Experimental Research of Characteristics of Fluid-Induced Force in Eccentric Seal

2011 ◽  
Vol 291-294 ◽  
pp. 2034-2040
Author(s):  
Wan Fu Zhang ◽  
Jian Gang Yang ◽  
Hao Cao ◽  
Rui Guo ◽  
Dan Sun
Keyword(s):  
Dynamic Analysis ◽  
Experimental Research ◽  
System Stability ◽  
Inlet Pressure ◽  
Analysis Model ◽  
Rotating Speed ◽  
Stiffness Coefficients ◽  
System A ◽  
The Difference ◽  
The Stability

This paper sets up a dynamic analysis model for cylinder-seal system. A new identification method for fluid-induced force and stiffness coefficients in eccentric seal is presented. The study shows that the system stability decreases with increasing cross-coupled stiffness in a certain range. Beyond this range, the system will be destabilized. Influences of rotating speed, inlet pressure, eccentricity and clearance on fluid-induced force were tested in the rig. It was found that a large tangential fluid-induced force was produced in the direction perpendicular to the eccentric displacement of rotor. The difference between the tangential and radial fluid-induced force became larger and larger with the increasing rotating speeds. Under the action of the seal force, the logarithmic decrement descended with increasing rotating speeds, and the stability of the system decreased. These effects became more and more serious for higher inlet pressure and tighter clearance.

Theoretical Study on Instability Boundary of Rotor-Hydrodynamic Bearing Systems: Part II — Rotor With External Flexible Damped Support

2001 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
Theoretical Study ◽  
System Stability ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
Alternative Means ◽  
The Stability

Abstract The situation of a rotor-hydrodynamic bearing system in external flexible damped support is more complicated than that discussed before in Part I but it can become an alternative means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is built first. Then, the analytical study on the vertical rotor is conducted. The results show that there might be up to four threshold speeds in this configuration that form a consecutive regional pattern taken turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results of the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of value for support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

Instability Boundary for Rotor-Hydrodynamic Bearing Systems, Part 2: Rotor With External Flexible Damped Support

2003 ◽  
Vol 125 (4) ◽  
pp. 423-426 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
System Stability ◽  
Regional Pattern ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
The Stability ◽  
Bearing System

A rotor-hydrodynamic bearing system having external flexible damped bearing supports is more complicated than that discussed in Part 1 but it can provide a means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is developed first. Then, the analytical study on the vertical rotor is conducted. The results show that there can be up to four threshold speeds in this configuration that form a consecutive regional pattern, taking turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results for the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

The Analysis of the Systems Stability of Linear Differential Equations Based on the Transformation of Difference Schemes

2019 ◽  
Vol 20 (9) ◽  
pp. 542-549 ◽  
Author(s):  
S. G. Bulanov
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computer Analysis ◽  
Linear Differential Equations ◽  
System Stability ◽  
The Difference ◽  
Linear Differential ◽  
The Stability

The approach to the analysis of Lyapunov systems stability of linear ordinary differential equations based on multiplicative transformations of difference schemes of numerical integration is presented. As a result of transformations, the stability criteria in the form of necessary and sufficient conditions are formed. The criteria are invariant with respect to the right side of the system and do not require its transformation with respect to the difference scheme, the length of the gap and the step of the solution. A distinctive feature of the criteria is that they do not use the methods of the qualitative theory of differential equations. In particular, for the case of systems with a constant matrix of the coefficients it is not necessary to construct a characteristic polynomial and estimate the values of the characteristic numbers. When analyzing the system stability with variable matrix coefficients, it is not necessary to calculate the characteristic indicators. The varieties of criteria in an additive form are obtained, the stability analysis based on them being equivalent to the stability assessment based on the criteria in a multiplicative form. Under the conditions of a linear system stability (asymptotic stability) of differential equations, the criteria of the systems stability (asymptotic stability) of linear differential equations with a nonlinear additive are obtained. For the systems of nonlinear ordinary differential equations the scheme of stability analysis based on linearization is presented, which is directly related to the solution under study. The scheme is constructed under the assumption that the solution stability of the system of a general form is equivalent to the stability of the linearized system in a sufficiently small neighborhood of the perturbation of the initial data. The matrix form of the criteria allows implementing them in the form of a cyclic program. The computer analysis is performed in real time and allows coming to an unambiguous conclusion about the nature of the system stability under study. On the basis of a numerical experiment, the acceptable range of the step variation of the difference method and the interval length of the difference solution within the boundaries of the reliability of the stability analysis is established. The approach based on the computer analysis of the systems stability of linear differential equations is rendered. Computer testing has shown the feasibility of using this approach in practice.

A model for the onset of penetrative convection

1988 ◽  
Vol 188 ◽  
pp. 571-583 ◽  
Author(s):  
P. C. Matthews
Keyword(s):  
Deep Layer ◽  
Finite Depth ◽  
Internal Heating ◽  
Penetrative Convection ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
System A ◽  
The Difference ◽  
The Stability ◽  
Rayleigh Numbers

The stability of an S-shaped, cubic temperature profile, maintained by internal heating, is considered as a model for circumstances in which an unstably stratified layer of fluid is bounded by two stable layers. Critical Rayleigh numbers are computed for the cases of an infinitely deep layer, and for a layer of finite depth with symmetrically placed free or rigid boundaries. It is found that the introduction of boundaries can reduce the stability of the system. A weakly nonlinear analysis shows that the bifurcation is supercritical and that rolls are preferred to squares for all values of the Prandtl number. This result prompts a re-examination of the model of penetrative convection in water above ice, in which the bifurcation is subcritical, in order to understand the difference between the two models.

Numerical Analysis for the Stability of Cylinder Gas Film Seal

2013 ◽  
Vol 655-657 ◽  
pp. 526-530
Author(s):  
Gang Ma ◽  
Jun He ◽  
Xin Min Shen
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Reynolds Equation ◽  
Working Condition ◽  
Critical Mass ◽  
System Stability ◽  
Dynamics Analysis ◽  
Rotor Speed ◽  
Analysis Model ◽  
The Stability

Non-contacting gas film seal applies to the high speed working condition and a numerical method was presented for analyzing the effect of speed on the stability of cylinder gas film seal. The dynamics analysis model was established, solving the time-dependent Reynolds equation coupling with the dynamic equations. Through numerical simulation, the critical speed of cylinder gas film seal system and the diagram of critical mass versus rotor speed were obtained. The influence of the speed on dynamic stability was studied. The results show that the system stability becomes worse as rotor speed increases.

scholarly journals Flow stability and correctness of the Cauchy problem for a two-speed medium model with different phase pressures

2021 ◽  
Vol 52 ◽  
pp. 66-77
Author(s):  
Alexander Evgenievich Kroshilin ◽  
Mikhail Evgenievich Kroshilin
Keyword(s):  
Cauchy Problem ◽  
Fluid Model ◽  
Stationary Solutions ◽  
System Of Equations ◽  
Two Phase ◽  
System A ◽  
The Cauchy Problem ◽  
The Difference ◽  
Two Fluid Model ◽  
The Stability

At present, to describe the two-velocity flow of a dispersed mixture, as a rule, a two-fluid model is used with equal pressure of the phases of the medium and different velocities of the phases. The corresponding system of equations without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. Recently, it has been proposed to use similar models more widely, but with different pressures of the phases of the medium. Such models allow one to take into account new physical effects associated with different phase pressures and often provide hyperbolicity of the corresponding system of equations. This article analyzes the influence of the difference in the pressure of the phases of the medium on the properties of the system: the importance of the corresponding new effects, the hyperbolicity of the system of equations, the stability of its stationary solutions, and the correctness of the corresponding Cauchy problem are investigated. Three systems are considered. The first, simplest model system is based on the well-known non-hyperbolic system, which has been modernized. It is shown that the Cauchy problem for the modified system is formally correct, but the practical possibility of using the calculation results obtained from the solution of this system should be investigated in each specific case, and depends on the calculated step and duration of the process under study. The techniques worked out to solve the first simplest system were used for other systems. As the second system, a model of the flow of a two-phase medium with different phase pressures and two momentum equations is considered. We will assume the phases are barotropic. Let us postulate an equation relating the pressure in the phases. It is proved that this system is always hyperbolic. The stability of its stationary solutions is investigated. Relationships are derived that make it possible to determine under what conditions, due to instability, the obtained solutions are unreliable. The properties of this system are compared with the system of two-speed flow of a dispersed mixture with equal pressure of the phases of the medium. As a third system, a two-pressure model describing bubble pulsations is considered. We will assume the phases are barotropic. Conditions are determined when the system is non-hyperbolic and the Cauchy problem is incorrect. It is investigated for what conditions the ill-posedness of the Cauchy problem leads to the unreliability of the solution, and under what conditions the ill-posedness of the Cauchy problem does not lead to the unreliability of the solution.

Rotordynamic Performance of the Interlocking Labyrinth Seal With a Tilting Rotor

2021 ◽  
Vol 143 (1) ◽  
Author(s):  
Wanfu Zhang ◽  
Yingfei Wang ◽  
Qianlei Gu ◽  
Lu Yin ◽  
Jiangang Yang
Keyword(s):  
Flow Rate ◽  
Labyrinth Seal ◽  
System Stability ◽  
Dynamic Force ◽  
Misalignment Angle ◽  
Analysis Model ◽  
Force Coefficient ◽  
Leakage Flow Rate ◽  
The Stability ◽  
Positive Effect

Abstract Numerical analysis model of an interlocking labyrinth seal (ILS) is established for studying the effect of tilting rotor on its rotordynamic characteristics. The dynamic characteristic identification method based on infinitesimal theory is applied to solve the dynamic force coefficient of the seal with arbitrary elliptical orbits and eccentric positions under field conditions. The paper investigated the dynamic characteristics of the interlocking labyrinth seal with various misalignment angles (θ = 0, 0.1 deg, 0.2 deg, 0.3 deg, 0.4 deg, 0.5 deg, 0.6 deg), different pressure ratios (Pin = 6.9 bar, PR = 0.5, 0.8), locations of misalignment center (Loc = 0, L/2, L). Results show that the tilting rotor could minimize the leakage flow rate of the ILS. When the misalignment angle θ = 0.6 deg, the mass flow rate can be reduced about 2.5%. The effect of each cavity in the ILS on the stability of the system is different. The cavity with the inlet close to the rotor and the outlet away from the rotor helps to improve the system stability due to its locally antirotational flow. The effective damping of the entire ILS increases as the misalignment angle increases. The system shows the best stability when the misalignment center is close to the seal inlet. The tilting rotor has a positive effect on the stability of the ILS only except for high whirling frequency (>100 Hz) under Loc = L.

scholarly journals Experimental Investigation on Rotordynamic Characteristics and Rotor System Stability of a Novel Negative Dislocated Seal

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Dan Sun ◽  
Xudong Wang ◽  
Chengwei Fei ◽  
Huan Zhao ◽  
Guochen Zhang ◽  
...  
Keyword(s):  
Pressure Ratio ◽  
Hydrodynamic Pressure ◽  
Labyrinth Seal ◽  
Rotor System ◽  
Logarithmic Decrement ◽  
System Stability ◽  
Rotating Speed ◽  
Outlet Pressure ◽  
Stiffness Coefficients ◽  
Decrement Rate

Air-induced force generated in seals is one key factor on the stability of the rotor system. In this paper, a novel negative dislocated seal (NDS) was developed in respect of dislocated bearing theory, to reduce hydrodynamic pressure effect and air-induced force and improve rotor stability as well. A test rig was built to test rotordynamic characteristics and rotor stability of the NDS. The rotordynamic characteristics of seals were investigated based on the unbalanced synchronous excitation method, and seal-rotor system stability was evaluated by the identification method with an electromagnetic bearing exciter. The effects of both rotating speed and inlet/outlet pressure ratio on the rotordynamic characteristics and rotor stability of both NDS and conventional cylindrical labyrinth seal were experimentally investigated. The results show that with the increasing rotating speed, inlet/outlet pressure ratio is promising to reduce the direct stiffness coefficients of seals and the logarithmic decrement rate of seal-rotor system and enhance both cross stiffness and damping coefficient as well. Besides, the developed NDS effectively reduces cross-stiffness coefficients and increases direct damping coefficients and the logarithmic decrement rate of the seal-rotor system, relative to the conventional cylindrical seal. The proposed seal can effectively improve seal stability of turbomachinery.

Rotordynamic Performance of the Interlocking Labyrinth Seal With a Tilting Rotor

2020 ◽  
Author(s):  
Wanfu Zhang ◽  
Yingfei Wang ◽  
Qianlei Gu ◽  
Lu Yin ◽  
Jian-gang Yang
Keyword(s):  
Flow Rate ◽  
Labyrinth Seal ◽  
System Stability ◽  
Radial Clearance ◽  
Dynamic Force ◽  
Misalignment Angle ◽  
Analysis Model ◽  
Force Coefficient ◽  
Annular Seal ◽  
The Stability

Abstract Numerical analysis model of an interlocking labyrinth seal (ILS), including 6 seal cavities and 7 seal teeth (3 teeth on the rotor, 4 teeth on the stator), is established for studying the effect of tilting rotor on its rotordynamic characteristics. The dynamic characteristic identification method based on infinitesimal theory is applied to solve the dynamic force coefficient of the annular seal with arbitrary elliptical orbits and eccentric positions under field conditions. The paper investigated the dynamic characteristics of the interlocking labyrinth seal with various misalignment angles (θ = 0, 0.1°, 0.2°, 0.3°, 0.4°, 0.5°, 0.6°), different pressure ratios (Pin = 6.9 bar, PR = 0.5, 0.8), locations of misalignment center (Loc = 0, L/2, L). Results show that the tilting rotor could minimize the leakage flow rate of the ILS. When the misalignment angle θ = 0.6°, the mass flow rate can be reduced about 2.5%. The tilting rotor will cause the geometric deformation of the ILS cavity and the changes in the radial clearance of the teeth, which results in an increasing pressure drop in the seal cavity. The effect of each cavity in the ILS on the stability of the system is different. The cavity with the inlet close to the rotor and the outlet away from the rotor helps to improve the system stability due to its locally anti-rotational flow. The effective damping of the entire ILS increases as the misalignment angle increases. The system shows the best stability when the misalignment center is close to the seal inlet. The stability of the seal cavity C1 can be improved for any misalignment centers. The stability of the seal cavity C2 decreases when the misalignment center moves toward the seal outlet. For the seal cavities C3∼C6, their stability can be improved for Loc = 0, L/2, and decreases for Loc = L. The tilting rotor has a positive effect on the stability of the ILS only except for high whirling frequency (> 100 Hz) under Loc = L.

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