# Latest papers in fluid mechanics

### Large-eddy simulation of flow past a circular cylinder for Reynolds numbers 400 to 3900

The benchmarking case of flow past a circular cylinder at the Reynolds number (Re) of 3900 is computed with two open-source codes, OpenFOAM and Nektar++, which are based on the conventional finite volume method (FVM) and the high-order spectral/hp element method, respectively. By using the Nektar++ model, mesh convergence for the case Re = 3900 is demonstrated (perhaps for the first time) through a systematic mesh dependence study, which includes separate examinations of the spanwise domain length (Lz/D), spanwise resolution, and the resolution in the plane perpendicular to the spanwise direction. The computational efficiencies for the Nektar++ and OpenFOAM approaches are then compared. This benchmarking study adds value to the broad Nektar++ and OpenFOAM communities and to the numerical modeling of bluff-body flows in general. Based on the Nektar++ approach, the computations are then generalized to a range of Re = 400–3900. It is found that Lz/D = 3 is adequate for Re = 2500–3900, while an increased Lz/D = 6 is recommended for Re = 400–2000. Based on the present high-fidelity numerical data, the physical mechanisms for the variations in the wake recirculation length and the hydrodynamic forces and pressure on the cylinder with Re are explored. In particular, the physics behind the inverse correlation between the root mean square lift coefficient (CL′) and the wake recirculation length, which includes a significant decrease in CL′ over Re = 270–1500, is highlighted.

### Numerical instability investigation of inward radial Rayleigh–Bénard–Poiseuille flow

The spatial instability of inward radial Rayleigh–Bénard–Poiseuille flow was investigated using direct numerical simulations with random and controlled inflow forcing. The simulations were carried out with a higher-order-accurate compact finite difference code in cylindrical coordinates. Inward radial Rayleigh–Bénard–Poiseuille flows can be found, for example, in the collectors of solar chimney power plants. The conditions for the present simulations were chosen such that both steady and unsteady three-dimensional waves are amplified. The spatial growth rates are attenuated significantly in the downstream direction as a result of strong streamwise acceleration. For the oblique waves, the growth rates and wave angles decrease and the phase speeds get larger with increasing frequency. As the oblique waves travel downstream, the phase speeds decrease and the wave angles increase. Overall, steady waves with a wave angle of 90 ° are the most amplified. In general, because of the finite azimuthal extent, only certain azimuthal wavenumbers are possible. As a result, the steady waves appear to merge in the streamwise direction. When the inflow is at an angle such that a spiral flow is formed, one family of oblique waves is favored over the other and the mode shapes of the left- and right-traveling oblique waves are asymmetric with respect to the radius. As the inflow angle increases, this asymmetry is aggravated and the wavenumber of the most amplified disturbances is diminished.

### Direct numerical simulation of electroconvection with thin Debye layer matching canonical experiments

Electroconvection has the potential to be applied in electrochemical technologies such as electrodialysis and energy storage, and has thus aroused considerable research interest. This paper describes the direct numerical simulation (DNS) of the dimensionless Poisson–Nernst–Planck and Stokes equations for electroconvection to determine why the dimensionless thin Debye layer in existing simulations does not match the results of canonical experiments. Our DNS results show that the discrepancy between the simulation results and the experimental data is mainly caused by differences in the structural characteristics of the extended space charge layer. A dimensionless thin Debye layer matching those in canonical experiments enhances the driving force of the extended space charge layer, resulting in massive vortices near the permselective membranes that cause the electroconvective flow to transition from the steady state to time-dependent spatiotemporal dynamics. Our DNS results show that choosing the thickness of the dimensionless thin Debye layer to be consistent with canonical experiments is a key factor in the high-precision quantitative analysis of electroconvection characteristics such as the vortex height, dynamic evolution, and pattern formation. These results provide important guidance for the design and instability control of microfluidic chips.

### Applying deep reinforcement learning to active flow control in weakly turbulent conditions

Machine learning has recently become a promising technique in fluid mechanics, especially for active flow control (AFC) applications. A recent work [Rabault et al., J. Fluid Mech. 865, 281–302 (2019)] has demonstrated the feasibility and effectiveness of deep reinforcement learning (DRL) in performing AFC over a circular cylinder at Re = 100, i.e., in the laminar flow regime. As a follow-up study, we investigate the same AFC problem at an intermediate Reynolds number, i.e., Re = 1000, where the weak turbulence in the flow poses great challenges to the control. The results show that the DRL agent can still find effective control strategies, but requires much more episodes in the learning. A remarkable drag reduction of around 30% is achieved, which is accompanied by elongation of the recirculation bubble and reduction of turbulent fluctuations in the cylinder wake. Furthermore, we also perform a sensitivity analysis on the learnt control strategies to explore the optimal layout of sensor network. To our best knowledge, this study is the first successful application of DRL to AFC in weakly turbulent conditions. It therefore sets a new milestone in progressing toward AFC in strong turbulent flows.

### On the time irreversibility of compressible turbulence reflected by particles of various inertias

Time irreversibility of compressible homogeneous isotropic turbulence (HIT) is investigated from a Lagrangian point of view and single-particle statistics. For this purpose, direct numerical simulation (DNS) is implemented for compressible HIT at Taylor-mircoscale Reynolds number [math] and turbulent Mach number Mt up to 1.01, in which tracers and inertial particles in a wide Stokes number (St) range are instantaneously tracked with time. The statistics of instantaneous power of particles corroborates that the violation of detailed balance of turbulence in compressible HIT is much stronger than in incompressible HIT. It turns out that the third moment of dimensionless instantaneous power (Ir) of tracers scales as [math]. A possible explanation based on Kolmogorov-like argument proves to be plausible due to the lacks of direct verification and generality for other moments of the power. A further analysis from an Eulerian point of view suggests that the underlying mechanism for time irreversibility of highly compressible turbulence is quite different from that for weakly compressible or incompressible turbulence. For inertial particles, the moments of instantaneous power are suggested to scale as [math] at relatively large St numbers, and be dependent only on Mach number or Reynolds number at the small-St number end, which are manifested by the present numerical data. It is further shown that the empirical [math] scaling of Ir also approximately applies to various inertial particles, but only at high Mt numbers due to the diminishing effect of compressibility to the low-Mach number end. The time irreversibility announced by the Lagrangian statistical properties of particles of different inertias is shown to be highly associated with their responses to the vortex and shocklet structures in compressible turbulence.

### Dynamics of flame extinction in narrow channels with cold walls: Heat loss vs acceleration

Propagation of a premixed flame from a closed to an open end in micro-channels with smooth non-slip isothermal walls is considered in the context of flame extinction dynamics. Powerful exponential flame acceleration in micro-channels with adiabatic walls has been demonstrated at the initial quasi-isobaric stage of the process [Bychkov et al., Phys. Rev. E 72, 046307 (2005)]. In contrast to the previous studies, here we investigate flame propagation in channels with isothermal walls. The problem is solved by means of high-fidelity laminar numerical simulations of the complete set of the Navier–Stokes combustion equations. For most of the problem parameter sets chosen, we obtain initial flame acceleration after ignition at the closed channel end. This acceleration resembles qualitatively the adiabatic case, but it develops noticeably slower, in an approximately linear regime instead of the exponential one and persists only for a limited time interval. Subsequently, heat loss to the walls reduces the temperature and hence the volume of the burnt gas behind the flame front, which produces a reverse flow in the direction of the closed channel end. When the amount of the burnt gas becomes sufficiently large, the reverse flow stops the acceleration process and drives the flame backwards with modifications of the flame front shape from convex to concave. Eventually, the flame extinguishes. Qualitatively, the process obtained reproduces a possible combustion failure during deflagration-to-detonation transition observed in previous experiments. We investigate the key characteristics of initial flame acceleration such as the acceleration rate and the maximum speed of the flame tip.

### Hybrid lattice Boltzmann model for atmospheric flows under anelastic approximation

Lattice Boltzmann (LB) method for atmospheric dynamics is developed by considering the characteristics of the anelastic approximation. After introducing reference base state values in atmospheric flows, an LB model, with an external force term, has been constructed in anelastic framework. In the proposed anelastic LB model, mass and momentum conservation equations are solved by the LB method with a regularization procedure, and temperature field or scalar transport is simulated by finite volume method. The derived macroscopic governing equations from the anelastic model are analyzed and discussed in Chapman–Enskog asymptotic expansion. The anelastic LB model is assessed considering three benchmarks including a non-hydrostatic atmospheric inviscid convection, two-dimensional density currents, and inertia-gravity waves in stably stratified atmospheric layer. The validations demonstrate that the anelastic extension of the LB method can simulate atmospheric flows effectively and accurately. Besides, the proposed model offers a unified framework for both Boussinesq approximation and anelastic approximation, which is largely free of characteristic depth of atmospheric flows.

### Surface wave scattering by multiple flexible fishing cage system

A study of the wave dynamics around a multiple cylindrical fishing cage system is carried out under the assumption of linear water wave theory and small-amplitude wave response. The Fourier–Bessel series expansion of the velocity potential is derived for the regions enclosed under the open-water and cage systems and the immediate vicinity. The scattering between the cages is accounted for by employing Graf's addition theorem. The porous flexible cage system is modeled using Darcy's law and the three-dimensional membrane equation. The edges of the cages are moored along their circumferences to balance its position. The unknown coefficients in the potentials are obtained by employing the matched eigenfunction method. In addition, the far-field scattering coefficients for the entire system are obtained by expanding the Bessel and Hankel functions in the plane wave representation form. Numerical results for the hydrodynamic forces, scattering coefficients, and power dissipation are investigated for various cage and wave parameters. The time simulation for the wave scattering from the cage system is investigated. The study reveals that wave loading on the cage system can be significantly reduced by the appropriate spatial arrangement, membrane tension, and porous-effect parameter. Moreover, the far-field results suggest that the cage system can also be used as a breakwater.

### Why do anguilliform swimmers perform undulation with wavelengths shorter than their bodylengths?

Understanding the connection between physiology and kinematics of natural swimmers is of great importance to design efficient bio-inspired underwater vehicles. This study looks at high-fidelity three-dimensional numerical simulations for flows over an undulating American eel with prescribed anguilliform kinematics. Particularly, our work focuses on why natural anguilliform swimmers employ wavelengths shorter than their bodylengths while performing wavy kinematics. For this purpose, we vary the undulatory wavelength for a range of values generally observed in different aquatic animals at Strouhal numbers 0.30 and 0.40. We observe that our anguilliform swimmer is able to demonstrate more suitable hydrodynamic performance for wavelengths of 0.65 and 0.80. For longer wavelengths, the swimmer experiences large frictional drag, which deteriorates its performance. The wake topology was dominated by hairpin-like structures, which are closely linked with the underlying physics of anguilliform swimming found in nature.

### Erratum: “A constitutive hemorheological model addressing both the deformability and aggregation of red blood cells” [Phys. Fluids 32, 103103 (2020)]

### Interpreting dynamics of snap-off in a constricted capillary from the energy dissipation principle

Snap-off usually occurs during two-phase fluid displacement in a constricted capillary, where the nonwetting phase fluid is cut into blobs or ganglia due to surface tension. Snap-off has been intensely recognized as a predominant pore-scale mechanism that may be responsible for the breakup and trapping of the nonwetting phase in complex geophysical structures. Herein, we investigated the dynamics of snap-off in a constricted pore and throat structure with a square cross-section using the volume of fluid method. Despite the geometric constraint dictated by Roof, a new judging diagram for the occurrence of snap-off was proposed as a function of Ca number and viscosity ratio. Our prediction from the numerical simulation is consistent with the analytical solution derived from the balance of capillary and hydrodynamic pressure. Furthermore, the associated transient energy balance was thoroughly studied, considering the alteration of the surface energy, kinetic energy, total input energy, and viscous dissipation during the period of snap-off. The results indicated that snap-off is always characterized by a sharp decline in the surface energy, which resulted in a surge in the kinetic energy and viscous dissipation. In addition, we observed a sharp surge in the viscous dissipation rate curve associated with such energy change, which is attributed to the redistribution of the velocity field. The sudden surge unanimously decreased while increasing the Ca number or viscosity ratio. Meanwhile, the position at which snap-off took place was shifted downstream of the throat, explaining the condition of the snap-off had become much more difficult.

### Bubble hydrodynamics and mass transfer in stirred tank with non-Newtonian fluids: Scale-up from laboratory to pilot-scale

Mass transfer is a crucial phenomenon in designing and scaling up chemical and biochemical stirred tanks. The literature lacks a pilot-scale study on investigating mass transfer in non-Newtonian fluids. A pilot-scale study is a prerequisite step before scaling up the process from laboratory to industrial-scale. Thus, a study using pilot-scale stirred tank was conducted to investigate bubble hydrodynamics and mass transfer in non-Newtonian fluids. This work is a scale-up study from laboratory to pilot-scale. Axial distributions of bubble–liquid mass transfer coefficient and interfacial area were obtained using dedicated in situ optical endoscope probes (oxygen and bubble size) simultaneously. Volumetric mass transfer coefficient was determined by recording local dissolved oxygen concentrations in liquid. Interfacial area was estimated by measuring local bubble size and global gas holdup. Bubble–liquid mass transfer coefficient was then deduced by combining the obtained values of volumetric mass transfer coefficient and interfacial area. Effects of operating conditions, fluid rheology, and probe axial positions (liquid height) on bubble–liquid mass transfer coefficient were considered. The operating conditions (power inputs and superficial gas velocities) were in the range of 30–250 W/m3 and 3.10–4.70 mm/s, respectively. Bubble–liquid mass transfer coefficient increased with an increase in operating conditions, whereas it decreased with an increase in fluid rheology and liquid height. Scale-up effects on mass transfer were higher for water than viscous fluids, as suggested by large deviation (9.6%) in values of bubble–liquid mass transfer coefficient.

### Capillary driven flow in oval tubes under microgravity

The capillary driven flow of a liquid in a tube of elliptical cross section under microgravity is studied in this paper. All the factors including the dynamic contact angle between the liquid and the tube wall, the pressure loss caused by convection, the viscous resistance in the tube and the reservoir, and the curved liquid surface in the reservoir are considered. The equation of capillary driven flow in the tube of elliptical cross section is derived. The flow equation can be transformed into an equation that combines external forces on the control body in the tube. In the case of low Ohnesorge ([math]) numbers, the flow behavior is divided into three time domains by using the capillary force as the driving force that balances with the inertial force in the reservoir, the convective pressure loss in the reservoir, and the viscous resistance in the tube in the three domains, respectively. The liquid climbing height in these three sections is proportional to [math], [math], and [math], respectively. However, in the case of high [math] numbers, the flow is divided into two regions, something which has not been proposed in previous work about capillary driven flow in cylinder tubes. This study is verified by drop tower experiments and numerical simulation with the volume of fluid method.

### Receptivity to forcing disturbances in subcritical liquid sheet flows

The receptivity to forcing harmonic disturbances of transverse velocity in subcritical liquid sheet flows subjected to gravity is studied. The investigation is carried out both by employing the linear stability theory applied to a simplified one-dimensional inviscid model and by performing fully two-dimensional numerical simulations based on the Volume-of-Fluid technique. The computation of global sinuous eigenmodes and eigenvalues has required the removal of the singularity of the governing equation, for the first time carried out in the case of unconfined gaseous ambient. Direct numerical simulations of the unsteady sheet when continuously forced by a perturbation in lateral velocity are reported. The harmonic forcing, applied at the inlet section, basically excites sinuous modes of the system, related to the natural impulse response. The results of receptivity have been treated by employing a proper one-dimensional reduction technique to compare numerical data with the corresponding findings of the stability theory. Depending on the Reynolds number, two different behaviors are observed: at low Re the large viscous effect makes the system overdamped; as Re increases and the inviscid conditions are approaching, the frequency response exhibits a peak frequency (resonance) which closely agrees with the frequency of the least stable eigenvalue. The various stations synchronize with the critical station as Re increases, and therefore it forces the global oscillations of the flow field. This behavior of the critical station retrieves the role of wavemaker, which fails for high-frequency forcing. The resonance characteristics of the sheet have been further analyzed by inspecting the fully two-dimensional velocity fields. A major finding at low forcing frequency is the nonlinear varicose distortion of the sheet thickness that progressively envelops the basic sinuous shape when the inviscid conditions are approaching.

### Characterization of H2O transport through Johnson Space Center number 1A lunar regolith simulant at low pressure for in-situ resource utilization

H2O transport through a packed bed of Johnson Space Center number 1A (JSC-1A) lunar regolith simulant was examined at relevant temperatures and pressures for in-situ resource utilization (ISRU) on the Moon. Experimentation was conducted over a range of pressures from 50 to 2065 Pa at ∼350 K, corresponding to Knudsen numbers of 0.3 < Kn < 11. Pressure and temperature conditions were relevant toward ISRU technologies. A piecewise function was used to evaluate transition and Knudsen regime flows. The piecewise model utilized a Knudsen number that predicted the transition point between advective and Knudsen flows. A transition Knudsen number of 1.66 ± 0.61 and a tortuosity shape parameter of 0.736 ± 0.13 were determined from non-linear regression, and Knudsen diffusivities of 10.62 cm2·s−1, 10.40 cm2·s−1, and 9.04 cm2·s−1 for packed beds of JSC-1A with porosities of 0.388, 0.385, and 0.365, respectively. The experimental measurements, methodology, and modeling provide useful information for ISRU technologies involving the transport of volatiles (e.g., thermal extraction of H2O).

### Simple extended lattice Boltzmann methods for incompressible viscous single-phase and two-phase fluid flows

The lattice Boltzmann method (LBM) is a numerical method with second-order spatial accuracy for incompressible viscous fluid flows based on an analogy with the kinetic theory of gases. Recently, the collision model of the LBM has become more and more complicated as its numerical stability has been enhanced. In this paper, conversely, we propose simple extended LBMs having good numerical stability with simple collision models by using the lattice kinetic scheme (LKS), which is an extended LBM. First, several schemes for single-phase flows based on the LKS are presented. The LKS is a simple stable scheme but has higher-order dissipation errors in the calculation of high-Reynolds-number flows. To solve this problem, the LKS is improved by using the linkwise artificial compressibility method (LWACM). Then, the numerical stability and accuracy of the LBM, the LKS, the LWACM, and the improved LKS are compared in a simulation of a doubly periodic shear layer at high Reynolds number with low-resolution grids. Next, a simple scheme for two-phase flows with large density ratio is constructed on the basis of the LKS and the improved LKS. The scheme is stable even for two-phase flows with large density ratio. The validation of the scheme is studied in a simulation of a binary droplet collision.

### An improved equation of state for air plasma simulations

This work is concerned with the development of a novel, accurate equation of state for describing partially ionized air plasma in local thermodynamic equilibrium. One key application for this new equation of state is the simulation of lightning strike on aircraft. Due to the complexities of species ionization and interaction, although phenomenological curve fitting of thermodynamic properties is possible, these curves are intractable for practical numerical simulation. The large difference in size of the parameters (many orders of magnitude) and complexity of the equations means they are not straightforward to invert for conversion between thermodynamic variables. The approach of this paper is to take an accurate 19-species phenomenological model and use this to generate a tabulated dataset. Coupled with a suitable interpolation procedure, this offers an accurate and computationally efficient technique for simulating partially ionized air plasma. The equation of state is implemented within a multiphysics methodology which can solve for two-way coupling between a plasma arc and an elastoplastic material substrate. The implementation is validated against experimental results, both for a single material plasma and an arc coupled to a substrate. It is demonstrated that accurate, oscillation-free thermodynamic profiles can be obtained, with good results even close to material surfaces.

### Double-D2Q9 lattice Boltzmann models with extended equilibrium for two-dimensional magnetohydrodynamic flows

The vast majority of the existing lattice Boltzmann methods (LBMs) suggest to relax relevant quantities to a second-order truncated equilibrium state. Despite its simplicity and popularity, this choice does not fully exploit the potential of any lattice discretization. In this paper, an extended equilibrium state is adopted to evaluate the suitability of different LBMs (i.e., the Bhatnagar–Gross–Krook, the multiple-relaxation-time in terms of raw and central moments, and the simplified one) to simulate two-dimensional magnetohydrodynamic flows by means of the D2Q9 velocity space. Two sets of particle distribution functions are employed: one for the flow field and the other for the magnetic one. Even if the minimal five-velocities discretization is sufficient to represent the evolution of the latter, a nine-velocities model enhances the capability to enforce the divergence-free condition of the magnetic field, as shown. Therefore, a double-D2Q9 approach is herein devised. Eventually, the computational cost involved by all the schemes is discussed both in terms of virtual memory and run time. Interestingly, the simplified LBM for magnetohydrodynamic flows is herein presented for the first time.

### Coiling of a viscoelastic fluid filament

Author(s): Yunxing Su, Bernardo Palacios, and Roberto Zenit

Coiling of a fluid filament is observed when the fluid viscosity is sufficiently large. The coiling frequency depends on several parameters (shown in the image) but most notably on viscosity. In this study we found that viscoelastic fluid filaments coil at a much smaller frequency than that of Newtonian fluids, under equivalent conditions. The reduction results from the increased value of the extensional viscosity typically observed for these liquids.

[Phys. Rev. Fluids 6, 033303] Published Thu Mar 18, 2021

### Parametric transition from deflagration to detonation in stellar medium

Author(s): Peter V. Gordon, Leonid Kagan, and Gregory Sivashinsky

The nature of thermonuclear explosions of white-dwarf stars is a fundamental astrophysical issue, the first principle interpretation of which is still commonly regarded as an unresolved problem. There is a general consensus that stellar explosions are a manifestation of the deflagration-to-detonatio...

[Phys. Rev. E 103, 033106] Published Wed Mar 17, 2021