Numerical Predictions of High-Speed Rotating Labyrinth Seal Performance: Influence of Rotation on Power Dissipation and Temperature Rise

The development of new labyrinth seals, operating at high pressure ratios, temperature levels and rotational speeds, has led to thermally and mechanically heavy loaded labyrinth configurations. Thus, our recent studies were concerned with the influence of rotation on discharge behaviour and heat transfer of labyrinth seals, considering different labyrinth shapes. Another important aspect is the windage power dissipation occurring in the labyrinth seal, which may lead to a significant temperature rise of the labyrinth flow with a direct influence on heat transfer and the discharge behaviour of the seal. Moreover, material stresses induced by this effect may decrease the life time of the seal including the coatings of the labyrinth fins and therefore the efficiency of the machine. It is relatively difficult to study the seal performance exclusively by experimental means, as it is nearly impossible to separate various effects which are encountered at the measurements of labyrinth flows. Therefore, our numerical code for the prediction of labyrinth flows, which has been presented at a former presentation (Waschka et al. (1991)), has been extended in order to account for the windage power dissipation. The numerical code has been developed during the past years at our Institute. Based on a quasi three-dimensional finite volume method, it accounts for the elliptic character of the labyrinth flow. The three components of velocity are solved as well as the equation of energy. The well- known SIMPLEC method is adopted in order to calculate the pressure distribution of the flow field. The influence of turbulence is considered by the standard k−ε -model. Two different solution schemes are employed: at first, a semi implicit procedure (SIP) has been tested, which has been extended by a conjugate gradient method (CG) recently. As the flow through step labyrinth seals with relatively high ratios of clearance to fin height is numerically extremely complex, concerning the convergence behaviour of the code, the stable upwind scheme has been used. The present paper illustrates the theoretical approach considering windage power dissipation, which is taken into account by an additional term in the equation of energy. The results of the computations are compared with experimental data, taken in our experimental facility as well as elsewhere (McGreehan and Ko (1989)), with emphasis on the different parameters of influence. Correlations are tested, which have been described by Stoff (1988) in order to account for the effect of power dissipation in a simplified manner. Finally, the application of the numerical code in describing the influence of windage power dissipation is discussed critically.