机翼跨声速非常绕流IA型反命题变域变分有限元解

以文[1]提出的二维振荡机翼含激波跨声速非定常绕流IA型反命题变分原理为基础，构建求解IA型反命题的有限元解法。构造了三维时空可变节点有限元来捕获自由尾涡面和翼面几何形状，跨声速流中的激波用人工密度法捕获。在远场边界上采用简化的无反射边界条件，新型非定常Kutta条件被用于处理尾缘条件。用该方法，根据翼型跨声速非定常绕流翼面压力分布求解IA型反命题，得到了NACA64A010翼型的几何形态，计算结果令人满意。     

使用非正交曲线坐标与非正交速度分量的跨声速S_2流面势函数方程人工可压缩性迭代解

本文推导建立了适于求解跨声速轴流式压气机转子中S_2流面正问题的全守恒型势函数方程,方程的求解采用人工密度的方法和一种新的Φ-ρ(Γ)迭代方法,能在S_2流面上自动捕获激波.用本方法编制的计算机程序对西德DFVLR单级跨声速轴流式压气机转子的一个最高效率点实验工况进行了验算,并将计算结果与实验结果作了比较。     

导弹超声速尾退分离干扰特性试验

超/高超声速尾退分离在防热、保形、隐身、多次投放、回收等方面具有明显优势,有望成为高超声速飞行器载荷投放的优选方案。由此面临一类新的多体分离问题：超/高超声速尾退分离问题(aft super/hypersonic ejection separation, ASES)。超/高超声速尾退分离问题本质上是带空腔底部流动与多体分离构成的耦合问题,具有流场结构复杂、气动非定常非线性非对称效应显著的特点。针对超声速尾退分离问题,采用网格测力和轨迹捕获(captive trajectory system, CTS)风洞试验方法探索了尾退分离干扰流场的结构,发现可根据流场结构和舵效变化分为低速-亚声速无激波、高亚声速-跨声速弱激波、超声速激波和准自由流弱干扰4种典型干扰特征,揭示了尾流场影响后不同区域的全弹气动特性和舵效特性以及控制律、攻角、高度和Mach数对分离位移和姿态的影响规律。相关结论将有助于增强对尾退分离问题的认识,对尾退分离技术的工程实践具有参考价值。     

高精度非定常激波装配法

为正确模拟高超声速绕流中,来流小扰动与弓形激波之间的干扰对流动特征的影响,将弓形激波作为动边界,利用非定常特征关系处理激波处的边界条件.应用五阶精度迎风紧致格式和六阶精度的对称格式与三阶精度的R-K方法相结合,建立高精度非定常激波装配方法.采用该方法数值模拟钝锥高超声速定常流场和二维抛物外形高超声速边界层流动的感受性问题,数值模拟来流小扰动与弓形激波干扰激波后非定常扰动流场,研究扰动波进入边界层产生边界层不稳定波的特征.     

跨声速叶栅流的激波捕获-分区计算法

本文基于文献[1]提出的建议,即先用流函数方程或势函数方程计算压气机叶栅的跨声速流场,得到大致的通道激波位置后,再对激波的上、下游区分别进行计算;最后通过对激波位置的调整以满足Rankine-Hugoniot条件,得出确切和明晰的激波形状及气流参量通过激波的突跃变化.文中对具有实验数据的一个双圆弧叶栅分别用势函数方法和流函数方法捕获通道激波并将二者所得激波的平均位置作为分区计算时进行通道激波调整的初始波形.在计算结果同实验值的比较中,还考虑了平面跨声速叶栅实验时实际存在的轴向速度密度比和沿流线熵增对计算结果的影响,所得计算结果是接近实验值的。     

含激波跨声速S_2流面反问题的椭圆型方程间断解

在充分的理论依据之上,通过找到叶轮机械S_2流面反问题运动方程的适当守恒形式,把激波关系嵌入主方程,提出了求子午面速度为亚声速的含激波跨声速S_2反问题的椭圆型方程间断解的数值方法.由于方程是统一的椭圆型的,算法简单可靠.编制了计算机程序并试算了例题.本方法可用于与S_1“激波拟合——分区计算”的跨声速三元流动迭代求解方法中.     

跨音叶栅多种命题的流函数解法

在求解跨音叶栅反命题及形形色色混合型命题时,将该命题所规定的边界条件均设法转换成用流函数ψ来表示的边界条件,从而得出物理概念十分清晰的形式比较统一的迭代求解途径.对跨音反命题的一些计算指出,本文方法是可行的,且有算例表明,此方法也可用来作为设计无激波超临界叶栅的一种手段。     

跨流域高超声速绕流环境Boltzmann模型方程统一算法研究

如何准确可靠地模拟从外层空间高稀薄流到近地面连续流的航天器高超声速绕流环境与复杂流动变化机理是流体物理的前沿基础科学问题. 基于对Boltzmann方程碰撞积分的物理分析与可计算建模, 确立了可描述自由分子流到连续流区各流域不同马赫数复杂流动输运现象统一的Boltzmann模型速度分布函数方程, 发展了适于高、低不同马赫数绕流问题的离散速度坐标法和直接求解分子速度分布函数演化更新的气体动理论数值格式, 建立了模拟复杂飞行器跨流域高超声速飞行热环境绕流问题的气体动理论统一算法. 对稀薄流到连续流不同Knudsen数0.002 ≤Kn_∞ ≤1.618、不同马赫数下可重复使用卫星体再入过程(110–70 km)中高超声速绕流问题进行算法验证分析, 计算结果与典型文献的Monte Carlo直接模拟值及相关理论分析符合得较好. 研究揭示了飞行器跨流域不同高度高超声速复杂流动机理、绕流现象与气动力/热变化规律, 提出了一个通过数值求解介观Boltzmann模型方程, 可靠模拟高稀薄自由分子流到连续流跨流域高超声速气动力/热绕流特性统一算法.     

跨音速流场的变域变分间断有限元解法及激波位置的自动捕获

一、前言 近年来,刘高联教授提出了利用变域变分法求解含激波的跨声速流场及相应的变分原理。作者根据文献[1]提出的变分原理,在文献[2]的基础上,提出了可移动结点间断有限元模式,以楔形流场为例进行流场的求解。通过计算不仅求出了激波的精确位置,而且激波厚度为零,其解与解析解吻合得较好。     

不同来流马赫数下激光能量形成高超声速进气道虚拟唇口的特性

用基于三维非定常可压缩雷诺平均Navier-Stokes方程的有限体积法计算了马赫数低于设计值6时一种高超声速进气道的性能参数,发现其性能存在明显下降。为提升进气道性能,将功率为15kW的激光能量注入进气道固体唇口前的流场中,形成虚拟唇口,马赫数为4.5,5.0和5.5时,计算得到来流捕获率分别提高了34%,20.6%和15.6%。绘制了不同马赫数下来流捕获率达到峰值时的流场压强云图,说明了虚拟唇口的特性及形成机制。结果表明:来流马赫数越低,来流捕获率越小,但相对于无能量注入时的来流捕获率的提升程度越明显;在不同来流马赫数条件下,通过改变激光能量引致的激波结构和位置,可达到最优状态,即激波与进气道前缘斜激波相交后的透射波打在进气道肩部位置的状态。     

二维浅水波问题Galerkin解法的质量集中法

本文讨论了二维非定常流Galerkin解法的质量集中法,并用Galerkin法和质量集中法对长江口北支水域进行了模拟实算,并对两种方法的计算结果作了分析和比较。     

抛物方程基于自然边界归化的耦合法

将冯康和余德浩提出的自然边界归化方法^[1~4]应用于求解抛物方程初边值外区域问题,提出一种自然边界元与有限元耦合算法。先将控制方程对时间进行离散化,得到关于时间步长的离散化格式,给出圆外域上的自然积分方程,基于此研究抛物方程无界区域问题的自然边界元与有限元耦合法,最后给出相应的数值例子。     

Modification of Multiple Knot $B$-Spline Wavelet for Solving (Partially) Dirichlet Boundary Value Problem

A construction of multiple knot B-spline wavelets has been given in [C. K. Chui and E. Quak, Wavelet on a bounded interval, In: D. Braess and L. L. Schumaker, editors. Numerical methods of approximation theory. Basel: Birkhauser Verlag; (1992), pp. 57-76]. In this work, we first modify these wavelets to solve the elliptic (partially) Dirichlet boundary value problems by Galerkin and Petrov Galerkin methods. We generalize this construction to two dimensional case by Tensor product space. In addition, the solution of the system discretized by Galerkin method with modified multiple knot B-spline wavelets is discussed. We also consider a nonlinear partial differential equation for unsteady flows in an open channel called Saint-Venant. Since the solving of this problem by some methods such as finite difference and finite element produce unsuitable approximations specially in the ends of channel, it is solved by multiple knot B-spline wavelet method that yields a very well approximation. Finally, some numerical examples are given to support our theoretical results.     

Simulation of Viscous Flows Around a Moving Airfoil by Field Velocity Method with Viscous Flux Correction

Based on the field velocity method, a novel approach for simulating unsteady pitching and plunging motion of an airfoil is presented in this paper. Responses to pitching and plunging motions of the airfoil are simulated under different conditions. The obtained results are compared with those of moving grid method and good agreement is achieved. In the conventional field velocity method, the Euler solver is usually used to simulate the movement of the airfoil. However, when viscous effect is considered, unsteady Navier-Stokes equations have to be solved and the viscous flux correction must be taken into account. In this work, the viscous flux correction is introduced into the conventional field velocity method when non-uniform grid speed distribution is occurred. Numerical experiments for the flow around NACA0012 airfoil showed that the proposed approach can well simulate viscous moving boundary flow problems.     

一类各项异性半线性椭圆方程自然边界元与有限元耦合法

将冯康和余德浩提出的自然边界归化方法用于研究一类半线性椭圆方程外区域问题，提出一种自然边界元与有限元的耦合算法、针对某一类半线性椭圆方程，应用变分原理，研究其弱解性及Galerkin逼近，得到有限元解的误差估计及收敛阶O(h^n)，最后给出相应数值例子。     

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid–fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks.     

分析半透明单晶生长传热过程的边界元方法

论文发展了一个能求解带相变运动界面非定常传热和非线性热物理特性问题的双倒易边界元方法。数值模拟了半透明单晶生长中热过程的一个例子。由于方法是纯边界积分方法,计算量与计算内存都大大减少。获得了单晶生长过程瞬态温度场分布和固液相界面形状时间推进的一些结果。     

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

不同载流运行下冷绝缘高温超导电缆的温度场数值分析

针对冷绝缘高温超导电缆(Cold Dielectric High Temperature Superconducting cable,CD HTS cable)在不同载流下的运行稳定性,采用有限元数值分析方法对超导电缆内部温度场进行准确计算和分析。根据超导电缆内部各层传热特征,建立基于ANSYS的CD HTS电缆有限元模型,给出正常载流及故障载流下超导电缆温度场分析传热边界条件,计算得到不同载流情况下超导电缆本体温度分布变化规律,从而为其通流能力影响下的运行稳定性分析提供参考依据,对超导电缆的故障保护具有一定的指导意义。     

An axisymmetric hypersingular boundary integral formulation for simulating acoustic wave propagation in supercavitating flows

Flow supercavitation begins when fluid is accelerated over a sharp edge, usually at the nose of an underwater vehicle, where a phase change occurs and causes a low density gaseous cavity to gradually envelop the whole object (supercavity) thereby allowing for higher speeds of underwater vehicles. The supercavity may be maintained through ventilated cavitation caused by injection of gases into the cavity, which causes fluctuations at the vapor–water interface. A major issue that concerns the efficient operation of an underwater object’s guidance system (which is achieved by high frequency acoustic sensors mounted within the nose region), is the hydrodynamic noise produced due to the fluctuating vapor–water interface. It is important to carry out a detailed study on the effect of self-noise at the vehicle’s nose that is generated by the ventilating gas jet impingement on the supercavity wall. For this purpose, the present study uses a boundary element method which is more versatile compared to other numerical techniques such as the finite element/finite difference methods. The variation of acoustic pressure at the vehicle nose for various shapes of cavitators, boundary conditions and jet impact diameters are presented. Comparisons are made with the semi-analytical procedure of Howe et al. (Howe et al., On self-noise at the nose of a supercavitating vehicle. Journal of Sound and Vibration, 322 (2009a), 772–784) and finite element based COMSOL commercial package. Several issues pertaining to the behaviour of analytical and numerical results are highlighted. Finally, the proposed boundary element technique is used to study arbitrary shapes of supercavities which may encountered at various stages of supercavity development.