Form Shear Stress (FSS) Correction in Bulk Flow Analysis of Grooved Seals Based on Effective Film Thickness

Bulk flow models for grooved annular seals provide computationally efficient static and dynamic response predictions, though heavy reliance on empirical relationships often leads to undesirable levels of uncertainty. The flow complexity caused by the grooves adds difficulty to shear stress modeling for these seals. This study seeks to improve shear stress modeling for grooved seals through the identification and quantification of the additional bulk flow shear stress contributions within the groove region. Through single groove computational fluid dynamics (CFD) simulations and an effective film thickness analysis framework, the additional groove shear stress component is identified as a form shear stress (FSS) due to its clear relationship to the effective film thickness behavior. The FSS is quantified as a correction to traditional shear stress definitions. Predictive models for the FSS are developed as functions of the ratio of circumferential to axial Reynolds number and the total resultant Reynolds number. Implementation of the FSS models into a simplified bulk flow method delivers leakage predictions for three seal cases within 10% of the experimental results and qualitative agreement in predicted circumferential velocity profiles while eliminating the need for an assumed groove loss coefficient. This is the first paper to utilize an effective film thickness based procedure to quantify and model the FSS component in grooved seal bulk flow analysis. The demonstrated predictive capability and widespread applicability of the models and approach presented in this paper provide an avenue for significant improvements in grooved seal bulk flow prediction accuracy through improved shear stress modeling.