with a backward facing micro-step is investigated in this paper using the lattice Boltzmann method (LBM) in slip and transition flow regimes. In a novel approach, a two-relaxation-time LB equation is used to solve the flow velocity and the single-relaxation-time to handle the heat transfer. The asymmetric relaxation time is determined by equating the analytical second-order slip velocity boundary condition and the slip velocity obtained from applying the implemented bounce back specular boundary condition in the LBM. A second-order implicit temperature jump boundary condition is also implemented to capture the rarefaction effect on the fluid temperature at walls. Velocity slip, temperature jump, centerline temperature, and Nusselt number variations are evaluated for channels with and without the micro-step for a wide range of the Knudsen number. Effects of the micro-step on the rarefied gaseous flow and convective heat transfer are evaluated and discussed. The numerical model is verified by comparing with direct simulation Mont Carlo results.

### Thermal fluctuations and boundary layer properties of turbulent natural convection inside open cavities of different dimensions heated from below

We report the experimental measurement of the temperature fluctuation in the vicinity of different zones of the thermal boundary layer in water-filled open cubic cavities heated from below and open at the top. The experiments are performed on the cubic cavity of aspect ratio 1 and lateral dimension 30 mm; the results of our previously reported open cubic cavities of aspect ratio 1 and lateral dimensions (120 mm and 240 mm) are also considered here. The transient nature of the temperature has been measured from the temperature–time series recorded across the central axis of the cavity at different vertical positions z from the heated bottom plate. The Prandtl number and Rayleigh number ranges reported in this paper are 4 ≤ Pr ≤ 6 and 105 ≤ Ra ≤ 109, respectively. The different basic statistical properties, of temperature fluctuation such as mean temperature, root mean square, and probability density function, are studied and discussed. The power-law of power spectral density of the temperature fluctuations at different regions of the thermal boundary layer is studied, and the different roles of rate are compared with the previously established theories and models. The validity criteria for the Oberbeck–Boussinesq approximation are fulfilled. The trend of the dimensionless Nusselt number (Nu) representing the global convective heat transfer is obtained and discussed. We also study the variation in [math] for the heat transfer representation in the range of 0.04–0.24, where δth is the boundary layer thickness.

### Phase boundary dynamics of bubble flow in a thick liquid metal layer under an applied magnetic field

Author(s): Mihails Birjukovs, Valters Dzelme, Andris Jakovics, Knud Thomsen, and Pavel Trtik

Dynamic neutron radiography is used to observe the effect of a transverse magnetic field on argon bubbles rising through a thick layer of liquid gallium without interactions with the container walls.

[Phys. Rev. Fluids 5, 061601(R)] Published Thu Jun 18, 2020

### Oscillation in the temperature profile of the large-scale circulation of turbulent convection induced by a cubic container

Author(s): Dandan Ji and Eric Brown

In turbulent Rayleigh-Bénard convection in a cubic cell, a new oscillation is found in the temperature profile shape of the large-scale circulation (LSC). This geometry dependence is explained by a model which assumes that heat conducted to the LSC from thermal boundary layers is proportional to the LSC path length along the boundary layers at the top and bottom plates. In a non-circular cross-section cell, oscillations of the flow orientation around a corner lead to container shape oscillations in the LSC reference frame, and thus a path length oscillation of the LSC.

[Phys. Rev. Fluids 5, 063501] Published Thu Jun 18, 2020

### Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

Author(s): Alejandro Martinez-Cava, Miguel Chávez-Modena, Eusebio Valero, Javier de Vicente, and Esteban Ferrer

A discrete framework to calculate eigenvalue sensitivity gradients to geometrical changes is introduced and applied to the compressible Navier-Stokes equations. The novel formulation is used to control global instabilities in compressible turbulent flow scenarios, modeled through Reynolds-averaged Navier-Stokes approaches. The sensitivity gradients are exploited to include local surface deformations that delay or enhance the onset of instabilities and can modify their associated frequency.

[Phys. Rev. Fluids 5, 063902] Published Thu Jun 18, 2020

### Study on stretching liquid bridges with symmetric and asymmetric surface wettability

Author(s): Jiayi Zhao, Nan Zhou, Kaixuan Zhang, Shuo Chen, and Yang Liu

The rupture process of stretching liquid bridges is determined by competition between contact line slip velocity and liquid bridge thinning velocity. Poorer surface wettability and larger stretching velocity help increase slip velocity and enable the liquid bridge to slip off surfaces. In addition, the shift moment of minimal radius of stretching liquid bridges is related to surface wettability, regardless of plate stretching velocity. Finally, satellite drop formation is related to the sequential order of appearance of the liquid bridge slipping off the plate and the breakup of the filament.

[Phys. Rev. Fluids 5, 064003] Published Thu Jun 18, 2020

### Large eddy simulations of wall jets with coflow for the study of turbulent Prandtl number variations and data-driven modeling

Author(s): Ali Haghiri and Richard D. Sandberg

A machine-learning technique is used to develop data-driven models for turbulent heat flux prediction in wall jets with co-flow The training data are obtained by performing highly-resolved large-eddy simulations of nine cases covering various flow and geometry conditions. Robust Reynolds-averaged Navier-Stokes based heat-transfer closures are obtained, and a significant error reduction in predicting adiabatic wall effectiveness is achieved using the machine-learnt models.

[Phys. Rev. Fluids 5, 064501] Published Thu Jun 18, 2020

### Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: The effect of slope

Author(s): Yaokun Zheng, Zhiliang Lin, Yan Li, T. A. A. Adcock, Ye Li, and T. S. van den Bremer

Recent studies of surface gravity waves propagating over a sloping bottom have shown that an increase in the probability of extreme waves can be triggered by depth variations in sufficiently shallow waters. A boundary element method is used to show that this increase in probability is greatest when the slope is steepest, i.e., for a step. A harmonic separation technique shows that the second-order terms in wave steepness are responsible for the change in the statistical properties near the depth transition.

[Phys. Rev. Fluids 5, 064804] Published Thu Jun 18, 2020

### Resistance of velocity slip flow in pipe/channel with a sudden contraction

A novel approach based on the local entropy generation rate, also known as the second law analysis (SLA), is proposed to compute and visualize the flow resistance in mass transfer through a pipe/channel with a sudden contraction component (SCC) at low Reynolds number (Re) featuring velocity slip. The linear Navier velocity slip boundary condition is implemented using the explicit scheme. At small Reynolds number, i.e., Re ≤ 10.0, the flow resistance coefficient of the SCC, KSCC, is found to be a function of the dimensionless velocity slip length [math] and Re−1, and gradually increase to a constant value at contraction ratio Rarea ≥ 8, reaching a formula [math]. Over this range of Re, the equivalent length of the flow resistance is almost independent of Re, while out of this range, the equivalent length increases monotonically with Re. Moreover, the dimensionless drag force work around the SCC is negative and reaches a minimum at a critical [math]. The SLA reveals that the regions affected by the SCC mainly concentrate around the end section of the upstream pipe/channel rather than the initial partition of the downstream section reported in large Re turbulent flow, and this non-dimensional affected upstream length increases with [math]. The fluid physics are further examined using SLA to evaluate the energy loss over the entire domain, decomposed as the viscous dissipation inside the domain and the drag work on the wall boundary.

### Nonlinear evolution of interacting sinuous and varicose modes in plane wakes and jets: Quasi-periodic structures

A plane wake or jet supports sinuous and varicose instability modes. The nonlinear interaction between them following their linear development was described previously by Leib and Goldstein [“Nonlinear interaction between the sinuous and varicose instability modes in a plane wake,” Phys. Fluids A 1, 513–521 (1989)] using the strongly nonlinear non-equilibrium critical-layer approach in the case of the Bickley jet for which the frequencies of the sinuous and varicose modes have an integer ratio of 2. This paper develops the theory for general profiles where the frequencies of the sinuous and varicose modes are non-commensurable. The disturbance is quasi-periodic in time and space and must be expressed as a function of two phase variables. Using matched asymptotic expansions simultaneously with the multi-scale method, we derived a set of coupled evolution equations governing the development of the amplitudes and critical-layer vorticities of these modes. The evolution system is solved for the base-flow profiles mimicking those in experiments. The sinuous mode suppresses the varicose mode but also causes the latter to saturate in a highly oscillatory manner. The varicose mode inhibits the sinuous mode initially. However, in the later stage, it lends the sinuous mode a significantly higher saturating amplitude. For a wide range of initial modal compositions and Reynolds numbers, the ratio of the varicose mode amplitude to that of the sinuous mode eventually tends to an almost constant value in the range of 0.4–0.6, in line with the experimental measurement. Due to the self and mutual interactions, the vorticities roll up to form vortices, which are non-symmetric in the transverse direction and quasi-periodic in the streamwise direction as well as in time. With such an increased complexity, the vortices resemble those observed in experiments. The nonlinear interactions of the sinuous and varicose modes in the critical layer generate all harmonics in the main layer, as a result of which the perturbation is non-periodic and may even appear “random-like.”

### On the dynamics of Richtmyer–Meshkov bubbles in unstable three-dimensional interfacial coherent structures with time-dependent acceleration

Richtmyer–Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical RMI is induced by a steady shock and impulsive acceleration, whereas in realistic environments, the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to study the dynamics of regular bubbles. For early time linear dynamics, we find the dependence of the growth rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time nonlinear dynamics, we consider regular asymptotic solutions, find a continuous family of such solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear. The non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that the dynamics of nonlinear RM bubbles is characterized by two macroscopic length scales: the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined. These are the flat Atwood bubble, the curved Taylor bubble, the minimum shear bubble, the convergence limit bubble, and the critical bubble. We elaborate new theory benchmarks for future experiments and simulations.

### Zero-shear viscosity of Fraenkel dumbbell suspensions

Whereas rigid dumbbell suspensions predict, at least qualitatively, most of the viscoelastic material functions measured in the laboratory, Hookean dumbbells predict few of these. For instance, whereas rigid dumbbells predict a shear-thinning viscosity curve, as they should, Hookean dumbbells yield a constant for the steady shear viscosity. In this paper, we explore the addition of a Hookean spring to the end of a rigid rod, a dumbbell attributed to Fraenkel. In this way, we focus our attention on how macromolecular extensibility affects the configuration distribution in steady shear flow. We arrive at the exact solution to this configuration distribution in steady shear flow at low shear rate and then insert it into the Giesekus expression for the stress tensor to arrive at an exact solution for the zero-shear viscosity and the zero-shear values of the normal stress differences.

### A new insight on a mechanism of airborne and underwater sound of a drop impacting a liquid surface

We report on an experimental study of the impact of a water drop on a liquid surface in the regime of the so-called irregular entrainment. The hydrodynamics of the phenomenon has been correlated finely to the features of the acoustic signal, both underwater and in the air, thanks to the synchronization of images and sounds in a home-made setup. If the origin of the acoustic signal is known to be caused by the capture of a bubble during the hydrodynamic flow following the impact, for the first time, a new mechanism responsible for the formation of the air bubble is highlighted. The latter is caused by the closing, like a liquid zipper, of the cavity induced by the retraction of the Rayleigh jet, by a secondary droplet detached from this jet. The comparison of the experimental data with the Minnaert model and plane wave theories reveals: (i) the time-dependence of the instantaneous oscillation frequency, (ii) a dominant frequency about 30% higher than the Minnaert prediction, (iii) a higher damping characteristic time, and (iv) a two orders of magnitude higher water–air transmission coefficient. All these results can be explained by the proximity of the bubble to the air–water interface, and by the too small dimensions of the tank to avoid underwater echoes in the measured underwater signal.

### Effect of surfactant and evaporation on the thin liquid film spreading in the presence of surface acoustic waves

A theoretical model of a liquid film flow in the presence of surface acoustic waves (SAWs) is established by involving the effects of an insoluble surfactant and evaporation on the spreading process of the partially wetting thin liquid film. A numerical simulation is performed to investigate the liquid film spreading dominated by the SAWs-induced drift of mass and the capillary stress. The simulated results show that SAWs drive liquid films to spread and move, and surfactants promote the further spreading and movement of liquid films, while liquid evaporation suppresses the spreading and movement. The inhibiting contribution of liquid evaporation to the liquid film dynamics is greater than the promoting contribution of the surfactant in this simulation. The mass loss of the liquid film caused by evaporation leads the spreading range to gradually retract. In addition, the spreading range has a positive correlation with the coefficient between the disjoining pressure and surfactant concentration and has a negative correlation with the Marangoni number. The spreading stability of liquid films is strengthened by the surfactant effect, while it is weakened by the evaporation effect.

### Influence of liquid properties on the oblique splashing threshold of drops

This report investigates how different splashing mechanisms affect the oblique splash threshold of drops impacting a dry solid surface. The splashing behaviors of water, ethanol, and a water/ethylene glycol solution are observed over a wide range of drop diameters (0.7 mm < D < 2.2 mm) and Weber numbers (10 < We < 1040), and several published models are tested in order to predict the thresholds between deposition, one-sided splashing, and two-sided splashing. We found that the splash threshold of liquids that exhibit the corona splashing mechanism can be readily predicted by existing models. However, for liquids such as water that exhibit prompt splashing, the oblique splash threshold is not successfully predicted by any presently established correlation. Hence, our findings identify a critical knowledge gap in the drop impact field, since the behavior of water is of fundamental importance to countless engineering problems. Finally, combining our own results with others reported in the literature, we address some contradictory reports about the influence of liquid viscosity on the splash threshold and demonstrate that the presence or lack of thin-sheet in different experiments could explain the contradictions present in the literature.

### Complex system approach to investigate and mitigate thermoacoustic instability in turbulent combustors

Thermoacoustic instability in turbulent combustors is a nonlinear phenomenon resulting from the interaction between acoustics, hydrodynamics, and the unsteady flame. Over the years, there have been many attempts toward understanding, prognosis, and mitigation of thermoacoustic instabilities. Traditionally, a linear framework has been used to study thermoacoustic instability. In recent times, researchers have been focusing on the nonlinear dynamics related to the onset of thermoacoustic instability. In this context, the thermoacoustic system in a turbulent combustor is viewed as a complex system, and the dynamics exhibited by the system is perceived as emergent behaviors of this complex system. In this paper, we discuss these recent developments and their contributions toward the understanding of this complex phenomenon. Furthermore, we discuss various prognosis and mitigation strategies for thermoacoustic instability based on complex system theory.

### Dual vortex breakdown in a two-fluid confined flow

This experimental study reveals a spectacular and important phenomenon—double vortex breakdown—in a swirling flow of two immiscible fluids where vortex breakdown bubbles evolve simultaneously in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, topological metamorphoses occur, resulting in a multicellular flow. Two new circulation cells (vortex breakdown bubbles) simultaneously develop near the centers of both fluids while the flow remains steady and axisymmetric. Such a pattern can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors.

### Steady and oscillatory flow in the human bronchial tree

Author(s): Sahar Jalal, Tristan Van de Moortele, Omid Amili, and Filippo Coletti

Magnetic resonance velocimetry is used to investigate the steady inhalation, steady exhalation, and oscillatory flow in a 3D-printed realistic airway geometry for physiologically relevant regimes ranging from quiet breathing to respiration under high-frequency ventilation. Additionally, the pendulluft phenomenon is demonstrated experimentally for the first time, using both Eulerian velocity fields and Lagrangian path lines.

[Phys. Rev. Fluids 5, 063101] Published Wed Jun 17, 2020

### Unsteady fluid-structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number

Author(s): Tanmay C. Inamdar, Xiaojia Wang, and Ivan C. Christov

What happens when a fluid is pumped into a soft microchannel with height as small as the diameter of a human hair? The microchannel inflates under the flow pressure, while the flow within is affected by the resistance of the wall to deformation. We develop a mathematical model and simulate the ensuing fluid–structure interaction. Even after complex oscillations of the channel wall, we show that the final inflated state is stable. Our model highlights the parameter sets that determine the steady state wall deformation and hydrodynamic pressure distribution across a wide range of systems.

[Phys. Rev. Fluids 5, 064101] Published Wed Jun 17, 2020

### Separating adverse-pressure-gradient and Reynolds-number effects in turbulent boundary layers

Author(s): C. Sanmiguel Vila, R. Vinuesa, S. Discetti, A. Ianiro, P. Schlatter, and R. Örlü

Wall turbulence is characterized by a near-wall cycle of streaks and quasistreamwise vortices apparent as an invariant inner peak in the premultiplied energy spectra. A second, outer peak is known to emerge in this spectral view and become energized with increasing Reynolds number (Re) as well as adverse pressure gradient (APG). An analysis of experimental data sets examines how this outer peak scales with Re and APG and whether their imprint on the near-wall small scales are different.

[Phys. Rev. Fluids 5, 064609] Published Wed Jun 17, 2020