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Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

Chinese Physics B 2015年第6期24卷 378-384页

作者：张伟王勇钱跃竑 Department of Mechanical Enignneering National University of Singapore Department of Mechanical and Aerospace Engineering University of California Shanghai Institute of Applied Math and Mechanics Shanghai University

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.

关键词： lattice Boltzmann dynamic mode decomposition stability analysis graphical processing unit

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MACROSCOPIC BEHAVIOR OF VIBRATING BEDS OF SMOOTH INELASTIC SPHERES

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PHYSICS OF FLUIDS 1995年第8期7卷 1818-1831页

作者： LAN, YD ROSATO, AD Department of Mechanical Engineering Center for Applied Mathematics and Statistics New Jersey Institute of Technology Newark New Jersey 07102

Three-dimensional, granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Gamma=a omega(2), even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low-density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g less than or equal to Gamma less than or equal to 2.0g, and subsequently flattens out at Gamma congruent to 2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data. (C) 1995 American Institute of Physics.

关键词： DISTRIBUTION FUNCTIONS FLUIDIZED BEDS GRANULAR MATERIALS INELASTIC SCATTERING mechanical VIBRATIONS NUMERICAL SOLUTION SPHERICAL CONFIGURATION

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Optimized thermoelectric generation for efficient low-medium temperature geothermal energy harvesting

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Renewable Energy 2025年 239卷

作者： Khan, Zafar Hayat Xie, Heping Sun, Licheng Yang, Wei Khan, Waqar A. Li, Bixiong Long, Xiting Wang, Jun Li, Cunbao Gao, Mingzhong Ruan, He Center for Applied Mathematics of Guangxi Nanning Normal University Nanning530100 China School of Mathematics and Statistics Nanning Normal University Nanning530100 China Guangdong Provincial Key Laboratory of Deep Earth Sciences and Geothermal Energy Exploitation and Utilization Institute of Deep Earth Sciences and Green Energy College of Civil and Transportation Engineering Shenzhen University Shenzhen518060 China State Key Laboratory of Hydraulics and Mountain River Engineering College of Water Resource & Hydropower Sichuan University Chengdu610065 China Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd University Al Khobar31952 Saudi Arabia Key Laboratory of Deep Underground Science and Engineering for Ministry of Education Sichuan University Chengdu610065 China

This paper aims to design and evaluate a thermoelectric generation system optimized for low-to-medium temperature geothermal energy, focusing on maximizing power output and system efficiency. A one-dimensional mathematical model based on energy balance is employed for a single thermoelectric element and subsequently scaled to a 600 thermoelectric generators (TEGs) module. The Peltier, Fourier, and Joule heating effects are included in the analysis, whereas the radiation and convection effects are neglected. The impact of various 2D and 3D layouts of thermoelectric generators (TEGs) and temperature variations on power generation and performance is examined. An experiment is performed to observe the power capacity of a module consisting of five thermoelectric generators. These experimental observations validate the analytical model, and reference properties are adopted to predict more complex modules. This work aims to simulate the optimal design of a TEG module, utilizing the temperature difference to generate 1 kW of power. For this purpose, a module comprising of 600 TEGs is analyzed in various layouts. Based on experimental results for the temperature difference ΔT=96.4Co, it is proposed that a compact module consisting of 600 TEGs with a 3D design of 10 × 12 × 5 will be suitable and cost-effective to generate 1 kW power. © 2024 Elsevier Ltd

关键词： Geothermal Modeling Optimization Thermoelectric generator

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mathematical models of carbide tool crater surfaces

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International Journal of Machine Tool Design and Research 1967年第n 4期v 7卷 p445-463页

作者： Wu, S.M. Meyer, R.N. Associate Professor Department of Mechanical Engineering and Department of Statistics The University of Wisconsin Madison Wisconsin 53706 USA Analyst Applied Mathematics and Statistics Department Minnesota Mining and Manufacturing Company St. Paul Minnesota 55101 USA

Carbide cutting tool crater surfaces are expressed by both second and third order polynomials;fitting of actual crater surfaces is illustrated by example;criterion of suitable models, effects of second and third order coefficients, repeatability and " weighting" of crater center are discussed in detail;many applications may be developed once crater surface can be represented by mathematical model;both determinations of crater volume and crater top area by numerical integration methods are illustrated by examples;close agreement was observed between new mathematical approach and old time-consuming approximation technique.

关键词： Cutting tools

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The Blood Flow of Prandtl Fluid Through a Tapered Stenosed Arteries in Permeable Walls with Magnetic Field

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Communications in Theoretical Physics 2015年第3期63卷 353-358页

作者： R.Ellahi S.U.Rahman S.Nadeem K.Vafai Department of Mechanical Engineering University of California Riverside Department of Mathematics and Statistics Faculty of Basic Applied Sciences International Islamic University Department of Mechatronics University of Engineering and Technology TexilaChakwal Campus Department of Mathematics Quaid-i-Azam University

This Communication deals with the blood flow of Prandtl fluid through a tapered stenosed arteries having permeable *** governing equations of two-dimensional Prandtl fluid model are modelled in cylindrical *** highly nonlinear equations are simplified with the help of non-dimensional variables under the assumption of mild *** solution of reduced nonlinear equation subject to boundary condition of porous walls having the effects of Darcy's number and slip parameter are computed analytically with the help of perturbation *** of emerging parameters such as impedance A,slip parameter a,stenosis height 6,magnetic parameter and stress component Srz on velocity are illustrated *** streamlines have also been presented to discuss the trapping bolus discipline.

关键词： Prandtl fluid magnetic field blood flow tapered stenosed arteries permeable walls analytical solutions

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Modelling maintenance practice of production plant using the delay-time concept

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IMA Journal of Management mathematics 1995年第1期6卷 67-83页

作者： Christer, A.H. Wang, W. Baker, R.D. Sharp, J. Centre for OR and Applied Statistics University of Salford United Kingdom Department of Aeronautical and Mechanical Engineering University of Salford United Kingdom

In this paper we present a study carried out for a copper products manufacturing company, developing and applying the delay-time modelling technique to model and thus optimize preventive maintenance (PM) of the plant. A key machine in the plant is used to illustrate the modelling process and management *** parameter values of the process by which faults arise and of the delay-time distribution are estimated from maintenance record data of failures and faults found at PM, using the method of maximum likelihood. A test of the model fit to data is carried out. Based upon the estimated model parameters and the failure delay time, an inspection model is proposed to describe the relationship between the total downtime and the PM interval. © 1995 Oxford University Press.

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Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

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applied mathematics and Mechanics(English Edition) 2018年第2期39卷 169-180页

作者： Xinyin ZOU Xiang QIU Jianping LUO Jiahua LI P.N.KALONI Yulu LIU School of Mechanical Engineering Shanghai Institute of Technology School of Science Shanghai Institute of Technology College of Urban Construction and Safety Engineering Shanghai Institute of Technology Department of Mathematics and Statistics University of Windsor Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman （J-S） fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.

关键词： Johnson-Segalman (J-S) fluid slowly varying pipe double perturbationstrategy velocity distribution

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Robust multi-task regression with grossly corrupted observations 15

Robust multi-task regression with grossly corrupted observat...

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15th International Conference on Artificial Intelligence and statistics, AISTATS 2012

作者： Xu, Huan Leng, Chenlei Department of Mechanical Engineering National University of Singapore Singapore Department of Statistics and Applied Probability National University of Singapore Singapore

We consider the multiple-response regression problem, where the response is subject to sparse gross errors, in the high-dimensional setup. We propose a tractable regularized M-estimator that is robust to such error, where the sum of two individual regularization terms are used: the first one encourages row-sparse regression parameters, and the second one encourages a sparse error term. We obtain non-asymptotical estimation error bounds of the proposed method. To the best of our knowledge, this is the first analysis of the robust multi-task regression problem with gross errors. © Copyright 2012 by the authors.

关键词： Error analysis

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Cross-thermal streamline patterns and heat transfer in EP-nanofluids: a neural network approach with uncertainty analysis

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Case Studies in Thermal engineering 2025年 70卷

作者： Umar Farooq Ali Alshamrani M. Mahtab Alam Khadija Rafique Department of Mathematics COMSATS University Islamabad Pakistan Department of Mechanical Engineering College of Engineering Taif University P.O. Box 11099 Taif 21944 Saudi Arabia Department of Basic Medical Sciences College of Applied Medical Science King Khalid University Abha Saudi Arabia Department of Mathematics and Statistics Hazara University Mansehra Pakistan

This study presents a mathematical model of tissue adhesive based on stretched surfaces with emphasis on flow and thermal characteristics using artificial neural networks with a Levenberg-Marquardt backpropagation scheme (ANN-LMBS). The model investigates Eyring-Powell nanofluids (EP-NF) with ferric oxide ( F e 2 O 3 ) and silicon dioxide ( S i O 2 ) nanoparticles dispersed in water ( H 2 O ) , focusing on magnetic strength, Darcy drag, viscous dissipation, joule heating and thermal radiation effects. Validation consists of 70 % training, 15 % testing, and 15 % validation. This dataset covers four scenarios and nine EP-NF cases. The resulting domain is divided into 300 grid points for velocity and temperature profiles. The ANN-LMBS model demonstrated excellent robustness in terms of accuracy, precision, and convergence, as verified by error histograms and regression optimization. The main findings include: as M increases from 1 to 4, the Nusselt number decreases by 2.48 %–2.16 % for F e 2 O 3 and by 1.71 %–1.54 % for S i O 2 ; as R d increases from 0.3 to 1.2, the Nusselt number increases by −10.17 % to −6.52 % for F e 2 O 3 and by −10.19 % to −6.58 % for S i O 2 ; The influence of porosity ( ϵ ) and Eckert number ( E c ) is less pronounced but still noticeable (∼3 % and 1.2 %, respectively). The governing equations, solved numerically via non-similarity transformation and the BVP4C algorithm, align with boundary conditions across all scenarios, with uncertainty analysis confirming solution robustness. Cross-thermal streamline patterns further enhance insights into flow dynamics, underscoring the model's potential in biomedical applications.

关键词： Cross-thermal streamline Eyring-powell nanofluid ANN MATLAB Non-similar analysis

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Streamlining the teaching of unsteady heat conduction in regular solid bodies with heat convection to neighboring fluids

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International Journal of mechanical engineering Education 2017年第3期45卷 245-259页

作者： Campo, Antonio Chang, Jane Y. Department of Mechanical Engineering University of Texas San AntonioTX78249 United States Department of Applied Statistics and Operations Research Bowling Green State University Bowling GreenOH United States

In the analysis of unidirectional, unsteady heat conduction for simple solid bodies (large slab, long cylinder and sphere), the modern tendency adopted by authors of heat transfer textbooks is to calculate the temperatures and total heat transfer with "one-term" series accounting for the proper eigenquantities, which are expressed in terms of the Biot number. The supporting information is available in tables for a large slab, a long cylinder and a sphere. To avoid linear and quadratic interpolation for the Biot numbers listed in the tables, the goal of the present study is to use regression analysis in order to develop compact correlation equations for the first eigenvalues, the first eigencontants and the first constants (for the total heat transfer) varying with the Biot number for large slabs, long cylinders and spheres, all in the ample range 0 © SAGE Publications.

关键词： Spheres

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