An Annular Gas Seal Analysis Using Empirical Entrance and Exit Region Friction Factors

1990 ◽  
Vol 112 (2) ◽  
pp. 196-204 ◽  
Author(s):  
D. A. Elrod ◽  
D. W. Childs ◽  
C. C. Nelson
Keyword(s):  
Shear Stress ◽  
Friction Factor ◽  
Factor Models ◽  
Exit Region ◽  
Dynamic Coefficients ◽  
Friction Factors ◽  
Direct Stiffness ◽  
Gas Seals ◽  
Rotor Dynamic ◽  
Better Than

Wall shear stress results from stationary-rotor flow tests of five annular gas seals are used to develop entrance and exit region friction factor models. The friction factor models are used in a bulk-flow seal analysis which predicts leakage and rotor-dynamic coefficients. The predictions of the analysis are compared to experimental results and to the predictions of Nelson’s analysis (1985). The comparisons are for smooth-rotor seals with smooth and honeycomb-stators. The present analysis predicts the destabilizing cross-coupled stiffness of a seal better than Nelson’s analysis. Both analyses predict direct damping well and direct stiffness poorly.

Test Results for Liquid “Damper” Seals Using a Round-Hole Roughness Pattern for the Stators

1999 ◽  
Vol 121 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Dara W. Childs ◽  
Patrice Fayolle
Keyword(s):  
Friction Factor ◽  
Round Hole ◽  
Test Results ◽  
Partial Explanation ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Friction Factors ◽  
Direct Stiffness ◽  
Factor Data ◽  
Pressure Driven Flow

Test results are reviewed for two annular liquid seals (L = 34.9 mm; D = 76.5 mm) at two clearances (.1 and .12 mm). The seal stators use hole-pattern-roughened stators that are identical except for hole depths of .28 and 2.0 mm. Tests are conducted at three speeds out to 24,600 rpm and three pressures out to 68 bars. Test data consist of leakage rates and rotordynamic coefficients at centered and eccentric positions with static eccentricity ratios out to 0.5. Test results are consistent with expectations in regard to the reduction of cross-coupled stiffness coefficients due to stator roughness. However, the measured direct stiffness coefficients were unexpectedly low. A partial explanation for these results is provided by measured friction factor data which show an increase in the friction factors for pressure-driven flow with an increase in clearance. A prediction model for rotordynamic coefficients, incorporating the friction-factor data, predicted a substantial loss in direct stiffness but could not explain the very low (or negative) values that were measured. The model did explain the measured drop in cross coupled stiffness (k) and provides an alternative explanation to observed reductions in k values; specifically, an increase in the friction factor with increasing clearance causes a reduction in k irrespective of any parallel reduction in the average circumferential velocity.

scholarly journals Dynamic Characteristics and Stability Prediction of Steam Turbine Rotor Based on Mesh Deformation

2020 ◽  
Vol 66 (3) ◽  
pp. 164-174
Author(s):  
Heyong Si ◽  
Lihua Cao ◽  
Pan Li
Keyword(s):  
Dynamic Characteristics ◽  
Rotational Velocity ◽  
Pressure Ratio ◽  
Cross Coupling ◽  
Steam Flow ◽  
Mesh Deformation ◽  
Dynamic Coefficients ◽  
Excited Vibration ◽  
Direct Stiffness ◽  
Rotor Dynamic

In order to study the steam flow excited vibration caused by the eccentricity of a rotor, three-dimensional rotor whirl motion is simulated based on mesh deformation. The mechanism of steam flow excited vibration and its influence on the dynamic characteristics of the rotor are investigated. The results show that the exciting forces change with the displacement of the rotor’s centre. Rotor dynamic coefficients are nonlinear when the rotor whirls pass the mesh deformation. The rotor dynamic coefficients and effective damping increase with the increase of whirl frequency. When the whirl frequency is 24.41 Hz, the rotor dynamic coefficients are strongly affected by rotational velocity. The maximum fluctuations of average direct stiffness, cross-coupling stiffness, direct damping and cross-coupling damping are 8.1 %, 113.2 %, 45.8 %, and 121.0 %, respectively. Effective damping fluctuates greatly when both whirl and rotational frequency are 24.41 Hz. The direct stiffness, direct damping, and effective damping increase with the increase of pressure ratio, which can improve rotor stability. The pressure fluctuation on the rotor’s surface is a primary reason for steam flow excited vibration. The stability margin of the rotor can be estimated precisely via effective damping.

scholarly journals Choosing Factors for the Vietnamese Stock Market

2021 ◽  
Vol 14 (3) ◽  
pp. 96
Author(s):  
Nina Ryan ◽  
Xinfeng Ruan ◽  
Jin E. Zhang ◽  
Jing A. Zhang
Keyword(s):  
Stock Returns ◽  
Factor Model ◽  
Five Factor Model ◽  
Explanatory Power ◽  
Factor Models ◽  
Marginal Contribution ◽  
Return On Equity ◽  
Factor Modeling ◽  
Three Factor ◽  
Better Than

In this paper, we test the applicability of different Fama–French (FF) factor models in Vietnam, we investigate the value factor redundancy and examine the choice of the profitability factor. Our empirical evidence shows that the FF five-factor model has more explanatory power than the FF three-factor model. The value factor remains important after the inclusion of profitability and investment factors. Operating profitability performs better than cash and return-on-equity (ROE) profitability as a proxy for the profitability factor in FF factor modeling. The value factor and operating profitability have the biggest marginal contribution to a maximum squared Sharpe ratio for the five-factor model factors, highlighting the value factor (HML) non-redundancy in describing stock returns in Vietnam.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

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.

An Experimental and Analytical Study of Single-Phase Liquid Flow in a Horizontal Well

1997 ◽  
Vol 119 (1) ◽  
pp. 20-25 ◽  
Author(s):  
H. Yuan ◽  
C. Sarica ◽  
S. Miska ◽  
J. P. Brill
Keyword(s):  
Experimental Data ◽  
Friction Factor ◽  
Horizontal Well ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Test Facility ◽  
Phase Liquid ◽  
Rate Ratios ◽  
Friction Factor Correlation ◽  
Better Than

A new test facility was designed and constructed to simulate flow in a horizontal well with a single perforation. A total of 635 tests were conducted with Reynolds numbers ranging from 5000 to 60,000 with influx to main rate ratios ranging from 1/5 to 1/100, and also for the no-influx case. The flow behavior in a single-perforation new friction expression for a single-perforation horizontal well was developed. A new simple correlation for the horizontal well friction factor was developed by applying experimental data to the general friction factor expression. The new friction factor correlation and experimental data were compared with the Asheim et al. (1992) data and model, and showed that the new correlation performed better than the Asheim et al. (1992) model.

The Equation of State and the Temperature, Pressure, and Shear Dependence of Viscosity for a Highly Viscous Reference Liquid, Dipentaerythritol Hexaisononanoate

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Scott Bair ◽  
Tsuyoshi Yamaguchi
Keyword(s):  
Molecular Weight ◽  
Shear Stress ◽  
Equation Of State ◽  
High Molecular Weight ◽  
Free Volume ◽  
Newtonian Limit ◽  
Scaling Models ◽  
The Difference ◽  
Better Than ◽  
Low Shear

Measurements are reported for dipentaerythritol hexaisononanoate (DiPEiC9) of pressure–volume–temperature (pVT) response to pressures to 400 MPa and temperatures to 100 °C, and of viscosity at pressures to 700 MPa and temperatures to 90 °C and shear stress to 18 MPa. These data complement the low-shear viscosities published by Harris to pressures to 200 MPa and the compressions by Fandiño et al. to 70 MPa. The improved Yasutomi correlation reproduces all viscosity measurements with accuracy better than the Doolittle free volume and the Bair and Casalini thermodynamic scaling models which require an equation of state (EoS). The interaction parameter for thermodynamic scaling, γ = 3.6, is less than that reported by Harris (γ = 4.2) and the difference is primarily in the choice of EoS. The shear stress at the Newtonian limit, about 6 MPa, is exceptionally large given the high molecular weight of DiPEiC9. The large Newtonian limit is also seen in the oscillatory shear response.

A Review of Explicit Friction Factor Equations

1985 ◽  
Vol 107 (2) ◽  
pp. 280-283 ◽  
Author(s):  
D. J. Zigrang ◽  
N. D. Sylvester
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Explicit Equation ◽  
Flow Friction ◽  
Friction Factors ◽  
High Degree ◽  
Very High

A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

Friction factor analysis for a nanofluid circulating in a microchannel filled with a homogeneous porous medium

2022 ◽  
Author(s):  
Francisco Fernando Hernandez ◽  
Federico Mendez ◽  
Jose Joaquin Lizardi ◽  
Ian Guillermo Monsivais
Keyword(s):  
Porous Medium ◽  
Friction Factor ◽  
Porous Matrix ◽  
Velocity Profiles ◽  
Momentum Equation ◽  
Volumetric Concentration ◽  
Forchheimer Equation ◽  
Viscosity Models ◽  
Friction Factors ◽  
Homogeneous Porous Medium

Abstract This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.

scholarly journals Impact of Modified Spacer on Flow Pattern in Narrow Spacer-Filled Channels for Spiral-Wound Membrane Modules

Environments ◽  
2018 ◽  
Vol 5 (11) ◽  
pp. 116
Author(s):  
Zhiming Han ◽  
Mitsuharu Terashima ◽  
Bing Liu ◽  
Hidenari Yasui
Keyword(s):  
Shear Stress ◽  
Flow Pattern ◽  
Friction Factor ◽  
Flow Direction ◽  
Dead Zone ◽  
Three Dimensional ◽  
Stress Contour ◽  
Directional Change ◽  
Low Shear Stress ◽  
Membrane Modules

A modified spacer, which was constructed with arched filaments and zigzag filaments, was designed to improve vortex shedding and generate a directional change in flow patterns of membrane modules, especially in the vicinity of the feed spacer filament, which is most affected by fouling. A unit cell was investigated by using a three-dimensional computational fluid dynamics (CFD) model for hydrodynamic simulation. The results of CFD simulations were carried out for the fluid flow in order to understand the effect of the modified spacer on vortices to the performance of arched filaments at different distances. From 2D velocity vectors and shear stress contour mixing, the flow pattern and dead zone flushing were depicted. The ratio of low shear stress area to the total area increased with the inlet velocity closed to 20%. The energy consumption with respect to flow direction for the arched filament was 80% lower than that in the zigzag filament. Compared with previous commercial spacers’ simulation, the friction factor was lower when the main flow was normal to the arched filament and the modified friction factor was close to the commercial spacers. The homogenization was realized through the flow pattern created by the modified spacer.

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