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.

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.

Analysis of Eccentric Annular Incompressible Seals: Part 2—Effects of Eccentricity on Rotordynamic Coefficients

1988 ◽  
Vol 110 (2) ◽  
pp. 361-366 ◽  
Author(s):  
C. C. Nelson ◽  
D. T. Nguyen
Keyword(s):  
Flow Model ◽  
Element Model ◽  
Analysis Procedure ◽  
Governing Equations ◽  
Zeroth Order ◽  
Static Displacement ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Flow Variables ◽  
Factor Equation

In Part 1 of this paper, a new analysis procedure is presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. This part of the paper (Part 2) incorporates the solutions from Part 1 to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations by means of the method described in Part 1, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare very well with available experimental data, and are clearly more accurate than the predictions based on a Finite Element model.

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.

scholarly journals Rotordynamic Coefficients for Partially Roughened Annular Gas Seals

1991 ◽  
Author(s):  
Joseph K. Scharrer ◽  
Clay C. Nelson
Keyword(s):  
Pressure Distribution ◽  
Order Continuity ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Complex Differential Equations ◽  
Gas Seals ◽  
Basic Equations ◽  
Perturbation Pressure

The basic equations are derived for compressible flow in an annular seal with partially roughened surfaces. 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 test data exist for this type of seal, the results of a parametric study on the effect of the rough length/smooth length ratio on the seal leakage and rotordynamic coefficients is presented.

Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals: Part I—A Two Control Volume Model

1988 ◽  
Vol 110 (3) ◽  
pp. 270-280 ◽  
Author(s):  
Joseph K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Control Volume ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Wall Friction ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Volume Model ◽  
Gas Seals

The basic equations are derived for a two-control-volume model for compressible flow in a labyrinth seal. The recirculation velocity in the cavity is incorporated into the model for the first time. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. 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 variable 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.

Calculation of Rotordynamic Coefficients and Leakage for Annular Gas Seals by Means of Finite Difference Techniques

1989 ◽  
Vol 111 (3) ◽  
pp. 545-552 ◽  
Author(s):  
R. Nordmann ◽  
F. J. Dietzen ◽  
H. P. Weiser
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Zeroth Order ◽  
Navier Stokes Equations ◽  
First Order ◽  
Fluid Forces ◽  
Rotordynamic Coefficients ◽  
Gas Seals ◽  
Finite Difference Techniques

The compressible flow in a seal can be described by the Navier-Stokes equations in connection with a turbulence model (k–ε model) and an energy equation. By introducing a perturbation analysis in these differential equations we obtain zeroth order equations for the centered position and first order equations for small motions of the shaft about the centered position. These equations are solved by a finite difference technique. The zeroth order equations describe the leakage flow. Integrating the pressure solution of the first order equations yields the fluid forces and the rotordynamic coefficients, respectively.

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.

Development of Scallop Cut Type Damper Seal for Centrifugal Compressors

2014 ◽  
Author(s):  
Naohiko Takahashi ◽  
Haruo Miura ◽  
Mitsuhiro Narita ◽  
Noriyo Nishijima ◽  
Yohei Magara
Keyword(s):  
High Pressure ◽  
Perturbation Analysis ◽  
Flow Model ◽  
Frame Of Reference ◽  
Bulk Flow ◽  
Rotating Frame ◽  
Rotordynamic Coefficients ◽  
Neighboring Region ◽  
Rotor Surface ◽  
Honeycomb Seals

This paper deals with a new type of damper seal developed for a high-pressure centrifugal compressor. Honeycomb seals and hole-pattern seals are popularly used as damper seals and provide superior rotordynamic damping characteristics. Honeycomb seals are expensive because the manufacturing process is complex. Hole-pattern seals are easier to manufacture, but they are still expensive. Use of a scallop pattern is one way to reduce manufacturing cost and time. A new seal that has a scallop pattern and small teeth on the stator surface is proposed. This pattern is cut on the stator surface using a disc type tool. To estimate the rotordynamic coefficients of this new seal, a bulk flow model code that is based on a two-control-volume model developed by Matsuda for labyrinth seals was newly developed. This model uses the Hirs model for the viscous shear stresses. The friction factor coefficients for the rotor surface, the stator surface and the surface between the two control volumes were determined by CFD steady analysis. The rotordynamic coefficients can also be obtained by using CFD perturbation analysis. The high accuracy of the bulk flow model was demonstrated by comparing its results with CFD perturbation analysis results. In the perturbation analysis, the whirling motion was treated as a steady state problem by using a rotating frame of reference. For the damper seal, the rotor surface and its neighboring region were treated with a rotating frame of reference and the neighboring region of the stator was treated with a stationary frame of reference. The damping property of the new seal was evaluated by conducting rotor stability tests using a high-pressure compressor with an electromagnetic exciter. The new seal equipped with swirl brakes was used for the balance piston of the compressor. Stability was evaluated by exciting the rotor during operation and identifying the eigenvalues of the rotor. The experimental results showed that the new seal increases damping. Comparison of the damping effect with calculations based on the bulk flow analysis showed good agreement.

Development of Scallop Cut Type Damper Seal for Centrifugal Compressors

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Naohiko Takahashi ◽  
Haruo Miura ◽  
Mitsuhiro Narita ◽  
Noriyo Nishijima ◽  
Yohei Magara
Keyword(s):  
High Pressure ◽  
Perturbation Analysis ◽  
Flow Model ◽  
Frame Of Reference ◽  
Bulk Flow ◽  
Rotating Frame ◽  
Rotordynamic Coefficients ◽  
Neighboring Region ◽  
Rotor Surface ◽  
Honeycomb Seals

This paper deals with a new type of damper seal developed for a high-pressure centrifugal compressor. Honeycomb seals and hole pattern seals are popularly used as damper seals and provide superior rotordynamic damping characteristics. Honeycomb seals are expensive because the manufacturing process is complex. Hole pattern seals are easier to manufacture, but they are still expensive. Use of a scallop pattern is one way to reduce manufacturing cost and time. A new seal that has a scallop pattern and small teeth on the stator surface is proposed. This pattern is cut on the stator surface using a disk type tool. To estimate the rotordynamic coefficients of this new seal, a bulk flow model code that is based on a two-control-volume model developed by Matsuda for labyrinth seals was newly developed. This model uses the Hirs model for the viscous shear stresses. The friction factor coefficients for the rotor surface, the stator surface, and the surface between the two-control-volumes were determined by computational fluid dynamics (CFD) steady analysis. The rotordynamic coefficients can also be obtained by using CFD perturbation analysis. The high accuracy of the bulk flow model was demonstrated by comparing its results with CFD perturbation analysis results. In the perturbation analysis, the whirling motion was treated as a steady-state problem by using a rotating frame of reference. For the damper seal, the rotor surface and its neighboring region were treated with a rotating frame of reference and the neighboring region of the stator was treated with a stationary frame of reference. The damping property of the new seal was evaluated by conducting rotor stability tests using a high-pressure compressor with an electromagnetic exciter. The new seal equipped with swirl brakes was used for the balance piston of the compressor. Stability was evaluated by exciting the rotor during operation and identifying the eigenvalues of the rotor. The experimental results showed that the new seal increases damping. Comparison of the damping effect with calculations based on the bulk flow analysis showed good agreement.

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.

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