Numerical Simulation of Anisotropic Preheating Ablative Rayleigh-Taylor Instability

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability （ARTI） is studied by numerical simulations. The preheating model κ （T）=κSH [1＋f（T）] is applied, where f（T） is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 （2007） 245001].     

Direct Numerical Simulation of the Rayleigh-Taylor Instability with the Spectral Element Method

A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows.     

Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

Role of Viscosity Stratification and Insoluble Surfactant in Instability of Two-Layer Channel Flow

We study, for the case of the two layer plane Poiseuille flow, the effect of viscosity stratification and interracial surfactant on the flow instability. Considering a normal mode of the streamwise wave number α, both the linear and energy analyses are presented. The expressions of perturbation energy supplied at the interface are derived. The result demonstrates that the jumps of horizontal velocity and tangential stress of the perturbed flow across the interface could be induced by the presence of viscosity stratification and surfactant. This is expected to be responsible for the Yih and Marangoni instability.     

Compressible Rayleigh-Taylor Instability with Preheat in Inertial Confinement Fusion

The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.     

Formation of the preheated zone ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation transition

The Letter presents analytical, numerical and experimental studies of the mechanism underlying the deflagration-to-detonation transition (DDT). Insight into how, when, and where DDT occurs is obtained by analyzing analytically and by means of multidimensional numerical simulations dynamics of a flame accelerating in a tube with no-slip walls. It is shown that the deflagration-to-detonation transition exhibits three separate stages of evolution corroborating majority experimental observations. During the first stage flame accelerates and generates shocks far ahead of the flame front. During the second stage the flame slows down, shocks are formed in the immediate proximity of the flame front and the preheated zone ahead of the flame front is created. The third stage is self-restructuring of the steep temperature profile within the flame, formation of a reactivity gradient and the actual formation of the detonation wave itself. The mechanism for the detonation wave formation, given an appropriate formation of the preheated zone, seems to be universal and involves a reactivity gradient formed from the initially steep flame temperature profile in the presence of the preheated zone. The developed theory and numerical simulations are found to be well consistent with extensive experiments of the DDT in hydrogen-oxygen and ethylene-oxygen mixtures in tubes with smooth and rough walls.     

Essence of Inviscid Shear Instability: a Point View of Vortex Dynamics

The essence of shear instability is reviewed both mathematically and physically, which extends the instability theory of a sheet vortex from the viewpoint of vortex dynamics. For this, the Kelvin-Arnol＇d theorem is retrieved in linear context, i.e., the stable flow minimizes the kinetic energy associated with vorticity. Then the mechanism of shear instability is explored by combining the mechanisms of both Kelvin Helmholtz instability （K-H instability） and resonance of waves. The waves, which have the same phase speed with the concentrated vortex, have interactions with the vortex to trigger the instability. The physical explanation of shear instability is also sketched by extending Batchelor＇s theory. These results should lead to a more comprehensive understanding on shear instabilities.     

Influence of Rayleigh-Taylor Instability on Liquid Propellant Reorientation in a Low-Gravity Environment

A computational simulation is conducted to investigate the influence of Rayleigh-Taylor instability on liquid propellant reorientation flow dynamics for the tank of CZ-3A launch vehicle series fuel tanks in a low-gravity environment. The volume-of-fluid （VOF） method is used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially flat and curved interfaces are numerically studied. These two different initial conditions of the gas-liquid interface result in two modes of liquid flow. It is found that the Rayleigh Taylor instability can be reduced evidently at the initial gas-liquid interface with a high curve during the process of liquid reorientation in a low-gravity environment.     

Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

Universality in crossover function for convection in fluids with a free surface

We show that in the onset of convection in a thin fluid layer with a free surface, the passage from surface tension driven to buoyancy driven convection with changing thickness of the fluid layer follows a universal curve and can be calculated very accurately using a variational method. We have shown that the balance between surface tension traction to buoyancy force determines the crossover length scale of the fluid which is independent of viscosity or thermal diffusivity. We suggest a scenario near critical point of fluids in which this crossover can be observed.     

A note on Burgers' equation with time delay: Instability via finite-time blow-up

Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time.     

Three-Dimensional Waves in Tilt Thermal Boundary Layers

We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed： the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30° and 64°, it is expected to play an important role in the transition to turbulence.     

Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background. It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation （LBE）, especially for shock calculation. Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.     

A weighted network evolution with traffic flow

In this paper, we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure. In the model, the nodes in the network are represented by the traffic flow states, the links in the network are represented by the transform of the traffic flow states, and the traffic flow transported when performing the transform of the traffic flow states is considered as the weight of the link. Several topological features of this generalized weighted model, such as the degree distribution and strength distribution, have been numerically studied. A scaling behavior between the strength and degree s∼klogk is obtained. By introducing some constraints to the generalized weighted model, we study its subnetworks and find that the scaling behavior between the strength and degree is conserved, though the topology properties are quite sensitive to the constraints.     

A Novel Oblique Detonation Structure and Its Stability

Oblique detonation structures induced by the wedge in the supersonic combustible gas mixtures are simulated numerically. The results show that the stationary oblique detonation structures are influenced by the gas flow Math number, and a novel critical oblique detonation structure, which is characterized by a more complicated wave system, appears in the low Mach number cases. By introducing the inflow disturbance, its nonstationary evolution process is illustrated and its stability is verified.     

Thermo-Hydrodynamic Lattice BGK Schemes with Lie Symmetry Preservation

A new class of lattice Bhatnagar-Gross-Krook （BGK） models is proposed, based on the Lie symmetry preservation ansatz for the local equilibria. This class extends the range of stability of previous models, especially for thermohydrodynamic lattice BGK schemes.     

Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows

In this Letter, a three-dimensional (3D) lattice-Boltzmann model is presented following the non-free-parameter lattice-Boltzmann method of Qu et al. [K. Qu, C. Shu, Y.T. Chew, Phys. Rev. E 75 (2007) 036706]. A simple function, which satisfies the zeroth- through third-order moments of the Maxwellian distribution function, is introduced to replace the Maxwellian distribution function as the continuous equilibrium distribution function in 3D space. The function is then discretized to discrete-velocity directions via a 25-point Lagrangian interpolation polynomial. To simulate compressible flows with shock waves, an implicit-explicit finite-difference scheme based on the total variation diminishing flux limitation is adopted to solve the discrete Boltzmann-BGK equation in order to capture the shock waves in compressible flows with a finite number of grid points. The model is validated by its application to some typical inviscid compressible flows ranging from 1D to 3D, and the numerical results are found to be in excellent agreement with the analytical solutions and/or other numerical results.     

Order parameter equation and model equation for high Prandtl number. Rayleigh-Bénard convection in a rotating large aspect ratio system

We derive the order parameter equation which describes the evolution of spatio-temporal patterns close to the Bénard instability in a rotating large aspect ratio system for high Prandtl number fluids. Since this order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order parameter equation by suitable simplification of the nonlinearity. For this model equation we calculate the family of roll solutions and investigate their stability with respect to long scale instabilities and examine the onset of the Küppers-Lortz instability. Then we present spatiotemporal patterns which are obtained from a numerical evaluation of the model equation.