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STABILITY ANALYSIS IN spatial mode FOR CHANNEL FLOW OF FIBER SUSPENSIONS

Applied Mathematics and Mechanics(English Edition) 2003年第8期24卷 871-879页

作者：林建忠游振江 Department of Mechanics State Key Laboratory of Fluid Power Transmission and ControlZhejiang University Hangzhou 310027 P.R.China Department of Mechanics State Key Laboratory of Fluid Power Transmission and ControlZhejiang University Hangzhou 310027 P.R.Chinaifferent from previous temporal evolution assumption the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number a decrease of corresponding wave number a slowdown of the decreasing of phase velocity a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole long wave disturbances are susceptible to fibers.

Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.

关键词： flow stability spatial mode fiber suspensions channel flow

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Critical Transition Reynolds Number for the Incompressible Flat-plate Boundary Layer as Searched by Numerical Simulation

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Advances in Applied Mathematics and Mechanics 2023年第4期15卷 1056-1075页

作者： Yongming Zhang Di Liu Ning Li Laboratory for High-Speed Aerodynamics Tianjin UniversityTianjin 300072China Department of Mechanics Tianjin UniversityTianjin 300072China Tianjin Key Laboratory of modern Engineering Mechanics Tianjin 300072China Research Institute of Petroleum Exploration&Development PetroChinaBeijing 100083China

The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.

关键词： Critical transition Reynolds number flat-plate boundary layer DNS temporal mode spatial mode

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Aerodynamic system instability identification with sample entropy algorithm based on feature extraction

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Propulsion and Power Research 2023年第1期12卷 138-152页

作者： Mingming Zhang Jia Zhang Anping Hou Aiguo Xia Wei Tuo Yongzhao Lv Faculty of Science Beijing University of TechnologyBeijing 100124China School of Energy and Power Engineering Beihang UniversityBeijing 100191China Beijing Aeronautical Technology Research Center Beijing 100076China Zhengzhou Aerotropolis Institute of Artificial Intelligence ZhengzhouHenan 451162China

Based on the sample entropy algorithm in nonlinear dynamics,an improved sample entropy method is proposed in the aerodynamic system instability identification for the stall precursor detection based on the nonlinear feature extraction algorithm in an axial compressor.The sample entropy algorithm is an improved algorithm based on the approximate entropy algorithm,which quantifies the regularity and the predictability of data in time series.Combined with the spatial modes representing for the rotating stall in the circumferential direction,the recognition capacity of the sample entropy is displayed well on the detection of stall inception.The indications of rotating waves are extracted by the circumferential analysis from modal wave energy.The significant ascendant in the amplitude of the spatial mode is a pronounced feature well before the imminence of stall.Data processing with the spatial mode effectively avoids the problems of inaccurate identification of a single measuring point only depending on pressure.Due to the different selections of similarity tolerance,two kinds of sample entropy are obtained.The properties of the development process of the identification model show obvious mutation phenomena at the boundary of instability,which reveal the inherent characteristic in aerodynamic system.Then the dynamic difference quotient is computed according to the difference quotient criterion,after the smooth management by discrete wavelet.The rapid increase of difference quotient can be regarded as a significant feature of the system approaching the flow instability.It is proven that based on the principle of sample entropy algorithm,the nonlinear characteristic of rotating stall can be well described.The inception can be suggested by about 12-68 revolutions before the stall arrival.This prediction method presenting is accounted for the nonlinearity of the complex flow in stall,which is in a view of data fusion system of pressure for the spatial mode tracking.

关键词： Sample entropy algorithm spatial mode Data fusion Inception identification Nonlinear dynamics

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mode decomposition of nonlinear eigenvalue problems and application in flow stability

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Applied Mathematics and Mechanics(English Edition) 2014年第6期35卷 667-674页

作者：高军罗纪生 Department of Mechanics Tianjin University

Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an Nth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.

关键词： nonlinear eigenvalue problem mode decomposition spatial mode adjoint equation orthogonal relationship

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Programmable unitary operations for orbital angular momentum encoded states

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National Science Open 2022年第3期1卷 26-45页

作者： Shikang Li Xue Feng Kaiyu Cui Fang Liu Wei Zhang Yidong Huang Department of Electronic Engineering Tsinghua UniversityBeijing 100084China

We have proposed and demonstrated a scalable and efficient scheme for programmable unitary operations in orbital angular momentum(OAM)domain.Based on matrix decomposition into diagonal and Fourier factors,arbitrary matrix operators can be implemented only by diagonal matrices alternately acting on orbital angular momentum domain and azimuthal angle domain,which are linked by Fourier transform.With numerical simulations,unitary matrices with dimensionality of 3×3 are designed and discussed for OAM domain.Meanwhile,the parallelism of our proposed scheme is also presented with two 3×3 matrices.Furthermore,as an alternative to verify our proposal,proof of principle experiments have been performed on path domain with the same matrix decomposition method,in which an average fidelity of 0.97 is evaluated through 80 experimental results with dimensionality of 3×3.

关键词： unitary transformation orbital angular momentum spatial mode spatial light modulator

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A New Bottom-Up Process: The Rural Urbanization Driven by E-Commerce in China

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China City Planning Review 2017年第4期26卷 25-33页

作者： Luo Zhendong He Heming Li Caige(译) School of Architecture and Urban Planning Nanjing University Research Center for Regional Planning Nanjing University Center for Strategic Planning Institute of Urban Planning and DesignNanjing University 不详

Rural urbanization driven by e-commerce is a new bottom-up urbanization process originating in the information era.The systematical restructuring that this process brings about in the social life,economic environment,and physical space of the countryside,which is reflected in characteristics such as the leaping non-agriculturalization of employment,the comprehensive modernization of rural life,and the intensive spatial urbanization.Obviously,there are many common features between this new process and the old one in the past three decades,but progresses also exist.The distinctions of the countryside,such as a low-cost entrepreneurial environment,local non-agricultural industry,and resources of specialty agricultural products,are manifested in the process.Combined with the Internet and e-commerce by the rural grassroots entrepreneurs,they enable rural area to break the location constrains and join in the national even global industry division,and further realize the leaping development of scale and function.Meanwhile,the capital and talents back to the rural areas are an important guarantee for the upgrading of rural development.Consequentially,the developing and planning idea of smart shrinking is necessary for the rural urbanization process driven by e-commerce in China.

关键词： bottom-up urbanization e-commerce rural urbanization characteristics spatial mode mechanism

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The Hindcast of Winter and Spring Arctic and Antarctic Oscillation with the Coupled Climate models

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Acta meteorologica Sinica 2011年第3期25卷 340-354页

作者：钱卓蕾王会军孙建奇 Institute of Atmospheric Physics Chinese Academy of Sciences Climatic Change Research Center Chinese Academy of Sciences Graduate School of Chinese Academy of Sciences

This study evaluates the ability of the global coupled climate models in hindcasting the Arctic Oscillation （AO） and Antarctic Oscillation （AAO）. The results show that the models can well simulate the spatial distribution of AO with better results in winter than in spring. In the troposphere in spring, the simulation of AO on the whole is still relatively good with a comparatively high correlation with the NCEP/NCAR reanalysis. The models can also well reproduce the spatial distribution of AAO throughout the year at all levels of the troposphere, and the spatial simulation is better at 850 hPa than at the surface. Although the simulation is better in winter than in other seasons, the seasonal variation is not so significant and the differences among different models are relatively smaU. In addition, the capability of the models for ＂predicting＂ the AO and the AAO index time series is limited, because only a few models can capture their observed interannual variability at the 95% significance level.

关键词： Arctic Oscillation （AO） Antarctic Oscillation （AAO） EOF spatial mode time series

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STUDY OF MECHANISM OF BREAKDOWN IN LAMINARTURBULENT TRANSITION OF SUPERSONIC BOUNDARY LAYER ON FLAT PLATE

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Applied Mathematics and Mechanics(English Edition) 2006年第4期27卷 425-434页

作者：曹伟黄章峰周恒 Department of Mechanics Tianjin University Tianjin 300072P. R. China Liuhui Center of Applied Mathematics Nankai University and Tianjin UniversityTianjin 300072P. R. China

spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a fiat 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 disturbance, when they became larger, leads to 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 spatial mode

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The urbanization process of Bohai Rim in the 1990s by using DMSP/OLS data

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Journal of Geographical Sciences 2006年第2期16卷 174-182页

作者： HE Chunyang LI Jinggang CHEN Jing SHI Peijun CHEN Jin PAN Yaozhong LI Jing ZHUO Li Ichinose Toshiaki Key Laboratory of Environmental Change and Natural Disaster Ministry of Education of ChinaBeijing Normal University College of Resources Science ＆ Technology Beijing Normal UniversityBeijing 100875 China Institute of Remote Sensing Applications CAS. Beijing 100101 China Japan National Institute of Environmental Studies 16-2 Onogawa Tsukuba 305-8506 Japan

This paper firstly derived urban information from Defense Meteorological Satellite Program/Operational Linescan System （DMSP/OLS） data in 1992, 1996 and 1998 with the support of statistical data, and then developed three basic urban models of polygon-urbanization, line-urbanization and point-urbanization in urban agglomerations from viewpoint of spatial analysis. The conclusions are as follows：（1） Urban patch numbers in the Bohai Rim increased from 1659 to 2053 with an annual average increase number of about 66. Meanwhile, the small urban patches accounted for a larger proportion in the region and the patch density increased fast. In addition, the urban barycenter of the region showed a moving trend toward northwest from 1992 to 1998. Urbanization in the Bohai Rim in the 1990s is fast and obvious. （2） Urbanization in the Bohai Rim can be reflected by three basic processes, i.e., the polygon-urbanization around the big cities, the line-urbanization around the transportation lines and the point-urbanization emerging in large areas. Of them, the polygon-urbanization has been in dominance. It is obviously within an effective range of 3-4 km surrounding the urban patches. The line-urbanization and point-urbanization in the region was relatively small, both of which showed an obvious increasing trend.

关键词： DMSP/OLS urbanization agglomeration urbanization spatial mode process Bohal Rim

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NONLINEAR EVOLUTION ANALYSIS OF T-S DISTURBANCE WAVE AT FINITE AMPLITUDE IN NONPARALLEL BOUNDARY LAYERS

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Applied Mathematics and Mechanics(English Edition) 2002年第6期23卷 660-669页

作者： TANG Deng-bin(唐登斌) XIA Hao(夏浩) Department of Aerodynamics Nanjing University of Aeronautics and Astronautics Nanjing 210016 P R China Department of Aerodynamics Nanjing University of Aeronautics and Astronautics Nanjing 210016 P R China

The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.

关键词： boundary layer stability nonlinear evolution nonparallelism T-S disturbance wave compact scheme spatial mode parabolized stability equation

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