الفهرس 
AcknowledgementOnly 14 pages are availabe for public view
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Abstract
The analysis of the rectangular labyrinth seals having several geometrical configurations is carried out in this work. Prior to any experimental work a theoretical prediction of the labyrinth performance and dynamic characteristics for different geometries at different eccentricity ratios is required. The laminar, incompressible and three-diinensional flow in labyrinth seals is treated and the performance and dynamic characteristics are obtained.The analysis is restricted here to the case where the labyrinth height to shaft radius ratio m« 1. Such restriction enables the velocity components and pressure to be put in ascending powers of m. Because of rotor eccentricity the flow in the seal is not axisymmetric and the seal height must be specified at any circumferential position. The governing equations are put in transformed coordinate system by introducing a new radial coordinate whereby the eccentric shaft is converted to be concentric with the seal gland. For steady, laminar and incompressible flow the nature of the flow inside the labyrinth cavity depends on geometrical configuration of the seal (grooved shaft, grooved casing, up-the step and down-the step) and rotation of the shaft. The velocity components and pressure are introduced as components due to rotation of the- shaft superimposed on the resulting components due to the labyrinth geometry at a certain amount of axial leakage velocity. Determination of direct and cross-coupled stiffness ahd damping coefficients of the seal can be obtained using the method of small disturbances. The labyrinth height is assumed to have small variations superimposed on the steady state specified height. This will cause similar variations in the flow velocity components and pressure. The equations of_ ”notion are derived for small motion• of the shaft center in tWo onhogonal . coordinate directions and the ~quations goven$g the variations of the flowvariables are obtained for stationary and rotating seals. The variations of pressure distribution are then calculated for different geometries and at different shaft eccentricities for stationary and rotating seals. By integration in the axial and circumferential directions, the aerodynamic forces, direct and cross-coupled stiffness and damping coefficients can be detennined.Successful attempts have been made to use fluid blowing to pressurize labyrinth seals in order to prevent leakage through the glands and to control the stiffuess and damping coefficients of labyrinth seals. Glands provided with circumferential slots are used , it is to be noted that the effect of geometrical shape on the . seal performance is of great importance as far as a search for an optimum blowing amount is concerned. The effect of blowing on the leakage rate through seals of different geometrical configurations is examined. Also, the effect of blowing on the dynamic coefficients of stationary gro~ved shaft labyrinth seal is obtained here.
To obtain the performance and dynamic characteristics of rectangular labyrinth seals having rotor misalignment without great difficulty and with saving in computer running cost, the perturbation method is also introduced in this work. The perturbation analysis is used to study the problem of axial leakage through the stationary grooved shaft labyrinth seal and to obtain the dynamic characteristics for different values of eccentricity ratios. Also, the perturbation analysis presented in this work deals, with the mesh size that depends on the rotor misalignment. The results of the perturbation analysis based on the eccentricity ratio show that the agreement with the general solution is satisfactory.
The mathematical model obtained is not generally tractable by analytical methods leading to solutions in closed forms. The governing equations and the boundary conditions for the flow in rectangular labyrinth seals as presented in this work are suited to nWIlerical computations by fmite difference approximations and solved using the Gauss-Seidel, successive overrelaxation and successive underrelaxation iterative methods.
The height to width ratio of the labyrinth cavity y , the clearance ratio termed as radial clearance to height of the cavity c, the eccentricity ratio E and the rotation of the shaft are the factorS investigated in this work for different geometries (grooved shaft,’grooved casing, up-the step and down-the step). In the absence of shaft rotation, the effects of height to width ratio y Bud the eccentricity ratio’ E on the performance and dynamic characteristics are examined for the geometries considered. The results show that the rotation
of the shaft gives no sensible differences in the performance of the, grooved end grooved casing seals. For’up-the step and ’down-the step seals the