The simulation and control of the severe slugging flow in the subsea multiphase pipeline is the focus of research in the production and exploitation of oil companies. Severe slug flow results in severe fluctuations of pressure and flow rate at both the wells end and the receiving host processing facilities, causing safety and shutdown risks. To prevent the severe slugging flow regime in multiphase transport pipelines, an Ordinary Differential Equation (ODE) model is established by using the mass conservation law for individual phases in the pipeline and the riser sections. Then, the proposed model is compared to the results from the OLGA simulation. A comparative study of different slugging flow control solutions is conducted. Unscented Kalman Filter (UKF), Wavelet Neural Network (WNN) and UKF&WNN are used for state estimation and combined with PI controller. The UKF and WNN are good nonlinear filters. However, when the nominal choke opening is increased, they work unsatisfying. The UKF&WNN observer shows slightly better results than UKF and WNN when the system has high input disturbance.

Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system. Oil-lubricated bearings are widely used in high speed rotating machines. However, environmental issues and risk-averse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water decreases film thickness significantly. Crowning and tapers are two main ways to maintain the film thickness requirements in water lubrication, but no studies about the influence of these parameters on the film thickness in water-lubricated bearings have been reported. Therefore, further understanding of the performance associated with optimizing the bearing design with different weighted performance and their relationships to bearing design variables could be invaluable to bearing design engineers. This study explores the impact of three crowning and taper design variables on the performance of one tilting pad thrust bearing using the design of experiments techniques applied to a thermoelastohydrodynamic (TEHD) bearing model. The bearing design variables analyzed in this study include the radius of the ground-in crown, taper circumferential angle offset, and the vertical taper distance at the inner and outer radii. Each of the design variables is first varied over five levels, each in central composite design. The outputs from the TEHD numerical simulations used as performance measures for each bearing design point were the minimum film thickness, the film thickness at the pivot location, maximum film pressure and power loss. Multi-objective optimization was performed. A range of weighting parameters was selected for the optimization function to find a bearing design that maintains the minimum film thickness criterion while minimizing power loss. The resulting optimum design points allowed for a comparison between the design optimization at different weightings. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearing for a wide range of applications.

A thrust bearing is a particular type of rotary bearing permitting rotation between parts but designed to support a predominately axial load. Part I of this study was submitted to ASME 5th Joint US-European Fluids Engineering Summer Meeting. It compared the experimental, TEHD and CFD results for a thrust bearing. Reasonable relative errors between these three results were observed. The outlet oil film thickness at low speeds and the inlet oil film thickness at high speeds as calculated using TEHD were found to be more accurate than their counterparts. Isothermal, non-deforming CFD was found to predict outlet film thickness accurately as thermal deformation has a lower impact in the outlet region. Isothermal and non-deforming CFD was also found to produce a qualitatively accurate film thickness and pressure distribution. Experimental data from a second paper reported by the same authors in Part I, provides temperature measurements in two different pads and showed some variation of temperature from pad to pad. A thermal CFD, different from isothermal CFD in Part I, was performed in this Part II. Different data analysis methods will be included in Part II including a comparison of leading edge, mid-plane and trailing edge temperature at two loads, two speeds. 24 different speed-load combination TEHD cases and 12 CFD cases were run in Part II in addition to the 32 TEHD cases and 8 CFD cases in Part I. Both TEHD and CFD underpredict the slope between temperature and shaft speeds. TEHD also underpredicts the slope between temperature and bearing loads while CFD can get an accurate slope between temperature and bearing loads. An improved inlet temperature model would fix the error between temperature and bearing load in CFD, and also can enable CFD to have the same accuracy as TEHD analysis for the temperature versus shaft speed relation. The inlet film thickness from both TEHD and CFD is underestimated. TEHD is more accurate than CFD in outlet film thickness, or minimum film thickness, which is a critical performance characteristic in fluid film thrust bearings. While CFD is more accurate than TEHD in inlet film thickness and power loss.

Bearings are machine elements that allow components to move with respect to each other. A thrust bearing is a particular type of rotary bearing permitting rotation between parts but designed to support a predominately axial load. Oil-lubricated bearings are widely used in high speed rotating machines such as those found in the aerospace and automotive industries. With the increase of velocity, the lubrication regime will go through boundary lubrication, mixed lubrication, and hydrodynamic lubrication (full film). In this paper, the analysis was in the hydrodynamic lubrication region. THRUST is used to predict the steady-state operating characteristics of oil-lubricated thrust bearings. As a thermoelastohydrodynamic prediction tool, THRUST assumes a 3D turbulence model, 3D energy equation, and 2D Reynolds equation. Turbulence is included by obtaining average values of eddy momentum flux (Reynolds stress) and averaging the influence down to a 2D Reynolds equation. Convergence is achieved by iterating on the pad tilt angles and pivot film thickness until the integrated pressure matches the load applied to the pad. Despite the multiple experimental, CFD, and TEHD studies of thrust bearings that have been performed to date, no validation has yet been performed to confirm the accuracy of TEHD methods in modeling the performance of thrust bearings by both experimental and advanced computational means simultaneously. This study addresses this need by comparing TEHD and CFD simulation results of film thickness, temperature, power loss, and pressure in thrust bearings taken from the literature at multiple speeds and loads with results from experimental data. Starting from the case of the lowest speed and load, it was verified that this case is indeed laminar and with negligible thermal and elastic effects. Four cases were run in THRUST, a TEHD solver, combining thermal and deformation in each rotational speed and load combination. Additionally, a CFD study was performed in ANSYS CFX with the assumptions of isothermal, non-deforming. The average viscosity from THRUST was used in CFD to follow the effects of the isoviscous assumption. Then, the experimental, TEHD and CFD results were compared at each case. Experimental, TEHD, and CFD results show acceptable agreement when turbulence is negligible.

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], ε m /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.

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.

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries. However, with some applications including underwater machinery and environmentally friendly applications, water lubricated bearings have become increasingly used. Due to the different fluid properties between oil and water — namely viscosity — the use of water increases the Reynolds numbers drastically and, therefore, makes water-lubricated bearings prone to turbulence and fluid inertia effects. In other words, the linear approximation of the fluid film reaction forces due to the stiffness and damping parameters — as suggested in the traditional Reynolds equation — is not adequate and should be amended to include lubricant added mass. This is because water-lubricated bearings exhibit large lubricant inertia forces on the order of viscous forces. Additionally, stiffness and damping coefficients should be calculated with the turbulence effects included. The aim of this study was to investigate the methodology of modifying the traditional Reynolds equation to include lubricant inertia effects. This paper reviews the current status of research in the lubricant inertia of bearings and explores the development of methodologies to modify the Reynolds equation to include lubricant inertia in bearings. The Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films in lubrication theory. The thin film hypothesis is used to directly relate the bearing film thickness to the lubricant film pressure. Adding lubricant inertia to the Reynolds equation is vital to improving the accuracy of the bearing model and more specifically its film pressure which is essential to predicting load carrying capabilities. The film pressure relates the gradient of the velocity tensor through the Reynolds equation, and resulting shear stresses then allow the turbulent momentum equations to be written in terms of an eddy-viscosity value. An extended Reynolds equation should be developed which takes into account turbulence and both convective and temporal inertia. The most complete form of the temporal inertia effect model should be developed and applied to the turbulent regime, consisting of both primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu’s approach. This analysis develops a lubricant inertia model applicable to water-lubricated bearings. The results of this study could aid in improving future designs and models of water-lubricated bearings.