# Latest papers in fluid mechanics

### Effects of resolution inhomogeneity in large-eddy simulation

Author(s): Gopal R. Yalla, Todd A. Oliver, Sigfried W. Haering, Björn Engquist, and Robert D. Moser

Discretizations with inhomogeneous resolution affect large-eddy simulations (LES) through the commutator of the filtering and differentiation operators. We employ a multiscale asymptotic analysis to investigate the statistical characteristics of this commutator, which can serve as a target for commutation models. Further, we demonstrate how the neglect of this commutator manifests numerically, drawing a connection between the so-called commutation error and the dispersion relation of the underlying numerics. A modeling approach for the commutator is proposed that is based on the numerical properties of the LES evolution equation.

[Phys. Rev. Fluids 6, 074604] Published Thu Jul 08, 2021

### Representing rectangular jet dynamics through azimuthal Fourier modes

Author(s): Surya Chakrabarti, Datta Gaitonde, and S. Unnikrishnan

Rectangular propulsion nozzles have advantages over circular nozzles, including easier thrust-vectoring and air-frame-integration. Jet noise is easier to study with circular jets (CJ), however, due to azimuthal homogeneity, which, together with low-rank acoustic dynamics enables simpler acoustic models. Using Large Eddy Simulations of rectangular jets (RJ) of various aspect ratios we show that acoustic fluctuation components exhibit comparably rapid convergence in azimuthal Fourier space even for high aspect ratios. A reduced-order model for RJ that retains near-field acoustic asymmetry can be constructed using only three leading azimuthal modes, but with two additional terms relative to CJ.

[Phys. Rev. Fluids 6, 074605] Published Thu Jul 08, 2021

### Radiometric force on a sphere in a rarefied gas based on the Cercignani–Lampis model of gas–surface interaction

The radiometric force on a sphere due to its thermal polarization in a rarefied gas flow being in equilibrium is investigated on the basis of a kinetic model to the linearized Boltzmann equation. The scattering kernel proposed by Cercignani and Lampis to model the gas–surface interaction using two accommodation coefficients, namely, the tangential momentum accommodation coefficient and the normal energy accommodation coefficient, is employed as the boundary condition. The radiometric force on the sphere, as well as the flow field of the gas around it, is calculated in a wide range of the gas rarefaction, defined as the ratio of the sphere radius to an equivalent free path of gaseous particles, covering the free molecular, transition, and continuum regimes. The discrete velocity method is employed to solve the kinetic equation numerically. The calculations are carried out for values of accommodation coefficients considering most situations encountered in practice. To confirm the reliability of the calculations, the reciprocity relation between the cross phenomena is verified numerically within a numerical error of 0.1%. The temperature drop between two diametrically opposite points of the spherical surface in the direction of the gas flow stream, which characterizes the thermal polarization effect, is compared to experimental data for a spherical particle of Pyrex glass immersed in helium and argon gases.

### Numerical investigation of truncated-root rib on heat transfer performance of internal cooling turbine blades

Due to the great heat obtained from the combustion chamber, the turbine blades of a jet engine always operate at high temperatures. Therefore, to minimize the temperature of the turbine rotor and stator blades, the internal cooling system was developed. The original rib called the squared-rib has been developed as a turbulence generator to enhance heat transfer ability. This technique is to cast ribs in the serpentine passage inside the turbine blades. By this technique, the vortex exists in the rear rib region that causes a low heat transfer zone. In this investigation, a new rib configuration called the truncated-root rib was designed to reduce the squared-rib disadvantage. The configuration of the truncated-root rib forms a small extra-passage into which the coolant passes through and the vortex is comparatively removed. To investigate the heat transfer performance and fluid flow characteristic of the internal cooling turbine blades, a parametric study of the truncated-root rib with the height and shapes of the extra-passage was performed using three-dimensional Reynolds-averaged Navier–Stokes equations with the shear stress transport turbulence model. The numerical results showed that all the heat transfer performance of the truncated-root rib configuration is greater than that of the squared-rib. The Nusselt number in the case of the truncated-root rib increases by 8.56% with the Reynolds number of 37 392, and the thermal performance is 39.24% higher than that of the original shape in the case with Reynolds number 53 697.

### Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: A way to an original and versatile numerical approach

Author(s): Roxane Letournel, Ludovic Goudenège, Rémi Zamansky, Aymeric Vié, and Marc Massot

The characterization of intermittency in turbulence has its roots in the refined similarity hypotheses of Kolmogorov, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in an attempt to reproduce it. The first ...

[Phys. Rev. E 104, 015104] Published Wed Jul 07, 2021

### Dynamics of an externally driven cavitation bubble in an elastic microconfinement

Author(s): Konstantin Leonov and Iskander Akhatov

The subject of the present study is the dynamics of a single cavitation bubble in a spherical liquid cell surrounded by an infinite elastic solid. It is shown that volume confinement strongly affects the manifestation of the classical cavitation Blake threshold. In particular, at liquid cell sizes s...

[Phys. Rev. E 104, 015105] Published Wed Jul 07, 2021

### Exact trajectory solutions of a spherical microswimmer under flow and external fields

Author(s): M. Guedda, J. Chaiboub, M. Benlahsen, and C. Misbah

Exact trajectoires of microswimmers under flow are determined analytically exhibiting intriguing patterns such as a spherical helix.

[Phys. Rev. Fluids 6, 074102] Published Wed Jul 07, 2021

### Cascades and reconnection in interacting vortex filaments

Author(s): Rodolfo Ostilla-Mónico, Ryan McKeown, Michael P. Brenner, Shmuel M. Rubinstein, and Alain Pumir

Vortex reconnection is the process whereby two interacting vortex tubes modify their topology. Earlier studies had focused mostly on a very symmetric configuration, where the singular nature of the problem was manifesting itself by the formation of very intense vortex sheets. As revealed by our numerical study, this is just one of the possible scenarios. When the strong symmetry assumptions of earlier studies are relaxed, and the vortex tubes initially make a small angle to each other, the interactions lead to the development of small-scales of motion, via a cascade process involving the deformation of the vortex cores.

[Phys. Rev. Fluids 6, 074701] Published Wed Jul 07, 2021

### Measurement and modeling of bulk viscosity for polystyrene melts

Bulk viscosity describes the irreversible resistance to the rate of volume change. Bulk viscosity, which is more than ten thousand times higher than shear viscosity, has been ignored in the field of polymer processing for the past decades. Bulk viscosity may play an important role for compressible polymer melts undergoing strong compression during processing, especially during the packing and holding stage in injection molding. In this study, bulk viscosity of an amorphous Polystyrene melt is investigated through measurements, modeling, and implementation in an injection molding simulation. The results demonstrated that bulk viscosity can be derived from a cooling rate-controlled PVT (pressure-specific volume–temperature) measurement. A new pressure-specific volume–temperature–cooling rate model was developed to obtain smooth and reliable bulk viscosity results. Furthermore, a Cross-William–Landel–Ferry–Arrhenius model was found capable of describing the dependence of temperature, rate of volume change, and mechanical pressure on bulk viscosity of this polymer melt. The proposed modeling was first verified using the non-equilibrium PVT and then was implemented into an injection molding simulation. Simulation results showed that the effects of bulk viscosity not only prevent the material from changing its size but also reduce mechanical pressure variations during the injection molding packing stage.

### Insight on the evaporation dynamics in reducing the COVID-19 infection triggered by respiratory droplets

In this paper, the lifetime of coronavirus infected droplets under a stick-slip evaporation mode has been investigated, which may play a pivotal role in reducing the spread of COVID-19 infection. It is showed that the survival time of the virus can be reduced by increasing the receding contact angle or by reducing the initial contact angle of a drop deposited on a solid surface. It has been found that the lifetime of the virus increases almost five times under highly humid conditions as compared to dry conditions. It is further observed that the normalized lifetime does not depend upon thermo-physical properties, ambient temperature, relative humidity, and initial drop volume. A model has been proposed to estimate the shear stress acting on a virus taking into account the effect of a Marangoni flow. The presented model unveils that the magnitude of computed shear stress is not enough to obliterate the virus. The findings of the present model have been discussed in the context of reducing the COVID-19 infection, but the model can also be applied for coughed/sneezed droplets of other infectious diseases. Moreover, this physical understanding of evaporation dynamics on solid surfaces with a stick-slip mode may help in better design of a face mask, PPE kit, and other protective equipment used in public places in order to minimize the chances of infection and tackle the current pandemic. However, the reported model for estimating the survival time of the virus does not consider the effect of the thermo-capillary convection (the Marangoni effect).

### Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels

High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. Deep learning (DL) techniques have been demonstrated to be effective for super-resolution (SR) tasks, which, however, primarily rely on sufficient HR labels for training. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNNs), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. Moreover, the proposed CNN-SR solution unifies the forward SR and inverse data assimilation for the scenarios where the physics is partially known, e.g., unknown boundary conditions. A new network structure is designed to enable not only the parametric SR but also the parametric inference for the first time. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. A series of different LR scenarios, including LR input with Gaussian noises, non-Gaussian magnetic resonance imaging noises, and downsampled measurements given either well-posed or ill-posed physics, are investigated to illustrate the SR, denoising, and inference capabilities of the proposed method.

### Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers

Rayleigh–Taylor-instability (RTI) induced flow and mixing are of great importance in both nature and engineering scenarios. To capture the underpinning physics, tracers are introduced to make a supplement to discrete Boltzmann simulation of compressible RTI flows. By marking two types of tracers with different colors, the tracer distribution provides a clear boundary of two fluids during the evolution. Fine structures of RTI flow and thermodynamic non-equilibrium behavior around the interface in a miscible two-fluid system are delineated. Distribution of tracers in their velocity phase space makes a charming pattern showing quite dense information on the flow behavior, which opens a new perspective for analyzing and accessing significantly deep insights into the flow system. RTI mixing is further investigated via tracer-defined local mixedness. The appearance of Kelvin–Helmholtz instability is quantitatively captured by the abrupt increase in mixedness averaged along the direction of acceleration. The role of compressibility and viscosity on mixing are investigated separately, both of which show a two-stage effect. The underlying mechanism of the two-stage effect is interpreted as the development of large structures at the initial stage and the generation of small structures at the late stage. At the late stage, for a fixed time, a saturation phenomenon of viscosity is found that a further increase in viscosity cannot lead to an evident decline in mixedness. The mixing statues of heavy and light fluids are not synchronous and the mixing of an RTI system is heterogeneous. The results are helpful for understanding the mechanism of flow and mixing induced by RTI.

### Birthing of a daughter vesicle in a model system for self-reproduction vesicles

Sakuma and Imai [Phys. Rev. Lett. 107, 198101 (2011)] established a temperature-controlled cyclic process for a model system of self-reproducing vesicles without feeding. The vesicle generates a smaller inclusion vesicle called “daughter vesicle” inside the original vesicle (we call this “mother vesicle”) and then the daughter vesicle is expelled through a small pore on the mother vesicle. This self-reproducing process is called birthing. In the present study, we present a theoretical model on the birthing process of a single, rigid daughter vesicle through a pore. By using a simple geometric picture, we derive the free energy constituting the material properties of the bending, stretching, and line tension moduli of the mother vesicle, as a function of the distance between the centers of the daughter and mother vesicles, and the size of the daughter vesicle. We see clearly the disappearance of the energy barrier by selecting appropriate moduli. The dynamics of the system is studied by employing the Onsager principle. The results indicate that translocation time decreases as the friction parameter decreases or the initial size of the daughter vesicle decreases.

### The influence of gas volume fractions on deformation and volumetric efficiency of twin-screw multiphase pump based on fluid–thermal–structure coupling numerical calculation

The twin-screw multiphase pump shows a significant phenomenon of fluid–thermal–structure physics field coupling. The method of studying dynamics, thermodynamic characteristics, and deformation of the screw pump is biased from the actual boundary conditions without considering multi-field coupling. To enhance the calculation accuracy of the twin-screw pump integrated deformation field and further determine the clearances between rotors and pump liner, the fluid–thermal–structure coupling calculation is completed by ANSYS WORKBENCH. The calculation results of the leakage rate are verified by experiments. The moving reference frame dynamic mesh method is used in the fluid domain numerical simulation, and the non-equilibrium wall function method is used to solve the boundary layer. The rotor and pump liner deformations and their influences on volumetric efficiency are studied under different gas volume fractions. The optimal installation clearances are proposed to reduce the leakage flow rate and prevent the rotor from sticking due to large deformation. The results show that the calculated results of the leakage rate are in good agreement with the experimental values, and the average deviation is less than 4%. The research program effectively ensures the calculation accuracy and efficiency of the whole model and provides an important basis for the optimal design of the twin-screw pump.

### Two typical collective behaviors of the heavy ions expanding in cold plasma with ambient magnetic field

We have numerically studied the evolution of heavy ions that expand in a cold background plasma at a large scale. Two typical collective behaviors of the heavy ions are identified with the conditions where only the traversing heavy ions' initial total mass is different. Our work has demonstrated that a difference in the initial total mass of the moving heavy ions is able to induce completely different collective behaviors of the plasma. The simulation is performed via the hybrid model in which the ions and electrons are treated as classical particles and mass-less fluids, respectively. Due to the imbalance of the electric and magnetic force on the heavy ions, these particles will evolve into different collective patterns eventually. These patterns manifest a rather different stopping behavior of the moving ions and an opposite drifting direction of the electron fluid at the rim of the expanding plasma. Further numerical and analytical calculations show that the imbalance depends not only on the number densities of the plasma ions but also on the spatial variations of the magnetic fields. Our work reveals that the collective behavior of the heavy ions is highly non-linear, and the non-linearity is able to induce different phenomena in the evolution of the system at a large scale.

### Preferential alignment and heterogeneous distribution of active non-spherical swimmers near Lagrangian coherent structures

We report the interaction between active non-spherical swimmers and a long-standing flow structure, Lagrangian coherent structures (LCSs), in a weakly turbulent two-dimensional flow. Using a hybrid experimental–numerical model, we show that rod-like swimmers have a much stronger and more robust preferential alignment with attracting LCSs than with repelling LCSs. Tracing the swimmers' Lagrangian trajectories, we reveal that the preferential alignment is the consequence of the competition between the intrinsic mobility of the swimmers and the reorientation ability of the strain rate near the attracting LCSs. The strong preferential alignment with attracting LCSs further leads to a strong accumulation near the attracting LCSs. Moreover, we show the self-similarity of this accumulation, which reduces the intricate interaction to only one control parameter. Our results generically elucidate the interaction between active and non-spherical swimmers with LCSs and, thus, can be widely applied to many natural and engineered fluids.

### Numerical investigation of natural transitions of bow boundary layers over underwater axisymmetric bodies

The natural transitions of bow boundary layers over underwater axisymmetric bodies are investigated using numerical methods. The laminar flow fields over the underwater axisymmetric bodies are first calculated, and then the linear stability of the boundary layers is analyzed considering both the streamwise and circumferential curvatures of the wall. Based on the stability results, the eN method is employed to predict the transition locations. Numerical calculations are performed for seven forebody shapes under six oncoming flow velocities, allowing the influences of the forebody shapes and the oncoming flow velocities on the transition to be investigated. For the different forebody shapes, the boundary layer stability is generally the same behind the streamwise location of twice the forebody length, but varies within in the range of twice the forebody length. The transition locations are significantly different for the different forebody shapes. As the oncoming flow velocity increases, the dimensional unstable zone expands significantly, and the transition location moves upstream. The SUBOFF forebody shape proposed by Groves et al. [“Geometric characteristics of DARPA SUBOFF models (DTRC model numbers 5470 and 5471),” Report No. DTRC/SHD-1298-01 (David Taylor Research Center, West Bethesda, MD, 1989)] has a particularly late transition location and a large diameter close to the leading edge. This delayed transition location is caused by two separated unstable zones. Considering multiple factors, our analyses indicate that the SUBOFF forebody shape is quite valuable for practical engineering problems.

### The hydrodynamics of an inertial squirmer rod

The hydrodynamic behavior of a two-dimensional elongated micro-swimmer (squirmer rod) in a bulk fluid is studied numerically with an immersed boundary-lattice Boltzmann method. The swimming Reynolds numbers, the number of the squirmers (squirmer is a self-propelled model to assemble the elongated micro-swimmer), and the relative distance between two adjacent squirmers' centers are, respectively, set being 0.05 ≤ Res ≤ 5, 2 ≤ i ≤ 8, and 0.75d ≤ s ≤ 1.5d (d is the diameter of the squirmer) to investigate the swimming speed, the power expenditure, and the hydrodynamic efficiency of the micro-swimmer. The results show that the swimming speed of the puller rod (a type of elongated micro-swimmers propelled from the front) increases monotonically with enhancing i. The pusher rod (a type of elongated micro-swimmers propelled from the rear) with more pushers i swims faster at Res ≤ 0.1, whereas it swims slower at Res > 0.1. The speed of the pusher rod increases monotonously with the decrease in the distance s, whereas a non-monotonous variation is found for the puller rod. Meanwhile, the more i or smaller s for the puller and pusher rods, the more power P they expend, and no appreciable distinction is found for their P at 0.05 ≤ Res ≤ 1. By continuing to increase Res (Res > 1), P increases monotonically for both the puller and pusher rods, and it is more appreciably for the pusher rods. Finally, the hydrodynamic efficiency η of the pusher rods increases monotonically with the translational Reynolds number ReU, in contrast to that of the puller rods, which decreases (ReU ≤ 1) and then increases (ReU > 1) with ReU. For the pusher rods at ReU > 1, the increasing ratio of η is proportional to [math]. The higher η is found for the squirmer rods with smaller i or greater s.

### Microscopic phenomena inferred from the rheological analysis of an emulsion

The rheological behavior of an emulsion is determined by microstructural changes caused by external loads. Some of these changes are irreversible due to the occurrence of the destabilization processes. Therefore, a deeper understanding of the system may be acquired by linking rheological characterization results with microscopic events. It is important to understand the rheological consequences of the occurrence of destabilization phenomena such as coalescence and flocculation. An experimental study was performed to verify the destabilization of samples during shear in a rheometer. Coalescence was assessed by measuring changes in the droplet size distribution functions, while the degree of flocculation was determined with the use of consecutive flow curves. Additionally, the occurrence of the non-equilibrium condition was studied. As a case study, the method developed in this paper was applied to a water-in-oil crude emulsion.

### DSMC study of hypersonic rarefied flow using the Cercignani–Lampis–Lord model and a molecular-dynamics-based scattering database

This study proposes a scattering database method to model gas–solid interaction based on a database of distributions of scattering velocity obtained by a molecular dynamics simulation. The proposed method is used as the boundary condition in the direct simulation Monte Carlo method to simulate hypersonic flow over a rounded wedge at different Knudsen numbers (Kn). The effects of different wall models [e.g., the scattering database method and the Cercignani–Lampis–Lord (CLL) model] on the flow simulation were compared and analyzed. When Kn ≥ 1, the results based on the CLL model are evidently different from those of the scattering database model, where this difference increases with the degree of rarefication of flow. The mechanism of this discrepancy is such that when the flow is rarefied, a large number of freestream molecules from the far-field directly collide with the wall. In particular, near the stagnation point, the tangential reflection kinetic energy of freestream molecules is amplified due to the conversion of their normal incident kinetic energy. The scattering feature of this conversion is challenging to reproduce based on the theoretical framework of the CLL model. Still, a specific local parameter can describe the ratio of this conversion. Therefore, compared with the traditional wall model, the scattering database method can show more detailed scattering features and, hence, could be a promising tool for the study of gas–solid interaction in hypersonic rarefied flow.