Numerical simulation of turbulent cascade flows involving high turning angles

Numerical simulations of three dimensional turbulent incompressible flows through linear cascades of turbine rotor blades with high turning angles have been performed using a generalized k−ɛ model which is a high Reynolds number form and derived by RNG (renormalized group) method to account for the variation of the rate of strain. The convective terms are approximated by using a second order upwind scheme to suppress numerical diffusion. Boundary-fitted coordinates are adopted to represent the complex cascade geometry accurately. For the case without tip clearance, secondary flows and flow losses are shown to be in good agreement with previous experimental results. For the case with tip clearance, the effects of the passage vortex and tip clearance flow on the total pressure loss as well as their interactions are discussed. The flow within the tip clearance has been analyzed to illustrate the existences of the tip clearance vortex and vena contracta.     

Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions

In this article we present a validation study involving the full-scale NREL Phase VI two-bladed wind turbine rotor. The ALE–VMS formulation of aerodynamics, based on the Navier–Stokes equations of incompressible flows, is employed in conjunction with weakly enforced essential boundary conditions. We find that the ALE–VMS formulation using linear tetrahedral finite elements is able to reproduce experimental data for the aerodynamic (low-speed shaft) torque and cross-section pressure distribution of the NREL Phase VI rotor. We also find that weak enforcement of essential boundary conditions is critical for obtaining accurate aerodynamics results on relatively coarse boundary layer meshes. The proposed numerical formulation is also successfully applied to the aerodynamics simulation of the NREL 5MW offshore baseline wind turbine rotor.     

Aerodynamic experimental investigation using stereolithography fabricated test models: the case of a linear compressor blading cascade

The purpose of this work is to demonstrate that rapid prototyping can be effectively applied for fabricating test models to be used in aerodynamic experimental investigations. The present work, in particular, concerns a linear cascade of 2½-D blades, with NACA 65-12(A10)10 profile section. Each one of the nine separate (identical) blades of the cascade has been fabricated using a stereolithography rapid prototyping technique. The cascade has been installed in an aerodynamic test rig, in order to simulate the flow conditions through a compressor blading. Aspects concerning the fabrication of the test models/blades, their functionality, their post-processing, the mounting arrangement and the pressure tubing and ports are discussed in detail. Experimental results for the distribution of the blade surface airflow pressure for various incidence angles compare favourably with computational results obtained with a panel inviscid flow numerical scheme. This implicitly indicates the effectiveness of employing stereolithography for fabricating wind tunnel test models.     

气体涡轮流量传感器叶轮压力的数值模拟

在严格按照实际涡轮流量传感器几何结构的基础上,运用Solidworks三维建模,通过运用计算流体动力学的方法对内径为80mm的气体涡轮流量传感器进行了数值模拟,给出了流量计在不同流量下内部的压力场并特别给出叶轮表面的压力分布.从压力分布分析叶轮部分的受力情况,以此来讨论叶轮动受力.     

Use of a residual distribution Euler solver to study the occurrence of transonic flow in Wells turbine rotor blades

 The aim of the present study is to investigate the occurrence of transonic flow in several cascade geometries and blade sections that have been considered in the design of Wells turbine rotor blades. The calculations were performed using an implicit Euler solver for two-dimensional flow. The numerical method uses a multi-dimensional upwind matrix residual distribution scheme formulated on a new symmetrized form of the Euler equations, both in time and in space, that decouples the entropy and the enthalpy equations. Second-order accurate steady-state solutions where obtained using a compact three-point stencil. The results show that unwanted transonic flow may occur in the turbine rotor at relatively low mean-flow Mach numbers. Received: 29 November 2001 / Accepted: 28 May 2002     

风力机翼型动态失速气动特性仿真

基于Beddoes-Leishman(B-L)半经验动态失速模型,从附着流、分离流和动态涡三个方面阐述了风力机翼型在动态失速情况下非定常气动力系数的计算方法。在此基础上根据风力机翼型工作时的实际特点对原B-L模型中分离流和动态涡气动力系数的计算进行了改进,并将模型扩充到适用于全范围攻角的动态失速计算。利用所编制的程序仿真了风力机翼型S809和NACA4415动态失速下的升力、阻力和力矩系数。计算结果与实验数据吻合良好。改进模型与原B-L模型计算结果的对比表明,改进后的模型提高了对非定常气动力系数计算的精确性和适用区间,能更好地预测动态失速气动力的变化。     

叶栅内非定常不可压流动的数值模拟

基于SMAC(SimplifiedMarkerandCell)方法推导出直接求解二维非定常、不可压N-S方程的隐式数值方法。求解的基本方程是任意曲线坐标系中以逆变速度为变量的N-S方程和椭圆型的压力Poisson方程。采用该方法,对二维叶栅非定常分离流场进行了数值模拟,叶栅表面压力的计算结果与试验结果相比比较吻合,从而验证了这种方法的可靠性。同时对叶栅非定常流场的流场结构和流动机理做了初步的探讨。在均匀来流和定常边界条件下,叶栅内部流动表现出强烈的非定常性;在小冲角和高雷诺数时,叶栅尾部产生类似卡门涡街的周期性流动。     

Faceted design of channels for low-dispersion electrokinetic flows in microfluidic systems

A novel methodology for designing microfluidic channels for low-dispersion, electrokinetic flows is presented. The technique relies on trigonometric relations that apply for ideal electrokinetic flows, allowing faceted channels to be designed using common drafting software and a hand calculator. Flows are rotated and stretched along the abrupt interface between adjacent regions having differing specific permeability--a quantity with dimensions of length that we introduce to derive the governing equations. Two-interface systems are used to eliminate hydrodynamic rotation of bands injected into channels. Regions bounded by interfaces form faceted flow "prisms" with uniform velocity fields that can be combined with other prisms to obtain a wide range of turning angles and expansion ratios. Lengths of faceted prisms can be varied arbitrarily, simplifying chip layout and allowing the ability to reduce unwanted effects such as transverse diffusion and Joule heating for a given faceted prism. Designs are demonstrated using two-dimensional numerical solutions of the Laplace equation.     

Numerical analysis of two-dimensional compressible turbulent flows in a turbine stage

A numerical analysis based on the compressible Reynolds-averaged Navier-Stokes equation has been developed for the analysis of two-dimensional compressible turbulent flows in a turbine stage (nozzle and bucket). In the present flow analysis, governing equations are solved by the use of a time dependent explicit method and a two-equation model of turbulence is employed to estimate turbulence effects. To calculate nozzle and bucket flow fields simultaneously, a steady interaction between these flows is assumed. For spatial discretization of the governing equations, a control volume method combined with a body-fitted curvilinear coordinate system is developed to calculate the flows in arbitrarily shaped cascades. In order to assure the effectiveness of the present method, computations are carried out for a two-dimensional section at a blade midspan in a turbine stage. The method gives satisfactory results about boundary layers on blade surfaces, nozzle wake profiles and pitchwise averaged turbine design parameters at each blade exit.     

Extended kinetic theory applied to inclined granular flows: role of boundaries

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction.     

飞艇大攻角绕流气动特性模拟及湍流模型与参数影响研究

飞艇大攻角绕流作为一种典型的分离与漩涡流动,相关研究具有较高难度和十分重要的意义。该文基于数值模拟方法,研究了飞艇大攻角绕流条件下的气动特性,分析了湍流模型选择和湍流强度设置等关键因素对模拟结果的影响。气动力、压力系数、流场显示细节等结果表明:SST 模型和Realizable 均能较准确地模拟飞艇周边流体流动现象,计算得到的气动参数和实验结果吻合良好,而S-A模型和实验存在较大差异;同时发现湍流强度对飞艇气动力存在较大影响,升阻力系数在湍流强度I > 0.5%时随之线性增长。进一步引入了等效雷诺数的概念,证明与原始雷诺数类似,等效雷诺数对气动力影响存在相应的敏感区间,在计算和实验中值得加以注意。     

Construction of a Mixed FEM Approximation to Solve a Problem on Bending of a Plate on the Basis of Zienkiewicz's Triangle

To solve a problem on bending of a plate, a special three-node triangular finite element has been constructed on the basis of Zienkiewicz's triangle. A mixed approximation is used for the plate deflection and turning angles. The numerical solution is shown to converge to an exact one with a decrease in the triangle dimensions. The results of the numerical analysis of the convergence and accuracy of the solution of a number of test problems are presented.     

Application of an Eulerian granular numerical model to an industrial scale pneumatic conveying pipeline

In this paper, an Eulerian granular numerical model is applied in the modelling of an industrial scale pneumatic-based cement conveying system. Steady-state simulation results are found to match pressure and outlet flowrate values with actual system data. By modifying the inlet pressure and material feed rate, data that predicts the performance of the conveying system have been obtained within the present study. Transient simulations have also been conducted and the results reveal intricate details of the cement flows along the pneumatic pipes and pipe bends. In particular, particle roping behaviour is observed to follow the sides of the wall before, during and after the pipe bends. A sloshing-like cement flow motion is also observed after the cement exits the bend. The concentration distribution of the cement particles is found not only to be partly due to gravitational effects but also the pneumatic pipe configuration. Lastly, close inspection of the secondary flows within the pneumatic pipe shows that their directional changes lead to a corresponding change in the particle roping direction, indicating that particle roping is closely associated with the secondary flow structures induced by the exact pipe configuration.     

Entropy minimization in turbine cascade using continuous adjoint formulation

A complete continuous adjoint formulation is presented here for the optimization of the turbulent flow entropy generation rate through a turbine cascade. The adjoint method allows one to have many design variables, but still afford to compute the objective function gradient. The new adjoint system can be applied to different structured and unstructured grids as well as mixed subsonic and supersonic flows. For turbulent flow simulation, the k–ω shear-stress transport turbulence model and Roe's flux function are used. To ensure all possible shape models, a mesh-point method is used for design parameters, and an implicit smoothing function is implemented to avoid the generation of non-smoothed blades. To analyse the capability of the presented algorithm, the shape of a turbine cascade blade is redesigned and a few physical observations are made on how the scheme improves the blade performance.     

Elastoplastic state of a thin-walled pipe under pressure in the process of bending with tension (Compression)

We analyze the elastoplastic state of a rectilinear element of a thin-walled pipeline under pressure in the process of bending with tension (compression) and determine the characteristics of its stiffness. To solve this problem, we use a numerical method based on the deformation theory of plasticity and the momentless theory of shells. The problem is reduced to a one-dimensional problem and the proposed approach enables us to substantially simplify the procedure of numerical calculations. The idea of this approach can be described as follows: the longitudinal stresses and the components of strains are decomposed into two parts, one of which depends only on internal pressure and the second of which reflects the work of the pipe as a rod. By using this computational procedure and also the Mathcad PLUS-6.0 mathematical package, we analyzed the influence of internal pressure and longitudinal forces on the bending strength of the rectilinear elements of main pipelines. A numerical example is presented. The results of numerical calculations are displayed in the form of plots. “L’vivs’ka Politekhnika” State University, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 99–105, November–December, 1998.     

Transformations of the equations of motion for the unsteady rectilinear flow of a perfect gas

Summary Unsteady rectilinear flows of a perfect gas have usually been studied in the Eulerianx, t-plane and less frequently in Lagrangian or other independent variables. In the homentropic case, when Riemann invariants exist, these may be used with advantage as independent variables.In the present paper some simple techniques are applied to the equations of motion in Lagrangian variables in order to obtain a survey of the equations of motion when the independent variables are varied in a systematic fashion. This transformation theory reveals some connections in the problem, which appeared in the literature in a fragmentary and puzzling fashion. Also several results obtained before are simplified, unified and hence clarified by the present treatment. No new and detailed solutions are presented but it is expected that the study will be of some help for further work on unsteady rectilinear flows.     

Transsonische Strömung in einem Gasturbinenlaufrad – experimentelle Untersuchungen im ebenen Gitter und im rotierenden Ringgitter

Using a straight cascade and a rotating annular cascade the transonic flow field within a gas turbine rotor according to design conditions was investigated (β₁?=?140°, Ma_2is?≈?1.1). By means of conventional measuring technic using pneumatic pressure transducers within probes and on surfaces wake flow traverses were carried out as well as static pressure measurements and boundary layer measurements. Determination of the flow velocity was done within different planes parallel to the cascade exit using a L2F-anemometer. Finally, heat transfer measurements and flow visualisation by means of the Schlieren technic were part of the research program. The experiments clearly show that the results from the two dimensional and the three dimensional investigations supplement each other and contribute to a deeper understanding of the aerodynamics of the flow field within a gas turbine rotor. As well, the results can be used as basic data to validate (improved) numerical procedures for flow field computations.     

An efficient numerical method for highly loaded transonic cascade flow

In this paper, an efficient numerical method for transonic viscous flow in a highly loaded turbine vane cascade, where the interaction of a shock wave and boundary layer often leads to very complicated flow phenomena, is developed. The numerical code, a modified implicit flux-vector-splitting solver of the Navier–Stokes equations (MIFVS), is extended to simulate such transonic cascade flow. A compressible low-Reynolds-number k–ɛ model, together with a transition-modified damping function, has been implemented into the MIFVS code. With this extended MIFVS solver, the main feature of transonic flow and shock and boundary-layer interactions in the highly loaded transonic turbine vane are efficiently predicted with satisfactory accuracy. The convergence rate is found to be three times faster than that of flux-vector-splitting (FVS) methods.     

Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations

The composite pipes manufactured by filament winding technology have anisotropic behavior owing to different reinforced ply angles. Composite pipes can be exposed to the thermomechanical loading due to hot fluid that flows into them. In this paper, based on the three-dimensional anisotropic elasticity, an exact elastic solution for thermal stresses and deformations of the pipes under internal pressure and a temperature gradient has been studied. Giving heat convection conditions the variation of temperature field within the pipe is obtained by solving the conduction equation at the wall. The influence of temperature field in the governing equations of thermoelasticity has been considered via a constitutive law. The shear extension coupling is also considered because of lay-up angles. Stress, strain and deformation distributions for different angle-ply pipe designs are investigated using the present theory.     

高拱坝表孔宽尾墩流道内水流特性的数值模拟研究

宽尾墩应用于高拱坝表孔后,其下泄水流的空中扩散特性与宽尾墩流道内的水流特性密切相关。采用k-ε双方程紊流模型对宽尾墩应用在高拱坝坝身泄洪表孔时的水流特性进行了3维数值模拟,给出了孔流道水面线、压力、流场等水流特性。计算值与模型试验值对比,两者吻合较好。计算结果发现,坝面中线压力分布与侧墙压力分布存在相似规律,所不同的是侧墙压力在宽尾墩转折点位置存在局部增大;墩尾压力分布受墩内水流流线弯曲影响,其分布不再符合净水压力分布规律;墩尾水流流速大小沿水深方向变化不大,但流速方向变化比较明显。