# Latest papers in fluid mechanics

### Aerodynamic drag modification induced by free-stream turbulence effects on a simplified road vehicle

We report an extensive experimental investigation into the effects of inflow turbulence on a simplified road vehicle, the so-called square back Ahmed body. Variations reaching up to [math] and −17% of the drag coefficient are observed for free-stream turbulence representative of open-road conditions [J. W. Saunders and R. B. Mansour, “On-road and wind tunnel turbulence and its measurement using a four-hole dynamic probe ahead of several cars,” SAE Trans. 109, 477 (2000)]. Regular turbulence grids are mounted upstream the Ahmed body. The turbulence intensity and the integral length scale of turbulence are varied using different mesh, bar sizes, and solidity. The boundary layer developing around the body together with the structure of the wake is strongly altered by free-stream turbulence where both the length of the recirculation and the shear layer characteristics are modified. A weakly non-parallel stability analysis of the shear layers together with a momentum budget, both bounding the recirculation region, shows that coherent structures, traced through the Reynolds stresses and streamwise turbulent fluctuations, are the key mechanisms that control drag. Subsequently, the analysis of the shear layer together with the stability analysis demonstrate that the mean vertical shear is the key component that controls the Reynolds stresses and thereby the drag experienced by the vehicle. These findings raise the question of the importance of free-stream turbulence when considering studies dedicated to car aerodynamics and subsequent control strategies, most of which neglect the influence of inflow conditions. This issue is also of major importance for guiding the design of the next generation of control strategies for drag reduction.

### Saturation mechanism of the fluctuation dynamo in supersonic turbulent plasmas

Author(s): Amit Seta and Christoph Federrath

The physical mechanism of converting the kinetic energy of turbulence to magnetic energy is known as a dynamo. Fluctuation dynamo amplifies magnetic fields at scales smaller than the driving scale of turbulence. We show that the fluctuation dynamo in subsonic turbulent plasma is similar to the supersonic case in some aspects and very different in others.

[Phys. Rev. Fluids 6, 103701] Published Mon Oct 04, 2021

### Predator-prey plankton dynamics in turbulent flow past an obstacle

Author(s): Alice Jaccod, Stefano Berti, Enrico Calzavarini, and Sergio Chibbaro

A predator-prey model of plankton dynamics in a turbulent flow past an idealized island is studied through fully-resolved numerical simulations to understand the complex interplay between biological excitable behavior and flow transport. We provide evidence that for a certain relation between advective and biological time scales, plankton accumulates in localized filamentary regions where velocity gradients compete with reaction-diffusion spreading, favoring persistence and primary production. The impact of small turbulent scales and of the geometrical details of the obstacle are investigated as well, quantifying their effects on plankton dynamics and patchiness.

[Phys. Rev. Fluids 6, 103802] Published Mon Oct 04, 2021

### Contribution of Mach number to the evolution of the Richtmyer-Meshkov instability induced by a shock-accelerated square light bubble

Author(s): Satyvir Singh

The Richtmyer-Meshkov (RM) instability has long been an interesting subject due to its fundamental significance in scientific research. In the current study, the contribution of shock Mach number on the evolution of the RM instability induced by a shock-accelerated square light bubble is investigated numerically. The shock Mach number causes significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. The Mach number effects are explored in detail through various physical phenomena such as vorticity production, kinetic energy, dissipation rate, and enstrophy.

[Phys. Rev. Fluids 6, 104001] Published Mon Oct 04, 2021

### Polymer drag reduction in surfactant-contaminated turbulent bubbly channel flows

Author(s): Daulet Izbassarov, Zaheer Ahmed, Pedro Costa, Ville Vuorinen, Outi Tammisola, and Metin Muradoglu

Interface-resolved direct numerical simulations are performed to investigate the effects of clean (top) and contaminated (bottom) bubbles driven upward in Newtonian and viscoelastic turbulent channel flows. It is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows. An addition of a minute amount of Triton X-100 to the viscoelastic turbulent bubbly flow system is found to be sufficient to revive the polymer drag reduction effects.

[Phys. Rev. Fluids 6, 104302] Published Mon Oct 04, 2021

### Fluid dynamics beyond the continuum: A physical perspective on large-eddy simulation

Author(s): Max Okraschevski, Sven Hoffmann, Katharina Stichling, Rainer Koch, and Hans-Joerg Bauer

In our work, we motivate and rederive the Large-eddy simulation (LES) framework by coarse-graining of Lagrangian fluid elements making use of a statistical mechanics approach. Consequently, we understand that LES is much more than a numerical turbulence model, namely a perspective commonly taken by modern fluid dynamicists, not only in numerical simulations but also in experiments. From this point of view, we see the potential to develop a unified theory for LES and the Reynolds-averaged Navier-Stokes (RANS) framework and additionally reveal a link to uncertainty quantification in particle image velocimetry (PIV).

[Phys. Rev. Fluids 6, L102601] Published Mon Oct 04, 2021

### Simulation of upward gas—hydrate slurry multiphase flow in a vertical concentric annulus for natural gas hydrate solid fluidization exploitation

The accurate simulation of upward multiphase flow of hydrate slurry in the annulus is one of the key scientific unsolved issues in natural gas hydrate solid fluidization exploitation. In this work, the upward multiphase flow of hydrate slurry in a vertical concentric annulus is simulated. The hydrate slurry hydrodynamic models suitable for pseudo-single-phase flow, bubbly flow, slug flow, and annular flow are proposed, respectively. Finally, the hydrate decomposition kinetic model is combined with the established annulus hydrate slurry multiphase flow model to simulate the multiphase flow of hydrate slurry in the annulus. The factors affecting flow behaviors are analyzed. During the upward flow in the annulus, the hydrate slurry temperature first decreases and then increases. As the inlet temperature increases, the fluid temperature, hydrate decomposition rate, and gas superficial velocity increase. During the upward flow in the annulus, hydrate may be formed again, which indicates that the error may be magnified due to ignoring hydrate formation. The larger the flow rate, the smaller the length of the slug flow. The larger the hydrate volume fraction, the higher the starting point of hydrate decomposition. These findings are of practical value to give a further understanding of hydrate slurry multiphase flow, which can promote further engineering application of natural gas hydrate solid fluidization exploitation.

### Spectral proper orthogonal decomposition of compressor tip leakage flow

To identify the spatiotemporal coherent structure of compressor tip leakage flow, spectral proper orthogonal decomposition (SPOD) is performed on the near-tip flow field and the blade surface pressure of a low-speed compressor rotor. The data used for the SPOD analysis are obtained by delayed-detached eddy simulation, which is validated against the experimental data. The investigated rotor near-tip flow field is governed by two tip leakage vortices (TLV), and the near-tip compressor passage can be divided into four zones: the formation of main TLV (Zone I), the main TLV breakdown (Zone II), the formation of tip blockage cell (Zone III), and the formation of secondary TLV (Zone IV). Modal analysis from SPOD shows that a major part of total disturbance energy comes from the main TLV oscillating mode in Zone I and the main TLV vortex shedding mode in Zone III, both of which are low-frequency and low-rank; on the contrary, modal components in Zones II and IV are broadband and non-low-rank. Unsteady blade forces are mainly generated by the impingement of the main TLV on the blade pressure surface in Zone III, rather than the detachment of the secondary TLV from the blade suction surface in Zone IV. These identified coherent structures provide valuable knowledge for the aerodynamic/aeroelastic effects, turbulence modeling, and reduced-order modeling of compressor tip leakage flow.

### Active external control effect on the collective locomotion of two tandem self-propelled flapping plates

The self-organization of active swimmers is interesting but not fully understood. Lighthill conjectured that the orderly configurations may emerge passively from the hydrodynamic interactions rather than active control mechanism. To further test Lighthill's conjecture, the effect of active control on the propulsive performance of two self-propelled flapping plates in tandem configuration is studied. Different types of external horizontal forces are applied at the leading edge of the following plate. It is found that the collective dynamic and propulsive performance of the two-plate system are mainly affected by the mean value of the external horizontal force rather than its specific form. The two-plate self-propelled system has certain ability to counteract a limited external intervention and maintain the orderly configuration by adjusting the gap spacing between two plates. For a stable configuration, the external intervention hardly affects the propulsion velocity but has a significant monotonic effect on the gap spacing and input work. Further, a simplified model is proposed to relate the external horizontal force to the gap spacing between two plates and verified to be reliable by the numerical results. Moreover, the momentum and energy transferred to fluid are investigated in terms of local vortical structures. It is revealed that the impulse of the wake vortex pair is hardly affected by the external horizontal force, while its kinetic energy and the local dissipative energy vary monotonically with it. These results may shed some light on the understanding of collective behaviors of living swimmers and robotic fish.

### Interaction of two out-of-phase underwater explosion bubbles

This study presents an experimental investigation of the dynamic properties of underwater explosion (UNDEX) bubble pairs produced with a range of phase differences Δθ, defined as 2π(t1−t2)/Tosc, where ti (i = 1,2) represents the bubble inception moment and Tosc is the experimentally obtained first period of a single UNDEX bubble. Each bubble was generated by a spherical hexogen explosive charge detonated in a cubical tank and observed via high-speed photography. The phase difference was adjusted by setting different delays between the two detonations, with an accuracy of 1.0 ms. Experiments were conducted with both horizontally and vertically positioned bubble pairs and with single bubbles as well. UNDEX bubble pairs are subject to a larger buoyancy effect than cavitation or spark-generated bubble pairs. The resultant bubble behavior in the bubble–bubble interaction is more complex and is yet to be understood. In our experiments, various bubble parameters, including bubble pulsation periods, bubble elongation ratios, and collapse-induced shock wave pressures bubble, were measured and studied. Dependence of the bubble dynamics on Δθ was found, demonstrating the significant influence of Δθ on the morphology and shock wave pressure of bubble pairs. The findings suggest a method of strengthening or weakening the damage potential of an UNDEX bubble pair based on the proper adjustment of the delay between two detonations. It may also lead to a better understanding of the dynamics of interacting bubbles with buoyancy effects.

### Gravity effects on oil–water two-phase displacement in homogeneous porous media

Gravity plays an important role in enhanced oil recovery and groundwater hydrology. A two-dimensional visual homogeneous micromodel was used in this study to describe the role of gravity in displacement processes. A theoretical analysis is proposed for three flow modes, i.e., vertical-upward, vertical-downward, and horizontal displacements, in which water and decane are used for the displacing and the displaced phases, respectively. A relatively compact displacement front was obtained at high flow rates in the three displacement modes, and the front gradually became unstable with a decrease in the flow rate. Compared with horizontal displacement, in vertical-upward displacements, gravity can hinder the evenness of the flow and aggravate the front finger formations at the inlet. This process forces the heavier displacing phase to expand horizontally at the midpoint and weakens the front's fingers. In the vertical-downward displacement process, two states occurred at the same low flow rate: stable flow and unstable flow. Unstable flows occurred more frequently with a decrease in the flow rate. To better understand the role of gravity in displacement, we proposed a theoretical prediction model for the flow state transition of the three displacement modes by combining the capillary force, viscous force, and gravity based on pore-filling events. Finally, to predict the final recovery factor for various displacement modes, four dimensionless formulations were produced using the capillary number, the gravity number, the bond number, and the viscosity ratio.

### Peripheral heat transfer prediction of the subcooled falling liquid film on a horizontal smooth tube

The peripheral heat transfer correlation of the subcooled falling liquid film outside the horizontal tube was established using the present numerical data under different liquid flow rates, heat fluxes, tube sizes, distributor heights, and liquid temperatures. The results indicated that the present correlation can predicate 93% of 2654 data within ±25% in θ = 2°–15°, 92% of 2254 data within ±15% in θ = 15°–165°, and 80% of 1442 data within ±30% in θ = 165°–178°. The peripheral heat transfer correlation can predict 74% of 903 data and 80% of 700 data, respectively, within 0°–180° and 15°–165° with the deviations of ±30%. The sensitivity analysis indicated that the parameter angle and the distributor height have the most and least significant impact on the peripheral heat transfer correlation, respectively.

### Active control for enhancing vortex induced vibration of a circular cylinder based on deep reinforcement learning

In the current paper, the active flow control for enhancing vortex induced vibration (VIV) of a circular cylinder, which can be potentially applied in ocean energy harvesting, is achieved by an artificial neural network (ANN) trained through deep reinforcement learning (DRL). The flow past a circular cylinder with and without jet control located on the cylinder is numerically investigated using OpenFOAM, and the ANN is applied to learn an active flow control strategy through experimenting with different mass flow rates of the jets. According to our results, the jets on the cylinder are able to dramatically destabilize the periodic shedding of the cylinder wake, which leads to a much larger VIV and work capability of the cylinder. Through controlling the flow rate of the jets based on the observation of the instantaneous flow field, the ANN successfully increases the drag by 30.78%, and the magnitude of the fluctuation of the drag and lift coefficient by 785.71% and 139.62%, respectively, while the energy consumption of the jets is almost negligible. Furthermore, the net energy output by VIV with jet control increases by 357.63% (case of water) compared with the uncontrolled situation. The results demonstrate that the performance of the active jet control strategy established by DRL for enhancing VIV is outstanding and promising for realizing the transformation from the ocean energy to electrical energy. Therefore, it is encouraged to perform further investigations on VIV enhancement using active flow control based on DRL.

### Micro-rheology of a particle in a nonlinear bath: Stochastic Prandtl–Tomlinson model

The motion of Brownian particles in nonlinear baths, such as, e.g., viscoelastic fluids, is of great interest. We theoretically study a simple model for such a bath, where two particles are coupled via a sinusoidal potential. This model, which is an extension of the famous Prandtl–Tomlinson model, has been found to reproduce some aspects of recent experiments, such as shear-thinning and position oscillations [R. Jain et al., “Two step micro-rheological behavior in a viscoelastic fluid,” J. Chem. Phys. 154, 184904 (2021)]. Analyzing this model in detail, we show that the predicted behavior of position oscillations agrees qualitatively with experimentally observed trends; (i) oscillations appear only in a certain regime of velocity and trap stiffness of the confining potential, and (ii), the amplitude and frequency of oscillations increase with driving velocity, the latter in a linear fashion. Increasing the potential barrier height of the model yields a rupture transition as a function of driving velocity, where the system abruptly changes from a mildly driven state to a strongly driven state. The frequency of oscillations scales as [math] near the rupture velocity [math], found for infinite trap stiffness. Investigating the (micro-)viscosity for different parameter ranges, we note that position oscillations leave their signature by an additional (mild) plateau in the flow curves, suggesting that oscillations influence the micro-viscosity. For a time-modulated driving, the mean friction force of the driven particle shows a pronounced resonance behavior, i.e., it changes strongly as a function of driving frequency. The model has two known limits: For infinite trap stiffness, it can be mapped to diffusion in a tilted periodic potential. For infinite bath friction, the original Prandtl–Tomlinson model is recovered. We find that the flow curve of the model (roughly) crosses over between these two limiting cases.

### Multiplicity for idealized rotational detonation waves

Simulations of three-dimensional rotational detonation waves are conducted to understand the mechanisms of wave bifurcation. A compressible reacting Euler solver is developed within the framework of OpenFOAM, and a fixed mass flux boundary condition is developed to avoid complex injector dynamics. Influences of inflow mass flow rates and initiations of ignition spots are studied. As the inflow mass flow rate increases, one detonation wave is maintained. Constrained by the circumference of the combustor, the maximum fill height is achieved when the maximum post-shock pressure expansion is reached. Further increasing mass flow rates does not lead to wave bifurcation or higher mean fill height. By introducing multiple ignition regions, an identical number of stable waves are ignited and maintained, which signifies that wave numbers are not uniquely determined by the inlet boundary conditions. The minimum fill height (or largest velocity deficit) owing to either the lowest mass flow rate or the maximum wave number is obtained when the pressure expansion distance is comparable to the hydrodynamic thickness. The scaling of fill height is subsequently explained through a theoretical relation based on mass conservation. It is shown that neither increasing mass flow rates nor existence of multiple waves is a sufficient condition for wave bifurcation. The fill height is intrinsically connected with wave numbers, and both cannot be predicted solely based on boundary conditions. Future work will relax some idealizations in this work to further quantify the limit for the fill height.

### Dilute sodium dodecyl sulfate droplets impact on micropillar-arrayed non-wetting surfaces

Impinging dilute sodium dodecyl sulfate (SDS) droplets on micropillar-arrayed polydimethylsiloxane surfaces were experimentally investigated. It was found that the behaviors of impinging droplets greatly depend on surface roughness and SDS concentration. Similar to pure water droplets, there exists a narrow range of dimensionless Weber number, We, for the complete rebound of impacting SDS droplets. The lower and upper limits of impact velocity were theoretically analyzed and compared with experimental data. The addition of SDS could greatly shorten the contact time of bouncing droplets. Besides, surface roughness has little influence on the maximum spreading factor while SDS concentration has an obvious influence and the maximum spreading factor nearly follows a scaling law of [math].

### On the dissipative extended Kawahara solitons and cnoidal waves in a collisional plasma: Novel analytical and numerical solutions

Two novel analytical solutions to the damped Gardner Kawahara equation and its related equations are reported. Using a suitable ansatz and with the help of the exact solutions of the undamped Gardner Kawahara equation, two general high-accurate approximate analytical solutions are derived. Moreover, the Crank–Nicolson implicit finite difference method is introduced for analyzing the evolution equation numerically. The comparison between the obtained solutions is examined. All the obtained solutions are able to investigate many types of the dissipative traveling wave solutions such as the dissipative solitary and cnoidal waves. Also, the obtained solutions help many researchers understand the mechanisms underlying a variety of nonlinear phenomena that can propagate in optical fiber, physics of plasmas, fluid mechanics, water tank, oceans, and seas. The obtained solutions could be applied for investigating the characteristics of the dissipative higher-order solitary and cnoidal waves in electronegative plasmas. Numerical results depending on the physical plasma parameters are presented.

### Erratum: “Investigation of the three-dimensional flow past a flatback wind turbine airfoil at high angles of attack” [Phys. Fluids 33, 085106 (2021)]

### Deep learning for reduced order modelling and efficient temporal evolution of fluid simulations

Reduced order modeling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using significantly lesser parameters. Conventional ROMs accomplish this by linearly projecting higher-order manifolds to lower-dimensional space using dimensionality reduction techniques such as proper orthogonal decomposition (POD). In this work, we develop a novel deep learning framework DL-ROM (deep learning—reduced order modeling) to create a neural network capable of non-linear projections to reduced order states. We then use the learned reduced state to efficiently predict future time steps of the simulation using 3D Autoencoder and 3D U-Net-based architectures. Our model DL-ROM can create highly accurate reconstructions from the learned ROM and is thus able to efficiently predict future time steps by temporally traversing in the learned reduced state. All of this is achieved without ground truth supervision or needing to iteratively solve the expensive Navier–Stokes (NS) equations thereby resulting in massive computational savings. To test the effectiveness and performance of our approach, we evaluate our implementation on five different computational fluid dynamics (CFD) datasets using reconstruction performance and computational runtime metrics. DL-ROM can reduce the computational run times of iterative solvers by nearly two orders of magnitude while maintaining an acceptable error threshold.

### Pre-breakdown processes in water under ultra-long pulses: Bubble–streamer dynamics and their transition

Pre-breakdown processes in water are usually accompanied by the developments of bubble and streamer. Therefore, the dynamic behaviors of bubble and streamer and their transition process are essential to understand the mechanism of underwater discharge. In this work, the pre-breakdown processes in water (60 μS/cm) under ultra-long pulses (>100 ms) are investigated, and two fundamental but unclear issues are clarified: What is the intrinsic difference between bubble and streamer, and how does a bubble transit into a streamer? The research results manifest that the pre-breakdown processes under ultra-long pulses follow the pattern of bubble cycle evolution and streamer triggered breakdown, and the final breakdown occurs only if the bubble attached to the electrode surface expands to a critical size (0.5–1.2 mm). Further analysis indicates that the huge conductivity disparity between bubble and streamer leads to their diverse dynamic behaviors. The development of bubble belongs to bottom-up type that the growth of bubble is driven by the expansion of its root near the electrode surface. Meanwhile, the development of streamer belongs to top-down type that the propagation of streamer is guided by the evolvement of its head. As the bubble expands, the voltage drops and pressure of bubble increases and decreases, respectively, which provides a necessary condition for the internal breakdown of bubble triggering the bubble–streamer transition. However, the transition from bubble to streamer is a competitive process: The dynamic equilibrium between growth and expansion (development boost) and detachment/rupture (development resistance) of bubble determines whether the bubble can develop continuously into a streamer.