Self-oscillatory regimes of the penetration of vertical free turbulent jets through a liquid surface

The results of an experimental investigation of the penetration of vertical plane and round free turbulent jets through the surface of a liquid contained in a relatively narrow channel are presented. It is established that there exist the ranges of jet thicknesses, their velocities, and free region lengths, on which regular self-oscillatory regimes of the displacement of submerged jet regions and two-phase flow regions are observable. The mechanism of the generation of these regimes and the special features of the observable flows are discussed. The dependences of the self-oscillation periods on the main control parameters of the problem are established.     

基于元胞自动机模型的C型交织区交通流特性

根据C型双侧交织区的车辆换道特征建立相应的换道规则,采用多车道元胞自动机模型研究交织区系统的交通流特性. 通过数值模拟得到了不同交织区长度下的相图,表明当主路和匝道交通流均为自由流时,交织区长度对系统影响不大,但当主路或匝道拥挤时,交织区长度的增加可以明显改善入口匝道的交通流状况. 进一步讨论了主路畅通而交织流量较大情形下主路上的车辆密度、速度和换道频率分布,发现换道集中在合流区和分流区附近,并造成相应路段上的局部拥堵.      

Heat transfer effects on particle motion under rarefied conditions

Gas–solid flows occurring on very small spatial scales (of the order of micro and nanometres) are of great relevance in a number of industrial applications. It is currently not well established how particle motion and filtration are affected by non-isothermal conditions at such scales. Furthermore, when the particle size is comparable to the mean free path of the gas, rarefaction effects become important. In the present work we investigate the effects of heat transfer and non-isothermal conditions on the motion of small particles in rarefied flow. For that purpose, a suitable framework is developed here as a generic multiphase DNS method for rarefied flows. The resulting model is valid for low particle Reynolds number flows, irrespective of the Biot number, and for particle Knudsen numbers up to unity in unbounded flow. Using this model, we show that there is different settling behaviour of particles with an internal heat source in rarefied and continuum cases of the carrier gas respectively. It is shown that the chances for thermal levitation and/or lifting up of a particle due to buoyancy effects are significantly reduced under rarefied conditions.     

On the Von Neumann Paradox of Weak Mach Reflection*

Recent experimental and numerical studies of weak Mach reflections are examined. It is shown that the fundamental reason for the von Neumann paradox is that his theory of Mach reflection is based on the assumption that the flow downstream of the reflected wave and the Mach shock near the wave triple point is uniform. The assumption is shown to be valid for strong Mach reflection which agrees with experiment, but invalid for weak Mach reflection which does not agree with experiment. It is also shown that viscous effects are dominant when the incident shock is within about 100 mean free path lengths of the corner, but not otherwise. The analytical theory of the entire subsonic region supports these conclusions.     

A Dissipation Rate Equation for Low-Reynolds-Number and Near-Wall Turbulence

Two-equation turbulence models are usually formulated for specific flow types and are seldom validated against a variety of flows to account for near-wall and low-Reynolds-number effects simultaneously. In addition to low-Reynolds-number effects, near-wall flows also experience wall blocking, which is absent in free flows. Consequently, near-wall modifications to two-equation models could be quite different from low-Reynolds-number corrections. Besides, it is known that existing two-equation models perform poorly when used to calculate plane wall jets and two-dimensional backstep flows. These problems could be traced to the modeling of the dissipation rate equation. In this paper an attempt is made to improve the modeling of the dissipation rate equation so that it could successfully predict both free and wall-bounded shear flows including plane wall jets and backstep flows. The predictions are compared with experimental and direct numerical simulation data whenever available. Most of the data used are obtained at low Reynolds numbers. Good correlation with data is obtained. Therefore, for the first time, a model capable of correctly predicting free and wall-bounded shear flows, backstep flows, and plane wall jets is available. Received: 12 December 1995 and accepted 12 November 1996     

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Frequency analysis of turbulent compressible flows by laser vibrometry

The objective of this work was the application of laser vibrometry as a tool for non-intrusive measurement of frequency spectra in turbulent flows. A laser vibrometer system together with a signal analyser was used to obtain frequency spectra of density fluctuations across a turbulent free jet. Since laser vibrometry is based on interferometric techniques, the derived signals are path integrals along the measurement beam. Frequency spectra recorded in the rotational symmetric flow were then treated using Abel inversion in order to derive information on local density fluctuations. Results for two different flow conditions were compared to spectral data from a constant temperature anemometer and a pitot-mounted pressure sensor. Received: 21 February 2000/Accepted: 13 December 2000     

A unified gas-kinetic scheme for multiscale and multicomponent flow transport

Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.     

Studying disturbance waves in vertical annular flow with high-speed video

In many annular two-phase gas–liquid flows, large disturbance waves propagate liquid mass. These waves are important for modeling of gas-to-liquid momentum transfer and liquid film behavior. High-speed videos of vertical upflow have been analyzed to extract individual and average wave data. Two types of structures, coherent waves and piece waves, have been identified in these flows. Velocities, lengths, and temporal spacings of individual waves and average velocities, lengths, frequencies, and intermittencies have been studied as functions of both gas and liquid flow rates. Velocity and frequency increase with liquid and gas flow rates, length decreases with increasing gas flow and increases with increasing liquid flow, and intermittency is predominantly an increasing function of liquid flow.     

Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers

Collisions of high Mach number flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large. Therefore, most shock waves in astrophysics are “collisionless”, since they form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at the laser facilities can achieve the conditions necessary for the formation of collisionless shocks, and will provide a unique avenue for studying the nonlinear physics of collisionless shock waves. We are performing a series of experiments at the Omega and Omega-EP lasers, in Rochester, NY, with the goal of generating collisionless shock conditions by the collision of two high-speed plasma flows resulting from laser ablation of solid targets using ∼10¹⁶ W/cm² laser irradiation. The experiments will aim to answer several questions of relevance to collisionless shock physics: the importance of the electromagnetic filamentation (Weibel) instabilities in shock formation, the self-generation of magnetic fields in shocks, the influence of external magnetic fields on shock formation, and the signatures of particle acceleration in shocks. Our first experiments using Thomson scattering diagnostics studied the plasma state from a single foil and from double foils whose flows collide “head-on”. Our data showed that the flow velocity and electron density were 10⁸ cm/s and 10¹⁹ cm⁻³, respectively, where the Coulomb mean free path is much larger than the size of the interaction region. Simulations of our experimental conditions show that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur. This paper presents the results from these first Omega experiments.     

A semi‐implicit numerical method for the free‐surface Navier–Stokes equations

Semi‐implicit methods are known for being the basis of simple, efficient, accurate, and stable numerical algorithms for simulating a large variety of geophysical free‐surface flows. Geophysical flows are typically characterized by having a small vertical scale as compared with their horizontal extents. Hence, the hydrostatic approximation often applies, and the free surface can be conveniently represented by a single‐valued function of the horizontal coordinates. In the present investigation, semi‐implicit methods are extended to complex free‐surface flows that are governed by the full incompressible Navier–Stokes equations and are delimited by solid boundaries and arbitrarily shaped free‐surfaces. The primary dependent variables are the velocity components and the pressure. Finite difference equations for momentum, and a finite volume discretization for continuity, are derived in such a fashion that, after simple manipulation, the resulting pressure equation yields a well‐posed piecewise linear system from which both the pressure and the fluid volume within each computational cell are naturally derived. This system is efficiently solved by a nested Newton type iterative scheme, and the resulting fluid volumes are assured to be nonnegative and bounded from above by the available cell volumes. The time step size is not restricted by stability conditions dictated by surface wave speed, but can be freely chosen just to achieve the desired accuracy. Several examples illustrate the model applicability to a large range of complex free‐surface flows and demonstrate the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

An efficient quasi-Newton method for two-dimensional steady free surface flow

Steady free surface flows are of interest in the fields of marine and hydraulic engineering. Fitting methods are generally used to represent the free surface position with a deforming grid. Existing fitting methods tend to use time-stepping schemes, which is inefficient for steady flows. There also exists a steady iterative method, but that one needs to be implemented with a dedicated solver. Therefore a new method is proposed to efficiently simulate two-dimensional (2D) steady free surface flows, suitable for use in conjunction with black-box flow solvers. The free surface position is calculated with a quasi-Newton method, where the approximate Jacobian is constructed in a novel way by combining data from past iterations with an analytical model based on a perturbation analysis of a potential flow. The method is tested on two 2D cases: the flow over a bottom topography and the flow over a hydrofoil. For all simulations the new method converges exponentially and in few iterations. Furthermore, convergence is independent of the free surface mesh size for all tests.     

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Acoustic waves propagating through a rarefied gas between two plates induced by both oscillation and unsteady heating of one of them are considered on the basis of a model of the linearized Boltzmann equation. The gas flow is considered as fully established so that the dependence of all quantities on time is harmonical. The problem is solved for several values of two main parameters determining its solution, namely, the gas rarefaction defined as the ratio of the distance between the plates to the equivalent free path of gaseous molecules, and the oscillation parameter given as the ratio of the intermolecular collision frequency to the wave frequency. The reciprocal relation for such flows is obtained and verified numerically. An influence of the gas–surface accommodation coefficients on the wave characteristics is analyzed by employing the Cercignani–Lampis scattering kernel to the boundary conditions.     

简单剪切流动中转捩的低维模式与数值模拟

回顾了过去10年在壁湍流和自 由剪切流转捩问题的数值研究中取得的重要进展, 介绍了数值方法和模式研究方面 的进展, 以及由此带来的关于转捩理论认识上的进展. 对于壁面流动, 文中主要介 绍了渐进稳定流动中``跨越(bypass)转捩'研究中的各种观点. 本文也简要介绍了 对感受性和转捩控制方面的研究.     

A marker-and-cell approach to viscoelastic free surface flows using the PTT model

This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien–Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.     

A novel multiphase DNS approach for handling solid particles in a rarefied gas

A comprehensive model is proposed for multiphase DNS simulations of gas–solid systems involving particles of size comparable to the mean free path of the gas and to that of the bounding geometry. The model can be implemented into any multiphase Direct Numerical Simulation (DNS) method. In the current work, the Volume of Fluid (VOF) method is used, and it is extended to allow for the incorporation of rarefaction effects. For unbounded flow, the model is in excellent agreement with experimental data from the literature. For flows in closed conduits, the model outperforms the alternate approach of using a slip boundary condition at the particle surface for the most relevant degrees of rarefaction and confinement. The proposed model is also able to correctly handle particle–particle interception. The model is intended for low particle Reynolds number flows, and can be applied to resolve in great detail phenomena in a large number of industrial applications (such as filtration of fine particles in porous media).     

Density-stratified Sadovskii flow in a channel

Stably density-stratified and nonstratified flows in a channel past a pair of symmetrical closed-streamline vortices on the channel axis are considered. The numerical results obtained cover the whole range of subcritical stratification and eddy lengths. An asymptotic solution for a very long closed-streamline region is found. The results can be used directly in the asymptotic theory of separated flows at high Reynolds number. Sadovskii flows are plane potential inviscid flows past a pair of closed-streamline regions of uniform vorticity. The flow velocity may be discontinuous at the boundary of the closed-streamline region. The analysis below is restricted to the specific case of continuous velocity distribution, so that the Bernoulli constant jump at the eddy boundary is zero. Unbounded nonstratified flows of this kind were studied in [1, 2]. Calculations of the corresponding channel flow were restricted to relatively wide channels. Closely related problems were also considered in [3, 4].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 118–123, May–June, 1993.     

自由漂浮空间机器人路径优化的Legendre伪谱法

基于Legendre 伪谱法研究自由漂浮空间机器人非完整路径规划的最优控制问题. 自由漂浮是空间机器人执行任务常用的工作模式,其路径优化是空间机器人完成复杂空间任务的基础. 由于空间机器人不具有固定基座,机械臂和载体之间存在非完整约束,使得自由漂浮空间机器人路径规划完全不同于地面机器人而变得具有挑战性. 本文提出自由漂浮空间机器人路径规划的最优控制伪谱方法. 首先,利用多体动力学理论建立自由漂浮空间机器人动力学模型,给定系统的初始和目标位形,选取机械臂关节耗散能最小为性能指标,并考虑实际控制输入受限,建立其路径规划的Bolza 问题. 然后,应用Legendre 伪谱法,将状态和控制变量在Legendre-Gauss-Lobatto (LGL) 点上离散,并构造Lagrange 插值多项式逼近系统状态和控制变量,将连续路径优化问题离散化为非线性规划问题求解. 最后通过数值仿真表明,应用Legendre 伪谱法求解自由漂浮空间机器人非完整路径规划问题,得到的机械臂和载体最优运动轨迹,较好地满足各种约束条件,且计算精度高、速度快,并具有良好的实时性.      

Nonlinear Knudsen boundary layer on an infinitely thin permeable membrane

The state of a gas in the neighborhood of an infinitely thin permeable membrane whose sides have different temperatures is investigated. The dimensions of orifices in the membrane are much less than the mean molecular free path. The gas temperatures and pressures on both sides of the membrane outside the nonlinear Knudsen layers adjacent to the membrane and variations in these parameters in the Knudsen layers are determined. The investigation is carried out by solving the Boltzmann kinetic equation by means of the direct simulation Monte-Carlo method. The semiempirical Maxwell method is also used for consideration of the molecular flows on both sides of the membrane when analyzing the temperatures and the pressures. The solution to the nonlinear problem is compared with the solution to the linear problem of a jump temperature near a nonisothermal porous body obtained earlier.