# Latest papers in fluid mechanics

### Experimental investigation of effects of pulsed injection on flow structure and flame development in a kerosene-fueled scramjet with pilot hydrogen

The effects of pulsed injection on the flow structure and flame development in a scramjet were investigated experimentally with a pilot hydrogen equivalence ratio (ER) of 0.1 and a kerosene ER of 0.3; the pilot hydrogen was used to enhance the kerosene combustion. In the steady injection flow, the non-reacting flow structure changed periodically, and the monitor pressure built up rapidly when the pilot hydrogen self-ignited at t = 0.0096 s, increasing from 0.03 to 0.037 MPa. The pilot flame was stable and filled the whole cavity until the kerosene began to be injected into the combustor at t = 0.05 s; the kerosene combustion occurred only in the cavity shear layer. After a very short time, the pilot flame was blown off by the kerosene. In the pulsed injection flow, the kerosene kept burning with the help of the pilot flame, and the monitor pressure remained at a high value that was about six times that in the non-reacting flow. The mixture of pilot hydrogen and kerosene flame could propagate into the isolator, which was discontinuous and a distinct fault could be seen in the flame images. The kerosene combustion under pulsed injection was very intense, and even when the pilot hydrogen was removed, the cold room-temperature kerosene could still burn steadily for some time. Comparing with the flame development process under steady injection conditions, it is concluded that pulsed injection helps greatly to realize kerosene ignition and stable combustion.

### Wake stabilization behind a cylinder by secondary flow over the leeward surface

Porous coating and blowing jets are both effective flow control methods for a bluff body. In the present study, we conducted wind tunnel experiments to investigate the combined control effects on a circular cylinder. The flow control was achieved by active steady blowing flows through the structured porous surface on the leeward side of the cylinder. The Reynolds number Re in the experiments, based on the cylinder outer diameter, was [math]. The control effects were evaluated by a non-dimensional blowing momentum coefficient [math], which was determined by various blowing mass flow rates, incoming wind speed, and the geometry of the porous surface. Reduced-order models, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were employed to analyze the wake stabilization effects of the secondary jet flows. We found that, under the control of secondary flows ejected from the porous region of the cylinder, POD modal characteristics in the global flow wake were changed; temporal and spatial properties of DMD transformed; frequency and mode of the vortex shedding process shifted; statistical turbulent flow characteristics ameliorated; and the estimated drag coefficients restrained. Experimental results in the present study demonstrated that the secondary flow ejected from the structured porous surface and the resultant small-scale vortices could stabilize the cylinder wake with proper [math] values.

### Effect of contact angles on dynamical characteristics of the annular focused jet between parallel plates

Focused jets have been widely studied owing to the abundance of attractive flow phenomena and industrial applications, whereas annular focused jets are less studied. This study combines experiments, numerical simulations, and analytical modeling to investigate the effect of the contact angle on the generation position and focusing efficiency of annular focused jets between parallel plates. In the experiment, a pulsed laser generates a cavitation bubble inside the droplet, and the rapidly expanding cavitation bubble drives an annular-focused jet on the droplet surface. Changing the plate wettability creates different contact angles and droplet surface shapes between the droplet and plates, which modulates the position and focusing efficiency of the annular jet. Based on the jet singularity theory and by neglecting gravity, the derived formula for the jet position offset is found to depend only on the contact angle, which is in good agreement with the experimental and numerical simulation results. Combined with numerical simulations to analyze the flow characteristics of the droplets between the parallel plates, a new calculation method for the jet focusing efficiency is proposed. Interestingly, when the liquid surface radius is small, the focusing efficiency can be improved by adjusting the contact angle to make the jet position closer to the flat plate, whereas the same operation reduces the focusing efficiency when the radius is large. The study of annular jets can expand the scope of traditional jet research and has the potential to provide new approaches for applications such as high-throughput inkjet printing and liquid transfer.

### Effective entropy production and thermodynamic uncertainty relation of active Brownian particles

Understanding stochastic thermodynamics of the active Brownian particles system has been an important topic in very recent years. However, thermodynamic uncertainty relation (TUR), a general inequality describing how the precision of an arbitrary observable current is constraint by energy dissipation, has not been fully studied for a many-body level. Here, we address such an issue in a general model of an active Brownian particles system by introducing an effective Fokker–Planck equation, which allows us to identify a generalized entropy production only by tracking the stochastic trajectory of particles' position, wherein an activity and configuration dependent diffusion coefficient come into play an important role. Within this framework, we are able to analyze the entropic bound as well as TUR associated with any generalized currents in the systems. Furthermore, the effective entropy production has been found to be a reliable measure to quantify the dynamical irreversibility, capturing the interface and defects of motility induced phase separation. We expect the new conceptual quantities proposed here to be broadly used in the context of active matter.

### Bifurcation in flows of wormlike micellar solutions past three vertically aligned microcylinders in a channel

This study presents a numerical investigation of path switching and selection phenomena in flows of wormlike micellar solutions (WLMs) past three vertically aligned microcylinders in a channel in the creeping flow regime. The flow characteristics of the wormlike micellar solution are examined with the help of a two-species Vasquez–Cook–McKinley constitutive model, which considers both the breakage and re-formation dynamics of wormlike micelles. At low Weissenberg numbers (ratio of the elastic to that of the viscous forces, Wi), the flow field in the present system is found to be steady and symmetric. Furthermore, the WLM solution passes through all the passages present between the microcylinders and channel walls. However, as the Weissenberg number reaches a critical value Wicri, a transition in the flow field from steady to unsteady occurs. Furthermore, the flow field is found to be bifurcated (a transition from symmetric to asymmetric flow field also occurs) as the Weissenberg number gradually increases. However, we observe that all these transitions are strongly dependent on the micelle breakage rate (i.e., how easy or hard to break a micelle) and the intercylinder gap. This study is an extension of our earlier studies on the flow of WLMs past a single and two vertically aligned microcylinders, which are often considered as model porous media for studying the flow dynamics of various complex fluids. The results presented in this work will be relevant for understanding the path switching phenomena of complex fluids during their flow through a porous media.

### Nanoparticle dispersion in porous media: Effects of attractive particle-media interactions

Author(s): Deepak Mangal, Jacinta C. Conrad, and Jeremy C. Palmer

We investigate the effects of physicochemical attractions on the transport of finite-sized particles in three-dimensional ordered nanopost arrays using Stokesian dynamics simulations. We find that weak particle-nanopost attractions negligibly affect diffusion due to the dominance of Brownian fluctua…

[Phys. Rev. E 105, 055102] Published Tue May 10, 2022

### Forcing of a flame by a periodic flow in a Hele-Shaw burner

Author(s): Basile Radisson, Bruno Denet, and Christophe Almarcha

Understanding how time-dependent flows affect the propagation of a flame is of prime importance for engineering applications. We experimentally study the case of a quasi-two-dimensional flame propagating in a flow that varies periodically in time. The flow acts as a parametric forcing and induces parametric restabilization and parametric destabilization of the flame front. The comparison of our experimental measurements of these destabilization and restabilization thresholds with a low frequency theory indicates how the flame response varies with the time scale associated with the dynamics of the flow.

[Phys. Rev. Fluids 7, 053201] Published Tue May 10, 2022

### Study on the radial sectional velocity distribution and wall shear stress associated with carotid artery stenosis

Atherosclerosis is an important cause of cardiovascular disease. The wall shear stress (WSS) is one of the key factors of plaque formation and dislodgement. Currently, WSS estimation is based on the measurement of the blood velocity gradient. However, due to the lack of flow field measurements in carotid stenosis vessels, the two distribution forms (parabolic and non-parabolic) commonly considered in numerical simulations could cause WSS estimates to differ by more than 40%, which could seriously affect the accuracy of mechanical analysis. This study applied three-dimensional (3D) printing technology to create an experimental model of real-structure carotid arteries. Microparticle image velocimetry was adopted to comprehensively measure blood velocity field data at the stenosis location, providing experimental validation of numerical simulation (Fluent; finite volume method) results. Then, the flow field was simulated at a normal human heart rate (45–120 beats per minute). The radial sectional velocity exhibited a plateau-like distribution with a similar velocity in the central region (more than 65% of the total channel width). This study provides an accurate understanding of the WSS at the carotid stenosis location and proposes a reliable method for the study of flow fields under various blood flow conditions.

### Do-it-yourself rheometry

We describe the structure and outcomes of a course project for do-it-yourself (DIY) rheometry. Although the project was created in response to the shelter-in-place orders of the COVID-19 pandemic, the student learning outcomes were so positive that we have continued implementing the project even when students have access to laboratory rheometers. Students select an interesting complex fluid, collect qualitative visual evidence of key rheological phenomena, and then produce their own readily available flows that they quantitatively analyze to infer rheological properties, such as yield stress, extensional viscosity, or shear viscosity. We provide an example rubric, present example student project outcomes, and discuss learning outcomes that are achieved with DIY measurements.

### Penetration and aerosolization of cough droplet spray through face masks: A unique pathway of transmission of infection

The advent of the COVID-19 pandemic has necessitated the use of face masks, making them an integral part of the daily routine. Face masks occlude the infectious droplets during any respiratory event contributing to source control. In the current study, spray impingement experiments were conducted on porous surfaces like masks having a different porosity, pore size, and thickness. The spray mimics actual cough or a mild sneeze with respect to the droplet size distribution (20–500 [math]) and velocity scale (0–14 [math]), which makes the experimental findings physiologically realistic. The penetration dynamics through the mask showed that droplets of all sizes beyond a critical velocity penetrate through the mask fabric and atomize into daughter droplets in the aerosolization range, leading to harmful effects due to the extended airborne lifetime of aerosols. By incorporating spray characteristics along with surface tension and viscous dissipation of the fluid passing through the mask, multi-step penetration criteria have been formulated. The daughter droplet size and velocity distribution after atomizing through multi-layered masks and its effects have been discussed. Moreover, the virus-emulating particle-laden surrogate respiratory droplets are used in impingement experiments to study the filtration and entrapment of virus-like nanoparticles in the mask. Furthermore, the efficacy of the mask from the perspective of a susceptible person has been investigated.

### Characterization of reflected shock tunnel air conditions using a simple method

A new method to characterize air test conditions in hypersonic impulse facilities is introduced. It is a hybrid experimental–computational rebuilding method that uses the Fay–Riddell correlation with corrections based on thermochemical nonequilibrium computational fluid dynamic results. Its benefits include simplicity and time-resolution, and using this method, a unique characterization can be made for each individual experimental run. Simplicity is achieved by avoiding the use of any optical techniques and overly expensive numerical computations while still maintaining accuracy. Without making any assumptions to relate the reservoir conditions to the nozzle exit conditions, the work done characterizing four test conditions in a reflected shock tunnel is presented. In this type of facility, shock compression is used to produce an appropriate reservoir, which is then expanded through a nozzle to produce hypersonic flow. Particular focus is given to the nozzle exit total enthalpy where a comparison is made with the reservoir enthalpy obtained using the measured shock speed and pressure in the shock tube. Good agreement is observed in all cases providing validation of the new approach. Additionally, static pressure measurements showed clearly that conditions III and IV have a thermochemical state which likely froze shortly after the nozzle throat. Also, the nozzle flow is shown to be almost isentropic. Due to the simplicity of the current method, it can be easily implemented in existing facilities to provide an additional independent estimate alongside existing results.

### Droplet impact on immiscible liquid pool: Multi-scale dynamics of entrapped air cushion at short timescales

We have detected unique hydrodynamic topology in thin air film surrounding the central air dimple formed during drop impact on an immiscible liquid pool. The pattern resembles spinodal and finger-like structures typically found in various thin condensed matter systems. However, similar structures in thin entrapped gas films during drop impacts on solids or liquids have not been reported to date. The thickness profile and the associated dewetting dynamics in the entrapped air layer are investigated experimentally and theoretically using high-speed reflection interferometric imaging and linear stability analysis. We attribute the formation of multi-scale thickness perturbations, associated ruptures, and finger-like protrusions in the draining air film as a combined artifact of thin-film and Saffman–Taylor instabilities. The characteristic length scales depend on the air layer dimensions, the ratio of the liquid pool to droplet viscosity, and the air–water to air–oil surface tension.

### Extensions to the Navier–Stokes equations

Historically, the mass conservation and the classical Navier–Stokes equations were derived in the co-moving reference frame. It is shown that the mass conservation and Navier–Stokes equations are Galilean invariant—they are valid in any arbitrary inertial reference frame. From the mass conservation and Navier–Stokes equations, we can derive a wave equation, which contains the speed of pressure wave as its parameter. This parameter is independent of the speed of the source—the fluid element velocity. The speed of pressure wave is determined from the thermodynamic equation of state of the fluid, which is reference frame independent. It is well known that Lorentz transformation ensures wave speed invariant in all inertial frames, and the Lorentz invariance holds for different inertial observers. Based on these arguments, general Navier–Stokes equations (conservation law for the energy–momentum) can be written in any arbitrary inertial reference frame, they are transformed from one reference frame into another with the help of the Lorentz transformation. The key issue is that the Lorentz factor is parametrized by the local Mach number. In the instantaneous co-moving reference frame, these equations will degrade to the classical Navier–Stokes equations—the limit of the non-relativistic ones. These extended equations contain a square of the Lorentz factor. When the local Mach number is equal to one (the Lorentz factor approaches infinity), the extended Navier–Stokes equations will embody an intrinsic singularity, meaning that the transitions from the subsonic flow to the supersonic flow will happen. For the subsonic flow, the square of the Lorentz factor is positive, while for the supersonic flow, the square of the Lorentz factor becomes a negative number, which represents that the speed of sound cannot travel upstream faster than the flow velocity.

### Relationship between the base pressure and the velocity in the near-wake of an Ahmed body

Author(s): Bérengère Podvin, Stéphanie Pellerin, Yann Fraigneau, Guillaume Bonnavion, and Olivier Cadot

We investigate the joint dynamics of the near-wake velocity and the base pressure of a square back Ahmed body. We identify two modes that are responsible for most of the pressure drag variations. We show that the turbulent large-scale velocity field in the wake can be recovered from base pressure measurements.

[Phys. Rev. Fluids 7, 054602] Published Mon May 09, 2022

### Pattern selection for thermocapillary flow in rectangular containers in microgravity

Author(s): P. Salgado Sánchez, J. Porter, J. M. Ezquerro, I. Tinao, and A. Laverón-Simavilla

The performance of Phase Change Material (PCM) devices in microgravity can be significantly improved by thermocapillary convection. However, the melting process in this case is affected by a series of instabilities and mode transitions due to the evolving size and shape of the liquid domain. We perform a numerical investigation of pattern selection for thermocapillary flow in ideal rectangular containers of liquid n-octadecane in microgravity and show how this can be applied to explain the more complex dynamics of melting PCMs. In particular, the locations of travelling and standing wave instabilities predicted in this way show very good agreement with numerical simulations of PCM melting.

[Phys. Rev. Fluids 7, 053502] Published Mon May 09, 2022

### Research on the force mechanism of two tandem cylinders in a stratified strong shear environment

A large-eddy simulation of a three-dimensional numerical wave flume is used to study the forces on two tandem cylinders in a stratified strong shear internal wave (IW) environment. By analyzing the pressure distribution and the flow field around two cylinders compared with that of a single cylinder, the mechanism for the influence of the center-to-center (CTC) spacing (L), which is normalized by the cylinder diameter (D), i.e., (L/D), between the two tandem cylinders on the vortex disturbance intensity is explored, further revealing the mechanical response characteristics of the upstream (P1) and downstream (P2) cylinders. The results show that the vortex between two cylinders is the key factor affecting the pressure resistance of the cylinders in the IWs of the depression environment. The vortex disturbance intensity can be distinguished by a normalized critical CTC spacing (Lc/D): when L/D ≤ Lc/D = 2.5, the disturbance is strong, causing P1 and P2 to undergo large forces along and in the opposite direction of the waves, respectively. In addition, the vortex disturbance is more severe in the upper layer than in the lower layer. The correlation between the nondimensional force amplitude (CFn-max) and L/D and that between CFn-max and the nondimensional IW amplitude (ηo/H) is quantified. In the strong disturbance area (L/D ≤ Lc/D), CFn-max has an exponential relationship with (L/D)/(ηo/H) for P1 and is a power function of (L/D)/(ηo/H) for P2.

### Impact of CaCl2 concentration and in situ rheometric setup configuration on fast alginate–Ca2+ reaction

Recording kinetics during a reaction is a challenging effort that provides significant insight into gelation. We recently published our work based on a novel custom-made rheometric setup for in situ cross-linking reaction [Besiri et al., Carbohydr. Polym., 2020, 246, 116615]. It facilitates the instant injection of CaCl2 solution into alginate via micro-holes of the lower plate configuration to initiate the process. Considering that the time evolution of the viscoelastic parameters is related to the developed structure, we can obtain the reaction kinetics. This study aims to improve the setup by increasing the number of micro-holes from 2 to 4, investigating the mass ratio effects, and considering the proposed design as a batch reactor. As the volume and concentration of the reactants can be controlled during the initiation of the process, we investigate the molarity effect on the gelation. The long-term behavior of rheological oscillatory shear experiments indicates that the reaction is based on the mass of cations. The stoichiometry of reactants affects the diffusion of ions to alginate since, at high concentration and low volume of CaCl2, the mechanical properties are increased compared to lower concentration and higher volume of the cationic solution. Systematic time sweep experiments prove that at low angular frequencies, ω, the driving force of the reaction is the distribution of ions to the polymer. For higher values of ω, the force acting on the oscillating geometry of the rheometer is possibly the factor causing an enhanced mixing of the reactants, with a corresponding increase in moduli.

### Vibrations of wind turbine blades in standstill: Mapping the influence of the inflow angles

The present investigation used numerical simulations to study the vibrations of a wind turbine blade in standstill. Such vibrations are presumed to affect horizontal axis wind turbine designs and can jeopardize the structural integrity of the machine. The applied numerical methods relied on a fluid–structure interaction (FSI) approach, coupling a computational fluid dynamics (CFD) solver with a multibody finite-element structural solver. A 96-m-long wind turbine blade was studied for a large parametric space, accounting for the variation of both pitch and inclination. The inclination was defined as the angle between the freestream velocity and the cross-sectional plane at the root, allowing for the introduction of a flow component in the spanwise direction. The pitch variation corresponded to the rotation of the inflow around the spanwise axis, steering the angles of attack seen by the airfoils. Two regimes of vibrations were characterized, depending on the considered range of the inclination angle. For high inclinations, the pitch angles leading to vibrations clustered around a particular region of the parametric space, and the appearance of large oscillations was accompanied by the synchronization of the loading with the frequency of motion. At low inclination angles, the mechanism triggering vibrations was relatively similar, even if the excitation spectrum was richer, and the critical pitch angles seemed to be more scattered. Regardless of the inflow, the problem was highly three-dimensional, and several complex flow phenomena such as oblique shedding and phase dislocations were identified.

### Boundary condition induced passive chaotic mixing in straight microchannels

When fluids flow through straight channels sustained turbulence occurs only at high Reynolds numbers [typically [math]]. It is difficult to mix multiple fluids flowing through a straight channel in the low Reynolds number laminar regime [[math]] because in the absence of turbulence, mixing between the component fluids occurs primarily via the slow molecular diffusion process. This Letter reports a simple way to significantly enhance the low Reynolds number (in our case [math]) passive microfluidic flow mixing in a straight microchannel by introducing asymmetric wetting boundary conditions on the floor of the channel. We show experimentally and numerically that by creating carefully chosen two-dimensional hydrophobic slip patterns on the floor of the channels, we can introduce stretching, folding, and/or recirculation in the flowing fluid volume, the essential elements to achieve mixing in the absence of turbulence. We also show that there are two distinctive pathways to produce homogeneous mixing in microchannels induced by the inhomogeneity of the boundary conditions. It can be achieved either by (1) introducing stretching, folding and twisting of fluid volumes, i.e., via a horse-shoe type transformation map, or (2) by creating chaotic advection, achieved through manipulation of the hydrophobic boundary patterns on the floor of the channels. We have also shown that by superposing stretching and folding with chaotic advection, mixing can be optimized in terms of significantly reducing mixing length, thereby opening up new design opportunities for simple yet efficient passive microfluidic reactors.

### Characteristics of the wake of an inclined prolate spheroid in uniform shear flow

Flow around an inclined 5:2 prolate spheroid with the incidence angle α = 45° is numerically investigated in a uniform shear flow. The Reynolds number based on the inflow center velocity Uc and the volume-equivalent sphere diameter De of the spheroid are considered at Re = 480, 600, 700, and 750. The non-dimensional shear rate K is ranged from 0 to 0.1. Five qualitatively different wake modes are observed, including a new mode characterized by multi-periodic shedding of hairpin vortices with regular rotation of the separation region. In general, the wake transition is suppressed with increasing shear rate. At high shear rates, the flow even reverts from unsteady to steady state at Re = 480, which we attributed to the reduction of the local Reynolds number at the leading-edge side of the spheroid. The time-averaged drag/lift coefficients and the Strouhal number increase with increasing the shear rate and the Reynolds number (except for K = 0). Finally, the effect of a sign-change of the incidence angle of the prolate spheroid on wake evolution is investigated. A physical exploration of the effect of the sign of the incidence angle and the amount of inlet shear is provided to give deeper insight into the physical mechanisms acting in the wake behind inclined non-axisymmetric bluff bodies in a shear flow.