热力学理论与空化现象

有关空化现象的理论研究大多建立在1917年由Rayleigh[1]开始的,后由Plesset等人发展起来的单个空泡运动理论的基础上.该理论仅从流体动力学的某些观点出发,考虑了力的作用,对诸如水下爆炸等问题的讨论,无疑是合适的.由于忽视了空泡生长或消失过程中气、液两相间的物质交换及能量转化,因此对空化现象的讨论则认为是不完备的. 本文主要从热力学观点.分析高速水流中的空化现象、空泡形成条件、空化数以及讨论空化模型实验的相似性问题.     

栅格翼空化干扰水动力建模研究

对水下超空泡栅格翼水动力进行了研究.分析了叶片数、叶片间距、叶片厚度、叶片攻角和空化数对栅格翼水动力的影响.揭示了叶片间隙中的空泡流动对水动力的干扰机理.建立了超空泡栅格翼水动力数学模型,并用实验结果进行了验证.最后基于模型解释了实验中发现的栅格翼水动力变化规律.     

初生空化状态相似性问题

在前文中[1],讨论了热力学条件与初生空化的关系.在此基础上,引进空泡群的体积函数z₀(r),代替前文中的能量方程式,讨论相似流动体系中的空化状态相似性问题.分析结果表明,在两个满足Froude准则的相似流动体系中,空化状态是不相似的,其初生空化数随几何比尺的增加而增加.理论结果与实践是符合的.     

空化问题中的相变现象与接近平衡的速率

前文[9]我们已经说明用单个空泡的急剧膨胀和收缩来说明空化现象是不合适的.原因是空化现象中的实际气泡的变动与急剧膨胀和收缩的变化情形差距很大,而和平衡状态比较接近,本文紧接着前文[9]给出了气泡趋于平衡的速率和弛豫时间.并且给出空化现象中气泡可以作为平衡状态的判断准则.     

线性不确定系统的鲁棒D型迭代学习控制

研究一类线性不确定系统的鲁棒D型迭代学习控制问题.首先针对一类线性标称控制对象,建立其迭代学习控制的二维模型;然后基于获得的二维模型,利用二维系统稳定性理论,获得系统在迭代初态与期望初态一致和不一致两种情形下的D型迭代学习控制律的存在条件和设计方法;进一步,将所得结果推广至控制对象包含不确定性的情形.所得结果以线性矩阵不等式(LMI)的形式给出,可以方便地利用Matlab中的LMI工具箱求解.最后,数值仿真实例验证了本文所提方法的有效性.     

一种基于新锥模型的自适应信赖域算法

本文提出一种自动确定信赖域半径的新锥模型信赖域算法.该算法在每步迭代中利用以前迭代点的二次信息和水平向量信息自动产生一个信赖域半径.且证明了全局收敛性及超线性收敛性,数值结果验证了新算法的有效性.     

基于IRT的一种多级评分模型的参数估计

基于项目反应理论,文章先将双参数Logistic模型中的答对概率视为被试的得分率,采用最小二乘估计法先后对多级评分模型中的项目参数和能力参数进行估计,再根据已知条件将所得的结果加以迭代,提出了一种实用性很强的参数估计方法.     

无约束优化的自适应信赖域方法

本文对无约束优化问题提出一个自适应信赖域方法,每次迭代都充分利用前迭代点的信息自动产生一个恰当的信赖域半径,在此区域内,二次模型与原目标函数尽可能一致,避免盲目的尝试,提高了计算效率。文中在通常条件下证明了全局收敛性及局部超线性收敛结果,给出了新算法与传统信赖域方法的数值结果,证实了新方法的有效性。     

纵向数据半参数建模中的迭代加权偏样条最小二乘估计

考虑了纵向数据半参数建模中的估计问题, 提出了参数分量的一个迭代加权偏样条最小二乘估计. 在渐近方差意义下该估计比加权偏样条最小二乘估计更加有效, 且具有渐近正态性. 另外, 给出了一个自适应方法, 该方法能保证经过有限次迭代后, 迭代过程会终止, 并且产生的估计渐近等价于使用迭代方法所能产生的最好的估计, 这些结果是Chen和Shao的结果在半参数回归上的推广.     

迭代的计算与估计

对高次多项式函数这类非线性映射给出了一般 n次迭代的一个计算结果 ,还讨论了一维欧氏空间中一些非多项式型映射的迭代 .在二维欧氏空间中 ,我们给出了几类特殊的非线性迭代的结果 .对于一些难以精确计算迭代表达式的映射 ,我们给出了其迭代的估计 .     

Numerical Investigations of Relaxation Phenomena in Cavitating Nozzle Flows

Numerical simulations of cavitating flows are frequently performed by applying simple law of state‐models. In this study an advanced law of state‐model on the basis of a Landau‐type approach is used that focusses on the physical treatment of relaxation phenomena. Relaxation phenomena or phase non‐equilibrium effects occur within the scope of two‐phase fluid dynamics if the time scale of the flow problem is small. This appears e.g. in the case of cavitating flow in injector nozzles of diesel engines. The aim of this study is the determination of the relaxation parameter of the advanced law of state‐model. For this reason a theoretical approach is presented as well as simulations of unsteady cavitating nozzle flows that are compared with experimental data. Concerning the calculation of 2‐D unsteady cavitating flow the evolution equation for the vapor fraction is solved by a modified Volume‐of‐Fluid algorithm.     

Modified k – ω Model for Simulation of Cavitating Flows

Although cavitating flows are generally turbulent, the interaction of turbulence and cavitation dynamics is still not well understood. In general, two‐equation models are employed, which were originally developed for single‐phase flows. Therefore they fail by handling cavitation based flow phenomena with very high density variations (dependent on operating condition up to 40000:1). This sudden change of the density causes strong pressure gradients, secondary flows and local compressibility. The aim of this study is to enhance the Wilcox's k‐? model with empirical correlations in order to simulate turbulent cavitating flows more precisely and effciently.     

Numerical Investigation of Cavitation Interacting with Pressure Wave

A computational fluid dynamics solver based on homogeneous cavitation model is employed to compute the two-phase cavitating flow. The model treats the two-phase regime as the homogeneous mixture of liquid and vapour which are locally assumed to be under both kinetic and thermodynamic equilibrium. As our focus is on pressure wave formation, propagation and its impact on cavitation bubble, the compressibility effects of liquid water have to be accounted for and hence the flow is considered to be compressible. The cavitating flow disturbed by the introduced pressure wave is simulated to investigate the unsteady features of cavitation due to the external perturbations. It is observed that the cavity becomes unstable, locally experiencing deformation or collapse, which depends on the shock wave intensity and freestream flow speed.     

Modeling the Effect of Supply Pressure Fluctuations on Cavitation Processes in Injection Nozzles

In this study cavitating flows in an injection nozzle under time‐depended inlet pressure are calculated using a dispersed bubble dynamics model. The calculations confirm that a transient rise of the nozzle inlet pressure forces cavitation to recede and a sharp decrease of the injection pressure enhances cavitation.     

Comparison of Inviscid and Viscous Two‐Phase Calculations of Cavitating Pump Flow

In cavitating flows there is a strong interaction between the fine dispersed vapor bubbles and turbulence. Therefore in two‐phase flow calculations the prediction of turbulence is a matter of great difficulties and uncertainties. To get an idea of the influence of turbulence modelling on the calculated result, viscous and inviscid two‐phase calculations of cavitating pump flow were performed. In the inviscid calculations the influence of cavitation is isolated from turbulence effects. In the viscous calculations the effect of turbulence is modelled with a k – ϵ turbulence model. The results show that the influence of viscous effects on the flow field is weak in comparison to cavitation. However, in contrast to the steady cavitation behaviour predicted by the viscous calculations, the inviscid calculations show unsteady behaviour of the cavitation (as can be seen in the experiment).     

Constraints on equation of state for cavitating flows with thermodynamic effects

Thermodynamic effects play an important role in the cavitation dynamics of cryogenics fluids. Such flows are characterized by strong variations in fluid properties with the temperature. A compressible, multiphase, one-fluid solver was developed to study and to predict thermodynamic effects in cavitating flows. To close the system, a cavitation model is proposed to capture metastable behaviours of fluids and non isothermal thermodynamic path. The thermodynamical consistency based on entropy conditions and the evolution of the mixture speed of sound are investigated. These constraints are applied to other models. The considered working fluid is the refrigerant R-114.     

有限超空泡机翼的研究

我们把在机翼上方建立了人为的空泡低压区的机翼称为“空泡机翼”.本文利用推广了的Blasius定理和保角映射,研究了在空泡上方具有喷流的空泡机翼的机翼绕流问题,并给出了机翼的举力和推力公式.     

A Model for Kidney Tissue Damage under High Speed Loading

In a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime. The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small‐strain to the finite deformation range. In that way the time‐discretized version of the porous‐viscoplastic constitutive updates is described in a fully variational manner. By numerical experiments we study the shock‐wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary element formulation for nonlinear applications in geomechanics

Several types of nonlinearities are considered, using the boundary element method, with emphasis on geomechanical applications. Numerical algorithms to model ‘no-tension’ plastic, viscoplastic and viscoelastic responses are presented. Extension of the method to two-dimensional piecewise homogeneous problems is shown.The overlay technique is adapted for the boundary element formulation to model complex plastic and viscoplastic responses. In particular, the technique is shown to be extremely useful to model time-dependent behaviour. It has also proved suitable for the Bauschinger-effect representation in elastoplastic analysis.Tunnel examples are presented and are shown to be very well suited to solution by boundary elements. The method deals with infinite domains without requiring the definition of an artificial outer boundary. As a result little discretization is needed.     

Buckling analyses of three characteristic-lengths featured size-dependent gradient-beam with variational consistent higher order boundary conditions

In this work, a three characteristic-lengths featured size-dependent gradient-beam is constructed by adopting the modified nonlocal model, resulting in much more general constitutive equation with stress gradient up to four-order and strain gradient to two-order. The six-order differential governing equation for transverse displacement is formulated. All boundary conditions especially variational consistent higher order boundary conditions of the present model are derived with the aid of weighted residual approach. The closed-form solutions to critical buckling loads under different sets of boundary conditions are systematically formulated with higher order boundary conditions incorporated. The numerical results show that both nonlocal parameters have significant effect on the buckling behaviors. Meanwhile, if two nonlocal parameters are taken as same, the present results cannot always reduce to that from Eringen's nonlocal model. Due to its clear physical meaning, the present model is expected to be widely adopted in mechanical analyses of nano-structures.