Bulk-flow Model Research Articles

ELASTOHYDRODYNAMIC EFFECTS IN LUBRICATION OF JOURNAL BEARINGS UNDER TURBULENT CONDITIONS

The current paper is aimed to investigate the deformability effects of the bearing surface on the lubrication performance of cylindrical journal bearing with finite length under turbulent conditions. The bush is coated with a thin resilient layer with a smooth surface, the radial distortions of which are of the same order of magnitude as the film thickness. The elastohydrodynamic problem is studied under elasticity conditions in accordance with the plain strain hypothesis (Winkler model). The modified Reynolds equation is carried out on the base of the turbulent lubrication model of Hirs (bulk flow model). The partial differential equation is solved numerically by successive over-relaxation technique on a finite difference grid, considering different values of coating materials, lubricant viscosity, and journal speed. Results for the performance characteristics of the bearing are given for several selected values of Reynolds number and elasticity parameters of the soft liner on the bush.

Computational Fluid Dynamics Analysis and Experimental Results for the Dynamic Performance of Two Long Smooth Surface Annular Seals Operating With a Liquid in Air Mixture

Abstract Compressors in subsea oil and gas production must handle wet gases to reliably operate for extended periods of time. Annular clearance seals contribute to compressor performance and do affect system rotordynamic stability. Prior experimental work with two smooth surfaces, uniform clearance seals supplied with a light oil in air mixture and undergoing similar operating conditions produced direct stiffnesses (K) with distinct trends as the liquid content increased to 8% in volume. Both seals differ in length and diameter albeit having similar radial clearance. Other force coefficients for both seals, namely, cross-coupled stiffness (k) and direct damping (C) increase as the inlet liquid volume fraction (LVF) grows. Rationale for the peculiar differences in centering stiffness (K) is missing. Hence, a computational fluid dynamics (CFD) model and its predictions, the thrust of this paper, unveil flow field details (pressure, velocity fields, and liquid content evolution) for the oil in air mixture. Besides the CFD model, an enhanced bulk-flow model (BFM) also predicts the seals' leakage and dynamic force coefficients. Both models predict through flows agreeing well with the measured ones, the maximum difference is less than 16%. The BFM direct stiffness (K) does reproduce closely the experimental K whereas the direct damping coefficient (C) is up to ∼41% lower than the test result. The CFD model captures the variation trend of K versus inlet LVF for the first seal, albeit its magnitude is thrice the experimental stiffness. The CFD C agrees well with the test data for both seals, the largest difference is less than 10%. In spite of the complexity of the CFD model, significant differences with the experimental results persist, in particular for K. When considering the seal inlet corner as round, the CFD model produces a significant reduction in K to better approach the test result for a seal supplied with air. Attention to the seal geometry is paramount to produce accurate predictions.

Development of a New Loss Model for Turbomachinery Labyrinth Seals

Abstract The preliminary design of labyrinth seals requires fast and accurate estimate of the leakage flow. While the conventional bulk flow models can quickly predict labyrinth seal discharge characteristics, they lack the accuracy and pragmatism of modern computational fluid dynamics (CFD) techniques and vice-a-versa. This paper presents a new one-dimensional loss model for straight-through gas labyrinth seals that can provide quick seal leakage flow predictions with CFD-equivalent accuracy. The present seal loss model is developed using numerical experimentation technique. Multiple CFD computations are conducted on straight-through labyrinth seal geometries for a range of pressure ratios. A distinct postprocessing methodology is developed to extract the through-flow stream tube in seal. Total pressure losses and flow area variations experienced by the flow in seal stream-tube are systematically accounted for based on the well-known knife-to-knife (K2K) methodology. Regression analyses are conducted on the trends of variations of loss and area coefficients to derive the independent pressure loss and flow area correlations. These novel correlations can predict the bulk leakage flow rate, windage flow rate, and interknife static pressures over a wide range of variations of flow and geometry parameters. Validation study shows that the leakage mass flow rate predicted by this model is accurate within ±8% of measured test data. This fast and accurate model can be employed for various applications such as in seal design-analysis workflows, for secondary air system (SAS) performance analysis, and for the rotor-dynamic and aeroelastic assessments of seals.

Circumferentially Grooved Seal Flow Field Analysis Based on Effective Film Thickness to Improve Bulk Flow Models

Abstract Bulk flow methods for circumferentially grooved seals use simplified physics models to predict leakage and rotordynamic coefficients efficiently, but uncertainty in empirical quantities like friction factors and loss coefficients leads to limited accuracy. To develop a more fundamental understanding of incompressible grooved seal flow, this study utilizes computational fluid dynamics (CFD) and an effective film thickness, a physical boundary between the jet and recirculating flows, to investigate Reynolds number effects on flow fields and shear stresses. Simulations are run using ansyscfx for a single groove seal model where streamlined analysis produces the effective film thickness. Flow structures, film thicknesses, shear stresses, and net flow expansion into the groove are found to be described completely by the ratio of circumferential to axial Reynolds number and the total resultant Reynolds number. Decreases in leakage with rotor speed are found to be dictated by increased land shear stresses and a decreased role of the groove in inducing pressure drop. An optimal groove aspect ratio between 0.07 and 0.19 is presented based on maximizing expanded film area while retaining a main groove recirculation region. This is the first paper to analyze circumferentially grooved seal flow from an effective film thickness standpoint. The results highlight bulk flow analysis areas where an effective film thickness approach could lead to new, physics-motivated model development and the elimination of particular empirical coefficients, thus providing a foundation on which substantial improvements in bulk flow modeling accuracy can be achieved.

A Nonhomogeneous Bulk Flow Model for Gas in Liquid Flow Annular Seals: An Effort to Produce Engineering Results

Abstract Seals in multiple-phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous bulk flow model (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0% (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (∼38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ∼0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate), and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1. Compared to the test data, the two models generally under predict C and k by ∼25%. Both models deliver a whirl frequency ratio (fw) ∼ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ∼0.35 as the GVF approaches 0.1. For the low-pressure seal, the flow is laminar; the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ∼30% below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate that the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal that the fluid flow maintains the homogeneous character known at the inlet condition.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based on the Applicability Analysis of Leakage Models Using Bulk-Flow Method

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial to the analysis of the fluid excitation rotordynamics of labyrinth seals. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of seventy-two leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Investigation of the Dynamic Characteristics of an Eccentric Annular Seal on the Basis of a Transient CFD Method with Three Whirl Models

Many annular seals suffer eccentricity because of rotor–stator misalignment or the deflection of a flexible rotor, which has a strong influence on the vibration characteristics and stability of rotating machines. In this article, a transient CFD method based on three whirl models is employed to research the dynamic characteristics of annular seals at various static eccentricities. The influence of the whirl amplitude on the dynamic characteristics of eccentric annular seals are also explored. The results of the transient CFD method are compared with the bulk flow model results and the experimental results. It is shown that the transient CFD method possesses high prediction precision for direct damping, with a maximum error of 25%. Negative kyx increases by 166% when the static eccentricity ratio is increased from 0 to 0.5. The dynamic characteristics of the annular seal operating at high static eccentric ratio are sensitive to whirl amplitude, and the model with an amplitude of 1% Cr has great advantages for the prediction of direct virtual-mass, while the model with an amplitude of 10% Cr has great advantages for the prediction of cross-coupled damping.

Gravitational waves from bubble walls

We present a general method for computing the gravitational radiation arising from the motionof bubble walls or thin fluid shells in cosmological phase transitions.We discuss the application of this method to different wall kinematics.In particular, we derive general expressions for thebubble collision mechanism in the envelope approximation and the so-called bulk flow model,and we also consider deformations from the spherical bubble shape.We calculate the gravitational wave spectrum for a specific model of deformations on a definite size scale,which gives a peak away from that of the bubble collision mechanism.

Behaviors of a Hole-Pattern Seal With Wet-Gas

Abstract Hole-pattern (HP) seals are widely used in centrifugal compressors to control leakage. This paper investigates the behaviors of an HP with wet-gas mixtures. The mixture consists of oil and air with inlet liquid volume fraction (LVF) up to 8%. Injecting oil into the air stream increases the leakage mass flowrate. Direct stiffness K is frequency-dependent and increases with increasing excitation frequency Ω. Injecting oil into the airflow makes this stiffening effect more pronounced. At low frequencies, increasing inlet LVF shows no appreciable impact on K; however, as Ω increases, the effects of changing LVF become more pronounced; i.e., at high frequencies, increasing LVF increases K. The effective damping Ceff value at half of the running speed is indicative of the system stability because many compressor rotors frequently show instabilities at ∼50% of the running speed. At 50% of the running speed, Ceff is positive, and it increases with increasing inlet LVF. Predictions based on San Andrés's (2011) homogenous-mixture bulk-flow model show a good agreement with test results for leakage mass flowrate, K, and the Ceff value near 50% of the running speed. When Ω = 0.5ω, the predicted value of Ceff is smaller than the measured value by ∼12.5%, giving a safe margin for the compressor design.

Static Characteristics and Leakage Rates of Smooth Annular Seals Based on a New Solution Method for Gas-Liquid Two-Phase Conditions

This paper proposes a new solution method for the leakage and static characteristics of smooth annular seal under a homogeneous gas-liquid two-phase flow based on a bulk-flow model. In this solution method, the Rayleigh–Plesset equation is introduced into the governing equations to describe the behavior of bubbles considering mixture compressibility. Detailed comparisons between Childs’ experimental leakage rates and predicted ones based on the proposed method are conducted, and the predicted results show good agreement with the experimental results, with a maximum error of 11.2%. Moreover, static characteristics of the seal, including leakage rates, gas volume fraction (GVF) distribution, pressure distribution, mixture density, and viscosity within the seals, are investigated based on the present method. The results show that as the inlet gas volume fraction increases from 0% to 10%, the local gas volume fraction of each axial position will increase, however, the seal leakage, mixture density, and mixture viscosity will decrease. Bubble radius has little effect on the leakage rates and the static characteristics of the seals. Additionally, comparisons between the characteristics of the model seals with different clearances show that the leakages of the seals with bigger clearance behave more sensitively to the inlet GVF changes.

Test Results for the Static and Rotordynamic Characteristics of a Long (L/D = 0.75) Smooth Seal in Two-Phase (Mainly Gas) Conditions With a 62-Bar Inlet Pressure

Abstract Recent multiphase-pump developments encountered several rotordynamic issues with smooth balance-piston seals, creating a need to better understand the performance of annular seals under multiphase-flow operation. This paper presents measurements of static and dynamic characteristics of a long smooth seal (L/D = 0.75, D = 114.686 mm, and Cr = 0.200 mm) operating under pure- and mainly air condition in which air is mixed with silicone oil (PSF-5cSt). Tests are performed at a supply pressure of 62.1 bars-g, three rotation speeds (5, 10, and 15 krpm), three pressure ratios (PRs) (0.6, 0.5, 0.4), for a range of inlet liquid volume fraction (LVFi) from 0% to 8%. The results are then compared to: (1) the previous test reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) with similar testing condition but a different seal geometry (L/D = 0.65, D = 89.306 mm, and Cr = 0.188 mm) and (2) the predictions from a bulk-flow model developed by San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503). Results show a significant increase of direct dynamic stiffness KΩ as LVFi increases, especially at low PR. Test results reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) has an opposite tendency of KΩ as an impact of increasing LVFi values. Concerning cross-coupled dynamic stiffness kΩ and cross-coupled damping c, the results from Zhang et al. (2017) and the present results agree to the effects of changing speed, PR, and LVFi under pure- and mainly air conditions. As LVFi increases, direct damping C increases while test results reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) showed no significant increase. A steady-state computational fluid dynamics (CFD) result for a testing case suggests a significant difference happening inside the two seals (present seal and Zhang et al.'s (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) seal). A full investigation in CFD is needed. Except for the direct dynamic stiffness and the impact of changing LVFi on the cross-coupled dynamic stiffness, the bulk-flow model of San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) predicts decently the tendencies and magnitudes of the rotordynamic coefficients.

On the Leakage and Dynamic Force Coefficients of a Novel Stepped Shaft Pocket Damper Seal: Experimental and Numerical Verification

Abstract High-performance turbomachinery favors annular seals with a large damping coefficient to ensure rotor system stability. Pocket damper seals (PDSs), a variation of labyrinth seals with axial blades (ribs) and adding circumferential partition walls (ridges), produce a favorable damping performance. To further enhance the damping characteristic and reduce leakage, a novel stepped shaft PDS is hereby introduced. The invention has a unique arrangement of steps on the rotor surface, each facing an upstream rib in a pocket row. Thus, the step and a blade tip form a tight clearance (c1), while the rotor surface and the downstream blade tip make a larger clearance (c2). The convergence–divergence variation of cross-sectional areas along the flow direction increases the PDS damping coefficient. To validate the performance of the novel design, a stepped shaft PDS (c1/c2 = 0.5) with four axial ribs and eight circumferential pockets is built and tested. A comprehensive investigation, experimental and computational, produces the seal leakage and dynamic force coefficients for the stepped shaft PDS, as well as similar performance characteristics for an identical PDS with a smooth rotor surface (c1/c2 = 1, i.e., a uniform clearance PDS). The stepped shaft PDS operates with air at supply pressure (PS) ranging from 1.1 bar to 3.2 bar. The measured leakage for the stepped shaft PDS is 50% of that for the uniform clearance PDS. Computational fluid dynamics (CFD) and bulk flow model (BFM) predictions of leakage agree well with the test data. For PS = 2.3 bar, the test damping coefficient (C) for the stepped shaft PDS is ~1.5 times greater than the one for the uniform clearance PDS. With an increase in PS to 3.2 bar, the stepped shaft PDS shows a two and one half increase in damping coefficient. In comparison to the test data, a CFD model overestimates C by 29% for operation at PS = 3.2 bar, though capturing the variation trend versus whirl frequency. The BFM largely underpredicts C for the stepped shaft PDS and is abandoned for future work. Both the test data and CFD predictions demonstrate the superior damping performance of the stepped shaft PDS, thus providing a novel alternative seal configuration for turbomachinery usage.

On the Effect of Clearance on the Leakage and Cavity Pressures in an Interlocking Labyrinth Seal Operating With and Without Swirl Brakes: Experiments and Predictions

Abstract Gas labyrinth seals (LSs) improve turbomachinery operational efficiency and mechanical reliability by reducing secondary leakage. As interlocking labyrinth seals (ILSs) restrict more leakage than conventional see-through LSs, attention is due to their performance. An earlier paper (San Andrés et al. 2019, “Leakage and Cavity Pressures in an Interlocking Labyrinth Gas Seal: Measurements Vs. Predictions,” ASME J. Eng. Gas Turbines Power, 141(10), p. 101007.) details the performance of a particular ILS in an ad hoc test rig via measurements of mass flow (leakage) and cavity pressures while supplied with pressurized air at ambient temperature and operating with a rotor speed to a maximum of 10 krpm (surface speed 79 m/s). The test seal comprises two teeth on the rotor and three teeth on the stator to make a four cavity seal with radial clearance Cr = 0.2 mm. The experimental and numerical leakages for the ILS produce a modified flow factor (Φ¯) that is independent of the seal operating conditions, namely, inlet pressure, discharge pressure and rotor speed. The finding leads to an orifice-like loss coefficient cd = 0.36 and an effective clearance (cd × Cr) for the test seal, thus evidencing its effectiveness in reducing leakage. To complement the former research, this paper reports measurements of the leakage and cavity pressures for the same geometry interlocking labyrinth seals configured with two other clearances Cr = 0.3 mm and 0.13 mm. For the ILS with Cr = 0.3 mm, a first configuration is without a swirl brake (baseline), the second is with a swirl brake with 0 deg teeth pitch (axial ribs), and the third configuration is with a swirl brake with teeth angled at 40 deg in the direction of shaft rotation. For tests conducted without shaft rotation and with rotor spinning at 7.5 krpm (surface speed= 59 m/s), the inlet air pressure (Pin) ranges from 0.29 MPa to 0.98 MPa, while the exit pressure (Pout) is set to pressure ratios PR = (Pout/Pin) = 0.3, 0.5, 0.8. As to the ILS with Cr = 0.13 mm, it operates with an upstream swirl brake with axial ribs (0° teeth pitch) and w/o rotor speed. The supply pressure (Pin) varies from 0.59 MPa to 1.4 MPa and PR = 0.3, 0.5. The measurements and bulk-flow model predictions show that the seal mass leakage is proportional to the inlet pressure (Pin), increases as PR decreases and is not affected by either shaft speed or the swirl brake configuration. Seal cavity static pressures drop linearly for all inlet pressures (Pin) and PR = 0.5 and above, except under a choked flow condition at PR = 0.3. Processing of the test data to consolidate the numerous leakage measurements delivers a nearly invariant flow factor Φ¯ for each seal clearance and from this follows a unique orifice-like loss coefficient cd = 0.36 for the ILS with Cr = 0.3 mm and cd = 0.33 for the ILS with Cr = 0.13 mm. This finding is remarkable as the test results obtained for the ILS with Cr = 0.2 mm also deliver a similar loss coefficient (cd = 0.36). Finally, predictions of ILS leakage and cavity pressures are within 5% of the measurements for all test conditions. The test data and predictions are of significant value to better the selection and design of gas labyrinth seals in turbomachinery.

Rotordynamic force estimation of turbulent, annular seals using OpenFOAM®

3D CFD simulations are performed to resolve the leakage rates, axial pressure drops, and dynamic force coefficients of smooth annular seals. Simulations are performed for several, simple annular seal geometries subject to water and gas flows in order to verify and validate the open-source CFD library OpenFOAM for such applications. Rotordynamic force coefficients are determined using the whirling-rotor method. Accuracy of CFD-predicted results is assessed through direct comparison with published experimental data and bulk-flow model predictions. For the three water seals analyzed, the open-source, CFD-predicted dynamic coefficients closely agree with their experimental counterparts. The k- $$\omega $$ family of turbulence models is shown to outperform the k- $$\epsilon $$ models. For the gas seals, the open-source CFD solver is shown to be unsatisfactory in predicting damping coefficients and simulations are alternatively performed with ANSYS Fluent.

Gas Labyrinth Seals: Improved Prediction of Leakage in Gas Labyrinth Seals Using an Updated Kinetic Energy Carry-Over Coefficient

Abstract Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict the mass flow inaccurately. The BFM models rely on classical Neumann's equation model to characterize the flow through a labyrinth tooth. Presently, a computational fluid dynamics (CFD) analysis quantifies the effects of tip clearance (Cr) and operating conditions on the prediction of LS mass flow, and then derives an updated kinetic energy carry-over coefficient (μ1i) to improve the accuracy of Neumann's leakage equation. μ1i is a function of the seal tip clearance (Cr), the tooth pitch, and the total teeth number; but it does not depend on the seal supply or discharge pressures. The analysis selects a 14-teeth on stator LS (length/diameter = L/D = 0.29) with clearance Cr = (1/733)D and operating at nominal supply (Pin) and discharge (Pout) pressures equal to 73 bar and 51 bar, respectively, and at a rotor speed of 12 krpm (surface speed = 138 m/s). The CFD produces flow fields for LSs with a clearance varying from 80% to 200% of the nominal Cr, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR = Pout/Pin) ranging from 0.40 to 0.85. The numerous predictions deliver the mass flow as well as the bulk-flow velocities and cavity pressures within the seals. The kinetic energy carry-over coefficient (μ1i) increases with respect to the seal radial clearance (Cr). μ1i shows a parabolic correlation with PR; at first, μ1i increases with a rise in PR from a low value; and then, a further increase in PR leads to a decrease in μ1i. The coefficient μ1i is only sensitive to the PR and not to the magnitude of either the supply or discharge pressures. Lastly, for use with Neumann's leakage model, the CFD predictions produce an updated μ1i, a function of the seal geometry and the PR condition. Integration of the new μ1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% difference against test data reduces to within 6%. A TOS LS tested by Ertas et al. (2012, Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbine Power, 134(4), p. 4250301) serves to further validate the accuracy of the modified leakage model.

저널 래버린스 실이 임펠러 추력 및 누설에 미치는 영향

In recent years, turbomachinery pursue high speed operations in compact volume to achieve high specific power. An impeller operating at high rotating speeds increases the compression ratio and results in significant axial thrust forces which must be balanced with balance piston or thrust bearing. A leakage flow flowing through Labyrinth seals located in the gap between the rotor and stator parts also influences the magnitude of the thrust forces. This study develops a predictive model of an impeller coupled with a labyrinth seal to predict the resulted axial thrust force. Firstly, a comparison between the predicted cavity pressure and leakage to the published test data validates the bulk-flow model of the labyrinth seal used in the paper. Then the coupled model of the impeller to the labyrinth seal is verified by comparison of the predicted pressure distributions and leakage flow rates to those from CFD analyses using the k-ε turbulence model. Additionally, the study reports the effects of the labyrinth seal design, operating speed, and lubricant type on the axial thrust force and the leakage flow rate. The results show that the labyrinth seal decreases the leakage flow rate but increases the axial force, implying the need of trade-off between the impeller axial force and leakage flow rate. As the gap between the impeller and casing wall decreases, both the impeller axial force and leakage flow rate decrease. The impeller axial force and the leakage flow rate predicted using refrigerant gas are smaller and less sensitive to the change of the labyrinth seal design when compared to those predicted using air.

Numerical Study on Gas Transport in Shale Kerogen with Adsorption Effect Using LBM

Gas transport and storage mechanism in gas reservoirs with complex pore size distribution play a key role in gas production. In the nano-scale, during the process of density disturbance caused by depressurization development, notable output gas collides with the wall as they convey along the channel. The continuum assumption of fluid flow is therefore invalid, and taking the influence of particles to collide with solid walls into account is necessary. The effective viscosity and slip boundary conditions were introduced in the simulation. Meanwhile, because of the adsorption effect is one of the most important intrinsic properties of shale, the impact of surface adsorption on the solid wall by using Langmuir adsorption kinetics was also involved in our investigation. In this work, a unified LB model was developed for gas multiple transports and surface adsorption in nanopores. In the model, the double distribution function was employed for a coupled bulk flow and gas diffusion model. The model is valid within the range of the continuum regime to the transition regime and has been verified by the analytical solution and the results of some previously published works. The results show that (1) the driven force of the fluid, the combination coefficient of slippage and the Knudsen number of the flow have an impact on the adsorption rate, (2) adsorption effect only directly influence the local small region of the solid surface, and the induced concentration gradient makes the global concentration variation, (3) once acting the surface adsorption on the boundary, the flux falls more significant as Knudsen number increases.

Influences of Floating-ring Seal Parameters on Clearance Leakage

For a type of floating-ring seal widely used in the fields of aeronautics and astronautics, power and energy, and petrochemical engineering, the influences of various parameters on clearance leakage behavior of floating-ring seal are analyzed using numerical method and by means of MATLAB programming. Based on Bulk-flow model, the governing equations of the flow field in the clearance of floating-ring seal are established. The finite difference method and the staggered grid are used to discretize the governing equations. The SIMPLE algorithm is used to solve the discretized equations. The self-locking position of the floating-ring is calculated by analyzing the equilibrium condition of the floating ring, and accordingly the leakage flowrate of the flow field in the clearance of the floating-ring seal are obtained. Finally, the influences of fluid viscosity, inlet swirl, width of floating ring, and relative roughness of floating-ring and rotor surface s on the leakage flowrate are discussed.

Preswirl and Mixed-Flow (Mainly Liquid) Effects on Rotordynamic Performance of a Long (L/D = 0.75) Smooth Seal

Abstract Measured results are presented for rotordynamic coefficients and mass leakage rates of a long smooth annular seal (length-to-diameter ratio L/D = 0.75, diameter D = 114.686 mm, and radial clearance Cr = 0.200 mm) tested with a mixture of silicone oil (PSF-5cSt) and air. The test seal is centered, the seal exit pressure is maintained at 6.9 bars-g while the fluid inlet temperature is controlled within 37.8–40.6 °C. It is tested with three inlet-preswirl inserts, namely, zero, medium, and high (the preswirl ratios (PSRs), i.e., the ratio between the fluid's circumferential velocity and the shaft surface's velocity, are in ranges of 0.10–0.18, 0.30–0.65, and 0.65–1.40 for zero, medium, and high preswirls, respectively), six inlet gas-volume fractions GVFi (0%, 2%, 4%, 6%, 8%, and 10%), four pressure drops PDs (20.7, 27.6, 34.5, and 41.4 bars), and three speeds ω (3, 4, and 5 krpm). The targeted test matrix could not be achieved for the medium- and high-preswirl inserts at PD ≥ 27.6 bars due to the test-rig stator's dynamic instability issues. Spargers were used to inject air into the oil, and GVFi values higher than 0.10 could not be consistently achieved because of unsteady surging flow downstream from the sparger mixing section. Leakage mass flow rate m˙ and rotordynamic coefficients are measured, and the effect of changing inlet preswirl and GVFi is studied. The test results are then compared with predictions from a two-phase, homogeneous-mixture, bulk-flow model developed in 2011. Generally, both measurements and predictions show little change in m˙ as inlet preswirl changes. Measured m˙ remains unchanged or slightly increases with increasing GVFi, but predicted m˙ decreases. Measured m˙ is comparable to predicted values but consistently lower. Dynamic-stiffness coefficients are measured using an ensemble of excitation frequencies and curve-fitted well by frequency-independent stiffness Kij, damping Cij, and virtual mass Mij coefficients. Planned tests with the medium- and high-preswirl inserts could not be accomplished at PD = 34.5 and 41.4 bars because the seal stator became unstable with any finite injection of air. The test results show that the instability arose because the seal's direct stiffness K became negative and increased in magnitude with increasing GVFi. The model predicts a drop in K as GVFi increases, but the test results dropped substantially more rapidly than predicted. Also, the model does not predict the observed strong tendency for K to drop with an increase in preswirl in moving from the zero-to-medium and medium-to-high preswirl inserts. The authors believe that the observed drop in K due to increasing GVFi is not explained by either (a) a reverse Lomakin effect from operating in the transition flow regime or (b) the predicted drop in K at higher GVFi values from the model. A separate and as yet unidentified two-phase flow phenomenon probably causes the observed results. The negative K results due to increasing GVFi and moving from the zero to medium, and medium to high preswirl observed here could explain the instability issue (sudden subsynchronous vibration) on a high-differential-pressure helico-axial multiphase pump (MPP), reported in 2013. Effective damping Ceff combines the stabilizing effect of direct damping C, the destabilizing effect of cross-coupled stiffness k, and the influence of cross-coupled mass mq. As predicted and measured, increasing inlet preswirl significantly increases k and decreases Ceff, which decreases the seal's stabilizing properties. Ceff increases with increasing GVFi—becomes more stable.

Auxiliary bearing squeeze film dampers for magnetic bearing supported rotors

Auxiliary bearings (AB) support the rotor and protect the magnetic bearing (AMB) system when the AMB is disabled due to power loss or excessive loads. The paper demonstrates that installing a damping device along with the AB can yield extended AB fatigue life, protect the AMB, and reduce vibration, contact force and AB heating. A squeeze film damper (SFD) is an energy dissipation device that has been widely used in the turbo-machinery industry, and as demonstrated in the paper can also work effectively in combination with an AB. Usually, the SFD implements a supply groove to ensure adequate lubricant flow into the film lands. The supply groove can provide significant added mass coefficients and significantly influence the overall impedance of the SFD. Past literature has analyzed the transient response of the rotor dropping onto AB's with squeeze film dampers, none though have considered the influence of the SFD's center groove and its added mass effect on rotor's drop behavior. This paper develops a high fidelity finite element grooved SFD model considering the fluid inertia, and an effective groove clearance is used following the practice appearing in the literature. SFD force coefficients are benchmarked with results of a linear fluid inertia, bulk-flow model developed in the literature, before including them in the rotor – AB system model. The SFD model is integrated into a high fidelity nonlinear auxiliary bearing (angular contact ball bearing) model, which considers the movements, contact force, stress, and temperature of bearing balls, the inner race and outer race. The instantaneous reaction forces from the SFD are calculated with a finite element based solution of Reynold equation at each time step due to the intermittent and large sudden loads. The flexibility of the rotor is included utilizing a Timoshenko beam, finite element model. The fatigue life of the auxiliary bearing when integrated into the SFD is also calculated based on the rain flow counting method. The influence of the added mass of the SFD on the rotor's drop behavior is demonstrated showing that the added mass increases the contact force and peak temperature and reduces the fatigue life of the AB. Therefore, the added mass effect of the SFD should be considered to avoid over predicting the AB fatigue life. The influence of the SFD clearance on the rotor's drop behavior is also studied showing that an optimal clearance exists for increasing the AB fatigue life. Too small of a clearance will yield excessive damping making the effective stiffness too large, and causing high contact forces. Too large of a clearance lowers damping which may lead to a destructive backward whirl. This paper provides key guidelines for auxiliary bearing damper system design.