On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.

Surface-ray tracing on hybrid surfaces of revolution for UTD mutual coupling analysis

An angle invariance property based on Hertz's principle of particle dynamics is employed to facilitate the surface-ray tracing on nondevelopable hybrid quadric surfaces of revolution (h-QUASOR's). This property, when used in conjunction with a Geodesic Constant Method, yields analytical expressions for all the ray-parameters required in the UTD formulation. Differential geometrical considerations require that some of the ray-parameters (defined heuristically in the UTD for the canonical convex surfaces) be modified before the UTD can be applied to such hybrid surfaces. Mutual coupling results for finite-dimensional slots have been presented as an example on a satellite launch vehicle modeled by general paraboloid of revolution and right circular cylinder.

Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body

Boundary layers are subject to favorable and adverse pressure gradients because of both the temporal and spatial components of the pressure gradient. The adverse pressure gradient may cause the flow to separate. In a closed loop unsteady tunnel we have studied the initiation of separation in unsteady flow past a constriction (bluff body) in a channel. We have proposed two important scalings for the time when boundary layer separates. One is based on the local pressure gradient and the other is a convective time scale based on boundary layer parameters. The flow visualization using a dye injection technique shows the flow structure past the body. Nondimensional shedding frequency (Strouhal number) is calculated based on boundary layer and momentum thicknesses. Strouhal number based on the momentum thickness shows a close agreement with that for flat plate and circular cylinder.

Control of vortex shedding at moderate Reynolds numbers

The suppression method of vortex shedding from a circular cylinder has been studied experimentally in the Reynolds number range from 300 to 1600. The test is performed in a water channel. The model cylinder is 1 cm in diameter and 38 cm in length. A row of small rods of 0.18 cm in diameter and 1.5 cm in length are perpendicularly connected to the surface of the model cylinder and distributed along the meridian, The distance between the neighboring rods and the angle of attack of the rods can be changed so that the suppression effect on vortex shedding can be adjusted. The results show that vortex shedding can be suppressed effectively if the distance between the neighboring rods is smaller than 3 times and the cylinder diameter and the angle of attack is in the range of 30degreesless than or equal tobeta<90&DEG;.

Computation of Viscous Incompressible Flow using Pressure Correction Method on Unstructured Chimera Grid

In this paper, a pressure correction algorithm for computing incompressible flows is modified and implemented on unstructured Chimera grid. Schwarz method is used to couple the solutions of different sub-domains. A new interpolation to ensure consistency between primary variables and auxiliary variables is proposed. Other important issues such as global mass conservation and order of accuracy in the interpolations are also discussed. Two numerical simulations are successfully performed. They include one steady case, the lid-driven cavity and one unsteady case, the flow around a circular cylinder. The results demonstrate a very good performance of the proposed scheme on unstructured Chimera grids. It prevents the decoupling of pressure field in the overlapping region and requires only little modification to the existing unstructured Navier–Stokes (NS) solver. The numerical experiments show the reliability and potential of this method in applying to practical problems.

Elastodynamic erosion of thermal barrier coatings

The finite element method is used to analyze the elastodynamic response of a columnar thermal barrier coating due to normal impact and oblique impact by an erosive particle. An assessment is made of the erosion by crack growth from preexisting flaws at the edge of each column: it is demonstrated that particle impacts can be sufficiently severe to give rise to columnar cracking. First, the transient stress state induced by the normal impact of a circular cylinder or a sphere is calculated in order to assess whether a 2D calculation adequately captures the more realistic 3D behavior. It is found that the transient stress states for the plane strain and axisymmetric models are similar. The sensitivity of response to particle diameter and to impact velocity is determined for both the cylinder and the sphere. Second, the transient stress state is explored for 2D oblique impact by a circular cylindrical particle and by an angular cylindrical particle. The sensitivity of transient tensile stress within the columns to particle shape (circular and angular), impact angle, impact location, orientation of the angular particle, and to the level of friction is explored in turn. The paper concludes with an evaluation of the effect of inclining the thermal barrier coating columns upon their erosion resistance. © 2011 The American Ceramic Society.

A Pressure-Correction Method And Its Applications On An Unstructured Chimera Grid

In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios of U-m to U-0 are of O(10(-1)), O(10) and O(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re = 10(2), 10(3) and 3 x 10(3) are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Karman vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method.

Domain decomposition hybrid method for numerical simulation of bluff body flows:theoretical model and application

The discrete vortex method is not capable of precisely predicting the bluff body flow separation and the fine structure of flow field in the vicinity of the body surface. In order to make a theoretical improvement over the method and to reduce the difficulty in finite-difference solution of N-S equations at high Reynolds number, in the present paper, we suggest a new numerical simulation model and a theoretical method for domain decomposition hybrid combination of finite-difference method and vortex method. Specifically, the full flow. field is decomposed into two domains. In the region of O(R) near the body surface (R is the characteristic dimension of body), we use the finite-difference method to solve the N-S equations and in the exterior domain, we take the Lagrange-Euler vortex method. The connection and coupling conditions for flow in the two domains are established. The specific numerical scheme of this theoretical model is given. As a preliminary application, some numerical simulations for flows at Re=100 and Re-1000 about a circular cylinder are made, and compared with the finite-difference solution of N-S equations for full flow field and experimental results, and the stability of the solution against the change of the interface between the two domains is examined. The results show that the method of the present paper has the advantage of finite-difference solution for N-S equations in precisely predicting the fine structure of flow field, as well as the advantage of vortex method in efficiently computing the global characteristics of the separated flow. It saves computer time and reduces the amount of computation, as compared with pure N-S equation solution. The present method can be used for numerical simulation of bluff body flow at high Reynolds number and would exhibit even greater merit in that case.

用非结构网格研究旋转振荡圆柱绕流

研究了雷诺数Re=200,1000,线速度比α=0.5,2.0,4.0,强迫振荡频率fs=0.1～2.0情况下的旋转振荡圆柱绕流问题.通过基于非结构同位网格有限体积法对Navier-Stokes方程进行数值求解.对流项、扩散项和非恒定项的离散格式均具有二阶精度,利用SIMPLE算法处理压力-速度耦合.计算得到了作用力系数随不同控制参数的变化规律.通过对升力系数的频谱分析得到自然脱落频率和强迫振荡频率下的作用力振幅.通过对不同频率作用力幅值的分析,得到频率之间的竞争关系,进而定量地给出了不同尾迹涡脱落模式的分区图.

圆柱振荡绕流的三维不稳定性研究

通过数值求解三维不可压缩Navier-Stokes方程，研究了振荡圆柱绕流的旋涡不稳定性。研究表明，在一定的参数范围内，由于旋涡不稳定性，振荡流出由二维演化成三维流动，并沿圆柱轴向形成交错排列的三维涡结构。数值计算合理地预测了三维涡结构的空间失稳波长，并与实验测试值相符很好。文中还进一步研究了圆柱的受力特性，通过求解Morison方程，计算了圆柱的阻力和惯性力特性，其计算结果与已有的实验数据相吻合。

Generalization of the JTZ model to open plane wakes

The JTZ model [C. Jung, T. T¶el and E. Ziemniak, Chaos 3, (1993) 555], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is ex- tended here to describe an open plane wake without the con¯ned nar- row channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and ex- perimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the in- teraction between small spherical particles and vortices in an extended JTZ model °ow is studied. It is shown that the particle size has signif- icant in°uences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.

Vortex dislocations in wake-type flow induced by spanwise disturbances

Vortex dislocations in wake-type flow induced by three types of spanwise disturbances superimposed on an upstream velocity profile are investigated by direct numerical simulations. Three distinct modes of vortex dislocations and flow transitions have been found. A local spanwise exponential decay disturbance leads to the appearance of a twisted chainlike mode of vortex dislocation. A stepped spanwise disturbance causes a streamwise periodic spotlike mode of vortex dislocation. A spanwise sinusoidal wavy disturbance with a moderate waviness causes a strong unsteadiness of wake behavior. This unsteadiness starts with a systematic periodic mode of vortex dislocation in the spanwise direction followed by the spanwise vortex shedding suppressed completely with increased time and the near wake becoming a steady shear flow. Characteristics of these modes of vortex dislocation and complex vortex linkages over the dislocation, as well as the corresponding dynamic processes related to the appearance of dislocations, are described by examining the variations of vortex lines and vorticity distribution. The nature of the vortex dislocation is demonstrated by the substantial vorticity modification of the spanwise vortex from the original spanwise direction to streamwise and vertical directions, accompanied by the appearance of noticeable vortex branching and complex vortex linking, all of which are produced at the locations with the biggest phase difference or with a frequency discontinuity between shedding cells. The effect of vortex dislocation on flow transition, either to an unsteady irregular vortex flow or suppression of the Kaacutermaacuten vortex shedding making the wake flow steady state, is analyzed. Distinct similarities are found in the mechanism and main flow phenomena between the present numerical results obtained in wake-type flows and the experimental-numerical results of cylinder wakes reported in previous studies.

Phase variations and phase shift in a TE011 mode microwave cavity used for in a miniature Rb fountain frequency standard

It is the first time in China that the phase variations and phase shift of microwave cavity in a miniature Rb fountain frequency standard are studied, considering the effect of imperfect metallic walls. Wall losses in the microwave cavity lead to small traveling wave components that deliver power from the cavity feed to the walls of cavity. The small traveling wave components produce a microradian distribution of phase throughout the cavity ity, and therefore distributed cavity phase shifts need to be considered. The microwave cavity is a TE011 circular cylinder copper cavity, with round cut-hole of end plates (14mm in diameter) for access for the atomic flux and two small apertures in the center of the side wall for coupling in microwave power. After attenuation alpha is calculated, field variations in cavity are solved. The field variations of the cavity are given. At the same time, the influences of loaded quality factor QL and diameter/height (2a/d) of the microwave cavity on the phase variations and phase shift are considered. According to the phase variation and phase shift of microwave cavity we select the parameters of cavity, diameter 2a = 69.2mm, height d = 34.6mm, QL = 5000, which will result in an uncertainty delta(Delta f / f0 ) < 4.7 x 10(-17) and meets the requirement for the miniature Rb fountain frequency standard with accuracy 10(-15).