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 modelling fidelity is for rotating cavity flows. Although it is a widely held opinion that 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/LES type approaches such as 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 behaviour 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 non-physical modelled 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.

LES-CHT for a Rotating Cavity With Axial Throughflow

“…This wall normal spacing gives an average z + of 1.26 on the disks, and an average r + of 0.72 on the shroud. This gave average cell aspect ratios (wall-normal spacing divided by the square root of the cell face area on the wall) of 22 on the disks and 17 on the shroud, inline with previous wall resolved LES investigations on rotating cavities [1] and common LES resolution requirements [19]. 240 time-steps are used per revolution of the cavity, giving an volume-average convective CFL number of 0.4.…”

“…Both the near-disk and the near-shroud flow is very sensitive to thermal effects: on the shroud, buoyancy generated flow structures that enhance the local heat transfer have been observed by several authors [1][2][3][4] On the disks, Gao et al [5,6] found that the inclusion of viscous heating can affect heat transfer predictions due to the laminar nature of the disk Ekman layers. Similarly, Hickling and He [1] showed that the average disk shear stress was different when comparing an adiabatic and an isothermal disk with the same overall temperature difference.…”

“…It is becoming widely accepted that LES is the most appropriate turbulence modelling fidelity for the flow within rotating cavities. Hickling and He [1] showed that although unsteady Reynolds averaged Navier-Stokes (URANS) can give sensible area-averaged results in some cases, this is due to a fortunate cancellation of errors, and that the model does not predict the correct details of the flow structure and is not suitable for use in rotating cavities. This paper also showed that it is not suitable to use wall modelling approaches such as detached eddy simulation (DES) in these flows.…”

“…This challenge in rotating cavities is that the slip of the large-scale flow structure causes a very low frequency temperature fluctuation near the disks [1], which may have a penetration depth that is similar to (or even greater than) the solid domain thickness. This means that it is desirable to develop an approach that allows us to capture frequencies of unsteadiness in the solid domain when the thermal penetration depth is of a similar magnitude to the solid domain thickness so that any non-local interactions can be captured, but also allows us to use the wall transfer function approach for fluctuations that we do not need to solve/are not able to resolve properly in the solid domain.…”

Plume Model for Buoyancy-Induced Flow and Heat Transfer in Closed Rotating Cavities

“…Ekman-layer flow depends on differential rotation between the discs and the core, although in closed cavities the speed difference is very small. (Even at the high rotational speeds found in engines, the Coriolis forces can be large enough to suppress turbulence, and there is considerable evidence in the papers to support the assumption of laminar Ekman layer flow [15][16][17][18][19][20][21]. )…”