# Latest papers in fluid mechanics

### Vortex-induced vibrations of an elliptic cylinder of low mass ratio: Identification of new response branches

The classical resonance branches that construct the response of a freely vibrating circular or elliptic cylinder at low Reynolds numbers, Re, are “initial” and “lower.” The existence of additional response branches, if any at low Re via alteration of controlling parameters, is unavailable in the literature. In this computational work, relating to a low mass ratio (m* = 1) and zero damping, i.e., m*ζ = 0 transverse-only vortex-induced vibrations of an elliptic cylinder over Re = 50–180, four response branches that are unreported in the literature are identified. The lock-in at such a low mass ratio is non-classical, and the new response branches are resolved close to the lock-in boundaries. These additional branches are designated as extended initial branch, extended lower branch, terminal branch, and quasi-periodic desynchronization branch. The method proposed by Kumar et al. [“Identification of response branches for oscillators with curved and straight contours executing VIV,” Ocean Eng. 164, 616–627 (2018b)] has been employed to identify the branches by locating the Re region concerning the change of slope and discontinuous jumps of oscillation frequency. It is further shown that branching at a low mass ratio depends on structural damping, oscillator shape, and degree-of-freedom.

### Mixed convection in gravity-driven thin nano-liquid film flow with homogeneous–heterogeneous reactions

A modified nanofluid model for homogeneous–heterogeneous reactions in a gravity-driven liquid film is proposed based on the assumptions of the homogeneous reaction governed by isothermal cubic autocatalytic kinetics and the heterogeneous reaction given by first-order kinetics. The Buongiorno model is introduced to describe behaviors of nanofluids with the Boussinesq approximation being used for simplification of the buoyancy term. Multiple solutions are captured, whose stabilities are checked and discussed based on the theory of Sturm–Liouville. The influence of various physical parameters on important physical quantities is presented for different cases, including buoyancy assisting, no buoyancy, and buoyancy opposing. Different from previous studies on chemical reactions in which reactants are presumed in nanometer scale, we assume that the chemical species are of regular size, which react with each other in a nanofluid. This configuration makes our model physically more realistic than previous ones.

### Upper edge of chaos and the energetics of transition in pipe flow

Author(s): Nazmi Burak Budanur, Elena Marensi, Ashley P. Willis, and Björn Hof

Numerical experiments demonstrate that the edge state of pipe flow can be reached by scaling down three-dimensional perturbations that are “too strong” to trigger turbulence. Further analysis reveals the importance of energy amplification in the bulk region for the transition in pipe flow.

[Phys. Rev. Fluids 5, 023903] Published Fri Feb 21, 2020

### Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

Author(s): Stergios Katsanoulis, Mohammad Farazmand, Mattia Serra, and George Haller

The idea of defining vortex boundaries as material curves that minimize the leakage of vorticity from the fluid mass they enclose when compared to other nearby material curves is put forward. The exact solution to this calculus of variations problem provides a mathematical criterion that unites common features of empirical observations: the material and vorticity-transporting nature of observed vortex cores. Moreover, an algorithm for the automated extraction of diffusive vortex boundaries is proposed and tested on analytical and numerical examples.

[Phys. Rev. Fluids 5, 024701] Published Fri Feb 21, 2020

### Collinear interaction of vortex pairs with different strengths—Criteria for leapfrogging

We formulate a system of equations that describe the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves along the same axis in the same sense. In much of the literature, the vortex pairs have equal strength. The vortex pairs can either escape to infinite separation or undergo a periodic leapfrogging motion. We determine an explicit criterion in terms of the initial horizontal separation of the vortex pairs given as a function of the ratio of their strengths to describe a periodic leapfrogging motion when interacting along the line of symmetry. In the Appendix, we also contrast a special case of interaction of a vortex pair with a single vortex of the same strength in which a vortex exchange occurs.

### Analysis of drop-on-demand piezo inkjet performance

For a particular printing ink and drop-on-demand piezoelectric inkjet printhead, piezoelectric voltage and temperature of the ink were varied to change the inkjet performance, and the jetting velocity of the inkjet was analyzed under various conditions. The ink was cooled by using a Peltier module, which was attached to the nozzle plate as a heat sink. The inkjet drops were captured by the shadowgraphic method using a high-speed camera. The positions and velocities of these drops were then estimated after image processing. The drop state was distinguished by dimensionless numbers, such as the Weber and Z numbers, to decide whether it was stable for ejection and printing. Increasing the piezoelectric voltage increased the ejection velocity but with an associated generation of satellite drops. Cooling the ink increased the viscosity, which in turn decreased the drop velocity while diminishing the satellite drops. Therefore, it was shown that the cooled ink enabled stabilized inkjet ejection.

### Effect of variation in density on the stability of bilinear shear currents with a free surface

We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor [“Effect of variation in density on the stability of superposed streams of fluid,” Proc. R. Soc. London, Ser. A 132, 499 (1931)], a geometrical approach to the problem is proposed, which allows us to present simple analytical criteria under which the flow is stable. A strong destabilizing effect of stratification in density is perceived when the results are compared with those obtained for the physical setting where the vorticity interface is also a density interface separating two immiscible fluids with constant densities. In contrast with the homogeneous case, the stratified bilinear shear current is mostly unstable and can only be stabilized when the background current in the upper layer is constant.

### Theory of acoustic trapping of microparticles in capillary tubes

Author(s): Jacob S. Bach and Henrik Bruus

We present a semianalytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of th...

[Phys. Rev. E 101, 023107] Published Thu Feb 20, 2020

### On-off switching of vortex shedding and vortex-induced vibration in crossflow past a circular cylinder by locking or releasing a rotational nonlinear energy sink

Author(s): Antoine B. Blanchard and Arne J. Pearlstein

Numerical simulations in two dimensions of the flow past a cylinder restrained by an elastic support find that the vortex-induced vibration can be suppressed using a nonlinear energy sink consisting of a rotating mass inside the cylinder.

[Phys. Rev. Fluids 5, 023902] Published Thu Feb 20, 2020

### Nonlinear delayed feedback model for incompressible open cavity flow

Author(s): F. Tuerke, F. Lusseyran, D. Sciamarella, L. Pastur, and G. Artana

A model based on hydrodynamic feedback mechanisms that is able to correctly reproduce power spectra commonly found in open cavity flows is presented. Using a delay differential equation, it takes into account time lags from the reflection of instability waves and the recirculation region inside the cavity.

[Phys. Rev. Fluids 5, 024401] Published Thu Feb 20, 2020

### Retraction: “Numerical study of a bubble driven micromixer based on thermal inkjet technology” [Phys. Fluids 31, 062006 (2019)]

### A self-propelled flexible plate with a Navier slip surface

The hydrodynamics of a three-dimensional self-propelled flexible plate with a Navier slip surface was explored in an effort to assess its role in the hydrodynamics of a slip boundary that mimics the mucus layer. The Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The immersed boundary method was employed to simulate the flow. For comparison, simulations were also performed with the no-slip condition. The clamped leading edge of the flexible plate was forced into a prescribed harmonic oscillation in the vertical direction but was free to move in the horizontal direction. For validation of the results obtained with the Navier slip, experiments were performed on a solid surface with a seaweed covering. The average cruising speed ([math]), the input power ([math]), and the propulsion efficiency (η) of the plate were determined as a function of the flapping frequency (f) to characterize its kinematics. The drag reduction due to the Navier slip was determined by examining the changes in the powers resulting from its effects on the Lagrangian momentum forces. The reduction in the power in the tangential direction due to the Navier slip condition is greater than that in the normal direction. The effects of the Navier slip on the force (F), power (P), and propulsion performance of the plate were evaluated. The hydrodynamic benefits of the slip condition for a self-propelled flexible body were elucidated in detail.

### Theoretical investigation of electroviscous flows in hydrophilic slit nanopores: Effects of ion concentration and pore size

Nanopores with various shapes are well developed in unconventional reservoirs, and the transport phenomena of solutions in these reservoir rocks are ubiquitous but have not yet been fully understood. This article investigates the flow characteristics of solutions in hydrophilic slit nanopores through the combination of a modified Poisson–Boltzmann (MPB) model and the modified Navier–Stokes (NS) equation. To account for the nanoconfinement effects on ion concentration and fluid viscosity, an electrochemical potential term is used in the MPB model and a varying viscosity model (VVM) is introduced in the NS equation. The model rationality is first confirmed, and then the influences of ion concentration and pore size on the transport capacities of solutions in nanopores are illuminated. In addition, the hydrodynamic features of liquids in nanopores and the limitations of this coupled model are discussed as well. The results show that the dimensionless apparent permeability of the slit increases with an increase in ion concentration and pore size. The relative contributions of the electroviscous effect (EVE) and VVM to the total flow resistance reveal different varying trends as ion concentration or pore size increases, which is greatly related to the surface charge density and the sign of the charged wall. Additionally, although the effects of EVE and VVM resulting from the nanoconfinement are considered, average velocities of fluids in nanopores exhibit a linear correlation with the pressure gradient, which cannot be used to explain the nonlinear flow mechanism occurring in tight reservoirs. Furthermore, we also compare the velocity difference between the classical PB and MPB models. We hope that the findings in this work can help improve our understanding of the characteristics of liquid flow in tight reservoirs and provide vital practical implications for diverse engineering applications.

### A non-isentropic model of aluminized explosives involved with the reaction degree of aluminum powder for post-detonation burning behavior

The post-detonation burning effect of aluminum (Al) powder plays an important role during the expansion of detonation products (DPs) of aluminized explosives (AEs). Lithium fluoride (LiF) is an inert substitute for Al, and hence, a comparison of the performance of composite explosives based on cyclotrimethylenetrinitramine (RDX), such as RDX/Al and RDX/LiF, clearly illustrates its contribution to accelerating ability due to Al oxidation. A series of metal plate tests is conducted to measure the velocity history of a metal plate driven by RDX/Al and RDX/LiF through a photonic Doppler velocimetry system with 5%, 15%, and 25% Al or LiF contents. The detonation and expansion process of the AEs is generally divided into two stages: the detonation zone (DZ) and the post-detonation zone (PDZ). In the DZ, the Al powder remains inert, while it absorbs the detonation energy from pure explosives. Therefore, the equivalent inert dilution model is established and the equivalent inert dilution coefficient of the Al powder is introduced. In the PDZ, the Al powder reacts with DPs, and the Al oxidation reaction results with a change in entropy related to the reaction degree of the Al powder. Based on the local isentropic assumption, as well as the function of the reaction degree of the Al powder, a non-isentropic model is established. The method of the non-linear characteristic line is applied to theoretically calculate the metal plate velocity based on the non-isentropic model. In addition, the theoretical results show good agreement with the metal plate test results with an acceptable error (less than 10%), indicating that the non-isentropic model can be effectively applied to analyze the accelerating ability of the AEs.

### Large deformation of a conductive nanodroplet in a strong electric field

Despite their remarkable effect on printing accuracy and uniformity, charge migrations that dominate the deformation of ink droplets during electrohydrodynamic jet printing have not been widely investigated. In this work, the large deformation mechanisms of a conductive nanodroplet under a strong electric field are examined from the point of view of charge migrations. It is found that the charge migrations include the charge relaxation in the bulk of the droplet and surface charge convection at the fluid interface. A conductive nanodroplet first evolves into an ellipsoid through charge relaxation. Then, the ellipsoid is deformed by the convection of the surface charges in four modes, namely, tip streaming (mode 1), lobe formation (mode 2), finger stretching (mode 3), and dumbbell stretching (mode 4). Finally, the stretched nanodroplet is broken into secondary droplets. Modes 1, 2, and 4 are in agreement with the experimental observations. Furthermore, it is found that over 20% of the charges are distributed inside the bulk nanodroplet and the other charges are distributed at the surface, causing the four deformation modes. Analysis based on the electric Reynolds number (the ratio of electric field force to viscous force) and the Coulombic capillary number (the ratio of surface tension to Coulombic force) shows that the nanodroplet is prolate if the electric field force is dominant. When the Coulombic force plays a crucial role, the nanodroplet deforms into an ellipsoid with wide cones. By contrast, the nanodroplet will generate hemispherical ends if the deformation is dominated by the effect of surface tension.

### Radial deformation and disintegration of an electrified liquid jet

Droplets stretched by electric stresses emit jets from their pointed tips. We observed in the experiment a new tip-streaming phenomenon by applying a radial electric field to a liquid jet. Droplets in the jet are stretched in the radial direction and develop into a disk-like shape. The growth of non-axisymmetric harmonics leads to the formation of tens of Taylor cones evenly distributed at the equator of a droplet. At the tip of each cone, a tiny secondary jet is emitted, which breaks up into progeny droplets orders of magnitude smaller than the parent ones. This tip-streaming pattern may provide a new spraying route to the generation of micro- and nanosized droplets.

### Dynamics of a circular cylinder with an attached splitter plate in laminar flow: A transition from vortex-induced vibration to galloping

Flow-induced vibration (FIV) of a circular cylinder with an attached splitter plate in a laminar flow with Re = 100 is studied numerically. First, the mechanical model along with mathematical formulations is proposed to describe the fluid-structure interaction (FSI) between the elastically supported cylinder–plate body and the surrounding flow. Subsequently, an FSI solution procedure is developed based on the characteristic-based split finite element method, and its accuracy and stability are validated using vortex-induced vibrations (VIVs) of a plain circular cylinder with benchmark solutions. Finally, using FSI simulations, effects of the plate length (L), reduced velocity, mass ratio and damping coefficient on the dynamic response, fluid load, and flow pattern of the cylinder–plate assembly are investigated in detail. As the plate length increases from L/D = 0–1.5 (D is the cylinder diameter), three FIV modes are observed successively: VIV, coupled VIV and galloping, and separated VIV and galloping, along with three vortex modes in the wake: 2S (two separated vortices in one cycle), P+S (a vortex pair and a separated vortex in one cycle), and 2P (two vortex pairs in one cycle). Moreover, it is found that the lift components generated from the splitter plate and the cylinder behave, respectively, as the driving force and the suppressing force of galloping, and the transition from VIV to galloping can be taken as a result of the competition between them. The cylinder–plate model presented could be taken as a benchmark model demonstrating the VIV-galloping interaction and applied to the design of novel FSI-based energy harvesters.

### A kinetic Fokker–Planck approach to model hard-sphere gas mixtures

Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker–Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad’s 13 moment equations on a Navier–Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He–Ar mixture.

### On the spreading of non-canonical thermals from direct numerical simulations

We present results from direct numerical simulations on laminar and turbulent non-canonical thermals with an initial rectangular density distribution at a Reynolds number of Re = 500 and Re = 5000, respectively. We find the non-canonical shape to induce strong azimuthal variations in the thermal for both the laminar and turbulent cases. These include noticeable differences in downward and horizontal propagation speeds as well as differences in the strength of the vortex tube. These differences persist over a significant period of time and help generate a cross-flow component that is otherwise not present in canonical cases. The cross-flow component is in the opposite direction to that observed in gravity currents with the same initial density distribution. This is counterintuitive seeing that both flows are solely driven by buoyancy. By extracting the three-dimensional streamlines, we find the descending vortex tube to force the dense fluid to follow a helical path.

### Experimental investigation of unstart dynamics driven by subsonic spillage in a hypersonic scramjet intake at Mach 6

Understanding start–unstart behavior of intakes in hypersonic Mach numbers is essential for seamless operation of scramjet engines. We consider a high compression ratio intake (CR = 40) at a Mach number of M = 6 in this work. Start–unstart characteristics are studied in a hypersonic wind tunnel at a flight realistic Reynolds number (Re = 8.7 × 106/m, M = 6). A flap provided at the rear end of the isolator simulates the effect of backpressure for throttling ratios in the range of 0–0.69. Experiments are conducted in two modes: (a) with the flap fixed at a particular throttling ratio and (b) the flap moved to a particular throttling ratio after the started flow has been established. Unsteady pressure measurements and time-resolved Schlieren visualization are undertaken. Modal analysis of pressure (using fast Fourier transform) and Schlieren images (using dynamic mode decomposition) are carried out. The intake shows started behavior for throttling ratios up to 0.31 and a dual behavior, where it remains started in dynamic flap runs but unstarted in fixed flap runs for throttling ratios of 0.35 and 0.42. The intake exhibits a staged evolution to a large amplitude oscillatory unstart for throttling ratios of 0.55 and 0.69, with frequencies of 950 Hz and 1100 Hz, respectively. For the first time, a staged evolution (5 stages) to a subsonic spillage oscillatory unstart of a hypersonic intake is detailed using corroborative evidence from both time-resolved Schlieren and pressure measurements. A precursor to the final large amplitude oscillatory unstart is identified, and the flow mechanism for sustained oscillations is explained.