# Latest papers in fluid mechanics

### Development of zinc oxide-multi-walled carbon nanotube hybrid nanofluid for energy-efficient heat transfer application: A thermal lens study

This paper addresses the need for developing an energy-efficient hybrid nanofluid with zinc oxide–multi-walled carbon nanotube (ZnO-MWCNT) for overcoming the bottleneck of efficient heat transfer in thermal systems. The concentration-dependent thermal diffusivity modifications are analyzed using the highly sensitive mode mismatched thermal lens technique. The hybrid composite is prepared by the solid-state mixing and annealing of a pure multi-walled carbon nanotube (MWCNT) and zinc oxide (ZnO), synthesized by the solution combustion method. The composite formation is studied by structural, morphological, and optical characterization techniques. Among the three nanofluids ZnO, MWCNT, and ZnO-MWCNT, the composite exhibits a drastic enhancement in thermal diffusivity at a lower solid volume fraction of 0.047 mg/ml containing 0.009 mg/ml of MWCNT. All the nanofluids show an optimum concentration beyond which the thermal diffusivity decreases with the nanoparticle concentration. Thus, this study suggests the potential application of ZnO-MWCNT hybrid nanofluids in thermal system design to enhance internal combustion engines' efficiency during cold-start.

### Effect of an adverse pressure gradient on hypersonic wall pressure fluctuations

Measurements based on a plate-perpendicular fin model were conducted to investigate the effect of an adverse pressure gradient on hypersonic wall pressure fluctuations. The leading edge diameter of the perpendicular fin is designed to be 25 mm with a height of 200 mm. A linear sensor-array was used to measure the wall pressure fluctuation, and a numerical computation was carried out to validate the measurement. Wall pressure fluctuations were discussed in terms of two aspects: the time–frequency domain and spatial correlation. The flow types on the plate could be estimated by the sound pressure level distribution, and the dominant flow type that substantially contributes to the wall pressure fluctuations could be determined. The spatial correlation of wall pressure fluctuations was analyzed using the phase array technique, and two disturbance modes could be identified from the wavenumber map obtained using the beamforming algorithm. The investigation results revealed that the change in the unit Reynolds number caused by the variation in the inflow dynamic pressure leads to the change in the flow type and the distribution of wall pressure fluctuations. The small-scale vortices within the hypersonic laminar flow lead to the difference in the signs of the convective mode wavenumber and that generated by hypersonic turbulence.

### Effect of momentum and heat losses on the hydrodynamic instability of a premixed equidiffusive flame in a Hele–Shaw cell

The linear stage of hydrodynamic instability of a laminar premixed flame propagating in a Hele–Shaw cell is investigated. Our theoretical model takes into account momentum and heat losses, temperature-dependent transport coefficients, and the continuous internal structure of the flame front. The dispersion relation is obtained numerically as a solution to an eigenvalue problem for the linearized governing equations. The obtained results are in good qualitative and quantitative agreement with previous studies. It is shown that the wall heat losses tend to weaken the hydrodynamic flame instability. On the contrary, momentum losses enhance the flame instability. It is demonstrated that for the adiabatic walls, an increase in the Hele–Shaw cell width results in a reduction of the instability growth rate. For the non-adiabatic walls, there is a competition between momentum and heat losses in narrow channels that may result in a non-monotonic dependence of the instability growth rate on the Hele–Shaw cell width. It is shown that the effects of the Prandtl number and the thermal expansion vary with the wall heat loss coefficient. A possibility of non-monotonic dependence of the maximum instability growth rate on the thermal expansion has been demonstrated.

### Mechanism of separation hysteresis in curved compression ramp

A new spatial-related mechanism is proposed to understand separation hysteresis processes in curved compression ramp flows discovered recently [Hu et al., Phys. Fluids 32(11), 113601 (2020)]. Two separation hystereses, induced by variations of Mach number [math] and wall temperature Tw, are investigated numerically. The two hystereses indicate that there must exist parameter intervals of Mach number [math] and wall temperature [math], wherein both attachment and separation states can be established stably. The relationships between the aerodynamic characteristics (including wall friction, pressure and heat flux) and the shock wave configurations in these two hystereses are analyzed. Further, the adverse pressure gradient (APG) [math] induced by the upstream separation process and APG [math] induced by the downstream isentropic compression process are estimated by classic theories. The trend of boundary layer APG resistence [math] is evaluated from the spatial distributions of the physical quantities such as the shape factor and the height of sonic line. With the stable conditions of separation and attachment, a self-consistent mechanism is obtained when Isb, Icw, and Ib have appropriate spatial distributions.

### An investigation of particles effects on wall-normal velocity fluctuations in sand-laden atmospheric surface layer flows

Based on the high-quality observational data in the Qingtu Lake Observation Array (QLOA), the difference in the energy distribution, the scale of the coherent structures, and the amplitude modulation effect of the wall-normal velocity fluctuations between particle-free and particle-laden flow in the atmospheric surface layer are analyzed. The results show that the presence of particles enhanced the wall-normal turbulence intensity, especially the increase at the top of the logarithmic region is more significant though the particle mass loading decreases with the wall-normal distance. A further insight indicates that the increase in the length scale of the wall-normal fluctuating velocity coherent structure by particles is more significant further from the wall, which is supported by the premultiplied energy spectra and the two-point correlation. This leads to a drastic increase in kinetic energy of the large-scale coherent structures by the particle away from the wall and thus results in increased amplitude modulation effects of large-scale wall-normal velocity fluctuations onto small-scales.

### Wall-attached structures over a traveling wavy boundary: Scalar transport

The wall-attached structures of scalar fluctuations over a traveling wavy boundary are investigated using large eddy simulations (LESs) at a moderate Reynolds number ([math]) and various Prandtl numbers ([math]). The wave slope is [math], where a is the wave amplitude and k is the wavenumber. The prescribed wave age is [math], where c is the wave phase speed and [math] is the friction velocity. For comparison, the results of an LES over a smooth wall are also discussed. The results provide evidence for the presence of self-similar wall-attached structures of scalar fluctuations in both turbulent flow over a traveling wavy boundary and that over a smooth wall. In particular, the population density of the attached structures exhibits an inverse power-law distribution, reminiscent of a hierarchy of attached structures. The conditionally averaged scalar variance reconstructed from the superposition of attached structures has a near-wall peak and a logarithmic variation in the log region. The magnitude of this peak varies logarithmically with the hierarchical length scale, and the variation slope decreases with increase in the Prandtl number. In addition, the correlations between the attached structures and vertical scalar transport are examined by direct observation of instantaneous snapshots. The ejection event of the fluid leads the negative wall-attached structures to contribute positive vertical scalar flux and the positive wall-attached structures to contribute negative vertical scalar flux.

### Laminar flow characterization using low-field magnetic resonance techniques

Laminar flow velocity profiles depend heavily on fluid rheology. Developing methods of laminar flow characterization, based on low-field magnetic resonance (MR), contribute to the widespread industrial application of the MR technique in rheology. In this paper, we outline the design of a low-cost, palm-sized permanent magnet with a 1H resonance frequency of 20.48 MHz to measure the laminar flow. The magnet consists of two disk magnets, which were each tilted at an angle of 1° from an edge separation of 1.4 cm to generate a constant gradient, 65 G/cm, in the direction of flow. Subsequently, a series of process methods, for MR measurements, were proposed to characterize Newtonian and non-Newtonian fluid flows in a pipe, including phase-based method, magnitude-based method, and a velocity spectrum method. The accuracy of the proposed methods was validated by simulations, and experiments in Poiseuille flow and shear-thinning flow with the designed magnet. The new velocity profile methods proposed are advantageous because the MR hardware and measurement methods are simple and will result in a portable instrument. Although the governing equations are complicated, the data analysis is straightforward.

### Smallest scale of wrinkles of a Huygens front in extremely strong turbulence

Author(s): V. A. Sabelnikov, A. N. Lipatnikov, and A. I. Troshin

By analyzing the statistically stationary stage of propagation of a Huygens front in homogeneous, isotropic, constant-density turbulence, a length scale l0 is introduced to characterize the smallest wrinkles on the front surface in the case of a low constant speed u0 of the front when compared to th...

[Phys. Rev. E 104, 045101] Published Mon Oct 11, 2021

### Helical trajectories of swimming cells with a flexible flagellar hook

Author(s): Zonghao Zou, Wilson Lough, and Saverio Spagnolie

A model bacterium with a flexible flagellar hook generically swims along a helical trajectory, even when incorporating detailed hydrodynamics. A bifurcation in the hook’s equilibrium bending angle below a critical bending stiffness can have a dramatic effect on the trajectory’s helical pitch angle. Analytical predictions for the bifurcation’s dependence on the hook’s spontaneous curvature, the shape of the cell body, and the flagellum geometry are provided.

[Phys. Rev. Fluids 6, 103102] Published Mon Oct 11, 2021

### Effects of spanwise confinement on stratified shear instabilities

Author(s): Yves-Marie Ducimetière, François Gallaire, Adrien Lefauve, and Colm-cille P. Caulfield

We study the influence of transverse confinement on the linear instability properties of velocity and density distributions evoking exchange flows in stratified inclined ducts. In the chosen parameter space, we find that the presence of lateral walls has a stabilizing effect. The growth-rate predictions for the spanwise-invariant cases are almost systematically an upper bound to the growth-rate corresponding to the confined geometry. In addition, accounting for spanwise-varying perturbations result in the proliferation of unstable modes that present an odd-even regularity in their spatial structures, which is rationalized by comparison to the dispersion relation obtained for oblique waves.

[Phys. Rev. Fluids 6, 103901] Published Mon Oct 11, 2021

### Hessian-based Lagrangian closure theory for passive scalar turbulence

Author(s): Taketo Ariki and Kyo Yoshida

A self-consistent closure theory of the passive scalar turbulence has been developed on the basis of the Hessian of the scalar field, where the characteristic timescale of the scalar is properly incorporated via Lagrangian time-advancement of the Hessian. Without relying on any empirical parameter, the theory reasonably predicts the Obukhov-Corrsin spectrum of the inertial-convective range with its universal constant.

[Phys. Rev. Fluids 6, 104603] Published Mon Oct 11, 2021

### Multiphase smoothed particle hydrodynamics modeling of diffusive flow through porous media

This paper presents a numerical model using smoothed particle hydrodynamics for simulating diffusive flow in porous media with spatially varying porosity, especially when high permeability permits fast flow. The governing equations are based on a two-phase mixture theory that describes porosity in terms of stationary solid particles carrying information about volume fraction. The diffusion equation is first validated by application to two-dimensional diffusion within a square box. The continuity and momentum equations taking account of porosity are then validated by simulating Darcy seepage flow in a U-tube filled with a porous medium. Good agreement between numerical results and predicted data is obtained, demonstrating the validity of the multiphase model. Finally, the model is applied to diffusion in a two-dimensional dam-break flow through a porous structure.

### Hydrodynamic instabilities of a viscous liquid film flowing down an inclined or vertical plane

In this paper, we have investigated theoretically linear as well as weakly nonlinear stability of a viscous liquid film flowing down an inclined or vertical plane under the action of gravity. The classical momentum-integral method, which is applicable for small as well as large values of Reynolds number Re, has been used to formulate the single nonlinear free surface equation in terms of the dimensionless perturbed film thickness [math]. Using sinusoidal perturbation in the linearized part of the surface evolution equation, we obtain the stability criterion and the critical value of the wave number kc which conceives the physical parameters Re, inclination angle θ and Weber number We. However, the linear stability analysis reveals the stabilizing influence of We as well as the destabilizing influence of Re and θ on this flow dynamics. The multiple-scale analysis has been used to derive the complex Ginzburg–Landau type nonlinear equation for investigating the weakly nonlinear stability analysis. We demarcate all the four states of the flow in the Re-k (or θ-k)-plane which are found after the critical value of Rec (or θc) depending upon the values of the other parameters. A novel result which emerges from the nonlinear stability analysis is a simple relationship among the parameters k, Re, We, and θ. This relationship essentially gives us the conditions needed for the existence of an explosive unstable zone when [math] 0; otherwise, the flow system will be free from this zone. Indeed, this zone decreases with the increase in We, whereas it increases with the increase in Re and θ confirming the stabilizing role of We and destabilizing role of Re and θ as found in linear stability analysis.

### Flow boiling in geometrically modified microchannels

Microchannels are a promising solution for high-heat-flux thermal management scenarios, including high-performance microelectronics cooling and power electronics cooling. However, thermohydraulic instabilities result from the rapid vapor bubble formation. The prior literature has examined several methods, including constricted inlet microchannels, expanding microchannels, and auxiliary jetting microchannels, to mitigate the effect of these instabilities. Computational fluid dynamics and heat transfer (CFD/HT) modeling of the flow boiling phenomena in these microchannel configurations has seen limited examination, and one-to-one numerical comparisons of the different mitigation strategies have not been performed. In the present investigation, CFD/HT analyses using a three-dimensional (3D) volume of fluid model coupled with a phase-change model for the interfacial heat and mass transfer were performed for multiple microchannel configurations (constricted inlet, expanding, and auxiliary jetting microchannels). A benchmark case of a rectangular microchannel was examined to quantify baseline thermohydraulic performance. Results demonstrated slight to significant thermal performance improvements for all cases, and significant pressure benefits for the expanding and jetting cases, consistent with experimental results in the literature. Bubble dynamics and visualization for the baseline and alternative configurations are provided to give insight into their underlying physics, and the differences in performance were investigated and compared with available literature.

### Deep learning method for identifying the minimal representations and nonlinear mode decomposition of fluid flows

We propose a deep learning method to learn the minimal representations of fluid flows. It uses the deep variational autoencoder (VAE) to decouple the independent representations for fluid flows. We apply this method to several simple flows and show that the network successfully identifies the independent and interpretable representations. It shows that the proposed method can extract the physically suggestive information. We further employ the VAE network to improve the mode decomposing autoencoder framework. It decomposes the cylinder flow fields into two independent ordered states. The cylinder flow at different Reynolds numbers and time can be described as the composition of the two decomposed fields. The present results suggest that the proposed network can be used as an effective nonlinear dimensionality reduction tool for flow fields.

### Multi-population analysis of the Cuban SARS-CoV-2 epidemic transmission before and during the vaccination process

In this work, several mathematical models for the spread of viruses and diseases are presented. In particular, the work focuses on the coronavirus disease 2019 (COVID-19) pandemic. A multi-population model is presented for the study of the interaction of various populations and the contagion of the virus between them. A second model on vaccination is presented, which allows analyzing the behavior of the disease taking into account the effectiveness of the vaccine and the speed of COVID-19 after the vaccination process. Finally, both models are applied to analyze the epidemic in Cuba. For this study, the official data reported by the Cuban Ministry of Health from March 2020 to August 2021 is used.

### Determination of the symmetry groups of radiation hydrodynamics equations and the compatible equations of state and opacities

The purpose of this study was to find all the symmetry groups of the radiation hydrodynamics equations with no a priori assumptions on the equations of state (EOS) and opacities. As shown in earlier works, the application of the Lie group technique to such a system of equations leads to invariance conditions in the form of linear differential equations, which, up until now, were only partially solved. In this paper, using the same technique and under the same assumptions, but with a simpler formulation, we show that these equations can be entirely solved analytically. This result enables us to list all the one-parameter groups that may be symmetry groups of the system. To be actually so, they must be associated with suitable EOS and opacities whose general expressions are also given. The interesting point is that some of them can be chosen so as to fit realistic data for EOS and opacities. Using this property, we propose a method to design low-scale experiments to simulate radiative processes, which would involve too much energy to have experimented with at their full scale. In addition, we derive the reduced systems associated with the one-parameter symmetry groups found. We show that some classical self-similar problems can be extended to more general EOS and opacities, and we treat in detail the self-similar expansion of a semi-infinite medium submitted to an internal source of energy.

### Stability of similarity solutions of viscous thread pinch-off

Author(s): Michael C. Dallaston, Chengxi Zhao, James E. Sprittles, and Jens Eggers

We show for the first time that only one similarity solution that describes the break-up of viscous liquid threads is linearly stable, while other similarity solutions are unstable. Complex eigenvalues lead to the presence of oscillations close to the break-up.

[Phys. Rev. Fluids 6, 104004] Published Fri Oct 08, 2021

### Preferential concentration by mechanically driven turbulence in the two-fluid formalism

Author(s): Sara Nasab and Pascale Garaud

Direct Numerical Simulations are employed to investigate preferential concentration of heavy inertial particles in a system in which turbulence is mechanically-driven. Using the two-fluid equations, we study this process and the resulting particle concentration enhancement for particles with St≲O(0.01). The results are similar to those found in previous work, where we established scaling laws to predict maximum and typical particle concentration enhancements in the context of the particle-driven convective instability.

[Phys. Rev. Fluids 6, 104303] Published Fri Oct 08, 2021

### Granular avalanches of entangled rigid particles

Author(s): Damien P. Huet, Maziyar Jalaal, Rick van Beek, Devaraj van der Meer, and Anthony Wachs

We explore the behavior of granular avalanches of nonconvex cross-shaped particles as a step forward in the modeling of entangled granular media. We conduct experiments and simulations of a dam break setup and report several flow regimes such as the top-driven collapse and the intermittent regime, in which the granular column sometimes remains stable and the flow outcome is determined by the random initial microstructure.

[Phys. Rev. Fluids 6, 104304] Published Fri Oct 08, 2021