A theoretical model for ingress through turbine rim seals based on physically-observed unsteadiness

Recent experimental and computational research has demonstrated unsteady large-scale flow structures rotating in the rim seal clearance of aero-engine turbines. This intrinsic unsteadiness dominates the physical mechanism for the detrimental ingress of hot gases. Existing theoretical models of ingress lack this physical connection; nor can they predict the change in pressure across rim seals, important to the engine designer setting a superposed sealing flow to suppress ingress. This paper presents a new low-order model, named the Ingress Wave Model, relating ingress to the strength of the large-scale flow structures. Sinusoidal functions are used to represent the radial and circumferential velocities within the structures. For a given superposed sealing flow rate, a sealing effectiveness is determined by the non-dimensional amplitude of the sinusoidal function for the radial velocity, Phi(A), an empirical term that depends on the seal geometry as well as the annulus and wheel-space flow conditions. The circumferential and radial velocity are linked via the equations for continuity and angular momentum, yielding the radial pressure drop across the seal. Using appropriate empirical values of Phi(A), the model is validated over a wide range of experimental data from the literature. It is also demonstrated that the model is a practical tool in the preliminary design process, estimating the degree of ingress under different operating conditions.