A comparative assessment of fluid flow and heat transfer parameters in laminar flow around a circular cylinder and a sphere

Theoretical studies have been carried out for a comparative assessment of hydrodynamic boundary layer thickness, displacement thickness and shear stress at the wall for laminar flow around a circular cylinder and a sphere with the help of the approximate method due to Karman and Pohlhausen for two dimensional flow and the method as applied to bodies of revolution based on the work of F. W. Scholkemeier, respectively. Thermal boundary layer thickness and Nusselt number have been evaluated around the surface of the solids. Comparison is made with available solutions. The graphical presentation of the results depicts a concise and relative assessment of fluid flow and heat-transfer parameters for flow around cylinder and sphere.     

A review of flow-induced noise from finite wall-mounted cylinders

This paper reviews previous studies on the flow around and flow-induced noise produced by a finite wall-mounted cylinder (FWMC) of circular and square cross section. The flow around a square FWMC is somewhat understood. Conversely, the flow around a circular FWMC is not well understood, particularly because of the phenomenon of spanwise cellular shedding. The effect of the aspect ratio (the ratio of cylinder span to diameter) on the near wake structure has been most extensively studied in the literature. However, the effect of the height of the incoming boundary layer on the near wake structure has not been comprehensively investigated and is therefore unclear, despite it being identified as a major influencing parameter on the development of the wake. Similarly, only a few studies have been conducted on the flow-induced noise of FWMCs and there is a general lack of data on the flow-induced noise characteristics and mechanisms of an FWMCs in cross flow. Nevertheless, the amalgamation of the limited data set has led to several noise generation hypotheses: (1) lower frequency tonal noise generation is due to the development of separate structures along the span of both circular and square FWMCs and (2) that increasing the boundary layer thickness will promote tonal noise generation.     

MODELLING AND CALCULATION OF THE TURBULENT BOUNDARY LAYER ON A ROTATING CYLINDER SURFACE WITH STRONG SUCTION 1)

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.     

An experimental study on the effects of uniform injection through one perforated surface of a square cylinder on some aerodynamic parameters

It is well known that injection/suction (transpiration) through a perforated surface is an efficient way of influencing the characteristics of a turbulent boundary layer. Injection application creates a thicker boundary layer on a flat plate and it thus decreases drag. In aeronautical applications, suction is frequently used to delay boundary layer separation. This paper presents an experimental study on the effects of uniform injection through one perforated surface of a square cylinder on the pressure distribution and drag coefficient in a two-dimensional turbulent flow. For this purpose, surface pressure measurements around a square cylinder have been performed at three different Reynolds numbers in a wind tunnel. The parameters taken into account were injection rate, position of perforated surface (i.e., front, top, and rear), and pressure coefficient and drag coefficient. The results show that variation in pressure coefficient around the square cylinder and drag coefficient were influenced by the position of perforated surface and by injection rate.     

强吸气旋转圆筒壁面湍流边界层建模及计算

提出了湍流边界层的一种简单、快速计算方法,用以求解强吸气作用下旋转圆筒表面边界层流动.首先,理论分析了同心圆筒间的旋转流体运动,外筒静止、内筒旋转且为多孔吸气条件.强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动,基于这一事实得到了周向速度分布的解析表达式.其次,通过引入新参数扩展Cebeci-Smith代数湍流模型,使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素.针对这些因素的综合影响,采用解析修正和经验参数对模型进行调整.同时,基于Reynolds应力湍流模型的仿真结果,校准代数湍流模型中的经验参数.最后,给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法,该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况.计算了不同旋转速度和吸气强度组合工况下的边界层流动,其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近.并且表明,当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时,该方法也再现了相同初始条件下的层流边界层.     

Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall

The flow around a circular cylinder placed close to a horizontal plane wall was investigated experimentally. Fluctuations of lift and drag of the cylinder and wall interference effects were studied in terms of the gap height between the cylinder and wall and the thickness of the turbulent wall boundary layer. The fluctuating fluid forces acting on the cylinder sharply increased, and the regular vortex shedding, i.e. Kárman vortex streets, started to form beyond a critical gap height. The formation of Kárman vortex streets was abruptly interrupted when the bottom of the cylinder came in contact with the outer layer of the boundary layer developed on the wall. This critical gap height correlated well with the thickness of the boundary layer.     

圆柱表面包覆电磁场消涡与增涡实验研究

利用电磁体积力改变流体边界层的结构，用作用于流体边界层上的电磁力进行消涡与增涡控制。交替分布的电极和磁极包覆在圆柱体的表面置于电介质溶液中，简单调整电磁力的时间与空间分布可以方便地控制圆柱绕流的形态。通过理论分析和数值模拟确定了实验控制的关键参数，实现了电磁力消涡和增涡的连续控制，电磁力作用下的圆柱绕流的分离点可以在前驻点和后驻点之间变动。     

流体边界层上电磁力的控制效应研究

利用作用于流体边界层上的电磁体积力改变流体边界层的结构，研究电磁力对流场的控制 作用效果. 电极与磁极交替分布的电磁场激活板包覆在圆柱体表面置于流动的电解质溶液 中，产生的电磁力沿圆柱体表面分布，可以改变流体边界层的结构，从而实现对流场的控制. 用电磁屏蔽和时域控制的方法调整电磁力的时空分布参数，圆柱绕流分离点可以在前驻点和 后驻点之间变动，产生不同的控制效果. 流体边界层上的电磁力能连续控制圆柱绕流、尾流 涡街的形态. 正向电磁力具有较好的消涡、减震和减阻控制效应. 反向电磁力具有明显的增 涡控制效应，具有较强的制动控制效应，此时圆柱体表面涡量分布的对称性和稳定性被破坏.     

Mode i and mixed mode fields with incomplete crack tip plasticity

Plane strain slip line fields, in which plasticity does not fully surround the crack tip have been developed for mode I and mixed mode I\II cracks under contained yielding. Analytical solutions have been assembled using slip line theory for the plastic sectors and semi-infinite wedge solutions for the elastic sectors. These solutions are compared with finite element solutions based on modified boundary layer formulations. The analytical solutions agree well with numerical solutions, and form a family of fields with incomplete plasticity around the crack tip.     

基于格子Boltzmann方法的粘弹性流体圆柱绕流分析

将光滑界面法引入到格子Boltzmann方法中分析粘弹性流体绕流问题,分别采用单松弛模型和对流扩散模型求解运动方程和Oldroyd-B本构方程,针对圆形和椭圆内部边界条件,给出连续界面插值函数,在此基础上,运用光滑界面法将内部边界转换为作用力项施加到演化方程中。首先分析圆柱绕流问题,给出不同材料参数情况下的流场分布和阻力系数计算结果,比较发现与宏观数值模拟结果相吻合。将模型拓展到绕椭圆流动中,分析椭圆形状和材料参数对粘弹性流体绕柱流的影响,发现随着椭圆长轴与短轴比值的增加和维森伯格数的增加,阻力系数逐渐下降,并且长短轴比对迭代收敛有较大影响。     

A viscoplastic strain gradient analysis of materials with voids or inclusions

A finite strain viscoplastic nonlocal plasticity model is formulated and implemented numerically within a finite element framework. The model is a viscoplastic generalisation of the finite strain generalisation by Niordson and Redanz (2004) [Journal of the Mechanics and Physics of Solids 52, 2431–2454] of the strain gradient plasticity theory proposed by Fleck and Hutchinson (2001) [Journal of the Mechanics and Physics of Solids 49, 2245–2271]. The formulation is based on a viscoplastic potential that enables the formulation of the model so that it reduces to the strain gradient plasticity theory in the absence of viscous effects. The numerical implementation uses increments of the effective plastic strain rate as degrees of freedom in addition to increments of displacement. To illustrate predictions of the model, results are presented for materials containing either voids or rigid inclusions. It is shown how the model predicts increased overall yield strength, as compared to conventional predictions, when voids or inclusions are in the micron range. Furthermore, it is illustrated how the higher order boundary conditions at the interface between inclusions and matrix material are important to the overall yield strength as well as the material hardening.     

Design sensitivity analysis for parameters affecting geometry,elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method

This paper presents a design sensitivity analysis method by the consistent tangent operator concept-based boundary element implicit algorithm. The design variables for sensitivity analysis include geometry parameters, elastic–viscoplastic material parameters and boundary condition parameters. Based on small strain theory, Perzyna’s elastic–viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis. The related elastic–viscoplastic radial return algorithm and the formula of elastic–viscoplastic consistent tangent operator are derived and discussed. Based on the direct differentiation approach, the incremental boundary integral equations and related algorithms for both geometric and elastic–viscoplastic sensitivity analysis are developed. A 2D boundary element program for geometry sensitivity, elastic–viscoplastic material constant sensitivity and boundary condition sensitivity has been developed. Comparison and discussion with the results of this paper, analytical solution and finite element code ANSYS for four plane strain numerical examples are presented finally.     

A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part II: Finite deformations

This paper generalizes to finite deformations our companion paper [Gurtin, M.E., Anand, L., 2004. A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. Journal of the Mechanics and Physics of Solids, submitted]. Specifically, we develop a gradient theory for finite-deformation isotropic viscoplasticity in the absence of plastic spin. The theory is based on the Kröner–Lee decomposition F = F^eF^p of the deformation gradient into elastic and plastic parts; a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:

• the microstresses to depend on D^p, the gradient of the plastic stretching,

• the free energy ψ to depend on the Burgers tensor G = F^pCurlF^p.

The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for F^p. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the microstresses are partially energetic, and this, in turn, leads to backstresses and (hence) Bauschinger-effects in the flow rule. The typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with viscoplastic flow, and, as an aid to numerical solution, a weak (virtual power) formulation of the nonlocal flow rule is derived. Finally, the dependences of the microstresses on D^p are shown, analytically, to result in strengthening and possibly weakening of the body induced by viscoplastic flow.     

Interfacial energy effects within the framework of strain gradient plasticity

In the framework of strain gradient plasticity, a solid body with boundary surface playing the role of a dissipative boundary layer endowed with surface tension and surface energy, is addressed. Using the so-called residual-based gradient plasticity theory, the state equations and the higher order boundary conditions are derived quite naturally for both the bulk material and the boundary layer. A phenomenological constitutive model is envisioned, in which the bulk material and the boundary layer obey (rate independent associative) coupled plasticity evolution laws, with kinematic hardening laws of differential nature for the bulk material, but of nondifferential nature for the layer. A combined global maximum dissipation principle is shown to hold. The higher order boundary conditions are discussed in details and categorized in relation to some peculiar features of the boundary surface, and their basic role in the coupling of the bulk/layer plasticity evolution laws is pointed out. The case of an internal interface is also studied. An illustrative example relating to a shear model exhibiting energetic size effects is presented. The theory provides a unified view on gradient plasticity with interfacial energy effects.     

考虑法向压力梯度的三维旋转边界层计算

本文以量级分析为基础,建立了一般曲线坐标系上的三维旋转边界层方程。对旋转在边界层中的影响进行分析之后,提出了一个能够处理壁面法向压力梯度不为零问题的压力梯度迭代方法。在传统的Box法的基础上发展了一套完整的求解三维旋转边界层的方法和程序,并对螺旋面、压气机转子叶面以及圆柱面上的旋转边界层进行了计算,与他人的计算和实验的对比分析表明,该方法和程序是正确的,可用于求解任意几何物面上的三维旋转边界层。     

A spatial laminar boundary layer on a streamline in conical external flow of a uniform gas in the absence of sources and sinks

Theoretical study of a three-dimensional laminar boundary layer is a complex problem, but it can be substantially simplified in certain particular cases and even reduced to the solution of ordinary differential equations.One such particular case is the flow of a compressible gas on a streamline in conical external flow. The case is of considerable practical importance because the local heat fluxes may take extremal values on such lines.Such flow, except for the conical case, has been examined [1–4], and an approximate method has been given [1] on the basis of integral relationships and a special form for the approximating functions. A numerical solution has been given [2, 3] for such flow around an infinite cylinder. It was assumed in [1–3] that the Prandtl number and the specific heats were constant, and that the dynamic viscosity was proportional to temperature. Heat transfer has been examined [4] near a cylinder exposed to a flow of dissociated air.Here we give results from numerical solution of a system of ordinary differential equations for the flow of a compressible gas in a laminar boundary layer on streamlines in conical external flow, with or without influx or withdrawal of a homogeneous gas. It is assumed that the gas is perfect and that the dynamic viscosity has a power-law temperature dependence.     

Stress intensity factors around a cylindrical crack in an interfacial zone in composite materials

Axisymmetric stresses around a cylindrical crack in an interfacial cylindrical layer between an infinite elastic medium with a cylindrical cavity and a circular elastic cylinder made of another material have been determined. The material constants of the layer vary continuously from those of the infinite medium to those of the cylinder. Tension surrounding the cylinder and perpendicular to the axis of the cylinder is applied to the composite materials. To solve this problem, the interfacial layer is divided into several layers with different material properties. The boundary conditions are reduced to dual integral equations. The differences in the crack faces are expanded in a series so as to satisfy the conditions outside the crack. The unknown coefficients in the series are solved using the conditions inside the crack. Numerical calculations are performed for several thicknesses of the interfacial layer. Using these numerical results, the stress intensity factors are evaluated for infinitesimal thickness of the layer.     

Experimental results of pure and simultaneous heat and mass transfer by free convection about a vertical cylinder for Pr=0.71 and Sc=0.63

In this paper experimental results are given concerning stationary heat and mass transfer in the laminar boundary layer of a vertical cylinder placed in still air. The combined effect is considered as well as the two separate effects. Measurements are carried out on heat transfer and evaporation of water. Results are in close agreement with the classical free convection boundary layer theory for a vertical flat plate, if only a small cylinder correction is applied.     

变高度圆柱诱导的激波边界层干扰

采用分区方法及Ｒｏｅ三阶流通量差分分裂格式求解雷诺平均Ｎ－Ｓ方程,湍流附加黏性系数用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ模型计算,数值模拟了高超声速条件下变高度圆柱诱导的激波边界层层干扰,其流场的主要特性均与实验结果一致或规律相同,结果清晰地展示了流场结构以及气动载荷分布随柱高度的变化特征,产说明激波碰撞和旋涡运动都可能导致飞行器表面局部气动载荷的增加。