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Research Papers

# Large-Eddy Simulation of Buoyancy-Induced Flow in a Sealed Rotating Cavity

[+] Author and Article Information
Diogo B. Pitz

Thermo-Fluid Systems,
University Technology Centre,
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK;
CAPES Foundation,
Ministry of Education of Brazil,
Brasília 70040-020, Brazil
e-mail: d.bertapitz@surrey.ac.uk

John W. Chew

Thermo-Fluid Systems,
University Technology Centre,
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: j.chew@surrey.ac.uk

Olaf Marxen

Thermo-Fluid Systems,
University Technology Centre,
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK

1Corresponding author.

Manuscript received July 3, 2018; final manuscript received July 15, 2018; published online October 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(2), 021020 (Oct 04, 2018) (9 pages) Paper No: GTP-18-1429; doi: 10.1115/1.4041113 History: Received July 03, 2018; Revised July 15, 2018

## Abstract

Buoyancy-induced flows occur in the rotating cavities of gas turbine internal air systems, and are particularly challenging to model due to their inherent unsteadiness. While the global features of such flows are well documented, detailed analyses of the unsteady structure and turbulent quantities have not been reported. In this work, we use a high-order numerical method to perform large-Eddy simulation of buoyancy-induced flow in a sealed rotating cavity with either adiabatic or heated disks. New insight is given into long-standing questions regarding the flow characteristics and nature of the boundary layers. The analyses focus on showing time-averaged quantities, including temperature and velocity fluctuations, as well as on the effect of the centrifugal Rayleigh number on the flow structure. Using velocity and temperature data collected over several revolutions of the system, the shroud and disk boundary layers are analyzed in detail. The instantaneous flow structure contains pairs of large, counter-rotating convection rolls, and it is shown that unsteady laminar Ekman boundary layers near the disks are driven by the interior flow structure. The shroud thermal boundary layer scales as approximately $Ra−1/3$, in agreement with observations for natural convection under gravity.

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## References

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## Figures

Fig. 1

Geometrical model used for the investigation of buoyancy-induced flow in a sealed rotating cavity. The outer and inner cylindrical surfaces are kept at constant temperatures Tb and Ta, respectively, with Tb > Ta, whereas the disks are either adiabatic or heated.

Fig. 2

Spectral element mesh in a radial-axial plane with Nel = 160, showing (a) element boundaries and (b) element boundaries with internal nodes for P = 7

Fig. 3

Instantaneous contours of normalized (a) temperature T*, (b) radial velocity ur*, and (c) tangential velocity uθ*, at the midaxial position for Ra=108 with adiabatic disks. The cavity rotates in the counter-clockwise direction.

Fig. 4

Near-disk profiles of normalized mean radial velocity ur*¯ and radial velocity fluctuation ur,rms* at different radial locations r*, for Ra=108 and adiabatic disks. The dashed lines correspond to the thickness of a laminar Ekman layer, (π/d)ν/Ω.

Fig. 6

(a) Near-disk profiles of normalized radial velocity fluctuations ur,rms* at r*=0.5, for the case of adiabatic disks at different Ra and (b) radial velocity fluctuation normalized by its maximum value versus z/δrms

Fig. 7

Near-disk profiles of normalized (a) radial velocity fluctuation ur,rms* and (b) temperature fluctuation Trms* at r*=0.5, for Ra=108

Fig. 8

Instantaneous profiles of ur* and uθ* at different azimuthal locations for r*=0.5, Ra=108 with adiabatic disks. The profiles are compared with Ekman-type solutions given by Eqs. (8) and (9).

Fig. 9

Profiles of (a) ur,rms⋆ and (b) uθ,rms⋆ as a function of the radial coordinate r*, for Ra=107 (solid line), Ra=108 (dashed line) and Ra=109 (dash-dot line), with adiabatic disks. The profiles were obtained by averaging over 0.25≤z*≤0.75. The superscript ⋆ indicates that the fluctuations are normalized by Ωa.

Fig. 5

((a) and (b)) Normalized disk boundary layer thicknesses δ0* and δrms* as a function of the radial location r*, for the case of adiabatic disks for Ra = 107 and Ra = 108, respectively, (c) δrms* averaged over 0.25≤r*≤0.75 as a function of the Reynolds number Re. The three circles correspond to Ra=107, Ra=108, and Ra=109, respectively.

Fig. 10

Normalized profiles of ((a) and (c)) mean temperature and ((b) and (d)) temperature fluctuation for Ra=107 (solid line), Ra=108 (dashed line), and Ra=109 (dash-dot line), with adiabatic disks. The profiles were obtained by averaging over 0.25≤z*≤0.75.

Fig. 11

(a) Temperature fluctuation normalized by its maximum value as a function of the distance from the shroud (b−r) normalized by the thermal boundary layer thickness λrms, forRa=107 (solid line), Ra=108 (dashed line), and Ra=109 (dash-dot line) and (b) λrms* versus Ra, showing a scaling of λrms*∝Ra−0.323

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