谈工科理论力学教学中数学工具的应用

分析了当前理论力学教学由于缺乏对数学工具的充分应用而带来问题,提出在理论力学教学中应充分利用矢量、矩阵等数学工具,重视对学生计算机数值求解方法的训练. 在具体的求解过程中选用MATLAB或Maple软件作为数值计算的工具.     

Mathematical model of two-phase fluid nonlinear flow in low-permeability porous media with applications

IntroductionItisasuccessfulexampleinadevelopmentstoryofscienceandtechnologyformechanicsoffluidsinporousmediatocombinewithengineeringtechnology .Fieldsinfluencedbythemechanicsinvolveddevelopmentofoil_gasandgroundwaterresources,controlonseawaterintrusionandsubsidenceandgeologichazards,geotechnicalengineeringandbioengineering ,andairlineindustry[1～ 7].Aproblemonnonlinearflowinlow_permeabilityporousmediaisbutonlyabasiconeindifferentkindsofengineeringfields,butalsooneoffrontlineresearchfieldsofmod…     

On optimization of many-revolution low-thrust orbit transfers: Part 1

The paper proposes a numerical approach to the problem of optimal control of low-thrust spacecraft in a strong central gravity field. The approach employs the solution of the averaged equations of optimal motion. For an optimal variable-thrust maneuver, it is shown that quasioptimal trajectories are close to the averaged ones. It is established that in the case of constant thrust, the averaged solutions can be used as a satisfactory first approximation for finding a quasioptimal solution by minimizing the discrepancy at the right end of the trajectory __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 110–119, July 2008.     

A shape optimisation method of a body located in adiabatic flows

The purpose of this study is to derive an optimal shape of a body located in adiabatic flow. In this study, we use the equation of motion, the equation of continuity and the pressure–density relation derived from the Poisson’s law as the governing equation. The formulation is based on an optimal control theory in which a performance function of fluid force is taken into consideration. The performance function should be minimised satisfying the governing equations. This problem can be solved without constraints by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimisation technique, the Galerkin finite element method is used as a spatial discretisation and the implicit scheme is used as a temporal discretisation to solve the state equations. The mixed interpolation, the bubble function for velocity and the linear function for density, is employed as the interpolation. The optimal shape is obtained for a body in adiabatic flows.     

The correlation of engineering data reconsidered

Rowe¹ highlights some of the pitfalls resulting from correlating engineering data by the use of dimensionless groups. He illustrates his points elegantly by ‘correlating’ sets of data taken from random number tables. Although Rowe's paper is over 20 years old, errors of the type he reveals are still made, resulting in his paper being cited regularly. Yet, contrary to his advice, dimensionless groups and log—log plots are universally used. This may be attributable to custom, convenience or ignorance of a feeling or conviction that Rowe's views are untenable. It is appropriate, therefore, to re-examine the pitfalls Rowe revealed and to study his suggestions for avoiding them. A number of errors and misconceptions have been identified and an alternative approach is recommended. Use of dimensionless groups in the presentation of heat transfer and fluid flow data can lead to the development of spurious correlations, unless great care is exercised. This paper considers the pitfalls and discusses techniques for their avoidance.     

On the use of characteristic‐based split meshfree method for solving flow problems

This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time‐dependent and steady‐state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. Copyright © 2007 John Wiley & Sons, Ltd.     

基于CFD-DEM的高炉风口回旋区形状和传热特性数值模拟研究

采用计算流体力学-离散单元法(CFD-DEM)耦合方法,对高炉风口回旋区进行了数值模拟研究。首先通过与实验结果对比,验证了CFD-DEM模型的正确性;然后考察了不同气速对风口回旋区形状和传热特性及颗粒接触的影响。数值模拟结果表明:风口回旋区的大小和形状均受气速影响较大,在较大进气速度下,颗粒受到的曳力大于颗粒间的摩擦阻力并破坏颗粒间的桥力,形成较大尺寸的回旋区;且颗粒之间接触力较小,形成较大的空隙结构,更有利于热气体向周围扩散以强化传热。目前考察的三种气速结果表明:当气速为11m/s时,热量向下方传递速度最快;当气速为13m/s时,热量向上方传递速度最快;而当气速为15m/s时,热量向右方传递速度最快;此外,气速越大流态化越明显,颗粒间接触越少,接触力也越小。     

MHD flow and heat transfer from continuous surface in uniform free stream of non-Newtonian fluid

An analysis is carried out to study the steady flow and heat transfer charac- teristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid.The flow is subjected to a transverse uni- form magnetic field.The constitutive equation of the fluid is modeled by that for a second grade fluid.Numerical results are obtained for the distribution of velocity and temperature profiles.The effects of various physical parameters like viscoelastic param- eter,magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.     

Effects of slip,viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.     

On shock layer method for the hypersonic flow problems

Chernyi’s series method[1] is not proper for the case that(γ-l)/(γ+l)<<2/(γ+1)×M²sin²β (γ=c_p/c_v-adiabatic index number, M-Much number, β-shock incidence). In this paper, we only suppose that in the neighbour of the shock, there exists a shock layer in which the density of the gas is very big, but we do not remove the case that (γ-1)/(γ+1)<<2/(γ+1)M²sin²β.     

Mathematical simulation of conjugate mixed convection in a rectangular region with a heat source

Conjugate convective-conductive heat transfer in a rectangular region with forced flow and a heat source is simulated numerically. Distributions of the thermal and hydrodynamic characteristics of the flow regimes studied are obtained. The evolution of the process analyzed is shown. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 69–81, November–December, 2008