*Modern high-bypass-ratio and high-pressure-ratio turbofan engine design presents multiple challenges. To achieve these design targets the size of the engine core has to be reduced. Without corresponding reductions in blade tip gap tolerance this will result in a larger blade tip clearance-to-blade span ratio, which will in turn lead to proportionally higher tip clearance losses. The blade tip clearance of the last axial compressor stage at near nominal engine speed is of the same order of magnitude as the thermal and centrifugal growths of the compressor rotor disc \[1\]. The thermal growth is controlled by the ﬂow and heat transfer in the rotating compressor disc cavities. In many cases these flows are buoyancy-dominated. Therefore, designing a tight blade tip clearance for modern jet engine requires improved knowledge of buoyancy-driven convection and reliable prediction tools.*

*This paper presents direct numerical simulation (DNS) and large-eddy simulation (LES) of buoyancy-driven convection in a sealed rapidly rotating annulus for Rayleigh number conditions 10^7^≤Ra≤10^9^. An incompressible Navier-Stoke (N-S) equation solver with the Boussinesq approximation is used for the DNS, whilst a fully compressible N-S code is employed for the LES. The Boussinesq approximation assumes density as a linear function of static temperature, and is considered to be valid up to a buoyancy parameter βΔ≤0.2. In the incompressible formulation the complete energy equation is simplified as a temperature transport equation, i.e. neglecting terms associated with kinetic energy, viscous, pressure and body force effects, for low Eckert number conditions. Closer agreement with the experiment, in terms of the shroud Nusselt number (Nu), and with the Nu-Ra scaling for gravitational convection is achieved by the compressible solver. As found in earlier studies the kinetic boundary layers on the rotating disc behave as unsteady Ekman layers: This effect is referred to as Ekman layer scrubbing. Analysis of the disc thermal boundary layer shows that viscous heating due to Ekman layer scrubbing can be important despite the small Eckert number (∼0.01, at Ra=10^9^). In this condition the velocity is fluctuating around a negligible mean value, and the energy dissipation is accumulated which raises the temperature in the Ekman layer. This is considered as the major contribution to the difference in shroud Nu between the two solvers, for the higher Ra condition.*

*Further to the sealed cavity configuration, a configuration with an axial throughflow is investigated using the compressible solver for axial throughﬂow Reynolds numbers 1000≤Re~z~≤5600. Compared with the sealed configuration, reduction in core static temperature is observed. Despite the presence of forced convection near the bore of the rotating annulus, the natural convection occurs near the shroud and shows similar Nu-Ra scaling exponent to the sealed natural convection test cases. The viscous heating effect is examined for this configuration and scaling of the effect to typical engine conditions is considered.*

Keywords: Ekman layer scrubbing, viscous heating, centrifugal buoyancy, rotating cavity.

Reference

\[1\] Luberti, D., Tang, H., Scobie, J. A., Pountney, O. J., Owen, J. M., Lock, G. D., 2019. “Inﬂuence of temperature distribution on radial growth of compressor discs”. *In Proceedings of the ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition*. Paper GT2019-91848.


Ekman Layer Scrubbing and Shroud Heat Transfer in Centrifugal Buoyancy-Driven Convection

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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