Precessing Vortex Structures in Turbulent Flow within Rotor-Stator Disc Cavities

Several studies of enclosed turbulent flows within rotating discs or cylinders (e.g. [6, 7]) have revealed that, while the geometry may be strictly axisymmetric, it is possible for non-axisymmetric flow patterns to be created within the space. Here we report a visualization study off low induced in the cavity formed between two discs, one rotating, the other stationary. This is an idealization of the flow configuration that occurs between successive stages in the `hot section' of a gas turbine. Such rotor-stator cavities have hitherto been regarded as creating asymmetric flow pattern but Owen [8] has conjectured that the failure to predict heat transfer coefficients accurately for certain radius-to-height ratios may indicate that here, too, organized rotating vortex structures were playing a crucial role. The present study has made an experimental visualization of this flow over a range of conditions in order to test this conjecture and to help guide future numerical explorations. The apparatus comprised a rotating disc over which is fitted a Perspex stationary disc and shroud. The lower disc was rotated for a number of distinct speeds between 30 and 120 rpm and for two ratios of gap-height to radius (H/R). The spin Reynolds number based on gap height and maximum rotational speed, ρΩRh/μ, ranged from 3.7 × 10E4 to 2.24 × 10E5. The flow structures were visualized by injecting ink through a small hypodermic tube at various radii and depths within the cavity and recording the ensuing dye streaks with a video camera mounted above the discs. The results show that, for a wide range of conditions,structured flow with large-scale vortices does indeed arise, the number of vortices diminishing as the spin Reynolds number is increased. The two-vortex S-shaped pattern is stable over a wide range of conditions but three, five and seven vortices have also been observed. These results suggest that an accurate numerical simulation of the flow within rotor-stator disc cavities may require unsteady,three-dimensional CFD modelling over at least certain ranges of flow parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigation of horizontal-axis wind turbine (HAWT) blade threedimensional rotational effect based on field experiments

Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coefficients. The 3D rotational effect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental differential pressure of the blade section airfoil increases at first and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational effect has a significant impact on the blade surface flow and the aerodynamic load, leading to an increase of the differential pressure on the airfoils and their lift coefficient than that with the 2D one because of the stall delay. The influence of the 3D rotational effect on the wind turbine blade especially takes place on the sections with flow separation.     

Superposed flow between two discs contrarotating at differential speeds

This paper describes a combined computational and experimental study of the flow between two contrarotating discs for −1 ≤ Γ ≤ 0 (where Γ is the ratio of the speed of the slower disc to that of the faster one) for the case where there is a superposed radial outflow of air. The computations were conducted using an elliptic solver and a low-Reynolds-number k-ε turbulence model, and velocity measurements were made using a laser-Doppler anenometry system. Two basic flow structures can occur: Batchelor-type flow, where there are separate boundary layers on each disc with a rotating core of fluid between, and Stewartson-type flow, where there is virtually no core rotation. The main effect of a superposed flow is to reduce the core rotation and to promote the transition from Batchelor-type flow to Stewartson-type flow. For most of the results, there is good agreement between the computed and measured velocities. Computed moment coefficients show that, for Γ = −1, superposed flow has little effect on C_m: an accepted correlation of C_m for a free disc should provide a useful estimate for design purposes.     

Bifurcation and chaotic response of a cracked rotor system with viscoelastic supports

Cracks appearing in the shaft of a rotary system are one of the main causes of accidents for large rotary machine systems. This research focuses on investigating the bifurcation and chaotic behavior of a rotating system with considerations of various crack depth and rotating speed of the system’s shaft. An equivalent linear-spring model is utilized to describe the cracks on the shaft. The breathing of the cracks due to the rotation of the shaft is represented with a series truncated time-varying cosine series. The geometric nonlinearity of the shaft, the masses of the shaft and a disc mounted on the shaft, and the viscoelasticity of the supports are taken into account in modeling the nonlinear dynamic rotor system. Numerical simulations are performed to study the bifurcation and chaos of the system. Effects of the shaft’s rotational speed, various crack depths and viscosity coefficients on the nonlinear dynamic properties of the system are investigated in detail. The system shows the existence of rich bifurcation and chaos characteristics with various system parameters. The results of this research may provide guidance for rotary machine design, machining on rotary machines, and monitoring or diagnosing of rotor system cracks.     

Air-cooled gas-turbine discs: a review of recent research

The flow between corotating compressor or turbine discs and the flow between a turbine disc and an adjacent stationary casing can be respectively modelled by a rotating cavity and by a rotor-stator system. This paper reviews some of the recent experimental and theoretical work on flow and heat transfer in these two classes of rotating-disc systems. Comparisons between the theoretical and measured distributions of velocity, pressure, and Nusselt numbers are made for the rotating cavity with a superimposed radial flow of cooling air. For the rotor-stator system, some recent work on the fluid dynamics is outlined, and particular mention is made of the so-called “ingress problem” and of the use of pre-swirl air to improve the blade-cooling effectiveness.     

模型昆虫翼作非定常i运动时的气动力特性

基于Navier-Stokes方程的数值解,研究了一模型昆虫翼在小雷诺数(Re=100)下作非定常运动时的气动力特性.这些运动包括翼启动后的常速转动,快速加、减速转动,常速转动中快速上仰(模拟昆虫翼的上挥或下拍、翻转等运动).有如下结果在小雷诺数下,模型昆虫翼以大攻角(α=35°)作常速转动运动时,由于失速涡不脱落,可产生较大的升力系数.其机理是翼转动时,翼尖附近(该处线速度大)上翼面压强比翼根附近(该处线速度小)的小得多,因而存在展向压强梯度,同时存在着沿展向的离心力,此展向压强梯度和离心力导致的展向流动在失速涡的轴向方向,其可避免失速涡脱落.模型昆虫翼在快速加、减速转动和快速上仰运动中,虽然雷诺数小,但由于在短时间内产生了大涡量,也可产生十分大的气动力,例如在快速上仰运动中,升力系数可大于10.     

航空发动机轴承腔润滑的气液两相均匀流研究

基于轴承腔中润滑油的两相均匀流动模型,采用湍流模式和有限差分数值方法计算轴承腔内三维定常N-S方程,对腔内润滑油的气液两相均匀流动特性进行研究,以获得气液两相均匀流条件下润滑油流场、压力场和速度场在轴承腔内的分布情况,分析转子转速、含气率和润滑油进口速度对润滑油出口压力以及润滑油与壁面之间剪切力的影响,同时对单相流和两相均匀流润滑性能差异进行比较.结果表明,转子转速、含气率和润滑油进口速度对润滑油出口压力和腔内壁面与润滑油间的平均剪切力具有不同影响,而采用2种流动模型计算出的轴承腔润滑油出口压力的差异较大,同时支持了开展航空发动机轴承腔润滑两相流动分析的必要性.     

Pressure drop for flow in channels subjected to strong system rotation

A disc stack centrifuge is an industrial example of a fluid machine in which all the internal flow takes place in a rapidly rotating frame. The present report gives a survey of the experimental and theoretical work performed at Alfa-Laval in order to estimate the pressure drops in the different internal passages in the centrifuge, including both laminar and turbulent flow.For the laminar flow between the discs, a theory has been developed using the concept of a rotating Hele Shaw cell and conformal mapping. The theory is valid in the limit of very small Rossby numbers. For moderately large Rossby numbers, this model overestimates the pressure drop. The linear theory was extended by introducing advecting vortices in a computer model. The vortices cause vertical fluid transport between the Ekman and geostrophic layers by Ekman pumping, an effect which decreases the pressure drop in the disc stack. The linear model and the enhanced model have both been confirmed by experiments.The flow is turbulent in most parts of the centrifuge, except in the disc stack. The theoretical or numerical modelling for rotating turbulent flows is very difficult and no reliable models exist so far. We therefore have to rely on measurements, which show that the pressure is significantly influenced by rotation for Rossby numbers below unity.     

双旋转附属圆柱对主圆柱尾流控制的影响

基于Fluent 软件平台,采用数值模拟方法对非稳态圆柱体结构尾流流动特性进行了研究．对在Re = 50~200范围内,双旋转附属圆柱的转速对主圆柱体尾流流动特性的影响进行了分析．研究结果表明：随着附属圆柱旋转速率的增加,主圆柱体表面所受阻力系数平均值与均方根值、升力系数均方根值均会减小．同时,旋转速率的变化对柱体结构表面压力分布的影响显著,压力系数在附属圆柱的位置产生了跳跃性变化．另外,当附属圆柱转速达到临界值时,尾流涡街变窄,涡脱落现象消失,并且系统的能量效率到达最佳状态．     

微载荷含油轴承摩擦性能研究Ⅱ.摩擦试验分析

采用自行研制的径向轴承微载荷摩擦试验机研究了微载荷下径向含油轴承的摩擦性能,采用小波方法对试验数据进行滤波降噪.结果表明,含油轴承在稳定微载荷状态下的瞬态摩擦系数不固定,且随着润滑剂、轴承转速、径向载荷与混合润滑状态等因素而变化.在微载荷状态下,当600 r/min、采用液晶添加剂(5CB)与46号机械油以体积比1%～2%配制的润滑剂润滑时,平均摩擦系数达到最小值;当转速从600 r/min增至3 000 r/min时,平均摩擦系数由小变大、再变小;瞬态摩擦系数随着载荷从0.5 N增至10.0 N呈现高-低-稳定的变化趋势.与混合润滑状态相比,充分润滑下的摩擦系数较大;当混合润滑时,在主轴转速为1 500～2 400 r/min下的摩擦系数出现不稳定.     

考虑空化影响的水润滑橡胶合金轴承冲蚀磨损研究

用计算流体力学方法,数值模拟水润滑轴承空化-冲蚀交互作用时气液固三相流场的动力学特性(压力场、速度场、气含率分布),然后在水润滑轴承摩擦磨损装置上,进行试件磨损试验,并观察试件表面形貌.结果表明:考虑空化影响后,水润滑轴承整个流场压力分布更接近实际;数值模拟所得的流场压力、速度、气含率最大值,均出现在发生空化的位置附近,其余位置基本不变,说明交互磨损比单一磨损严重.观察试件表面磨痕,存在短程犁沟、空蚀针孔、麻点状气蚀坑和蚀坑,磨痕呈现规律性,磨痕与轴转速的方向基本一致.试验结果和数值计算吻合较好,证明了理论分析的正确与合理.上述仿真与试验初步探讨了水润滑轴承空化与冲蚀交互作用的磨损机理与影响因素.     

瞬态载荷下L4/L5椎间盘内流固耦合效应

中医正脊治疗通过对腰椎施加瞬态拉伸和旋转来治疗腰椎间盘退变, 本文采用考虑流固耦合效应的数值模拟研究其生物力学机制. 通过实验测量和文献调研, 确定了合理的拉伸和旋转的载荷参数; 发展了使用人体断层扫描图像结合解剖学数据建立详细腰椎几何模型的方法; 将松质骨、终板、椎间盘考虑为多孔弹性介质, 其他组织考虑为线性弹性介质, 进而建立了考虑生物组织中流固耦合效应的物理模型; 通过数值模拟得到了不同瞬态载荷及其组合作用下椎间盘内应力?应变与流体流动的变化规律. 研究发现, 瞬态载荷通过改变L4/L5椎间盘基质应力和髓核内外压力梯度, 在髓核中产生流体流动; 拉伸加载引起流体先流出髓核、再流入髓核, 产生含水量变化; 顺时针旋转加载在髓核左右产生相反的流动, 髓核右侧的含水量变化较左侧大. 本研究所采用的方法为流动过程相关的人体椎间盘退变病理生理机制研究提供了新的方法, 为中医正脊研究提供科学化思路, 也为相关的力学-生物学耦合研究和髓核再生的基础研究提供了一个切入点.      

Numerical investigation on dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication

The dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication (MQL) is investigated. According to the features of the compressible fluid Reynolds equation in oil/air feature, a time-dependent mathematical model is established to describe the pressure distribution of cutting fluid with nonlinearity in MQL deep hole drilling. By introducing the differential transformation approach, the time-dependent pressure equation arising from cutting fluid is solved by the use of direct integral method. The influences of the rotational speed, the transverse displacement ratio, and radial clearance on the hydrodynamic pressure distribution of cutting fluid are obtained. The advantage of this method is to overcome much of the computational cost and has its rapid convergence rate. Furthermore, the nonlinear responses of drilling shaft influenced by MQL are analyzed, and the instability rotational speeds of drilling tool are discussed while the design parameters of drilling shaft system changing.     

Lift force on rotating sphere at low Reynolds numbers and high rotational speeds

The lift force on an isolated rotating sphere in a uniform flow was investigated by means of a three-dimensional numerical simulation for low Reynolds numbers (based on the sphere diameter) (Re<68.4) and high dimensionless rotational speeds (Г5). The Navier-Stokes equations in Cartesian coordinate system were solved using a finite volume formulation based on SIMPLE procedure. The accuracy of the numerical simulation was tested through a comparison with available theoretical, numerical and experimental results at low Reynolds numbers, and it was found that they were in close agreement under the above mentioned ranges of the Reynolds number and rotational speed. From a detailed computation of the flow field around a rotational sphere in extended ranges of the Reynolds number and rotational speed, the results show that, with increasing the rotational speed or decreasing the Reynolds number, the lift coefficient increases. An empirical equation more accurate than those obtained by previous studies was obtained to describe both effects of the rotational speed and Reynolds number on the lift force on a sphere. It was found in calcttlations that the drag coefficient is not significantly affected by the rotation of the sphere. The ratio of the lift force to the drag force, both of which act on a sphere in a uniform flow at the same time, was investigated. For a small spherical particle such as one of about 100μm in diameter, even if the rotational speed reaches about 10^6 revolutions per minute, the lift force can be neglected as compared with the drag force.     

Characteristics of ventilating flow generated by a rotating swirler in a vortex vent

A vortex ventilation system with a rotating annular disk installed coaxially with the exhaust inlet is a very effective local ventilator. A swirling flow generated by a rotating swirler makes the ventilation flow concentrated around the axis of rotation, which can increase the ventilation depth by a factor of five compared to a conventional exhaust hood. Despite the well-documented excellent ventilation performance of such a system, detailed flow characteristics are not well understood. In this study, the swirling flow field in the vortex vent was tested, and a number of peculiar flow characteristics were observed. When the rotational speed was varied, a series of different flow patterns appeared, and the changes in the flow pattern showed rapid transition, hysteresis, and flow instability similar to the vortex. The transition of the flow pattern could be explained based on the ratio of the centrifugal force to exhaust pressure. Hysteresis of the flow transition occurred in an unstable equilibrium mode between the two forces, and an unstable flow pattern occurred when the secondary recirculating flow was located beneath the swirler. A formula for the critical rotational speed was derived, which showed satisfactory agreement with experimental observation.     

Experimental study of wall curvature and bypass flow effects on orifice discharge coefficients

This paper presents the results of an experimental study investigating the impact of wall curvature and bypass flow on the discharge coefficients of circular orifices. To extend the range of currently available discharge coefficients, the ratio of the orifice to the pipe diameter is varied from 0.25 to 0.67. Functional relationships are developed that relate a free-discharge orifice coefficient to the ratio of the orifice diameter to the pipe diameter and the total head (velocity and pressure heads) upstream of the orifice. In addition, the use of the projected area versus surface area of the orifice for determining discharge coefficients is investigated and the results show that both approaches yield similar observations. The results of this experimental study are particularly useful for the case of sparger design.     

Experimental study of rotation effect on film cooling over the flat wall with a single hole

A new rotating test rig was set up to investigate the rotation effect on the film cooling over the flat wall. A simple flat blade with an inclined 30° film hole, which is parallel to the hot mainstream, was installed. And different rotation orientations were selected to simulate the blade pressure or suction side of a turbine blade. A steady liquid crystal technique was applied to obtain detailed distribution of the temperature over the blade surface. And the average adiabatic film cooling effectiveness of the area adjacent to the film hole was selected to evaluate the cooling effect. Five different rotational speeds, i.e., 0, 300, 500, 800, 1000 r/min, were considered. Experimental results indicate that the film trajectory could bend under the rotating condition. With the increase of the rotational speed, on the pressure side, the film trajectory inclines centripetally firstly and then centrifugally; whereas, on the suction side the film trajectory bends centrifugally. On the other hand, as the rotational speed increases, the cooling effect is improved firstly and then worsened when Ω > 500–600 r/min on the pressure side. On the suction side, however, the cooling effect is not sensitive to the rotational speed.     

Flow and heat transfer in a rotating cavity with a radial inflow of fluid Part 1: The flow structure

Flow visualization has been conducted in a rotating cavity, comprising two steel discs and a peripheral polycarbonate shroud, for dimensionless flow rates of air up to |C_w|8000 and rotational Reynolds number up to Re_φ10⁶. For all the experiments, the ratio of the inner to outer radii of the discs was 0.1 and the ratio of the axial clearance between the discs to their outer radii was 0.133; five different shroud geometries were tested. The flow visualization has confirmed that the flow structure comprises a source region near the shroud, laminar or turbulent Ekman layers on the discs, a sink layer near the centre of the cavity, and an interior core of rotating fluid. Above a certain flow rate, this structure was found to be unstable; heating one disc tended to stabilize the flow. For isothermal flow, measurements of the size of the source region were in good agreement with values predicted from a simple theoretical model.     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

Heat transfer from rotating finned heat exchangers with different orientation angles

The local and average heat transfer characteristics of spoke like fins that extend outward from a rotating shaft have been determined experimentally. The experiments encompassed a number of geometrical parameters, including the length and chord of the fins, the number of fins deployed around the circumference of the shaft and the orientation angles of the fin. The experiments cover a wider range of rotational speeds, which varies from 25 up to 2,000 rpm. Three wire heat flux sensors have been used in conjunction with a slip ring apparatus to evaluate the local and average heat transfer coefficients. The output results indicated that, the heat transfer transition on rotating fins occurs at Reynolds number lower than encountered on the stationary rectangular fins in crossflow. In general, with non zero incidence angle, the rotating system acts as a fan and creates axial air motion, which enhance the heat transfer rate. However, the effect of orientation angle reduces with increasing the rotational speed. The Nusselt number data are independent of the number of fins in the circumferential array at high rotational speed and are weakly dependent at low Reynolds numbers. To facilitate the use of the results for design, correlations were developed which represent the fin heat transfer coefficient as a continuous function of the investigated independent parameters.