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.

Analysis of Leakage Flow and Dynamic Characteristics in Floating Ring Seals for High Pressure Turbopump

2006 ◽  
Author(s):  
Yong-Bok Lee ◽  
Chang-Ho Kim ◽  
Wenbo Duan ◽  
Fulei Chu
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Stokes Equations ◽  
Descent Method ◽  
Bulk Flow ◽  
Steepest Descent Method ◽  
Leakage Flow ◽  
Transform Method ◽  
Flow Equations ◽  
Numerical Predictions

Because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming, the bulk-flow model was used for calculating the static and the dynamic characteristics of floating ring seals. The bulk-flow model is governed by three partial differential equations on eccentric working conditions with steepest descent method to find the seal’s equilibrium position efficiently. A finite difference scheme has been used to solve the nonlinear governing equations. Compared to Nelson and Nguyen’s Fast Fourier Transform Method, this scheme has better consistency. Perturbation analysis of the flow variables yields a set of zeroth and first-order equations. The SIMPLE algorithm is used to integrate the system of bulk-flow equations. Comparisons of the numerical predictions (lock-up eccentricity ratio, leakage flow rate and rotordynamic coefficients) with Ha’s results, which were formulated using the Fourier series, and experimental data are presented subsequently.

Combined Navier–Stokes and Bulk-Flow Analysis of Hybrid Bearings: Radial and Angled Injection

2004 ◽  
Vol 127 (3) ◽  
pp. 557-567 ◽  
Author(s):  
M. Hélène ◽  
M. Arghir ◽  
J. Frêne
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Pressure Field ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Favourable Effect ◽  
Alternative Analysis ◽  
Pressure Pattern ◽  
Numerical Predictions

The present work deals with the Navier–Stokes and bulk-flow analysis of hybrid bearings intended for use in aerospace applications. These bearings are expected to work at high rotational speeds and high feeding pressures. In such a case, the pressure in the shallow pockets of the bearing is no longer constant and is influenced by hydrostatic and hydrodynamic effects. It has been shown in the literature that the recess pressure pattern can have an important influence on the dynamic characteristics of the bearing. The present work investigates the pressure field in the recess of centered hybrid bearings with radial and angled injection by using a numerical Navier–Stokes analysis. The recess pressure pattern is then subsequently characterized by combining these results with some parametric descriptions. For calculating the dynamic characteristics of the bearing, the parametric pressure pattern is then injected into a bulk-flow model. The proposed model is an alternative analysis to the one advanced by San Andrés [ASME J. Tribole, 112, pp. 699–707; 119, 179–187] and in order to evaluate the validity of the bulk-flow code, the numerical predictions are compared with experimental data taken from the literature for radial and angled injection. The favourable effect of the counter-rotating angled injection is then explained by using the velocity field issued from the Navier–Stokes analysis and the pressure field given by the bulk-flow model.

Combined Navier-Stokes and Bulk-Flow Analysis of Hybrid Bearings: Radial and Angled Injection

2004 ◽  
Author(s):  
Mathieu Helene ◽  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Pressure Field ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Favorable Effect ◽  
Alternative Analysis ◽  
Pressure Pattern ◽  
Numerical Predictions

The present work deals with the Navier-Stokes and bulk-flow analysis of hybrid bearings intended for use in aerospace applications. These bearings are expected to work at high rotational speeds and high feeding pressures. In such a case, the pressure in the shallow pockets of the bearing is no longer constant and is influenced by hydrostatic and hydrodynamic effects. It has been shown in the literature that the recess pressure pattern can have an important influence on the dynamic characteristics of the bearing. The present work investigates the pressure field in the recess of centered hybrid bearings with radial and angled injection by using a numerical Navier Stokes analysis. The recess pressure pattern is then subsequently characterized by combining these results with some parametric descriptions. For calculating the dynamic characteristics of the bearing, the parametric pressure pattern is then injected into a bulk-flow model that is an alternative analysis of the one introduced by San Andre´s [3, 4]. In order to evaluate the validity of the bulk-flow code, the numerical predictions are compared with experimental data taken from the literature for radial and angled injection. The favorable effect of the counter-rotating angled injection is then explained by using the velocity field issued from the Navier Stokes analysis and the pressure field given by the bulk-flow model.

Tip Leakage Flow in Axial Compressors

1991 ◽  
Vol 113 (2) ◽  
pp. 252-259 ◽  
Author(s):  
J. A. Storer ◽  
N. A. Cumpsty
Keyword(s):  
Pressure Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Tip Clearance ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Local Pressure ◽  
Flow Measurements ◽  
Tip Leakage ◽  
Numerical Predictions

Experimental measurements in a linear cascade with tip clearance are complemented by numerical solutions of the three-dimensional Navier–Stokes equations in an investigation of tip leakage flow. Measurements reveal that the clearance flow, which separates near the entry of the tip gap, remains unattached for the majority of the blade chord when the tip clearance is similar to that typical of a machine. The numerical predictions of leakage flow rate agree very well with measurements, and detailed comparisons show that the mechanism of tip leakage is primarily inviscid. It is demonstrated by simple calculation that it is the static pressure field near the end of the blade that controls chordwise distribution of the flow across the tip. Although the presence of a vortex caused by the roll-up of the leakage flow may affect the local pressure field, the overall magnitude of the tip leakage flow remains strongly related to the aerodynamic loading of the blades.

Thermal Effects in Cryogenic Liquid Annular Seals—Part I: Theory and Approximate Solution

1993 ◽  
Vol 115 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Zhou Yang ◽  
Luis San Andres ◽  
Dara W. Childs
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Thermal Effects ◽  
Approximate Analytical Solution ◽  
Cryogenic Liquid ◽  
Bulk Flow ◽  
Absolute Pressure ◽  
Fluid Temperature ◽  
Numerical Predictions ◽  
Annular Seals

A thermohydrodynamic (THD) analysis is introduced for calculation of the performance characteristics of cryogenic liquid annular seals in the turbulent flow regime. A full-inertial bulk-flow model is advanced for momentum conservation and energy transport. The liquid material properties depend on the local absolute pressure and temperature. Heat flow to the rotor and stator is modeled by bulk-flow heat transfer coefficients. An approximate analytical solution is obtained to the governing equations when the seal operates at a steady-state and concentric condition. The temperature-rise in the fluid film of a cryogenic liquid seal is found to be composed of four sources due to viscous dissipation, pressure extrusion work, surface heat transfer and kinetic energy variation. For incompressible adiabatic flows, the fluid temperature rises linearly along the axial direction. The approximate analytical solution provides a useful tool for preliminary design and a better understanding of seal performance. Full numerical predictions of load, leakage, temperature, and rotordynamic coefficients for a high speed liquid oxygen seal are given in Part II to show the importance of thermal effects on seal performance. The accuracy of the approximate concentric seal analysis is then demonstrated by comparison to the results from the full numerical solution.

Distributed Control of Two-Dimensional Navier–Stokes Equations in Fourier Spectral Simulations

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Behrooz Rahmani ◽  
Amin Moosaie
Keyword(s):  
Differential Equations ◽  
Distributed Control ◽  
Nonlinear Equations ◽  
Stokes Equations ◽  
Control Method ◽  
Grid Point ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Flow ◽  
Mode Interaction ◽  
Flow Equations

A method for distributed control of nonlinear flow equations is proposed. In this method, first, Takagi–Sugeno (T–S) fuzzy model is used to substitute the nonlinear partial differential equations (PDEs) governing the system by a set of linear PDEs, such that their fuzzy composition exactly recovers the original nonlinear equations. This is done to alleviate the mode-interaction phenomenon occurring in spectral treatment of nonlinear equations. Then, each of the so-obtained linear equations is converted to a set of ordinary differential equations (ODEs) using the fast Fourier transform (FFT) technique. Thus, the combination of T–S method and FFT technique leads to a number of ODEs for each grid point. For the stabilization of the dynamics of each grid point, the use is made of the parallel distributed compensation (PDC) method. The stability of the proposed control method is proved using the second Lyapunov theorem for fuzzy systems. In order to solve the nonlinear flow equation, a combination of FFT and Runge–Kutta methodologies is implemented. Simulation studies show the performance of the proposed method, for example, the smaller settling time and overshoot and also its relatively robustness with respect to the measurement noises.

scholarly journals Tip Leakage Flow in Axial Compressors

1990 ◽  
Author(s):  
J. A. Storer ◽  
N. A. Cumpsty
Keyword(s):  
Pressure Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Tip Clearance ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Local Pressure ◽  
Flow Measurements ◽  
Tip Leakage ◽  
Numerical Predictions

Experimental measurements in a linear cascade with tip clearance are complemented by numerical solutions of the three-dimensional Navier-Stokes equations in an investigation of tip leakage flow. Measurements reveal that the clearance flow, which separates near the entry of the tip gap, remains unattached for the majority of the blade chord when the tip clearance is similar to that typical of a machine. The numerical predictions of leakage flow rate agree very well with measurements and detailed comparisons show that the mechanism of tip leakage is primarily inviscid. It is demonstrated by simple calculation that it is the static pressure field near the end of the blade which controls chordwise distribution of the flow across the tip. Although the presence of a vortex caused by the roll-up of the leakage flow may affect the local pressure field, the overall magnitude of the tip leakage flow remains strongly related to the aerodynamic loading of the blades.

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.

Analysis of Tangential-Against-Rotation Injection Lomakin Bearings

2003 ◽  
Author(s):  
Mihai Arghir ◽  
Mathieu He´le`ne ◽  
Jean Frene
Keyword(s):  
Thin Film ◽  
Dynamic Characteristics ◽  
Flow Model ◽  
Flow Equation ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Thin Film Model ◽  
High Reynolds ◽  
Annular Seals

This work presents a thin film flow model for analyzing the static and dynamic characteristics of centered, eccentric or misaligned tangential-against-rotation injection Lomakin bearings. The Lomakin bearing is a recent device intended for use in modern turbomachinery and having characteristics similar to hybrid bearings. It can be described as an ensemble of two opposing straight annular seals separated by a circumferential feeding groove. The fluid is supplied to the groove via orifice restrictors. Their tangential inclination generates an against-rotation circumferential flow in the groove that further penetrates into the thin film. This effect, known from annular seals as the pre-rotation speed, improves the dynamic characteristics of the bearing. The zero and first order analyses are carried out by recognizing the crucial importance of taking into account the interaction between the flow in the thin film lands, the circumferential groove and the supply orifices. Due to the high Reynolds number regime, the land flow is governed by the two dimensional thin film inertia equations (the “bulk flow” model). A one-dimensional circumferential flow dominated by inertia forces is assumed to take place in the groove and is described by an appropriate bulk flow equation. The flows in the supply orifices, the groove and the thin film lands are linked together by the same mass flow rate balance algorithm as used for hydrostatic and hybrid bearings analysis. The algorithm is extended to Lomakin bearings by considering the groove areas surrounding each orifice as a row of intercommunicating feeding pockets. This approach enables the analysis of centered, eccentric or misaligned Lomakin bearings. Comparisons with water-lubricated test results are used to validate the present model. For the zero eccentricity case a good agreement is obtained for the cross-coupled stiffness and for the whirl frequency ratio. A parametric study shows the variation of the bearing characteristics with increasing static eccentricity or misalignment. The limits of the developed thin film model are further estimated by comparing the static and zero eccentricity thin film results with a full Navier Stokes calculation.

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.

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