# Latest papers in fluid mechanics

### Grid resolution requirement for resolving rare and high intensity wall-shear stress events in direct numerical simulations

Author(s): Xiang I. A. Yang, Jiarong Hong, Myoungkyu Lee, and Xinyi L. D. Huang

Wall-shear stress becomes more intermittent as the Reynolds number (Re) of a flow increases. To properly resolve wall shear stress events in direct numerical simulations thus requires finer grids at higher Re. In this work we examine the grid resolution required to resolve a given percentage of wall shear stress events as a function of Re. We find that the standard grid resolution does not capture a fraction of high intensity events which increases with Re and quantify the grid resolution needed to do so.

[Phys. Rev. Fluids 6, 054603] Published Fri May 07, 2021

### Relation between the spectral properties of wall turbulence and the scaling of the Darcy-Weisbach friction factor

Author(s): Francesco Coscarella, Roberto Gaudio, Gabriel G. Katul, and Costantino Manes

Empirical formulae describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulae have remained without theoretical interpretation for many decades. To close this knowledge gap we provide, using a co-spectral budget model, a clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes.

[Phys. Rev. Fluids 6, 054601] Published Thu May 06, 2021

### Stochastic dynamical model for space-time energy spectra in turbulent shear flows

Author(s): Ting Wu and Guowei He

A dynamic autoregressive (DAR) random forcing model is proposed for space-time energy spectra in turbulent shear flows. This model starts with Taylor’s convection model and introduces the DAR random forcing to represent the random sweeping effect. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations.

[Phys. Rev. Fluids 6, 054602] Published Thu May 06, 2021

### Growth of barchan dunes of bidispersed granular mixtures

Barchans are dunes of crescentic shape found on Earth, Mars, and other celestial bodies, growing usually on polydisperse granular beds. In this Letter, we investigate experimentally the growth of subaqueous barchans consisting of bidisperse grains. We found that the grain distribution within the dune changes with the employed pair, and that a transient stripe appears on the dune surface. We propose that observed patterns result from the competition between fluid entrainment and easiness of rolling for each grain type, and that grains segregate with a diffusion-like mechanism. Our results provide new insights into barchan structures found in other environments.

### An efficient deep learning framework to reconstruct the flow field sequences of the supersonic cascade channel

Accurate and comprehensive flow field reconstruction is essential for promptly monitoring the flow state of the supersonic cascade. This paper proposes a novel data-driven method for reconstructing the slices of the two-dimensional (2D) pressure field in three-dimensional (3D) flow of the supersonic cascade by using deep neural networks. Considering the complicated spatial effects of 2D pressure field slices, the architecture embeds the convolution into the long short-term memory (LSTM) network to realize the purpose of using the upstream pressure to reconstruct downstream pressure. Numerical simulations of the supersonic cascade under different back pressures are performed to establish the database capturing the complex relationship between the upstream and downstream flow. The pressure of different upstream slices can be used as a spatial-dependent sequence as the input of the model to reconstruct the pressure of different downstream slices. A deep neural network including special convolutional LSTM layers and convolutional layers is designed. The trained model is then tested under different back pressures. The reconstruction results are in good agreement with the computational fluid dynamics, especially for the identification of shock wave position changes and the recognition of complex curved shock waves in 3D flow with high accuracy. Moreover, analyzing the frequency distribution of reconstructed pressure at different positions can clearly distinguish the flow separated zone, which will further improve the accuracy of the state monitoring. Specifically, it is of great significance for identifying the stall of the flow field promptly.

### Statistical properties of a model of a turbulent patch arising from a breaking internal wave

The turbulent patch arising from internal gravity wave breaking is investigated with direct numerical simulation of a stably stratified flow over a two-dimensional hill. The turbulent patch is distinguished from the non-turbulent wave region with potential vorticity. The turbulent patch is highly intermittent, and its location fluctuates with space and time. The buoyancy Reynolds number slowly decays with time in the turbulent patch and the mixing efficiency stays around 0.2. The turbulent patch is separated from the non-turbulent wave region by a turbulent/non-turbulent interfacial (TNTI) layer, whose thickness is about five times the Kolmogorov scale. The kinetic energy dissipation rate also sharply decreases from the turbulent to the wave region while the potential energy dissipation rate has a large peak within the TNTI layer. Both shear and stable stratification are strong in the upper area of the turbulent patch. On the other hand, the lower area has a small mean density gradient, i.e., weak stratification, which is related to the strong intermittency of the turbulent patch in the lower area. Furthermore, weak stratification in the lower area results in a low gradient Richardson number, which is below the critical value for the shear instability, and the roller vortex appears. The outer edge of the turbulent patch aligns with the perimeter of the roller vortex, and the vortex affects the spatial distribution of the turbulent patch.

### Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

We introduce two new approaches, called A-LSOB and N-MR, for boundary and interface-conjugate conditions on flat or curved surface shapes in the advection-diffusion lattice Boltzmann method (LBM). The Local Second-Order, single-node A-LSOB enhances the existing Dirichlet and Neumann normal boundary treatments with respect to locality, accuracy, and Péclet parametrization. The normal-multi-reflection (N-MR) improves the directional flux schemes via a local release of their nonphysical tangential constraints. The A-LSOB and N-MR restore all first- and second-order derivatives from the nodal non-equilibrium solution, and they are conditioned to be exact on a piece-wise parabolic profile in a uniform arbitrary-oriented tangential velocity field. Additionally, the most compact and accurate single-node parabolic schemes for diffusion and flow in grid-inclined pipes are introduced. In simulations, the global mass-conservation solvability condition of the steady-state, two-relaxation-time (S-TRT) formulation is adjusted with either (i) a uniform mass-source or (ii) a corrective surface-flux. We conclude that (i) the surface-flux counterbalance is more accurate than the bulk one, (ii) the A-LSOB Dirichlet schemes are more accurate than the directional ones in the high Péclet regime, (iii) the directional Neumann advective-diffusive flux scheme shows the best conservation properties and then the best performance both in the tangential no-slip and interface-perpendicular flow, and (iv) the directional non-equilibrium diffusive flux extrapolation is the least conserving and accurate. The error Péclet dependency, Neumann invariance over an additive constant, and truncation isotropy guide this analysis. Our methodology extends from the d2q9 isotropic S-TRT to 3D anisotropic matrix collisions, Robin boundary condition, and the transient LBM.

### Input-output framework for actuated boundary layers

Author(s): I. Gluzman and D. F. Gayme

The input-output approach is expanded to investigate actuated wall-bounded shear flows whose geometries and input signals span a range of pulse-width modulated signals common in experimental flow control studies. The model is validated through comparisons to experiments and simulations of three different plasma actuator geometries. An important benefit of this analytical method is the low computational cost associated with its use, enabling efficient parametric studies.

[Phys. Rev. Fluids 6, 053901] Published Wed May 05, 2021

### Vertical distribution and longitudinal dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow

Author(s): Bohan Wang, Weiquan Jiang, Guoqian Chen, Luoyi Tao, and Zhi Li

A more concise and accurate generalized Taylor dispersion theory is applied to dispersion of active gyrotactic microorganisms in a plane Poiseuille flow. The joint effect of boundary conditions, cell shape anisotropy, swimming speed, and flow speed leads to the nonmonotonic variations of the phenomenological dispersion coefficients.

[Phys. Rev. Fluids 6, 054502] Published Wed May 05, 2021

### Numerical analysis of two-phase flow in heterogeneous porous media during pre-flush stage of matrix acidizing: Optimization by response surface methodology

Oil trapping behavior during the pre-flush stage is critically important to evaluate the effectiveness of matrix acidizing for the oil well stimulation. In this study, the visco-capillary behavior of the two-phase flow in the pore-scale is analyzed to investigate the influence of wetting properties for a natural rock sample. A two-dimensional model, based on Cahn–Hilliard phase-field and Navier–Stokes equations, was established and solved using the finite element method. A stability phase diagram for log capillary number (Ca)–log viscosity ratio (M) was constructed and then compared with the reported experimental works. The maximum and minimum ranges of capillary number and viscosity ratio to identify both viscous and capillary fingering regions were found to be Log M ≈ −2.5, Log Ca ≈ −5, and Log M ≈ −0.5, Log Ca ≈ −5, respectively. However, the most stable displacement region was found to be located at Log M ≈ 0.5 and Log Ca ≈ −2. Furthermore, the impact of four independent variables, including pore volume of injection (1 < PV < 5), capillary number (−6 < Log Ca < 0), viscosity ratio (−5 < Log M < 2), and contact angle ([math]), on recovery factor (RF) was investigated using central composite design of response surface methodology. For the chosen range of independent variables, the optimum conditions for the immiscible two-phase flow (e.g., RF > 0.95) occurred at Log M > 0, −4.5 < Log Ca < −2, PV > 1, θ > π/6 condition. It is worth mentioning that for Log M< 0, the optimum condition occurred at Log M ≈ 0, Log Ca ≈ −3.5, PV ≈ 4, and θ ≈ π/6.

### Unsteady analysis of turbulent flow and heat transfer behind a wall-proximity square rib using dynamic delayed detached-eddy simulation

In the present study, turbulent wall heat transfer behind a wall-proximity square rib is numerically modeled using dynamic delayed detached-eddy simulations, with the objective of clarifying unsteady flow behaviors and their influence on wall heat transfer. Three configurations with gap-to-height ratios (G/d) of 0, 0.25, and 0.5 are comparatively evaluated at a Reynolds number (Red) of 7600. The wall heat transfer is overwhelmingly affected by the interaction between the upper separated shear layer and the lower wall jet flow, exhibiting distinctly different global characteristics with increases in the wall gap. A proper orthogonal decomposition analysis of the turbulent flow fields is conducted to effectively identify the energetic flow structures superimposed on the shear layers and demonstrates that transformative features are present, from energetic bubble-flapping modes ([math] 0, 0.25) to Karman-like vortex street modes ([math] 0.25, 0.5). Finally, the phase-dependent variation of the spatiotemporally varying flow structures is examined. In the [math] configuration, the suppressed lower vortical structure oscillated irregularly, leading to a locally thin thermal boundary layer and strong wall heat-transfer augmentation in the [math] region. In the [math] configuration, the wall jet flow constantly disrupted the thermal boundary layer, causing [math] to plateau in the [math] region. The periodic shedding of the vortical structures in the upper shear layer intermittently spread onto the wall surface in the [math] region, resulting in the gradual decline of [math]. Accordingly, the cause-and-effect mechanism linking the unsteady flow behaviors with wall heat removal is determined, and the coupling between the large-scale vortical structures and the corresponding thermal boundary distribution is established.

### Linear stability of a surfactant-laden viscoelastic liquid flowing down a slippery inclined plane

A study of linear stability analysis of a surfactant-laden viscoelastic liquid flowing down a slippery inclined plane is carried out under the framework of Orr–Sommerfeld type eigenvalue problem. It is assumed that the viscoelastic liquid satisfies the rheological property of Walters' liquid [math]. The Orr–Sommerfeld type eigenvalue problem is solved analytically and numerically based on the long-wave analysis and Chebyshev spectral collocation method, respectively. The long-wave analysis predicts the existence of two temporal modes, the so-called surface mode and surfactant mode, where the first order temporal growth rate for the surfactant mode is zero. However, the first order temporal growth rate for the surface mode is non-zero, which leads to the critical Reynolds number for the surface mode. Further, it is found that the critical Reynolds number for the surface mode reduces with the increasing value of viscoelastic coefficient and ensures the destabilizing effect of viscoelastic coefficient on the primary instability induced by the surface mode in the long-wave regime. However, the numerical result demonstrates that the viscoelastic coefficient has a non-trivial stabilizing effect on the surface mode when the Reynolds number is far away from the onset of instability. Further, if the Reynolds number is high and the inclination angle is sufficiently low, there exists another mode, namely the shear mode. The unstable region induced by the shear mode magnifies significantly even for the weak effect of viscoelastic coefficient and makes the transition faster from stable to unstable flow configuration for the viscoelastic liquid. Moreover, the slip length exhibits a dual role in the surface mode as reported for the Newtonian liquid. But it exhibits only a stabilizing effect on the shear mode. In addition, it is found that the Marangoni number also exhibits a dual nature on the primary instability induced by the surface mode in contrast to the result of the Newtonian liquid.

### Numerical simulation of adiabatic/cooled/heated spherical particles with Stefan flow in supercritical water

When droplets or particles are in complex fluid-temperature-environment conditions, the spatial variation in temperature-dependent properties affects the overall particle-laden flow behavior. Particularly, in a high-temperature environment, the components on the particle surface are heated and volatilize to form a mass flow, named the Stefan flow, that influences the mass, momentum, and energy transfer between particles and the fluid. For supercritical fluids, small changes in temperature and pressure cause substantial changes in thermophysical properties. Hence, in this work, we study the characteristics of supercritical water flowing past an adiabatic/cooled/heated sphere for Re = 10–200 with and without Stefan flow. The three-dimensional numerical simulations that are conducted consider the exact water thermophysical properties. The flow field, the Nusselt number (Nu), the drag coefficient (Cd), and the velocity and temperature distribution around the particle are analyzed. The results demonstrate that the vortex is strongly influenced by the variation in viscosity near the particle. The Cd and Nu values of the cooled and heated spheres show different deviations in different conditions. The influence of Stefan flow cannot be ignored as it increases the vortex size and decreases both Cd and Nu. Finally, the effect of Stefan flow on both Cd and Nu of the cooled sphere is greater than that of the heated sphere.

### Effect of multibanded magnetic field on convective heat transport in linearly heated porous systems filled with hybrid nanofluid

The paper attempts to enhance the control of convective transport phenomena in magnetothermal devices applying a technique of multibanded magnetic field. For this demonstration, a typical cavity-like thermal system is considered involving linear heating, porous substance, hybrid nanofluid, and magnetic field. Four identical bands of magnetic fields are applied horizontally with uniform inactive zones between the bands. The transport equations of the coupled multiphysics evolving from the thermal buoyancy (due to linear heating at one sidewall and isothermal cooling at the opposite sidewall), filled porous medium, spatially intermittently active magnetic fields, and the engineered working fluid of Cu–Al2O3/water hybrid nanofluid are solved by an indigenously developed computing code. The study is conducted using the pertinent dimensionless parameters for the following ranges: Darcy–Rayleigh number (Ram = 1–104), Darcy number (Da = 10−5 − 10−1), Hartmann number (Ha = 0–70), and concentration of hybrid nanoparticles [math] (= 0–2%). The convective phenomena are analyzed using the heatlines (for heat transport), streamlines (flow pattern), isotherms (static temperature), and the average Nusselt number (for heat transfer). The outcomes of this technique of multibanded magnetic field are rigorously compared with other established application methods of magnetic fields. It establishes different local behaviors along with an improved heat transfer. Heatline visualization reveals the definite portraits of heat flow paths depending upon parametric values. Furthermore, the presence of linear heating is in particular treated to explore the insight of linear heating (that featuring multiple heating and cooling zones along with the linear heater), utilizing the local Nusselt number and heatlines. One of the important advantages of this new technique is it is more energy-efficient particularly for the square or shallow cavity. The multibanded magnetic field shows a promising technique for the control of convective transport phenomena involving coupled multiphysics used during sophisticated applications (such as materials processing, biomedical applications, etc.).

### Dynamics of two coaxially rising gas bubbles

In this study, the coalescence dynamics of two unequal sized vertically inline bubbles rising in a liquid column have been investigated using the coupled level-set and volume-of-fluid (CLSVOF) method. A wide range of bubble radius ratios of trailing bubble and leading bubble ([math]) and separation distances between the bubbles ([math]) have been deployed to investigate the evolution of the bubble wakes and bubble shapes. It is discovered that the coalescence time increases with R, the maxima being around [math], and then it decreases. With the increase in S, the coalescence time gradually increases. The existence of a pair of counter-rotating vortex rings has been observed between the bubbles, which are seen to accelerate the bubble coalescence process. For the present range of R and S, we show a regime map with four distinct coalescence pathways: coalescence with liquid entrapment, coalescence without liquid entrapment, penetration of the leading bubble, and premature splitting of the trailing bubble.

### Dissipation scaling and structural order in turbulent channel flows

Scaling and structural evolutions are contemplated in a new perspective for turbulent channel flows. The total integrated turbulence kinetic energy and the total dissipation can be viewed as global constraints on the turbulence structure, leading to predictable, ordered scaling for u′2 and v′2 through its first and second gradients, respectively. This self-similarity allows for profile reconstructions at any Reynolds numbers based on a common template through simple multiplicative operations. Using these scaled variables in the Lagrangian transport equation derives the Reynolds shear stress, which in turn computes the mean velocity profile through the Reynolds-averaged Navier–Stokes equation. The dissipation scaling along with the transport equations renders succinct views of the turbulence dynamics and its structural characteristics. In this way, variable profiles can be analytically reconstructed, which bears potential implications toward solvability and computability of turbulent flows in canonical and other geometries.

### Reduction of monomeric friction coefficient for linear isotactic polypropylene melts in very fast uniaxial extensional flow

For the first time, the monomeric friction coefficient for fully aligned chains, ζaligned, was determined for three linear isotactic polypropylene melts (iPP) using a high-strain-rate limiting value of uniaxial extensional viscosity, ηE,U,∞, obtained from our recent experimental data [Drabek and Zatloukal, Phys. Fluids 32(8), 083110 (2020)] and expression relating ηE,U,∞ with ζaligned, which was derived for a fully stretched Fraenkel chain [Ianniruberto et al., Macromolecules 53(13), 5023–5033 (2020)]. It was found that the obtained ζaligned value is lower by a factor of 2.9–5.0 (or even by a factor of 8.7–16.5 if the effect of polydispersity is included) compared to the equilibrium friction coefficient, ζeq, defined according to Doi and Edwards. This strongly supports recent arguments from rheological data and molecular simulations that a reduction in the friction coefficient must be considered in order to understand dynamics of polymer melts in very fast flows.

### Influence of thermalization protocol on Poiseuille flow of confined soft glass

Using extensive molecular dynamics simulations, we study how the Poiseuille flow of a model confined soft glass is determined by thermalization protocols. We contrast the steady-state behavior as well as the onset of flow, using two different thermostats, one where the confined glass is directly thermalized, whereas in the other case the glass is thermalized via the confining walls. The latter setup leads to a spatially non-uniform temperature profile within the channel, during flow, which allows for probing the rheological response of the confined glass under this additional perturbation and thereby investigate the deviations from bulk rheology. Finally, we also examine how this response depends upon varying the channel widths. Our study illustrates the competing effects due to the stress gradients, the intrinsic non-local correlations of glassy systems, and the presence or absence of thermal gradients.

### Ab initio simulation of hypersonic flows past a cylinder based on accurate potential energy surfaces

For the first time in the literature, we present 2D simulations of hypersonic flows around a cylinder obtained from accurate ab initio potential energy surfaces (PESs). We compare results obtained from a low fidelity (empirical) and a high fidelity (ab initio) PES, thus demonstrating the impact of PES accuracy on the entire aerothermodynamic field around the body. We observe that the empirical PES is not adequate to accurately reproduce rotational and vibrational relaxation in the hypersonic flow, both in the compression and expansion regions of the flow field. This approach, enabled by advancements in large-scale computing, paves the way to the direct simulation of hypersonic flows where the only modeling input is the PES that describes molecular interactions between the various air constituents. Such flow field simulations provide benchmark solutions for the validation of reduced-order models.

### Self-propelled slender objects can measure flow signals net of self-motion

The perception of hydrodynamic signals by self-propelled objects is a problem of paramount importance ranging from the field of bio-medical engineering to bio-inspired intelligent navigation. By means of a state-of-the-art fully resolved immersed boundary method, we propose different models for fully coupled self-propelled objects (swimmers, in short), behaving either as “pusher” or as “puller.” The proposed models have been tested against known analytical results in the limit of Stokes flow, finding excellent agreement. Once tested, our more realistic model has been exploited in a chaotic flow field up to a flow Reynolds number of 10, a swimming number ranging between zero (i.e., the swimmer is freely moving under the action of the underlying flow in the absence of propulsion) and one (i.e., the swimmer has a relative velocity with respect to the underlying flow velocity of the same order of magnitude as the underlying flow), and different swimmer inertia measured in terms of a suitable definition of the swimmer Stokes number. Our results show the following: (i) pusher and puller reach different swimming velocities for the same, given, propulsive force: while for pusher swimmers, an effective slender body theory captures the relationship between swimming velocity and propulsive force, this is not for puller swimmers. (ii) While swimming, pusher and puller swimmers possess a different distribution of the vorticity within the wake. (iii) For a wide range of flow/swimmer Reynolds numbers, both pusher and puller swimmers are able to sense hydrodynamic signals with good accuracy.