Study of Critical Flow for Supercritical CO₂ Turbomachinery Seal Design

The S-CO₂ leakage flow from turbo-machinery via seal becomes one of the important issues since not only it influences the cycle efficiency due to parasitic loss but also it is important for evaluating the system safety under various operating conditions. In the previous authors' study, the effect of the tooth length on the critical flow and comparing the results to the existing two phase system analysis code calculation were presented. However, since the code is limited to fully reflect the gap effect and the number of tooth effect, a separate numerical model had to be developed. In this paper, the number of tooth effect in a labyrinth seal geometry nozzle are presented by using the same experimental facility described in the previous paper. Predicting the leak flow rate in turbo-machinery seals is imperative to secure high performance of an S-CO₂ power cycle. This paper includes the experimental data obtained under various conditions. Although this study does not immediately contribute for reducing the leakage flow, it provides useful information for further understanding of labyrinth seal leakage performance and eventually leading to the design optimization. The model suggested by Hodkinson for predicting the critical flow in the seal geometry gave a good agreement with the experimental data. The newly developed model should reflect the gap effect, the number of tooth effect as well as the two phase effect to capture all important physical processes in the seal and showing a good prediction capability for the seal design.