Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Static Stability ◽  
Operating Conditions ◽  
Eccentricity Ratio ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Experiment Data ◽  
High Eccentricity ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Gas Seals

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor–stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360 deg mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces, and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-averaged Navier–Stokes solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7000 rpm, 11,000 rpm, and 15,000 rpm) including the nonrotating condition, three pressure ratios (0.17, 0.35, and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions; no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal (PDS) would be statically unstable.

Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

2017 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Static Stability ◽  
Operating Conditions ◽  
Eccentricity Ratio ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Experiment Data ◽  
High Eccentricity ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Gas Seals

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor-stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully-partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360° mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-Averaged Navier-Stokes (RANS) solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7 000 rpm, 11 000 rpm and 15 000 rpm) including the non-rotating condition, three pressure ratios (0.17, 0.35 and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions, no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal would be statically unstable.

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Freˆne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons with the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint this behaviour is explained by the modification of the Lomakin effect that changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Vol 129 (4) ◽  
pp. 1028-1034 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Frêne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal, choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons to the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section, the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section, the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint, this behavior is explained by the modification of the Lomakin effect, which changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

Study on Dynamic Characteristics of a Hydrostatic and Hydrodynamic Journal Bearings for Small Diameter Grinding Spindle

2012 ◽  
Vol 497 ◽  
pp. 99-104 ◽  
Author(s):  
Zhi Quan Hou ◽  
Wan Li Xiong ◽  
Xue Bing Yang ◽  
Ju Long Yuan
Keyword(s):  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Small Diameter ◽  
Diameter Ratio ◽  
Design Parameters ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Supply Pressure ◽  
Stiffness Coefficients ◽  
Direct Stiffness

The dynamic characteristics of a hydrostatic and hydrodynamic journal bearing with two arrays of eight holes have been investigated theoretically by the three-dimensional Computational Fluid Dynamics (CFD) models with respect to equilibrium position. The various dynamic coefficients for design parameters, such as orifice diameter, length to diameter ratio, eccentricity ratio, supply pressure, and rotational speed, are analyzed systematically under the action of displacement disturbance and velocity disturbance which are considered by the User Definition Function (UDF) programs. Results show that the dynamic coefficients greatly affected by design parameters. The cross stiffness coefficients increase rapidly more than direct stiffness with an increase of length to diameter ratio and rotational speed. Conversely, the direct stiffness coefficients are larger than cross stiffness with an increase of supply pressure and eccentricity ratio. It indicates that the journal bearing with two arrays of eight holes is suitable for their applications to small diameter grinding spindle by the means of optimizing the operating parameters and the structural parameters in order to obtain a better dynamic characteristic.

Influence of Annular/Pocket Groove on the Static and Rotordynamic Characteristics of Hole-Pattern Seals

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Dynamic Stiffness ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Static Stability ◽  
Mesh Deformation ◽  
Radial Clearance ◽  
Static Stiffness ◽  
Force Coefficients ◽  
Piston Seal ◽  
Direct Stiffness

Abstract Annular damper seals, such as hole-pattern seals, are widely used to control leakage and enhance rotordynamic stability in turbomachinery, especially, for the balance-piston seal in the straight-through multistage centrifugal compressor, and the center seal in the back-to-back compressor. To avoid negative static stiffness (zero frequency), annular grooves on seal stator have been used to increase the direct static stiffness of hole-pattern seals by dividing a long seal to several shorter seal sections. However, few literatures are available for understanding the influences of grooves on seal static and rotordynamic characteristics. To comprehensively understand the effects of grooves on the static and rotordynamic characteristics of annular damper seals, a proposed three-dimensional (3D) transient CFD-based method was used to predict the rotordynamic characteristics of annular damper seals, based on the multifrequency one-dimensional rotor whirling model and mesh deformation technique. Moreover, a 3D steady CFD-based method based on the mesh deformation technique was also proposed to predict the static characteristics of annular damper seals. The accuracy and reliability of the present transient CFD-based method were demonstrated with the experimental data of frequency-dependent rotordynamic force coefficients for an experimental hole-pattern seal at three inlet preswirl conditions (μ0 = −0.244, 0, 0.598). Numerical results such as leakage flowrates, static and rotordynamic force coefficients were presented and compared for a conventional straight-through hole-pattern seal (without grooves, HPS) and two types of grooved hole-pattern seals (one with annular groove on stator, HPS-AG; one with pocket groove on stator, HPS-PG) with three groove positions (20%, 40%, 60% of seal axial length), at zero (μ0 = 0) and positive (μ0 = 0.598) inlet preswirl conditions. These seals are long (L/D = 0.75), with a diameter of 114.5 mm and a radial clearance of 0.2 mm. The effects of groove types (annular and pocket) and groove positions on seal's static and rotordynamic force coefficients were numerically discussed. Results show that compared to the conventional HPS seal, two types of grooves (annular and pocket) both produce a significant increase (20–150%, especially for the larger rotor eccentric ratios) in static direct stiffness, and the HPS-PG seal possesses the relatively optimal static stability. Two types of grooves (annular and pocket) both result in a slight increase (less than 5%) in seal leakage. The annular groove will significantly weaken the seal dynamic stiffness capability, however, the pocket groove shows only very weak influences. Compared to the conventional HPS seal, the HPS-PG seal possesses the similar increasing effective damping and decreasing crossover frequency with the HPS-AG seal. This suggests that the pocket groove is a more suitable design to improve the seal static and rotordynamic characteristics. The rotordynamic force coefficients show a strong dependence on the groove location for the HPS-AG seal, but which is insensitive for the HPS-PG seal. The optimal location of annular groove is strongly related to the inlet preswirl conditions.

Static and Dynamic Performance of Pressure Dam Bearings With Dam Steps That Are (I) Square and (II) Filleted

2008 ◽  
Author(s):  
Dara Childs ◽  
Andrew Schaible ◽  
Bader Al Jughaiman
Keyword(s):  
Dynamic Performance ◽  
Operating Conditions ◽  
The Other ◽  
Step Test ◽  
Radial Clearance ◽  
Static Characteristics ◽  
Stiffness Coefficients ◽  
Test Conditions ◽  
Minimum Film Thickness ◽  
Direct Stiffness

Measured rotordynamic force coefficients (stiffness, damping, and added-mass) and static characteristics (eccentricity and attitude angle) are presented for two nearly identical pressure-dam bearings. One bearing has a square step at the dam; the other has a filleted step. Because of reduced manufacturing costs, the filleted-step design is used widely. The bearings’ groove dimensions are close to the optimum predictions of Nicholas and Allaire [2] and are consistent with current field applications. The bearings have a diameter of 117.1 mm (4.61 in), a length-to-diameter ratio of 0.655, and a nominal radial clearance of 0.133 mm (5.25 mils). The bottom pad has a deep, centered relief track over 25% of the pad’s axial length. The upper pad for both bearings has a step located at 130° from the horizontal and a 0.620 mm (15.75 mils) deep dam. The dam on the upper pad of one bearing has a square step; the other bearing has a filleted step. Test conditions include four shaft speeds (4000, 6000, 8000 and 10000 rpm) and bearing unit loads from 0 to 1034 kPa (150 psi). Laminar flow was produced for all test conditions within the bearing lands. For the same operating conditions, the filleted step bearing operates at a lower eccentricity ratio (has a larger minimum film thickness). The filleted step design has higher direct stiffness coefficients. Both cross-coupled stiffness coefficients are positive (favorable for stability) for both designs but the filleted design produces higher values. In regard to direct damping, the filleted-step design has higher damping in the load direction and comparable values in the unloaded direction. Hence, for the same operating conditions, a filleted step design should produce reduced amplitudes at or near a critical speed. With respect to stability as defined by WFR, the filleted design is consistently better (lower value) than the square step design, resulting in an elevated onset speed of instability for the filleted-step design.

Analysis of the Experimental and CFD-Based Theoretical Methods for Studying Rotordynamic Characteristics of Labyrinth Gas Seals

2010 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Martin Deckner
Keyword(s):  
Measurement Techniques ◽  
Experimental Results ◽  
Theoretical Methods ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Dynamic Methods ◽  
Inlet Swirl ◽  
Direct Stiffness ◽  
Gas Seals ◽  
Stiffness And Damping

This paper presents an analysis of the experimental and theoretical methods used to study rotordynamic characteristics of short staggered labyrinth gas seal. Two experimental identification procedures referred to as static and dynamic methods are presented. The static method allows determining direct and cross-coupled stiffness coefficients of the seal by integrating measured circumferential pressure distribution in cavities at various shaft eccentric positions. In the dynamic method, identification of stiffness and damping coefficients is based on the rotor excitation using a magnetic actuator and utilizes the effect of alternation of rotor vibrations due to aerodynamic forces acting in the seal. The experimental results obtained by the static and dynamic methods demonstrate an apparent discrepancy most of all in the direct stiffness coefficients. A CFD-based model of the seal is used to predict rotordynamic coefficients and to analyze the discrepancies between the static and dynamic measurements. The seal forces are calculated in two ways similar to the experimental procedures. The predictions are in good agreement with experimental results obtained by both measurement techniques. The effects of pressure differential, inlet swirl, shaft rotational speed, shaft eccentricity, and inflow cavity on seal stiffness and damping are presented. The discrepancies between different methods must be kept in mind while studying rotordynamic characteristics of seals.

Prediction of the Flow and Force Characteristics of Safety Relief Valves

2006 ◽  
Author(s):  
W. Dempster ◽  
C. K. Lee ◽  
J. Deans
Keyword(s):  
Operating Conditions ◽  
Cfd Analysis ◽  
Flow Conditions ◽  
Relief Valve ◽  
Good Correspondence ◽  
Geometry Modeling ◽  
Valve Opening ◽  
Satisfactory Prediction ◽  
Force Characteristics

The design of safety relief valves depends on knowledge of the expected force-lift and flow-lift characteristics at the desired operating conditions of the valve. During valve opening the flow conditions change from seal-leakage type flows to combinations of sub-sonic and supersonic flows It is these highly compressible flow conditions that control the force and flow lift characteristics. This paper reports the use of computational fluid dynamics techniques to investigate the valve characteristics for a conventional spring operated 1/4” safety relief valve designed for gases operating between 10 and 30 bar. The force and flow magnitudes are highly dependent on the lift and geometry of the valve and these characteristics are explained with the aid of the detailed information available from the CFD analysis. Experimental determination of the force and flow lift conditions has also been carried out and a comparison indicates good correspondence between the predictions and the experiment. However, attention requires to be paid to specific aspects of the geometry modeling including corner radii and edge chamfers to ensure satisfactory prediction.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

Prediction of Threshold Sand Rates from Acoustic Monitors Using Artificial Intelligence

2021 ◽  
Author(s):  
Ronald E. Vieira ◽  
Bohan Xu ◽  
Asad Nadeem ◽  
Ahmed Nadeem ◽  
Siamack A. Shirazi
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Noise Level ◽  
Background Noise ◽  
Pipe Wall ◽  
Flow Patterns ◽  
Operating Conditions ◽  
Flow Conditions ◽  
Background Noise Level ◽  
Input Parameters

Abstract Solids production from oil and gas wells can cause excessive damage resulting in safety hazards and expensive repairs. To prevent the problems associated with sand influx, ultrasonic devices can be used to provide a warning when sand is being produced in pipelines. One of the most used methods for sand detection is utilizing commercially available acoustic sand monitors that clamp to the outside of pipe wall and measures the acoustic energy generated by sand grain impacts on the inner side of a pipe wall. Although the transducer used by acoustic monitors is especially sensitive to acoustic emissions due to particle impact, it also reacts to flow induced noise as well (background noise). The acoustic monitor output does not exceed the background noise level until a sufficient sand rate is entrained in the flow that causes a signal output that is higher than the background noise level. This sand rate is referred to as the threshold sand rate or TSR. A significant amount of data has been compiled over the years for TSR at the Tulsa University Sand Management Projects (TUSMP) for various flow conditions with stainless steel pipe material. However, to use this data to develop a model for different flow patterns, fluid properties, pipe, and sand sizes is challenging. The purpose of this work is to develop an artificial intelligence (AI) methodology using machine learning (ML) models to determine TSR for a broad range of operating conditions. More than 250 cases from previous literature as well as ongoing research have been used to train and test the ML models. The data utilized in this work has been generated mostly in a large-scale multiphase flow loop for sand sizes ranging from 25 to 300 μm varying sand concentrations and pipe diameters from 25.4 mm to 101.6 mm ID in vertical and horizontal directions downstream of elbows. The ML algorithms including elastic net, random forest, support vector machine and gradient boosting, are optimized using nested cross-validation and the model performance is evaluated by R-squared score. The machine learning models were used to predict TSR for various velocity combinations under different flow patterns with sand. The sensitivity to changes of input parameters on predicted TSR was also investigated. The method for TSR prediction based on ML algorithms trained on lab data is also validated on actual field conditions available in the literature. The AI method results reveal a good training performance and prediction for a variety of flow conditions and pipe sizes not tested before. This work provides a framework describing a novel methodology with an expanded database to utilize Artificial Intelligence to correlate the TSR with the most common production input parameters.

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