# Latest papers in fluid mechanics

### Onset of instability in Hadley–Prats flow in a weakly heterogeneous porous layer with viscous dissipation

The stability of a flow subjected to an inclined temperature gradient (Hadley-type flow) in a horizontal porous media is studied in the presence of a basic horizontal mass flow (Prats flow). Therefore, the basic flow is called the Hadley–Prats flow. A weak vertical heterogeneity in permeability and conductivity is considered. The effect of viscous dissipation is taken to be non-negligible. The Rayleigh number corresponding to the vertical thermal gradient RaC is considered as an eigenvalue. Other parameters are the Péclet number (Pe) associated with the horizontal through flow, horizontal Rayleigh number [math] associated with the horizontal temperature gradient, Gebhart number (Ge) associated with viscous dissipation; parameters γ1 and γ2 represent the changes in permeability and conductivity, respectively. A linear stability analysis is done and the governing equations are solved numerically to obtain the critical Rayleigh number and wave number. Longitudinal and transverse rolls are discussed. Longitudinal rolls are the preferred modes for instability in most scenarios. It is found that when throughflow is present, the heterogeneity in permeability can show a stabilizing effect for longitudinal rolls but destabilizing effect for transverse rolls and vice versa depending on the direction of the throughflow. Increase in conductivity also may stabilize or destabilize the flow depending on the mass flow and viscous heating. The horizontal thermal gradient shows interesting effects in the presence of weak heterogeneity and horizontal throughflow. Significant change in the critical Rayleigh number is observed even for small values of the horizontal Rayleigh number.

### Onset of dynamic stall of tubercled wings

In the present study, numerical simulation of the flow field of the tubercled NACA0021 (National Advisory Committee for Aeronautics) wing has been conducted with the large eddy simulation model. Then, proper orthogonal decomposition (POD) analysis has been carried out at trough and peak sections. According to the spatial distributions and temporal coefficients in the case of [math], the physical backgrounds of corresponding POD modes could be identified, including flow attachment, separation, and the dynamic stall vortex (DSV). The onsets of local dynamic stall could be indicated with the extremum values of the DSV mode coefficients, which stay almost synchronized at trough and peak. Actually, the DSV is originally generated at trough and then moves to peak due to the spanwise convection induced by streamwise vorticity. The generation of the secondary vortex at trough is triggered with the streamwise pressure gradient, the development of which pinches off the feeding vorticity of the DSV and results in the detachment of the DSV. Eventually, the influence of pitching amplitude has also been discussed. The strength of the DSV at peak is increased with a larger pitching amplitude, which could be interpreted with the feeding sheet connected with the leading edge.

### Effect of surface heat exchange on phase change materials melting with thermocapillary flow in microgravity

A numerical analysis of the melting of n-octadecane in microgravity is presented for a small aspect ratio rectangular container. The container is bounded above by an air layer that exchanges heat with the phase change material (PCM) and supports thermocapillary convection in the liquid phase. The air temperature is assumed to match the applied temperatures at the lateral walls and to change linearly between them. The effect of key dimensionless parameters is investigated including the Marangoni number (Ma), which quantifies the heat transport due to the thermocapillary flow, and the Biot (Bi) number, which characterizes the heat exchanged across the PCM/air interface. Several different dynamic regimes are distinguished according to whether the flow is quasi-steady or oscillatory; the latter may be characterized by an oscillatory standing wave (OSW), a hydrothermal traveling wave, or a novel type of thermal traveling wave (TTW). The results are summarized with a stability map in terms of Bi and Ma. Notably, there are parameters where the flow undergoes transitions between distinct regimes during melting, including a transition between the TTW and OSW modes and other regions where the oscillatory flow undergoes a homoclinic bifurcation. The effect of Bi on heat transport is also investigated and shown to be particularly relevant for small Ma.

### Irreversibilities in natural convection inside a right-angled trapezoidal cavity with sinusoidal wall temperature

Analysis on natural convective heat transfer in different engineering systems allows optimization of the technical apparatus. For this purpose, numerical simulation of the fluid flow and heat transport within the system is combined with study of entropy generation. The latter is very important considering the Gouy–Stodola theorem of thermodynamics. The present research deals with the mathematical modeling of thermal convection and entropy generation in a right-angled trapezoidal cavity under the influence of sinusoidal vertical wall temperature distribution. Control Oberbeck–Galerkin finite element technique has solved Boussinesq equations formulated using the non-dimensional primitive variables. Analyses of flow structures, thermal and entropy generation patterns for different values of the Rayleigh number, and parameters of non-uniform wall temperature were performed. It was found that a rise in the sinusoidal wall temperature amplitude increases the average Nusselt and Bejan numbers and average entropy generation. Moreover, growth in the non-uniform wall temperature wave number decreases the energy transport strength and Bejan number.

### Numerical study on the drag characteristics of rigid submerged vegetation patches

Aquatic plants play a crucial role in the hydrodynamic and material transport processes within the aquatic environments due to the additional flow resistance induced by vegetation stems. In this study, high-resolution numerical experiments were performed to investigate the drag characteristics of circular vegetation patches fully immersed in a turbulent open channel flow. The submerged vegetation patch was modeled as a rigid cylinder array with a diameter D composed of N cylinder elements with a diameter d. The effects of vegetation density Φ (0.023 ≤ Φ ≤ 1) and relative diameter d/D (d/D = 0.051 and 0.072) were tested. The simulation results show that Φ and d/D affect the flow resistance exerted by the vegetation patch by modifying the bleeding flow intensity. With the increase in Φ, the drag forces acting on the individual cylinder elements decrease, whereas the total drag forces of the patch increase. The oscillation strength of the drag force of individual cylinders depends on Φ and the fixed positions within the patch. The presence of the free end of submerged cylinder array leads to enhanced wake entrainment with the increase in Φ. The drag coefficient of the submerged patch is smaller than that of the emergent patch when the dimensionless frontal area aD > 3. However, the two patches exhibit comparable drag coefficients for smaller aD values.

### The shape of a falling jet formed by concentrated polymer solutions

We studied the shape of free-falling stable jets created by viscoelastic concentrated poly(acrylonitrile) solutions that were pressed out of a capillary at different outputs. The viscosity of the solutions varied by more than 1000 times, and the elasticity increased along with growing concentration. The main goal of the study was to compare theoretical predictions with experimental data. The theoretical argumentations were based on the momentum and rheological equations. We analyzed the superposition of viscoelastic, capillary, and inertial forces for fluids with different rheological properties flowing with different velocities changing more than 100 times. Although elasticity is definitely present, the Weissenberg number in all cases under study appeared less than one and, respectively, played a secondary role except for the most concentrated solution. Then we discussed the applicability of two main models based on the combination of visco-inertial and capillary-inertial forces. The best fitting and dominant input of different forces appeared dependent on the properties of the fluids and conditions of flow. At low polymer concentration, the jet profile corresponds better to the capillary-inertial model, while the visco-inertial regime of flow becomes dominant at higher velocities and highly viscous solutions. At very high concentrations (25% in our case), both of the considered models do not allow describing the complete experimental data due to the increasing role of elasticity.

### Effect of cavity on hypersonic flat-plate boundary layer instability

The effects of a cavity on hypersonic boundary layer instabilities are investigated experimentally. First- and second-mode wave amplitude evolution is determined using pressure sensors and high-resolution Schlieren technology. The results indicate that when a cavity is located downstream of the fast- and slow-mode synchronization points, it suppresses the second-mode wave and promotes first-mode wave growth. In contrast, when the cavity is located upstream of the synchronization point, the growth of the second-mode wave is promoted while that of the first-mode wave is suppressed. During disturbance evolution, nonlinear interactions are observed due to the phase-locked mechanism that relates the two unstable modes. The transition locations for various cases are confirmed using temperature-sensitive paint technology, and the influences of the cavity on the transition are explained from the perspective of unstable mode amplitude evolution.

### On dispersion of solute in a hydromagnetic flow between two parallel plates with boundary absorption

It is well known that the widely applied Taylor diffusion model predicts the longitudinal distribution of tracers. Some recent studies indicate that the transverse concentration distribution is highly significant for large dispersion times. The present study describes an analytical approach to explore the two-dimensional concentration dispersion of a solute in the hydromagnetic laminar flow between two parallel plates with boundary absorption. The analytical expressions for the transverse concentration distribution and the mean concentration distribution of the tracers up to second-order approximation are derived using Mei's homogenization technique. The effects of the Péclet number and Hartmann number on the Taylor dispersivity are shown. It is also observed how the transverse and longitudinal mean concentration distributions are influenced by the magnetic effect, dispersion times, and boundary absorption. It is remarkable to note that the boundary absorption creates a large non-uniformity on the transverse concentration in a hydromagnetic flow between two parallel plates.

### Coupling response of flow-induced oscillating cylinder with a pair of flow-induced rotating impellers

An innovative device transforming the active control of rotating rods to passive control with a pair of impellers is proposed and numerically examined in this paper. The coupling response of a vortex-induced vibrating (VIV) circular cylinder symmetrically equipped with two impellers that are free to rotate is analyzed based on the results of computations that carried out for a reduced velocity range of Ur = 2–14 at a low Reynolds number of 150. In comparison with the bare cylinder, both the in-line and cross-flow responses are significantly augmented in the VIV initial branch with the introduction of a pair of passively rotating impellers, which is mainly attributed to the unstable rotation response in both direction and speed and the wake adjustment including the reduction in vortex formation length and broadening of flow wake. In the VIV lower branch, although the response amplitude is close to that of a bare cylinder, the strong interaction between two directional responses occurs with the same dominant frequency locking on the natural one. Nevertheless, the coexistence of multiple vibration frequencies leads to irregular oscillation trajectories and irregular vortex shedding. Moreover, the secondary vortex street is observed in the whole Ur range, but the number of merged vortices for the formation of secondary vortex street varies with Ur, depending on the response amplitude and the interaction between the shear layers of the main cylinder and impellers. In terms of time-averaged rotation, the symmetrical inward counter-rotating pattern is achieved despite the intermittent alteration of rotation direction. Furthermore, the vibration–rotation coupling is demonstrated from the variation of time-averaged rotation speed that closely follows the variation of vibration amplitude against Ur.

### Chiral propulsion: The method of effective boundary conditions

We propose to apply an “effective boundary condition” method to the problem of chiral propulsion. For the case of a rotating helix moving through a fluid at a low Reynolds number, the method amounts to replacing the original helix (in the limit of small pitch) by a cylinder, but with a special kind of partial slip boundary conditions replacing the non-slip boundary conditions on the original helix. These boundary conditions are constructed to reproduce far-field velocities of the original problem and are defined by a few parameters (slipping lengths) that can be extracted from a problem in planar rather than cylindrical geometry. We derive the chiral propulsion coefficients for spirals, helicoids, helically modulated cylinders and some of their generalizations using the introduced method. In the case of spirals, we compare our results with the ones derived by Lighthill and find a very good agreement. The proposed method is general and can be applied to any helical shape in the limit of a small pitch. We have established that for a broad class of helical surfaces the dependence of the chiral propulsion on the helical angle θ is universal, [math] with the maximal propulsion achieved at the universal angle [math].

### Numerical simulation of clogging in a microchannel with planar contraction

Clogging is the mechanism that interrupts the flow in confined geometries due to the complete blockage of the channel cross section. It represents a critical issue in the processing of particle suspensions for both industrial and biological applications, and it is particularly relevant in microfluidics and membrane technology due to the high particle confinement and the difficult device cleaning. Although numerous experimental and numerical studies have been carried out to understand the mechanism governing this complex multiscale phenomenon, the picture is not yet clear and many questions still remain, especially at the particle level. In this regard, the numerical simulations may represent a useful investigation tool since they provide a direct insight to quantities not easily accessible from experiments. In this work, a detailed computational fluid dynamics-discrete element method simulation study on the clogging mechanism in a microchannel with planar contraction is carried out. Both constant flow rate and constant pressure drop conditions are investigated, highlighting the effect of flow conditions, particle volume fraction, cohesion forces, and contraction angle. The onset of clogging conditions is discussed.

### On the compressible biglobal stability of the mean flow motion in porous tubes

In this work, a compressible biglobal stability approach is used to investigate the growth characteristics of hydrodynamic and vorticoacoustic waves in porous tubes with uniform wall injection. The retention of compressibility effects enables us to construct a physics-based formulation that is capable of predicting both hydrodynamic and vorticoacoustic wave motions simultaneously with no need for mode decomposition. At first, we show that, in the absence of a mean flow, the stability framework reproduces traditional Helmholtz frequencies and modal shapes. This confirms the embedment of the wave equation within the compressible Navier–Stokes framework. We then proceed to simulate the idealized motion in solid rocket motors, often modeled as porous tubes, where a mean flow expression is available. Specifically, using the compressible Taylor–Culick profile as a base flow, our solver produces a comprehensive frequency spectrum that returns both hydrodynamic and vorticoacoustic modes in one swoop with the added benefit of pinpointing the flow-induced longitudinal, radial, and mixed frequencies at user-prescribed tangential modes. Moreover, we find that increasing the flow Mach number leads to a slight reduction in the vorticoacoustic frequencies relative to their strictly acoustic counterparts. Similar results are obtained while increasing the Reynolds number and aspect ratio, thus affirming the origin of frequency shifts often observed in motor firings. Finally, the vorticoacoustic velocity fluctuations are shown to resemble those obtained asymptotically. Particularly, their depths of penetration appear to be controlled by the penetration number, a dimensionless parameter that combines the effects of sidewall injection, oscillatory frequency, viscosity, and chamber radius.

### On the compressible biglobal stability of the mean flow motion in porous tubes

In this work, a compressible biglobal stability approach is used to investigate the growth characteristics of hydrodynamic and vorticoacoustic waves in porous tubes with uniform wall injection. The retention of compressibility effects enables us to construct a physics-based formulation that is capable of predicting both hydrodynamic and vorticoacoustic wave motions simultaneously with no need for mode decomposition. At first, we show that, in the absence of a mean flow, the stability framework reproduces traditional Helmholtz frequencies and modal shapes. This confirms the embedment of the wave equation within the compressible Navier–Stokes framework. We then proceed to simulate the idealized motion in solid rocket motors, often modeled as porous tubes, where a mean flow expression is available. Specifically, using the compressible Taylor–Culick profile as a base flow, our solver produces a comprehensive frequency spectrum that returns both hydrodynamic and vorticoacoustic modes in one swoop with the added benefit of pinpointing the flow-induced longitudinal, radial, and mixed frequencies at user-prescribed tangential modes. Moreover, we find that increasing the flow Mach number leads to a slight reduction in the vorticoacoustic frequencies relative to their strictly acoustic counterparts. Similar results are obtained while increasing the Reynolds number and aspect ratio, thus affirming the origin of frequency shifts often observed in motor firings. Finally, the vorticoacoustic velocity fluctuations are shown to resemble those obtained asymptotically. Particularly, their depths of penetration appear to be controlled by the penetration number, a dimensionless parameter that combines the effects of sidewall injection, oscillatory frequency, viscosity, and chamber radius.

### A combined oscillation cycle involving self-excited thermo-acoustic and hydrodynamic instability mechanisms

The paper examines the combined effects of several interacting thermo-acoustic and hydrodynamic instability mechanisms that are known to influence self-excited combustion instabilities often encountered in the late design stages of modern low-emission gas turbine combustors. A compressible large eddy simulation approach is presented, comprising the flame burning regime independent, modeled probability density function evolution equation/stochastic fields solution method. The approach is subsequently applied to the PRECCINSTA (PREDiction and Control of Combustion INSTAbilities) model combustor and successfully captures a fully self-excited limit-cycle oscillation without external forcing. The predicted frequency and amplitude of the dominant thermo-acoustic mode and its first harmonic are shown to be in excellent agreement with available experimental data. Analysis of the phase-resolved and phase-averaged fields leads to a detailed description of the superimposed mass flow rate and equivalence ratio fluctuations underlying the governing feedback loop. The prevailing thermo-acoustic cycle features regular flame liftoff and flashback events in combination with a flame angle oscillation, as well as multiple hydrodynamic phenomena, i.e., toroidal vortex shedding and a precessing vortex core. The periodic excitation and suppression of these hydrodynamic phenomena is confirmed via spectral proper orthogonal decomposition and found to be controlled by an oscillation of the instantaneous swirl number. Their local impact on the heat release rate, which is predominantly modulated by flame-vortex roll-up and enhanced mixing of fuel and oxidizer, is further described and investigated. Finally, the temporal relationship between the flame “surface area,” flame-averaged mixture fraction, and global heat release rate is shown to be directly correlated.

### Analytic solutions of the variable force effect in lattice Boltzmann methods for Poiseuille flows

Various external forcing formulations of the lattice Boltzmann method (LBM) are analyzed by deriving the analytic solutions of the fully developed Poiseuille flows with and without the porous wall. For uniform driving force, all the forcing formulations recover the second-order accurate discretized Navier–Stokes equation. However, the analytic solutions show that extra force gradients arise due to variable force, and this form differs from the analysis using Chapman–Enskog expansion. It is possible to remove these extra terms of single relaxation time (SRT) LBM using specific relaxation time depending on the force formulation adopted. However, this limits the broader applicability of the SRT LBM. Moreover, the multiple-relaxation-time LBM may provide an option to remove the variable-force gradient term benefiting from separating relaxation parameters for each moment.

### Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach

Author(s): Georgia Nykteri and Manolis Gavaises

A droplet exposed to a high-speed gas flow is subject to a violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet under the shear-induced entrainment regime. The numerical investigation is conducted within a physically consistent multiscale framework, which provides insight into the mist dynamics and the distribution of the produced secondary droplets under different postshock conditions.

[Phys. Rev. Fluids 6, 084304] Published Tue Aug 17, 2021

### Multiphase CFD modeling of front propagation in a Hele-Shaw cell featuring a localized constriction

Author(s): Jonatan R. Mac Intyre, Antti Puisto, Marko Korhonen, Mikko Alava, and Jordi Ortín

Liquid-gas front propagation in disordered media exhibits unique behavior during a repeated series of drainage-imbibition displacements. Such complex behavior in a disordered media can be simplified to a single mesa-shaped defect, which provides new insight into the collective behavior at the macro-scale. We show how the morphological difference in imbibition and drainage is affected by the capillary number and wetting properties.

[Phys. Rev. Fluids 6, 084305] Published Tue Aug 17, 2021

### Structure functions in nocturnal atmospheric boundary layer turbulence

Author(s): Eliezer Kit, Eli Barami, and H. J. S. Fernando

Turbulence in a nocturnal stably stratified flow draining from a mountain range was captured using a probe system consisting of sonic and hot-film anemometers that communicate with each other through a neural network for optimal operation without any human intervention. This unique ‘Combo’ system allowed probing turbulence continuously down to energy dissipation scales, at Taylor Reynolds number greater than 1200. The data analyses, together with direct numerical simulation, reveal that, contrary to the Kolmogorov Self-Similarity Hypothesis, turbulence at dissipation scales is anisotropic, suggesting a new line of inquiry on turbulence in stable atmospheric boundary layers.

[Phys. Rev. Fluids 6, 084605] Published Tue Aug 17, 2021

### Erratum: Quantized orbital-chasing liquid metal heterodimers directed by an integrated pilot-wave field [Phys. Rev. Fluids <b>5</b>, 053603 (2020)]

Author(s): Jianbo Tang, Xi Zhao, and Jing Liu

[Phys. Rev. Fluids 6, 089902] Published Tue Aug 17, 2021

### Model reduction of traveling-wave problems via Radon cumulative distribution transform

Author(s): Jie Ren, William R. Wolf, and Xuerui Mao

Due to their sizeable Kolmogorov n-width, travel-wave problems have brought critical challenges to conventional model reduction techniques. This study aims to provide new insights into this problem by exploiting the Radon cumulative distribution transform (R-CDT) that emerged in the sector of computer vision science. By virtue of the unique property that nonlinear invertible R-CDT renders both traveling and scaling components into amplitude modulations, a substantial model-reduction is achieved in the R-CDT space, while sustaining high accuracy. The method is parameter-free and data-driven, which lends itself to problems regardless of the dimensions or boundary conditions.

[Phys. Rev. Fluids 6, L082501] Published Tue Aug 17, 2021