# Latest papers in fluid mechanics

### Universal nature of rapid evolution of conservative gravity and turbidity currents perturbed from their self-similar state

Author(s): Santiago L. Zúñiga, Jorge S. Salinas, S. Balachandar, and Mariano I. Cantero

We explore the nature of gravity and conservative turbidity currents perturbed from their self-similar state and, in particular, we elucidate the cyclic sequence that universally arise in these rapidly-varying regimes. This sequence comprises four states determined by the bulk Richardson number and the acceleration/deceleration of the flow, and its universal nature is supported by six highly resolved direct and large eddy simulations. We study the details of this complex nonmonotonic rapid evolution and explore the how and why of this unique behavior.

[Phys. Rev. Fluids 7, 043801] Published Fri Apr 22, 2022

### Unsteady and inertial dynamics of a small active particle in a fluid

Author(s): T. Redaelli, F. Candelier, R. Mehaddi, and B. Mehlig

In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997), to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere.

[Phys. Rev. Fluids 7, 044304] Published Fri Apr 22, 2022

### Optimal eddy viscosity in closure models for two-dimensional turbulent flows

Author(s): Pritpal Matharu and Bartosz Protas

We consider fundamental limitations on the performance of eddy-viscosity closure models for turbulent flows focusing on the Leith model for two-dimensional Large Eddy Simulation (LES). Optimal eddy viscosities depending on the vorticity gradient magnitude are determined subject to minimum assumptions by solving partial-differential-equation-constrained optimization problems defined such that the corresponding optimal LES best matches the filtered Direct Numerical Simulation. Since the optimal eddy viscosities do not converge to a well-defined limit as the regularization vanishes, we conclude that the problem of finding an optimal eddy viscosity does not have a solution and is ill-posed.

[Phys. Rev. Fluids 7, 044605] Published Fri Apr 22, 2022

### Ferrofluid annulus in crossed magnetic fields

Author(s): Pedro O. S. Livera, Pedro H. A. Anjos, and José A. Miranda

We study the dynamics and pattern formation of a ferrofluid annulus enveloped by two nonmagnetic fluids in a Hele-Shaw cell, subjected to an in-plane crossed magnetic field configuration involving the combination of radial and azimuthal magnetic fields. A perturbative, second-order mode-coupling ana…

[Phys. Rev. E 105, 045106] Published Thu Apr 21, 2022

### Critical pressure in liquids due to dynamic choking

Author(s): Jiří Vacula and Pavel Novotný

The existence of a critical pressure ratio due to gas-dynamic choking is well known for an ideal gas. It is reasonable to assume that liquids whose compressibility is defined by the bulk modulus also have a critical pressure ratio. The problem discussed here is a fundamental one because it deals wit…

[Phys. Rev. E 105, 045107] Published Thu Apr 21, 2022

### Bursting on a vortex tube with initial axial core-size perturbations

Author(s): Lingbo Ji and Wim M. Van Rees

Axisymmetric rectilinear vortex tubes develop twist waves if their core size varies along the centerline. These twist waves propagate, and when two opposite-signed twist waves meet their interaction leads to vortex bursting. We perform numerical simulations of vortex tubes with a range of initial core-size perturbation amplitudes, and provide a detailed analysis of the bursting dynamics. Our results explain the main mechanisms driving and subsequently arresting the bursting process; quantify the accelerated energy dissipation due to bursting; and show that bursting is susceptible to non-axisymmetric instabilities that further accelerate the decay of the vortex tube.

[Phys. Rev. Fluids 7, 044704] Published Thu Apr 21, 2022

### Early detection of the combustion instabilities by quantifying diagonal-wise measurements of joint recurrence plots of pressure and radiant energy fluctuations

This article presents a study of the early detection of combustion instabilities of a [math] liquid rapid premixed oil swirled burner. The main objective was the calculation of indexes, based on a chaotic analysis, able to detect in advance the combustion instabilities. In the combustor, the air mass flow rate was kept constant, and in order to induce the combustion instabilities, the fuel mass flow rate was adjusted during the experiments in which pressure and radiant energy fluctuations were simultaneously measured from the combustion chamber. In this chaotic analysis, joint recurrence plots were calculated in order to analyze the dependence between the pressure and radiant energy fluctuations. Hence, a diagonal-wise quantification was applied to the joint recurrence plots to calculate four indexes: the τ-recurrence rate index [math], the τ-determinism index [math], the τ-average diagonal line length index [math], and the τ-entropy index [math]. The results show that all four indexes were capable of sorting all cases under analysis into two groups: the “combustion noise regime” due to the low-amplitude aperiodic oscillations and the “combustion instability regime” due to the high-amplitude periodic oscillations. In addition, early detection of the transitions were also detected. Therefore, the results presented in this research showed that the four indexes were effective precursors in order to detect in advance the combustion instabilities.

### A novel approach to quantify ventilation heterogeneity in occluded bronchial tree based on lung admittance

Obstructions in airways result in significant alterations in ventilation distribution and consequently reduce the ventilation to perfusion ratio, affecting gas exchange. This study presents a lumped parameter-based model to quantify the spatial ventilation distribution using constructal theory. An extension of the existing theory is made for the conductive bronchial tree and is represented in matrix frame incorporated with airway admittances. The proposed lung admittance model has a greater advantage over the existing methodologies based on lung impedance, as it can be applicable for both fully and partially blocked regions. We proved the well-posedness of the problem, and the generated matrix is highly sparse in nature. A modified block decomposition method is implemented for symmetric and asymmetric trees of various obstructions [math] to reduce the memory size. The asymmetry is considered in every left branch of the bronchial tree recursively, following the mathematical relations: [math] and [math], where L and D are the length, diameter of the jth branch at ith generation, respectively, for [math]. It is observed that relative flow rate [math] decreases exponentially with the generation index. In tidal breathing, the regional ventilation pattern is found to vary spatially instead of spatio-temporally. The comparison of our result with the clinical data is found to be accurate when 40% or more obstruction is considered in the proximal region (observed in asthma). Moreover, this predicts an increment of lung impedance by 6%, which can be used for further improvement of clinical observations.

### Large-eddy simulations of self-excited thermoacoustic instability in a premixed swirling combustor with an outlet nozzle

Reducing the footprint of greenhouse gases and nitrogen oxides (NOx) emissions from combustion systems means that they have been operating under lean or ultra-lean fuel–air premixed conditions. Under such conditions, self-excited large-amplitude pulsating thermoacoustic instabilities may occur, characterized by deafening combustion noises and even “violent” structural vibrations, which is, therefore, highly undesirable in practice. By conducting chemical reaction-thermodynamics-acoustics-swirling flow coupling investigations, we have numerically explored the generation and mitigation mechanisms of self-excited pulsating oscillations in a methane-fueled swirling combustor in the presence and absence of an outlet nozzle. Hence, a large-eddy simulation was performed on a fully three-dimensional compressible flow via an open-source platform, OpenFOAM. Furthermore, a thorough assessment was made to understand the fundamental physics of the interaction of the swirling flame, either constructively or destructively, to the acoustic pressure perturbations by examining the local Rayleigh criterion/index. A further explanation was made on implementing the outlet nozzle that can mitigate such periodic pulsating combustion via attenuating the fuel fraction fluctuations, vortices processing, and changing temperature field. It was also found that the dominant pulsating mode is switched from the 1/4 standing-wave wavelength mode to the 3/4 wavelength mode. Finally, more physical insights were obtained by conducting a proper orthogonal decomposition analysis on the energy distribution between the thermoacoustic modes.

### Temporary velocity correction-based immersed boundary–lattice Boltzmann method for incompressible flows in porous media at representative elementary volume scale

The immersed boundary (IB)–lattice Boltzmann (LB) method is an effective strategy for complex boundary condition treatment. By adding an extra body force term in the LB equation properly, the specific velocity boundary condition can be enforced in this method. However, when it comes to incompressible flows through porous media at the representative elementary volume (REV) scale, the conventional IB–LB method fails because the velocity and the force term induced by porous media are coupled. In order to solve this problem, a temporary velocity is used to construct the IB-induced force term with the enforcement of the velocity boundary condition. The temporary velocity is decomposed into the intermediate temporary velocity and the corresponding correction. By this treatment, the temporary velocity correction is the linear function of the IB-induced force term. Furthermore, to obtain the force term accounting for the IB, the velocity boundary condition is transformed to the temporary velocity. Consequently, a temporary velocity correction-based IB–LB method is established for the incompressible flows at the REV scale. To avoid the error of explicitly calculating the IB-induced force term, the multi-direct-forcing scheme is employed in which iteration is carried out in terms of the specific boundary condition. The proposed IB–LB method for REV-scale incompressible flows is applied for the Couette flow in a porous annulus and lid driven flow in a square cavity filled with porous matrix. Numerical results show the computational accuracy of the developed IB–LB method.

### A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water

The aim of this paper is to calculate the time dependence of the mean position (and orientation) of a fluid particle when a fluid system at thermodynamic equilibrium is submitted to a mechanical action. The starting point of this novel theoretical approach is the introduction of a mechanical energy functional. Then using the notions of inertial modes and action temperature, and assuming a mechanical energy equipartition principle per mode, the model predicts the existence of a dynamic phase transition where the rheological behavior of the medium evolves from a solid-like to a liquid-like regime when the mechanical action is increased. The well-known Newtonian behavior is recovered as the limiting case. The present modeling is applied to the analysis of recent liquid water viscoelastic data pointing out a prevalent elastic behavior in confined geometry. It is demonstrated that the model makes it possible to understand these data in a coherent and unified way with the transport properties (viscosity and self-diffusion coefficient). It is concluded that any finite volume of fluid at rest possesses a static shear elasticity and should therefore be considered as a solid-like medium.

### Granular mixtures discharging through a silo with lateral orifice

Here, we studied the flow dynamics of a mixture of dumbbells and disks flowing through an orifice situated on the lateral wall of a two-dimensional silo using the discrete element method. When two constituent parts of a dumbbell are simultaneously in contact with either a disk or one part of another dumbbell, it hinders the relative motion of both the particles. An increase in the fraction of dumbbells increases the number of contacts exhibiting the aforementioned mechanism, thus increasing the dynamic friction. This leads to a decrease in the flow rate with an increase in the fraction of dumbbells. To relate the flow rate with the fraction of dumbbells and the orifice width, we proposed modified Beverloo's law scaling. Moreover, we presented coarse-grained flow fields, which reveal the presence of stagnant zones that hinder the free flow of particles adjacent to them.

### Analysis of turbulence generation and dissipation in shear layers of methane–oxygen diffusion flames using direct numerical simulations

A turbulent methane–oxygen diffusion flame is studied using a direct numerical simulation setup. The operating regime and turbulence characteristics are chosen to resemble those of a modern methane rocket combustor. Local flame characteristics and dimensionless numbers are defined and evaluated, and their relationship with the turbulent kinetic energy transport budget is studied. Positive net turbulence generation is observed in the reaction shear layer. It is found that the underlying mechanisms for these results are similar to those encountered in premixed flames, with pressure terms acting as the primary turbulent kinetic energy sources. Models for predicting turbulent transport through mean pressure gradients, fluctuating pressure gradients, and turbulent flux of turbulent kinetic energy are adapted. The accuracy of the proposed formulations is assessed, and the involved challenges are discussed.

### Development of subgrid-scale model for LES of Burgers turbulence with large filter size

A neural network (NN) with one hidden layer is implemented to establish a relationship between the resolved-scale flow field and the subgrid-scale (SGS) stress for large eddy simulation (LES) of the Burgers equation. Five sets of input are considered for the neural network by combining the velocity gradient and the filter size. The training datasets are obtained by filtering the direct numerical simulation (DNS) results of the Burgers equation with random forcing function. The number of modes is sufficiently large (N = 65 536) to resolve extremely small scales of motion. In the a priori test, a correlation coefficient over 0.93 is achieved for the SGS stress between the NN models and the filtered DNS data. The results of the a posteriori test reveal that the obtained solutions are stable for all NN models without applying any stabilization techniques. However, not all NN models have a reasonable performance when embedded in the LES code. The applicability of the NN models to the Burgers equation with higher and lower viscosity is also investigated, and it is indicated that the most reliable NN models obtained in this paper can be applied to a set of parameters which are different from those used in training. The results of the SGS models constructed using the neural network are also compared with the existing models, and it is shown that the best obtained NN models outperform the Smagorinsky model and the gradient model, and are comparable to the dynamic Smagorinsky model. However, the NN models have an advantage over the dynamic Smagorinsky model in numerical cost.

### Machine-learning flow control with few sensor feedback and measurement noise

A comparative assessment of machine-learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number (Re = 100). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylinder. The feedback employs several velocity sensors. Two probe configurations are evaluated: 5 and 11 velocity probes located at different points around the cylinder and in the wake. The control laws are optimized with Deep Reinforcement Learning (DRL) and Linear Genetic Programming Control (LGPC). By interacting with the unsteady wake, both methods successfully stabilize the vortex alley and effectively reduce drag while using small mass flow rates for the actuation. DRL has shown higher robustness with respect to different initial conditions and to noise contamination of the sensor data; on the other hand, LGPC is able to identify compact and interpretable control laws, which only use a subset of sensors, thus allowing for the reduction of the system complexity with reasonably good results. Our study points at directions of future machine-learning control combining desirable features of different approaches.

### Active learning of tandem flapping wings at optimizing propulsion performance

In the present work, we propose an optimization framework based on the active learning method, which aims to quickly determine the conditions of tandem flapping wings for optimal performance in terms of thrust or efficiency. Especially, multi-fidelity Gaussian process regression is used to establish the surrogate model correlating the kinematic parameters of tandem flapping wings and their aerodynamic performances. Moreover, the Bayesian optimization algorithm is employed to select new candidate points and update the surrogate model. With this framework, the parameter space can be explored and exploited adaptively. Two optimization tasks of tandem wings are carried out using this surrogate-based framework by optimizing thrust and propulsion efficiency. The response surfaces predicted from the updated surrogate model present the influence of the flapping frequency, phase, and separation distance on thrust and efficiency. It is found that the time-average thrust of the hind flapping wing increases with the frequency. However, the increase in frequency may lead to a decrease in propulsive efficiency in some circumstances.

### Long-wave instabilities of evaporating/condensing viscous film flowing down a wavy inclined wall: Interfacial phase change effect of uniform layers

The interfacial phase change effect on a thin film flowing down an undulated wall has been investigated in the present study. The study is performed for a general periodic undulated bottom of moderate steepness that is long compared to the film thickness, followed by a case study over the sinusoidal bottom. The long-wave instabilities of the ununiform film are used by deriving a nonlinear evolution equation in the classical long-wave expansion method framework. The one-equation model can track the free surface evolution and involve the bottom undulation, viscosity, gravity, surface tension, and phase change (evaporation/condensation) effects. Linear stability analysis shows that the bottom steepness ζ has a dual role. In the downhill region, increasing ζ destabilizes, whereas increasing ζ stabilizes in the uphill region. Weakly nonlinear waves are studied using the method of multiple scales to obtain the complex Ginzburg–Landau equation. The results show that both supercritical and subcritical solutions are possible for evaporating and condensate film. Interestingly, while one subcritical region is visible for an evaporating film, two subcritical unstable regions are found for condensate film. The numerical solution of the free-surface equation demonstrates the finite-amplitude behavior that tends to dry out for an evaporating film. For condensate film, the thickness increases rapidly. The rupture dynamics highly depend on the initial perturbation, and the bottom steepness has a negligible effect on it. Kutateladze number has a significant impact on the stability characteristic of the film flow as it represents a sort of efficiency of phase change that occurs at the interface.

### Study of the secondary droplet breakup mechanism and regime map of Newtonian and power law fluids at high liquid–gas density ratio

This work reports the numerical investigation of the secondary breakup of non-Newtonian droplets at different Weber [math] and Ohnesorge [math] numbers. As part of this work, an in-house coupled level set volume of fluid solver is developed based on OpenFOAM libraries. It uses improved curvature calculation techniques like smoothening and the closest point search method. Flow is assumed to be axisymmetric. Approximately 95 different cases were simulated to investigate the effect of [math] and [math] numbers on secondary breakup for Newtonian, shear-thinning, and shear-thickening fluids. [math] varies from [math] to [math], and, correspondingly, [math] varies from [math] to [math]. The non-Newtonian rheology is modeled as a power-law fluid, and the power-law index [math] ranged from [math]. The present work describes the flow field near the droplet and the effects of non-Newtonian parameters and viscosity on the flow field. The various aspects of droplet dynamics like droplet deformation ratio [math], deformation rate [math], and coefficient of pressure [math] are studied and compared with the internal flow theory. A generalized relation for critical Weber number [math] is proposed for both Newtonian and non-Newtonian fluids and is shown in a phase diagram plot to map the different regimes of secondary droplet breakup.

### Ganglia dynamics during imbibition and drainage processes in nanoporous systems

We study the gas–water transient imbibition and drainage processes in two-dimensional nanoporous media using our recently developed lattice Boltzmann model. To describe the microscopic molecular interactions, the model employs a pseudopotential that correlates the local density and interaction strength to perform simulation at a mesoscopic scale. The primary interest is ganglia dynamics in the nanoporous media affected by fluid and geometrical properties of the porous structure. We performed sensitivity analyses on the fluid and rock characteristics such as the Euler number, gas–water interfacial area, water film area, capillary pressure, pore size distribution, specific surface area, and wettability. The simulation results revealed the fingering nature of the nonwetting phase. In the imbibition process, the flow pathway of water results in isolated and trapped gas bubble clusters because of the strong attraction between water and solid surfaces. In the drainage process, the pressure difference between the gas phase and the water phase depends on both the capillary pressure and the disjoining pressure due to the presence of water film. Pore topography and specific surface area control the continuity of the fluid phases in the imbibition process. In nonwet systems, the water phase starts fingering in the nanoporous system. The present work elucidates the microscopic ganglia dynamics of gas–water two-phase flow in nanoporous media. The microscopic scale details will help establish the macroscopic flow equation to accurately predict two-phase flow in shale gas, tight oil, and caprock seals.

### Self-propulsion of a submerged sphere due to coupling of its deformation and internal mass shift

The self-propulsion of a deforming sphere through an unbounded inviscid fluid is investigated analytically. Its motion is only induced by the coupling of its radial alteration, centroid shift, and rotation of the internal masses without vortex shedding and external forces. The Lagrange equations are used to describe such self-motion since the fluid-body system is conservative. Then the expressions for translational and rotational velocities of the deforming body are obtained in algebraic forms. Several cases show that some typical moving patterns of the sphere would be obtained as long as its radius variation and internal mass shift are properly coupled.