# Latest papers in fluid mechanics

### Impact of fundamental molecular kinetics on macroscopic properties of high-enthalpy flows: The case of hypersonic atmospheric entry

Author(s): G. Colonna, F. Bonelli, and G. Pascazio

A state-to-state approach and GPU processors are used to find the nonequilibrium vibrational distributions of O2 and N2 in a hypersonic flow past a sphere.

[Phys. Rev. Fluids 4, 033404] Published Fri Mar 29, 2019

### Nonequilibrium air flow predictions with a high-fidelity direct simulation Monte Carlo approach

Author(s): Sergey F. Gimelshein and Ingrid J. Wysong

A conventional and high-fidelity direct simulation Monte Carlo approach is applied to a number of hypersonic cases where validation data is available. Changes in the collision model are found to have a small effect on surface properties, with nitrogen recombination being the only notable exception.

[Phys. Rev. Fluids 4, 033405] Published Fri Mar 29, 2019

### Disorder characterization of porous media and its effect on fluid displacement

Author(s): Zhongzheng Wang, Kapil Chauhan, Jean-Michel Pereira, and Yixiang Gan

Depending on topology of pore space, different patterns of multiphase flow in porous media are observed. By analyzing pore-scale mechanisms, a phase diagram is constructed showing that wettability and structural disorder collectively affect displacement efficiency and fluid-fluid interfacial area.

[Phys. Rev. Fluids 4, 034305] Published Fri Mar 29, 2019

### Investigation of inner-outer interactions in a turbulent boundary layer using high-speed particle image velocimetry

Author(s): Gokul Pathikonda and Kenneth T. Christensen

High-resolution, high-frame-rate particle image velocimetry measurements in a refractive index-matched flow facility are used to explore the spatiotemporal signature of outer, large-scale motions influencing near-wall, smaller scales (so-called inner-outer interactions) in a turbulent boundary layer.

[Phys. Rev. Fluids 4, 034607] Published Fri Mar 29, 2019

### Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects

Motivated by evaluating coating oil films within bearing chambers in an aero-engine application, an analysis is presented for the fluid dynamics relevant in their dual capacity as both the coolant and lubricant in highly sheared flows that may approach microscale thickness. An extended model is developed for isothermal rimming flow driven by substantial surface shear within a stationary cylinder. In particular, a partial slip condition replaces the no-slip condition at the wall whilst retaining inertial effects relevant to an intrinsic high speed operation. A depth-averaged formulation is presented that includes appropriate inertial effects at leading-order within a thin film approximation that encompasses a more general model of assessing the impact of surface slip. Non-dimensional mass and momentum equations are integrated across the film depth yielding a one dimensional problem with the a priori assumption of local velocity profiles. The film flow solutions for rimming flow with wall slip are modeled to a higher order than classical lubrication theory. We investigate the impact of wall slip on the transition from pooling to uniform films. Numerical solutions of film profiles are provided for the progressively increased Reynolds number, within a moderate inertia regime, offering evaluation into the effect of film slippage on the dynamics of rimming flow. We find that slip allows non-unique solution regions and existence of multiple possible steady state solutions evaluated in transforming from smooth to pooling film solutions. Additionally, boundary slip is shown to enhance the development of recirculation regions within the film which are detrimental to bearing chamber flows.

### Turbulent convection and large scale circulation in a cube with rough horizontal surfaces

Author(s): N. Foroozani, J. J. Niemela, V. Armenio, and K. R. Sreenivasan

Large-eddy simulations of thermal convection are presented and discussed for a cube with rough horizontal surfaces. Two types of roughness are considered: uniformly placed pyramids, and grooves aligned parallel to one set of sidewalls. The Rayleigh number is 108, the Prandtl number 0.7, and the aspe...

[Phys. Rev. E 99, 033116] Published Thu Mar 28, 2019

### Effect of electric field on an oscillatory film flow

The effect of a uniform electric field on the linear stability of a viscous liquid film flow on an oscillating plane is studied. The mechanism of the long-wave instability is deciphered based on the regular perturbation method along with the Floquet theory. The analytical solution predicts that long-wave unstable region increases in the presence of the electric field. On the contrary, the growth rate of the long-wave mode decreases in the presence of the surface tension. In addition, the Orr-Sommerfeld boundary value problem (OS BVP) is formulated to explore the numerical solution in the finite wavelength regime. The Chebyshev spectral collocation method along with the Floquet theory is applied to solve the OS BVP for infinitesimal disturbances of arbitrary wavenumbers. The stability limits exhibit U-shaped form curve in various ranges of the imposed frequency at a sufficiently small wavenumber. However, the oblique stability limits emerge from the branch points detected on the U-shaped form stability limits at a finite critical wavenumber and continue monotonically with the imposed frequency. Furthermore, with the increasing value of the electric field, folds occur on the finite wavelength stability limit and result in a pair of separated unstable regions. Similarly, with the decreasing value of the surface tension, the finite wavelength stability limit demonstrates folds on it and yields a pair of separated unstable regions.

### Comparison of free convection flow around an engineered porous fin with spherical connections and rigid fin under different positioning angles—An experimental and numerical analysis

In this paper, the free convective flow around an engineered porous fin with spherical connections is investigated experimentally and numerically. In addition, the effects of different positioning angles for different fin materials on thermal fin performance are analyzed. First, the copper, aluminum, and brass fins are made and their thermal performances under free convective flow are examined experimentally. Then, in order to extend the results, after validation the numerical analysis is carried out in steady and three-dimensional calculations. Then, at different positioning angles, the formed free convective flow around the porous fin is analyzed numerically and compared with the results of a rigid fin. The results show that the efficiency of the copper fins at all positioning angles is maximal. It was also found that the highest amount of Nusselt number occurs at the angle of 45°. In the numerical investigations, it is determined that the maximum increase in the Nusselt number of the engineered porous fins is about two times that of the rigid fin. Moreover, a relationship between the Nusselt number and the Rayleigh number is presented for a horizontal engineered porous fin in laminar free convection flow.

### Numerical simulation of two coalescing turbulent forced plumes in linearly stratified fluids

A computational fluid dynamic model that can solve the Reynolds-averaged Navier-Stokes equations and the species transport equation is developed to simulate two coalescing turbulent forced plumes, which are released with initial momentum and buoyancy flux into a linearly stable stratified environment. The velocity fields, turbulence structures, and entrainment of two plumes with different source separations and source buoyancy fluxes are analyzed quantitatively, in comparison with a series of physical experiments. An empirical parameterization is proposed to predict the amplification of the maximum rise height of two coalescing forced plumes caused by superposition and mutual entrainment. The maximum values of both turbulent kinetic energy and turbulence dissipation rate decrease monotonically with the increase in source separation of the two turbulent plumes. However, the trajectory of the maximum turbulent viscosity attained in the plume cap region presents two notable enhancements. This variation may be attributed to the turbulence transported from the touching region and the strong mixing around the neutrally buoyant layer between two plumes, while the mixing is caused by the lateral convection and the rebound after overshooting. The plume entrainment coefficient in near vent stems has a positive relationship with the source Richardson number. A transition of flow regimes to plume-like flows would occur when the contribution of initial momentum is important. The entrainment coefficient will decrease in the touching region of two plumes due to mutual entrainment, while the superposition of plumes can lead to distortion of the boundary of plume sectors.

### Analog cosmology with two-fluid systems in a strong gradient magnetic field

Author(s): Zack Fifer, Theo Torres, Sebastian Erne, Anastasios Avgoustidis, Richard J. A. Hill, and Silke Weinfurtner

Inflation refers to the exponential expansion of the early universe that can explain many of the properties we see today. The authors of this work propose an experimental analog in which the interface between two immiscible, magnetic fluids shows inflationary behavior. The work shows that waves created at the interface could reproduce known solutions of inflationary models, and suggests a variety of other cosmological scenarios that could be simulated.

[Phys. Rev. E 99, 031101(R)] Published Wed Mar 27, 2019

### Effect of pressure on joint cascade of kinetic energy and helicity in compressible helical turbulence

Author(s): Zheng Yan, Xinliang Li, Jianchun Wang, and Changping Yu

Direct numerical simulations of three-dimensional compressible helical turbulence are carried out at a grid resolution of 10243 to investigate the effect of pressure, which is important for the joint cascade of kinetic energy and helicity in compressible helical turbulence. The principal finding is ...

[Phys. Rev. E 99, 033114] Published Wed Mar 27, 2019

### Localized Faraday patterns under heterogeneous parametric excitation

Author(s): Héctor Urra, Juan F. Marín, Milena Páez-Silva, Majid Taki, Saliya Coulibaly, Leonardo Gordillo, and Mónica A. García-Ñustes

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiment...

[Phys. Rev. E 99, 033115] Published Wed Mar 27, 2019

### Liquid spreading on cold surfaces: Solidification-induced stick-slip dynamics

Author(s): Rémy Herbaut, Philippe Brunet, Laurent Limat, and Laurent Royon

Spreading of liquid on a cold substrate with freezing is investigated. Experimental investigation of the criterion for a solidification-induced pinning of the liquid near the triple line finds that below a temperature-dependent velocity, spreading shows stick-slip dynamics.

[Phys. Rev. Fluids 4, 033603] Published Wed Mar 27, 2019

### On the inherent bias of swirling strength in defining vortical structure

The traditional practice of using rotational motion as the principal attribute of coherent vortical structures in the buffer region of near-wall turbulent flow is shown to create a biased accounting of the role of vorticity within the structures. Vorticity associated with rotation is given a favored consideration against vorticity that is equally strong but not associated with rotation. Using data from a highly resolved direct numerical simulation of channel flow, it is shown that describing the structures based on the properties of the rotational field leads to a distorted view of the actual structures that are present. As a practical matter, this means that where hairpins are typically considered to be the flow structures, a more accurate description of the coherent events is that they are elongated mushroom-shaped vortical objects ejecting over low speed streaks. In this, hairpin-shaped rotational regions are embedded in the lobes of the mushrooms.

### Enhanced imbibition from the cooperation between wetting and inertia via pulsatile forcing

We study the dynamics of microfluidic interfaces driven by pulsatile pressures in the presence of neutral and hydrophilic walls. For this, we propose a new phase field model that takes inertia into account. For neutral wetting, the interface dynamics is characterized by a response function that depends on a non-dimensional frequency, which involves the time scale associated with inertia. We have found a regime, for large values of this non-dimensional frequency, in which inertia is relevant, and our model is necessary for a correct description of the dynamics. For hydrophilic walls, the dynamics of the contact line with pulsatile forcing is basically undistinguishable to the dynamics of imbibition solely due to wetting. However, we observe that the presence of inertia causes the interface to advance faster than in the absence of pulsatile forcing. This is because pulsatile forcing induces inertia at the bulk to cooperate with wetting creating an enhancement of the imbibition process. We characterize this complex dynamics with transitory exponents that, at early times, are larger than the Washburn ones, and tend to the Washburn exponent at long times, when the interface feels less and less the driving force applied at the entrance of the microchannel, and the dynamics is dominated solely by wetting.

### Harmonic linearized Navier-Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition

Laminar-turbulent transition is crucially influenced by wall roughness. This paper develops a numerical approach based on the harmonic linearized Navier-Stokes (HLNS) equations to accommodate the scattering effect of the rapidly distorted mean flow induced by a two-dimensional hump or indentation at the wall on the oncoming instability modes (including the Mack first and second modes) in a hypersonic boundary layer. Due to the ellipticity of the scattering system when the roughness width is comparable with the instability wavelength, the traditional linear stability theory and the linear parabolized stability equation do not apply, and therefore, the HLNS approach has advantages in both accuracy and efficiency. The impact of a roughness is characterized by a transmission coefficient, which is the ratio of the asymptotic amplitude downstream of the roughness to that upstream. At a Mach number of 5.92, the dependence of the transmission coefficient on the frequency and the oblique angle of the oncoming mode and the size and location of the hump/indentation is studied systematically. It is confirmed that the synchronization frequency appears as a critical frequency, above and below which the oncoming instability modes are suppressed and enhanced by the roughness, respectively, which provides fundamental basis to the laminar-flow control in hypersonic boundary layers.

### Using vortex identifiers to build eddy-viscosity subgrid-scale models for large-eddy simulation

Author(s): Xingjun Fang, Bing-Chen Wang, and Donald J. Bergstrom

A generalized framework of incorporating vortex identifiers into subgrid-scale models for large-eddy simulation is presented. The proposed models can automatically identify the under-resolved vortex stretching process and drain energy from the inertial subrange.

[Phys. Rev. Fluids 4, 034606] Published Tue Mar 26, 2019

### Scattering of surface shallow water waves on a draining bathtub vortex

Author(s): Semyon Churilov and Yury Stepanyants

Wave scattering on a bathtub vortex in shallow water is studied in the linear approximation. The results obtained are relevant to the interpretation of laboratory experiments and can be considered the hydrodynamic model of wave scattering by a rotating black hole in general relativity.

[Phys. Rev. Fluids 4, 034704] Published Tue Mar 26, 2019

### On two-dimensional self-similar axisymmetric vortices

Superpositions of Lamb-Oseen axisymmetric vortices with Gaussian vorticity having zero net circulation and finite kinetic energy in unbounded domain are considered. Their evolution is described by self-similar solutions depending on a certain combination of space, time, and viscous diffusion. It is shown that the structure of a popular self-similar solution for a shielded vortex with Gaussian fluid rotation rate corresponds to two Lamb-Oseen vortices with opposite sign and nearly the same spatial scale. The radial structure of a combined vortex with different spatial scales is well suited for characterization of realistic vortical structures like atmospheric hurricanes. The linear stability of the combined vortex is investigated. The results have important implications for better understanding of vortex structures in two-dimensional flow.

### A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.