# Latest papers in fluid mechanics

### Physics guided machine learning using simplified theories

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this Letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasize their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include the features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.

### Calculation of the flow velocity of a siphon

Siphons have been known and used since ancient times and are still widely used. We re-examine the siphon process and recognize that the existing classic formula of the flow velocity of a siphon is only applicable to continuous flow; however, the flow of a siphon may be discontinuous flow. This study proposes new formulas, which can cover continuous and discontinuous flow and can consider the influence of the release of air from liquid on the flow velocity. Sixteen experiments were performed to validate our proposed method. The main results show that (a) for some schemes, the calculated values from the existing formula have large errors and the maximum error rate reaches 96%, (b) our method not only calculates the flow velocity of a siphon well but also makes a good prediction of the bubbles observed in the experiments, and (c) Qup/Qw > 1 is an effective way to reduce bubble generation in a siphon pipe, where Qup and Qw are the volumetric flow rates of the liquid phase by analyzing the upward pipe and whole pipe using Bernoulli’s equation, respectively. Based on the above understanding, some new siphon systems could be designed to reduce bubble generation in a siphon; for example, a new siphon drainage system with variable diameters can be designed to reduce bubble generation and, hence, to weaken or even avoid cavitation in the process of a siphon.

### Proper orthogonal decomposition analysis of the large-scale dynamics of a round turbulent jet in counterflow

Author(s): Marc Rovira, Klas Engvall, and Christophe Duwig

The understanding of the large-scale dynamics of the turbulent jet in counterflow remains limited. By employing proper orthogonal decomposition and spectral proper orthogonal decomposition on large eddy simulation data, new insights are presented. The fundamental mode dynamics are described as varying penetration, precession, and an alternating stretching-contracting motion. Furthermore, intermittency in the temporal evolution of these modes is identified.

[Phys. Rev. Fluids 6, 014701] Published Fri Jan 08, 2021

### High-order gas kinetic flux solver for simulation of two dimensional incompressible flows

Within the framework of the high-order finite volume (FV) method, a high-order gas kinetic flux solver (GKFS) is developed in this work for simulation of two-dimensional incompressible flows. Generally, in the conventional high-order FV method, the inviscid and viscous fluxes are treated separately. However, different from the conventional high-order FV method, the high-order GKFS evaluates the inviscid and viscous fluxes simultaneously from the local asymptotic solution to the Boltzmann equation, which consists of the equilibrium distribution function and its substantial derivative at the cell interface. By introducing a difference scheme with the high-order accuracy in space to discretize the substantial derivative, a high-order accurate local asymptotic solution to the Boltzmann equation can be obtained. The numerical flux of the Navier–Stokes equations can then be calculated by the moments of the local asymptotic solution. Since this local asymptotic solution is relatively simple, the numerical fluxes of the Navier–Stokes equations can be given explicitly for the high-order GKFS, which is the function of the left and the right states and their first-order derivatives. Numerical results showed that the developed solver can achieve the desired accuracy on both the quadrilateral mesh and the triangular mesh and its efficiency is higher than the second-order counterpart when achieving comparable accuracy of solution.

### Principal strain rate evolution within turbulent premixed flames for different combustion regimes

The statistical behaviors of the principal strain rates and its evolution in turbulent premixed flames have been analyzed using a three-dimensional direct numerical simulations dataset of statistically planar turbulent premixed flames with different turbulence intensities spanning from the corrugated flamelet regime to the thin reaction zone regime. It has been found that the scalar gradient predominantly aligns collinearly with the most extensive principal strain rate eigendirection within the flame for large values of Damköhler numbers and small values of turbulence intensities and Karlovitz numbers. However, this tendency weakens with the increasing turbulence intensity, which, for a given integral length scale, amounts to a decrease (an increase) in the Damköhler (Karlovitz) number. Moreover, it has been observed that the terms due to molecular diffusion, pressure Hessian, and the correlation between pressure and density gradients play key roles in the evolution of principal strain rates for flames with large values of Damköhler numbers and small values of Karlovitz numbers. However, the relative importance of the terms arising from the correlation between pressure and density gradients and the pressure Hessian relative to the strain rate and vorticity contributions of the principal strain rate transport diminishes with the increasing Karlovitz number and decreasing Damköhler number. The statistical behaviors of the mean values of the terms of the transport equation of the principal strain rate have been explained based on the relative alignments of principal strain rate eigenvectors with vorticity, pressure gradient, and the eigenvectors of the pressure Hessian tensor. The findings of the current analysis suggest that the pressure gradient and pressure Hessian tensor play key roles in the evolution of principal strain rates within premixed turbulent flames, and their influence needs to be accounted for high fidelity modeling of the tangential strain rate and scalar–turbulence interaction terms of the flame surface density and scalar dissipation rate transport equations, respectively. This provides possible explanations for the modification in the alignment of the reactive scalar gradient with local principal strain rates in premixed flames in comparison to that in non-reacting turbulent flows.

### On the control volume arbitrariness in the Navier–Stokes equation

We present a continuum theory to demonstrate the implications of considering general tractions developed on arbitrary control volumes where the surface enclosing it lacks smoothness. We then tailor these tractions to recover the Navier–Stokes-αβ equation and its thermodynamics. Consistent with the surface balances postulated to propose this theory, we provide an alternative approach to derive the natural boundary conditions.

### Roles of solid effective stress and fluid-particle interaction force in modeling shear-induced particle migration in non-Brownian suspensions

Author(s): Rashid Jamshidi, Jurriaan J. J. Gillissen, Panagiota Angeli, and Luca Mazzei

The applicability of some constitutive equations for the solid stress tensor used in the mixture model to describe the shear-induced migration of neutrally buoyant particles in Newtonian fluids is investigated. It is shown that in moderately dense suspensions, where direct particle contacts and interparticle forces are negligible, migration must be due to the lubrication forces between the particles. Results highlight that the tensor accounting for these forces is part of the stress tensor of the fluid phase, not of the solid phase and, in particular, that it coincides with the part of the particle-presence stress tensor related to the lubrication forces.

[Phys. Rev. Fluids 6, 014301] Published Thu Jan 07, 2021

### Fiber alignment in oscillating confined shearing flows

Author(s): Scott Strednak, Jason E. Butler, Laurence Bergougnoux, and Élisabeth Guazzelli

Experiments and simulations reveal that rigid fibers suspended at high concentration in a viscous fluid can be aligned in the vorticity direction using a shearing flow. Creating vorticity alignment requires an oscillatory shear over a limited range of strain amplitudes. The suspension must also be confined, as only those particles near the bounding walls align.

[Phys. Rev. Fluids 6, 014302] Published Thu Jan 07, 2021

### Nonasymptotic elastoinertial turbulence for asymptotic drag reduction

Author(s): Lu Zhu (朱路) and Li Xi (奚力)

Polymer-induced drag reduction in turbulent flow is bounded by a universal upper limit with increasing fluid elasticity. For decades, efforts to understand this maximum drag reduction asymptote have focused on the search for an ultimate flow state whose dynamics is no longer influenced by polymer elasticity. Contrary to common assumption, this study shows that behind the converged mean flow, the underlying dynamics continues to evolve through distinct stages, with no sign of convergence.

[Phys. Rev. Fluids 6, 014601] Published Thu Jan 07, 2021

### Inertial forces in the Maxey–Riley equation in nonuniform flows

Author(s): Bhargav Rallabandi

Here, inertial forces on particles in nonuniform ambient flows, previously missing from the Maxey—Riley formulation of inertial particle dynamics, are identified. These forces involve both local and convective fluid inertia and depend on the curvature of the ambient flow. These new terms provide quantitative corrections and qualitative additions to the Maxey—Riley equation and are relevant when the particle size is appreciable relative to the characteristic length scale of the ambient flow.

[Phys. Rev. Fluids 6, L012302] Published Thu Jan 07, 2021

### Breakup of compound jets with inner droplets in a capillary flow-focusing device

The coupling between the multilayer interfaces in compound jets has notable effects on the structure and generation sequence of the formed double emulsions. These effects are important for the performance of double emulsions, such as the capacity, release rate, and controlled release threshold in medical and chemical applications. In this work, the influence of the inner droplet on the necking of compound jets is investigated in a horizontally placed capillary flow-focusing device based on microfluidics. Three types of interface coupling modes are explored. Scaling laws that describe the time evolution of the neck radius for these different coupling modes are analyzed, and the reasons for transitions between such scaling laws are discussed. The results show that the motion and deformation of the droplet have a large impact on the neck breakup in the inertial regime, causing the scaling law to change, but only a slight effect in the viscous regime. Moreover, the inner droplet can prevent the jet from breaking up owing to interface coupling. These findings could help us to understand the role of interface coupling in compound jets and provide a reference for controlling the generation of compound droplets.

### Nonintrusive manufactured solutions for ablation

The study of heat transfer and ablation plays an important role in many problems of scientific and engineering interest. As with the computational simulation of any physical phenomenon, the first step toward establishing credibility in ablation simulations involves code verification. Code verification is typically performed using exact and manufactured solutions. However, manufactured solutions generally require the invasive introduction of an artificial forcing term within the source code such that the code solves a modified problem for which the solution is known. In this paper, we present a nonintrusive method for manufacturing solutions for a non-decomposing ablation code, which does not require the addition of a source term.

### Linear to turbulent Görtler instability transition

We present results from a highly resolved large-eddy simulation of a freely developing Blasius profile over a concave boundary in a large spanwise domain. Due to the large initial Reynolds and Görtler numbers (Reθ,0 = 1175, Gθ,0 = 75), we observe the onset of two dominant wavelengths: the first dominating in the linear/transition region, λ1, and the second dominating in the turbulent region, λ2. Extending previous linear stability analysis (LSA) to higher Görtler numbers and non-dimensional wavenumbers, both dominant wavelengths of the Görtler instability correspond to predictions of LSA, the latter comparable to laminar theory by replacing the kinematic viscosity with the turbulent viscosity in the definition of the Görtler number. The predicted spatial modes compare well with the computed profiles for both λ1 and λ2. The skin friction coefficient Cf is found heterogeneous in the spanwise direction according to the emerging wavelengths λ1 and λ2 of the Görtler instability. We report a smooth increase in Cf from the theoretical predictions of a laminar boundary layer to those for a turbulent boundary layer over a flat plate. The values only slightly overshoot these predictions in the domain of existence of the second dominant wavelength λ2, very different from that reported at lower Reynolds numbers.

### Four-temperature kinetic model for CO2 vibrational relaxation

A four-temperature kinetic-theory approach for modeling vibrationally non-equilibrium carbon dioxide flows is developed. The model takes into account all kinds of vibrational–translational energy transitions and inter-mode vibrational energy exchange between symmetric, bending, and asymmetric CO2 modes. The key feature of the model is using the averaged state-resolved relaxation rates instead of conventional Landau–Teller expressions. Spatially homogeneous CO2 vibrational relaxation is studied using the state-to-state, new four-temperature and commonly used three-temperature models. Excellent agreement between four-temperature and state-to-state solutions is found, whereas using the three-temperature model with the Landau–Teller production rates leads to significant loss of accuracy. Numerical efficiency of various approaches is discussed as well as the ways for its improvement.

### Numerical study of the interaction between a pulsating coated microbubble and a rigid wall. I. Translational motion

Author(s): M. Vlachomitrou and N. Pelekasis

Coated microbubbles exhibit a complex surface rheology. When accelerated towards a wall subject to an acoustic disturbance they behave like a deformable solid and assume a prolate rather than oblate shape, as is the case with conventional bubbles, due to the dominance of friction over pressure drag. This results from the balance between viscoelastic stresses that develop on the protective shell and pressure and viscous stresses from the surrounding fluid which generate a progressively more prolate shape as the translational Reynolds number increases. Proper coating design can optimally control particle shape and motion in applications, notably in biomedical ones.

[Phys. Rev. Fluids 6, 013601] Published Wed Jan 06, 2021

### Numerical study of the interaction between a pulsating coated microbubble and a rigid wall. II. Trapped pulsation

Author(s): M. Vlachomitrou and N. Pelekasis

A coated microbubble approaching a solid substrate changes shape from prolate to oblate due to the balance of Bjerknes force and elasto-lubrication pressure. The bubble then undergoes trapped pulsations about an average static state corresponding to the Reissner response of a coated shell compressed by a rigid plate corrected for surface tension. The contact region length is inverse to shell stiffness, with thickness of tens of nanometers due to the balance of viscous shell and liquid stresses. The contact region flow is a Stokes layer generated in response to bubble translational and vibrational motion that are found to be in phase in our simulations, so steady streaming was not captured.

[Phys. Rev. Fluids 6, 013602] Published Wed Jan 06, 2021

### Using colloidal deposition to mobilize immiscible fluids from porous media

Author(s): Joanna Schneider, Rodney D. Priestley, and Sujit S. Datta

Deposition of colloidal particles in a porous medium is typically considered to be problematic in energy and water applications. Here, experiments demonstrate that colloidal deposition can, surprisingly, promote mobilization of a trapped immiscible fluid from a porous medium without requiring any surface activity. Analysis of the underlying physics provides a way to predict the characteristics of fluid that is mobilized as deposition progresses.

[Phys. Rev. Fluids 6, 014001] Published Wed Jan 06, 2021

### Lagrangian study of the particle transport past a lateral, open-channel cavity

This paper presents a Lagrangian laboratory study of the passive tracer transport in and around a lateral, open-channel (square) cavity. Using 3D-particle tracking velocimetry (PTV), the trajectories of neutrally buoyant seeding particles are measured and analyzed to investigate the processes governing the particle exchanges between the cavity and the adjacent main stream for a selected subcritical flow condition. The tracked particles are classified using a Lagrangian approach based on their start and end positions, i.e., the cavity or the main stream region. Next, the spatial distribution of the particles at the main stream–cavity interface is analyzed to distinguish the typical transport processes of the different particle classes and identify preferential zones of net particle inflow, net particle outflow, and local zigzagging across the interface. Finally, this paper investigates the influence of the zigzag motion of particles on the (net) mass exchange coefficient. Derived from the same 3D-PTV dataset, a comparison between the common Eulerian (velocity-based) and Lagrangian mass exchange coefficients suggests that the transverse velocity method overestimates the net exchange significantly because of the particle zigzag motions.

### Pilot hydrogen enhanced combustion in an ethylene-fueled scramjet combustor at Mach 4

This paper describes a numerical and experimental investigation of the combustion process in an ethylene-fueled scramjet combustor. The combustion process could be divided into six parts. Part 1 consists of a nonreacting flow before the hydrogen was injected. In part 2, hydrogen injection led to the generation of a shock wave, resulting in an increase in the monitor pressure. Part 3 involved hydrogen combustion, including ignition and flame stabilization. The ignition time of the pilot hydrogen was about 26 ms, and the shock train generated by hydrogen combustion moved at about 20 m/s. In part 4, with the injection of ethylene, there was a hydrogen and ethylene combustion flow, the combustion became more intense, and the shock waves were pushed into the isolator and disappeared from the schlieren images. In part 5, with the cessation of hydrogen injection, the combustion involved ethylene alone, and the ethylene flame moved from the front of the cavity to the back. The combustion mode changed from subsonic to supersonic, and the flame stabilization mode changed from cavity recirculation to cavity shear layer combustion. In part 6, the flame was blown out and combustion ceased.

### A Bayesian approach to the mean flow in a channel with small but arbitrarily directional system rotation

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrarily directional system rotation. Our approach is as follows. First, we apply dimensional analysis to the Reynolds-averaged momentum equation. We show that when a boundary-layer flow is subjected to small system rotation, the constant stress layer survives, and the mean flow U+ is a universal function of y+, [math], [math], and [math], where U is the mean flow, y is the distance from the wall, Ωi is the system rotation speed in the ith direction (in the locally defined coordinate), and the superscript + denotes normalization by the local wall units. Second, we survey the three-dimensional parameter space of [math] and determine [math] for small Ω+. Here, we conduct direct numerical simulation (DNS) of a Reτ = 180 channel at various rotation conditions. This approach is conventionally considered as “brutal force.” However, as we will show in this work, the Bayesian approach allows us to very efficiently sample the parameter space. Four independent surveys are conducted with 146 DNSs, and the resulting Bayesian surrogate agrees well with our DNSs. Finally, we upscale to high Reynolds numbers via wall-modeled large-eddy simulation. In general, the present framework provides a path for surrogate modeling in a high-dimensional parameter space at high Reynolds numbers when sampling in a designated parameter space is possible at only a few conditions and at a low Reynolds number.