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.     

Heat transfer in a rotor–stator system with a radial inflow

The object of the present work is to produce a better understanding of the flow and heat transfer process occurring in a rotor-stator system, with a low aspect ratio and subjected to a superposed radial inflow. The theoretical approach presented in a previous paper (Debuchy et al., Eur. J. Mech. B-Fluids 17 (6) (1998) 791–810) in the framework of laminar, steady, axisymmetric flow is extended to heat transfer effects. The asymptotic model is simplified and new integral relations including temperature are indicated. The experiments, made in a rotor–stator system with a heated stationary disc, are in agreement with the features of the model in the explored range of the gap ratio, Ekman and Rossby numbers. The data include radial and circumferential mean velocity components, air temperature inside the cavity, temperature and temperature-velocity correlations, and also local Nusselt numbers measured on the stationary disc. The flow structure near the axis is found to be strongly affected by the presence of a superposed inflow, as already observed under isothermal conditions. By contrast, the mean temperature, as well as the correlations concerning velocity and temperature are smaller when a radial inflow is assigned.     

高速转动圆盘流动数值模拟研究

重点研究高速离心压气机叶轮与机匣间的间隙流动及其温度分布。研究将离心压气机简化为高速转动圆盘,搭建了相关实验平台,并开展了相应的数值模拟研究。通过改变转动圆盘的转速和轴向进入的冷却流的流量,研究了转速和流量对于间隙内温度和速度分布的影响。结果显示,转速是影响温度变化的最主要因素,转速越大,温度越高;同等幅度的流量变化对温度的影响则较小。研究发现,在实验和模拟对应的大雷诺数条件下,无量纲的速度分布基本不受到圆盘转速、冷却流量和温度场的影响。     

Effect of an axial throughflow on buoyancy-induced flow in a rotating cavity

In this paper large-eddy simulation is used to study buoyancy-induced flow in a rotating cavity with an axial throughflow of cooling air. This configuration is relevant in the context of secondary air systems of modern gas turbines, where cooling air is used to extract heat from compressor disks. Although global flow features of these flows are well understood, other aspects such as flow statistics, especially in terms of the disk and shroud boundary layers, have not been studied. Here, previous work for a sealed rotating cavity is extended to investigate the effect of an axial throughflow on flow statistics and heat transfer. Time- and circumferentially-averaged results reveal that the thickness of the boundary layers forming near the upstream and downstream disks is consistent with that of a laminar Ekman layer, although it is shown that the boundary layer thickness distribution along the radial direction presents greater variations than in the sealed cavity case. Instantaneous profiles of the radial and azimuthal velocities near the disks show good qualitative agreement with an Ekman-type analytical solution, especially in terms of the boundary layer thickness. The shroud heat transfer is shown to be governed by the local centrifugal acceleration and by a core temperature, which has a weak dependence on the value of the axial Reynolds number. Spectral analyses of time signals obtained at selected locations indicate that, even though the disk boundary layers behave as unsteady laminar Ekman layers, the flow inside the cavity is turbulent and highly intermittent. In comparison with a sealed cavity, cases with an axial throughflow are characterised by a broader range of frequencies, which arise from the interaction between the laminar jet and the buoyant flow inside the cavity.     

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.     

Laminar thermal convection in rotating cavity between two disks

In solving several technical problems it is necessary to know what takes place in a closed rotating axisymmetric cavity filled with a nonuniformly heated viscous fluid. Such cavities are encountered, for example, in the rotors of steam and gas turbines. The thermal convection in these cavities is studied for a definite temperature condition of the rotors: in [1, 2] some qualitative considerations are presented, and quantitative estimates are given for thermal convection in cavities of turbine rotors; in [3,4] there is presented a very approximate calculation using the method of integral relations of the heat transfer coefficients in the case of a narrow cavity between two rotating disks which have different temperatures. We note that the thermal convection effect in a rotating cavity may be utilized in various technical devices, for example, in equipment for separating isotopes, etc. [5], A solution is presented for the problem of laminar thermal convection in a narrow cavity between two disks which are rotating with the same velocity and which have different temperatures which are constant along the radius. In the case of the narrow cavity we can neglect the influence of the cylindrical cavity rim on the flow in primary portion of the cavity (see [6]); therefore it is sufficient to solve the self-similar problem for two infinite disks.In conclusion I would like to thank A. Z. Serazetdinov and V. L. Karaseva for carrying out the computer calculations.     

Eclatement tourbillonnaire dans une cavité rotor–stator cylindrique

The rotating flow inside an enclosed cylindrical rotor–stator cavity is studied. Within a certain range of governing parameters, vortex breakdown phenomenon can arise along the axis. Very recent papers exhibiting some particular three-dimensional effects, have concentrated new interest on this topic. The study is carried out by a numerical resolution of the 3D Navier–Stokes equations, based on spectral approximations. Three-dimensional behaviours of the flow and in the structure of the associated vortex breakdown are numerically exhibited for the first time in a cavity of large axial aspect ratio.     

Velocity field investigation inside a bulb turbine runner using endoscopic PIV measurements

The flow in the inter-blade channels of a bulb turbine was measured using endoscopic cameras integrated to a stereoscopic particle image velocimetry (S-PIV) system. This paper presents results from the measurement campaign and also provides some key conclusions based on the dataset. The technical aspect of the measurement configuration is addressed. The main focus is on the novelties and challenges brought by the use of endoscopic cameras to achieve S-PIV measurements between the runner blades. For the first time in hydraulic rotating machinery, velocity measurements covered 62 % of a rotor inter-blade flow. After outlining the techniques used, comparison with laser Doppler velocimetry measurements allows assessing the intrusiveness of the endoscopes. Then, some velocity field analyses are shown. First, the rotor–stator interaction is outlined as the influence of the guide vane wakes on the runner flow. The size, localization, strength and dissipation of those structures are inferred from the information coming from measurements. Finally, the PIV data allow the identification of a vortex located near the suction side of the blades and originating from the corner between the leading edge and the hub when operating the bulb turbine at part-load.     

Construction of liquid flow past a solid body with an air layer

It is known that the friction drag for a body moving in a liquid may be reduced by varying the physical properties of the liquid at the body surface and, in particular, by creating an artificial air cavity on the body surface.The question of the magnitude of the drag gain in the case of the presence of a wall fluid layer with different physical constants was considered in [1–3].In [4, 5] results are presented of theoretical and experimental studies on the question of determining the parameters of artificial air cavities created on the lower surface of a horizontal wall in order to reduce the drag.In the following an attempt is made to construct the three-dimensional flow of an ideal liquid past a body which is enveloped entirely in an air cavity.     

Discharge coefficients for flow through holes normal to a rotating shaft

A possible design for a more compact gas turbine engine uses contra-rotating high pressure (HP) and intermediate pressure (IP) turbine discs. Cooling air for the IP turbine stages is taken from the compressor and transferred to the turbine stage via holes in the drive shaft. The aim of this work was to investigate the discharge coefficient characteristics of the holes in this rotating shaft, and, in particular, to ascertain whether the sense of rotation of the shaft with respect to the discs affected these significantly. This paper reports mostly on experimental measurements of the discharge coefficients. Some CFD modelling of this flow was carried out and this has helped to explain the experimental work. The experimental results show the effects on the discharge coefficient of rotational speed, flow rate, and co- and contra-rotations of the shaft relative to the discs. The measured values of the discharge coefficient are compared with established experimental data for non-rotating holes in the presence of a cross-flow. For stationary shaft and discs, co-rotation of the shaft and discs and differential rotation with the disc speed less than the shaft (in the same rotational direction), the discharge coefficients are in reasonable agreement with these data. For differential rotation (including contra-rotation) with the disc speed greater than the shaft, there is a significant decrease in discharge coefficient.     

Direct Numerical Simulation of Transitional Turbulent Flow in a Closed Rotor-Stator Cavity

The transitional turbulent regime in confined flow between a rotating and a stationary disc is studied using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows frequently arise in many industrial devices, especially in turbomachinary applications. The present contribution extends the DNS simulation into the turbulent flow regime, to a rotational Reynolds number Re =3 × 10⁵. An annular rotor-stator cavity of radial extension ΔR and height H, is considered with L = 4.72(L = ΔR/H) and Rm = 2.33 (Rm = (R ₁+ R ₀)/ΔR). The direct numerical simulation is performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached. A three-dimensional spectral method is used with the aim of providing both very accurate instantaneous fields and reliable statistical data. The instantaneous quantities are analysed in order to enhance our knowledge of the physics of turbulent rotating flows. Also, the results have been averaged so as to provide target turbulence data for any subsequent modelling attempts at reproducing the flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence manipulation in air–water flows on a stepped chute: An experimental study

In a stepped channel operating with large flow rates, the flow skims over the pseudo-bottom formed by the step edges as a coherent stream. Intense three-dimensional recirculation is maintained by shear stress transmission from the mainstream to the step cavities, while significant free-surface aeration takes place. The interactions between free-surface aeration and cavity recirculation are investigated herein with seven step cavity configurations. The experiments were conducted in a large stepped channel operating at large Reynolds numbers. For some experiments, triangular vanes, or longitudinal ribs, were placed across the step cavities to manipulate the flow turbulence to enhance the interactions between the mainstream flow and the cavity recirculation region. The results showed a strong influence of the vanes on the air–water flow properties in both free-stream and cavity flows. The findings demonstrate some passive turbulence manipulation in highly turbulent air–water flows.     

Calculation of laminar flow of a viscous fluid between rotating disks

The results are given of a numerical investigation of the laminar flow of a viscous incompressible fluid with heat transfer from the periphery to the center between two rotating disks. The system is a simplified model of one of the elements of the cooling circuit of a gas turbine. The complete Navier—Stokes equations in the vortlcity—flow function variables were solved by an explicit conservative scheme with appoximation of the convective terms of divergence type by directed differences. The calculations were made in a wide range of variation of the dimensionless determining parameters of the problem. The results agree well with the known experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–81, January–February, 1982.We thank V. M. Kapinos for discussion and helpful comments.     

Implementation of all‐Mach Roe‐type schemes in fully implicit CFD solvers – demonstration for wind turbine flows

This paper presents the implementation of all‐Mach Roe‐type schemes in a fully implicit CFD solver. Simple 2D cases, such as the flow around inviscid and viscous aerofoils, were used for an initial validation of these methods, along with more challenging computations consisting of the 3D flow around the Model Experiments in Controlled Conditions wind turbine, in parked and rotating conditions. This work is motivated by the increased interest of the wind turbine industry in larger diameter wind turbines where compressibility effects near the blade tips may be important. Instead of using an incompressible flow solver, this paper explores the option of modifying an existing, efficient, compressible flow solver for use at lower Mach numbers. The good performance of the Roe solver and its popularity influenced the selection of schemes for this work. The results suggest that effective all‐Mach solutions are possible with implicit solvers, and the paper defines the implementation of the new fluxes and Jacobian, including an investigation of some numerical parameters, using as platform the Helicopter Multi‐Block solver of Liverpool University. Copyright © 2013 John Wiley & Sons, Ltd.     

Étude des structures spirales à la périphérie d'une cavité rotor–stator aspiréeStudy of spiral structures at the periphery of an aspirated rotor–stator cavity

The influence of suction on the spirals pattern that appear on the periphery of an aspirated opened rotor–stator cavity is studied by means of tomography. A radial gap, located between the rotating disk and the fixed cylindrical wall allow the suction of an outer flux made up of a jet of fresh air and a high contrasted smoke thin sheet produced in the outside cavity Ekman layer. Sequences of tomographies allow the characterization of the apparition and disappearance thresholds according to Reynolds number, suction and wave number. To cite this article: D. Rémy et al., C. R. Mecanique 332 (2004).     

Experiments on dynamic behavior of near-field region in variable property jet with swirling flow

The dynamic behavior of the near-field region in a coaxial variable property jet has been experimentally investigated under a swirling flow produced by rotating cylindrical inner and outer tubes, focusing on how the swirl of the outer jet affects the formation of a stagnation point in the swirling inner jet. The inner and outer jets rotate in the same direction. Air, CO₂, or He is issued from the inner tube as a variable property jet, and air is issued from the outer tube in this work. In the case of a CO₂ jet (a high-density, low-viscosity gas jet), a stagnation point flow is more easily formed than in the case of an air jet, and the stagnation point location is significantly lower than in that of the air jet. When the swirl of the outer jet is introduced, a stagnation point flow is more easily formed than in the case of a nonswirling outer jet, and the stagnation point location is much lower than in the case of a nonswirling outer jet. In the case of a He jet (a low-density and high-viscosity gas jet), the inner jet does not have a stagnation point flow, and its overall behavior remains nearly unchanged even under high swirl numbers of the inner and outer jets. These results clearly show that the density and viscosity differences between the inner and outer jets have a significant impact on the dynamic behavior of the near-field region in the coaxial swirling jet. The significant lowering of the stagnation point location can be physically explained by considering the theoretical equation obtained in this work.     

考虑水弹性影响的水下航行体结构动响应研究

考虑水弹性的影响,计及惯性力、水动力和弹性力之间的相互耦合作用,将水动力学方程和结构动力学方程联合求解,采用三维势流理论和边界元法推导并计算了水下航行体结构的附加质量矩阵,对带空泡水下航行体出水过程中的结构动响应问题进行了分析.      

Observations of “granular jump” in the pneumatic conveying system

This paper presents a preliminary study of a previously unreported phenomenon of the “gas driven granular jump”, observed in the gas–solids flow within the pneumatic conveying system. From the phenomenological point of view, it resembles the already known processes such as hydraulic jumps in shallow water or granular jumps in granular flows in chutes or avalanches (although it seems most appropriate to explain it by analogy to a propagating granular bore). Clearly, unlike in classical phenomena of this type, the flow itself is driven by the aerodynamic forces related to the gas flow and the behaviour of the front of the “jump” is modified significantly by their presence. A series of high-speed camera visualisations are presented, which focus on this unusual behaviour of the flow on the border-line between cluster and stratified flow regimes in a horizontal pipe. Some similarities are drawn between the observed phenomenon and the broader class of problems exhibiting transition between super- and sub-critical flows. The fluid dynamical aspects and possible mechanisms behind the new phenomenon are discussed and the results obtained are compared quantitatively with simple theoretical models.     

Development of a computer program for the prediction of flow in a rotating cavity

A computer program has been developed to predict laminar source-sink flow in a rotating cylindrical cavity. Although the program is based on a standard finite difference technique for recirculating flow, it incorporates two novel features. Step changes in grid size are employed to obtain sufficient resolution in the boundary layers and special treatment is given to the solution of the pressure correction equations, in the ‘SIMPLE’ algorithm, in order to improve the convergence properties of the method. Results are presented both for the flow in an infinite rotating cylindrical annulus and a finite rotating cylindrical cavity, with the inner cylindrical surface acting as a uniform source and the outer cylinder as a sink. These show good agreement with existing analytical solutions and illustrate some of the problems associated with the computation of rapidly rotating flows.     

Application de l'approximation polytropique à la Simulation Numérique Directe de gaz chaudsApplication of the polytropique approximation to Direct Numerical Simulation of heated gases

As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003).