Static and Dynamic Analysis of Annular Seals

2006 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Static Problem ◽  
Bulk Flow ◽  
Friction Coefficients ◽  
Flow Equations ◽  
Static And Dynamic Analysis ◽  
Dynamic Coefficients ◽  
Theoretical Approaches ◽  
Eccentric Rotor ◽  
Inertia Forces ◽  
Annular Seals

This work is an overview of theoretical approaches used for estimating the characteristics of straight or grooved annular seals. The flow in annular seals is dominated by inertia forces. The goal of the static analysis is to describe the relation between the pressure difference across the seal and the (mass) flow rate. The presentation introduces different approaches of the static problem (analytic, simplified–“bulk flow” and CFD) and underlines the main difficulties in analysing annular seals. The forces on an eccentric rotor are described as a superposition between three effects (Lomakin, viscous and Bernoulli forces). This approach is then used to describe the dynamic characteristics of the seal for a rotor whirling around its centred position. The specific aspects that compressibility adds to gas annular seals analysis are next discussed, with its most important consequence, the flow choking in the exit section. Finally, some recent findings concerning the analysis of textured stator annular seals are presented. The results show that the presence of textures engenders stator and rotor friction coefficients obeying different laws. The use of these new friction coefficients in the bulk-flow equations enables to match the values of the experimental dynamic coefficients. A discussion about the further needs (development and research) in annular seals analysis is carried out at the end of this work.

Comparison Between Numerical and Experimental Dynamic Coefficients of a Hybrid Aerostatic Bearing

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Mohamed Amine Hassini ◽  
Mihai Arghir ◽  
Manuel Frocot
Keyword(s):  
Experimental Data ◽  
Theoretical Models ◽  
Bulk Flow ◽  
Major Influence ◽  
Aerostatic Bearing ◽  
Complex Flow ◽  
Flow Equations ◽  
Dynamic Coefficients ◽  
Equivalent Area ◽  
Feeding Pressure

Hybrid journal bearings have been considered for many years as a possible replacement for ball bearings in turbopumps used by the aerospace industry. Due to flow regimes dominated by inertia and due to the nature of the lubricant (cryogenic fluids), the prediction of the linearized dynamic coefficients in these bearings must be based on the compressible bulk-flow equations. Theoretical models based on these equations were validated for hybrid bearings working with water or for liquid or gas annular seals. Validations for hybrid compressible bearings are missing. Experimental data obtained for an air lubricated hybrid aerostatic bearing designed with shallow pockets were recently presented; the data consist of linearized dynamic coefficients obtained for rotation speeds up to 50 krpm and up to 7 bars feeding pressure. The present work introduces a consolidated numerical approach for predicting static and linearized dynamic characteristics. Theoretical predictions are based on bulk flow equations in conjunction with CFD analysis. It was found that, for a given feeding pressure, the value of the pressure downstream the orifice has a major influence on all results. Special care was then taken to describe the complex flow in the feeding system and the orifice. Three dimensional CFD was employed because the bulk-flow equations are inappropriate in this part of the bearing. The pressure downstream the orifice stemming from CFD results and the feeding pressure were next imposed in the bulk flow model and the equivalent area of the orifice was obtained from the numerical solution of the steady flow in the bearing. Since the pockets of the hybrid bearing are shallow, this equivalent area is considered as being the harmonic average of the orifice cross section area and of the cylindrical curtain area located between the orifice and the rotor. The comparisons between theoretical dynamic coefficients and experimental data validated this approach of the equivalent area of the orifice.

Comparison Between Numerical and Experimental Dynamic Coefficients of a Hybrid Aerostatic Bearing

2012 ◽  
Author(s):  
Mohamed Amine Hassini ◽  
Mihai Arghir ◽  
Manuel Frocot
Keyword(s):  
Experimental Data ◽  
Theoretical Models ◽  
Bulk Flow ◽  
Major Influence ◽  
Aerostatic Bearing ◽  
Complex Flow ◽  
Flow Equations ◽  
Dynamic Coefficients ◽  
Equivalent Area ◽  
Feeding Pressure

Hybrid journal bearings are considered since many years as a possible replacement for ball bearings in turbo-pumps used by the aerospace industry. Due to flow regimes dominated by inertia and due to the nature of the lubricant (cryogenic fluids), the prediction of the linearized dynamic coefficients in these bearings must be based on the compressible bulk-flow equations. Theoretical models based on these equations were validated for hybrid bearings working with water or for liquid or gas annular seals. Validations for hybrid compressible bearings are missing. Experimental data obtained for an air lubricated hybrid aerostatic bearing designed with shallow pockets were recently presented; the data consist of linearized dynamic coefficients obtained for rotation speeds up to 50 krpm and up to 7 bar feeding pressure. The present work introduces a consolidated numerical approach for predicting static and linearized dynamic characteristics. Theoretical predictions are based on bulk flow equations in conjunction with CFD analysis. It was found that for a given feeding pressure, the value of the pressure downstream the orifice has a major influence on all results. Special care was then taken for describing the complex flow in the feeding system and the orifice. Three dimensional CFD was employed because the bulk-flow equations are inappropriate in this part of the bearing. The pressure downstream the orifice stemming from CFD results and the feeding pressure were next imposed in the bulk flow model and the equivalent area of the orifice was obtained from the numerical solution of the steady flow in the bearing. Since the pockets of the hybrid bearing are shallow, this equivalent area is considered as being the harmonic average of the orifice cross section area and of the cylindrical curtain area located between the orifice and the rotor. The comparisons between theoretical dynamic coefficients and experimental data validated this approach of the equivalent area of the orifice.

On the Dynamic Properties of Pump Liquid Seals

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Vahe Hayrapetian ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Bruno Schiavello ◽  
...  
Keyword(s):  
Complex Geometry ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Damping Factor ◽  
Steam Turbines ◽  
Fluid Inertia ◽  
Flow Equations ◽  
Dynamic Coefficients ◽  
Aspect Ratios ◽  
Rotor Dynamic

Rotordynamic instability due to fluid flow in seals is a well known phenomenon that can occur in pumps as well as in steam turbines and air compressors. While analysis methods using bulk-flow equations are computationally efficient and can predict dynamic properties fairly well for short seals, they often lack accuracy in cases of seals with complex geometry or with large aspect ratios (L/D above 1.0). This paper presents the linearized rotordynamic coefficients for a liquid seal with large aspect ratio subjected to incompressible turbulent flow. The fluid-induced forces acting on the rotor are calculated by means of a three-dimensional computational fluid dynamics (3D-CFD) analysis, and are then expressed in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients. For comparison, the seal dynamic coefficients were calculated using two other codes: one developed with the bulk flow method and one based on the finite difference method. The three sets of dynamic coefficients calculated in this study were used then to predict the rotor dynamic behavior of an industrial pump. These estimations were then compared to the vibration characteristic measured during the pump shop test, results indicating that the closest agreement was achieved utilizing the CFD generated coefficients. The results of rotor dynamic analysis using the coefficients derived from CFD approach, improved the prediction of both damped natural frequency and damping factor for the first mode, showing substantially smaller damping factor which is consistent with the experimentally observed instability of the rotor-bearing system. As result of continuously increasing computational power, it is believed that the CFD approach for calculating fluid excitation forces will become the standard in industry.

A Bulk-Flow Analysis of Static and Dynamic Characteristics of Eccentric Circumferentially-Grooved Liquid Annular Seals

2004 ◽  
Vol 126 (2) ◽  
pp. 316-325 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Differential Equations ◽  
Dynamic Characteristics ◽  
Pressure Field ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Bulk Flow ◽  
Elliptic Type ◽  
Flow Equations ◽  
Numerical Predictions ◽  
Annular Seals

The bulk-flow equations used for inertia dominated thin-film flows is an attractive model for the analysis of circumferentially grooved annular seals because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming. By using three types of control volumes and some user-tuned constants, the bulk-flow model can be used for calculating the static and the dynamic characteristics. Until now, this has been carried out for centered seals where the flow is governed by ordinary differential equations but no solutions have yet been given for eccentric working conditions. In this latter case, the model is governed by partial differential equations of an elliptic type. The main problem is that for describing the groove effects, the pressure field must incorporate the concentrated drop or recovery effects that occur at the interface between the groove and the land zone. This means that the numerical procedure used for solving the elliptic equations should be able to handle a pressure field having discontinuous values and discontinuous first order derivatives. In the present work, the method used for integrating the system of bulk-flow equations is the SIMPLE algorithm. The algorithm is extended for handling pressure jumps by adding two pressure values on each side of the discontinuity. These values are then expressed in terms of cell centered pressures by imposing the mass conservation and the generalized Bernoulli equation at the discontinuity. This numerical solution is original and has never previously been presented in the finite volume related literature. Comparisons between the numerical predictions (leakage flow rate and rotordynamic coefficients) and experimental data taken from the literature Marquette and Childs (1997) are subsequently presented for an eccentric ten-groove annular seal.

scholarly journals Fluid Flow Equations for Rotordynamic Flows in Seals and Leakage Paths

2001 ◽  
Vol 124 (1) ◽  
pp. 176-181 ◽  
Author(s):  
Y. Hsu ◽  
C. E. Brennen
Keyword(s):  
Fluid Flow ◽  
Numerical Method ◽  
Bulk Flow ◽  
Experimental Measurements ◽  
Flow Equations ◽  
Flow Models ◽  
Annular Seal ◽  
Rotordynamic Forces ◽  
Annular Seals

Fluid-induced rotordynamic forces produced by the fluid in an annular seal or in the leakage passage surrounding the shroud of a pump or turbine, are known to contribute substantially to the potential excitation forces acting on the rotor. The present research explores some of the important features of the equations governing bulk-flow models of these flows. This in turn suggests methods which might be used to solve these bulk-flow equations in circumstances where the linearized solutions may not be accurate. This paper presents a numerical method for these equations and discusses comparison of the computed results with experimental measurements for annular seals and pump leakage paths.

Hybrid Analysis of Gas Annular Seals With Energy Equation

2013 ◽  
Author(s):  
Patrick J. Migliorini ◽  
Alexandrina Untaroiu ◽  
William C. Witt ◽  
Neal R. Morgan ◽  
Houston G. Wood
Keyword(s):  
Experimental Data ◽  
Hybrid Method ◽  
Energy Equation ◽  
Flow Analysis ◽  
Experimental Studies ◽  
Rotor System ◽  
Bulk Flow ◽  
Outlet Temperature ◽  
Cfd Analysis ◽  
Annular Seals

Annular seals are used in turbomachinery to reduce secondary flow between regions of high and low pressure. In a vibrating rotor system, the non-axisymmetric pressure field developed in the small clearance between the rotor and the seal generate reactionary forces that can affect the stability of the entire rotor system. Traditionally, two analyses have been used to study the fluid flow in seals, bulk-flow analysis and computational fluid dynamics (CFD). Bulk-flow methods are computational inexpensive, but solve simplified equations that rely on empirically derived coefficients and are moderately accurate. CFD analyses generally provide more accurate results than bulk-flow codes, but solution time can vary between days and weeks. For gas damper seals, these analyses have been developed with the assumption that the flow can be treated as isothermal. Some experimental studies show that the difference between the inlet and outlet temperature temperatures is less than 5% but initial CFD studies show that there can be a significant temperature change which can have an effect on the density field. Thus, a comprehensive analysis requires the solution of an energy equation. Recently, a new hybrid method that employs a CFD analysis for the base state, unperturbed flow and a bulk-flow analysis for the first order, perturbed flow has been developed. This method has shown to compare well with full CFD analysis and experimental data while being computationally efficient. In this study, the previously developed hybrid method is extended to include the effects of non-isothermal flow. The hybrid method with energy equation is then compared with the isothermal hybrid method and experimental data for several test cases of hole-pattern seals and the importance of the use of energy equation is studied.

Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratio

2012 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Paul E. Allaire
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Flow Method ◽  
Dynamic Coefficients ◽  
Aspect Ratios

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with large aspect ratio are calculated by means of a three dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor. For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method. These two sets of dynamic coefficients were compared with those obtained from CFD. Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD. In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD predicts also the highest value; however a much larger discrepancy can be observed for this term (73% higher than value predicted by finite difference method and 79% higher than bulk flow code prediction). Similar large differences in predictions one can see in the estimates for damping and direct mass coefficients, where highest values are predicted by the bulk flow method. These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (i.e. the large aspect ratio AR>1.0 of this seal model vs. the short seal configuration the bulk flow code is usually calibrated for, using an empirical friction factor).

A Bulk-Flow Model of Angled Injection Lomakin Bearings

2002 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Soulas ◽  
Florence Challier ◽  
Patrice Fayolle
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Performance ◽  
Bulk Flow ◽  
Computational Method ◽  
Design Parameters ◽  
Dynamic Force ◽  
Injection Angle ◽  
Flow Equations ◽  
Force Coefficients

The paper introduces a bulk-flow model for prediction of the static and dynamic force coefficients of angled injection Lomakin bearings. The analysis accounts for the flow interaction between the injection orifices, the supply circumferential groove, and the thin film lands. A one control-volume model in the groove is coupled to a bulk-flow model within the film lands of the bearing. Bernoulli-type relationships provide closure at the flow interfaces. Flow turbulence is accounted for with shear stress parameters and Moody’s friction factors. The flow equations are solved numerically using a robust computational method. Comparisons between predictions and experimental results for a tangential-against-rotation injection water Lomakin bearing show the novel model predicts well the leakage and direct stiffness and damping coefficients. Computed cross-coupled stiffness coefficients follow the experimental trends for increasing rotor speeds and supply pressures, but quantitative agreement remains poor. A parameter investigation evidences the effects of the groove and land geometries on the Lomakin bearing flowrate and force coefficients. The orifice injection angle does not influence the bearing static performance, although it largely affects its stability characteristics through the evolution of the cross-coupled stiffnesses. The predictions confirm the promising stabilizing effect of the tangential-against-rotation injection configuration. Two design parameters, comprising the feed orifices area and groove geometry, define the static and dynamic performance of Lomakin bearing. The analysis also shows that the film land clearance and length have a larger impact on the Lomakin bearing rotordynamic behavior than its groove depth and length.

Convergent-Tapered Annular Seals: Analysis and Testing for Rotordynamic Coefficients

1985 ◽  
Vol 107 (3) ◽  
pp. 307-316 ◽  
Author(s):  
D. W. Childs ◽  
J. B. Dressman
Keyword(s):  
Dynamic Pressure ◽  
Momentum Equation ◽  
Computational Method ◽  
Centrifugal Pumps ◽  
Zeroth Order ◽  
Taper Angle ◽  
First Order ◽  
Dynamic Coefficients ◽  
Direct Stiffness ◽  
Annular Seals

A combined analytical-computational method is developed to calculate the pressure field and dynamic coefficients for tapered 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 by Hirs’ bulk-flow turbulent-lubrication equations. Linear zeroth- and first-order perturbation equations are developed for the momentum equations and continuity equations. The development of the circumferential velocity field is defined from the zeroth-order circumferential-momentum equation, and a leakage relationship is defined from the zeroth-order axial-momentum equation. A short-bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients for the seal. Numerical results are presented and compared to previous results for straight and tapered seals. The direct stiffness and leakage increase with increasing taper angle, while the remaining dynamic coefficients decrease. An optimal taper angle is shown to exist with respect to (a) the direct stiffness, and (b) the ratio of direct stiffness to leakage. Stiffness increases on the order of 40-50 percent are predicted. Experimental results are presented for seals with three taper angles which show generally good agreement between theory and prediction.

Computational Modeling and Experimental Investigation of Static Straight-Through Labyrinth Seals

2008 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Christopher P. Goyne ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Robert Rockwell ◽  
...  
Keyword(s):  
Experimental Data ◽  
Flow Behavior ◽  
Optimization Techniques ◽  
Bulk Flow ◽  
Numerical Code ◽  
Cfd Modeling ◽  
Leakage Flow ◽  
Dynamic Coefficients ◽  
Seal Design ◽  
Flow Parameters

To design highly efficient and stable turbomachines, engineers require accurate methods to model seal flows and calculate clearance-excitation forces generated by the eccentric position of the rotor. One of the most widely used methods to predict leakage flow and dynamic coefficients is the use of computer codes developed based on bulk flow theory. In recent years, computational fluid dynamics (CFD) modeling is increasingly being recognized as an accurate assessment tool for flow parameters and dynamic coefficients evaluation as compared to the bulk flow codes. This paper presents computational and experimental investigations that were carried out to calculate flow parameters in a stationary straight-through model labyrinth seal. The main objective of this study is to explore the capabilities of Ansys-CFX, a commercially available state of the art 3D numerical code, to accurately model compressible flow through the seals. The flow behavior is analyzed using CFD and the flow parameters calculated by CFD are validated against experimental data taken for the same seal configuration. The integrated values of leakage flow rates estimated from the computational results agree with the experimental data within 7.6%. This study serves as a benchmark case that supports further efforts in applying CFD analysis in conjunction with automatic design optimization techniques for seals used for compressible media. It was shown that optimization algorithms combined with CFD simulations have good potential for improving seal design.

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