Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model

In this paper, we proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.     

Linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model

Double diffusive convection in a fluid-saturated rotating porous layer is studied when the fluid and solid phases are not in local thermal equilibrium, using both linear and nonlinear stability analyses. The Brinkman model that includes the Coriolis term is employed as the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. It is found that small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of thermal diffusion, solute diffusion, and rotation that causes the convection to set in through either oscillatory or finite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modified conductivity ratio, Lewis number, diffusivity ratio, Vadasz number, and Taylor number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study.     

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.     

Effect of rotation on ferromagnetic porous convection with a thermal non-equilibrium model

The effect of rotation on the onset of thermal convection in a horizontal layer of ferrofluid saturated Brinkman porous medium is investigated in the presence of a uniform vertical magnetic field using a local thermal non-equilibrium (LTNE) model. A two-field model for temperature representing the solid and fluid phases separately is used for energy equation. The condition for the occurrence of stationary and oscillatory convection is obtained analytically. The stability of the system has been analyzed when the magnetic and buoyancy forces are acting together as well as in isolation and the similarities as well as differences between the two are highlighted. In contrast to the non-rotating case, it is shown that decrease in the Darcy number Da and an increase in the ratio of effective viscosity to fluid viscosity Λ is to hasten the onset of stationary convection at high rotation rates and a coupling between these two parameters is identified in destabilizing the system. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient H _t are presented and compared with those computed numerically. Besides, the influence of magnetic parameters and also parameters representing LTNE on the stability of the system is discussed and the veracity of LTNE model over the LTE model is also analyzed.     

Plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic rotating half-spaces with two relaxation times

The present paper concentrates on the study of reflection and refraction characteristics of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic rotating half-spaces with different elastic and thermal properties. In this type of problem of orthotropic thermoelastic rotating medium, there are three types of plane waves quasi longitudinal (QL-) wave, quasi thermal (T-mode) wave and quasi transverse (QT-) wave, whose velocities depend on the angle of incidence, imperfection and rotation. The amplitude ratios of reflected waves to that of incident one in each case have been derived. Some special cases of boundaries, i.e. normal stiffness, transverse stiffness, thermal contact conductance, slip boundary and welded contact boundary have been deduced from an imperfect one. Effect of rotation on the amplitude ratios of different reflected and refracted waves with respect to incident QL-wave at different boundaries have been studied graphically. It is observed that thermal properties, imperfect boundary and rotation have significant effect on the propagation of waves.     

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated.     

Effect of rotation speed on the temperature of starter alternator machine

This paper presents a study on the effect of rotation speed on the temperature distribution of starter alternator machine. The effect of the outer conditions of the machine on its temperature is also studied. The numerical solution of the thermal model of the machine is solved by using a nodal approach during a numerical code (SAME). This code is established at our laboratory and is written by MATLAB. The results show that when the rotation speed of the machine increases, the temperature of the machine increases. They also show that increasing the rotation speed of the machine more than five times increases the power loss from the machine three times and the maximum temperature difference of the machine about 40 %.     

单轴旋转对惯导系统误差特性的影响

分析了单轴旋转惯导系统自动补偿的基本原理,对陀螺和加速度计常值漂移、安装误差、标度因数误差等因素在单轴旋转下的调制情况进行了研究。通过仿真分析了转动速度对各种误差的影响规律,指出了实际系统旋转速度和方式的选择要综合考虑陀螺的常值漂移和标度因数误差的影响。利用激光捷联惯导系统在实验室中进行了单轴旋转IMU实验,其定位精度优于1nm／24h。研究结果可以为单轴旋转惯导系统的进一步优化和工程设计提供理论参考。     

Throughflow and Quadratic Drag Effects on Thermal Convection in a Rotating Porous Layer

A linear stability analysis is implemented to study thermal convective instability in a horizontal fluid-saturated rotating porous layer with throughflow in the vertical direction. The modified Forchheimer-extended Darcy equation that includes the time-derivative and Coriolis terms is employed as a momentum equation. The criterion for the occurrence of direct and Hopf bifurcations is obtained using the Galerkin method. It is shown that if a Hopf bifurcation is possible it always occurs at a lower value of the Darcy?CRayleigh number than the direct bifurcation. Increase in the throughflow strength and inertia parameter is to decrease the domain of Prandtl number up to which Hopf bifurcation is limited but opposite is the trend with increasing Taylor number. The effect of rotation is found to be stabilizing the system, in general. However, in the presence of both rotation and Forchheimer drag a small amount of vertical throughflow as well as inertia parameter show some destabilizing effect on the onset of direct bifurcation; a result of contrast noticed when they are acting in isolation. The existing results in the literature are obtained as limiting cases from the present study.     

Rotating Brinkman–Lapwood Convection with Modulation

The purpose of this article is to analyze, theoretically, the effect of modulation on rotating Brinkman–Lapwood convection, i.e., buoyancy-driven convection in a sparse porous medium subjected to rotation. Darcy–Brinkman momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about an axis with non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. A linear stability analysis has been performed to find the critical Rayleigh number in modulated case. The effect of modulated rotation speed is found to have a stabilizing effect on the onset of convection for different values of modulation frequency and the other physical parameters involved.     

Fluid convection in a rotating porous layer under modulated temperature on the boundaries

The linear stability of thermal convection in a rotating horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation, using Brinkman’s model. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The combined effect of rotation, permeability and modulation of walls’ temperature on the stability of flow through porous medium has been investigated using Galerkin method and Floquet theory. The critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Taylor number, porous parameter and Prandtl number. It is found that both, rotation and permeability are having stabilizing influence on the onset of thermal instability. Further it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature.     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

Effect of the Velocity Mode of a Modulationally Rotating Ampoule on the Thermal Structure of a Melt in Growing Single Crystals by the Stockbarger Method FORENAME = V. É

The effect of the velocity mode of the ACRT on the thermal structure of a melt and the flow rates in it in growing single crystals by the Stockbarger method in ampoules of diameter 100 mm at values of the Taylor number Ta > 10⁸ is studied. Optimum conditions for mixing of the melt for trapezoidal modes of modulated rotation are found.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

Numerical investigation of natural convective motions in a rotating cube

On the basis of a numerical integration of the Navier-Stokes equations in the Boussinesq approximation, the natural thermal convection in a rotating cube heated from below is investigated for three values of the Rayleigh number. The effect of the rotation velocity on the establishment of various forms of convection flows is studied. The existence of several types of convection flows is noted. Each of the motions is realized on a specific range of the rotation velocity of the cube. The domains of existence of the different types are determined. The results obtained are compared with experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 53–60, July–August, 1995.     

NONLINEAR THERMAL ANALYSIS FOR THE INTER-SHAFT BEARING UNDER THE DYNAMIC LOAD 1)

中介轴承作为双转子系统高低压转子重要的支承部件,其内圈和外圈均随着低压转子和高压转子高速旋转, 其传热问题更加突出.本文研究中介轴承在非线性动载荷作用下的非线性热行为.基于双转子系统动力学响应定义中介轴承动载荷,考虑中介轴承的径向游隙、分数指数非线性和参数激励等非线性因素,中介轴承动载荷会出现跳跃和双稳态等非线性行为. 考虑润滑剂的黏温关系,根据Palmgren经验公式建立动载荷作用下中介轴承的热传递模型,通过数值求解得到中介轴承稳态温度,发现动载荷的非线性行为导致中介轴承温度出现跳跃和双稳态等非线性热行为.分析转速比、偏心距、中介轴承径向游隙、Hertz接触刚度和滚子数目对中介轴承温度及非线性热行为的影响,表明偏心距、径向游隙和刚度只影响非线性热行为,而转速比和滚子数目对两者都有重要影响. 本文研究表明,动载荷相较于静载荷更适合描述中介轴承的实际载荷,由于双转子系统具有非线性振动特性, 中介轴承的热行为也表现出复杂的非线性行为.     

动载荷作用下中介轴承的非线性热行为研究

中介轴承作为双转子系统高低压转子重要的支承部件,其内圈和外圈均随着低压转子和高压转子高速旋转, 其传热问题更加突出.本文研究中介轴承在非线性动载荷作用下的非线性热行为.基于双转子系统动力学响应定义中介轴承动载荷,考虑中介轴承的径向游隙、分数指数非线性和参数激励等非线性因素,中介轴承动载荷会出现跳跃和双稳态等非线性行为. 考虑润滑剂的黏温关系,根据Palmgren经验公式建立动载荷作用下中介轴承的热传递模型,通过数值求解得到中介轴承稳态温度,发现动载荷的非线性行为导致中介轴承温度出现跳跃和双稳态等非线性热行为.分析转速比、偏心距、中介轴承径向游隙、Hertz接触刚度和滚子数目对中介轴承温度及非线性热行为的影响,表明偏心距、径向游隙和刚度只影响非线性热行为,而转速比和滚子数目对两者都有重要影响. 本文研究表明,动载荷相较于静载荷更适合描述中介轴承的实际载荷,由于双转子系统具有非线性振动特性, 中介轴承的热行为也表现出复杂的非线性行为.      

旋转惯导系统中转轴方向对系统调制精度的影响

不同轴向的惯性器件误差在惯导系统中的误差传播特性不同,因此在旋转惯导系统中转动机构选择不同转轴方向对系统精度的调制效果不同。分析了在选择不同轴向作为旋转轴时对导航系统精度的影响,并根据转台转轴与机体系、惯性器件(IMU)系之间存在的夹角关系,将其分为两种方案进行讨论,转轴与IMU系存在夹角以及转轴与机体系存在夹角。通过分析,前者在调制效果上与传统的单轴旋转惯导系统相同,而后者会改变调制效果。在此基础上,进一步推导分析了第二种方案下不同转轴方向与系统定位精度之间的内在关系,提出了一种在长时间导航情况下的转轴方向选择方案,并进行了仿真验证。仿真结果表明,与传统单轴旋转惯导系统相比,该方案显著提高了系统的导航定位精度,对在不同情况下转台转轴方向的选择具有一定的工程应用参考价值。     

转动驱动圆角立方体颗粒有序堆积的离散元模拟

宏观颗粒体系的有序堆积研究可以为热系统中微观粒子的自组装提供研究模型,也有助于工业生产中提高颗粒材料的填充率.实验发现圆筒中的圆角立方体颗粒受容器往复旋转剪切作用会实现有序堆积.为探究旋转圆筒中立方体颗粒有序堆积过程的内部结构演化过程和动力学机理,采用超二次曲面方程构造了圆角立方体颗粒,基于离散元方法对旋转剪切作用下圆...     

Numerical investigation of viscous gas secondary flows in a rotating cylinder with sources and sinks

A source-sink model of secondary flow excitation in a rotating cylinder, which describes the interaction between a circulator and a rotating gas, is proposed for a nonlinear system of Navier-Stokes equations, and the results of a numerical calculation of the resulting circulating flows are presented. The modified Newton's method employed in the numerical solution makes use of regularizing perturbations to ensure its stability and convergence at low Ekman numbers and high rates of rotation of the cylinder. The combined effect of mechanical and thermal means of flow excitation and the influence of viscous energy dissipation are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–44, July–August, 1989.