# Latest papers in fluid mechanics

### Three-dimensional direct numerical simulations of vortex-induced vibrations of a circular cylinder in proximity to a stationary wall

Author(s): Weilin Chen, Chunning Ji, Dong Xu, and Zhimeng Zhang

In this paper three-dimensional direct numerical simulations (3-D DNS) on vortex-induced vibrations of an elastically mounted circular cylinder near a stationary wall at a subcritical Reynolds number of 500 and a gap ratio of 0.8 are conducted. It is found that the three-dimensionality increases linearly with amplitude, leading to substantial variations in the vortex dynamics. The interactions of the vortices with the wall-generated boundary layer play significant roles in altering the cylinder vibration.

[Phys. Rev. Fluids 7, 044607] Published Thu Apr 28, 2022

### Dynamical landscape of transitional pipe flow

Author(s): Anna Frishman and Tobias Grafke

The transition to turbulence in pipes is characterized by a coexistence of laminar and turbulent states. At the lower end of the transition, localized turbulent pulses, called puffs, can be excited. Puffs can decay when rare fluctuations drive them close to an edge state lying at the phase-space bou…

[Phys. Rev. E 105, 045108] Published Wed Apr 27, 2022

### Quasistatic magnetoconvection with a tilted magnetic field

Author(s): Justin A. Nicoski, Ming Yan, and Michael A. Calkins

Convection is the primary driver of magnetic fields in planets and stars. This self-generated magnetic field can then react back on the underlying convection by influencing its structure and dynamics. Numerical simulations are used to explore the convective dynamics in the presence of an externally imposed magnetic field that has a component perpendicular to gravity. New flow regimes are identified and their quantitative behavior is analyzed.

[Phys. Rev. Fluids 7, 043504] Published Wed Apr 27, 2022

### Modulation of interphase, cross-scale momentum transfer of turbulent flows by preferentially concentrated inertial particles

Author(s): Miralireza Nabavi, Mario Di Renzo, and Jeonglae Kim

Inertial particles can interact in two ways with carrier-phase turbulence, exchanging mass, momentum, and energy. This study proposes a wavelet multiresolution framework that analyzes spectral energy transfer involving two phases and multiple scales simultaneously. Its application to preferentially concentrated particle-laden turbulence shows the role of particle clusters in spectral energy transfer as well as the physical consistency of the subgrid-scale (SGS) Stokes number useful to analyze and develop an SGS model for two-way coupled particle-laden turbulence.

[Phys. Rev. Fluids 7, 044305] Published Wed Apr 27, 2022

### A new hybrid lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation

A new low-Mach algorithm for the thermal lattice Boltzmann method (LBM) is proposed aiming at reducing the computational cost of thermal flow simulations in the low Mach number limit. The well-known low Mach number approximation is adopted to accelerate the simulations by enlarging the time step through re-scaling the psuedoacoustic speed to the same order of the fluid motion velocity. This specific process is inspired by the similarity between the artificial compressibility method and the isothermal LBM and is further extended to its thermal counterpart. It must be emphasized that such low-Mach acceleration strategy is in a general form, thus can be easily applied to other compressible LB methods. The present method overcomes the drawback of the classical pressure gradient scaling method due to the pressure gradient changing. The new algorithm is validated by various well-documented academic test cases in laminar [one dimensional gravity column, 2D (two dimensional) rising thermal bubble, and 2D differentially heated square cavity] and turbulent [3D (three dimensional) Taylor–Green vortex and 3D heated cylinder] regimes. All the results show excellent agreement with the reference data and high computational efficiency.

### Correlation analysis of flow and sound in non-isothermal subsonic jets based on large eddy simulations

The sound radiation mechanism is investigated in non-isothermal subsonic jets at acoustic Mach number 0.9 and at temperature ratios of 0.86, 1.0, and 2.7, using causality methods on the results predicted by large eddy simulations. Turbulence signals in the jet flows are rearranged according to the acoustic analogies, such as the streamwise and radial shear signals, [math] and [math], the self-signal, [math], the entropy fluctuation, [math], and the vortex norm, [math]. The ray-tracing method is applied to locate the acoustically correlated regions, and the two-point correlation is employed to analyze the acoustic correlation. The results show that the cancelation between the [math] and [math], and between the [math] and [math], vary with temperature ratio, and, thus, may affect the radiation directionality. The density fluctuation, [math], suppresses the acoustic correlations of the shear- and self-signals in the cold jet, respectively, but strengthens them in the hot jet; thus, the [math] enhances the cancelation both in cold and in hot jets. The intense negative fluctuation of the [math] is found to be associated with the cancelation mechanism. It induces the peaks of [math] and [math] by disturbing the average fields. The jet temperature changes the averaged density and entropy so as to change the cancelation mechanism. Two large-scale acoustically correlated parts of the coherent structures are visualized by the zonal correlation of the [math]. Their acoustic correlations cancel each other in the hot jets, but enhance each other in the cold jets. The acoustically correlated regions represented by the zonal correlations of the [math] and [math] are in small scale and gather around the end of the potential core region.

### Detection and evaluation of cavitation in the stator of a torque converter using pressure measurement

Cavitation is a transient phase transition between liquid and vapor, and it often occurs in fluid machinery, especially in a hydraulic torque converter that uses oil as the working medium to transmit speed and torque. The complex and strongly coupled fluid flow in the torque converter is prone to cavitation due to high rotating speed and high-temperature working conditions. Cavitation seriously affects the working performance, transmission smoothness, and service life of the torque converter. The flow pressure in the stator of a torque converter under various charging conditions and high rotating speeds was measured. The pressure data on the stator blade were analyzed in the time domain and frequency domain to identify and evaluate the cavitation characteristic. The transient cavitation flow inside the torque converter was also simulated with the computational fluid dynamics model. The results show that the shedding of cavitation seriously reduced the hydraulic performance, hindered the fluid flow, and destroyed the stability of the flow field. Moreover, cavitation aggravates the complexity and nonlinearity of the pressure frequency and hydraulic performance oscillation of the torque converter, and seriously affected the shaft/blade interaction frequency between the pump and stator. Meanwhile, the occurrence and degree of cavitation in the torque converter can be evaluated by APS.shaft/APS.blade (the amplitude ratio of the shaft interaction frequency and blade interaction frequency between pump and stator) with spectrum analysis of the dynamic pressure, and the critical value was 1.6 for the test torque converter. The research revealed the influence of cavitation on the internal flow field of the torque converter and provided a novel practical cavitation evaluation technique.

### Effects of various inlet parameters on the computed flow development in a bidirectional vortex chamber

We vary the inflow properties in a finite-volume solver to investigate their effects on the computed cyclonic motion in a right-cylindrical vortex chamber. The latter comprises eight tangential injectors through which steady-state air is introduced under incompressible and inviscid conditions. To minimize cell skewness around injectors, a fine tetrahedral mesh is implemented first and then converted into polyhedral elements, namely, to improve convergence characteristics and precision. Once convergence is achieved, our principal variables are evaluated and compared using a range of inflow parameters. These include the tangential injector speed, count, diameter, and elevation. The resulting computations show that well-resolved numerical simulations can properly predict the forced vortex behavior that dominates in the core region as well as the free vortex tail that prevails radially outwardly, beyond the point of peak tangential speed. It is also shown that augmenting the mass influx by increasing the number of injectors, injector size, or average injection speed further amplifies the vortex strength and all peak velocities while shifting the mantle radially inwardly. Overall, the axial velocity is found to be the most sensitive to vertical displacements of the injection plane. By raising the injection plane to the top half portion of the chamber, the flow character is markedly altered, and an axially unidirectional vortex is engendered, particularly, with no upward motion or mantle formation. Conversely, the tangential and radial velocities are found to be axially independent and together with the pressure distribution prove to be the least sensitive to injection plane relocations.

### Direct simulation of blood flow with heterogeneous cell suspensions in a patient-specific capillary network

Three-dimensional (3D) simulations on blood flow in a complex patient-specific retina vascular network were performed considering deformable red blood cells, white blood cells (WBCs), and obstructed vessels. First, the impact of blockage on flow rate distribution (without cells) was investigated. It showed that the blockage might change the flow rate significantly on distant vessels that were not directly connected with the blocked vessel. The flow rate in some vessels could increase up to 1200% due to an obstruction. However, with cells, it showed a fluctuating flow pattern, and the cells showed complicated transport behavior at bifurcations. Cell accumulation might occur in some bifurcations such as a T-shaped junction that eventually led to a physical blockage. The addition of WBCs impacted the local flow rate when they were squeezed through a capillary vessel, and the flow rate could be decreased up to 32% due to the larger size of WBCs. The simulation of flow under stenosis with cells showed that cells could oscillate and become trapped in a vessel due to the fluctuating flow. Finally, a reduced order model (ROM) with multiple non-Newtonian viscosity models was used to simulate the blood flow in the network. Compared with the 3D model, all ROMs reproduced accurate predictions on hematocrit and flow rate distribution in the vascular network. Among them, the Fåhræus–Lindqvist model was found to be the most accurate one. The work can be used to build a multiscale model for blood flow through integration of ROMs and 3D multiphysics models.

### Flameless combustion of low calorific value gases, experiments, and simulations with advanced radiative heat transfer modeling

Thermal radiation is the dominant mode of heat transfer in many combustion systems, and in typical flameless furnaces, it can represent up to 80% of the total heat transfer. Accurate modeling of radiative heat transfer is, thus, crucial in the design of these large-scale combustion systems. Thermal radiation impacts the thermochemistry, thereby the energy efficiency and the temperature sensitive species prediction, such as NOx and soot. The requirement to accurately describe the spectral dependence of gaseous radiative properties of combustion products interacts with the modeling of finite rate chemistry effects and conjugates heat transfer and turbulence. Additionally, because of the multiple injection of fuels and/or oxidizers of various compositions, case-specific radiative properties' expressions are required. Along these lines, a comprehensive modeling to couple radiation and combustion in reacting flows is attempted and applied to the simulation of flameless combustion. Radiation is modeled using the spectral line-based weighted-sum-of-gray-gases approach to calculate gaseous radiative properties of combustion products using the correlation of the line-by-line spectra of H2O and CO2. The emissivity weights and absorption coefficients were optimized for a range of optical thicknesses and temperatures encountered in the considered furnace. Efforts were also made on the development of a reliable and detailed experimental dataset for validation. Measurements are performed in a low calorific value syngas furnace operating under flameless combustion. This test rig features a thermal charge which can extract about 60% of combustion heat release via 80% of radiative heat transfer, making it of special interest for modeling validation. The comparison between the simulation and the experiment demonstrated a fair prediction of heat transfer, energy balance, temperature, and chemical species fields.

### Hydrodynamic correlation functions of chiral active fluids

Author(s): Debarghya Banerjee, Anton Souslov, and Vincenzo Vitelli

Spectroscopic measurements form the basis of understanding material properties characterized by the linear susceptibility. In this paper, the authors discuss how such linear susceptibilities are affected in the presence of odd viscosity. The authors also discuss a natural framework where odd viscosity arises due to the presence of injected torque in a fluid with a spin degree of freedom.

[Phys. Rev. Fluids 7, 043301] Published Mon Apr 25, 2022

### Relative role of short interfacial fingers and long internally driven streamers in convective flows below growing sea ice

Author(s): C. A. Middleton, S. S. Gopalakrishnan, I. Berenstein, B. Knaepen, J.-L. Tison, and A. De Wit

As sea ice grows from sea water, salt initially dissolved in the liquid is rejected from the solid. Buoyancy-driven flows develop under the ice layer in two ways: 1) interfacial boundary layer convection resulting in small-scale fingers and 2) internal convection originating from brine drainage channels inside the ice, flushing out longer-scale convective streamers. We study these dynamics experimentally by freezing salt water from above in a quasi-2D Hele-Shaw cell, observing with Schlieren and direct imaging systems. Interfacial fingers turn out more significant as a salt-transport pathway than previously thought, persisting throughout ice growth, whereas streamers show on-off behavior.

[Phys. Rev. Fluids 7, 043503] Published Mon Apr 25, 2022

### Physics of a strongly oscillating axisymmetric air-water interface with a fixed boundary condition

Author(s): Cong Wang and Morteza Gharib

A free-slip air-water interface with a fixed contact line boundary condition, when oscillating at certain frequencies with a large amplitude, can efficiently induce a fast-speed, far-propagating streaming jet. The extraordinary characters of the streaming jet can be employed to address engineering challenges across multiple disciplines.

[Phys. Rev. Fluids 7, 044003] Published Mon Apr 25, 2022

### Reorientation dynamics of microswimmers at fluid-fluid interfaces

Author(s): Harinadha Gidituri, Zaiyi Shen, Alois Würger, and Juho S. Lintuvuori

We show that a microswimmer trapped thermodynamically at fluid-fluid interfaces experiences a torque arising from the hydrodynamic boundary condition at the interface. This turns force dipoles corresponding to pullers perpendicular and pushers parallel to the interface. We demonstrate that in the general case, when there is a viscosity contrast across the interface, the steady state orientation is given by the interplay between the torques arising from the force dipoles and the self-propulsion which is sensitive to the viscosity difference between the two fluids.

[Phys. Rev. Fluids 7, L042001] Published Mon Apr 25, 2022

### Minimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous media

Author(s): Laurent Talon

Non-Newtonian fluids are found in many applications related to porous or fractured media. At a macroscopic scale, inelastic non-Newtonian fluid obeys a nonlinear Darcy’s equation. This paper show thats the solution of such a nonlinear equation in a heterogeneous permeability field obeys a minimum principle similar to the minimum dissipation principle of Stokes flow.

[Phys. Rev. Fluids 7, L042101] Published Mon Apr 25, 2022

### Less can be more: Insights on the role of electrode microstructure in redox flow batteries from two-dimensional direct numerical simulations

Understanding how to structure a porous electrode to facilitate fluid, mass, and charge transport is key to enhancing the performance of electrochemical devices, such as fuel cells, electrolyzers, and redox flow batteries (RFBs). Using a parallel computational framework, direct numerical simulations are carried out on idealized porous electrode microstructures for RFBs. Strategies to improve an electrode design starting from a regular lattice are explored. By introducing vacancies in the ordered arrangement, it is possible to achieve higher voltage efficiency at a given current density, thanks to improved mixing of reactive species, despite reducing the total reactive surface. Careful engineering of the location of vacancies, resulting in a density gradient, outperforms disordered configurations. Our simulation framework is a new tool to explore transport phenomena in RFBs, and our findings suggest new ways to design performant electrodes.

### Dynamics of a droplet-impact-driven cantilever making contact with the ground

To understand the mechanical principles of raindrop-based energy-harvesting systems, we experimentally investigate the dynamics of a cantilever, which deforms by a falling droplet and sequentially contacts the ground below. A new dimensionless parameter defined as the ratio of impact force to bending force is used to characterize the droplet–cantilever interaction. The bending stiffness of the cantilever, the impact velocity and size of the droplet, and the gap distance between the cantilever and the ground are varied to find how the transition boundary between contact and non-contact modes is affected by the dimensionless force ratio. The rebound amplitude, contact duration, and contact area of the cantilever are then analyzed. After the contact with the ground occurs, the rebound amplitude monotonically increases with the dimensionless force ratio. The contact duration of the cantilever with the ground is in a linear relation with the maximum contact area. We also examine the effects of the impact location and surface tension of the droplet on the contact responses. While the contact duration and area are changed notably by the impact location, the dynamics of the cantilever show minor variations with respect to the surface tension, despite a dramatic variation in droplet spreading behavior.

### Hydroelastic analysis of interaction between water waves and a floating laminated disk

This paper studies the interaction between water waves and a very large floating laminated disk in water of finite depth. The disk is a composite structure consisting of two surface sheets and a middle low-density elastic core layer. Based on the linear potential flow theory, an analytical solution of the hydroelastic problem is developed using the eigenfunction expansion method for the velocity potential of fluid motion. In the solution procedure, the laminated disk is regarded as double circular Euler sheets connected by a series of closely spaced and mutually independent vertical springs, and then an eighth-order differential equation of motion of the laminated disk is derived as the elastic boundary condition of the hydroelastic problem. An approximated model is then developed for the hydroelastic problem in shallow water. The deflection and bending moment of the disk and the free surface elevation near the disk are calculated, and it is found that the series solution for the velocity potential converges rapidly. Typical examples are presented to show the effects of different parameters, including wave frequency, the edge conditions of the disk, and the elastic coefficient of the core layer, on wave force, structural hydroelastic response, and wave field. Moreover, viscoelastic damping is introduced in the core layer, and its effect on the hydroelastic response is evaluated by adopting the complex stiffness method. The results indicate that the wave force on the laminated disk is larger than that on a corresponding rigid one over a very wide range of wave frequencies, and the local deformation of the lower sheet can be suppressed by designing a core layer with viscoelastic damping.

### A novel compressible enstrophy transport equation-based analysis of instability during Magnus–Robins effects for high rotation rates

The effects of compressibility on the instability of a two-dimensional flow past a rotating cylinder executing high rotation rates are investigated, in detail, using a novel analysis based on the compressible enstrophy transport equation (CETE). Accurate analysis of the instability necessitates the generation of high fidelity numerical solutions, and this is achieved by employing optimized numerical methods that enable high accuracy direct numerical simulation of compressible flows. To study the effects of compressibility induced by rotation alone, a low free stream Mach number and two high rotation rates are considered, as compared to that reported in the literature. Results demonstrate single-sided vortex shedding, the presence of significant compressibility in the flow field confirmed by local Mach number, and temperature and density gradient fields with transient formation of supersonic pockets noted for the higher rotation speed cases. The temporal instability is studied by analyzing the relative contributions of different terms in the CETE to the growth of enstrophy. As per the authors' knowledge, this is the first such research effort demonstrating an application of the CETE for instabilities. Analysis shows that viscous diffusion is the dominant mechanism in creating the flow instability with a secondary role played by the baroclinic mechanism.

### Predicting and optimizing multirow film cooling with trenches using gated recurrent unit neural network

The film cooling of cylindrical holes embedded in transverse trenches under superposition has shown promise for protecting the critical components of a high-pressure turbine from thermal damage. To optimize the relevant parameters and provide a suitable film cooling strategy, it is important to predict the effectiveness of lateral-averaged adiabatic film cooling with the trench effect on the surface of a blade. However, high-fidelity semi-empirical correlations for film cooling under superposition conditions with a trench have rarely been examined. This study establishes a gated recurrent unit (GRU) neural network model to predict the effectiveness of lateral-averaged film cooling under multiple-row superposition conditions with a trench. In general, a GRU neural network model is built with a large sequence of one-dimensional parameters, including the depth and width of the trench, compound angle, location of the hole, and blowing ratio. The computational fluid dynamics (CFD) method is used to provide a training dataset for the model. After careful testing and validation, the results predicted by the GRU agreed well with the CFD results. Moreover, the performance and robustness of the GRU were better than those of other recurrent neural network models, such as the long short-term memory model. Integrated with the GRU model, the sparrow search algorithm was adopted to optimize the parameters of the trench. The film cooling effectiveness of the optimized case improved by 1.6% compared with the best case, 28.5% compared with the worst case in dataset, and 23.5% compared with the no-trench case.