Flow In Rotating Cavity Research Articles

Parametric dependence and elementary modelling for compressor disc cavity heat transfer

A wall-modelled large-eddy simulation (WMLES) method previously validated against laboratory experiments is applied to a real engine disc cavity geometry with surface and air temperatures representative of maximum power conditions. An appropriate set of independent nondimensional parameters describing the problem is defined and the sensitivities to these parameters are investigated by independently varying each parameter in the WMLES. Effects of a change in disc temperature distribution and a reduction in radius of the downstream disc are also investigated. The flow and heat transfer mechanisms predicted are very similar to those found for the research rig configuration although rotating cavity flow structures with two or more lobes are found for the engine geometry rather than the single-lobed structures shown in previous work. The simulations are compared with an elementary model giving further insight into scaling of the flow and heat transfer with operating conditions. The model assumes a well-mixed core flow in the cavity with constant rothalpy, relates shroud heat transfer to that of natural convection under gravity for high Rayleigh number, and relates disc heat transfer to conduction across unsteady Ekman layers. An energy balance for the cavity is used to obtain an effective mass flow exchange rate between the axial throughflow and the disc cavity to the disc and shroud heat transfer and core temperature. The model is considered to give a useful basis for engineering calculations involving correlation and extrapolation of WMLES and experimental results.

Some Observations on the Computational Sensitivity of Rotating Cavity Flows

Abstract Across the open literature, there is no clear consensus on what the most suitable modeling fidelity is for rotating cavity flows. Although it is a widely held opinion that unsteady Reynolds-averaged-Navier–Stokes (URANS) approaches are unsuitable, many authors have succeeded in getting reasonable heat transfer results with them. There is also a lack of research into the validity of hybrid URANS/large eddy simulation (LES) type approaches such as detached eddy simulation (DES). This paper addresses these research challenges with a systematic investigation of a rotating cavity with axial throughflow at Grashof numbers of 3.03×109 and 3.03×1011. The disk near-wall layers remained laminar at both conditions, meaning that a turbulence model should not be active in these regions. The disk heat transfer was observed to affect the near-disk aerodynamics, which in turn affect the disk heat transfer: this feedback loop implies that conjugate heat transfer computations of rotating cavities may be worth investigating. On the shroud, additional eddy viscosity in URANS and DES was found to interfere with the formation of heat transfer enhancing streaks, whilst these were always captured by LES. DES exhibited a concerning behavior at the higher Grashof number. Locally generated eddy viscosity from the shroud was injected into the bulk fluid by the radial inflow. This contaminated the entire cavity with nonphysical modeled turbulence. As the radial inflow is a characteristic feature of rotating cavity flows, these results show that caution is necessary when applying hybrid URANS/LES approaches to this type of flow.

Investigation on the Radial Heat-Transfer of Pumping Secondary Flow in Semiclosed Rotating Disk Cavity

Abstract This study investigates the mean flow and radial heat-transfer behaviors in semiclosed rotating disk cavity within the canned reactor coolant pump. The flow in the semiclosed cavity contains the Stewartson type flow at inner region and the Batchelor type flow at outer region. The heat is radially transported from the outer rim of the semiclosed disk cavity to discharge-hole through the nondirect discharge (ND) portion of the superimposed flow from inlet. The effects of rotating Reynolds numbers, cavity aspect ratio and radial location of discharge-hole on the discharge ratio, pumping mass flow rate, local wall shear stress and radial heat-transfer coefficient are examined in the semiclosed rotating cavity flow, respectively. Based on the radial heat transfer behaviors of pumping secondary flow, an equivalent thermal network is proposed and validated by experiments, which can effectively predict the radial temperature distribution from the discharge hole to periphery with the viscous-heating and nonisothermal effects.

Stability and control of an annular rotor/stator cavity limit cycle

Rotating cavity flows have been widely studied for years because of many implications that these have on industrial applications. These flows can indeed generate, under specific conditions, self-sustained oscillations that can be noisy or even dangerous for the integrity of a system. The coherent structures or flow modes composing this unsteady phenomenon usually called “pressure band phenomenon” are misunderstood and therefore difficult to control. In the present study, the dynamics of an annular rotor/stator cavity is investigated to shed some light on the flow organization and identify control strategies based on reliable theory and analysis to stabilize the observed undesired flow modes. No specific tool is known today to control a multi-frequency phenomenon. To address this first issue, the mode dominance and interactions appearing in this multi-frequency problem are investigated, thanks to dynamic mode tracking and control [M. Queguineur et al., “Dynamic mode tracking and control with a relaxation method,” Phys. Fluids 31, 034101 (2019)]. The benefit of this method is to be able to follow in time several modes while controlling them one by one and observe mode dominance and interactions. This purely numerical controller shows that, here, the dominant mode of the annular cavity is at the source of another low frequency mode. Based on this information and to develop a physically relevant control strategy, the global linear stability framework previously used by Queguineur et al. [“Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles,” Phys. Fluids 31, 104109 (2019)] is further developed to make use of the sensitivity to a base flow modification theory. This specific analysis indeed enables us to point out the exact location where the base flow should be modified to shift the dominant mode frequency and/or growth rate. In this context, passive controller positioning is identified for the studied annular cavity flow. Such strategies are then validated through new large eddy simulations of a controlled cavity using low amplitude injection/suction demonstrating the adequacy of the analysis and control strategy.

Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles

Although rotating cavity flows are essential components of industrial applications, their dynamics is still largely misunderstood. From computer hard-drives to turbopumps of space launchers, designed devices often produce flow oscillations that can destroy the component prematurely, or produce disturbing noise or undesired operating modes of the system. The fundamentals of encountered static and rotating flow boundary layers have evidenced, a long time ago now, the presence of specific boundary layer instabilities and structures for low Reynolds numbers. For higher Reynolds numbers and fully enclosed systems, features are, however, more complex with the apparition of multifrequency oscillations populating the entire cavity limit cycle. For these flows, Large Eddy Simulation (LES) has illustrated the capacity of reproducing features and limit cycles. However, identifying the origin and region within these flows that are responsible for mode selections remains difficult if not impossible using such computational fluid dynamics tools. The present contribution evaluates a LES and a global stability analysis framework to identify the mechanisms responsible for the observed limit-cycles of two types of rotor-stator cavities. In particular, the presence of a central body or shaft and its impact on the instability selection is of interest here, i.e., the identification of the regions of mode activation for a cylindrical as well as an annular cavity is detailed. Results issued by the conjunct use of dynamical mode decomposition and Global Linear Stability Analysis (GLSA) confirm the observed LES dynamics. Most importantly, GLSA gives access to the triggering mechanisms at the root of the limit-cycles expression as well as hints on the mode selection. In that respect, a cylindrical cavity is shown to sustain more complex features than an annular cavity because of an enhanced flow curvature near the central shaft.

Rotationally-induced unstable flow characteristics and structural optimization of rim seals

In view of rotationally-induced unsteady rim sealing flow issues in the absence of mainflow nonuniform pressure fields, the large eddy simulation method validated by the enclosed rotating cavity flow measurement was adopted to investigate the instability of the flow in the enclosed rim seal cavity. On this basis, the unsteady Reynolds-averaged numerical calculation was carried out for three structures: typical axial and radial rim seals as well as the chute seal that is visible in actual engines. The unsteady sealing flow characteristics for typical rim seal structures are investigated. The dynamic characteristics of the large-scale vortex structures in the rim seal region are revealed by fast Fourier transform and cross-correlation analysis methods. Finally, the rotationally-induced sealing characteristics for different rim seal structures and the enlightenment of the seal structure optimization are given. The results show that the rotationally-induced rim sealing flow has inherent instability characteristics; a series of large-scale vortex structures are generated in the rim clearance region, which propagate in the circumferential direction at a speed lower than the rotor, and the vortex frequency, number of revolutions and number of vortices depend on the rim seal type; overall, the chute rim seal has the highest rotationally-induced sealing effectiveness.

Flow development through HP & LP turbines, Part I: Inward rotating cavity flow with superimposed throughflow

With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1st part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface’s boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn’t happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re φ and C w is not considered in the current two parts paper.

Large scale motions of multiple limit-cycle high Reynolds number annular and toroidal rotor/stator cavities

Rotating cavity flows are essential components of industrial applications but their dynamics are still not fully understood when it comes to the relation between the fluid organization and monitored pressure fluctuations. From computer hard-drives to turbo-pumps of space launchers, designed devices often produce flow oscillations that can either destroy the component prematurely or produce too much noise. In such a context, large scale dynamics of high Reynolds number rotor/stator cavities need better understanding especially at the flow limit-cycle or associated statistically stationary state. In particular, the influence of curvature as well as cavity aspect ratio on the large scale organization and flow stability at a fixed rotating disc Reynolds number is fundamental. To probe such flows, wall-resolved large eddy simulation is applied to two different rotor/stator cylindrical cavities and one annular cavity. Validation of the predictions proves the method to be suited and to capture the disc boundary layer patterns reported in the literature. It is then shown that in complement to these disc boundary layer analyses, at the limit-cycle the rotating flows exhibit characteristic patterns at mid-height in the homogeneous core pointing the importance of large scale features. Indeed, dynamic modal decomposition reveals that the entire flow dynamics are driven by only a handful of atomic modes whose combination links the oscillatory patterns observed in the boundary layers as well as in the core of the cavity. These fluctuations form macro-structures, born in the unstable stator boundary layer and extending through the homogeneous inviscid core to the rotating disc boundary layer, causing its instability under some conditions. More importantly, the macro-structures significantly differ depending on the configuration pointing the need for deeper understanding of the influence of geometrical parameters as well as operating conditions.

A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

The present work proposes a collocation spectral method for solving the three-dimensional Navier–Stokes equations using cylindrical coordinates. The whole diameter -R⩽r⩽R is discretized with an even number of radial Gauss–Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectral convergence that reduces the number of grid points with respect to lower-order numerical methods. The grid-points distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in tall cylinders and thin inter-disc cavities. Associated to a spectral vanishing viscosity [E. Séverac, E. Serre, A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities, J. Comp. Phys. 226 (2007) 1234–1255], the method provides very promising LES results of turbulent cavity flows.

Toward Defining Objective Criteria for Assessing the Adequacy of Assumed Axisymmetry and Steadiness of Flows in Rotating Cavities

The need to make a priori decisions about the level of approximation that can be accepted—and subsequently justified—in flows of industrial complexity is a perennial problem for computational fluid dynamics (CFD) analysts. This problem is particularly acute in the simulation of rotating cavity flows, where the stiffness of the equation set results in protracted convergence times, making any simplification extremely attractive. For example, it is common practice, in applications where the geometry and boundary conditions are axisymmetric, to assume that the flow solution will also be axisymmetric. It is known, however, that inappropriate imposition of this assumption can lead to significant errors. Similarly, where the geometry or boundary conditions exhibit cyclic symmetry, it is quite common for analysts to constrain the solutions to satisfy this symmetry through boundary condition definition. Examples of inappropriate use of these approximating assumptions are frequently encountered in rotating machinery applications, such as the ventilation of rotating cavities within aero-engines. Objective criteria are required to provide guidance regarding the level of approximation that is appropriate in such applications. In the present work, a study has been carried out into: (i) The extent to which local three-dimensional features influence solutions in a generally two-dimensional (2D) problem. Criteria are proposed to aid in decisions about when a 2D axisymmetric model is likely to deliver an acceptable solution; (ii) the influence of flow features which may have a cyclic symmetry that differs from the bounding geometry or imposed boundary conditions (or indeed have no cyclic symmetry); and (iii) the influence of unsteady flow features and the extent to which their effects can be represented by mixing plane or multiple reference frame approximations.

Three‐Dimensional Thermo Fluid Analysis of Large Scale Electric Motor

In the present work, the flow and temperature fields in large scale rotating electric motor are studied by solving the Navier–Stokes equations along with the temperature equation on the basis of finite difference method. All the equations are written in terms of relative velocity with respect to the rotating frame of reference. Generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. Differential terms with respect to time are approximated by forward differences, diffusion terms are approximated by the implicit Euler form, convection terms in the Navier–Stokes equations are approximated by the third order upwind difference scheme. The results of calculation led to a good understanding of the flow behavior, namely, the rotating cavity flow in between the supporting bar of the motor, the flow stagnation and region of temperature rise due to flow stagnation, etc. Also the measured average temperature of the motor coil wall is predicted quite satisfactorily.

Assessment of Two- and Three-Scale k–ε Models for Rotating Cavity Flows

A three-scale k–ε turbulence model was recently developed for complex flows such as the rotor–rotor and rotor–stator cavities found in gas turbine engines. The three-scale model is a logical extension of the previous two-scale k–ε model of Ko and Rhode (1990). Both multiscale turbulence models are presented and assessed via comparison with measurements for possible adoption in future cavity computations. A single computer code solving the two-dimensional axisymmetric Navier–Stokes equations with a “switch” for selecting among the various turbulence models being compared was used. It was found for both cavity cases that the three-scale model gives a marginal improvement over the two-scale model. Further, both multiscale models give a substantial improvement over the standard k–ε model for the rotor–stator case, especially in the near-wall region where different eddy sizes are found. However, the feasibility of using a multiscale model for the rotor–rotor case is unclear since it gives improved values over the standard high-Re model in some regions but worse values in other regions. In addition, the solutions provide enhanced insight concerning the large changes in flow pattern previously photographed in the rotor–rotor case as rotation increases. In particular, it is shown how: (a) the number of recirculation zones increase with increasing rotation rate and (b) the recirculation zones decrease in size with a decreasing G ratio.

Digital vector image processing of lid-driven rotating cavity flow

A flow visualization method entitled Digital Vector Velocimetry (DVV) method is introduced to extract the flow field quantitatively from particle images. This methodis applied to a lid-driven rotating cavity flow. In the DVV method, a time sequence of images are captured by a CCD (Charge Coupled Device) video camera with each frame containing a single-exposure image. All possible velocity vectors between two temporally successive images in the interrogating window are digitally constructed on the digital vectorgram. The most probable velocity vector is identified as the velocity vector of the maximum intensity in the digital vectorgram. The DVV system provides measurement with subpixel accuracy. The dynamic range of the velocity is expanded using feedback analysis that selects consistent velocity vectors.

Flow and Thermal Fields in Channels Between Corotating Disks

Flow and thermal fields in disk packs are analyzed numerically. These flows are a subset of enclosed rotating cavity flows in which the disks are rotating with the same angular velocity and contained within a fixed cylindrical shroud. The axisymmetric model under consideration consists of a pair of corotating disks with mid-line symmetry. The corotating disks are assumed to be fully shrouded. Computed velocity and temperature fields in the gap between corotating disks are given for a 5.25-in. disk geometry drive. Estimates of disk windage for corotating disks were found to be 30 to 40% of those obtained for a rotor/stator geometry.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>