亚声速段横向射流对C0il性能影响的数值研究

在化学氧碘激光的混合喷管内发生的是一个气体动力学、化学反应动力学以及光学等相互耦合的复杂过程,每个过程都对COIL性能有着至关重要的影响.利用三维CFD技术,通过求解层流Navier-Stokes方程与组分输运方程,对简化后的化学氧碘激光RADICL模型进行数值模拟与分析,对COIL的气动和增益特性进行探讨.在不同的射流穿透条件下,计算COIL混合喷管中的混合与化学反应过程,发现穿透深度决定了增益的分布特性以及过度穿透条件下的非定常结构.     

COIL基于小信号增益系数的最佳流量配比选择

 氧碘化学激光器(COIL)的混合喷管内发生的是气体动力学、化学反应动力学以及光学等相互耦合的复杂过程,每个过程都对COIL性能有着至关重要的影响。利用3维CFD技术,通过求解层流Navier-Stokes方程与组分输运方程,结合10种组分和21个基元反应的化学反应模型,对简化后的化学氧碘激光RADICL模型在亚声速段横向射流情况下,不同的主副流流量配比对小信号增益系数的影响情况进行了比较与分析。结果证明:过高或过低的碘分子浓度均不利于产生合理的小信号增益系数;存在最佳流量配比使小信号增益系数得到显著提高且分布均匀。     

流量配比对Coil增益分布影响的数值研究

利用三维CFD技术,通过求解层流Navier-Stokes方程与组分输运方程,对简化后的化学氧碘激光RADICL模型进行数值模拟与分析,结合10种组分和21个基元反应的化学反应模型,对COIL亚声速段横向射流情况下,不同的主副流流量配比对化学氧碘激光器性能的影响进行分析与比较.结果证明,过高或过低的碘分子浓度状态均不利于合理、可观的小信号增益系数产生.存在一个最佳流量配比范围,与之对应的工作状态下,COIL的小信号增益系数会得到显著提高.     

VICON程序模拟氧碘化学激光器3维喷管流场的可行性探讨

 用VICON程序对化学氧碘激光器(COIL)喷管冷流场进行了3维模拟，得出的计算区几何较准确地反映了模拟装置的几何变化。主气流方向和副气流方向的分点数反映出了此2维平面内的气动特性，对不同流量的模拟结果对比分析得出穿透过度与穿透不够一样，致使主副气流混合不好。对带化学反应的情况进行了模拟，显现出副气流从喷孔出来后穿进主气流的马蹄形结构的变化过程，这些说明VICON程序可用来模拟研究COIL喷管流场特性。     

化学反应与饱和模型对化学氧碘激光性能的影响

 将速率方程（RE）模型与化学动力学模型相结合，讨论了增益饱和模型与化学反应系统对COIL性能的影响。流动为预混的一维模型，考虑了10种成分和21个化学反应，分析计算了未分解碘分子，激发态氧产率，水含量以及温度等因素对COIL性能的影响。计算结果表明，碘流量过多，混合和反应过程中消耗大量能量；碘流量过低，导致粒子数反转和增益过低，对于能量的提取不利。     

流量大小对混合流场特性等的影响

在主、副气流各组份的流量比不变的情况下,改变输入氧碘化学激光器(COIL)光腔总气流流量,数值模拟给出了COIL拉伐尔喷管主、副气流混合状况和各物理量的分布等,通过对这些结果进行对比分析得出输入COIL光腔总气流流量增加三倍,氧碘气流的混合状况稍稍变差,但Mach数和密度等的分布和变化规律基本不变.     

基于混合发展的超声速段射流式COIL的数值优化

应用CFD技术,发展三维多组分化学反应流计算程序,对采用超声速段射流方式的氧碘化学激光进行数值模拟,考察分解率与增益等参考变量的详细三维分布.计算结果说明,超声速区域的高速流动以及混合效率降低使COIL无法在有限空间内完成整个运转流程;提高碘含量以加快反应速度的手段导致主流无法提供足够的载能介质,无法形成合理增益.在不改变喷管长度的前提下,提出主流无载气方式的探索,结果证明了超声速段射流方式采用无载气主流配置的可行性与优势,通过减小气流速度保证混合与化学反应在光腔上游完成,在合理的流量配比下光腔位置处可得到1.3%cm^-1的增益峰值.     

副气流中He流量变化对流场混合状态的影响*

在保持主气流流量和副气流中I2的流量不变的条件下,改变副气流中He的流量,数值模拟氧碘化学激光器拉伐尔喷管内的流场混合特性.结果表明,随着副气流中He的流量的增加,副气流垂直穿透主气流的深度逐渐变大,主、副气流混合状态也逐渐变好,直至氧碘气流混合均匀.     

高马赫数高压力的氧碘化学激光器阵列喷管的数值模拟

 采用计算流体力学方法,研究了以氮气为载气的新型高总压氧碘化学激光器(COIL)阵列喷管。模拟结果表明:采用高马赫数的氮气流引射低马赫数的氧气流,可以提高光腔出口的驻点压力;高超声速的氮气与声速的氧气混合较慢,在喷管出口安装翼片有利于增强气流混合;喷管出口安装大翼片,翼片诱导的横向涡可以到达氮喷管的中心,光腔内混合比较充分。通过采用10组分21反应的化学反应模型,模拟了阵列喷管内多组分气体的混合和化学反应过程。模拟结果表明：光腔内生成了激发态碘原子和基态碘原子,光腔中获得了正增益,而且光腔出口的总压也由2.6 kPa提升至28.9 kPa。     

以氮气为载气的千瓦极COIL的初步实验研究

首次在氯气流量为110mmol/s、采用方列管型射流式O^2(^1△）发生器（SPJSOG）以及列阵式超音速氧碘混合喷管的COIL装置上，以氮气替代拟气作为载气进行出光实验研究。初步实验获得1.8kW的激光输出功率以及18％的化学效率。     

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.     

Implementation of a constrained Ritz series modeling technique for acoustic cavity-structural systems

A prior study [Ginsberg, J. H. (2010b). J. Acoust. Soc. Am. 127, 2749-2758] used Ritz series in conjunction with Hamilton's principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure. The equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity's surface. These constraints are imposed by the surface traction, which is represented by unknown coefficients of Ritz-type series. The resulting set of equations are differential-algebraic type. Three methods are presented to convert the governing equations to forms that are familiar to structural acoustics, including one that transforms them from differential-algebraic type to the standard ordinary differential equations associated with linear multi-degree-of-freedom vibratory systems. In cases where only the structure is excited, the formulation offers options as to how displacement/velocity boundary conditions on the nonstructural boundary are enforced, as well as whether zero pressure boundary conditions are enforced at all. An example of a one-dimensional waveguide that is closed at one end by an oscillator is used to explore the quality of solutions obtained from each of these options. Results for natural frequencies and mode functions are examined for accuracy and convergence.     

From the Becker–Döring to the Lifshitz–Slyozov–Wagner Equations

Connections between two classical models of phase transitions, the Becker–Döring (BD) equations and the Lifshitz–Slyozov–Wagner (LSW) equations, are investigated. Homogeneous coefficients are considered and a scaling of the BD equations is introduced in the spirit of the previous works by Penrose and Collet, Goudon, Poupaud and Vasseur. Convergence of the solutions to these rescaled BD equations towards a solution to the LSW equations is shown. For general coefficients an approach in the spirit of numerical analysis allows to approximate the LSW equations by a sequence of BD equations. A new uniqueness result for the BD equations is also provided.     

微分方程的部分Hamilton化与积分

将微分方程部分地表示为Hamilton系统的方程并写成逆变代数形式.用动力学代数建立方程的Poisson积分理论，并举例说明结果的应用. 关键词： 微分方程 部分Hamilton化 逆变代数形式 Poisson积分理论     

Three-dimensional modelling and dynamic analysis of an automatic ball balancer in an optical disk drive

Dynamic behaviours and stability of an automatic ball balancer (ABB) in an optical disk drive are analyzed based on the proposed three-dimensional dynamic model. For dynamic analysis, the feeding deck with the ball balancer and a spindle motor is modelled as a rigid body with six degrees of freedom. The nonlinear equations of motion are derived using Lagrange's equation in order to describe the translational and rotational motions of the system. From the derived nonlinear equations, the linearized equations of motion in the neighbourhood of a balanced equilibrium position are obtained by the perturbation method. These equations are coupled, linear, differential equations with time-dependent periodic coefficients, from which the stability of the system is analyzed by using the Floquet theory. Finally, the time responses are computed to verify the results of the stability analysis, and to investigate the balancing performance of the ABB.     

Variable-stepsize Runge–Kutta methods for stochastic Schrödinger equations

Stochastic wave equations of Schrödinger type are widely employed in physics and have numerous potential applications in chemistry. While some accurate numerical methods exist for particular classes of stochastic differential equations they cannot generally be used for Schrödinger equations. Efficient and accurate methods for their numerical solution therefore need to be developed. Here we show that existing Runge–Kutta methods for ordinary differential equations (odes) can be modified to solve stochastic wave equations provided that appropriate changes are made to the way stepsizes are selected. The order of the resulting stochastic differential equation (sde) scheme is half the order of the ode scheme. Specifically, we show that an explicit 9th order Runge–Kutta method (with an embedded 8th order method) for odes yields an order 4.5 method for sdes which can be implemented with variable stepsizes. This method is tested by solving systems of equations originating from master equations and from the many-body Schrödinger equation.     

Solutions of Two Kinds of Non-Isospectral Generalized Nonlinear Schrodinger Equation Related to Bose-Einstein Condensates

Two non-isospectral generalized nonlinear Schrodinger （ONLS） equations, which are two important models of nonlinear excitations of matter waves in Bose-Einstein condensates, are studied. Two novel transformations are constructed such that these two GNLS equations are transformed to the well-known nonlinear Schr6dinger （NLS） equation, which is an isospectral equation. Therefore, once one solution of the NLS equation is provided, we can immediately obtain one solution for two ONLS equations by these transformations. Thus it is unnecessary to solve these two non-isospectral GNLS equations directly. Soliton solutions and periodic solutions are obtained for them by two transformations from the corresponding solutions of the NLS equation, which are generated by Darboux transformation.     

剪切流动条件下液滴变形和断裂的数值模拟

本文采用扩散界面法研究了剪切流动条件下悬浮液滴变形和断裂的动力学机制。控制方程采用考虑表面张力影响的Navier-Stokes-Cahn-Hilliard方程描述。计算网格采用均匀矩形交错网格。采用基于压力增量的近似投影法计算 Navier-Stokes方程,采用完全近似多重网格法计算Cahn-Hilliard方程。稳态液滴变形规律及液滴拉伸断裂过程的计算结果与试验结果符合较好,表明本文模型能够很好的研究液滴变形及断裂机理。     

Dynamical aspects in the optical bloch equations

In quantum optics, some models are considered to describe many aspects of the dynamics of atoms coupled to an electromagnetic field (laser). The simplest atomic model is of course the two-level-atom which is governed by the Bloch optical equations. In general this system is solved in the steady state or by using some approximations. An extended analytic approach is considered for this coupled equations. The separation approach of coupled differential equations is always possible with a sequence of special transformation into nonlinear differential equations. The conditions that permit an exact solution of three coupled systems are extracted in a natural manner. The case of sodium atom moving along the axis of a standing-wave is investigated in some details.     

Poloidal–toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.