# Latest papers in fluid mechanics

### Impact of turbulence forcing schemes on particle clustering

This letter investigates the clustering of particles in isotropic turbulence sustained by linear and spectral forcing. The Stokes numbers range from 0.1 to 100. The time series of particles are analyzed with autocorrelation functions of the particle velocity and local fluid velocity. The spatial distributions of particles are analyzed with probability density functions of Voronoï volumes. These statistics show significant differences between the clustering of particles in linearly and spectrally forced turbulence.

### Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation

Three-dimensional (3D) routes of transition affected by the frequency of monochromatic wall excitation started impulsively are studied by performing direct numerical simulation. The computed results for the two frequencies of excitation reported here resemble the experimental setup of Klebanoff et al. [“The three-dimensional nature of boundary-layer instability,” J. Fluid Mech. 12(1), 1–34 (1962)], where a two-dimensional boundary layer is excited using 3D disturbances. Such a monochromatic wall excitation creates three-component disturbance field: a near-field followed by the Tollmien-Schlichting wave-packet and a spatiotemporal wave-front (STWF), which is responsible for eventual transition. It is noted that the case of moderate frequency of excitation shows a complete noninteracting nature of the near-field solution and the STWF. We report another route of transition computationally for a lower frequency of excitation. This case shows an interacting nature of the near-field solution and the STWF. While both frequency of excitations can cause transition for moderate spanwise wavelength (λz) disturbances, dependence of transition on λz is reported here for the first time. It is noted that doubling the spanwise wavenumber leads to the disappearance of STWF and no transition of the flow. We use the recently developed disturbance enstrophy transport equation in Sengupta et al. [“An enstrophy based linear and nonlinear receptivity theory,” Phys. Fluids 30, 054106 (2018)] for a better quantitative method to trace the evolution of disturbance field of the imposed 3D disturbances.

### Dissipation in cone-jet electrosprays and departure from isothermal operation

Author(s): M. Gamero-Castaño

Electrospraying in the cone-jet mode has being regarded an isothermal process, and the laws obtained under this assumption are considered valid throughout the operational range. However, self-heating due to dissipation is expected to be significant at sufficiently high electrical conductivities. Thi...

[Phys. Rev. E 99, 061101(R)] Published Wed Jun 26, 2019

### Electrohydrodynamics of an ionic liquid meniscus during evaporation of ions in a regime of high electric field

Author(s): Chase S. Coffman, Manuel Martínez-Sánchez, and Paulo C. Lozano

Numerical investigations are presented for an ionic liquid meniscus undergoing evaporation of ions in a regime of high electric field. A detailed model is developed to simulate the behavior of a stationary meniscus attached to a liquid feed system. The latter serves as a proxy for commonly utilized ...

[Phys. Rev. E 99, 063108] Published Wed Jun 26, 2019

### Propulsion performance of a two-dimensional flapping airfoil with wake map and dynamic mode decomposition analysis

Author(s): Hongyu Zheng, Fangfang Xie, Yao Zheng, Tingwei Ji, and Zaoxu Zhu

In the present study, we use the dynamic mesh method based on the radial basis function interpolation for the two-dimensional simulation of harmonically oscillating NACA0015 airfoil. Under various flapping frequencies, heaving and pitching amplitudes, the observed wake flows can be divided into seve...

[Phys. Rev. E 99, 063109] Published Wed Jun 26, 2019

### Drop impact on hairy surfaces

Author(s): Alice Nasto, P.-T. Brun, and A. E. Hosoi

A study of the impact of liquid drops on millimeter-scale hairy surfaces finds that the behavior of the impacting drops depends on the amount of kinetic energy dissipated through the hairs via a balance of inertia, viscosity, and surface tension.

[Phys. Rev. Fluids 4, 064004] Published Wed Jun 26, 2019

### Universal molecular-kinetic scaling relation for slip of a simple fluid at a solid boundary

Author(s): Gerald J. Wang and Nicolas G. Hadjiconstantinou

A molecular-kinetic model, based on thermally activated processes, is developed for the slip of a simple fluid on a smooth solid boundary. Navier slip is recovered at low shear-rates. Predictions at higher shear-rates are tested against experiments and MD simulations.

[Phys. Rev. Fluids 4, 064201] Published Wed Jun 26, 2019

### Exact and asymptotic solutions to magnetohydrodynamic flow over a nonlinear stretching sheet with a power-law velocity by the homotopy renormalization method

We apply an asymptotic analysis to a nonlinear magnetohydrodynamic boundary-layer flow over a nonlinear stretching sheet with two types of boundary conditions: slip and no-slip. The original partial differential equations governing the flow regime are first transformed into a nonlinear ordinary equation by using a special type of similarity transformation. Asymptotic solutions are then obtained in simple explicit form via the homotopy renormalization method. These solutions satisfy the boundary conditions, and, for special values of the parameters, the asymptotic solutions are just the exact solutions. In addition, the impacts of the magnetic energy effect, the electrical conductivity, and the slip boundary are shown graphically. The validity of the asymptotic solutions is evaluated by comparison with numerical solutions. The results show that the explicit solutions, with finite numbers of terms, perform very well over the whole domain, indicating that our solutions are almost exact.

### Deep-ocean inertial subrange small bandwidth coherence and Ozmidov-frequency separation

The inertial subrange of turbulence in a density stratified environment is the transition from internal waves to isotropic turbulence, but it is unclear how to interpret its extension to anisotropic “stratified” turbulence. Knowledge about stratified turbulence is relevant for the dispersal of suspended matter in geophysical flows, such as in most of the ocean. For studying internal-wave-induced ocean-turbulence, moored high-resolution temperature (T-)sensors are used. Spectra from observations on episodic quasiconvective internal wave breaking above a steep slope of large seamount Josephine in the Northeast-Atlantic demonstrate an inertial subrange that can be separated in two parts: A large-scale part with relatively coherent portions adjacent to less coherent portions and a small-scale part that is smoothly continuous (to within standard error). The separation is close to the Ozmidov frequency and coincides with the transition from anisotropic/quasideterministic stratified turbulence to isotropic/stochastic inertial convective motions as inferred from a comparison of vertical and horizontal cospectra. These observations contrast with T-sensor observations of shear-dominated internal wave breaking in an equally turbulent environment above the slope of a small Mid-Atlantic ridge-crest, which demonstrate a stochastic inertial subrange throughout.

### An improved discrete gas-kinetic scheme for two-dimensional viscous incompressible and compressible flows

In this work, we propose an improved discrete gas-kinetic scheme (DGKS) for viscous incompressible and compressible flows based on the modified circular function. The improved scheme restores the flaw of the previous DGKS and recovers the correct macroscopic energy equation. Modifications are first made on the previous circular function by relocating some portion of the particles in the phase velocity space from the circle to the circular center. By adjusting the portion of particles at the circular center, the true diffusive flux for the energy equation can be recovered, and thus, the correct macroscopic energy equation is obtained. Based on the modified circular function, a D2Q5 discrete velocity model is developed, which enhances the computational efficiency. This discrete velocity model is then incorporated into the finite volume framework for the reconstruction of numerical fluxes on the cell interface. Numerical tests on incompressible and compressible flows are performed for comprehensive validation of the proposed solver. Improved accuracy is observed in the test examples, and the computational results show good agreement with the reference data.

### An objective version of the Rortex vector for vortex identification

Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortex definition should maintain its objectivity. Currently, most of the vortex identification methods rely on velocity gradient tensors. The calculation of the velocity gradient tensor is based on the reference frame of the observer, and the velocity gradient tensor will vary with the observer’s motion. By these vortex identification methods, very different vortex structures could be visualized and described in a moving reference frame. Recently, a mathematical definition of the Rortex vortex vector was proposed to represent the local fluid rotation. The definition used velocity gradient tensor to derive the local rigid rotation axis and strength. However, the original definition of the Rortex vector is nonobjective. In order to obtain the objectivity, in this paper, by a definition of a net velocity gradient tensor, an objective Rortex vortex vector is defined which uses a spatially averaged vorticity to offset the impact of the motion frame. Some typical numerical examples, such as an implicit large-eddy simulation result for shock and boundary layer interaction and a direct numerical simulation for boundary layer transition, are provided to show the objectivity of the developed method.

### A posteriori tests of subgrid-scale models in strongly anisothermal turbulent flows

This paper studies the large-eddy simulation of anisothermal low Mach number turbulent channel flows. We consider the large-eddy simulations of the low Mach number equations in two formulations, the velocity formulation and the Favre formulation. In both formulations, we investigate the subgrid-scale modeling of the two most significant subgrid terms of the filtered low Mach number equations: the momentum convection subgrid term and the density-velocity correlation subgrid term. To this end, the predictions of large-eddy simulations implementing the models are compared to filtered direct numerical simulations. We address several types of subgrid-scale models: functional eddy-viscosity or eddy-diffusivity models, structural models, tensorial models, and dynamic versions of these models. For the momentum convection subgrid term, we recommend the use of the scale-similarity model and the constant-parameter or dynamic tensorial anisotropic minimum-dissipation (AMD) model. For the density-velocity correlation subgrid term, several models are able to improve temperature-related statistics, for instance, the AMD model and the scale-similarity model. More accurate results are obtained with the Favre formulation than with the velocity formulation.

### Attached cavitation in laminar separations within a transition to unsteadiness

Attached sheet cavitation is usually observed in turbulent water flows within small laminar separation bubbles which can provide favorable conditions for inception and attachment of cavities. In the present study, viscous silicone oils are used within a small scale Venturi geometry to investigate attached cavitation into laminar separated flows for Reynolds numbers from 346 to 2188. Numerical simulations about single phase flows are performed with steady simulations for a Reynolds number range Re ∈ [50; 1400] and with unsteady simulations for Re ∈ [1000; 2000]. They reveal the emergence of two large laminar boundary layer separations downstream of the Venturi throat in addition to low pressure zones which can possibly induce both degassing or cavitation features. Experiments are performed with high-speed photography, and several multiphase dynamics are observed in these viscous flows, which are considered as quasisteady flows at low Reynolds numbers Re ≤ 1400. Degassing phenomenon with air bubble recirculation has been first observed at pressures far above liquid vapor pressure whereas typical attached cavities have been identified for low pressure conditions as “band” and “tadpole” cavities into the different separations of the laminar flows. For higher Reynolds numbers, a flow regime transition can be noticed in the wake of well-developed gas structures, characterized by wake instabilities, causing vortex cavitation above a critical Reynolds number associated with the bubble width [math]. This regime transition can possibly occur either quasicontinuously in the wake of an attached “band” vapor cavity or intermittently behind a recirculating air bubble generated with degassing. This last phenomenon is associated in our study to classical “patch” cavitation.

### Understanding droplet collisions through a model flow: Insights from a Burgers vortex

Author(s): Lokahith Agasthya, Jason R. Picardo, S. Ravichandran, Rama Govindarajan, and Samriddhi Sankar Ray

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significan...

[Phys. Rev. E 99, 063107] Published Tue Jun 25, 2019

### Data-based modeling of gas-surface interaction in rarefied gas flow simulations

In this work, a data-based approach to gas-surface interaction modeling, which employs the recently introduced distribution element tree (DET) method, is proposed. The DET method allows efficient data-driven probability density function (PDF) estimations with the possibility of conditional and unconditional random number resampling from the constructed distributions. As part of our ongoing research on gas-surface interaction, a comprehensive molecular dynamics (MD) study was performed, where the scattering of a nitrogen molecule from a graphite surface was investigated. Our aim here is to demonstrate how the DET method can be used in combination with the obtained MD database for constructing a generalized kernel of gas-surface interaction and for generating postscattered samples directly from the MD data itself. The major benefit of this approach is that it preserves all the relevant physics contained within numerical or experimental data, without the need for new kernel developments or accommodation coefficient calibrations. A direct comparison between the proposed approach and a classical scattering kernel used in rarefied gas flow simulations was carried out in the case of molecular beam scattering of rotationally hot and cold nitrogen from a solid surface. A further comparison between the proposed method and the available experimental data was also performed. Additionally, the ability of the DET-based kernel to satisfy the reciprocity condition, which ensures energy conservation in the case of thermal equilibrium, is demonstrated.

### Flow structures of a lobed mixer and effects of streamwise vortices on mixing enhancement

Large-scale vortices downstream of a lobed mixer are investigated experimentally using a nanoparticle-based planar laser scattering experimental system. The results are contrasted with additional measurements of a flat plate and a convoluted plate. Three streamwise vortices form downstream of the lobed mixer due to the pressure difference between the peak and trough regions of the trailing edge. This is not the case for the convoluted plate, where the streamwise structures are suppressed and do not appear downstream. Comparison of vortex sizes indicates that streamwise vortices contribute almost 80% of mixing enhancement, which is substantially higher than what could be expected from the increase of the interfacial surface area, especially in the far field of the present compressible mixing layer. It is also quite different from the effects of streamwise vortices on the mixing enhancement in incompressible mixing layers. That no streamwise vortices appear downstream of the convoluted plate indicates that the pressure difference around the corners of the peak and trough regions in the lobed mixer plays an important role for the appearance of the streamwise vortices. Three-dimensional views of the streamwise vortices show that a significant amount of fluid is entrained from the lower stream to the upper stream, resulting in the development of the streamwise vortices for the lobed mixer. The interaction of the streamwise and spanwise vortices then leads to the formation of a large number of small-scale vortices. These two mechanisms enlarge the interfacial surface area of the two streams greatly and substantially improve the turbulent mixing prominently. In addition, the presence of vortex clusters and T-shape vortices in the mixing layer indicate that they are common topological structures in such flows.

### A laboratory study of class III Bragg resonance of gravity surface waves by periodic beds

When moderately steep waves travel over a periodic rippled bed, class III Bragg resonance may occur due to the third-order quartet wave-bottom interaction among one bottom and three surface wave components. The theory, however, has not been experimentally confirmed. To verify the existence of class III Bragg resonance, we consider the simplest possible case involving a single incident wave and conduct a series of physical experiments. The experiments show that as the theory predicts, class III Bragg resonance could generate not only the reflected waves (from subharmonic resonance) but also the transmitted waves (from superharmonic resonance), and the reflection and transmission coefficients vary linearly along the rippled bottom patch. Furthermore, the experimental data of the reflected and transmitted waves (due to class III resonance) agree quantitatively well with the prediction by high-order spectral (HOS) method computations. To further understand the characteristics of class III resonance, we apply HOS simulations to study the more general cases including the presence of two incident waves of different frequencies as well as the presence of an incident wave group with Gaussian envelope. The results show that in addition to class I and class II Bragg resonances, class III Bragg resonance can significantly influence the evolution of surface wave fields passing over a rippled bottom, especially in the case of shallow water.

### A review and perspective on a convergence analysis of the direct simulation Monte Carlo and solution verification

In 1963, G. A. Bird published a research note on his investigation of a rigid sphere gas reaching translational equilibrium using a Monte Carlo type method. Since then, the method has been developed into a primary workhorse to computationally solve the Boltzmann kinetic equation. As it is increasingly applied to challenging problems in the real world, verification studies of the method have become a critical issue. In this paper, we review previous studies on this challenging subject and present a perspective on a convergence analysis of the direct simulation Monte Carlo (DSMC) method and solution verification. During this process, a verification method based on the physical laws of conservation is studied in depth. In particular, a convergence history plot on all three types of computational errors—decomposition, statistical, and round-off—is presented for two benchmark problems. Finally, future research topics to maximize the full potential of the DSMC method, pioneered by the late G. A. Bird, are suggested.

### Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales

Two-dimensional magnetohydrodynamics, forced at (a) large length scales or (b) small length scales, display turbulent, but statistically steady, states with widely different statistical properties. We present a systematic, comparative study of these two cases (a) and (b) by using direct numerical simulations. We find that, in case (a), there is energy equipartition between the magnetic and velocity fields, whereas, in case (b), such equipartition does not exist. By computing various probability distribution functions, we show that case (a) displays extreme events that are much less common in case (b).

### Propulsion driven by self-oscillation via an electrohydrodynamic instability

Author(s): Lailai Zhu and Howard A. Stone

When a flexible elastic filament is attached to a Quincke rotating sphere, an elasto-electro-hydrodynamic instability leads to self-propulsion of the composite system.

[Phys. Rev. Fluids 4, 061701(R)] Published Mon Jun 24, 2019