# Latest papers in fluid mechanics

### Kinetic equation for particle transport in turbulent flows

With a new approach based on the ensemble average over particle state transition paths in phase space, a kinetic equation for particles transported in turbulent flows is derived. The probability density function (PDF) for particles is defined as an ensemble average of a special fine-grained PDF, referred to as the local path density operator. The kinetic equation is derived from a Taylor series expansion of the PDF in terms of the cumulants with respect to particle paths in phase space and leads to a closed expression for its diffusion terms. It shows that the random forcing of eddy fluctuations, non-stationarity of turbulence, and inertia of particles are explicitly presented in the diffusion coefficient, which could help us to understand how particles are diffused by these underlying mechanisms. The kinetic equation is applicable to non-Markovian, non-Gaussian, and non-stationary stochastic processes, while for Markovian processes, it recovers the classical Fokker–Planck equation. The macroscopic equations for particle phase are derived based on the kinetic equation and compared with the direct numerical simulation of particles transported in turbulent flows.

### Stability of a non-Newtonian falling film due to three-dimensional disturbances

In this paper, we apply the normal modes method to study the linear stability of a liquid film flowing down an inclined plane, taking into account the complex rheology of the media. We consider generalized Newtonian liquids; the conditions of the Squire theorem do not hold for this case. We check if the flow is unstable due to three-dimensional (3D) disturbances that propagate at a certain angle to the flow direction but stable for the two-dimensional (2D) ones. We derived the generalized Orr–Sommerfeld equation, considered a long-wave approximation, and proved that 3D long-wave disturbances are less growing than the 2D ones for any rheological law. We solved the problem for finite wavenumbers numerically and found that for low inclination angles of the plane, instability due to 3D disturbances prevails. In this case, the shear mode of instability dominates, and the surface tension destabilizes the flow. For shear-thickening liquids, the critical Reynolds number decreases down to zero.

### Direct numerical simulation of drag reduction by spanwise oscillating dielectric barrier discharge plasma force

DBD (dielectric barrier discharge) plasma actuators have in recent years become increasingly attractive in studies of flow control due to their light structures and easy implementation, but the design of a series of actuators enabling drag reduction depends on many parameters (e.g., the length of the actuator, the space between actuators, and voltage applied) and remains a significant issue to address. In this study, velocities created by the DBD plasma actuators in stagnant flow obtained by the numerical model are compared with experimental results. Then, a DNS study is carried on, and spanwise oscillated DBD plasma actuators are examined to obtain a drag reduction in a fully developed turbulent channel flow. This study connects the conventional spanwise oscillated force in drag reduction studies with DBD plasma actuators. While the former is one of the most successful applications for the drag reduction, the latter is a most promising tool with its light and feasible structure.

### Liquid jet disintegration memory effect on downstream spray fluctuations in a coaxial twin-fluid injector

This paper intends to investigate the influence of unsteadiness in the liquid jet disintegration process on downstream fluctuations of spray characteristics in a coaxial twin-fluid injector. Time-resolved high-speed shadowgraphic imaging of the spray was obtained for different axial locations downstream of the injector exit at z = 0, 8Dl, and 30Dl, where Dl is the central liquid tube diameter. The primary jet breakup unsteadiness close to the injector exit was characterized by measuring both shear-driven Kelvin–Helmholtz (KH) instability and flapping instability in addition to jet breakup length fluctuations. Downstream of the liquid jet core region, the liquid shedding rate ([math]) was measured at z = 8Dl. The power spectrum of time series data of instantaneous volume mean diameter (VMD) measured at z = 30Dl indicated periodic variation of the droplet size. The corresponding frequency (fVMD) was obtained. It was found that for lower range of gas-to-liquid momentum flux ratio (M < 4), both [math] and fVMD are larger than the frequency of KH instability. Also, for such conditions, larger temporal variation of the droplet size is realized, and this leads to higher fluctuations of the local liquid mass flux. Proper orthogonal decomposition analysis of the shadowgraph images for different axial locations identified similar topology of the dominant mode that corresponds to flapping instability. The results suggest that even far downstream of the injector exit, some memory of the upstream unsteady jet breakup process is retained, which strongly influences spatio-temporal evolution of droplet characteristics, thereby contributing to local spray fluctuations.

### Thrust generation by pitching and heaving of an elastic plate at low Reynolds number

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

### Hydrodynamic forces on a clean spherical bubble translating in a wall-bounded linear shear flow

Author(s): Pengyu Shi, Roland Rzehak, Dirk Lucas, and Jacques Magnaudet

Fully resolved simulations are conducted to determine hydrodynamic forces on clean spherical bubbles translating near a flat rigid wall in a linear shear flow. Flows range from low-but-finite Re to nearly inviscid situations. Based on simulation results, semi-empirical expressions for drag and lift forces at arbitrary Re, relative shear rate, and separation distance are found. These improve over current ‘point-particle’ models which ignore wall effects, and may be used to predict realistic bubble trajectories and distributions in wall-bounded flows.

[Phys. Rev. Fluids 5, 073601] Published Wed Jul 01, 2020

### Modeling the dielectric strength variation of supercritical fluids driven by cluster formation near critical point

Density fluctuation driven by cluster formation causes drastic changes in the dielectric breakdown characteristics of supercritical fluids that cannot be described solely based on the conventional Townsend’s gas discharge theory and Paschen’s law. In this study, we model the dielectric breakdown characteristics of supercritical CO2 as a function of pressure based on the electron scattering cross section data of CO2 clusters that vary in size as a function of temperature and pressure around the critical point. The electron scattering cross section data of CO2 clusters are derived from those of gaseous CO2. We solve the Boltzmann equation based on the electron scattering cross section data to obtain critical electrical fields of various cluster sizes as a function of pressure. To validate our model, we compare the modeled breakdown voltage with the experimental breakdown measurements of supercritical CO2, which show close agreement.

### An investigation on the disturbance evolution and the transition by resonant-triad interactions with a side-frequency disturbance in a boundary layer

In practical engineering problems, there are always side-frequency components whose frequencies are close to those of the dominant-frequency waves. In this paper, the parabolized stability equations are employed to study the influence of a side-frequency component on the development of a dominant-frequency disturbance and on the transition by resonant-triad interactions. The numerical results are qualitatively consistent with the experimental data and the asymptotic analysis results. It is found that the resonant-triad waves and the mean flow distortion cannot trigger transition by themselves. We identify a new mechanism, which we refer to as the Steady-Spanwise-Waves-Working (SSWW) mechanism, which is necessary to cause transition, in that the steady spanwise waves generated by the nonlinear interaction between the pair of three-dimensional waves play an indispensable role. For the transition caused by resonant-triad interactions with a side-frequency component, the side-frequency wave makes transition occur earlier, and the relative amplitude rather than the absolute amplitude of the side-frequency disturbance plays the essential role in the transition advance. If the relative amplitude reaches the threshold level of 40%, the transition location can be affected substantially. In this kind of transition, the SSWW mechanism still works, and the side-frequency perturbation enhances the effects of the SSWW mechanism such that the transition occurs earlier.

### Wake and thermal characteristics for cross-buoyancy mixed convection around and through a porous cylinder

The influence of cross buoyancy on the steady flow and mixed convective heat transfer around and through a porous cylinder with internal heat generation is investigated numerically. Based on the Darcy–Brinkman–Forchheimer extended porous medium model, the finite volume method is applied to investigate the wake structure and thermal characteristics in terms of the streamlines, asymmetry of recirculating wakes, temperature distribution, and average Nusselt number. The ranges chosen for the Reynolds number (Re), Darcy number (Da), and Richardson number (Ri) are 5 ≤ Re ≤ 40, 10−6 ≤ Da ≤ 10−2, and 0 ≤ Ri ≤ 1, respectively. For certain ranges above, a pair of asymmetric recirculating wakes is observed, with the upper recirculating wake detached from and the lower one partially penetrating or also detached from the cylinder. The asymmetry of the recirculating wake increases with Ri but decreases with Re. Two or three regimes with the distinct asymmetric characteristics are identified over the range of Da investigated, depending on Re. For the heat transfer performance, cross buoyancy is found to have a certain impeditive impact on the average Nusselt number.

### Squirming in a viscous fluid enclosed by a Brinkman medium

Author(s): Herve Nganguia, Lailai Zhu, D. Palaniappan, and On Shun Pak

Cell motility plays important roles in a range of biological processes, such as reproduction and infections. Studies have hypothesized that the ulcer-causing bacterium *Helicobacter pylori* invades the gastric mucus layer lining the stomach by locally turning nearby gel into sol, thereby enhancing its...

[Phys. Rev. E 101, 063105] Published Tue Jun 30, 2020

### Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

Author(s): Anubhav Dwivedi, Nathaniel Hildebrand, Joseph W. Nichols, Graham V. Candler, and Mihailo R. Jovanović

Experimental studies of a transitional shock-wave–boundary-layer interaction identify robust streaklike flow structures. In order to account for the emergence of these three-dimensional flow features, growth of small initial perturbations around the two-dimensional laminar base flow is examined. The most significant transient amplification originates from the upstream streamwise vortices, which are not related to modal instabilities. Unique to separated high-speed flows, the impinging shock compresses the boundary layer, thereby causing the growth of the streaks.

[Phys. Rev. Fluids 5, 063904] Published Tue Jun 30, 2020

### Criteria for the onset of convection in the phase-change Rayleigh–Bénard system with moving melting-boundary

Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Bénard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra > 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height [math] and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.

### Gas density structure of supersonic flows impinged on by thin blades for laser–plasma accelerator targets

Density transition injection is an effective technique for controllably loading electrons into a trapped phase for laser plasma accelerators. One common technique to achieve the required fluid structure is to impinge a thin blade on the plume of a supersonic nozzle. Density transitions induced in this way are often assumed to be bow shocks and therefore sharp, but simulations and fluorescence measurements presented in this work show that in many cases of interest, the density transition accessible to a laser propagating transverse to the shock is an intercepting shock, and therefore, shock thickness and density vary with pressure, laser height, and blade position. The fluid dynamics of a supersonic nozzle impinged on by a thin, flat object are explored through simulations and relevant features are verified via planar laser-induced fluorescence measurements. The implications of the results for tuning electron beam injectors in laser plasma accelerators are discussed.

### Modeling the role of respiratory droplets in Covid-19 type pandemics

In this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing Covid-19. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, accounting for droplet cooling, heat and mass transfer, and finally, crystallization of the dissolved salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. The droplet evaporation/desiccation time is, indeed, dependent on ambient temperature and is also a strong function of relative humidity. The multi-scale model thus developed and the firm theoretical underpinning that connects the two scales—macro-scale pandemic dynamics and micro-scale droplet physics—thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets.

### Visualizing the effectiveness of face masks in obstructing respiratory jets

The use of face masks in public settings has been widely recommended by public health officials during the current COVID-19 pandemic. The masks help mitigate the risk of cross-infection via respiratory droplets; however, there are no specific guidelines on mask materials and designs that are most effective in minimizing droplet dispersal. While there have been prior studies on the performance of medical-grade masks, there are insufficient data on cloth-based coverings, which are being used by a vast majority of the general public. We use qualitative visualizations of emulated coughs and sneezes to examine how material- and design-choices impact the extent to which droplet-laden respiratory jets are blocked. Loosely folded face masks and bandana-style coverings provide minimal stopping-capability for the smallest aerosolized respiratory droplets. Well-fitted homemade masks with multiple layers of quilting fabric, and off-the-shelf cone style masks, proved to be the most effective in reducing droplet dispersal. These masks were able to curtail the speed and range of the respiratory jets significantly, albeit with some leakage through the mask material and from small gaps along the edges. Importantly, uncovered emulated coughs were able to travel notably farther than the currently recommended 6-ft distancing guideline. We outline the procedure for setting up simple visualization experiments using easily available materials, which may help healthcare professionals, medical researchers, and manufacturers in assessing the effectiveness of face masks and other personal protective equipment qualitatively.

### Direct numerical simulation of supersonic flow and acoustics over a compression ramp

We present direct numerical simulations of the shock wave boundary layer interaction (SBLI) at Mach number 2.9 over a 24° ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the monotonic upstream-centered scheme for conservation laws and the Weighted Essentially Non-Oscillatory (WENO) scheme, of accuracy ranging from 2nd- to 11th-order. Using the canonical Taylor–Green vortex test-case, a simple and computationally inexpensive rescaling of the candidate stencil values—within the context of the high-order WENO scheme—is proposed for reducing the numerical dissipation, particularly in under-resolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second- and fifth-order schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy (TKE) spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream, leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate ninth-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock.

### Experimental investigation of the solid-liquid separation in a stirred tank owing to viscoelasticity

Author(s): Weheliye Hashi Weheliye, Giovanni Meridiano, Luca Mazzei, and Panagiota Angeli

Experiments demonstrate that viscoelastic-induced particle migration concentrates solids at the core of vortices in particle suspensions. The findings can successfully be applied to the separation of solids suspended in a viscoelastic liquid with small density difference between the phases, high liquid viscosity, and small-sized particles. The proposed separation method is low cost and relevant to many chemical engineering processes.

[Phys. Rev. Fluids 5, 063302] Published Mon Jun 29, 2020

### Cooperation and competition of viscoelastic fluids and elastomeric microtubes subject to pulsatile forcing

Author(s): Aimee M. Torres Rojas and E. Corvera Poiré

The cooperation and competition of viscoelastic fluids, subject to pulsatile forcing, with the elastomeric microtubes that confine them is explored. Tuning of system parameters allows for the excitation of different modes, and resonances can be achieved by driving the fluid with the appropriate pulsatile pressure drop. The results are relevant at microscales and potentially useful for tailoring composite microfluidic devices, where one can induce an increase or decrease of the amplitude of the longitudinally averaged flow, relative to the one of tubes made of a single material.

[Phys. Rev. Fluids 5, 063303] Published Mon Jun 29, 2020

### Electrowetting diminishes contact line friction in molecular wetting

Author(s): Petter Johansson and Berk Hess

In electrowetting, an electrostatic potential is applied to a droplet to increase its wettability. As the droplet rapidly spreads to its new equilibrium state, contact line friction is greatly diminished. Molecular dynamics simulations show that this effect is present at molecular scales and is related to how liquid molecules advance the contact line.

[Phys. Rev. Fluids 5, 064203] Published Mon Jun 29, 2020

### Microroughness-induced disturbances in supersonic blunt body flow

Author(s): Thomas Schilden, Alexej Pogorelov, Sohel Herff, and Wolfgang Schröder

To identify the mechanism triggering boundary layer transition on a spherical forebody of an Apollo type re-entry capsule, direct numerical simulations of perturbed flow are analyzed. The perturbations are generated by deterministic distributed surface roughnesses that resemble model surface imperfections that are mounted on a capsule model in corresponding experiments. The receptivity of the capsule boundary layer to the roughness and the subsequent disturbance growth are analyzed.

[Phys. Rev. Fluids 5, 063903] Published Fri Jun 26, 2020