On the Sensitivity of the Asperity Pressures and Temperatures to the Fluid Pressure Distribution in Mixed-Film Lubrication

1999 ◽  
Vol 122 (1) ◽  
pp. 77-85 ◽  
Author(s):  
L. Chang ◽  
Yongwu Zhao
Keyword(s):  
Pressure Distribution ◽  
Fluid Pressure ◽  
Practical Interest ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Time Duration ◽  
Time Step ◽  
Wide Range ◽  
Mixed Film ◽  
Film Lubrication

This paper studies the sensitivities of the asperity pressures and temperatures to the fluid pressure distribution in concentrated contacts operating in the regime of mixed-film lubrication. Two fluid pressure distributions are used in the study. One is a Hertz-like distribution that neglects micro-EHL responses of the lubricant, and the other models the micro-EHL effects with significant pressure rippling. The asperity pressures and temperatures are deterministically calculated in time by numerically solving the asperity-contact and the transient energy equations as the two surfaces move relative to each other. The contact is simulated for sufficient time duration until the samples of the calculated asperity variables reach a statistical equilibrium that reflects the random-process nature of the problem. Parametric analyses are carried out that cover a wide range of operating conditions of practical interest. The results obtained consistently suggest that the asperity pressures and temperatures are not sensitively related to the fluid pressure. This insensitivity supports the use of any fluid pressure distribution consistent with the underlying mixed-film problem, rather than determining it by numerically solving the Reynolds equation at every time step of the simulation process. The study lays a foundation on which to advance modeling of the mixed-film contacts with a proper balance among model robustness, computational efficiency and solution accuracy. [S0742-4787(00)01101-2]

Unsteady Conjugate Heat Transfer Investigation of a Multistage Steam Turbine in Warm-Keeping Operation With Hot Air

2018 ◽  
Author(s):  
Piotr Łuczyński ◽  
Dennis Toebben ◽  
Manfred Wirsum ◽  
Wolfgang F. D. Mohr ◽  
Klaus Helbig
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Flow Patterns ◽  
Operating Conditions ◽  
Angle Of Incidence ◽  
Time Step ◽  
Hot Air ◽  
Wide Range ◽  
Vortex Systems ◽  
Operating Points

In recent decades, the rising share of commonly subsidized renewable energy especially affects the operational strategy of conventional power plants. In pursuit of flexibility improvements, extension of life cycle, in addition to a reduction in start-up time, General Electric has developed a product to warm-keep high/intermediate pressure steam turbines using hot air. In order to optimize the warm-keeping operation and to gain knowledge about the dominant heat transfer phenomena and flow structures, detailed numerical investigations are required. Considering specific warm-keeping operating conditions characterized by high turbulent flows, it is required to conduct calculations based on time-consuming unsteady conjugate heat transfer (CHT) simulations. In order to investigate the warm-keeping process as found in the presented research, single and multistage numerical turbine models were developed. Furthermore, an innovative calculation approach called the Equalized Timescales Method (ET) was applied for the modeling of unsteady conjugate heat transfer (CHT). The unsteady approach improves the accuracy of the stationary simulations and enables the determination of the multistage turbine models. In the course of the research, two particular input variables of the ET approach — speed up factor (SF) and time step (TS) — have been additionally investigated with regard to their high impact on the calculation time and the quality of the results. Using the ET method, the mass flow rate and the rotational speed were varied to generate a database of warm-keeping operating points. The main goal of this work is to provide a comprehensive knowledge of the flow field and heat transfer in a wide range of turbine warm-keeping operations and to characterize the flow patterns observed at these operating points. For varying values of flow coefficient and angle of incidence, the secondary flow phenomena change from well-known vortex systems occurring in design operation (such as passage, horseshoe and corner vortices) to effects typical for windage, like patterns of alternating vortices and strong backflows. Furthermore, the identified flow patterns have been compared to vortex systems described in cited literature and summarized in the so-called blade vortex diagram. The comparison of heat transfer in the form of charts showing the variation of the Nusselt-numbers with respect to changes in angle of incidence and flow coefficients at specific operating points is additionally provided.

scholarly journals Mixed and Fluid Film Lubrication Characteristics of Worn Journal Bearings

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Toshiharu Kazama ◽  
Yukihito Narita
Keyword(s):  
Frictional Coefficient ◽  
Journal Bearings ◽  
Mixed Lubrication ◽  
Operating Conditions ◽  
Fluid Film ◽  
Asperity Contact ◽  
Lubrication Regimes ◽  
Lubrication Characteristics ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The mixed and fluid film lubrication characteristics of plain journal bearings with shape changed by wear are numerically examined. A mixed lubrication model that employs both of the asperity-contact mechanism proposed by Greenwood and Williamson and the average flow model proposed by Patir and Cheng includes the effects of adsorbed film and elastic deformation is applied. Considering roughness interaction, the effects of the dent depth and operating conditions on the loci of the journal center, the asperity-contact and hydrodynamic fluid pressures, friction, and leakage are discussed. The following conclusions are drawn. In the mixed lubrication regime, the dent of the bearing noticeably influences the contact and fluid pressures. For smaller dents, the contact pressure and frictional coefficient reduce. In mixed and fluid film lubrication regimes, the pressure and coefficient increase for larger dents. Furthermore, as the dent increases and the Sommerfeld number decreases, the flow rate continuously increases.

Optimal Design of Squeeze Film Supports for Flexible Rotors

1983 ◽  
Vol 105 (3) ◽  
pp. 487-494 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Optimal Design ◽  
Vibration Amplitude ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rotor Vibration ◽  
Design Constraints ◽  
Supply Pressure ◽  
Flexible Rotors ◽  
Wide Range ◽  
Film Lubrication

Assuming central preloading, operation below the second bending critical speed, and full film lubrication, this paper presents a theoretical model which allows one, with minimum computation, to design squeeze film damped rotors under conditions of high unbalance loading. Closed form expressions are derived for the maximum vibration amplitudes pertaining to optimally damped conditions. The resulting vibration amplitude and transmissibility data of design interest are presented for a wide range of practical operating conditions on a single chart. It can be seen that for a given rotor, the lighter the bearing the more easily one can satisfy design constraints relating to allowable rotor vibration levels and lubricant supply pressure requirements. The data presented are shown to be applicable to a wide variety of rotors, and a recommended procedure for optimal design is outlined.

Development of a Piston Secondary Motion Model for Skirt Friction Analysis

2012 ◽  
Author(s):  
Ozgur Gunelsu ◽  
Ozgen Akalin
Keyword(s):  
Operating Conditions ◽  
Design Parameters ◽  
Asperity Contact ◽  
Motion Model ◽  
Film Rupture ◽  
Time Step ◽  
Elastic Deformations ◽  
Oil Film ◽  
Piston Skirt ◽  
Secondary Motion

A comprehensive piston skirt lubrication and secondary motion model that can be used for piston friction simulations was developed based on Greenwood and Tripp’s surface asperity contact model and Patir and Cheng’s modified Reynolds equation with surface flow factors. Oil flow between the skirt-liner clearances was modeled and hydrodynamic and asperity contact pressures around the skirt were calculated. Reynolds boundary conditions were applied to determine the film rupture boundaries and wetted areas. Surface roughness and roughness orientation were included in the model. Due to its important effect on pressure development in the oil film, change in the skirt profile due to elastic deformations was taken into account. Change of the skirt profile due to piston thermal expansion is also calculated using the steady-state temperature distribution of the piston corresponding to the investigated engine running conditions. A piston stiffness matrix obtained by finite element analysis was used to determine the elastic deformations of the piston skirt under the calculated oil film pressures. A two-degree-of-freedom system is formed with the forces and moments calculated by the lubrication model. These forces and moments require a coupled solution with piston position. This is achieved by applying an iterative numerical procedure based on Broyden’s scheme which seeks force and moment balance at each iteration phase making use of time step variation. The effects of various engine operating conditions and piston design parameters on piston secondary motion were investigated. Piston skirt friction force due to hydrodynamic shear forces and metal-to-metal contact is calculated.

scholarly journals Systematic derivation of a surface polarisation model for planar perovskite solar cells

2018 ◽  
Vol 30 (3) ◽  
pp. 427-457 ◽  
Author(s):  
N. E. COURTIER ◽  
J. M. FOSTER ◽  
S. E. J. O'KANE ◽  
A. B. WALKER ◽  
G. RICHARDSON
Keyword(s):  
Solar Cells ◽  
Numerical Solutions ◽  
Perovskite Solar Cells ◽  
Practical Interest ◽  
Operating Conditions ◽  
Asymptotic Approach ◽  
Perovskite Layer ◽  
Current Voltage ◽  
Wide Range ◽  
Vacancy Density

Increasing evidence suggests that the presence of mobile ions in perovskite solar cells (PSCs) can cause a current–voltage curve hysteresis. Steady state and transient current–voltage characteristics of a planar metal halide CH3NH3PbI3PSC are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width ~2 nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer (~600 nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplifiedsurface polarisationmodel in which the slow ion dynamics are replaced by interfacial (non-linear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.

Development of a Semi-implicit Solver for Detailed Chemistry in Internal Combustion Engine Simulations

2006 ◽  
Vol 129 (1) ◽  
pp. 271-278 ◽  
Author(s):  
Long Liang ◽  
Song-Charng Kong ◽  
Chulhwa Jung ◽  
Rolf D. Reitz
Keyword(s):  
Internal Combustion ◽  
Operating Conditions ◽  
Explicit Methods ◽  
Time Step ◽  
Ic Engine ◽  
Specific Internal Energy ◽  
Detailed Chemistry ◽  
Key Species ◽  
Wide Range ◽  
Implicit Solver

An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled stiff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver. Good agreement was achieved for a wide range of engine operating conditions, and 40-70% CPU time savings were achieved by the present solver compared to the standard CHEMKIN.

The Effect of Elastic Distortions on Journal Bearing Performance

1967 ◽  
Vol 89 (4) ◽  
pp. 409-415 ◽  
Author(s):  
J. O’Donoghue ◽  
D. K. Brighton ◽  
C. J. K. Hooke
Keyword(s):  
Exact Solution ◽  
Pressure Distribution ◽  
Elastic Deformation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Wide Range ◽  
Constant Viscosity ◽  
Outside Diameter

This paper presents a solution to the problem of hydrodynamic lubrication of journal bearings taking into account the elastic distortions of the shaft and the bearing. The exact solution for determining the elastic deformation for a given pressure distribution around a bearing is given, together with the reiterative procedure adopted to find the pressure distribution which satisfies both the hydrodynamic and elastic requirements of the system. Results are given which have been derived for a material with a Poisson’s ratio of 0.28, but other values such as 0.33 do not incur substantial errors. The results can be applied to a wide range of operating conditions using the nondimensional group of terms suggested in the paper. The bearing is assumed to be infinite in length, and infinite in thickness. The latter assumption is shown to be valid for a particular case where the outside diameter of the bearing shell is 3.5 times the shaft diameter. A further assumption in the calculation is a condition of constant viscosity of the lubricant existing around the bearing.

scholarly journals Identification of a Material–Lubricant Pairing and Operating Conditions That Lead to the Failure of Porous Journal Bearing Systems

2020 ◽  
Vol 68 (4) ◽  
Author(s):  
Guido Boidi ◽  
Stefan Krenn ◽  
Stefan J. Eder
Keyword(s):  
Mixed Lubrication ◽  
Operating Conditions ◽  
Maximum Temperature ◽  
Asperity Contact ◽  
Operational Conditions ◽  
Practical Applications ◽  
Custom Made ◽  
Wide Range ◽  
Lab Test ◽  
Wear Tests

AbstractIn this study, we perform accelerated wear tests with porous journal bearings (PJBs) on a lab test rig, providing statistically reliable results under realistic operational conditions. To this end, a custom-made tribometer consisting of 5 mechanically independent but centrally controlled units was used to test five identical bearings in parallel. The test parameters were tuned to promote enough wear under mixed lubrication by increasing the clearance gap and the radial load, while minimizing the bidirectional rotational speed. A wide range of lubricant and material combinations were evaluated, the vast majority of which performed excellently (i.e., negligible wear and low friction). Only one notable combination of a low-density iron bearing paired with a standard PAO-based lubricant failed when operating at low rotational speeds, exhibiting highly unstable frictional behavior and 10–20 times the typical wear in practical applications. An analysis of Stribeck curves, recorded periodically during the wear tests as a diagnostic tool, proved that this particular combination of materials and parameters failed to run in properly, with deteriorating tribological behavior over time. A direct relation between the total wear and the maximum temperature in the tribocontact during testing helped identify this pairing as the only one operating solely under mixed lubrication (high asperity contact), explaining the excessive wear. Graphical Abstract

Experimental and Numerical Investigations of Flowpath Profiling on Secondary Flow Losses in a Turbine Control Stage

2013 ◽  
Author(s):  
Nils Moser ◽  
Peter Steinhoff ◽  
Franz Joos
Keyword(s):  
Pressure Distribution ◽  
Secondary Flow ◽  
Guide Vane ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Formation Mechanisms ◽  
Guide Vanes ◽  
Numerical Investigations ◽  
Control Stage ◽  
Wide Range

The numerically and experimentally investigated industrial steam turbine control stage is derived from a real design. Due to the production process and costs of the guide vanes for control stages of steam turbines the flowpath profiling is rotationally symmetric. However the combination of the two-dimensional shroud contour and the flow deflection in the guide vane results in a fully three-dimensional end wall contour having a strong influence on the secondary flow features in the turbine control stage. To obtain an improved profile for the nozzle shroud the reduction of the total pressure loss over the guide vanes is taken as an optimization criterion. The three-dimensional contour generates a diffuser flowpath between the suction and the pressure side of two guide vanes perpendicular to the main flow direction. This diffuser geometry affects the pressure distribution over the guide vane and therefore the formation mechanisms of secondary flows. For the experimental and numerical investigations a baseline shroud design and two additional profiled contours are analyzed in detail. The control stage test rig is operated with air and is capable to represent a wide range of operating conditions. The measurements show a considerable increase of the stage efficiency and power output. The effect of the flowpath profiling on the pressure distribution over the guide vane is clearly proved.

scholarly journals Optimal Design of Squeeze Film Supports for Flexible Rotors

1982 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Optimal Design ◽  
Vibration Amplitude ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rotor Vibration ◽  
Design Constraints ◽  
Supply Pressure ◽  
Flexible Rotors ◽  
Wide Range ◽  
Film Lubrication

Assuming central preloading operation below the second bending critical speed and full film lubrication, this paper presents a theoretical model which allows one, with minimum computation, to design squeeze film damped rotors under conditions of high unbalance loading. Closed form expressions are derived for the maximum vibration amplitudes pertaining to optimally damped conditions. The resulting vibration amplitude and transmissibility data of design interest are presented for a wide range of practical operating conditions on a single chart. It can be seen that for a given rotor, the lighter the bearing the more easily one can satisfy design constraints relating to allowable rotor vibration levels and lubricant supply pressure requirements. The data presented are shown to be applicable to a wide variety of rotors, and a recommended procedure for optimal design is outlined.

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