An Iwatsubo-Based Solution for Labyrinth Seals: Comparison to Experimental Results

Abstract

The basic equations are derived for compressible flow in a labyrinth seal.The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and firstorder perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equation.The firstorder equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients.The results of this analysis are compared to published test results.

Rotordynamic Coefficients for Stepped Labyrinth Gas Seals

“…The leakage equation (8), flow coefficient, kinetic energy carryover coefficient, and the choked flow solution algorithm are the same as those used by Childs and Scharrer (1986a). The kinetic energy carryover coefficient has the added restriction of being unity when the step height is greater than the clearance.…”

“…The shear stress model is the same as that used by Childs and Scharrer (1986a). The differences are in the dimensionless shear stress lengths and the hydraulic diameter.…”

“…The stepped labyrinth seal is as prevalent in turbomachinery as the straight-through labyrinth seal; however, there has been very little or no experimental or analytical work done to quantify the rotordynamic characteristics of this type of seal. This paper presents an analysis of the stepped labyrinth seal which is a derivative of the straight-through analysis of Childs and Scharrer (1986a). The results of this analysis will be presented in the form of a parametric study, since there are no known experimental data.…”

“…Childs and Scharrer (1986a), Iwatsubo (1980), Jenny et al (1984) and Scharrer (1987). There has also been an extensive amount of experimental data collected for the rotordynamic coefficients of straight-through labyrinth seals, e.g.…”

A model of gas flow with friction in a slotted seal

“…In the description of the mass flow, the authors of this paper, using one-dimensional theory, applied the gas flow model for a short pipe. Paper [1] includes the model allowing for the influence of tangential tensions in a two disc, one-sided seal geometry. The experimental research on the determination of coefficients of friction losses for short segments of one-sided seals have been presented in [14,16].…”