Supersonic Shear Flows Research Articles

Supersonically sprayed PVDF and ZnO flowers with built-in nanocuboids for wearable piezoelectric nanogenerators

Healthcare implant devices that can internally generate a flow of electrical charge driven by mechanical stimuli are in demand. Such self-powered electromechanical devices are known as piezoelectric nanogenerators (PENGs). In this study, a piezo-ceramic element of hydrothermally synthesized ZnO flowers comprising built-in nanocuboids was supersonically sprayed with piezo-polymer polyvinylidene fluoride (PVDF) to fabricate ZnO-embedded PVDF films for flexible PENG devices. In the presence of ZnO, the catastrophic supersonic impact and shear flow transformed the nonpolar α-phase of PVDF into the polar β-phase. The combination of ZnO flowers with built-in nanocuboids and β-phase-rich PVDF can help enhance generated charges at interfacial sites under an applied force. The supersonically sprayed PVDF/ZnO composite exhibited a 32% increase in the β-phase compared to that exhibited by pure PVDF prior to supersonic coating. The effective piezoelectric coefficient values (d33*) of the pure PVDF and PVDF/ZnO composite films were 43 and 150 pm·V‐1, respectively; the corresponding open-circuit voltages were 1.2 and 25.5 V, respectively. These significant differences confirm the pivotal role of ZnO in increasing the β-phase within PVDF during supersonic spraying. The form of the externally applied force and frequency were varied to evaluate the electromechanical performance of PVDF/ZnO. The energy harvesting capability of the composite was demonstrated using 33 light-emitting diodes.

Tunable Spatial Resolution Focused Laser Differential Interferometer for Density Fluctuation Measurement

We first propose and demonstrate a novel approach for achieving a focused laser differential interferometer (FLDI) system with tunable spatial resolution. The spatial resolution of the FLDI can be adjusted continuously between 83 μm and 382 μm. The density fluctuation of a supersonic shear flow is measured using the FLDI system with a spatial resolution of 182 μm, and the density fluctuations at different locations of the supersonic shear flow are measured and analyzed. The ability to adjust the spatial resolution in this work is of great significance for enhancing the spatial resolution and flexibility of the FLDI system.

Boundary layers of accretion discs: Discovery of vortex-driven modes and other waves

ABSTRACT Disc accretion on to weakly magnetized objects possessing a material surface must proceed via the so-called boundary layer (BL) – a region at the inner edge of the disc, in which the velocity of accreting material abruptly decreases from its Keplerian value. Supersonic shear arising in the BL is known to be conducive to excitation of acoustic waves that propagate into both the accretor and the disc, enabling angular momentum and mass transport across the BL. We carry out a numerical exploration of different wave modes that operate near the BL, focusing on their morphological characteristics in the innermost parts of accretion disc. Using a large suite of simulations covering a broad range of Mach numbers (of the supersonic shear flow in the BL), we provide accurate characterization of the different types of modes, verifying their properties against analytical results, when available. We discover new types of modes, in particular, global spiral density waves launched by vortices forming in the disc near the BL as a result of the Rossby wave instability; this instability is triggered by the vortensity production in that region caused by the non-linear damping of acoustic waves. Azimuthal wavenumbers of the dominant modes that we observe appear to increase monotonically with the Mach number of the runs, but a particular mix of modes found in a simulation is mildly stochastic. Our results provide a basis for better understanding of the angular momentum and mass transport across the BL as well as the emission variability in accreting objects.

Effects of Flow Compressibility on Two-Phase Mixing in Supersonic Droplet-Laden Flows

This research addresses a numerical analysis on the effects of flow compressibility on the characteristics of droplet dispersion, evaporation, and mixing of fuel and air according to the simulation of the spatially developing supersonic shear flows laden with evaporating n-decane droplets. A sixth-order hybrid WENO numerical scheme is employed for capturing the unsteady wave structures. The influence of inflow convective Mach number ( M c ), representing the high-speed flow compressibility, on the two-phase mixing is analyzed, in which M c is specified from 0.4 to 1.0. It is found that the shearing vortex is compressed spatially as M c increases, associated with the alternate distributions of compression and expansion regimes in the flow field. The flow compressibility changes not only the vortex structures but also the aerothermal parameters of the shear flows, and further influences the dispersion and evaporation of droplets. The two-phase mixing efficiency is observed to decrease as M c increases.

Observation of dual-mode, Kelvin-Helmholtz instability vortex merger in a compressible flow

We report the first observations of Kelvin-Helmholtz vortices evolving from well-characterized, dual-mode initial conditions in a steady, supersonic flow. The results provide the first measurements of the instability's vortex merger rate and supplement data on the inhibition of the instability's growth rate in a compressible flow. These experimental data were obtained by sustaining a shockwave over a foam-plastic interface with a precision-machined seed perturbation. This technique produced a strong shear layer between two plasmas at high-energy-density conditions. The system was diagnosed using x-ray radiography and was well-reproduced using hydrodynamic simulations. Experimental measurements imply that we observed the anticipated vortex merger rate and growth inhibition for supersonic shear flow.

Kelvin–Helmholtz Instability in the Solar Atmosphere, Solar Wind and Geomagnetosphere

Modern views on the nature of the Kelvin–Helmholtz (KH) instability and its manifestations in the solar corona, in the interplanetary medium, and at the geomagnetospheric boundary are under consideration. We briefly describe the main theoretical results of the KH instability obtained in the linear approximation. Analysis of observational data, confirming the occurrence of the KH instability in magnetic formations of the solar coronal plasma and on the daytime magnetopause, was mainly performed in the approximation of incompressibility. We show that the Rayleigh–Taylor instability can significantly enhance the KH instability in the above regions due to interface accelerations or its curvature. Special attention is focused on the compressibility effect on the supersonic shear flow instability in the solar wind (SW) and at the geomagnetic tail boundary where this instability is usually considered to be ineffective. We have shown that the phase velocity of oblique perturbations is substantially less than the flow velocity, and values of the growth rate and frequency range are considerably higher than when only taking velocity-aligned disturbances into account. We emphasize that the magnetic field and plasma density inhomogeneity which weaken the KH instability of subsonic shear flows, in the case of a supersonic velocity difference weaken the stabilizing effect of the medium compressibility, and can significantly increase the instability. Effective generation of oblique disturbances by the supersonic KH instability explains the observations of magnetosonic waves and the formation of diffuse shear flows in the SW and on the distant magnetotail boundary, as well as the SW-magnetosphere energy and impulse transfer.

Observation of Single-Mode, Kelvin-Helmholtz Instability in a Supersonic Flow.

We report the first observation, in a supersonic flow, of the evolution of the Kelvin-Helmholtz instability from a single-mode initial condition. To obtain these data, we used a novel experimental system to produce a steady shock wave of unprecedented duration in a laser-driven experiment. The shocked, flowing material creates a shear layer between two plasmas at high energy density. We measured the resulting interface structure using radiography. Hydrodynamic simulations reproduce the large-scale structures very well and the medium-scale structures fairly well, and imply that we observed the expected reduction in growth rate for supersonic shear flow.

Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: “Towards an accurate description of compressibility effects in supersonic free shear flows”

A compressible supersonic mixing layer at convective Mach number (Mc) equal to 1 has been studied experimentally in a dual stream supersonic/subsonic wind-tunnel. Laser Doppler Velocimetry (L.D.V.) measurements were performed making possible a full estimation of the mean and turbulent 3D velocity fields in the mixing layer. The Reynolds stress tensor was described. In particular, some anisotropy coefficients were obtained. It appears that the structure of the Reynolds tensor is almost not affected by compressibility at least up to Mc=1.The turbulent kinetic energy budget was also experimentally estimated. Reynolds analogies assumptions were used to obtain density/velocity correlations in order to build the turbulent kinetic energy budget from LDV measurements. Results have been compared to other experimental and numerical results. Compressibility effects on the turbulent kinetic energy budget have been detected and commented. A study about thermodynamics flow properties was also performed using most recent DNS results experimentally validated by the present data. A non-dimensional number is then introduced in order to quantify the real effect of pressure fluctuations on the thermodynamics quantities fluctuations.

Effects of Density Stratification on Mixing Enhancement by Shock Wave in Supersonic Shear Layer Flows

We analyze the response of passive mixing to shock wave in a density-stratified supersonic shear layer by means of direct numerical simulation with a high-order hybrid compact-WENO scheme. The coexistence gradients of density and pressure have a complex influence on generation of baroclinic vorticity, depending on the gradient directions. The growth rate of mixing layer thickness is increased by the presence of shock wave, but the mixing layer thickness is not always increased. The passive mixing can be enhanced in a thickened shear layer by the incident shock wave if the homodromous vortexes are induced by the baroclinic torque. The mixing efficiency is also enhanced by increasing the density difference of two streams. The present study can be helpful to take measures to strengthen the mixing process in supersonic shear flows.

Excitation of low frequency oscillations in a planetary magnetosheath by supersonic shear flow

Abstract. We show that the slow magnetosonic (SM) perturbations generated in the vicinity of the magnetopause, due to the excitation of the Kelvin-Helmholtz (K.-H.) instability in the case of a supersonic flow velocity, are transformed into fast magnetosonic (FM) waves which can propagate into the magnetosheath. Under the conditions discussed in this paper, the FM wave has negative energy in the stationary (magnetospheric) coordinate frame. Due to this the outgoing FM wave increases the growth rate of the K.-H. instability excited at the magnetopause. Within the linear theory, we investigate the influence of the excited FM wave on the growth rate of the K.-H. instability. Simultaneously we predict the transformation of the SM mode into kinetic Alfvén (KA) mode. Thus, in general, two types of waves with different polarizations (the KA wave and the FM wave) should appear in the magnetosheath due to the excitation of the K.-H. instability. At the same time, the SM perturbations are only present in the localized region where the K.-H. instability is excited. To correctly describe the excitation of waves, we use two-fluid (for electrons and ions) magnetohydrodynamics. This approach is more general than the ideal magnetohydrodynamics and allows us to take into account the effects associated with the finite Larmor radius of ions. Also it can be used to investigate the K.-H. instability in a multi-component plasma, or in the case where the frequency of perturbations is of the order of the gyrofrequency of oxygen ions which may occur, for example, at the magnetosheath of Mars.

Generation of Ultrafast Jets Through the Implosion of a Nested Conical Wire Array

It is shown that in contrast to the electric pulse power driven implosion of a single conical wire array, the implosion of a nested conical wire array with opposite alternate opening angles can lead to the generation of fast jets, with velocities of the order 108 cm/s. This technique can be applied for the supersonic shear flow stabilization of a dense z-pinch, but possibly also for the fast ignition of a pre-compressed dense deuterium–tritium target.

ZONAL FLOWS AND LONG-LIVED AXISYMMETRIC PRESSURE BUMPS IN MAGNETOROTATIONAL TURBULENCE

We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to ten scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor two when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This in turn generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short time-scales creates zonal flow structures with life-times of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.

Numerical Investigation of High Speed Free Shear Flow Instability and Mach Wave Radiation

The linear stability theory is used to investigate the emergence, in supersonic free shear flows such as mixing layers and fully expanded plane jets, of supersonically travelling instability waves, which do not vanish in the ambient space. It is shown that, at supersonic convective Mach numbers, the slow and fast supersonic modes in the mixing layer as well as the sinuous supersonic mode in the plane jet should lead to Mach wave radiation. Direct numerical simulations are further used to study nonlinear stages of instability development in high-speed mixing layers and jets. They have shown that the formation of oblique shock waves attached to large-scale structures is observed in free shear flows forced by modes with supersonic phase speeds. The relevance of this phenomenon to the noise generation by high-speed jets is discussed.

How Can Jets Survive MHD Instabilities?

We present the main findings of two recent studies using high-resolution MHD simulations of supersonic magnetized shear flow layers. First, a strong large-scale coalescence effect partially countered by small-scale reconnection events is shown to dominate the dynamics in a two-dimensional layer subject to Kelvin-Helmholtz (KH) instabilities. Second, an interaction mechanism between two different types of instabilities (KH and current-driven modes) is shown to occur in a cylindrical jet configuration embedded in an helical magnetic field. Finally, we discuss the implications of these results for astrophysical jets survival.

On the predominance of oblique disturbances in the supersonic shear flow instability of the geomagnetic tail boundary

Abstract. A study is made of the influence of the longitudinal magnetic field and density inhomogeneity on the supersonic shear flow instability at the magnetospheric tail boundary. It is shown that the most unstable are slow oblique (3D) disturbances, with a phase velocity approaching at a sufficiently large angle (with respect to the flow direction) the magnetosonic velocity. Their growth rate and spectral width are much larger than those of the usually considered longitudinal (2D) supersonic disturbances. The magnetic field reduces the compressibility effect and, unlike the subsonic case, has a noticeable destabilizing effect on the excitation of oblique disturbances.

超音速せん断流中の水素ガス初期燃焼への気体分子運動論的アプローチ｀＊１´ 第１報：混合拡散過程

Direct Simulation Monte Carlo (DSMC) method based on the Boltzmann equation, in-cooperating a new reactive inelastic molecular collision model, has been employed to analyze the fuel gas mixing in two-dimensional supersonic shear flow which originates from the meeting at a thin plate (lip) edge of two parallel flows, a supersonic air stream and a sonic hydrogen gas flow. In the present study, the influence of hydrogen gas temperature upon the mixing within the shear layer is clarified. In a companion paper (the 2nd report), the relationship between mixing and chemical reaction will be presented.

プラズマトーチ応用の超音速燃焼初期促進に関する気体分子運動論的解析 第１報：活性基の種類と供給形態による特徴

The effects of various radical species, supplied from a plasma torch ignitor upon initiating hydrogen-air chemical reaction in a two-dimensional supersonic shear flow have been investigated by a new numerical approach based on the molecular gas dynamics. Direct Simulation Monte Carlo (DSMC) method has been employed to derive the microscopic reaction phenomena from the Boltzmann equation with a reactive inelastic molecular collision model (IE Model). The plasma species and injection mode into air stream have been varied. The result shows that fuel hydrogen initial combustion can be significantly enhanced by plasma injection of atomic oxygen supplying in diffusive mode.

Compressible turbulence and energetic scales: What is known from experiments in supersonic flows?

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction.

Compressibility and structure of turbulence in supersonic shear flows

In this paper, different aspects of supersonic turbulent flows are discussed, in connection with some properties of compressible turbulence. The discussion is based on experiments, in which particular features have been found. The first point is the influence of density gradients. It is shown that changing the density gradient in a boundary layer does not change the particularly small size of the energetic scales. This effect is attributed to compressibility and not to density stratification, probably by modifying the `inactive motions'. The second point is about the importance of acoustics in a mixing layer. The results show that turbulent transport of momentum and heat follows the same analogy as in boundary layers, and that the energy losses by acoustic radiation are too weak to explain the reduction of the spreading rate, which is the major global effect of compressibility.

Compressibility effects due to turbulent fluctuations

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.