Calibration of a four-hole pyramid probe and area traverse measurements in a short-duration transonic turbine cascade tunnel

A four-hole pyramid probe has been calibrated for use in a short-duration transonic turbine cascade tunnel. The probe is used to create area traverse maps of total and static pressure, and pitch and yaw angles of the flow downstream of a transonic annular cascade. This data is unusual in that it was acquired in a short-duration (5 s of run time) annular cascade blowdown tunnel. A four-hole pyramid probe was used which has a 2.5 mm section head, and has the side faces inclined at 60° to the flow to improve transonic performance. The probe was calibrated in an ejector driven, perforated wall transonic tunnel over the Mach number range 0.5–1.2, with pitch angles from -20° to + 20° and yaw angles from-23° to +23°. A computer driven automatic traversing mechanism and data collection system was used to acquire a large probe calibration matrix (～ 10,000 readings) of non dimensional pitch, yaw, Mach number, and total pressure calibration coefficients. A novel method was used to transform the probe calibration matrix of the raw coefficients into a probe application matrix of the physical flow variables (pitch, yaw, Mach number etc.). The probe application matrix is then used as a fast look-up table to process probe results. With negligible loss of accuracy, this method is faster by two orders of magnitude than the alternative of global interpolation on the raw probe calibration matrix. The blowdown tunnel (mean nozzle guide vane blade ring diameter 1.1 m) creates engine representative Reynolds numbers, transonic Mach numbers and high levels (≈ 13%) of inlet turbulence intensity. Contours of experimental measurements at three different engine relevant conditions and two axial positions have been obtained. An analysis of the data is presented which includes a necessary correction for the finite velocity of the probe. Such a correction is non trivial for the case of fast moving probes in compressible flow.     

两种湍流模型时域颤振计算方法研究

采用时域计算分析方法进行了机翼跨音速颤振特性研究。在结构运动网格的基础上,采用格点格式有限体积方法进行空间离散和双时间全隐式方法进行时间推进求解雷诺平均N-S方程。针对流动粘性分别应用了SST湍流模型和SSG雷诺应力模型,通过对跨音速标模算例AGARD445.6机翼的计算结果与实验值的对比分析,其中应用SST湍流模型得到的颤振速度与实验值最为接近,特别是在跨音速段平均相对误差在3%以内;并且计算结果整体上反映了跨音速颤振"凹坑"物理特性,验证了方法的有效性。     

The influence of acceleration and deceleration on shock wave movement on and around aerofoils in transonic flight

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s² (106 g), starting at Mach 0.1, and decelerated at −1041m/s², starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.      

Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.     

基于气动力降阶模型的跨音速气动弹性稳定性分析

基于离散型输入输出差分模型,运用非定常CFD方法训练信号,然后运用最小二乘方法进行参数辨识,得到降阶的非定常气动力模型,再将该离散差分模型转换为连续时间域内的状态方程。耦合气动状态方程和结构状态方程,得到耦合系统的气动弹性状态方程。求解不同动压下状态矩阵的特征值,根据根轨迹图分析系统的稳定性特性。分析结果与直接耦合CFD/CSD方法结果相吻合,可以计算跨音速非线性气动弹性问题。其计算效率比直接耦合CFD/CSD方法提高1~2个数量级。针对Isogai wing在跨音速出现的S型颤振边界进行了较为细致的分析,阐述了该现象是由于系统诱发颤振的分支随着速度(来流动压)的提高而发生转移所导致的。     

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, this-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption has been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5° semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers has been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5° circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. The asymmetric solutions show spatial vortex shedding which is qualitatively similar to the temporal vortex shedding of the unsteady locally conical flow. A cylindrical afterbody is also added to the same cone to study the effect of a cylindrical part on the flow asymmetry. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.     

Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows

The development of a three-hole pressure probe with back-flushing combined with a conductivity probe, used for measuring simultaneously the magnitude and direction of the velocity vector in complex air–water flows, is described in this paper. The air–water flows envisaged in the current work are typically those occurring around the rotors of impulse hydraulic turbines (like the Pelton and Cross-Flow turbines), where the flow direction is not known prior to the data acquisition. The calibration of both the conductivity and three-hole pressure components of the combined probe in a rig built for the purpose, where the probe was placed in a position similar to that adopted for the flow measurements, will be reported. After concluding the calibration procedure, the probe was utilized in the outside region of a Cross-Flow turbine rotor. The experimental results obtained in the present study illustrate the satisfactory performance of the combined probe, and are encouraging toward its use for characterizing the velocity field of other complex air–water flows.     

Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

CFD结合降阶模型预测阵风响应

传统的阵风响应主要在频域内进行分析,气动载荷基于线性方法计算,不能考虑黏性和跨声速流动影响. 飞机设计需考虑不同频率和不同形状阵风的响应,基于CFD的阵风响应预测由于计算工况太多,工作量巨大. 本文发展了一种CFD结合非定常气动力ARMA(autoregressive-moving-averagemodel)降阶模型的阵风响应分析方法,CFD只要针对给定频率和形状的一种阵风响应进行计算,对获得的气动力时间历程运用线性最小二乘法参数辨识ARMA降阶模型的系数,则对任意频率和形状的阵风,代入降阶模型即可确定该阵风的响应,大大提高了计算效率. 为效验发展的方法,先计算NACA0012翼型在低马赫数0.11的阵风响应,通过对比CFD、ARMA降阶模型及早期发展的不可压阵风响应预测方法的结果,验证了方法的有效性. 再对比CFD、ARMA在跨声速马赫数0.8的阵风响应预测结果,证实所发展的方法对跨声速阵风响应预测亦是有效的.      

Steam condensing flow modeling in turbine channels

The numerical method for modeling of the transonic steam flows with homogeneous and/or heterogeneous condensation has been presented. The experiments carried out for the Laval nozzles, for 2-D turbine cascades and for a 3-D flow in real turbine were selected to validate an in-house CFD code adjusted to the calculations of the steam condensing flows in complicated geometries. The sensitivity of the condensation model and difficulties in the validation process of the CFD code have been discussed. These difficulties limit the possibilities of verification and improvement of the condensation theory based on the existing experimental data.     

Stabilized finite‐element computation of compressible flow with linear and quadratic interpolation functions

The unsteady compressible flow equations are solved using a stabilized finite‐element formulation with C⁰ elements. In 2D, the performance of three‐noded linear and six‐noded quadratic triangular elements is compared. In 3D, the relative performance is evaluated for 6‐noded linear and 18‐noded quadratic wedge elements. Results are compared for the solutions to Euler, laminar, and turbulent flows at different Mach numbers for several flow problems. The finite‐element meshes considered for comparison have same location of nodes for the linear and quadratic interpolations. For the turbulent flow, the Spalart–Allmaras model is used for closure. It is found that the quadratic elements yield better performance than the linear elements. This is attributed to accurate representation of the stabilization terms that involve second‐order derivatives in the formulation. When these terms are dropped from the formulation with quadratic interpolation, the numerical results are similar to those obtained with linear interpolation. The absence of these terms result in added numerical diffusion that seems to give the effect of a relatively reduced Reynolds number. For the same location of nodes, the computations with the linear triangular and wedge elements are approximately 20% and 100% faster than those with quadratic triangular and wedge elements, respectively. However, if the same quadrature rule for numerical integration is used for both interpolations, the computations with quadratic elements are approximately 20% and 45% faster in 2D and 3D, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

Unsteadiness of the shock wave structure in attached and separated compression ramp flows

Wall pressure fluctuations have been measured upstream of the corner-line in several two dimensional, adiabatic, compression ramp flows. The nominal freestream Mach number was 3 and the Reynolds number, based on boundary layer thickness, was 1.4 million. The measurements show that the shockwave structure is unsteady in both separated and attached flows, resulting in a region in which the wall pressure signal is intermittent. Statistical properties of this intermittent region, and of the separated flow, are presented and correlated with results from other studies.     

Numerical study of unsteady turbulent cavitating flows

The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number, compressibility effects on turbulence and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models and Reynolds averaged codes, the turbulence modelling plays a major role in the capture of unsteady behaviours. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a simple equation of state (EOS) for the mixture. A special focus is devoted to the turbulence model influence. Unsteady numerical results are given for Venturi geometries and comparisons are made with experimental data.     

NUMERICAL INVESTIGATIONS OF THE AERODYNAMICS AND THE AEROELASTIC STABILITY OF OSCILLATING ANNULAR WINGS

The nacelles of modern aeroengines are constantly increasing in size. Thus, engine air-loads are becoming more powerful and their importance for the aeroelastic stability is becoming more significant. The principal goal of this study is to answer the question of how unsteady airloads vary while shifting to transonic Mach numbers. The investigations are carried out by applying a finite volume Euler method to a harmonically oscillating annular wing. The results show that transonic effects in the case of an annular wing are essentially weaker than in the case of an airfoil. The order of magnitude of the variations is around 10%. Possible consequences for the aeroelastic stability are examined with the example of an elastically mounted annular wing in transonic flow. The shifts of the stability curves also remain within a range of 10%. In addition, an actuator disk method, which is frequently used for the simulation of the fan jet, is expanded in such a way that unsteady flows can be treated. Some unsteady air-loads are strongly dependent on the pressure jump across the fan.     

An investigation of the heat transfer and static pressure on the over-tip casing wall of an axial turbine operating at engine representative flow conditions. (I). Time-mean results

The over-tip casing of the high-pressure turbine in a modern gas turbine engine is subjected to strong convective heat transfer that can lead to thermally induced failure (burnout) of this component. However, the complicated flow physics in this region is dominated by the close proximity of the moving turbine blades, which gives rise to significant temporal variations at the blade-passing frequency. The understanding of the physical processes that control the casing metal temperature is still limited and this fact has significant implications for the turbine design strategy. A series of experiments has been performed that seeks to address some of these important issues. This article reports the measurements of time-mean heat transfer and time-mean static pressure that have been made on the over-tip casing of a transonic axial-flow turbine operating at flow conditions that are representative of those found in modern gas turbine engines. Time-resolved measurements of these flow variables (that reveal the details of the blade-tip/casing interaction physics) are presented in a companion paper. The nozzle guide vane exit flow conditions in these experiments were a Mach number of 0.93 and a Reynolds number of 2.7 × 10⁶ based on nozzle guide vane mid-height axial chord. The axial and circumferential distributions of heat transfer rate, adiabatic wall temperature, Nusselt number and static pressure are presented. The data reveal large axial variations in the wall heat flux and adiabatic wall temperature that are shown to be primarily associated with the reduction in flow stagnation temperature through the blade row. The heat flux falls by a factor of 6 (from 120 to 20 kW/m²). In contrast, the Nusselt number falls by just 36% between the rotor inlet plane and 80% rotor axial chord; additionally, this drop is near to linear from 20% to 80% rotor axial chord. The circumferential variations in heat transfer rate are small, implying that the nozzle guide vanes do not produce a strong variation in casing boundary layer properties in the region measured. The casing static pressure measurements follow trends that can be expected from the blade loading distribution, with maximum values immediately upstream of the rotor inlet plane, and then a decreasing trend with axial position as the flow is turned and accelerated in the relative frame of reference. The time-mean static pressure measurements on the casing wall also reveal distinct circumferential variations that are small in comparison to the large pressure gradient in the axial direction.     

Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil

The preconditioning technique can address the stiffness of a low Mach number flow, while its stability is poor. Based on the conventional preconditioning method of Roe's scheme, a low-diffusion scheme is proposed. An adjustable parameter is introduced to control numerical dissipation, especially over the dissipation in the boundary layer and extremely in a low speed region. Numerical simulations of the low Mach number and low Reynolds number flows past a cylinder and the low Mach number and high Reynolds number flows past NACA0012 and S809 airfoils are performed to validate the new scheme. Results of the three tests well agree with experimental data, showing the applicability of the proposed scheme to low Mach number flow simulations.     

A numerical modelling of stator–rotor interaction in a turbine stage with oscillating blades

In real flows unsteady phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades and the development of predictive capabilities are essential for improved overall efficiency, durability and reliability. In the study presented, the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and the dynamics problem for rotor-blade motion by the action of aerodynamic forces, without separating the outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as a boundary condition for the other domain. 3-D transonic gas flow through the stator and rotor blades in relative motion with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite volume difference scheme of Godunov–Kolgan. The structural analysis uses the modal approach and a 3-D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations, with the modal coefficients depending on time. A calculation has been done for the last stage of the steam turbine, under design and off-design regimes. The numerical results for unsteady aerodynamic forces due to stator–rotor interaction are compared with results obtained while taking into account blade oscillations. The mutual influence of both outer flow non-uniformity and blade oscillations has been investigated. It is shown that the amplitude-frequency spectrum of blade oscillations contains the high-frequency harmonics, corresponding to the rotor moving past one stator blade pitch, and low-frequency harmonics caused by blade oscillations and flow non-uniformity downstream from the blade row; moreover, the spectrum involves the harmonics which are not multiples of the rotation frequency.