Measurement and analysis of unsteady flow structures in rotor blade wakes

Time-variant data are obtained to investigate the exit flow field from a rotor in a research compressor. In the free-stream region, the instantaneous data are analogous to one another and to the ensemble averaged free-stream results. However, in the wake region, some of the instantaneous signals are similar to one another and to the ensemble averaged wake, but others differ significantly. These variations in the instantaneous data are interpreted and shown to be due to a vortex street structure in the wake. This is accomplished by: (1) developing a mathematical model of the rotor blade exit flow field based on a wake vortex street structure analogous to the unsteady flow field behind bluff bodies due to classical von Karman vortex shedding; and (2) correlating predictions of both the ensemble averaged and instantaneous rotor blade exit flow fields as well as the velocity probability density distributions from this vortex wake flow field model with the corresponding data. The correlation of the ensemble averaged rotor blade exit flow fields is very good and the flow angle distribution correlation excellent. The predicted instantaneous rotor blade exit flow field exhibits many of the flow features found in the data. Also, the probability density distributions for the data and the vortex wake flow field model are analogous to one another.List of symbols N number of rotor revolutions - S _w rotor blade wake width - S _x vortex core horizontal spacing - S _y vortex core vertical spacing - u velocity component parallel to vortex street motion - v velocity component normal to vortex street motion - W instantaneous relative velocity - W _i velocity induced by vortex street - W free-stream relative velocity - W _s velocity of vortex street - x coordinate parallel to vortex street motion - y coordinate normal to vortex street motion - free-stream relative flow angle - _inst instantaneous relative flow angle - vortex strength     

高速列车穿越有竖井隧道流场的特性研究

给出了高速列车穿越隧道压力波的三维粘性流场数值模拟过程,控制方程为三维粘性、可压缩、等熵和非定常流的Navier-Stokes方程,空间离散采用了中心有限体积法格式,时间采用预处理二阶精度多步后差分格式进行离散,对隧道壁面采用壁面函数处理。在模拟中考虑了竖井的位置、竖井的断面积、竖井的数目等因素对隧道内压力及压力梯度的影响。计算结果表明,竖井的存在改变了压缩波的波前形状,从而使得隧道内的压力变化的最大值降低,因而能够降低隧道内的压力梯度最大值,但它并不能延长压力上升的时间。     

Calculation of the hydrodynamic interaction of blade cascades with consideration for the diffusion of unsteady wakes

A semianalytical method was developed to calculate the hydrodynamic interaction of two blade cascades moving relative to one another. The potential perturbation of the flow by the cascades and the vortex perturbation due to blade edge wakes are taken into account. Along with the steady wakes caused by boundary layer separation from the blade cascades, allowance is made of the unsteady wakes separating from the blade trailing edges because of change in velocity circulation on them. The unsteady wakes are calculated with allowance for their diffusion in the presence of flow viscosity using approximate boundarylayer theory. The method is implemented as a program for calculating the unsteady hydrodynamic characteristics of blade cascades on a personal computer. Examples of calculation and a comparison with experiment are given.     

Numerical simulation of axisymmetric unsteady incompressible flow by a vorticity-velocity method

A new numerical method for solving the axisymmetric unsteady incompressible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity field by means of a suitably chosen scalar potential and numerical treatment of the vorticity boundary condition are examined. The axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-staggered grid shows that the staggered grid is superior to the non-staggered grid. The computed scenario of the transition from zero-vortex to two-vortex flow at moderate Reynolds number agrees with that simulated using a pseudospectral method, thus validating the temporal accuracy of our method.     

Numerical simulation of unsteady multidimensional free surface motions by level set method

This paper presents a numerical method that couples the incompressible Navier–Stokes equations with the level set method in a curvilinear co‐ordinate system for study of free surface flows. The finite volume method is used to discretize the governing equations on a non‐staggered grid with a four‐step fractional step method. The free surface flow problem is converted into a two‐phase flow system on a fixed grid in which the free surface is implicitly captured by the zero level set. We compare different numerical schemes for advection of the level set function in a generalized curvilinear format, including the third order quadratic upwind interpolation for convective kinematics (QUICK) scheme, and the second and third order essentially non‐oscillatory (ENO) schemes. The level set equations of evolution and reinitialization are validated with benchmark cases, e.g. a stationary circle, a rotating slotted disk and stretching of a circular fluid element. The coupled system is then applied to a travelling solitary wave, and two‐ and three‐dimensional dam breaking problems. Some interesting free surface phenomena are revealed by the computational results, such as, the large free surface vortices, air entrapment and splashing of the water surge front. The computational results are in excellent agreement with theoretical predictions and experimental data, where they are available. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical simulation of unsteady inviscid flows with free surfaces

The boundary element method is used to calculate numerically the unteady flow of a capillary liquid associated with the interaction of an expanding gas cavity and the free surface of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–7, March–April, 1990.     

Numerical simulation of vibrational relaxation processes in unsteady gas jets

Minsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 55–60, September–October, 1994.     

Numerical simulation of 1-D unsteady two-phase flows with shocks

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the fiow parameters for the gas antiparticle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.     

高超声速非定常流动的数值模拟与气动热计算

高超声速飞行器研究中的一个重点问题是飞行器表面的气动加热,它对飞行器的气动、热特性及安全性有重要的影响.受到当前实验技术的限制,地面实验无法准确模拟真实飞行条件,所以采用数值模拟研究气动加热问题成为目前重要的研究手段.本文采用数值方法求解三维N-S方程,得到钝头体再入模型绕流的瞬态流场,驻点温度及表面热流沿轨道变化规律.计算中采用变边界条件模拟沿轨道飞行的非定常性.     

爆炸冲击波对肺损伤的数值模拟

采用数值模拟方法,分析了人体胸部在自由空间爆炸场中受冲击波作用的力学过程。利用Mimics软件对CT图像进行处理,建立人体胸部三维模型。根据人体胸部各生物组织的特性,选择合理的材料模型和参数,并利用LS-DYNA有限元程序中流固耦合方法,计算分析冲击波作用于人体胸部肺的受力过程。通过计算获得冲击波入射超压峰值和正压持续时间,参照Bowen损伤曲线评估出肺处于Dc 与D1损伤状态之间。观察肺部应力变化过程,获得肺部表面的正应力变化规律和损伤最严重的区域。分析剪切应力变化规律,了解肺受切应力作用损伤的可能性。     

Numerical investigation of forced convection heat transfer in unsteady flow past a row of square cylinders

This paper presents the unsteady laminar forced convection heat transfer from a row of five isothermal square cylinders placed in a side-by-side arrangement at a Reynolds number of 150. The numerical simulations are performed using a finite volume code based on the PISO algorithm in a collocated grid system. Special attention is paid to investigate the effect of the spacing between the cylinders on the overall transport processes for the separation ratios (spacing to size ratio) between 0.2 and 10. No significant interaction between the wakes is observed for spacing greater than four times the diameter at this Reynolds number. However, at smaller spacing, the wakes interact in a complicated manner resulting different thermo-hydrodynamic regimes. The vortex structures and isotherm patterns obtained are systematically presented and discussed for different separation ratios. In addition, the mean and instantaneous drag and lift coefficients, mean and local Nusselt number and Strouhal number are determined and discussed for various separation ratios. A new correlation is derived for mean Nusselt number as a function of separation ratio for such flows.     

Analysis of hysteresis and phase shifting phenomena in unsteady three-dimensional wakes

The aerodynamic characteristics of automobiles are greatly influenced by the unsteady change in the direction of relative airflow. The aim of this paper is to analyse how such a change influences vehicle wake flow patterns. An analysis was conducted on a simplified model capable of reproducing the typical structures encountered under the aerodynamic conditions of an automobile. The results were processed by mapping the steady and unsteady total pressure losses around the model. The findings should enable automobile development engineers inter alia to identify and analyse the physical phenomena that occur when a vehicle is subjected to a sudden gust of side wind.List of symbols B rod - l length of rod B (m) - angle of rod B (degrees) - D disk - P connection point between disk D and rod B - M _o drive motor of disk D - O centre of rotation of disk D - e radius of disk D (m) - angle of disk (degrees) - t moment of time t (s) - _o angle (degrees) at instant of time t=0 - d diameter of model (m) - C centre of rotation of model - x _c abscissa of centre of rotation C of model (m) - M connection point between model and rod B - pi value=3.14159 - incidence of model (degrees) - _M maximum value of incidence (degrees) - _m minimum value of incidence (degrees) - angular amplitude (degrees) - _c critical angle of incidence (degrees) for steady evolutions - critical angle of incidence (degrees) for the unsteady evolutions - ̄ mean angle of incidence (degrees) - angle (degrees) of the model such that =+ - pulse (rad s^–1) - T period (s) - f frequency (Hz) - R radius of model in meter (m) - velocity vector of incident airflow - V _o intensity of velocity vector (m s^–1) - P _io total pressure associated with upstream airflow velocity (Pa) - P _i local total pressure (Pa or J m^–3) - density (kg m^–3) - C _x drag coefficient - total pressure coefficient - (m, n) dimensions of grid: lines m, columns n - x X coordinate of sampling plane (m) - y _j Y coordinate of point of index j for j[1,n] - z _k Z coordinate of point of index k for k[1,m] - P _i (x,y _j ,z _k ,(t)) continuous data of unsteady total pressure (Pa) - discrete data of unsteady total pressure (Pa) - N number of tomographic images, from 1 upwards over an oscillation period T - maximum value of total pressure coefficients for steady evolutions - maximum value of total pressure coefficients for unsteady evolutions and increasing incidences - maximum value of total pressure coefficients for unsteady evolutions and decreasing incidences - differential between and - differential between and - phase shifting (degrees)     

过冷水滴撞击螺旋桨桨叶表面的数值模拟

本文介绍了某型螺旋桨在不同飞行状态下.求解桨叶水滴撞击特性的数值方法.该方法对桨叶运动模型进行简化,并在对绕桨叶运动的气流场计算的基础上,采用拉格朗日方法求解气流场中水滴运动方程,得到水滴运动轨迹.进而,确定了水滴对桨叶的撞击特性参数,为桨叶防冰系统设计提供条件.主要结论如下:(1)在巡航状态下,桨叶沿展向方向上总收集系数Em和局部收集系数β不断增大;(2)在爬升状态下,随着爬升高度H不断增大,飞行速度V0不断增大,水滴撞击在桨叶表面的范围有所增加,而且β随之增大;(3)随着水滴平均有效直径(MVD)的增大,水滴撞击在桨叶表面的范围明显增加同时,β在桨叶表面同一位置的值也随之增大.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 1 of this two-part paper,firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique.Then steady and unsteady simulations are conducted in a transonic compressor stage.The results from both simulations are compared to highlight the significance of the unsteady interactions.Furthermore,the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC).Lastly,steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results.The results from steady and time-averaging simulations are compared with the time-averaged unsteady results.The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.     

瓦斯爆炸诱导沉积煤尘爆炸的数值模拟

建立了描述瓦斯爆炸卷扬沉积煤尘参与爆炸的物理和数学模型,借助流场模拟平台,对瓦斯爆炸 卷扬沉积煤尘参与爆炸的过程进行了数值模拟;并把模拟值与实验值进行了对比;对爆炸过程中的速度场和 温度场进行了深入的分析。通过比较分析爆炸压力、速度场以及温度场,认为模拟结果清楚地展现了沉积煤 尘的扬起和爆炸过程,达到了瓦斯爆炸诱导沉积煤尘爆炸数值模拟的要求。     

Numerical simulation of blade coating with short dwell and roll application coaters

Paper and board are often coated at high speeds with a mineral-based aqueous suspension in order to improve their printing properties. This suspension is usually called coating colour. The flow behaviour of the coating colour in the cavity of the short dwell coater (SDC) and in the vicinity of the blade tip when paper is coated with a stiff blade has been analysed using the finite element method. The models used to simulate the flow incorporated free surfaces and shear-thinning colours. The Newtonian case was in some cases also included in the modelling. The viscosity level and the shear-thinning character of the coating colour had a significant influence on the flow in the SDC cavity, although the overall behaviour was to a large extent governed by the speed of the coater. The pressure distribution along the paper surface in the SDC cavity was also analysed.In agreement with earlier reported results, increasing the machine speed raised the pressure level in the colour close to the blade tip. The rheological properties of the coating colour also affected the flow field and the pressure distribution in this region; e.g. it was found here that a colour with a high viscosity level at low shear rates developed a high pressure level close to the blade tip. The most interesting result revealed by the analysis was that changes in the configuration close to the blade tip (converging flow between the blade tip and the paper and compression of the substrate under the blade tip) and boundary conditions at the blade tip surface had a very significant effect on the pressure distribution. The predictions of the numerical simulation were to some extent compared with experience from practical coating trials.     

油气在持续热壁下热着火发生的数值模拟

为了对油气在持续热壁下热着火发生过程进行数值模拟,耦合化学动力学模型、流体动力学模型及辐射传热模型,建立了油气热着火的统一模型。基于实验工况,模拟了受限空间中油气在持续热壁条件下热着火发生过程,并分析了温度、压力流场的演变特征,以及不同位置处温度、压力、层流速度、湍流速度和组分质量分数的变化曲线。通过模拟,发现油气热着火过程存在3个阶段,分别为加热初始阶段、加热中间阶段和热着火发生阶段。不同阶段存在的主要原因是化学反应和流动的主导作用不同。     

Numerical simulation of blast flow fields induced by a high-speed projectile

Numerical investigations on the launch process of a projectile in a nearly realistic situation have been performed in this article. The Arbitrary Lagrangian–Eulerian (ALE) of Euler equations is solved by the AUSMDV scheme and the dynamic chimera grid technique are used for describing the moving of the projectile. Based on our numerical results, the muzzle blast flow field of the transient launch process of a projectile at a relative high Mach number of 3.0 has been visualized numerically, and the prominent characteristics including the propagation of first and second blast waves, the generation of bow shock wave and moving of the projectile, etc. have been discussed in detail.      

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 2 of this two-part paper,the influence of DC on the time-averaged flow field was systematically studied.Several time-averaging computations were conducted with various boundary conditions and DC for the downstream stator in a transonic compressor stage,by employing the CFD solver developed in Part 1 of this two-part paper.These results were compared with the time-averaged unsteady flow field and the steady one.The study indicated that the circumferentialaveraged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compressors.Furthermore,it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.