Modeling Reichardt's Formula for Eddy Viscosity in the Fluid Film of Tilting Pad Thrust Bearings

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Xin Deng ◽  
Brian Weaver ◽  
Cori Watson ◽  
Michael Branagan ◽  
Houston Wood ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulence Model ◽  
High Speed ◽  
Eddy Viscosity ◽  
The Other ◽  
Fluid Film ◽  
Suitable Model ◽  
Velocity Gradients ◽  
Wall Shear

Oil-lubricated bearings are widely used in high-speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water-lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy viscosity, while eddy viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high-speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy viscosity for turbulence modeling. Eddy viscosity together with flow viscosity forms the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model's ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt's formula were used to model eddy viscosity in the fluid film. These methods are for determining where one wall's effects begin and the other wall's effects end. Trying to find a suitable model to capture the wall's effects of these bearings, with an aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil- and water-lubricated bearings.

Modeling Reichardt’s Formula for Eddy-Viscosity in the Fluid Film of Tilting Pad Thrust Bearings

2017 ◽  
Author(s):  
Xin Deng ◽  
Brian Weaver ◽  
Cori Watson ◽  
Michael Branagan ◽  
Houston Wood ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulence Model ◽  
High Speed ◽  
Eddy Viscosity ◽  
The Other ◽  
Fluid Film ◽  
Suitable Model ◽  
Velocity Gradients ◽  
Wall Shear

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy-viscosity, while eddy-viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy-viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy-viscosity for turbulence modeling. Eddy-viscosity together with flow viscosity form the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model’s ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt’s formula were used to model eddy-viscosity in the fluid film. These methods are for determining where one wall’s effects begin and the other wall’s effects end. Trying to find a suitable model to capture the wall’s effects of these bearings, with aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil and water lubricated bearings.

scholarly journals Impinging jets array: an experimental investigation and numerical modeling

2019 ◽  
Vol 85 ◽  
pp. 05004
Author(s):  
Nilesh Dhondoo ◽  
Ştefan-Mugur Simionescu ◽  
Corneliu Bălan
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Stagnation Point ◽  
High Speed ◽  
Jet Impingement ◽  
Impinging Jets ◽  
Stagnation Region ◽  
Jet Mixing ◽  
Point Pressure ◽  
Wall Shear

This paper reports on the measurements of wall shear stress and static pressure along a smooth static wall upon which jet impingement occurs. The effect of a single circular jet, respectively an array of jets is studied using a high speed/resolution camera. The areas of interest are the stagnation region and the wall jet region, where the jet is deflected from axial to radial direction. The effect of increasing the distance between the inlets is also investigated. The results are obtained by performing direct flow experimental visualizations and CFD numerical simulations, using the Reynolds averaged Navier-Stokes (RANS) approach with the commercial software ANSYS Fluent. The findings suggest that the smaller the nozzle-to-wall distance is, the higher the pressure peak. The wall shear stress has a bimodal distribution; at stagnation point, the wall shear stress is 0. An increase in the number of inlets produces the effect of a decrease in the stagnation point pressure. The greater the inter-inlet distance is, the greater the stagnation point pressure (there is less inter-jet mixing, less energy is lost in vortices formed between jets).

Comparison in High-Speed Droplet Impact Between Single and Multiple Collisions Against a Wall Covered With a Liquid Film

2019 ◽  
Author(s):  
Yoichiro Fukuchi ◽  
Tomoki Kondo ◽  
Keita Ando
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
High Speed ◽  
Water Layer ◽  
Liquid Jet ◽  
Surface Erosion ◽  
Single Droplet ◽  
Cleaning Efficiency ◽  
Droplet Impingement ◽  
Wall Shear

Abstract In semiconductor industry, liquid jet cleaning plays an important role because of its high cleaning efficiency and low environmental load. However, its cleaning mechanism is not revealed in detail because the experimental observation of high-speed and sub-micron droplets is challenging. Furthermore, higher impact velocity may give rise to surface erosion due to water-hammer shock loading from the impingement. To study cleaning mechanisms and surface erosion, numerical simulation of droplet impingement accounting for both viscosity and compressibility is an effective approach. In the previous study, wall-shear-flow generation has evaluated from the simulation of high-speed single droplet impingement. To evaluate more practical model of jet cleaning application, simulation of two droplets simplifying mono-dispersed splay of droplet train is favorable. Here, we numerically simulated impingement of two droplets, which allows for evaluating water-hammer pressure and wall shear stress. We consider the case of two water droplets (200 μm in diameter) that collides continuously, at speed 50 m/s, at the inter-droplet distance from 250 to 400 μm, with a no-slip rigid wall covered with a water layer (100 μm in thickness). The simulation is based on compressible Navier-Stokes equations for axisymmetric flow and the mixture of two components appears in numerically diffusion interface expressed by the volume average and advection equation. The simulation is solved by finite-volume WENO scheme that can capture both shock waves and material interface. In our simulation, the impingement of second droplet impingement gain higher shear stress than the single droplet impingement. At the case that the inter-droplet distance is 300 μm, maximum shear stress is 30.22 kPa (at the second droplet impingement), which is much larger than at the first droplet impingement (8.42 kPa). This result indicates how the second droplet impingement make wall shear flow induced by first droplet impingement stronger. From the parameter study of the inter-droplet distance, we can say that wall shear stress gets stronger as water layer thickness decreases. Furthermore, the maximum wall pressure is 1.96 MPa at the second droplet impingement, which is larger than at the first droplet impingement (1.46 MPa). From this study, the evaluation of surface erosion caused by jet cleaning is expected. The simulation suggests that multiple droplets impingement continuously may gain higher cleaning efficiency, which will give us a fundamental insight into liquid jet cleaning technologies. For further study, simulation of water column impingement and comparing the result of impingement of two droplets are expected.

Computational fluid dynamics simulations of cerebral aneurysm using Newtonian, power-law and quasi-mechanistic blood viscosity models

2020 ◽  
Vol 234 (7) ◽  
pp. 711-719 ◽  
Author(s):  
Khalid M Saqr
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Power Law ◽  
The Other ◽  
Lower Wall ◽  
Computational Fluid Dynamics Simulations ◽  
Wall Shear ◽  
Dynamics Simulations

Cerebral aneurysm is a fatal neurovascular disorder. Computational fluid dynamics simulation of aneurysm haemodynamics is one of the most important research tools which provide increasing potential for clinical applications. However, computational fluid dynamics modelling of such delicate neurovascular disorder involves physical complexities that cannot be easily simplified. Recently, it was shown that the Newtonian simplification used to close the shear stress tensor of the Navier–Stokes equation is not sufficient to explore aneurysm haemodynamics. This article explores the differences between the latter simplification, non-Newtonian power-law model and a newly proposed quasi-mechanistic model. The modified Krieger model, which treats blood as a suspension of plasma and particles, was implemented in computational fluid dynamics context here for the first time and is made available to the readers in a C# code in the supplementary material of this article. Two middle-cerebral artery and two anterior-communicating artery aneurysms, all ruptured, were utilized here as case studies. It was shown that the modified Krieger model had higher sensitivity for wall shear stress calculations in comparison with the other two models. The modified Krieger model yielded lower wall shear stress values consistently in comparison with the other two models. Moreover, the modified Krieger model has generally predicted higher pressure in the aneurysm models. Based on published aneurysm rupture studies, it is believed that ruptured aneurysms are usually correlated with lower wall shear stress values than unruptured ones. Therefore, this work concludes that the modified Krieger model is a potential candidate for providing better clinical relevance to aneurysm computational fluid dynamics simulations.

scholarly journals Wall shear stress from jetting cavitation bubbles

2018 ◽  
Vol 846 ◽  
pp. 341-355 ◽  
Author(s):  
Qingyun Zeng ◽  
Silvestre Roberto Gonzalez-Avila ◽  
Rory Dijkink ◽  
Phoevos Koukouvinis ◽  
Manolis Gavaises ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
High Speed ◽  
Temporal Distribution ◽  
Surface Cleaning ◽  
Shear Stresses ◽  
Rigid Boundary ◽  
Equivalent Radius ◽  
Wall Shear

The collapse of a cavitation bubble near a rigid boundary induces a high-speed transient jet accelerating liquid onto the boundary. The shear flow produced by this event has many applications, examples of which are surface cleaning, cell membrane poration and enhanced cooling. Yet the magnitude and spatio-temporal distribution of the wall shear stress are not well understood, neither experimentally nor by simulations. Here we solve the flow in the boundary layer using an axisymmetric compressible volume-of-fluid solver from the OpenFOAM framework and discuss the resulting wall shear stress generated for a non-dimensional distance, $\unicode[STIX]{x1D6FE}=1.0$ ($\unicode[STIX]{x1D6FE}=h/R_{max}$, where $h$ is the distance of the initial bubble centre to the boundary, and $R_{max}$ is the maximum spherical equivalent radius of the bubble). The calculation of the wall shear stress is found to be reliable once the flow region with constant shear rate in the boundary layer is determined. Very high wall shear stresses of 100 kPa are found during the early spreading of the jet, followed by complex flows composed of annular stagnation rings and secondary vortices. Although the simulated bubble dynamics agrees very well with experiments, we obtain only qualitative agreement with experiments due to inherent experimental challenges.

Turbulence Input Parameters Correction Methodology in Water Lubricated Thrust Bearings

2018 ◽  
Author(s):  
Xin Deng ◽  
Harrison Gates ◽  
Brian Weaver ◽  
Houston Wood ◽  
Roger Fittro
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Film Thickness ◽  
Turbulence Model ◽  
Thermal Deformation ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Water Lubrication ◽  
Low Viscosity ◽  
Eddy Viscosity Model

Oil-lubricated bearings are widely used in high speed rotating machines such as those found in the aerospace and automotive industries. However, environmental issues and risk-averse operations are resulting in the removal of oil and the replacement of all sealed oil bearings with reliable water-lubricated bearings. Due to the different fluid properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. This requires finer meshes when compared to oil-lubricated bearings as the low-viscosity fluid produces a very thin lubricant film. Analyzing water-lubricated bearings can also produce convergence and accuracy issues in traditional oil-based analysis codes. Thermal deformation largely affects oil-lubricated bearings, while having limited effects on water lubrication; mechanical deformation largely affects water lubrication, while its effects are typically lower than thermal deformation with oil. One common turbulence model used in these analysis tools is the eddy-viscosity model. Eddy-viscosity depends on the wall shear stress, therefore effective wall shear stress modeling is necessary in determining an appropriate turbulence model. Improving the accuracy and efficiency of modeling approaches for eddy-viscosity in turbulence models is of great importance. Therefore, the purpose of this study is to perform mesh refinement for water-lubricated bearings based on methodologies of eddy-viscosity modeling to improve their accuracy. According to Szeri [1], εm/v for the Boussinesq hypothesis is given by Reichardt’s formula. Fitting the velocity profile with experiments having a y+ in the range of 0–1,000 results in Ng-optimized Reichardt’s constants k = 0.4 and δ+ = 10.7. He clearly states that for y+ > 1000 theoretical predictions and experiments have a greater variance. Armentrout and others [2] developed an equation for δ+ as a function of the pivot Reynolds number, which they validated with CFD simulations. The definition of y+ can be used to approximate the first layer thickness calculated for a uniform mesh. Together with Armentrout’s equation, the number of required elements across the film thickness can be obtained. For typical turbulence models, the y+ must be within a certain range to be accurate. On the condition that the y+ is fixed to that of a standard oil bearing for which an oil bearing code was validated, the number of elements across the film thickness and coefficients used in the eddy-viscosity equation can be adjusted to allow for convergence with other fluids other than that which the traditional oil bearing code was designed for. In this study, the number of required elements across the film for improved prediction quality was calculated based on the proposed eddy-viscosity model mesh correction from the known literature. A comparison between water lubrication using the parameter correction and oil lubrication was also made. The results of this study could aid in improving future designs and models of water-lubricated bearings.

scholarly journals An In Vitro Comparative Study of Intracanal Fluid Motion and Wall Shear Stress Induced by Ultrasonic and Polymer Rotary Finishing Files in a Simulated Root Canal Model

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Jon Koch ◽  
John Borg ◽  
Abby Mattson ◽  
Kris Olsen ◽  
James Bahcall
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Root Canal ◽  
High Speed ◽  
Fluid Shear Stress ◽  
Distilled Water ◽  
Axial Motion ◽  
Fluid Shear ◽  
Wall Shear

Objective. This in vitro study compared the flow pattern and shear stress of an irrigant induced by ultrasonic and polymer rotary finishing file activation in an acrylic root canal model. Flow visualization analysis was performed using an acrylic canal filled with a mixture of distilled water and rheoscopic fluid. The ultrasonic and polymer rotary finishing file were separately tested in the canal and activated in a static position and in a cyclical axial motion (up and down). Particle movement in the fluid was captured using a high-speed digital camera and DaVis 7.1 software. The fluid shear stress analysis was performed using hot film anemometry. A hot-wire was placed in an acrylic root canal and the canal was filled with distilled water. The ultrasonic and polymer rotary finishing files were separately tested in a static position and in a cyclical axial motion. Positive needle irrigation was also tested separately for fluid shear stress. The induced wall shear stress was measured using LabVIEW 8.0 software.

The Effect of Disturbed Turbulence Structure on the Preston-Tube Method of Measuring Wall Shear Stress

1981 ◽  
Vol 32 (4) ◽  
pp. 354-367 ◽  
Author(s):  
S. Kiske ◽  
V. Vasanta Ram ◽  
K. Pfarr
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Abrupt Change ◽  
The Other ◽  
Turbulence Structure ◽  
Wall Roughness ◽  
Boundary Layer Flows ◽  
The Subject ◽  
Wall Shear

SummaryThe subject of this paper is the effect of a disturbance to the turbulence structure of the flow on the reading of a Preston tube used to measure wall shear stress. Two kinds of disturbance have been studied experimentally, one caused by reattachment and the other by an abrupt change in wall roughness. The apparent wall shear stress measured by the Preston tube both in channel and boundary layer flows with these kinds of disturbance has been compared with the wall shear stress measured by a sublayer fence. The results give an idea of the magnitude of the error that is likely to arise when the Preston tube is used in a flow with disturbed turbulence structure.

scholarly journals Movement of gas slug in annular channels with different diameter ratios

2021 ◽  
Vol 2119 (1) ◽  
pp. 012060
Author(s):  
O.N. Kashinsky ◽  
A.S. Kurdumov
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
High Speed ◽  
Capillary Tube ◽  
Tube Diameter ◽  
Outer Tube ◽  
Rise Velocity ◽  
Stress Measurements ◽  
Annular Channels ◽  
Wall Shear

Abstract The motion of gas slugs in annular channels was studied experimentally. The outer tube diameter was 32 mm. The inner tube diameter varied from 4 to 25 mm. The gas slugs were produced by injecting air through a capillary tube. The shapes of gas slugs were studied by high-speed videos. The paper presents data on the rise velocity of gas slugs in the channels, and wall shear stress measurements, performed by electrodiffusional technique. The probes were mounted on both walls of the channel. The evolution of wall shear stress during slug passage was recorded.

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