# Latest papers in fluid mechanics

### Newtonian and viscoelastic fluid flows through an abrupt 1:4 expansion with slip boundary conditions

In this work, we present a systematic numerical investigation of the 1:4 planar expansion creeping flow under the influence of slip boundary conditions for Newtonian and viscoelastic fluids, the latter modeled by the simplified Phan–Thien–Tanner constitutive model. The linear and nonlinear Navier slip laws were considered with the dimensionless slip coefficient [math] varying in the range [math] and the slip exponents m = 0.5, 1, and 2. The simulations were carried out for a low Reynolds number, Re = 0.001, and for Deborah numbers (De) between 0 and 100. Convergence could not be achieved for higher values of the Deborah number and large values of the slip coefficient due to the large stress gradients near the singularity point (reentrant corner). The results obtained allow us to conclude that for all De, the increase in slip velocity leads to vortex suppression. The flow characteristics are described in detail for low values of the Deborah number, De ≤ 5, while for higher De the main features are only shown for specific values of the slip coefficient. These results find application in polymer processing, where the use of lubricants that migrate to the wall is common, which promotes slip.

### Influence of spatial arrangements of roughness elements on turbulent Rayleigh-Bénard convection

Turbulent Rayleigh-Bénard convection in a square cavity with rough horizontal walls is investigated at a fixed Prandtl number Pr = 0.7 over the Rayleigh number range of 106 ≤ Ra ≤ 109. We have proposed five models with rough elements of the same height but different spatial distributions to evaluate their influences on the heat transport and flow structures of the system. It is found that the flow reversal can be promoted at a Rayleigh number around 107. In all the rough models, the heat transfer is impeded at a low Ra and enhanced at a Rayleigh number beyond a critical value. Interestingly, the heat transfer and flow structure can be clustered by the sparsity of the rough element distribution. Different scaling exponents for heat transfer are identified for sparsely distributed rough models and compactly distributed models. On the other hand, the spatial distribution of rough elements has little effect on the scaling of the Reynolds number.

### Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus

Author(s): Shraddha Mandloi and V. Shankar

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the comple...

[Phys. Rev. E 101, 043107] Published Thu Apr 23, 2020

### Flow induced deformation of vulnerable stenosis under pulsatile flow condition

Author(s): Woorak Choi, Jun Hong Park, Hojin Ha, and Sang Joon Lee

Deformation of vulnerable stenosis under pulsatile flow conditions and flow-induced stress acting on a fibrous cap are revealed to be proportional to the square of flow rate divided by fibrous cap thickness. Angle variation of jet flow at the throat of vulnerable stenosis is recommended as a diagnostic index for predicting the stress on the cap.

[Phys. Rev. Fluids 5, 043101] Published Thu Apr 23, 2020

### Shape transition and hydrodynamics of vesicles in tube flow

Author(s): Paul G. Chen, J. M. Lyu, M. Jaeger, and M. Leonetti

A numerical study of the steady motion and deformation of a vesicle freely suspended inside a circular tube in a pressure-driven flow is presented. A phase diagram of vesicle shapes is drawn and a shape transition line is proposed separating the parachute-shaped region from the bullet-shaped one in the reduced volume versus confinement phase space. High-resolution simulations allow examination of the hydrodynamic interaction between the wall boundary and vesicle surface at conditions of very high confinement. Furthermore, several correlations are presented and their practical implications discussed.

[Phys. Rev. Fluids 5, 043602] Published Thu Apr 23, 2020

### Hydrodynamic forces on randomly formed marine aggregates

Author(s): Eunji Yoo, Shilpa Khatri, and François Blanchette

A novel implementation of a boundary integral method is used to compute the flow around models of marine aggregates made of cubic particles. These aggregates have a fractal structure and two formation mechanisms, each with a corresponding fractal dimension. The drag, torque, and straining force on these aggregates is characterized as a function of an appropriate measure of their size.

[Phys. Rev. Fluids 5, 044305] Published Thu Apr 23, 2020

### Inertial/kinetic-Alfvén wave turbulence: A twin problem in the limit of local interactions

Author(s): Sébastien Galtier and Vincent David

In the framework of wave turbulence, it is shown analytically and numerically that rotating hydrodynamics and magnetized plasmas at kinetic scales can be described by the same nonlinear diffusion equation. This result means that laboratory experiments can be useful for better understanding solar wind turbulence and vice versa.

[Phys. Rev. Fluids 5, 044603] Published Thu Apr 23, 2020

### Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks and we demonstrate its ability to preserve accuracy with a significantly lower computational cost. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes the knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in the fast exploration of design space for diverse engineering applications. Comparison against a projection-based nonintrusive model order reduction method demonstrates that the proposed approach produces comparable accuracy and yet is orders of magnitude computationally cheap to evaluate, despite being agnostic to the physics of the problem.

### Vorticity transport in laminar steady rotating plumes

A steady laminar rotating thermal plume was investigated by the numerical solution of the 3D momentum and energy equations. The flow originated from a low momentum hot jet (Richardson number Ri = 173 and Grashof number Gr = 5000) issued from a small inlet in the bottom wall of a cylindrical domain with a permeable lateral surface that is rotating (Ekman number Ek = 12). Second order accurate calculations of the structure and dynamics of the buoyant vortex were investigated, with specific emphasis on the evolution of the vorticity distributions and their effects on the ensuing vortex. Budgets of the vorticity transport equations were investigated to analyze the genesis of the developed axial vorticity, explaining how the whirling flow was generated. Nonslip and slip bottom boundary conditions allowed the investigation of the impact of the boundary layer on the axial vorticity generation. The results showed that there is a conversion of radial vorticity into axial vorticity. The radial vorticity was found to be generated not only in the boundary layer but also by tilting of the tangential vorticity, which results from buoyancy. Additionally, the boundary layer was found to have a strong impact on the generation of axial vorticity, but not to be necessary to generate the whirl. In fact, a stronger whirl was originated without the effect of the boundary layer, since the axial vorticity was generated closer to the inlet, where additional stretching is provided by the acceleration of the flow.

### Clustering of inertial spheres in evolving Taylor–Green vortex flow

Clustering of inertial spheres in a statistically unsteady flow field is believed to be different from particle clustering observed in statistically steady flows. The continuously evolving three-dimensional Taylor–Green vortex (TGV) flow exhibits time-varying length and time scales, which are likely to alter the resonance of a given particle with the evolving flow structures. The tendency of homogeneously introduced spherical point-particles to cluster preferentially in the TGV flow is observed to depend on the particle inertia, parameterized in terms of the particle response time τp. The degree of the inhomogeneity of the particle distribution is measured by the variance σ2 of Voronoï volumes. The time evolution of the particle-laden TGV flow is characterized by a viscous dissipation time scale τd and the effective Stokes number Steff = τp/τd. Particles with low/little inertia do not cluster in the early stage when the TGV flow only consists of large-scale and almost inviscid structures and Steff < 1. Later, when the large structures have been broken down into smaller vortices, the least inertial particles exhibit a stronger preferential concentration than the more inertial spheres. At this stage, when the viscous energy dissipation has reached its maximum level, the effective Stokes number of these particles has reached the order of one. Particles are generally seen to cluster preferentially at strain-rate dominated locations, i.e., where the second invariant Q of the velocity gradient tensor is negative. However, a memory effect can be observed in the course of the flow evolution where high σ2 values do not always correlate with Q < 0.

### Two dimensional liquid flow focusing

Flow focusing of liquid in a gaseous medium is typically axisymmetric, and it is based on a round capillary positioned on top of a circular aperture, which restricts the gaseous flow from forming a pressure drop that accelerates the liquid into a fine jet. We report an experimental study on the two dimensional flow focusing enabled by a wedge over a slit that provides similar gas flow restriction. As the wedge-to-slit distance is gradually reduced, the liquid dripping transforms into a single continuous jet that then splits into two, three, and more approximately equally-spaced jets. Below a critical wedge-to-slit separation, the liquid undergoes random atomization. The complete set of phenomena is rationalized by the dispersion relation that suggests that the jet spacing is inversely proportional to the square root of the local pressure gradient of the gas flow field. Typical experiments in the incompressible gaseous flow regime can achieve the jet spacing as short as ∼100 µm at the pressure gradient maxima.

### An analytical solution of the inverse problem of capillary imbibition

The inverse problem of capillary imbibition involves determination of the capillary geometry from the measurements of the time-varying meniscus position. This inverse problem is known to have multiple solutions, and to ensure a unique solution, measurements of imbibition kinematics in both directions of the capillary are required. We here present a closed-form analytical solution of the inverse problem of determining the axially varying radius of a capillary from experimental data of the meniscus position as a function of time. We demonstrate the applicability of the method for solving the inverse capillary imbibition problem for two cases, wherein the data for imbibition kinematics are obtained (i) using numerical simulations and (ii) from published experimental work. In both cases, the axially varying capillary radius predicted by the analytical solution agrees with the true capillary radius. In contrast to the previously proposed iterative methods for solving the inverse capillary imbibition problem, the analytical method presented here yields a direct solution. This analytical solution of the inverse capillary imbibition problem can be helpful in determining the internal geometry of micro- and nano-porous structures in a non-destructive manner and design of autonomous capillary pumps for microfluidic applications.

### Flat-evaporator-type loop heat pipe with hydrophilic polytetrafluoroethylene porous membranes

This paper describes an experimental study of a flat-evaporator-type loop heat pipe (LHP) with wicks made from hydrophilic polytetrafluoroethylene (PTFE) porous membranes, which have small pore sizes but high porosity and permeability. To demonstrate the applicability of these membranes, the LHP was designed completely and fabricated, after which the performance was experimentally investigated under a 0.52 m anti-gravity condition at a constant heat sink temperature of 80 °C. Two types of membranes were used, possessing different pore diameters and permeabilities. The pore diameter and permeability of wick 1 were 0.44 µm and 2 × 10−14 m2, respectively, while wick 2 had a pore diameter and permeability of 1.40 µm and 5 × 10−14 m2, respectively. A special wick support was designed and fabricated to ensure contact between the wick and the groove fins and to prevent the shrinkage of the PTFE membranes. Pure water was used as the working fluid. The effect of the PTFE wick characteristics on the LHP thermal performance was investigated by measuring the temperature at each point and the compensation chamber pressure. The LHP achieved steady-state operation at heat loads up to 1000 W, with a minimum thermal resistance of 0.052 K/W. Wick 2, which had a larger pore size and higher permeability, exhibited better performance than wick 1. The LHP operating temperature decreased by 10 °C, and the thermal resistance decreased by approximately 20% between wick 1 and wick 2.

### Explicit unsteady Navier–Stokes solutions and their analysis via local vortex criteria

We construct a class of spatially polynomial velocity fields that are exact solutions of the planar unsteady Navier–Stokes equation. These solutions can be used as simple benchmarks for testing numerical methods or verifying the feasibility of flow-feature identification principles. We use examples from the constructed solution family to illustrate the deficiencies of streamline-based feature detection and those of the Okubo–Weiss criterion, which is the common two-dimensional version of the broadly used Q-, Δ-, λ2-, and λci-criteria for vortex-detection. Our planar polynomial solutions also extend directly to explicit, three-dimensional unsteady Navier–Stokes solutions with a symmetry.

### Soft material perforation via double-bubble laser-induced cavitation microjets

The resulting jet of two interacting laser-induced cavitation bubbles is optimized and studied as a technique for micro-scale targeting of soft materials. High controllability of double-bubble microjets can make such configurations favorable over single bubbles for applications where risk of ablation or thermal damage should be minimized such as in soft biological structures. In this study, double-bubble jets are directed toward an agar gel-based skin phantom to explore the application of micro-scale injection and toward a soft paraffin to quantify the targeting effectiveness of double-bubble over single-bubble jetting. The sharp elongation during the double-bubble process leads to fast, focused jets reaching average magnitudes of Ujet = 87.6 ± 9.9 m/s. When directed to agar, the penetration length and injected volume increase at ∼250 μm and 5 nl per subsequent jets. Such values are achieved without the use of fabricated micro-nozzles seen in existing needle-free laser injection systems. In soft paraffin, double-bubble jetting produces the same penetration length as single-bubble jetting, but with ∼45% reduction in damage area at a 3× greater target distance. Thus, double-bubble jetting can achieve smaller impact areas and greater target distances, potentially reducing collateral thermal damage and effects of strong shockwave pressures.

### Induced mixing in stratified fluids by rising bubbles in a thin gap

Author(s): Maathangi Ganesh, Sangkyu Kim, and Sadegh Dabiri

We study a bubbly flow confined in a Hele-Shaw cell in the presence of a linear stratification through numerical simulations. Under confinement, turbulence is suppressed, and mixing comes primarily from transport in bubble wakes. Simulations are run for a range of void fractions and Froude numbers Fr, which varies the stratification strength. Among other results we find that when the stratification strength is increased, the fraction of total energy lost to buoyancy increases while the cross isopycnal diffusion decreases.

[Phys. Rev. Fluids 5, 043601] Published Wed Apr 22, 2020

### Instability and transition in an elementary porous medium

Author(s): Xu Chu, Yongxiang Wu, Ulrich Rist, and Bernhard Weigand

Instability and transition in an elementary porous medium are investigated using global linear stability analysis and numerical simulation. The representative elementary volume porous medium consists of a staggered array of square cylinders. Two unstable modes are captured from the linear stability analysis: a two-dimensional oscillatory mode and a three-dimensional stationary mode. Both the lift-up and converging flow effects are responsible for the instability.

[Phys. Rev. Fluids 5, 044304] Published Wed Apr 22, 2020

### Fluid–structure interaction simulation based on immersed boundary-lattice Boltzmann flux solver and absolute nodal coordinate formula

Large deformation fluid–structure interaction (FSI) is a typical nonlinear problem in aero elastics. Engineering applications can be found in aviation, marine engineering, and bio-fluid mechanics. A three-dimensional (3D) parallel FSI solver based on an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) and absolute nodal coordinate formula (ANCF) is established. The computational efficiency of the parallel IB-LBFS with moving boundaries is improved by several acceleration techniques, including Euler–Lagrangian interpolation matrix parallel assembling and sparse matrix solving methods. Structure dynamics simulation discretized in high-order ANCF elements distinctly reduces the number of finite elements compared with the standard finite element method. A multiple body dynamics (MBD) solver including a rigid body, ANCF cable elements, and ANCF plate elements is developed. The IB-LBFS, MBD solver, and coupled FSI solver are tested by the corresponding validation examples. A framework of solving 3D FSI problems of complex multiple flexible structures with large deformation in incompressible flow is presented. An implicit boundary condition enforced method is applied to achieve a strong coupling approach. For application demonstration, the inflation process of several types of parachute systems is simulated in which different Young’s moduli of the parachute canopy are considered. The interaction between dynamic deformation and an unsteady vortex is obtained and discussed.

### Effect of the Reynolds number on the aeroacoustic fields of a transitional supersonic jet

The Reynolds number effect on the aeroacoustic fields of a supersonic jet was experimentally investigated via particle image velocimetry (PIV), schlieren visualization, and near-field acoustic measurements. Cold supersonic jets under ideally expanded conditions at a Mach number of 2.0 were produced with the Reynolds number, based on the diameter of the nozzle exit, ranging from 105 to 106. This study focuses on the laminar-to-turbulent transition of a supersonic jet, including a transitional condition (Re ≈ 105). The PIV results of the high-Reynolds-number jet (Re = 106), which exhibited a fully turbulent shear layer at the nozzle exit, show a linear growth of the shear layer width. Conversely, a significant increase in the turbulent fluctuations and a drastic change in the shear-layer-growth rate were observed near the transition region in the case of the low-Reynolds-number jet (Re = 105). The schlieren visualization and acoustic measurements imply that the turbulent fluctuations of the transition generated strong Mach waves. The effect of disturbing the nozzle flow was also investigated because the laminar-to-turbulent transition is sensitive to the initial disturbance. A physical disturbance added in the inlet of the low-Reynolds-number jet (Re = 105) can promote an earlier transition and suppress a significant increase in the turbulence fluctuations outside the nozzle. The changes in the flow fields due to the disturbance result in a decrease in the sound pressure level. Therefore, the aeroacoustic fields of the low-Reynolds-number jet with the disturbance show similar trends to those of the high-Reynolds-number jet (Re = 106), which already exhibited a fully turbulent shear layer at the nozzle exit.

### Vortex shedding characteristics in the wake of circular finned cylinders

The near wake flow development and vortex shedding characteristics downstream of straight circular finned cylinders are experimentally investigated. Different finned cylinders with the same fin pitch and fin thickness, but different diameter ratios, Df/Dr = 1.5, 2.0, 2.5, are investigated. Particle image velocimetry measurements are carried out at a Reynolds number of Re = 2.0 × 104 based on the cylinder effective diameter (Deff), which corresponds to the sub-critical flow regime. The spatial flow development in the near wake is elucidated using both time-averaged and phase-resolved flow field characteristics. The proper orthogonal decomposition analysis is used to characterize the unsteady vortex shedding process in the wake of the cylinders. The results show that adding fins to the cylinder changes the flow development around it. Moreover, the extent of the recirculation region reduces significantly downstream of the finned cylinders as their diameter ratio increases due to higher flow entrainment between the fins. This causes an increase in both the energy of the primary vortex shedding and the strength of the vortices in the wake. The combination of stronger vortices with amplified periodicity leads to a more energetic vortex shedding process in the wake of the finned cylinders.