Condensation induced water hammer: Numerical prediction

Contact of steam and subcooled water in a pipe or a pressurized vessel leads to intensive condensation accompanied by a pressure drop in the volume of condensing steam and an acceleration of the surrounding water mass towards the steam volume, which can result in a severe water hammer and plant damage. This phenomenon is known as the condensation induced water hammer (CIWH). A one-fluid model is developed for the prediction of pressure surges during CIWH. It is shown that the reliable prediction of pressure surges strongly depends on the calculation of the condensation rate, transient friction and the water column–steam interface tracking. Due to the lack of the CIWH condensation models, a new approach is derived. The one-fluid model predictions of pressure surges are compared with available measured data from a CIWH experimental facility and acceptable agreements are obtained. In addition, the ability of the developed model to simulate the water cannon event, which takes place during the steam drainage into the pool of subcooled water, is demonstrated. Experimentally observed considerable scattering of test data under the same conditions is related to the condensation rate and its dependence on the entrained droplets–steam interfacial area concentration in the vicinity of the water column head.     

Finite element for the dynamic analysis of pipes subjected to water hammer

An axisymmetric finite element is developed for the dynamic analysis of pipes subjected to water hammer. The analysis seamlessly captures the pipe response due to water hammer by solving first the water hammer mass and momentum conservation equations, to recover the spatial–temporal distribution of the internal pressure, and then uses the predicted pressure history to form a time-dependent energy equivalent load vector within a finite element model. The study then determines the pipe response by solving the finite element discretized equations of motion. The formulation of the pipe response is based on Hamilton’s principle in conjunction with a thin shell theory formulation, and captures inertial and damping effects. The results predicted by the model are shown to be in agreement with those based on an axisymmetric shell model in Abaqus for static, free vibration and transient responses for benchmark problems. The water hammer and structural models are seamlessly integrated to enable advancing the transient solution well into the time domain to capture the effect of reflected pressure wave due to water hammer. The results indicate that the radial stress/displacement oscillations approach those of the quasi-steady response when the valve closure time exceeds eight times the period of radial vibrations obtained for the case of instantaneous valve closure.     

改进的特征线方法及过载对水锤效应影响分析

传统特征线方法对过载作用下的水锤计算具有局限性,无法为水锤防护提供可靠性指导。本文在考虑过载效应和动态摩阻的基础上,提出了改进的特征线方法,该方法能准确模拟过载作用下水锤最大压力峰值及水锤波的衰减特性。基于该方法,建立了过载作用下水锤效应数学模型,通过分析结果与CFD数值仿真及实验数据对比,验证了改进特征线方法的正确性。分析结果表明,在恒定过载作用时,阀门位置的流体压力随过载量的增加而增大,且管轴向过载的影响大于横向过载;关阀过程受到瞬时过载作用时,过载效应对水锤最大压力峰值影响显著,而对关阀后水锤波的传播和衰减影响较小;同时,分析了过载效应下关阀特性和流体密度等参数对水锤效应的影响规律。     

Validation of CFD‐CSD coupling interface methodology using commercial codes

Coupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit^® and Fluent^® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS^® environment. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of bracings and motion coupling on resonance features of semi-submersible platform under irregular wave conditions

Resonance is a critical consideration in the design of offshore floating structures. This paper aims at analysing the nonlinear effects of bracings and motion coupling on the resonance features of a semi-submersible platform. An improved mathematical model based on potential theory is proposed to simulate the motion response of a semi-submersible platform under irregular wave conditions, considering both the variations of hydrostatic and hydrodynamic forces induced by the bracings entering and exiting the water and the nonlinear coupling induced by the platform motions. For comparison purposes, numerical simulations are also performed using a mathematical model without considering the aforementioned effects. Validated by results of wave basin tests and numerical simulations, the proposed model performs much better in capturing the characteristic resonance features of pitch motion in low-frequency region. The nonlinear hydrostatic effect of bracings leads to the increase of resonance frequency as the motion amplitude increases, while the hydrodynamic force on the bracings and the nonlinear motion coupling only influence the amplitude of resonance spectral peak. In addition, factors influencing the nonlinear effects such as the vertical position and diameter of bracings and the pitch restoring coefficient are further investigated. It is revealed that the deviation of pitch resonance frequency has evident dependence on the ratio between nonlinear and linear volumetric variations, and an empirical formula estimating the resonance frequency is proposed using the observed dependence. Theoretically, both smaller bracing radius and larger pitch restoring coefficient are beneficial for suppressing the resonance induced by the nonlinear effects. The proposed model can be an effective tool for predicting the motion response, and the understanding of the resonance features is helpful for the design of semi-submersibles.     

入水问题的Euler-Lagrange流固耦合数值模以技术研究

针对结构入水过程的特点,建立了一种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把结构对水作用的过程和结构动力学响应过程的计算结合起来,实现了结构与水之间流固耦合作用过程的模拟.其中水、空气的运动利用Eulerian过程的流体弹塑性有限差分计算程序进行模拟,结构的运动变形利用Lagrangian过程的结构动力学有限元计算程序模拟结构响应.通过板入水问题的计算结果与商业软件计算结果进行比较,验证了计算方法对流固间相互作用处理的正确性.本文计算程序可用于一般入水问题的结构响应-流场运动分析中.     

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

The closely coupled approach combined with the finite volume method (FVM) solver and the finite element method (FEM) solver is used to investigate the fluid-structure interaction (FSI) of a three-dimensional cantilevered hydrofoil in the water tunnel. The FVM solver and the coupled approach are verified and validated by comparing the numerical predictions with the experimental measurements, and good agreement is obtained concerning both the lift on the foil and the tip displacement. In the noncavitating flow, the result indicates that the growth of the initial incidence angle and the Reynolds number improves the deformation of the foil, and the lift on the foil is increased by the twist deformation. The normalized twist angle and displacement along the span of the hydrofoil for different incidence angles and Reynolds numbers are almost uniform. For the cavitation flow, it is shown that the small amplitude vibration of the foil has limited influence on the developing process of the partial cavity, and the quasi two-dimensional cavity shedding does not change the deformation mode of the hydrofoil. However, the frequency spectrum of the lift on the foil contains the frequency which is associated with the first bend frequency of the hydrofoil.     

Coexistence phenomenon in autoparametric excitation of two degree of freedom systems

Coexistence phenomenon refers to the absence of expected tongues of instability in parametrically excited systems. In this paper we obtain sufficient conditions for coexistence to occur in the generalized Ince equation

     

Study on influence of bending-torsion coupling in an impacting-rub rotor system

A mathematical model of an impacting-rub rotor system with bending-torsion coupling was established. It was compared with the model without bending-torsion coupling through the modem nonlinear dynamic theory . It is observed that periodical, chaotic, period adding phenomena in them and the two models have a similar bifurcation process in their bifurcation figures . But the influence of bending-torsion on the dynmaic characteristics of the system is not neglected. The results have considerable meanings to analyze and improve the characteristics of an impacting- rub rotor system .     

哈密顿体系下机电耦合问题的基本方程

利用多变量变分原理,针对具有机电耦合特性的压电材料,在哈密顿体系下推导出了机电耦合问题的对偶方程．求出了问题的零本征解和非零本征解的一般表达式。并就“二维压电平板对边受均布载荷”这一具体问题进行了完整的分析计算,得出了应力和电位移的具体解答,结果与一般弹性力学所得的结论相吻合,而且精度极高。表明哈密顿体系适用于压电材料的力学分析。     

地下爆炸地震强度与当量的比例关系

为了研究爆炸地震耦合强度与爆炸当量的关系,针对某一硬岩介质,在相同爆炸深度条件下,进行了系列不同爆炸当量的小当量化学爆炸试验,爆炸源附近的介质特性相同。应用近场地表记录的其中两次爆炸当量相差一倍的试验数据,比较研究了他们的爆炸震源函数折合速度势振幅谱比,得到他们的地震耦合强度地震矩M0比值近似等于2,与他们的爆炸当量比值相等,因此得到同爆炸深度的地下爆炸地震强度与爆炸当量成正比的结论。     

A new type of Maxwell stress in soft materials due to quantum mechanical-elasticity coupling

All dielectrics deform when subjected to an electric field. This behavior is attributed to the so-called Maxwell stress and the origins of this phenomenon can be traced to geometric deformation nonlinearities. In particular, the deformation is large when the dielectric is elastically soft (e.g. elastomer) and negligible for most “hard” materials. In this work, we develop a theoretical framework which shows that a striking analog of the electrostatic Maxwell stress also exists in the context of quantum mechanical-elasticity coupling. The newly derived quantum-elastic Maxwell stress is found to be significant for soft nanoscale structures (such as the DNA) and underscores a fresh perspective on the mechanics and physics of polarons. We discuss potential applications of the concept for soft nano-actuators and sensors and the relevance for the interpretation of opto-electronic properties.     

不同介质地下爆炸的地震耦合效应

对黄土、砂砾石和花岗岩等几种不同介质中的地下爆炸实验进行了地表速度测量,利用实测数据 获得爆炸源频谱以及以折合速度势低频稳态值表示的地震耦合强度。实验结果表明,对于相同当量、相当比 例埋深下的地下爆炸,地震耦合强度和源区介质特性有着强烈的依赖关系,其中介质强度是影响地震耦合效 率的最主要因素,而介质的干孔隙率和水饱和度也是影响地震耦合效率的重要因素。考察了M.D.Denny等 提出的经验公式在估算100kg级当量地下爆炸地震耦合强度的适用性和局限性。     

Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

硬球加强模型在CFD-DEM耦合计算中的验证与分析

针对CFD-DEM耦合计算中,颗粒计算时间步的选取影响颗粒碰撞计算精度和效率的问题。本文引入插值算法,将动量定理求解颗粒碰撞前后速度进行加权平均;根据弹性理论计算得到颗粒碰撞力,进行动力学方程求解;通过速度收敛准则修正初值速度并自动调整迭代求解次数,提出一种计算精度不受计算时间步长影响,无需对碰撞过程进行精细描述的高效率和高精度的加强硬球模型。对两个颗粒匀和变速碰撞算例进行数值模拟,碰撞后速度、碰撞力和碰撞时间与理论计算误差小于4%,与采用软球碰撞模型的DEM方法相比,颗粒碰撞计算精度不受计算时间步长影响,计算效率提高36.3%和36.8%。对单个颗粒在静水中沉降进行数值模拟,计算步长取10 s～5 s,颗粒与壁面即可得到精确解,计算效率提高33.5%。通过压力损失实验验证了该模型能够准确计算颗粒体积分数小于12%条件下两相流的压力损失。     

A master equation study of vibration-dissociation coupling in shock-heated oxygen molecules

The vibration-dissociation coupling phenomena in shock-heated oxygen molecules highly dilute in an argon heat-bath have been studied numerically. State-to-state transition rate coefficients were evaluated by using relatively simple models developed through the information theoretical approach. The master equation was solved by numerical integration to obtain time-resolved vibrational population distributions. The results of the master equation analysis are compared with those obtained by using a widely-used phenomenological vibration-dissociation coupling model. The results show that during the relaxation process the depletion of high-lying vibrational energy levels is severe and significantly affects bulk properties related to dissociation and that the phenomenological model can reproduce qualitatively the bulk relaxation process found in the master equation analysis. Received 26 June 2001 / Accepted 3 December 2002 Published online 4 February 2003     

A review of wave celerity in frictionless and axisymmetrical steel-lined pressure tunnels

Generally applicable approaches for estimating the “quasi-static”, which means without fluid-structure interaction and frequency-dependent water-hammer wave speed in steel-lined pressure tunnels are analyzed. The external constraints and assumptions of these approaches are discussed in detail. The reformulated formulas are then compared to commonly used expressions. Some special cases of wave speed calculation such as unlined pressure tunnels and open-air penstocks are investigated. The quasi-static wave speed is significantly influenced by the state of the backfill concrete and the near-field rock zone (cracked or uncracked). In the case when these two layers are cracked, the quasi-static wave speed is overestimated in between 1% and 8% compared to uncracked concrete and near-field rock layers. Depending on the stiffness of steel liner and penstock, the fluid-structure interaction leads to significant difference in wave speeds values. Compared to the quasi-static case, the fluid-structure interaction approach, applied to steel-lined tunnels, results up to 13% higher wave speed values in the high-frequency range (higher than 600 Hz) and up to 150% lower values for frequencies between 150 and 300 Hz in the considered test case.