Predictions of effect of swirl on flow and heat transfer in a rotating cavity

Abstract

Pre-swirl nozzles are used to deliver the cooling air to the rotating turbine blades in the cooling systems of gas turbine engines. This paper considers the case where the cooling air flows radially outward, between two corotating discs, to create a free vortex in the inviscid core between the boundary layers on the discs. A thermodynamic analysis is used to relate the temperature increase of the cooling air to the adiabatic work term (which reduces the air temperature) and to the heat transfer from the discs to the air (which increases the temperature). The Reynolds analogy has been used to determine an expression for the adiabatic-disc temperature and to draw conclusions about the moment coefficient and average Nusselt number. An important parameter is β p , the ratio of the tangential velocity of the pre-swirl air to the speed of the rotating disc, and the Reynolds analogy shows that the moment coefficient is zero when β p = β p,crit , a critical pre-swirl ratio, and that the average Nusselt number is a minimum when β p = β p,opt , an optimal pre-swirl ratio. Computations made using a steady-state axisymmetric elliptic-flow solver, incorporating a low-Reynolds-number k – ϵ turbulence model, are in good agreement with the pressure distribution, adiabatic-disc temperature and local Nusselt numbers predicted by the theoretical models. The computed values of β p,crit agree with the theoretical values, and the computations also confirm the occurrence of a minimum average Nusselt number. For β p < β p,opt , the computed temperature of the cooling air decreases as β p increases; for β p > β p,opt , whether the temperature decreases or increases depends on the relative magnitude of the adiabatic work term and the heat transfer from the discs.