Analysis for Rotordynamic Coefficients of Helically-Grooved Turbulent Annular Seals

1987 ◽  
Vol 109 (1) ◽  
pp. 136-143 ◽  
Author(s):  
Chang-Ho Kim ◽  
D. W. Childs
Keyword(s):  
Space Shuttle ◽  
Helix Angle ◽  
Circumferential Velocity ◽  
Surface Pattern ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seals

An analysis for helically-grooved turbulent annular seals is developed to predict leakage and dynamic coefficients, as related to rotordynamics. The grooved surface pattern is formulated as an inhomogeneous directivity in surface shear stress. The governing equations, based on both Hirs’ turbulent lubrication theory and “fine-groove” theory, are expanded in the eccentricity ratio to yield zeroth and first-order perturbation solutions. The zeroth-order equations define the steady-state leakage and the circumferential velocity development due to wall shear for a centered rotor position. The first-order equations define perturbations in the pressure and axial and circumferential velocity fields due to small motion of the rotor about the centered position. Numerical results are presented for proposed grooved seals in the High Pressure Oxygen Turbopump (HPOTP) of the Space Shuttle Main Engine (SSME) and for a water-pump application. The results show that an optimum helix angle exists from a rotordynamic stability viewpoint. Further, a properly designed helically-grooved stator is predicted to have pronounced stability advantages over other currently used seals.

Effects of Wall Flexibility on the Rotordynamic Coefficients of Turbulent Cryogenic Annular Seals

1996 ◽  
Vol 118 (3) ◽  
pp. 509-519 ◽  
Author(s):  
B. Venkataraman ◽  
A. B. Palazzolo
Keyword(s):  
Energy Transport ◽  
Space Shuttle ◽  
Element Formulation ◽  
Local Pressure ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Wall Flexibility ◽  
Main Engine ◽  
Symmetric Finite Element ◽  
Annular Seals

A theory for analyzing the effects of elastic deformations of the seal wall on the dynamic characteristics of high pressure cryogenic annular seals under concentric operation is presented. The bulk flow continuity, axial and circumferential momentum, and the energy transport equations are utilized to determine the pressure distribution in the seal. Thermophysical properties of the cryogenic fluid are assumed to be functions of the local pressure and temperature. The wall deformations are obtained using an iso-parametric, axi-symmetric Finite Element formulation of the seal wall. A perturbation analysis is employed to arrive at the first order solution which yields the rotordynamic coefficients. Results obtained for the case of Space Shuttle Main Engine Oxygen Turbopump (SSME-HPOTP) Preburner Seal show a significant impact of seal flexibility on the dynamic coefficients.

Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment

1997 ◽  
Vol 119 (3) ◽  
pp. 443-447 ◽  
Author(s):  
O. R. Marquette ◽  
D. W. Childs ◽  
L. San Andres
Keyword(s):  
High Speed ◽  
Small Motion ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Theory Versus ◽  
High Speed Data ◽  
Static Eccentricity ◽  
Good Signal ◽  
Good Agreement ◽  
Annular Seals

Reliable high-speed data are presented for leakage and rotordynamic coefficients of a plain annular seal at centered and eccentric positions. A seal with L/D = 0.45 was tested, and measured results have good signal-to-noise ratios. The influence on rotordynamic coefficients of pressure drop, running speed, and static eccentricity was investigated. There is an excellent agreement between experimental and theoretical results in the centered position, even for direct inertia terms, which have not shown good agreement with predictions in past studies. However, the rotordynamic coefficients are more sensitive to changes in eccentricity than predicted. These results suggest that, in some cases, annular seals for pumps may need to be treated more like hydrodynamic bearings, with rotordynamic coefficients which are valid for small motion about a static equilibrium position versus the present eccentricity-independent coefficients.

Dynamic Analysis of Turbulent Annular Seals Based On Hirs’ Lubrication Equation

1983 ◽  
Vol 105 (3) ◽  
pp. 429-436 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
High Pressure ◽  
Space Shuttle ◽  
Water Pump ◽  
Centrifugal Pumps ◽  
First Order ◽  
Lubrication Equation ◽  
Inlet Swirl ◽  
Main Engine ◽  
Perturbation Solutions ◽  
Annular Seals

Expressions are derived which define dynamic coefficients for high-pressure annular seals typical of neck-ring and interstage seals employed in multistage centrifugal pumps. Completely developed turbulent flow is assumed in both the circumferential and axial directions, and is modeled in this analysis by Hirs’ turbulent lubrication equations. Linear zeroth and first-order “short-bearing” perturbation solutions are developed by an expansion in the eccentricity ratio. The influence of inlet swirl is accounted for in the development of the circumferential flow field. Comparisons are made between the stiffness, damping, and inertia coefficients derived herein based on Hirs’ model and previously published results based on other models. Finally, numerical results are presented for interstage seals in the Space Shuttle Main Engine High Pressure Fuel Turbopump and a water pump.

The Effects of Fixed Rotor Tilt on the Rotordynamic Coefficients of Incompressible Flow Annular Seals

1993 ◽  
Vol 115 (3) ◽  
pp. 336-340 ◽  
Author(s):  
J. K. Scharrer ◽  
N. Rubin ◽  
C. C. Nelson
Keyword(s):  
Pressure Distribution ◽  
Incompressible Flow ◽  
Order Continuity ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Arbitrary Position ◽  
Basic Equations ◽  
Perturbation Pressure

The basic equations are derived for incompressible flow in an annular seal with large rotor tilt. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Moody’s friction factor equation. Linearized zeroth and first-order perturbation equations are developed for small motion about an arbitrary position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are solved using a Fast Fourier technique, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynamic coefficients. Results of a parametric study show that the detrimental effects of a tilted rotor are small.

Rotordynamic Coefficients for Compressible Flow in Tapered Annular Seals

1985 ◽  
Vol 107 (3) ◽  
pp. 318-325 ◽  
Author(s):  
C. C. Nelson
Keyword(s):  
Compressible Flow ◽  
Flow Model ◽  
Space Shuttle ◽  
Governing Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Stiffness And Damping ◽  
Main Engine

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs’ turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

Rotordynamic Coefficients for Partially Tapered Annular Seals: Part I—Incompressible Flow

1991 ◽  
Vol 113 (1) ◽  
pp. 48-52 ◽  
Author(s):  
J. K. Scharrer ◽  
C. C. Nelson
Keyword(s):  
Pressure Distribution ◽  
Incompressible Flow ◽  
Order Continuity ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Annular Seal ◽  
Complex Differential Equations ◽  
Basic Equations

The basic equations are derived for incompressible flow in an annular seal with a partially tapered clearance. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Hirs’ turbulent lubrication equations. 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 continuity and momentum equations are solved exactly, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are reduced to three ordinary, complex, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynamic coefficients. Since no component test data exist for this type of seal, the results of a parametric study on the effect of the taper length/total length ratio on the seal leakage and rotor-dynamic coefficients are presented.

scholarly journals Analysis for Leakage and Rotordynamic Coefficients of Surface-Roughened Tapered Annular Gas Seals

1984 ◽  
Vol 106 (4) ◽  
pp. 927-934 ◽  
Author(s):  
C. C. Nelson
Keyword(s):  
Flow Model ◽  
Computational Method ◽  
Governing Equations ◽  
Clearance Ratio ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Honeycomb Seals ◽  
Gas Seals ◽  
Rotor Dynamic

In order to soften the effects of rub, the smooth stators of turbine gas seals are sometimes replaced by a honeycomb surface. This deliberately roughened stator and smooth rotor combination retards the seal leakage and may lead to enhanced rotor stability. However, many factors determine the rotordynamic coefficients and little is known as to the effectiveness of these “honeycomb seals” under various changes in the independent seal parameters. This analysis develops an analytical-computational method to solve for the rotordynamic coefficients of this type of compressible-flow seal. The governing equations for surface-roughened tapered annular gas seals are based on a modified Hirs’s turbulent bulk flow model. A perturbation analysis is employed to develop zeroth and first-order perturbation equations. These equations are numerically integrated to solve for the leakage, pressure, density, and velocity for small motion of the shaft about the centered position. The resulting pressure distribution is then integrated to find the corresponding rotor-dynamic coefficients. Finally, an example case is used to demonstrate the effect of changing from a smooth to a rough stator while varying the seal length, taper, preswirl, and clearance ratio.

Finite-Length Solutions for Rotordynamic Coefficients of Turbulent Annular Seals

1983 ◽  
Vol 105 (3) ◽  
pp. 437-444 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Pressure Distribution ◽  
Finite Length ◽  
Reaction Force ◽  
Centrifugal Pumps ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Continuity Equations ◽  
Complex Differential Equations ◽  
Annular Seals

Expressions are derived which define dynamic coefficients for high-pressure annular seals typical of wear-ring and interstage seals employed in multistage centrifugal pumps. Completely developed turbulent flow is assumed in both the circumferential and axial directions, and is modeled by Hirs’ turbulent lubrication equations. Linear zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. The influence of inlet swirl is accounted for in the development of the circumferential flow. The zeroth-order momentum and continuity equations are solved exactly, while their first-order counterparts are reduced to three ordinary, complex, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and define the pressure distribution due to seal motion. Integration of the pressure distribution defines the reaction force developed by the seal and the corresponding dynamic coefficients. Finite-length solutions for the coefficients are compared to two “short-seal” solutions.

Rotordynamic Coefficients for Partially Tapered Annular Seals: Part II—Compressible Flow

1991 ◽  
Vol 113 (1) ◽  
pp. 53-57
Author(s):  
J. K. Scharrer ◽  
C. C. Nelson
Keyword(s):  
Pressure Distribution ◽  
Compressible Flow ◽  
Order Continuity ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Component Test ◽  
Annular Seal ◽  
Complex Differential Equations ◽  
Basic Equations

The basic equations are derived for compressible flow in an annular seal with a partially tapered clearance. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Moody’s equation for roughness. 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 continuity and momentum equations are solved exactly, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are reduced to three ordinary, complex, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynamic coefficients. Since no component test data exist for this type of seal, the results of a parametric study on the effect of the taper length/seal length ratio on the seal leakage and rotordynamic coefficients are presented.

scholarly journals Rotordynamic Coefficients for Stepped Labyrinth Gas Seals

1989 ◽  
Vol 111 (1) ◽  
pp. 101-107 ◽  
Author(s):  
J. K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Parametric Study ◽  
Separation Of Variables ◽  
Reaction Force ◽  
Zeroth Order ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Gas Seals ◽  
Basic Equations

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, then the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (1986b) for a 15 tooth seal.

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