Mode coupling in nonlinear Kelvin-Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.

NONLINEAR MHD KELVIN-HELMHOLTZ INSTABILITY IN A PIPE

Nonlinear MHD Kelvin-Helmholtz(K-H)instability in a pipe is treated with the deriva- tive expansion method in the present paper The linear stability problem was discussed in the past by Chandrasekhar(1961)and Xu et al.(1981).Nagano(1979)discussed the nonlinear MHD K-H instability with infinite depth.He used the singular perturbation method and extrapolated the ob- tained second order modifier of amplitude vs.frequency to seek the nonlinear effect on the instability growth rate γ.However,in our view,such an extrapolation is inappropriate.Because when the instabili- ty sets in,the growth rates of higher,order terms on the right hand side of equations will exceed the cor- responding secular producing terms,so the expansion will still become meaningless even if the secular producing terms are eliminated.Mathematically speaking,it's impossible to derive formula(39) when γ_0~2 is negative in Nagano's paper.Moreover,even as early as γ_0~2→O^+,the expansion be- comes invalid because the 2nd order modifier γ_2(in his formula(56))tends to infinity.This weak- ness is removed in this paper,and the result is extended to the case of a pipe with finite depth.

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability(KHI)of two superposed finite-thickness fluid layers with the magnetic field effect into consideration.The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased.When the thickness and the magnetic field act together on the KHI,the effect of thickness is more obvious when the magnetic field intensity is weak.The magnetic field transition layer destabilizes(enforces)the KHI,especially in the case of small thickness of the magnetic field transition layer.When considering the effect of magnetic field,the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness.The stronger the magnetic field intensity is,the more obvious the growth rate decreases with the total thickness.Thus,it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored,such as in double-cone ignition scheme for inertial confinement fusion.

K-H Instability of Dust Plasma

Areview about K-H instability related to comet tail is presented.The effect of dust graing on KHI is theoretically analysed and relations of critical shear to excit KHI with the properties of dust grains both for sheared ion flow and for sheared dust flow re put out.Their possible application in comet tail is suggested.

Applications of Non-Classical Equations and Their Approaches to the Solution of Some of Classes Equations Arise in the Kelvin-Helmholtz Mechanism and Instability

In the presented work, we consider applications of non-classical equations and their approaches to the solution of some classes of equations that arise in the Kelvin-Helmholtz Mechanism (KHM) and instability. In all areas where the Kelvin-Helmholtz instability (KHI) problem is investigated with the corresponding data unchanged, the solution can be taken directly in a specific form (for example, to determine the horizontal structure of a perturbation in a barotropic rotational flow, which is a boundary condition taken, as well as other types of Kelvin-Helmholtz instability problems). In another example, the shear flow along the magnetic field in the Z direction, which is the width of the contact layer between fast and slow flows, has a velocity gradient along the X axis with wind shear. The most difficult problems arise when the above unmentioned equation has singularities simultaneously at points and in this case, our results also remain valid. In the case of linear wave analysis of Kelvin-Helmholtz instability (KHI) at a tangential discontinuity (TD) of ideal magneto-hydro-dynamic (MHD) plasma, it can be attributed to the presented class, and in this case, as far as we know, solutions for eigen modes of instability KH in MHD plasma that satisfy suitable homogeneous boundary conditions. Based on the above mentioned area of application for degenerating ordinary differential equations in this work, the method of functional analysis in order to prove the generalized solution is used. The investigated equation covers a class of a number of difficult-to-solve problems, namely, generalized solutions are found for classes of problems that have analytical and mathematical descriptions. With the aid of lemmas and theorems, the existence and uniqueness of generalized solutions in the weight space are proved, and then general and particular exact solutions are found for the considered problems that are expressed analytically explicitly. Obtained our results may be used for all the difficult-to-solve processes of KHM and instabilities and instabilities, which cover widely studied areas like galaxies, Kelvin-Helmholtz instability in the atmospheres of planets, oceans, clouds and moons, for example, during the formation of the Earth or the Red Spot on Jupiter, as well as in the atmospheres of the Sun and other stars. In this paper, also, a fairly common class of equations and examples are indicated that can be used directly to enter data for the use of the studied suitable tasks.

The instability of water-mud interface in viscous two-layer flow with large viscosity contrast

The temporal instability of parallel viscous two-phase mixing layers is extended to current-fluid mud by considering a composite error function velocity profile. The influence of viscosity ratio, Reynolds number, and Froude number on the instability of the system are discussed and a new phenomenon never discussed is investigated based on our numerical results. It is shown that viscosity can enlarge the unstable wave number range, cause new instability modes, and certainly reduce the growth rate of Kelvin-Helmholtz （K-H） instability.

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin-Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin-Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.

Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model.Technically,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes.One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological functionals.Physically,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima simultaneously.The viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE intensities.Contrary to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution afterwards.The physical reasons are analyzed and presented.

Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability

The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.

Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (SF6) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction.The vortex dynamics of the Richtmyer-Meshkov instability and the turbulent mixing induced by the KelvinHelmholtz instability are discussed.A modified reconstruction model is proposed to predict the circulation for the shock triangular gas-cylinder interaction flow.Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated.Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case.The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin-Helmholtz vortices can gain energy from the mean flow in total.Consequently,small scale flow structures are generated therein by means of nonlinear interactions.Furthermore,the occasional 'pairing' between a vortex and its neighboring vortex will trigger the merging process of vortices and,finally,create a large turbulent mixing zone.

Study on the influences of interaction behaviors between multiple combustion-gas jets on expansion characteristics of Taylor cavities

The purpose of this study is to investigate means of controlling the interior ballistic stability of a bulk-loaded propellant gun（BLPG）.Experiments on the interaction of twin combustion gas jets and liquid medium in a cylindrical stepped-wall combustion chamber are conducted in detail to obtain time series processes of jet expansion,and a numerical simulation under the same working conditions is also conducted to verify the reliability of the numerical method by comparing numerical results and experimental results.From this,numerical simulations on mutual interference and expansion characteristics of multiple combustion gas jets（four,six,and eight jets） in liquid medium are carried out,and the distribution characteristic of pressure,velocity,temperature,and evolutionary processes of Taylor cavities and streamlines of jet flow Held are obtained in detail.The results of numerical simulations show that when different numbers of combustion gas jets expand in liquid medium,there are two different types of vortices in the jet flow field,including corner vortices of liquid phase near the step and backflow vortices of gas phase within Taylor cavities.Because of these two types of vortices,the radial expansion characteristic of the jets is increased,while changing numbers of combustion gas jets can restrain Kelvin-Helmholtz instability to a certain degree in jet expansion processes,which can at last realize the goal of controlling the interior ballistic stability of a BLPG.The optimum method for both suppressing Kelvin-Helmholtz instability and promoting radial expansion of Taylor cavities can be determined by analyzing the change of characteristic parameters in a jet flow field.

Study on three-dimensional expansion characteristics of four wall combustion-gas jets in confined liquid space

To explore further the launch mechanism of the new underwater launching technology proposed in this paper, the expansion characteristics of four wall combustion-gas jets in confined liquid space must be studied firstly. The experimental device is designed, and the high-speed digital photographic system is adopted to obtain the expansion sequence processes of Taylor cavities formed by the four wall jets. Meanwhile, the influence of the injection pressure on the axial expansion property of the four wall jets is discussed. Based on the experiments, a three-dimensional unsteady mathematical model is established to simulate the turbulent flow process of the four wall jets expanding in liquid, and the temporal and spatial distribution laws of phase, pressure, temperature, and velocity and the evolution rules of vortices are illustrated in detail. Results show that, accompanied by the jets expanding downstream, the four wall combustion-gas jets get close to each other and achieve convergence eventually under induction of the interference effect between multiple jets. Meanwhile, the heads of the Taylor cavities separate from the observation chamber wall and offset to the central axis of the observation chamber with time going on. The numerical simulation results of the four wall combustion-gas jets coincide well with the experimental data.

ON SEPARATED SHEAR LAYER OF BLUNT CIRCULAR CYLINDER

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8 x 10(3) to 1.0 x 10(5), with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2 similar to 3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5 similar to 6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed.

Dynamics of the outflow and its effect on the hydraulics of two-layer exchange flows in a channel

This paper reports that an experimental study is conducted to examine the dynamics of the outflow in two-layer exchange flows in a channel connecting between two water bodies with a small density difference. The experiments reveal the generation of Kelvin-Helmholtz (KH) instabilities within the hydraulically sub-critical flow region of the channel. During maximal exchange, those KH instabilities develops into large-amplitude KH waves as they escape the channel exit into the reservoir. The propagation speed of those waves, their generation frequency and their amplitudes are studied. The dynamics of the outflow and these waves are directly linked to the hydraulic conditions of the exchange flow within the channel.

NUMERICAL MODELING OF KELVIN-HELMHOLTZ INSTABILITY AND RAYLEIGH-TAYLOR INSTABILITY AT LARGE DEFORMATION STAGE——(Ⅰ) NUMERICAL METHOD AND NUMERICAL RESULTS OF RAYLEIGHTAYLOR INSTABILITY

This paper improves the discrete vortex method for modeling Kelvin-Helmholtz instability and Rayleigh-Tay- lor instability by proper choice of velocity weighted average coefficients, redistribution of markers and successive adding of computational points with the increase of interfacial deformation and gives the numerical results of Rayleigh-Taylor instability. The numerical results show that the first two techniques greatly enhance the ability of the discrete vortex method for modeling large interracial deformations and the last technique greatly reduces the computational amounts of the numerical modeling at large deformation stage. The numerical modeling of Rayleigh- Taylor instability not only reproduces some phenomena such as the roll up at the end part of the spike observed in experiments but also finds some new phenomena such as the splashes at the roll up parts which needs to be tested by experiment.

Influence of the tangential velocity on the compressible Kelvin–Helmholtz instability with nonequilibrium effects

Kelvin–Helmholtz(KH)instability is a fundamental fluid instability that widely exists in nature and engineering.To better understand the dynamic process of the KH instability,the influence of the tangential velocity on the compressible KH instability is investigated by using the discrete Boltzmann method based on the nonequilibrium statistical physics.Both hydrodynamic and thermodynamic nonequilibrium(TNE)effects are probed and analyzed.It is found that,on the whole,the global density gradients,the TNE strength and area firstly increase and decrease afterwards.Both the global density gradient and heat flux intensity in the vertical direction are almost constant in the initial stage before a vortex forms.Moreover,with the increase of the tangential velocity,the KH instability evolves faster,hence the global density gradients,the TNE strength and area increase in the initial stage and achieve their peak earlier,and their maxima are higher for a larger tangential velocity.Physically,there are several competitive mechanisms in the evolution of the KH instability.(i)The physical gradients increase and the TNE effects are strengthened as the interface is elongated.The local physical gradients decrease and the local TNE intensity is weakened on account of the dissipation and/or diffusion.(ii)The global heat flux intensity is promoted when the physical gradients increase.As the contact area expands,the heat exchange is enhanced and the global heat flux intensity increases.(iii)The global TNE intensity reduces with the decreasing of physical gradients and increase with the increasing of TNE area.(iv)The nonequilibrium area increases as the fluid interface is elongated and is widened because of the dissipation and/or diffusion.

Flow mechanism between purge flow and mainstream in different turbine rim seal configurations

The rim seal is used to prevent mainstream ingestion to the gap between the vane of a turbine and its blade. In this article, the dolphin lip with a hook configuration and a large seal cavity with hook structures are designed based on the high-pressure turbine datum single shark lip rim seal configuration. The sealing effect and parameters of the flow field are measured by an experiment method and a numerical simulation is used to explain the mechanism. For three configurations,the effect of the leakage slot vortex on the efficiency of the seal and the influence of leakage vortex,generated by the interaction between purge flow and mainstream flow, are discussed in depth. The result shows that the reverse vortex formed by the dolphin lip rim seal with hook structure will increase the sealing efficiency. The seal configuration with a large cavity improves sealing efficiency to a greater extent than the datum structure. At different purge flow rates and with unequal seal structures, the purge flow produces three types of leakage vortices in the passage. Besides, the seal configuration with dolphin lip produces a Kelvin-Helmholtz instability at the interface of the purge and the mainstream flows at a low purge flow rate to induce new leakage vortex branches in the passage of the blade.

Liutex core line and POD analysis on hairpin vortex formation in natural flow transition

In this study,the new method of the vortex core line based on Liutex definition,also known as Liutex core line,is applied to support the hypothesis that the vortex ring is not a part of theΛ-vortex and the formation of the ring-like vortex is formed separately from theΛ-vortex.The proper orthogonal decomposition(POD)is also applied to analyze the Kelvin-VHelmholtz(K-H)instability happening in hairpin ring areas of the flow transition on the flat plate to understand the mechanism of the ring-like vortex formation.The new vortex identification method named modified Liutex-Omega method is efficiently used to visualize and observe the shapes of vortex structures in 3-D.The streamwise vortex structure characteristics can be found in POD mode one as the mean flow.The other POD modes are in stremwise and spanwise structures and have the fluctuation motions,which are induced by K-H instability.Moreover,the result shows that POD modes are in pairs and share the same characteristics such as amplitudes,mode shapes,and time evolutions.The vortex core and POD results confirm that theΛ-vortex is not self-deformed to a hairpin vortex,but the hairpin vortex is formed by the K-H instability during the development of Lambda vortex to hairpin vortex in the boundary layer flow transition.

Simulating liquid-vapor phase separation under shear with lattice Boltzmann method

We study liquid-vapor phase separation under shear via the Shan-Chen lattice Boltzmann model. Besides the rheological characteristics, we analyze the Kelvin-Helmholtz (K-H) instability resulting from the tangential velocity difference of the fluids on two sides of the interface. We discuss also the growth behavior of droplets. The domains being close to the walls are lamellar-ordered, where the hydrodynamic effects dominate. The patterns in the bulk of the system are nearly isotropic, where the domain growth results mainly from the diffusion mechanism. Both the interfacial tension and the K-H instability make the liquid-bands near the walls tend to rupture. When the shear rate increases, the inequivalence of evaporation in the upstream and coagulation in the downstream of the flow as well as the role of surface tension make the droplets elongate obliquely. Stronger convection makes easier the transferring of material particles so that droplets become larger.