Rotordynamic Coefficients for Stepped Labyrinth Gas Seals

Abstract

The basic equations are derived for compressible flow in a stepped labyrinth gas 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 first-order 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 equations. The first order 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 presented in the form of a parametric study, since there are no known experimental data for the rotordynamic coefficients of stepped labyrinth gas seals. The parametric study investigates the relative rotordynamic stability of convergent, straight and divergent stepped labyrinth gas seals. The results show that, generally, the divergent seal is more stable, rotordynamically, than the straight or convergent seals. The results also show that the teeth-on-stator seals are not always more stable, rotordynamically, than the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (198613) for a 15 tooth seal.

Theory Versus Experiment for the Rotordynamic Coefficients of an Interlocking Labyrinth Gas Seal

“…Then, the stiffness and direct damping coefficients are presented versus inlet circumferential velocity ratio for three supply pressures and three shaft speeds, with a plotted line for each of four pressure ratios. The experimental results are compared to the predictions of Scharrer (1988…”

“…For all tests, the air temperature was between 296 and 310 K. The test seal geometry is shown in Figure 1. Scharrer (1988) extended an earlier one-control volume, bulk flow model for see-through labyrinth seals to analyze "stepped" labyrinth seals. The interlocking seal shown in Figure 1 is an example of a stepped labyrinth seal.…”

“…Although many turbomachines use interlocking labyrinth seals, very little research has been focused on determining their characteristics. This paper compares experimental results to theoretical predictions (Scharrer, 1988) of the rotordynamic coefficients of a full labyrinth or interlocking seal. The seal geometry tested is shown in Figure 1.…”

Research into the dynamic coefficient of the rotor-seal system for teeth-on-stator and teeth-on-rotor based on an improved nonlinear seal force model

“…A two-control-volume model was proposed by Wyssmann (1984). Scharrer (1989) and Childs (1986aChilds ( , 1993 gave a reasonable supplement and correction to make a two-control-volume model have more extensive application.…”

Rotordynamic Analysis of See-through-type Labyrinth Seal Using 3D CFD

“…은 two-control-volume model 해석법을 통한 개선된 결과를 발표하였다. 계단식 래 버린스 실에 대하여, Scharrer (6) 의 Blasius 마찰계수 식을 사용한 해석결과와 Ha (7) 의 Moody 마찰계수 식을 사용한 개 선된 해석 결과가 발표되었다. Ha (8) 는 (14) 을 기초로 제안하고자 한다.…”