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.

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).

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

2012 ◽  
Vol 135 (1) ◽  
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 a 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 also predicts the highest value; however, a much larger discrepancy can be observed for this term (73% higher than the value predicted by the finite difference method and 79% higher than the bulk flow code prediction). One can see similar large differences in predictions in the estimates for damping and direct mass coefficients, where the 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 versus the short seal configuration the bulk flow code is usually calibrated for using an empirical friction factor).

Fluid-Induced Forces in Pump Liquid Seals With Large Aspect Ratio

2011 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Vahe Hayrapetian ◽  
Costin D. Untaroiu ◽  
Paul E. Allaire ◽  
Houston G. Wood ◽  
...  
Keyword(s):  
Shear Stress ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Dynamic Properties ◽  
Fluid Velocity ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Aspect Ratios

The instability due to fluid flow in seals is a known phenomenon that can occur in pumps and compressors as well as in steam turbines. 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). Unlike the bulk flow models, computational fluid dynamics (CFD) makes no simplifying assumption on the seal geometry, shear stress at the wall, relationship between wall shear stress and mean fluid velocity, or characterization of interfaces between control volumes through empirical friction factors. This paper presents a method to calculate the linearized rotor-dynamic coefficients for a liquid seal with large aspect ratio (balance drum) subjected to incompressible turbulent flow by means of a three dimensional CFD analysis to calculate the fluid-induced forces acting on the rotor. The Reynolds-averaged Navier-Stokes equations for fluid flow are solved by dividing the volume of fluid into a discrete number of points at which unknown variables are computed. As a result, all the details of the flow field, including the fluid forces with potential destabilizing effects, are calculated. A 2nd order curve fit is then used to express the fluid-induced forces in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients.

Hole-Pattern Seals: A Three Dimensional CFD Approach for Computing Rotordynamic Coefficient and Leakage Characteristics

2009 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Patrick Migliorini ◽  
Houston G. Wood ◽  
Paul E. Allaire ◽  
John A. Kocur
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Bulk Flow ◽  
Fluid Inertia ◽  
Flow Equations ◽  
Flow Models ◽  
Rotordynamic Coefficients

Labyrinth and other annular seals are commonly used in the turbomachinery industry to limit the leakage between different pressure regions. The pressure driven flow these seals experience can produce significant forces on the rotor. These fluid-induced excitation forces can exert a strong influence on the dynamic characteristics of the machine. Such seal forces can cause the rotor to become unstable, or when properly designed, stabilize a troublesome machine. Thus, it is important to accurately quantify the fluid-induced forces exerted on the rotor to effectively predict the dynamic behavior. Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient, due to the assumptions made to simplify the flow equations, seal bulk flow models lack accuracy when dealing with more complex geometry seals, such as hole-pattern seals. Unlike the bulk flow model, computational fluid dynamics (CFD) makes no simplifying assumption on the seal geometry, shear stress at the wall, relationship between wall shear stress and mean fluid velocity, or characterization of interfaces between control volumes. This paper presents a method to calculate the linearized rotordynamic coefficients for a hole-pattern seal by means of a three dimensional CFD approach to estimate the fluid-induced forces acting on the rotor. The system is modeled as a rigid rotor, with rotational speed, ω, and whirl frequency, Ω, describing non-synchronous whirl orbits around a static operating point. The Reynolds-averaged Navier-Stokes equations for fluid flow are solved by dividing the volume of fluid into a discrete number of points at which unknown variables (velocity, pressure, etc.) are computed. As a result, all the details of the flow field, including the fluid forces with potential destabilizing effects, are calculated. A 2nd order regression method is then utilized to express the fluid induced forces in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients.

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.

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.

Effect of Surface Patterning on the Dynamic Response of Annular Hole-Pattern Seals

2017 ◽  
Author(s):  
Hanxiang Jin ◽  
Alexandrina Untaroiu ◽  
Gen Fu
Keyword(s):  
Dynamic Response ◽  
Regression Models ◽  
Dynamic Properties ◽  
Sensitivity Study ◽  
Leakage Rate ◽  
Surface Pattern ◽  
Design Parameters ◽  
Dynamic Coefficients ◽  
The Relationship ◽  
Rotor Dynamic

The performance of annular seals depends on the geometry of the leakage path as it facilitates the dissipation of the fluid kinetic energy. The goal of this study is to investigate potential correlations between the characteristics of the alternately arranged surface pattern and the corresponding rotor dynamic properties of the seal in addition to mapping its performance. Various patterning arrangements lining the stator surface are considered and the relative seal performance change is investigated using a hybrid method that calculates the seal dynamic response for each point in the design space. The design parameters selected in this DOE study are: the diameters of alternately arranged holes that are replicated in both axial and circumferential direction to construct the pattern, the hole depths for both types of holes, and the number of holes in both axial and circumferential directions. A sensitivity study is conducted to analyze the influence of each geometrical parameter on the seal response. Regression models are then generated for each response, including the leakage rate and the rotor dynamic coefficients. Quadratic regression models are used in this study to represent the relationship between the objective functions and the design parameters. The goal is to achieve a minimum leakage rate as well as an improved dynamic response. The results of the baseline model and the best performing design are compared. The results show that the patterning arrangements have crucial effects on the leakage rate as well as the dynamic coefficients of the seal. The results of this study are found to be helpful in designing a hole-pattern seal that can concurrently satisfy constraints on both the leakage rate and the rotor dynamic response while maintaining same design envelope.

scholarly journals Design and Analysis of CFD Experiments for the Development of Bulk-Flow Model for Staggered Labyrinth Seal

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Filippo Cangioli ◽  
Paolo Pennacchi ◽  
Leonardo Nettis ◽  
Lorenzo Ciuchicchi
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Flow Model ◽  
Control Volume ◽  
Computer Experiments ◽  
Bulk Flow ◽  
Labyrinth Seals ◽  
Dynamic Coefficients ◽  
Rotor Dynamic

Nowadays, bulk-flow models are the most time-efficient approaches to estimate the rotor dynamic coefficients of labyrinth seals. Dealing with the one-control volume bulk-flow model developed by Iwatsubo and improved by Childs, the “leakage correlation” allows the leakage mass-flow rate to be estimated, which directly affects the calculation of the rotor dynamic coefficients. This paper aims at filling the lack of the numerical modelling for staggered labyrinth seals: a one-control volume bulk-flow model has been developed and, furthermore, a new leakage correlation has been defined using CFD analysis. Design and analysis of computer experiments have been performed to investigate the leakage mass-flow rate, static pressure, circumferential velocity, and temperature distribution along the seal cavities. Four design factors have been chosen, which are the geometry, pressure drop, inlet preswirl, and rotor peripheral speed. Finally, dynamic forces, estimated by the bulk-flow model, are compared with experimental measurements available in the literature.

scholarly journals Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

2021 ◽  
Author(s):  
Mosayeb Shams ◽  
Kamaljit Singh ◽  
Branko Bijeljic ◽  
Martin J. Blunt
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Direct Numerical Simulation ◽  
Complex Geometry ◽  
Flow In Porous Media ◽  
Pore Scale ◽  
Contact Lines ◽  
Two Phase ◽  
X Ray ◽  
Aspect Ratios

AbstractThis study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We simulate multiphase flow in a limestone and compare our results with high-resolution synchrotron X-ray images of displacement previously published in the literature by Singh et al. (Sci Rep 7:5192, 2017). We use the results to interpret the observed displacement events that cannot be described using conventional metrics such as pore-to-throat aspect ratio. We show that the complex geometry of porous media can dictate a curvature balance that prevents snap-off from happening in spite of favourable large aspect ratios. We also show that pinned fluid-fluid-solid contact lines can lead to snap-off of small ganglia on pore walls; we propose that this pinning is caused by sub-resolution roughness on scales of less than a micron. Our numerical results show that even in water-wet porous media, we need to allow pinned contacts in place to reproduce experimental results.

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