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具有约束的动态投入产出最优控制模型

天津大学学报（自然科学与工程技术版） 2002年第3期35卷 384-388页

作者：亢京力毛云英杨正方天津大学理学院南开大学天津大学刘徽应用数学中心天津300072

研究了一类具有终端产出约束的动态投入产出问题的最优控制模型 ,分析了该模型最优控制的存在性和唯一性 .利用与其相应的无约束问题已有结论 ,把该模型最优控制的研究转化成一个较为简单的扰动模型最优控制的研究 ,利用罚函数法 ,推导... 详细信息

研究了一类具有终端产出约束的动态投入产出问题的最优控制模型 ,分析了该模型最优控制的存在性和唯一性 .利用与其相应的无约束问题已有结论 ,把该模型最优控制的研究转化成一个较为简单的扰动模型最优控制的研究 ,利用罚函数法 ,推导出扰动模型的最优反馈控制 .最终得到了具有终端产出约束最优控制问题的最优反馈控制 .实例仿真计算验证了结果的有效性 .

关键词：投入产出最优控制最优反馈控制转移矩阵

Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

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Science china(Physics,Mechanics & Astronomy) 2008年第8期51卷 1106-1115页

作者： HUANG ZhangFeng & ZHOU Heng Department of Mechanics,tianjin university,tianjin 300072,china Liu-Hui center of applied mathematics,nankai university and tianjin university,tianjin 300072,china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of applied mathematics Nankai University and Tianjin University Tianjin China

The inflow conditions for spatial direct numerical simulation(SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence,which is a puzzle. In this paper a new method is suggested,in which the flow field obtained by using temporal direct numerical simulation(TDNS) for fully developed turbulent flow(only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that,under a proper time-space transformation,all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other,not only qualitatively,but also quantitatively. The normal-wise distributions of mean flow profile,turbulent Mach number and the root mean square(RMS) of the fluctuations of various variables,as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS,bear similarity in nature.

关键词： inflow conditions spatial direct numerical simulation turbulent boundary layer similarity

Stochastic DEA model with undesirable outputs: An application to the prediction of anti-HIV therapy efficiency

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Progress in Natural Science:Materials International 2006年第7期16卷 753-759页

作者： BIAN Fuping and TANG Xiaoqin ( Department of mathematics, School of Science, tianjin university, tianjin 300072, china liuhui Institute of applied mathematics, nankai university and tianjin university, tianjin 300072, china) tianjin Univ Sch Sci Dept Math Tianjin 300072 Peoples R China nankai Univ Liuhui Inst Appl Math Tianjin 300072 Peoples R China

This paper proposes a stochastic prediction DEA model with undesirable outputs and simplifies the process using chance-constrained techniques in order to obtain an equivalent linear programming formulation. The existence and stability of the optimal solutions have been proved. And the model is used to describe and predict the efficiency of anti-HIV therapy in AIDS patients.

关键词： data envelopment analysis (DEA) decision making units (DMU) undesirable outputs stochastic DEA model anti-HIV therapy.

Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack

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Science china(Physics,Mechanics & Astronomy) 2009年第8期52卷 1223-1232页

作者： SU CaiHong1 & ZHOU Heng1,2 1 Department of Mechanics,tianjin university,tianjin 300072,china 2 Liu-Hui center of applied mathematics,nankai university and tianjin university,tianjin 300072,china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of applied mathematics Nankai University and Tianjin University Tianjin China

Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complexity of the *** eN method has been regarded as an effective method for the transition prediction of boundary ***,it heavily relies on experiment or *** in cases with three-dimensional base flow,for instance,the boundary layer on a cone with angle of attack,the result of its application is not *** authors have found its cause and proposed the method for its improvement,which did yield the fairly satisfactory result for a given test case,and also did not rely so much on experiment or ***,before people can really apply this method to practical problems,more test cases have to be *** this paper,more test cases for the application of the improved eN method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be *** results are compared with those obtained by experiments and/or direct numerical simulations,confirming that the improved eN method is effective and *** also find that there may be more than one ZARF for each meridian plane,and which one should be chosen for the eN method has been clarified.

关键词： angle of attack cone boundary layer transition eN method

Transition prediction of a hypersonic boundary layer over a cone at small angle of attack——with the improvement of e^N method

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Science china(Physics,Mechanics & Astronomy) 2009年第1期52卷 115-123页

作者： SU CaiHong1 & ZHOU Heng1,2 1 Department of Mechanics, tianjin university, tianjin 300072, china 2 Liu-Hui center of applied mathematics, nankai university and tianjin university, tianjin 300072, china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of applied mathematics Nankai University and Tianjin University Tianjin China

The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS.

关键词： angle of attack cone transition eN method

The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2 & ZHOU Heng 1,2 1. Department of Mechanics, tianjin university, tianjin 300072, china 2. Liu-Hui center of applied mathematics, nankai university and tianjin university, tianjin 300072, china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of applied mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2 & LUO Jisheng1,2 1. Department of Mechanics, tianjin university, tianjin 300072, china 2. Liu-Hui center of applied mathematics, nankai university and tianjin university, tianjin 300072, china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of applied mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows

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Science china(Physics,Mechanics & Astronomy) 2005年第2期48卷 228-236页

作者： LUO Jisheng, WANG Xinjun & ZHOU Heng Department of Mechanics, tianjin university Liu-Hui center of mathematics, nankai and tianjin university, tianjin 300071, china Department of Mechanics Tianjin University Tianjin China Liu-Hui center of mathematics Nankai and Tianjin University Tianjin China

Laminar-turbulent transition is an old yet unsolved problem. Notwithstanding the great effort made, there is an important question that seems not to have been addressed yet, that is, what is the inherent mechanism of breakdown that eventually leads to transition? The conventional idea is that the transition starts from the amplification of disturbances, and when the disturbances become larger, higher harmonics will be generated due to nonlinear effect, making the flow more and more complicated, and finally turbulent. Though the scenario seems clear, yet there is a missing link, that is, what happens in the breakdown process. Here we show by analyzing the results from direct numerical simulations that the change of stability characteristics of the mean flow profile plays a key role in the breakdown process.

关键词： laminar-turbulent transition, breakdown, plane channel flow.

A numerical investigation of the evolution of 2-D disturbances in hypersonic boundary layers and the effect on the flow structure due to the existence of shocklets

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Science china(Physics,Mechanics & Astronomy) 2004年第2期47卷 244-255页

作者： CAO Wei & ZHOU Heng Department of Mechanics,tianjin university Liu Hui center of applied mathematics,nankai and tianjin university,tianjin 300072,china Correspondence should be addressed to Zhou Heng(email:hzhou 1 @ ***) Department of Mechanics Tianjin University China Liu Hui center of applied mathematics Nankai China tianjin university Tianjin China

The evolution of 2-D disturbances in hypersonic boundary layer with Mach number 6,8, and 10 was investigated numerically by three different numerical schemes. At the entrance, second mode T-S waves with different amplitudes were introduced, and the relation between the Mach number and the amplitude of the disturbance when shocklets started to appear was investigated. By comparing the disturbance velocity profiles with those provided by linear stability theory, the effects of shocklets on flow structures were also investigated.

关键词： hypersonic boundary layers, T-S wave, shocklet, direct numerical simulation.