An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part I Non-isothermal flow

Tensor representation theory is used to derive an explicit algebraic model that consists of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for two-dimensional (2-D) incompressible non-isothermal turbulent flows. The representation methodology used for the heat flux vector is adapted from that used for the polynomial representation of the Reynolds stress anisotropy tensor. Since the methodology is based on the formation of invariants from either vector or tensor basis sets, it is possible to derive explicit polynomial vector expansions for the heat flux vector. The resulting EAHFM is necessarily coupled with the turbulent velocity field through an EASM for the Reynolds stress anisotropy. An EASM has previously been derived by Jongen and Gatski [10]. Therefore, it is used in conjunction with the derived EAHFM to form the explicit algebraic model for incompressible 2-D flows. This explicit algebraic model is analyzed and compared with previous formulations including its ability to approximate the commonly accepted value for the turbulent Prandtl number. The effect of pressure-scrambling vector model calibration on predictive performance is also assessed. Finally, the explicit algebraic model is validated against a 2-D homogeneous shear flow with a variety of thermal gradients. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

多学科设计优化中常用代理模型的研究

代理模型是多学科设计优化的关键技术之一。本文系统介绍了多项式响应面模型,径向基函数模型和Kriging模型等3种多学科设计优化中常用的代理模型。通过构造某机翼展向气动载荷分布的代理模型,对这3种模型的效果进行了评估,并对这些代理模型的构造方法、基本特性和适用范围进行了分析研究。     

结构可靠性问题研究的若干进展

主要介绍了结构可靠性研究的三种模型:随机模型、模糊模型及非概率模型的发展现状,重点综述了开展非概率模型研究的重大意义,以及非概率可靠性模型与另外两种模型的关系,并简述了结构可靠性研究的发展趋势．      

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

无磨损摩擦的原子理论

对描述原子级光滑表面之间的无磨损界面摩擦的微观过程的2个理论模型进行了综述,探讨了Frenkel-Kontorova(FK)模型的非线性静态和动态性质的复杂性,根据FK模型,静态特性在很大程度上依赖于表面晶格常数间的公度性,而动态特性则可分为周期解、准周期解和混沌解加以讨论。     

Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state,and the flow is frequently unsteady and turbulent.To assess the state-of-the-art of computational capabilities for unsteady cavitating flows,different cavitation and turbulence model combinations are conducted.The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics.The kε turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively.We have also blended these alternative cavitation and turbulence treatments,to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity.From the experimental validations regarding the force analysis,frequency,and the cavity visualization,no single model combination performs best in all aspects.Furthermore,the implications of parameters contained in different cavitation models are investigated.The phase change process is more pronounced around the detached cavity,which is better illus-trated by the interfacial dynamics model.Our study provides insight to aid further modeling development.     

RESEARCH ON AMSAA-BISE MODEL—AN ANSWER TO MEI MEN-HUA

The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA-BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given. Merits and demerits of AMSAA and AMSAA-BISE model are discussed.     

RESEARCH ON AMSAA-BISE MODEL—AN ANSWER TO MEI MEN-HUA

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎＭＥＩＷｅｎ＿ｈｕａ’ｓｐａｐｅｒ [1 ] ,ａｃｏｍｍｅｎｔｏｎＡＭＳＡＡ＿ＢＩＳＥｍｏｄｅｌｐｒｏｐｏｓｅｄｂｙａｕｔｈｏｒｅｔａｌ.(ｃｆ[2 ] )ｉｓｇｉｖｅｎ ,ａｎｄａｎａｐｐｒｏｘｉｍａｔｅｍｏｄｅｌａｔｔｅｍｐｔｉｎｇｔｏｓｏｌｖｅｔｈｉｓｐｒｏｂｌｅｍｉｓｐｒｅｓｅｎｔｅｄ .ＴｈｅＡＭＳＡＡ＿ＢＩＳＥｍｏｄｅｌｉｓｄｅｒｉｖｅｄｄｉｒｅｃｔｌｙｆｒｏｍａｎｏｔｈｅｒａｐｐｒｏａｃｈｔｈａｔｉｓｄｉｆｆｅｒｅｎｔｆｒｏｍｔｈｅａｐｐｒｏａｃｈｅｓｏｆ[2 ]ａｎｄ [3 ]…     

RESEARCH ON AMSAA-BISE MODEL—AN ANSWER TO MEI WEN-HUA

The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA- BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given.Merits and demerits of AMSAA and AMSAA-BISE model are discussed.     

Theory of nonlocal asymmetric quasicontinuum

In this article, the theory of nonlocal asymmetric quasicontinuum is developed on the basis of the atomic lattice model and theory of generalized function. The physico-mechanical model of the asymmetric stress is also discussed.     

Applying the generalized step-function to solve the bending problems of nonuniform beams with variable cross section

The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x-a}⁰ will be generalized, and a new function {x-a}⁰, n=0,1,2…,will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x-a}ⁿ{x-b}⁰. The reciprocal of the flexural of rigidity 1/EJ and the bending moment M(x) can all be expressed in terms of {x-a}ⁿ,and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given.     

A second-order dynamic subgrid-scale stress model

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎＬＥＳ,ｔｈｅｌａｒｇｅｓｃａｌｅｓｉｎｔｈｅｆｌｏｗａｒｅｃｏｍｐｕｔｅｄｅｘｐｌｉｃｉｔｌｙａｎｄｔｈｅｓｕｂｇｒｉｄ＿ｓｃａｌｅｓ(ＳＧＳ),ｗｈｉｃｈａｒｅｆｉｌｔｅｒｅｄｏｕｔｂｙａｎａｖｅｒａｇｅｐｒｏｃｅｓｓｏｐｅｒａｔｉｏｎｏｎｔｈｅＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓ,ａｒｅｍｏｄｅｌｅｄ.ＳｉｎｃｅＬＥＳｒｅｑｕｉｒｅｓｌｅｓｓｃｏｍｐｕｔｅｒｔｉｍｅｔｈａｎｔｈｅｄｉｒｅｃｔｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓａｎｄｕｓｅｓｓｉｍｐｌｅｒａ…     

Multi‐scale simulation with a hybrid Boussinesq‐RANS hydrodynamic model

A hybrid wave model is developed for simulation of water wave propagation from deep water to shoreline. The constituent wave models are the irrotational, 1‐D horizontal Boussinesq and 2‐D vertical Reynolds‐averaged Navier–Stokes (RANS). The models are two‐way coupled, and the interface is placed at a location where turbulence is relatively small. Boundary conditions on the interfacing side of each model are provided by its counterpart model through data exchange. Prior to the exchange, a data transformation step is carried out due to the differences in physical variables and approximations employed in both models. The hybrid model is tested for both accuracy and speedup performance. Tests consisting of idealized solitary and standing wave motions and wave overtopping of nearshore structures show that: (1) the simulation results of the current hybrid model compare well with the idealized data, experimental data, and pure RANS model results and (2) the hybrid model saves computational time by a factor proportional to the reduction in the size of the RANS model domain. Finally, a large‐scale tsunami simulation is provided for a numerical setup that is practically unapproachable using RANS model alone; not only does the hybrid model offer more rapid simulation of relatively small‐scale problems, it provides an opportunity to examine very large total domains with the fine resolution typical of RANS simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

Prediction of multiple overshoots in shear stress during fast flows of bidisperse polymer melts

We present a differential constitutive model of stress relaxation in polydisperse linear polymer melts and solutions that contains contributions from reptation, contour-length fluctuations, and chain stretching. The predictions of the model during fast start-up and steady shear flows of polymer melts are in accord with experimental observations. Moreover, in accordance with reported experimental literature (Osaki et al. in J Polym Sci B Polym Phys 38:2043–2050, 2000), the model predicts, for a range of shear rates, two overshoots in shear stress during start-up of steady shear flows of bidisperse polymer melts having components with widely separated molar masses. Two overshoots result only when the stretch or Rouse relaxation time of the higher molar mass component is longer than the terminal relaxation time of the lower molar mass component. The “first overshoot” is the first to appear with increasing shear rate and occurs as a result of the stretching of longer chains. Transient stretching of the short chains is responsible for the early time second overshoot. The model predictions in steady and transitional extensional flows are also remarkable for both monodisperse and bidisperse polymer solutions. The computationally efficient differential model can be used to predict rheology of commercial polydisperse polymer melts and solutions.     

A mesoscopic tube model of polymer/layered silicate nanocomposites

Rheology of isothermal suspensions of completely exfoliated silicate lamellae in polymer melts is investigated. In order to express more faithfully the physics involved in low shear rates and low frequencies, we model the polymer molecules composing the melt as chains whose motion is confined to a tube formed by surrounding chains and lamellae. In the absence of lamellae, the model reduces to the mesoscopic model of reptating chains developed in Eslami and Grmela (Rheol Acta, 2008). If the chains are seen only as FENE-P dumbbells, the model reduces to the model developed in Eslami et al. (J Rheol 51:1189–1222, 2007). Responses to oscillatory, transient, and steady shear flows are calculated and compared with available experimental data. Particular attention is payed to the region of low shear rate and low frequency.     

利用频响函数对阻尼结构进行模型修正的方法

基于频响函数和模型缩聚技术提出了一个动力结构模型修正方法。与传统频响函数法相比,由于引入了阻尼刚度比,减少了修正参数,提高了计算效率。并且针对传统频响函数法测试维数过高的缺点,引入模型缩聚技术,降低了模型测量维数的要求。数值算例证明了本方法的有效性与可行性。本方法可以对有阻尼的模型进行修正,克服了模态修正法的缺点;利用模型缩聚减小了测试点的数目,引进单元阻尼刚度比。与传统的频响函数修正法相比,减少了修正未知数,提高计算效率,并且修正结果也较准确。     

Validation of a Two-Dimensional Hyperbolic System Modelling a Gas Fluidized Bed

Numerical solutions of a gas fluidized bed model in two space dimensions are presented. This model is hyperbolic and contains particle pressure, but no particle viscosity. The results are compared with experimental data available in the literature for a wide variety of phenomena. Investigated are: the rise velocity of a single, isolated bubble; the frequency of variation of bubble diameter with time; bubble splitting; bubble frequency and the coalescence of a bubble chain formed by gas injected through a single orifice; analysis of the coalescence of bubbles aligned vertically, as well as that of those not in vertical alignment; the formation of slugs in narrow beds; and, eruption at the bed surface. The simulation results show both qualitative and quantitative agreement with the literature. This revised version was published online in July 2006 with corrections to the Cover Date.     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part II Buoyant flow

This paper presents a derivation of an explicit algebraic model for two-dimensional (2-D) buoyant flows. It is an extension of the work reported in Part I (So et al. [27]). The tensor representation method of Jongen and Gatski [14] is extended to derive an explicit algebraic Reynolds stress model (EASM) for 2-D buoyant flow invoking the Boussinesq approximation. The projection methodology is further extended to treat the heat flux transport equation in the derivation of an explicit algebraic heat flux model (EAHFM) for buoyant flow. Again, the weak equilibrium assumption is invoked for the scaled Reynolds stress and scaled heat flux equation. An explicit algebraic model for buoyant flows is then formed with the EASM and EAHFM. From the derived EAHFM, an expression for the thermal diffusivity tensor in buoyant shear flows is deduced. Furthermore, a turbulent Prandtl number (Pr_T) for each of the three heat flux directions is determined. These directional Pr_T are found to be a function of the gradient Richardson number. Alternatively, a scalar Pr_T can be derived; its value is compared with the directional Pr_T. The EASM and EAHFM are used to calculate 2-D homogeneous buoyant shear flows and the results are compared with direct numerical simulation data and other model predictions, where good agreement is obtained. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

航天器动力学模型试验验证技术研究进展

耦合载荷分析是航天器研制过程中的一个重要环节, 能够为航天器结构设计, 地面验证试验条件制定以及批准型号发射提供重要依据, 而精确地得到试验验证的航天器动力学分析模型是开展耦合载荷分析的基础. 对于大型复杂航天器结构系统, 动力学模型的试验验证需要统筹安排初始建模、动力学试验、相关分析和模型修正等工作, 这是一项极具挑战的任务. 本文首先给出了结构动力学模型验证的基本流程, 然后重点讨论动力学试验, 相关分析与模型修正等关键技术, 最后结合工程实际的需求, 提出了今后航天器动力学模型试验验证技术研究的重点.      

A Mathematical Model of Rainfall-Controlled Geothermal Fields

A mathematical model is developed, using a hydrothermal spring concept, for those geothermal fields which are controlled by infiltrated rainfall. Two limiting regimes are identified: when rainfall infiltration is so great that isothermal conditions exist in most of the downflow regions; and when rainfall infiltration is so small that a constant geophysical temperature gradient results. In either case, the ratio of downflow to upflow areas, and the energy output per unit area, are fixed, but the typical size of a geothermal field remains indeterminate. The additional assumption that the horizontal length scale of the downflow region is determined by the depth of the main heat sources, fixes the characteristic mass flows, energy outputs, and the number of geothermal fields in a geothermal region. These model predictions are compared with field data, and are shown to be in approximate agreement with geothermal field characteristics in the Taupo Volcanic Zone of New Zealand. The temperature dependence of water viscosity uses a correlation of Wooding (J. Fluid Mech. 2:273–285, 1957), while the temperature dependence of water density, enthalpy and boiling point use correlations from Elder (Geothermal Systems 508, 1981).