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.

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.

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.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2001 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Abstract Labyrinth seals are utilized inside turbomachinery to provide non-contacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure (Childs, 1993). In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2003 ◽  
Vol 125 (4) ◽  
pp. 427-433 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Labyrinth seals are utilized inside turbomachinery to provide noncontacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure.* In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

Rotordynamic Coefficients of Labseals for Turbines: Comparing CFD Results With Experimental Data on a Comb-Grooved Labyrinth

2005 ◽  
Author(s):  
Joachim Schettel ◽  
Martin Deckner ◽  
Klaus Kwanka ◽  
Bernd Lu¨neburg ◽  
Rainer Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Test Rig ◽  
Navier Stokes Equations ◽  
Detailed Model ◽  
Identification Methods ◽  
Rotating Speed ◽  
Flow Models ◽  
Rotordynamic Coefficients

The main goal of this paper is to improve identification methods for rotordynamic coefficients of labseals for turbines. This aim was achieved in joint effort of the Technische Universita¨t Mu¨nchen, working on experimental identification methods for rotordynamic coefficients, the University of Technology, Darmstadt, working on prediction methods, and Siemens AG, realizing the results. The paper focuses on a short comb-grooved labyrinth seal. Short labseals, amongst others the above mentioned comb-grooved labyrinth, were examined. by means of a very accurately measuring test rig. The rotor was brought into statically eccentric positions relative to the stator, in order to measure the circumferential pressure distribution as a function of pressure, rotating speed and entrance swirl. The data collected were used to validate results obtained with a numerical method. The theoretical approach is based on a commercial CFD tool, which solves the Navier Stokes equations using numerical methods. As a result, a detailed model of the flow within the test rig is produced. The efforts of computation here are greater than when compared with the likewise wide-spread Bulk flow models, however improved accuracy and flexibility is expected. As the validation of the model is successful, it could then be used to gain further insight in the flow within the seal, and to understand the results better. This showed that rotordynamic coefficients of labseals gained from different test rigs are not necessarily comparable.

Aerodynamic and Aeroacoustic Analyses of a Regenerative Blower

2015 ◽  
Author(s):  
Man-Woong Heo ◽  
Tae-Wan Seo ◽  
Chung-Suk Lee ◽  
Kwang-Yong Kim
Keyword(s):  
Shear Stress ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Side Channel ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Unsteady Flow Analysis

This paper presents a parametric study to investigate the aerodynamic and aeroacoustic characteristics of a side channel regenerative blower. Flow analysis in the side channel blower was carried out by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence closure. Aeroacoustic analysis was conducted by solving the variational formulation of Lighthill’s analogy on the basis of the aerodynamic sources extracted from the unsteady flow analysis. The height and width of the blade and the angle between inlet and outlet ports were selected as three geometric parameters, and their effects on the aerodynamic and aeroacoustic performances of the blower have been investigated. The results showed that the aerodynamic and aeroacoustic performances were enhanced by decreasing height and width of blade. It was found that angle between inlet and outlet ports significantly influences the aerodynamic and aeroacoustic performances of the blower due to the stripper leakage flow.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

High Level Languages Implementation and Analysis of 3D Navier-Stokes Solvers

2011 ◽  
Vol 3 (3) ◽  
pp. 370-388
Author(s):  
Valerio Grazioso ◽  
Carlo Scalo ◽  
Giuseppe de Felice ◽  
Carlo Meola
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Flamelet Model ◽  
Advection Scheme ◽  
Variable Ordering ◽  
Pressure Variable ◽  
High Level

AbstractIn this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.

Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening

2006 ◽  
Vol 128 (4) ◽  
pp. 573-578 ◽  
Author(s):  
Andrew L. Hazel ◽  
Matthias Heil
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Elastic Tube ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Steady Propagation

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

scholarly journals RUBBLE MOUND BREAKWATER OVERTOPPING: ESTIMATION OF THE RELIABILITY OF A 3D NUMERICAL SIMULATION

2012 ◽  
Vol 1 (33) ◽  
pp. 8 ◽  
Author(s):  
Luca Cavallaro ◽  
Fabio Dentale ◽  
Giovanna Donnarumma ◽  
Enrico Foti ◽  
Rosaria E. Musumeci ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Fluid Dynamic ◽  
Complete Solution ◽  
Three Dimensional ◽  
Design Tool ◽  
Physical Models ◽  
Navier Stokes ◽  
Free Boundaries ◽  
Navier Stokes Equations

Until recently, physical models were the only way to investigate into the details of breakwaters behavior under wave attack. From the numerical point of view, the complexity of the fluid dynamic processes involved has so far hindered the direct application of Navier-Stokes equations within the armour blocks, due to the complex geometry and the presence of strongly non stationary flows, free boundaries and turbulence. In the present work the most recent CFD technology is used to provide a new and more reliable approach to the design analysis of breakwaters, especially in connection with run-up and overtopping. The solid structure is simulated within the numerical domain by overlapping individual virtual elements to form the empty spaces delimited by the blocks. Thus, by defining a fine computational grid, an adequate number of nodes is located within the interstices and a complete solution of the full hydrodynamic equations is carried out. In the work presented here the numerical simulations are carried out by integrating the three-dimensional Reynolds Average Navier-Stokes Equations coupled with the RNG turbulence model and a Volume of Fluid Method used to handle the dynamics of the free surface. The aim of the present work is to investigate the reliability of this approach as a design tool. Two different breakwaters are considered, both located in Southern Sicily: one a typical quarry stone breakwater, another a more complex design incorporating a spill basin and an armoured layer made up by Coreloc® blocks.

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