Static Performance of Smooth Liquid Annular Seals in the Transition and Turbulent Regimes

2021 ◽  
Author(s):  
Dara W. Childs ◽  
Joshua Bullock
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Turbulent Regime ◽  
Swirl Ratio ◽  
Transition Flow ◽  
Transition Flow Regime ◽  
San Andres ◽  
Annular Seals

Abstract Static test results are presented for smooth annular seals with a length-to-diameter ratio of 0.50, radius R = 51.00 mm, at the nominal radial clearance Cr = 0.2032 mm. Tests were conducted for angular shaft speeds; ω = 2, 4, 6, 8 krpm, axial pressure drops; ΔP = 2.1, 4.13, 6.21, 8.27 bars, and eccentricity ratios ϵ0 = e0/Cr = 0.00, 0.27, 0.53, 0.8 where e0 is the static eccentricity. Three pre-swirl inserts were used to target zero, medium, and high (0., 0.4, and 0.8) pre-swirl ratios for a set of pre-determined operating conditions with ISO VG 2 oil at 46.1°C. Pitot tubes measured the circumferential velocity at separate upstream and downstream seal locations and were used to calculate pre-swirl ratio, PSR = vinlet/Rω, and outlet-swirl ratio, OSR = voutlet/Rω. For all tested pre-swirl inserts, PSR tended to converge to 0.4∼0.5 as ω increased. PSR and OSR were poorly correlated. Volumetric leakage rate Q ˙ versus pressure differential ΔP was measured. The measured vector Reynolds number Re, combining the axial and circumferential Reynolds numbers ranged from ∼1000 to ∼3500. Based on Zirkelback and San Andrés 1996 publication, almost all of the flow regime is predicted to lie in the transition regime, with fewer points in the turbulent regime. Generally, the seals’ static centering properties were obtained by applying a static load Fs and measuring the resulting displacement vector e0. At many low-speed, low-ΔP test conditions, the seal would not remain in the desired centered or near-centered position and had to be forced into place with a centering force Fs. The authors believe that the observed de-centering effects resulted from test operations in the transition flow regime where the friction factor λ does not drop with increasing ΔP and increasing Re. A positive centering Lomakin effect requires that λ drop with increasing axial Reynolds number. The seals had positive centering effects over a large portion of the predicted transition flow regime, supporting the view that the shift from transition-to-turbulent flow regularly occurred at lower Re values than the Re = 3000 boundary used by Zirkleback and San Andrés.

Experimental Study and Computational Fluid Dynamics Modeling of Pulp Suspensions Flow in a Pipe

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Carla Cotas ◽  
Bruno Branco ◽  
Dariusz Asendrych ◽  
Fernando Garcia ◽  
Pedro Faia ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Drop ◽  
Flow Regime ◽  
Turbulent Regime ◽  
Cfd Model ◽  
Dynamics Modeling ◽  
Transition Flow ◽  
Pulp Suspensions ◽  
Transition Flow Regime

Eucalyptus and Pine suspensions flow in a pipe was studied experimentally and numerically. Pressure drop was measured for different mean inlet flow velocities. Electrical impedance tomography (EIT), was used to evaluate the prevailing flow regime. Fibers concentration distribution in the pipe cross section and plug evolution were inferred from EIT tomographic images. A modified low-Reynolds-number k–ε turbulence model was applied to simulate the flow of pulp suspensions. The accuracy of the computational fluid dynamics (CFD) predictions was significantly reduced when data in plug regime was simulated. The CFD model applied was initially developed to simulate the flow of Eucalyptus and Pine suspensions in fully turbulent flow regime. Using this model to simulate data in the plug regime leads to an excessive attenuation of turbulence which leads to lower values of pressure drop than the experimental ones. For transition flow regime, the CFD model could be applied successfully to simulate the flow data, similar to what happens for the turbulent regime.

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

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Dung L. Tran ◽  
Dara W. Childs ◽  
Hari Shrestha ◽  
Min Zhang
Keyword(s):  
Dynamic Instability ◽  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Radial Clearance ◽  
Inlet Temperature ◽  
Test Results ◽  
Transition Flow ◽  
Two Phase ◽  
Rotordynamic Coefficients ◽  
Transition Flow Regime

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.

Experimental Investigation of Pressure Drop Characteristics of Viscous Fluid Flow Through Small Diameter Orifices

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Lalit Kumar Bohra ◽  
Leo M. Mincks ◽  
Srinivas Garimella
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Viscous Fluid ◽  
Euler Number ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Operating Conditions ◽  
Turbulent Regime ◽  
Pressure Drops

Abstract An experimental study on the flow of a highly viscous fluid through small diameter orifices was conducted. Pressure drops were measured for each of nine orifices, including orifices of nominal diameter 0.5, 1, and 3 mm and three different orifice thicknesses, over wide ranges of flow rates and temperatures. The fluid under consideration exhibits steep dependence of the properties (changes of several orders of magnitude) as a function of temperature and pressure and is also non-Newtonian at the lower temperatures. At small values of Reynolds number, an increase in aspect ratio (length/diameter ratio of the orifice) causes an increase in Euler number. It was also found that at extremely low Reynolds numbers, the Euler number was very strongly influenced by the Reynolds number, while the dependence becomes weaker as the Reynolds number increases toward the turbulent regime, and the Euler number tends to assume a constant value determined by the aspect ratio and the diameter ratio. A two-region (based on Reynolds number) model was developed to predict Euler number as a function of diameter ratio, aspect ratio, viscosity ratio, and generalized Reynolds number. It is shown that for such a highly viscous fluid with some non-Newtonian behavior, accounting for the shear rate through the generalized Reynolds number results in a considerable improvement in the predictive capabilities of the model. Over the laminar, transition, and turbulent regions, the model predicts 86% of the data within ±25% for the geometry and operating conditions investigated in this study.

scholarly journals A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

2015 ◽  
Vol 7 (2) ◽  
pp. 245-266 ◽  
Author(s):  
Songze Chen ◽  
Kun Xu ◽  
Qingdong Cai
Keyword(s):  
Kinetic Model ◽  
Flow Regime ◽  
Free Parameter ◽  
Numerical Solutions ◽  
Test Cases ◽  
Transition Flow ◽  
New Model ◽  
Transition Flow Regime ◽  
Generalized Kinetic Model ◽  
S Model

AbstractThe Ellipsoidal Statistical model (ES-model) and the Shakhov model (Smodel) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new parameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the continuum flow regime. Through the adjustment of the new parameter, it provides abundant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltzmann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the Smodel predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number.

Fibrous Filter Efficiency and Pressure Drop in the Viscous-Inertial Transition Flow Regime

2012 ◽  
Vol 46 (2) ◽  
pp. 138-147 ◽  
Author(s):  
J. A. Hubbard ◽  
J. E. Brockmann ◽  
J. Dellinger ◽  
D. A. Lucero ◽  
A. L. Sanchez ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Flow Regime ◽  
Transition Flow ◽  
Fibrous Filter ◽  
Filter Efficiency ◽  
Transition Flow Regime

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

2019 ◽  
Author(s):  
Dung L. Tran ◽  
Dara W. Childs ◽  
Hari Shrestha ◽  
Min Zhang
Keyword(s):  
Dynamic Instability ◽  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Radial Clearance ◽  
Inlet Temperature ◽  
Test Results ◽  
Transition Flow ◽  
Pressure Drops ◽  
Rotordynamic Coefficients ◽  
Transition Flow Regime

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 3 inlet-preswirl inserts, namely, zero, medium, and high (the preswirl ratios, 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), 6 inlet gas-volume-fractions GVFi (0%, 2%, 4%, 6%, 8%, 10%), 4 pressure drops PD (20.7, 27.6, 34.5, 41.4 bars), and 3 speeds ω (3, 4, 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 ṁ and rotordynamic coefficients are measured, and the effect of changing inlet preswirl and GVFi are studied. The test results are then compared with predictions from a 2-phase, homogeneous-mixture, bulk-flow model developed in 2011. Generally, both measurements and predictions show little change in ṁ as inlet preswirl changes. Measured ṁ remains unchanged or slightly increases with increasing GVFi, but predicted ṁ decreases. Measured ṁ 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 2-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 nonsynchronous vibration) on a high-differential-pressure helico-axial multiphase pump, 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 decrease the seal’s stabilizing properties. Ceff increases with increasing GVFi — becomes more stable.

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