Dynamic Characteristics of Spherically Converging Detonation Waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over Aat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were M-s = 1.30 and M-s = 2.032, dust loading ratios were alpha = 1 and alpha = 5, and particle diameters were d = 1, 10 and 50 mum. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure historics were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension.

一种易于并行求解Euler方程组的分区技术

在具有复杂边界的计算区域内,求解偏微分方程组时,经常需要分区和并行计算,分区方法直接关系到数值计算的并行化程度,本文在应用时间算子分裂方法求解Euler方程组的过程中,提出了一种非常容易实现并行化计算的分区技术.

Phase relaxation model for 2-phase flows

A phase relaxation model (PRM) for 2-phase flows is presented in this paper on the basis of three principal assumptions. The basic equations for PRM arc derived from the Boltzmann equations for gas-partlcle mixture, The general characteristics and solving process of the PRM's basic equations are also presented and discussed. Many terms in the PRM's basic equations contain a factor ε= ρgρp/ρg+ρp2 which is an intrinsic small parameter for 2-phase mixture, with ρg and ρp being respectively the densities of gas and particle phases.This makes it possible to simplify the computation of the PRM's basic equations. The model is applied to for example, studying file steady propagation of shock waves in gas-particle mixture. The analysis shows that with an increase of shock wave strength the relaxation process behind a gasdynamics shock front becomes a kind of dynamics relaxation instead of the standard exponential relaxation process. A method of determining experimentally the velocity and tem...更多perature relaxation rates (or times) of gas-particle flows is suggested and analyzed.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法，本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法，基于有限体积方法和迎风型矢通量分裂方法，建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件，区域内部采用隐式格式和局部时间步长等，以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较，二者基本吻合。计算结果表明采用分析“V”型多重网格方法，能提高计算效率，加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<equations computations for high Reynolds number flows, an idea of solving the conservation equations for discrete cells was proposed and named the discrete fluid dynamics (DFD) algorithm. Analysis shows that the basic conservative equations for discrete cells are the Euler equations, NS- and diffusion parabolized (DP) NS equations. In this paper, a new multiscale-domain decomposition method is developed for the high Reynolds number flow. First, the whole domain is decomposed to different sub-domains with the different characteristic scales. Then the different dominant equation of all sub-domains is defined according to the diffusion parabolized (DP) theory of viscous flow. Finally these different equations are solved simultaneously in whole computational region. For numerical tests of high Reynolds numerical flows, two-dimensional supersonic flows over rearward and frontward steps as well as an interaction flow between shock wave and boundary layer were solved numerically. The pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Transition Between Detonation and Deflagration in a Tube with a Cavity

In this paper, the transition of a detonation from deflagration was investigated numerically while a detonation wave propagates in a tube with a sudden change in cross section, referred to as the expansion cavity. The dispersion-controlled scheme was adopted to solve Euler equations of axis-symmetric flows implemented with detailed chemical reaction kinetics of hydrogen-oxygen (or hydrogen-air) mixture. The fractional step method was applied to treat the stiff problems of chemical reaction flow. It is observed that phenomena of detonation quenching and reigniting appear when the planar detonation front diffracts at the vertex of the expansion cavity entrance. Numerical results show that detonation front in mixture of higher sensitivity keeps its substantial coupled structure when it propagates into the expansion cavity. However, the leading shock wave decouples with the combustion zone if mixture of lower sensitivity was set as the initial gas.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

水下高速喷流噪声的产生机制与辐射特性

在对喷流噪声研究进展广泛调研的基础上，本论文采用柱坐标下轴对称的线化欧拉方程（LEE）、空间四阶时间二阶精度的MacCormack差分格式，对水下气体喷流的混合噪声产生与辐射特性进行数值模拟研究。采用基于经验公式的积分计算方法来确定求解线化欧拉方程所需的平均流场，对边界条件给予特殊处理以避免声波通过时产生反射。本文计算声明，线化欧拉方程及其相应的高阶数值方法提供了一个可以预报水下气体喷流混合噪声传播的省时高效的途径。给出的结果指出：由于水介质的密度很大，水下气体喷流远场收集到的噪声强度比同样情况下空中气体喷流要小，这说明水下发射导弹更具隐蔽性。同时，由于水介质中的声速很大，水下的高速喷流噪声场呈现更加均匀的性态，而不是象空中混合噪声在下游沿一定的方向辐射。鉴于本文只考虑常温情况，气体喷流速度是影响喷流噪声产生与辐射的重要参数：马赫数增大，远场的噪声强度随之增大。另外，水下喷流噪声的特性还与扰动频率有关。

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

Space and phase resolved plasma parameters in an industrial dual-frequency capacitively coupled radio-frequency discharge

The dynamics of high energetic electrons (>= 11.7 eV) in a modified industrial confined dual-frequency capacitively coupled RF discharge (Exelan, Lam Research Inc.), operated at 1.937 MHz and 27.118 MHz, is investigated by means of phase resolved optical emission spectroscopy. Operating in a He-O-2. plasma with small rare gas admixtures the emission is measured, with one-dimensional spatial resolution along the discharge axis. Both the low and high frequency RF cycle are resolved. The diagnostic is based on time dependent measurements of the population densities of specifically chosen excited rare gas states. A time dependent model, based on rate equations, describes the dynamics of the population densities of these levels. Based on this model and the comparison of the excitation of various rare gas states, with different excitation thresholds, time and space resolved electron temperature, propagation velocity and qualitative electron density as well as electron energy distribution functions are determined. This information leads to a better understanding of the dual-frequency sheath dynamics and shows, that separate control of ion energy and electron density is limited.

On how structural model variability influence transonic aeroelasticity stability.

This paper considers the ways in which structural model parameter variability can in?uence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, Interval and Perturbation calculations to allow this question to be investigated. Three routes are identi?ed. The ?rst involves variable normal mode frequencies only. The second involves normal mode frequencies and mode shapes. Finally, the third, in addition to normal mode frequencies and mode shapes, also includes their in?uence on the static equilibrium. Previous work has suggested only considering route 1, which allows signi?cant gains in computational e?ciency if reduced order models can be built for the aerodynamics. However, results in the current paper show that neglecting route 2 can give misleading results for the ?utter onset prediction.

Unsteady Gas Dynamic Engine Simulation

This paper provides an overview of the basic theory underlying 1D unsteady gas dynamics, the computational method developed at Queen’s University Belfast (QUB), the use of CFD as an alternative and some experimental results that demonstrate the techniques used to develop the mathematical models.