Hydrodynamic Pressure Distribution Research Articles

Seismic behavior of partially filled liquid tank with sloped walls

Abstract The seismic characteristics of liquid sloshing in partially filled sloped bottom tank are investigated numerically. Six different ground motions classified on the basis of low, intermediate and high frequency contents are selected to determine the dynamic characteristics of liquid in sloped bottom tanks. The effect of different slope angle on the frequency contents of earthquakes are investigated. The liquid domain is discretized as the combination of three node triangular and four node quadrilateral finite elements. The individual contribution of impulsive and convective response components of hydrodynamic behavior in terms of base shear force and hydrodynamic pressure distribution along the walls of the containers are successfully measured. The efficacy of the developed numerical model is validated with the existing published results.

Squeeze film dampers supporting high-speed rotors: Fluid inertia effects

This work represents closed-form analytical expressions for the operating parameters for short-length open-ended squeeze film dampers, including the lubricant velocity profiles, hydrodynamic pressure distribution, and lubricant reaction forces. The proposed closed-form expressions provide an accelerated calculation of the squeeze film damper parameters, specifically for rotordynamics applications. In order to determine the analytical solutions for the squeeze film damper parameters, the thin film equations for lubricant are introduced in the presence of the influence of lubricant inertia. Subsequently, two different analytical techniques, namely the momentum approximation method, and the perturbation method are applied to the thin film equations. Moreover, the solution for the lubricant flow equations are analytically determined to represent closed-form expressions for the hydrodynamic pressure distribution and the velocity component profiles in squeeze film dampers. Additionally, the expressions for the hydrodynamic pressure distribution are integrated over the journal surface, either numerically or analytically by using Booker’s integrals, to develop expressions for the fluid film reaction forces. Lastly, the developed squeeze film damper models are incorporated into simulation models in Matlab and Simulink®, and the results are compared against a well-established force coefficient model to verify the accuracy of the calculations. The results of the simulations verify the effect of the lubricant inertia components, namely the convective and temporal (i.e., unsteady) inertia components on the squeeze film damper dynamics, including hydrodynamic pressure distribution and fluid film reaction forces. Additionally, the simulation results suggest a close agreement between the proposed models and the results in the literature.

Analysis of non-Newtonian lubricated textured contact for mixed slip/no-slip configuration considering cavitation

The increasing use of non-Newtonian fluids as lubricants has received much attention due to their high shear. The present study explores a lubrication mechanism in lubricated textured contact for mixed slip/no-slip pattern considering cavitation. The effect of texturing depth on the bearing performance is also investigated. The numerical method based on commercial CFD (computational fluid dynamic) software is carried out to analyze the tribological characteristics (i.e., hydrodynamic pressure distribution) of lubricated textured contact. To model slip, the enhanced user-defined-function (UDF) in the FLUENT® package is developed. The analysis results show that giving textures as well as a slip to one of the parallel sliding surfaces can generate significant hydrodynamic pressure to affect the load support. The increase in the load support is also indicated by increasing the streamline recirculating flow. Besides, numerical results suggest that cavitation modeling has a significant effect on performance. Ignoring cavitation leads to less accurate results.

AN ANALYSIS OF HYDRODYNAMIC PRESSURE DISTRIBUTION AND LOAD CARRYING CAPACITY OF A CONICAL SLIDE BEARING LUBRICATED WITH NON -NEWTONIAN SECOND GRADE FLUI

In this paper, the authors present the equations of the hydrodynamic lubrication theory for conical slide bearings lubricated with the oil with properties described by the Rivlin-Ericksen model. It is assumed, that the considered lubricating oil shows non-Newtonian properties, i.e. it is an oil for which, apart from the classic dependence of oil viscosity on pressure, temperature and operating time, there is also a change in dynamic viscosity values caused by the changes of shear rate. The method of a small parameter was used to solve the conservation of momentum, stream continuity, and energy conservation equations. The small parameter method consists in presenting the sought functions (pressure, temperature, components of the velocity vector) in the form of a uniformly convergent series expansion in powers of a constant small parameter. These functions are substituted into the system of basic equations, and then the series are multiplied by the Cauchy method. By a comparison of the coefficients with the same powers of a small parameter, we obtain systems of partial differential equations, from which the subsequent approximations of unknowns of the sought functions are determined. The small parameter method separates the non-linear system of partial differential equations and creates several linear systems of equations. The aim of this work is to derive the equations describing and allowing the determination of the temperature distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction force and friction coefficient in the gap of conical slide bearing, lubricated with the oil of the properties described by the Rivlin-Ericksen model, taking into account its viscosity changes due to time of operation.

Necessary parameter setting of the finite‐difference method for determining selected rotor‐dynamics characteristics

AbstractThe aim of the study is to analyse the adequacy of the finite difference‐method (FDM) for determining the stability boundary of a rigid rotor mounted on short hydrodynamic plain journal bearings through the solution of the Reynolds partial differential equation (PDE). The Reynolds equation, obtained by coupling the equation of motion with the continuity equation, governs the pressure distribution in a lubricant film. The quasi stationary form of this equation requires normalization prior to solving, for the numerical error of the FDM to be minimized. Except for numerical benefits, the dimensionless form of the PDE is universally applicable to a bride spectrum of tribological problems, including hydrodynamic plain journal bearings. The present study first examines the adequacy of solver settings, including the computational grid, through comparison of the corresponding numerical results with an analytical solution obtained by means of the Short Bearing Theory (SBT). Two characteristic tribological quantities are selected as the basis for comparison: the modified Sommerfeld number and the bearing attitude angle. Further, dimensionless stiffness and damping tensors, valid for any short hydrodynamic plain journal bearing, are determined from the numerically obtained distribution of the dimensionless hydrodynamic pressure. These two dimensionless tensors allow for the subsequent estimation of the stability boundary, which marks the dimensionless speed at which a given rigid rotor becomes dynamically unstable. The results of the current study demonstrate sensitivity of the FDM results to the numerical step size. The corresponding numerical error is verified using the SBT and presented as function of the dimensionless (relative) journal eccentricity together with rotor start‐up curves. As a major finding, a dimensionless range of the step size is identified for the error to remain below 5%.

Numerical simulation of partially filled liquid containers with special type bottom geometry under earthquake excitation

Numerical simulation of liquid in partially filled tank of flat bottom and bottom box shape is investigated in the present paper. Previously, dynamic response of flat bottom tank has been carried out numerously, but the dynamic response of bottom box tank remains unclear. Therefor a parametric study on bottom box shape tank is carried out to understand the dynamic response of contained liquid under both harmonic excitation and real earthquake excitation. The efficacy of the present numerical model is verified by comparing the results with the published results. Galerkin’s finite element method is used to derive the modal equations of motion for sloshing. The slosh wave displacement, hydrodynamic pressure distribution and the base shear, are quantified for the bottom box shape tank. According to the dynamic analysis results larger size of bottom box significantly reduces the effective mass of liquid which keeps the container on safer side than the flat bottom container.

Study on Modal Dynamic Response and Hydrodynamic Added Mass of Water‐Surrounded Hollow Bridge Pier with Pile Foundation

This article presents an experiment program conducted to study the modal dynamic response of hollow bridge pier with pile foundation submerged in water. The forced vibration method was applied on a specimen designated with four levels of tip mass; and the dynamic characteristics of the first four lateral vibration modes of the specimen, including the first two modes along the x‐axis and the first two modes along the y‐axis, were tested for three different cases where the specimen contacts with only outer water, only inner water, and both outer and inner water, respectively. Finite element models were established using potential‐based fluid elements in accordance with the three different cases. The effects of fluid‐structure interaction on the dynamic characteristics of the first four lateral modes of the specimen were then investigated through numerical simulations, and the finite element models were verified by validating numerical results against the experimental data. Based on the verified models, hydrodynamic added mass (HAM) and modal hydrodynamic added mass (MHAM) along the x‐axis and y‐axis of the specimen, induced by fluid‐structure interaction, were studied with respect to the three cases. According to the distribution of modal acceleration and hydrodynamic pressure along the pier body, hydrodynamic added mass (HAM) distribution along the pier body was analyzed, and a simplified analytical model which equals the original fluid‐structure numerical model was proposed to determine the dynamic characteristics of hollow bridge piers submerged in water. The research provides a better understanding of the effect of fluid‐structure interaction on the modal dynamic response of deep‐water bridges with hollow piers.

An investigation of water-flow pressure distribution on bridge piers under flood loading

This study simulates the flood effect on piers using a finite volume method in the ANSYS-FLUENT package. The pier is modelled as a non-structural column with a rectangular and a circular cross-section. To simplify the methodology, the pier, as well as the bed and side walls, is assumed to have non-slip boundaries for the fluid domain. A crucial feature of this investigation is the consideration of the effect of water while it is flowing around an object like a bridge pier and the distribution of pressure along the pier height. A numerical model is proposed to explore the influence of variation of velocity on the hydrodynamic force and pressure distribution exerted on piers. A significant finding is that the shape of the pier cross-section has a significant effect on the fluid pressure exerted on bridge piers under flood loading. It is noted that the AS5100 method is appropriate for a conservative estimation of the pressure on rectangular piers, whereas the technique will have a risky safety margin for bridge piers with a circular cross-section and need to be used with caution.

Effect of Crankshaft and Crankcase Material Stiffness on Load Distribution in Main Bearings

In multi-cylinder diesel engines, hydrodynamic pressure distribution of main bearings has significant effect on the load distribution applied on engine crankcase, therefore, has an effect on the stress distribution and deflection of crankcase. Flexibility of crankshaft and crankcase assembly has significant effect on load distribution in engine main bearings. In this paper, the effect of elastic deformations of both crankshaft and crankcase on the load distribution in the main bearings is studied. Considering deformations of crankcase and crankshaft together with the elasto-hydrodynamic (EHD) analysis of main bearing is vital to obtain the realistic load distribution and accurate main bearing performance. At the beginning, the results of flexible body dynamic analysis of engine crank train with considering EHD joint for main bearings are presented and the main bearing force and moment are compared with rigid body dynamic analysis. Then, the effects of crankshaft and crankcase flexibilities on main bearing force and moment are studied. Several models with different flexibilities and stiffness of crankcase and crankshaft were prepared using Elasto-hydrodynamic simulation of diesel engine main bearings. According to the results, the load distribution on the engine main bearings and consequently the bearing shell deformation are affected by crankcase and crankshaft elasticities. A fast and time-saving method to obtain reasonably accurate results is proposed in the present paper.

Analysis of misaligned water-lubricated polymer bearing with axial grooves

PurposeThe purpose of this paper is to analyze the lubrication behavior of misaligned water-lubricated polymer bearings with axial grooves.Design/methodology/approachA lubrication model considering journal misalignment, bush deformation and grooves is established. In dynamic analyses of shaft systems, bearings are usually simplified as supporting points. Thus, an approach for solving the equivalent supporting point location is presented. The influence of misalignment angle and groove number on film thickness, hydrodynamic pressure distribution, load-carrying capacity and ESP location is investigated.FindingsAs the misalignment angle increases, the location of the maximum pressure and ESP are shifted toward the down-warping end, and the load-carrying capacity of the bearing decreases. In comparison to the nine-groove bearing, the six grooves bearing has a higher load-carrying capacity and the ESP is located closer to the down-warping end for an equivalent misalignment angle.Practical implicationsThe results of this study can be applied to marine propeller shaft systems and other systems with misaligned bearings.Originality/valueA study on the lubrication behavior of misaligned water-lubricated polymer bearings with axial grooves is of significant interest to the research community.

Earthquake induced sloshing and hydrodynamic pressures in rigid liquid storage tanks analyzed by coupled acoustic-structural and Euler-Lagrange methods

Three-dimensional (3-D) ground-supported cylindrical and rectangular rigid liquid storage tanks filled with water and subjected to seismic base excitation are investigated using finite element method (FEM). The analyses of the tanks are carried out using coupled acoustic-structural (CAS) and coupled Eulerian-Lagrangian (CEL) approaches of the FEM using Abaqus®. The CAS approach based on linear wave theory and the CEL approach based on non-linear wave theory are used here to study the fluid-structure interaction (FSI) behavior of the tanks. Sloshing displacement, impulsive, convective, and total hydrodynamic pressures are investigated for varying geometries of the tanks. The small amplitude sloshing and hydrodynamic pressure responses are compared between the two FE-based, CAS and CEL approaches. The results obtained from the present FE-based analysis approaches are found to be in close agreement with the experimentally obtained seismic response in the 3-D cylindrical and rectangular tanks subjected to seismic ground motions. The ratio of peak sloshing height (h) to liquid height in the tank (HL) obtained in the cylindrical tank using the CAS approach is 0.0425 and that by the CEL is 0.039, whereas for rectangular tank it is 0.060 by the CAS approach and 0.046 by the CEL approach; thereby, signifying relatively small sloshing amplitude response. It is concluded that the non-linearity of the sloshing wave displacement does not play a significant role while calculating the hydrodynamic pressure distribution on the rigid tank walls.

Measured and Predicted Operating Characteristics of a Tilting-Pad Journal Bearing with Jacking-Oil Device at Hydrostatic, Hybrid, and Hydrodynamic Operation

Jacking-oil pockets are applied in many journals and thrust bearing applications in order to provide a hydrostatic oil film force that ensures a wear free run-up following a successful lift-off procedure. However, all components of the jacking-oil system have to be carefully designed in order to limit costs and prevent significant disturbance of hydrodynamic operation after deactivation of lift-oil. Experimental data and predictions for a four-pad tilting-pad journal bearing in load between pivot configuration are presented. Dynamic processes of the lift-off procedure as well as characteristic parameters of stationary conditions are studied. Moreover, hydrodynamic operation and hybrid lubrication providing a combined hydrodynamic and hydrostatic pressure distribution are investigated for sliding speeds up to 20 m/s. Analyzes of lift-off procedure prove that characteristic parameters such as lift-off pressures and vertical lift displacements are considerably influenced by manufacturing tolerances and misalignments. The comparison of hydrodynamic and hybrid lubrication provides a significant increase of load carrying capacity by additional jacking-oil supply at the maximum journal speed. In summary, results of measurements and predictions correlate well for all three investigated lubrication conditions.

Hydrodynamic Pressure and Velocity Distributions in the Interlayer Crack of Ballastless Track under High-Speed Train Load: A Theoretical Analysis

In the abundant rain or poor drainage areas, there will be serious water damage existing in the interlayer of ballastless track. The essence of water damage of ballastless track is a dynamic development process of damage shape under the combined action of train load, hydrodynamic pressure, and flow velocity. In view of the distribution characteristics of hydrodynamic pressure and flow velocity in the interlayer crack of ballastless track under the high-speed train load, the simplified mechanics model for water and composite slab with interfacial crack is proposed in accordance with the water damage characteristics of ballastless track. Based on the conservation of mass and momentum theorem, the analytical expressions of water pressure and velocity in the saturated water crack were deduced. Similarly, the analytical expressions of water pressure and velocity in the unsaturated water crack were deduced by adding the state equation of ideal air. Considering that the water does not flow back timely, the analytical expressions of water pressure and velocity in another kind of unsaturated water crack were deduced. The results show that the hydrodynamic pressure and flow velocity in the interlayer crack are synthetically determined by multiple influencing factors such as fluid viscosity, load characteristic, crack shape, absolute pressure at the crack mouth, and initial volume of the air in the crack, and there is an intersecting phenomenon between influencing factors. When there is a small amount of air at the crack tip, the pressure and velocity distribution in the crack can be divided into three parts in terms of air-water interface and stagnation point. When the crack is filled with water, the hydrodynamic pressure tends to decrease along the direction of the crack mouth, and the distribution along the whole crack approximates to a cubic polynomial curve. Similarly, the flow velocity increases along the direction of crack mouth, and the distribution along the whole crack approximates to a quadratic polynomial curve.

ANALYSIS OF THE VALUES OF HYDRODYNAMIC PRESSURE AND LOAD CARRYING CAPACITIES FOR VARIOUS METHODS OF SOLVING A REYNOLDS TYPE EQUATION

Calculations of the hydrodynamic pressure distribution in the slide bearing gap occur most often on the basis of ready-made computer programs based on CFD methods or one’s own calculation procedures based on various numerical methods. The use of one’s own calculation procedures and, for example, the finite difference method, allows one to include in the calculations of various additional non-classical effects on the lubricant (e.g., the influence of the magnetic field on ferrofluid, the influence of pressure or temperature on viscosity changes, non-Newtonian properties of lubricant or various non-classical models of dynamic viscosity changes). The aim of the authors’ research is to check how large the differences in results may be obtained using the two most frequently used methods of solving a Reynolds type equation. In this work, the authors use the small parameter method and the method of subsequent approximations to determine the distribution of hydrodynamic pressure. For numerical calculations, the finite difference method and our own calculation procedures and Mathcad 15 software were used. With both methods, identical conditions and parameters were assumed and the influence of pressure and temperature on viscosity change was taken into account. In the hydrodynamic pressure calculations, a laminar flow of the lubricating liquid and a non-isothermal lubrication model of the slide bearing were adopted. The classic Newtonian model was used as a constitutive equation. A cylindrical-type slide bearing of finite length with a smooth pan with a full wrap angle was accepted for consideration. In the thin layer of the oil film, the density and thermal conduction coefficient of the oil were assumed to remain unchanged.

WAVE INDUCED COUPLED MOTIONS AND STRUCTURAL LOADS BETWEEN TWO OFFSHORE FLOATING STRUCTURES IN WAVES

As oil or gas field moves deeper offshore area, offshore offloading operations such as Tandem or Side-by-Side arrangement between two floating structures take place in many locations throughout the world and also have many hydrodynamic problems. Therefore, the researches on the motion response and hydrodynamic force including first and second order between two floating structures are needed to have the more safe offloading operability in waves. In this paper, prediction of wave induced motion responses and structural loads at mid-ship section with hydrodynamic interaction effect between two offshore floating structures in various heading waves are studied by using a linearized three-dimensional potential theory. Numerical calculations using three-dimensional pulsating source distribution techniques have been carried out for hydrodynamic pressure distribution, wave exciting force, twelve coupled linear motion responses, relative motions and wave loads of the barge and the ship in oblique waves. The computational results give a good correlation with the experimental results and also with other numerical results. As a result, the present computational tool can be used effectively to predict the wave induced motions and structural loads of multiple offshore floating structures in waves.

THE ANALYSIS OF HYDRODYNAMIC PRESSURE DISTRIBUTION AND LOAD CARRYING CAPACITY IN THE GAP OF SLIDE JOURNAL BEARINGS WITH MICRO-GROOVES

The purpose of this paper is to analyse the distribution of hydrodynamic pressure, load carrying capacities, and friction force in the gap of the slide bearing on account of the type, number, and size of micro-grooves on the surface of the sleeve. It was assumed that micro-grooves were distributed equally on the circumference of the sleeve as well as parallel to its axis. Micro-bearings with micro-grooves are more and more often utilized in the technical applications, e.g., in HDD disks or in computer fans. It is advisable to carry out a numerical analysis on the influence of the number and the size of micro-grooves on the value of the basic flow parameters in the slide micro-bearing. A laminar flow of lubricating fluid and an isothermal model of the lubrication of the slide bearing was used for the analysis. A classical Newtonian model was applied as the constitutive equation. A cylindrical slide bearing with the finished length and smooth sleeve, and a full wrap angle was used for the research. The density and thermal conductivity of the oil were considered to be constant in the thin film of oil. The results of measurements of shape and sizes of micro-grooves in real micro-slide bearings were presented by the author in the previous publications. The results of that research are used at present to determine the preliminary assumptions concerning the shape and the size of the micro-grooves. The results obtained in the research show the minor influence of micro-grooves on the value of the friction force and a few percentages rate influence of micro-grooves on the value of load carrying capacity.

ANALYSIS OF HYDRODYNAMIC LUBRICATION OF JOURNAL BEARINGS WITH OIL OF NON-NEWTONIAN PROPERTIES

In this paper, the presented issue concerns hydrodynamic lubrication of the journal bearings with the oil of non-Newtonian properties. For the analysis of the hydrodynamic lubrication, a constitutive model of the third order was assumed. The assumed model consist of a Newtonian part –pI+ηA1 and non-Newtonian part β3·tr(A1 2)A1. The main part of this paper concerns transformation, nondimensionalization, and an estimation of the order of magnitude of the equation, which describes the apparent viscosity. Apparent viscosity describes changes in the dynamic viscosity with shear rate. In this way, the prepared model of apparent viscosity is used in momentum equations. These equations are integrated in order to designate components of the velocity vector. By substitution of the proper boundary conditions, a modified Reynolds type equation is obtained. A further stage of the research will be proceeding of the numerical calculations of the hydrodynamic pressure distribution followed by the designation of the carrying capacity, friction force, and friction coefficient while taking changes of the viscosity from shear rate into account (apparent viscosity).

Analysis of the influence of train load characteristics on the water damage of slab tracks

High-speed train load is one of the main factors that causes the failure of a slab track and is also the direct cause for producing water pressure in the cracks. Hence, choosing the right loading method is the key to analyze the water damage of slab tracks. In order to identify the distribution characteristics of the vertical force acting on the slab track, the analytic expression of fastener load was derived, and the field test was conducted to verify the theoretical model. According to the distribution characteristics of fastener load and the area of crack filled with water, the loading method was presented to analyze the water damage of slab tracks, and the influence of loading characteristics on the hydrodynamic pressure and crack propagation was analyzed. The results show that the distribution of fastener load in the main affected zone approximately accords with the Gaussian distribution under the single wheel load. When under the action of double wheels, the superimposed effect makes the second derivative of the loading function to increase by 99.93%. The superimposed effect of three or more wheels is less than 1% and can be ignored. Considering that the hydrodynamic pressure is highly sensitive to the second derivative of loading function, the load applied on the track slab should be in the form of a bogie, and different loads should be applied step by step based on the time series. The distribution of hydrodynamic pressure along the crack is approximately equal to the cubic polynomial, and the pressure peak appears at the crack tip. Also, the pressure is proportional to the square of the running speed of the train. In the region with abundant rainwater and a poor drainage system, reducing the train speed and taking timely measures such as grouting can effectively reduce the water damage of slab tracks.

Near-field pressure waveform analysis of an excited Mach 0.9 jet

This work explores the effects of axisymmetric, helical, and flapping mode perturbations over a range of Strouhal numbers on the near-field pressure of an axisymmetric Mach 0.9 jet with a Reynolds number of 6.2 × 105. Excitation is generated by eight localized arc filament plasma actuators uniformly distributed around the nozzle exit. The excitation of jet shear layer instabilities resulted in large-scale structures. The signature of these structures in the irrotational near field appears as high-amplitude hydrodynamic pressure fluctuations with wavepacket-like growth, saturation, and decay. The excitation Strouhal number and, perhaps more importantly, the azimuthal mode, are seen to strongly affect the spatial evolution of the wavepacket in both axial and radial directions. The dominant excitation Strouhal number is around 0.3, and the most significant effect on the jet statistical properties (such as distributions of velocity and pressure) occurs further downstream for the flapping mode in comparison to the axisymmetric mode. Dynamic mode decomposition is performed to further describe the modal behavior and evolution of hydrodynamic pressure fluctuations. The pressure response in the near field of jet plumes in flapping mode excitation is shown to exhibit two azimuthal mode behaviors: axisymmetric and flapping. An empirical model of hydrodynamic pressure distribution is established with normalized axial and radial profiles. The amplitude and distribution of the hydrodynamic pressure component are well depicted by the empirical reconstruction.

Influence of short grooves on hydrodynamic lubrication of textured infinitely long sliders

The influence of geometrical parameters of the short grooves on the hydrodynamic lubrication is studied in this article. Based on Reynolds equation and Jakobsson–Floberg–Olsson cavitation theory, an analytical model is developed to investigate the hydrodynamic lubrication of the short grooves. The study employs a multigrid method to calculate the distribution of hydrodynamic pressure and the average pressure of textured surfaces. The results indicate that the interactions between neighboring short micro-grooves and the end effect on the hydrodynamic pressure should be considered in the process of numerical simulation. There exist the optimum values of horizontal spacing and short micro-groove depth to maximize the hydrodynamic pressure. The average film pressure decreases with the increase in the vertical spacing, but it increases alongside the short groove width. The increase rate of the average pressure declines gradually as the short groove length grows. Therefore, hydrodynamic lubrication performance can be improved by optimizing the geometrical parameters of the short grooves according to operating conditions.