bluuebunny/crossref_metadata_2025 huggingface dataset:
Laminar Natural Convection About Downward Facing Heated Blunt Bodies to Liquid Metals
Authors: Harpole G. M. , Catton I.
Published: November 2010

The laminar boundary layer equations for free convection over bodies of arbitrary shape (i.e., a three-term series expansion) and with arbitrary surface heat flux or surface temperature are solved in local Cartesian coordinates. Both two-dimensional bodies (e.g., horizontal cylinders) and axisymmetric bodies (e.g., spheres) with finite radii of curvature at their stagnation points are considered. A Blasius series expansion is applied to convert from partial to ordinary differential equations. An additional transformation removes the surface shape dependence and the surface heat flux or surface temperature dependence of the equations. A second-order-correct, finite-difference method is used to solve the resulting equations. Tables of results for low Prandtl numbers are presented, from which local Nusselt numbers can be computed.
Streakline Flow Visualization of Discrete Hole Film Cooling for Gas Turbine Applications
Authors: Colladay R. S. , Russell L. M.
Published: November 2010

Film injection from discrete holes in a three row staggered array with 5-dia spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the mainstream, and (3) slanted 30 deg to the surface and 45 deg laterally to the mainstream. The ratio of the boundary layer thickness-to-hole diameter and the Reynolds number were typical of gas turbine film cooling applications. Results from two different injection locations are presented to show the effect of boundary layer thickness on film penetration and mixing. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally-buoyant helium filled “soap” bubbles which follow the flow field. Unlike smoke, which diffuses rapidly in the high turbulent mixing region associated with discrete hole blowing, the bubble streaklines passing downstream injection locations are clearly identifiable and can be traced back to their point of ejection.
Mean Diameters in Parallel-Flow and Counter-Flow Aerosol Systems
Authors: Hollands K. G. T. , Goel K. C.
Published: November 2010

The general concept of the mean diameter of the disperse phase of an aerosol system, first introduced by Mugele and Evans in 1951, has proven to be a very useful one. In this concept, the proper mean diameter, xp,q, is characterized by a single pair of indices, p and q, which are dependent on the actual type of aerosol system under consideration. This paper re-examines the validity of this concept of mean diameter in heat and mass transfer aerosol systems. The concept is found to be applicable only under a very narrow range of conditions. Attention is then given to a more general definition of a mean diameter, applicable to aerosol heat or mass exchangers. Analyses of these devices shows that the more general mean diameter is a function of the capacity rate ratio, R, and effectiveness of the heat exchanger, ε. Solutions to the governing equations have permitted the mean diameter to be presented graphically as a function of these variables. These solutions are given for two types of particle size distributions, the Rosin-Rammler and the log-probability, and for both parallel-flow and counter-flow heat exchangers. The solutions are, however, restricted to cases where the resistance to heat or mass transfer lies exclusively in the continuous phase.
Thermal Radiative Properties of the Noble Metals at Cryogenic Temperatures
Authors: Toscano W. M. , Cravalho E. G.
Published: November 2010

Experimental values of the monochromatic, near normal emittance, ελN, of gold at cryogenic temperatures are presented and compared with values predicted by existing theoretical models. From this comparison recommendations are made regarding the engineering suitability of these models. Data obtained by the present authors for ελN of gold in the wavelength range 1 to 30μ and at temperatures of 300, 79, and 6.0 K are compared with the Drude free electron model, the anomalous skin effect theory for both specular and diffuse electron reflections, and the Holstein quantum mechanical model. Results show that the anomalous skin effect model with diffuse electron reflections predicts ελN most accurately. At room temperature and at liquid nitrogen temperature the agreement between this model and the data is within 5 percent. At liquid helium temperatures the agreement is somewhat poorer, i.e., within 30 percent.
Turbulent Heat Transfer Studies in Annulus With Inner Cylinder Rotation
Authors: Kuzay T. M. , Scott C. J.
Published: November 2010

Experimental investigations of turbulent heat transfer are made in a large-gap annulus with both rotating and nonrotating inner cylinder. The vertical annular channel has an electrically heated outer wall; the inner wall is thermally and electrically insulated. The axial air flow is allowed to develop before rotation and heating are imparted. The resulting temperature fields are investigated using thermocouple probes located near the channel exit. The wall heat flux, wall axial temperature development, and radial temperature profiles are measured. For each axial Reynolds number, three heat flux rates are used. Excellent correlation is established between rotational and nonrotational Nusselt number. The proper correlation parameter is a physical quantity characterizing the flow helix. This parameter is the inverse, of the ratio of axial travel of the flow helix in terms of hydraulic diameter, per half revolution of the spinning wall.
Dryout Heat Fluxes for Inductively Heated Particulate Beds
Authors: Dhir V. , Catton I.
Published: November 2010

Experimental observations of the dryout heat fluxes for inductively heated particulate beds have been made. The data were obtained when steel and lead particles in the size distribution 295–787 microns were placed in a 4.7-cm dia pyrex glass jar and inductively heated by passing radio frequency current through a 13.3-cm dia multiturn work coil encircling the jar. Distilled water, methanol and acetone were used as coolants in the experiments, while the bed height was varied from 1.9 to 8.9 cm. Different mechanisms for the dryout in deep and shallow beds have been identified. Dryout in shallow beds is believed to occur when the vapor velocity in the gas jets exceeds a certain critical velocity at which choking of the vapor, leading to obstruction in the flow of the liquid towards the bed occurs. However, deep beds dry out when gravitational force can no longer maintain a downward coolant flow rate necessary to dissipate the heat generated in the bed. Finally, the heat flux data of the present investigation and that from two previous investigations made at Argonne Laboratory and at UCLA have been correlated with semitheoretical correlations based on the proposed hydrodynamic models.
Thermal Performance Models and Drift Loss Predictions for a Spray Cooling System
Authors: Chen K. H. , Trezek G. J.
Published: November 2010

The relation between the Spray Energy Release (SER) and the spray nozzle efficiency (η) is considered with the view toward increasing the utility of previous spray thermal performance information. Through the approximate analysis of an assumed counter-flow process, the relevant parameters that η depends upon have been identified as the total heat transfer factor c′/cw, the sensible heat factor φ, and the SER. In general η cannot be correlated with wind speed alone. Similarities and differences between the NTU and SER methods are also considered. Values of SER are established from data obtained from a prototype spray system and a laboratory scale single column spray system. A simplified drift loss prediction model which is in good agreement with experimental data is proposed for an open atmosphere spray system.
Lambda—Transition (He II—He I) During Heat Flow at Supercritical Pressures
Authors: Caspi S. , Lee J. Y. , Frederking T. H. K.
Published: November 2010

New boiling-like phenomena are reported which have been observed during heat-induced lambda transitions in liquid Helium-II at pressures above the thermodynamic critical pressure.
Stability of a Submerged Frozen Crust
Authors: Epstein M.
Published: November 2010

Consideration is given to the stability of a thin frozen crust of infinite extent growing between two different fluid materials. A linear, inviscid stability analysis is employed to obtain an estimate for the crust breakup time. The stability formulation parallels that of Rayleigh and Kelvin for the generation of waves at the plane interface between two different fluids and is used to develop formulas defining necessary conditions for frozen crust breakup. An approximate crust breakup criterion is proposed, viz, that the crust growth (or crystallization) time exceed the crust breakup time. The criterion shows reasonable agreement with experimental observations of the stability of a growing frozen crust in a gravity field alone (Rayleigh instability).
Correlation Equations for Turbulent Thermal Convection in a Horizontal Fluid Layer Heated Internally and from Below
Authors: Cheung F. B.
Published: November 2010

High Rayleigh number thermal convection in a horizontal fluid layer with uniform volumetric energy sources and a constant rate of bottom heating is studied analytically by a simple boundary layer approach. Heat transfer characteristics of the layer are defined in terms of local boundary-layer variables. Correlation equations are derived for the upper and the lower surface Nusselt numbers as functions of two independent Rayleigh numbers, based respectively on the surface to surface temperature difference and the volumetric heating rate. Variation of the turbulent core temperature, which so far has not been determined successfully by existing analytical methods, is obtained. This is found to depend on a single dimensionless parameter which measures the relative rates of internal and external heating. Results of this study are presented with available experimental data.
Bubble Growth in Variable Pressure Fields
Authors: Jones O. C. , Zuber N.
Published: November 2010

The case of a spherical vapor bubble growing in an infinite, uniformly heated liquid, has been analyzed under the thin boundary layer approximation for the effects of a variable pressure field, including density variation. It has been shown that, in addition to the usually accepted effects of initial superheat, variable pressure effects can be quite important and dominate the rate of growth. For the case where pressure changes cause the vapor temperature to behave as tn, (t being time), the bubble radius will grow as tn+1/2, significantly faster than the t behavior usually expected. The analysis has been shown to compare favorably with existing data.
Aerothermochemistry of Metal Erosion by Hot Reactive Gases
Authors: Gany A. , Caveny L. H. , Summerfield M.
Published: November 2010

Analytical studies were conducted to investigate the mechanisms of metal erosion produced by short exposures (< 2 ms) to flowing high pressure (∼ 350 MPa), high temperature (∼ 3000 K) reactive gases. Previous experimental studies established that the intense heating during the short exposure produced melting and, when reactive gases were used, oxidation of the surface and enhanced erosion. The reactions were modeled as diffusion-limited, heterogeneous surface reactions which achieved equilibrium at the gas/metal interface. Calculated results for the sequential events of initial heating, surface reactions, and melting explained and correlated the experimental trends for Fe, Al, Ti, and Mo. Rapidly increasing erosion rates with increasing O2 concentration are the result of the surface reactions between the metal and O2. As O2 concentration increases, the heating produced by the surface reaction exceeds the forced convective heating which, in turn, greatly enhances the melting rate.
The Numerical Prediction of Viscous Flow and Heat Transfer in Tube Banks
Authors: Launder B. E. , Massey T. H.
Published: November 2010

A scheme for handling the numerical analysis of viscous flow and heat transfer in tube banks is presented. It involves the use of a cylindrical network of nodes in the vicinity of the tubes with a Cartesian mesh covering the remainder of the flow domain. The approach has been incorporated into the numerical solving algorithm for the Navier Stokes equations of Gasman, et al. [8]. A number of demonstration calculations is presented including a numerical simulation of the staggered square bank for which Bergelin and co-workers [4, 9] have reported experimental results for pressure drop and heat transfer rate. Agreement between predicted and measured characteristics is satisfactory when account is taken of end and entry effects that are present in the experiments but necessarily omitted from the calculations. Indeed the close agreement of the laminar predictions with measurements extends to Reynolds numbers in excess of 1000, a level at which it has hitherto been supposed that turbulent motion in the fluid made a substantial contribution to friction and heat transfer.
Forced Convection Heat Transfer from a Shrouded Fin Array with and without Tip Clearance
Authors: Sparrow E. M. , Baliga B. R. , Patankar S. V.
Published: November 2010

An analysis is made of the laminar heat transfer characteristics of an array of longitudinal fins with an adiabatic shroud situated adjacent to the fin tips. The analysis involves the solution of the velocity field in the inter-fin space and in the shroud clearance gap beyond the tips, after which the governing energy equations for the fluid and the fins are solved simultaneously. Solutions are obtained for representative values of dimensionless parameters which describe the system geometry and the fin conductance. For the fin, the results show that the heat loss is a minimum adjacent to the base and increases along the fin in the direction of the tip. The maximum fin heat loss occurs either at the tip or intermediate between the base and the tip, depending on whether or not there is clearance between the fin tips and the shroud. The calculated heat transfer coefficients vary along the fin and, in some cases, take on negative values. Heat loss variations are also encountered along the base surface, the extent of which depends on the fin conductance, the inter-fin spacing, and the extent of the clearance gap. With regard to the overall heat loss, the fin is, on a unit area basis, a more efficient transfer surface than is the base. The results demonstrate that the conventional uniform heat transfer coefficient model is inapplicable to shrouded fin arrays.
Supercritical Solutions for the Buoyancy Boundary Layer
Authors: Iyer P. A. , Kelly R. E.
Published: November 2010

Two-dimensional, finite amplitude solutions for the Prandtl buoyancy boundary layer are obtained for Reynolds numbers close to the critical values by an expansion in terms of disturbance amplitude. Supercritical nonlinear wave solutions are found to occur, rather than subcritical instabilities. The dependence of the wave amplitude and Nusselt number upon wall inclination, relative wall temperature, and Prandtl number is discussed.
Interacting Turbulent Boundary Layer over a Wavy Wall
Authors: Polak A. , Werle M. J.
Published: November 2010

This paper is concerned with the two-dimensional supersonic flow of a thick turbulent boundary layer over a train of relatively small wave-like protuberances. The flow conditions and the geometry are such that there exists a strong interaction between the viscous and inviscid flow. Here the interacting boundary layer equations are solved numerically using a time-like relaxation method with turbulence effects represented by the inclusion of the eddy viscosity model of Cebeci and Smith. Results are presented for flow over a train of up to six waves for Mach numbers of 2.5 and 3.5, Reynolds numbers of 10 and 32 × 106/meter, and wall temperature ratios Tw/T0 of 0.4 and 0.8. Limited comparisons with independent experimental and analytical results are also given.
Techniques for Reducing Thermal Conduction and Natural Convection Heat Losses in Annular Receiver Geometries
Authors: Ratzel A. C. , Hickox C. E. , Gartling D. K.
Published: November 2010

Analytical and experimental work has been undertaken to analyze thermal conduction and natural convection heat losses in annular receiver geometries. Techniques studied for reducing conduction heat loss include evacuation of the annulus gas, oversizing of the annular space while maintaining slight vacuum levels, and use of gases other than air in the annular space. For the geometry considered, total heat loss reductions of 10 percent to 50 percent may be obtained depending on the means by which the conduction heat loss is limited. In addition, natural convection studies considering the effects of nonuniform temperature distributions and eccentric cylinders are discussed. The numerical analysis performed indicates that highly nonuniform temperature distributions are required to appreciably affect the natural convection process between concentric cylinders and that rather large eccentricities cause only a slight increase in natural convection heat transfer.
Natural Convection Heat Transfer Characteristics of Flat Plate Enclosures
Authors: Randall K. R. , Mitchell J. W. , El-Wakil M. M.
Published: November 2010

Heat transfer by natural convection in rectangular enclosures has been experimentally studied using interferometric techniques. The effects of Grashof number, tilt angle, and aspect ratio on both the local and average heat transfer coefficients have been determined. The Grashof number range tested was 4 × 103 to 3.1 × 105, and the aspect ratio (ratio of enclosure length to plate spacing) varied between 9 and 36. The angles of tilt of the enclosure with respect to the horizontal were 45, 60, 75 and 90 deg. Correlations are developed for both local and average Nusselt number over the range of test variables. The effect of tilt angle is found to reduce the average heat transfer by about 18 percent from the value of 45 deg to that at 90 deg. No significant effect of aspect ratio over the range tested was found. A method for characterizing the flow regimes that is based on heat transfer mechanisms is proposed.
Effects of Multiple Sources in the Contact Conductance Theory
Authors: Beck J. V.
Published: November 2010

An analysis of regularly spaced disk sources on the surface of a semi-infinite body is given and related to steady-state contact conductance theory. It is shown that simple superposition utilizing the steady-state temperature distribution for a single typical disk source is not valid since a steady state does not exist for the temperature resulting for an infinite number of regularly spaced sources on the surface of a semi-infinite solid. A novel analysis is presented that treats the transient surface temperature in such a manner that a steady-state conductance is derived. The conductance results are compared with those obtained by Yovanovich who use a complementary analysis. The method of analysis can be applied to other disk spacings and to random distribution of contacts. Also considered is the case of contact radius being a uniformly-distributed random variable which yielded the results of increased contact resistance compared to that using the average contact radius.
Analysis of Turbulent Flow and Heat Transfer in Internally Finned Tubes and Annuli
Authors: Patankar S. V. , Ivanovic´ M. , Sparrow E. M.
Published: November 2010

The fully developed turbulent flow and heat transfer characteristics for tubes and annuli with longitudinal internal fins were analyzed via a mixing length model. The model takes account of the proximity of both the fin surfaces and the tube wall as well as of the gradients in the radial and circumferential directions. Application was made to air flows, and a single adjustable constant in the model was fixed by comparisons with experimental data for the friction factor and the circumferential-average Nusselt number for internally finned tubes. The local heat transfer coefficients exhibited a substantial variation along the fin height, with the smallest value (essentially zero) at the base and the largest value at the tip. Lesser and more gradual variations were exhibited by the local heat transfer coefficients on the wall of the tube or annulus. In general, the fins were found to be as effective a heat transfer surface as the wall (per unit area). Average Nusselt numbers and friction factors are presented for both the tube and the annulus.
Viscosity of Nitrogen near the Critical Point
Authors: Basu R. S. , Sengers J. V.
Published: November 2010

The viscosity of fluids exhibits an anomalous enhancement near the gas-liquid critical point. It is shown that the behavior of the viscosity of nitrogen as observed experimentally by Zozulya and Blagoi is consistent with current theoretical predictions. An equation is proposed for the viscosity of nitrogen that incorporates the observed critical enhancement in the viscosity near the critical point.
Calibration of a Fast Neutron Scattering Technique for Measurement of Void Fraction in Rod Bundles
Authors: Banerjee S. , Yuen P. , Vandenbroek M. A.
Published: November 2010

A technique based on scattering and transmission of fast neutron beams has been developed for measuring void fraction in two-phase flow through rod bundles. Experiments indicate that the scattered neutron flux varies linearly with void fraction and is largely independent of phase distribution. Measurements of the transmitted neutron flux have been used to determine phase distribution (or flow regime). The technique gives good sensitivity and count rates and appears suitable for void fraction and phase distribution measurements in transient flow boiling.
Dropwise Evaporation
Authors: Bonacina C. , Del Giudice S. , Comini G.
Published: November 2010

Evaporation of atomized liquids on hot surfaces is identified as an interesting technical process, characterized by very high values of specific heat fluxes. An experimental apparatus, expressely built for the evaluation of heat transfer mechanisms in mist cooling with low excess temperatures, is described. A mathematical model, based on the assumption of dropwise evaporation, is used to correlate the experimental results.
Entrainment by a Jet at a Density Interface in a Thermally Stratified Vessel
Authors: Lorenz J. J. , Howard P. A.
Published: November 2010

A study was conducted to determine the thermal behavior and upward movement of the density interface resulting from entrainment by an impinging jet in a thermally stratified vessel. Experiments were performed using a cylindrical vessel with water as the test fluid. The upward movement of the interface was detected by vertical strings of closely spaced thermocouples. As the interface passed a given thermocouple location, the temperature was observed to drop abruptly while oscillating in the process. It was found that vigorous entrainment and mixing maintain a relatively sharp temperature “step” in the impingement region. Using the theory of free submerged jets, a correlation was developed for the rise rate of the interface in terms of the Froude number based on local jet impingement parameters.
The Measurement of Natural Convective Heat Transfer in Triangular Enclosures
Authors: Flack R. D. , Konopnicki T. T. , Rooke J. H.
Published: November 2010

Heat transfer rates were experimentally measured for laminar convection air flows in two-dimensional triangular enclosures with two side walls which were heated and cooled and an adiabatic bottom. Both local and overall heat transfer data were obtained by the use of a Wollaston prism schlieren interferometer. The angle between the two isothermal side walls was varied between 60 and 120 deg, which resulted in a variation in aspect ratio (enclosure height/base width) between 0.29 and 0.87, while the Grashof number was varied between 2.9 × 106 and 9.0 × 106. Results are compared to previously obtained isothermal inclined flat plate data and rectangular enclosure data. Present results agree with rectangular enclosure results. One deviation from local rectangular enclosure data was found in the apex regions of the triangular enclosures, where complex thermal and flow interactions occurred due to proximity of the two side walls.
Periodic Thermal Storage: The Regenerator
Authors: Romie F. E.
Published: November 2010

The regenerator alternately stores and supplies heat to two gases which enter at different but constant temperatures and flow counter-currently and sequentially through the same flow passages for periods ta and tb. The periodic steady-state temperatures of the two gases and the regenerator solid are found as functions of time and position. The analysis is based on the use of polynomials of the position coordinate to represent the matrix temperature distributions at the beginning of each flow period. The subsequent gas and matrix temperatures are expressed in terms of functions which are readily evaluated by use of a computer. The initial, time average, and final temperatures of the gas leaving the regenerator are tabulated. Results for a single regenerator are applied to the rotating regenerator and to switched regenerators.
A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact
Authors: Cheng H. S.
Published: November 2010

A numerical solution of the elastohydrodynamic film thickness in an elliptical contact is developed. The two-dimensional Reynolds’ equation in the inlet region is solved by a finite-difference method. The deformation contour in the inlet region is calculated according to the classical Hertz theory for elliptical contacts. Results are presented as side leakage film reduction factors, which are defined as the ratios of the film thickness of the finite contact to that calculated by a line contact theory based on the same maximum Hertz stress. The results obtained for a b/a → ∞, which corresponds to a line contact, and for b/a = 1, which corresponds to a circular contact, agree with those obtained in [2]. Comparison with experimental data [1] indicates that this theory predicts a film thickness slightly higher than those measured by the experiment.
The Effect of Oil Supply on Cage and Roller Motion in a Lubricated Roller Bearing
Authors: Boness R. J.
Published: November 2010

Experimental results indicate that oil supply can have a significant effect on cage and roller motion in a lubricated roller bearing. A theoretical analysis is presented which enables cage and roller motion, for various operating conditions, to be predicted. The theoretical results imply that reducing the oil supply to a minimum value required to maintain full hydrodynamic conditions, reduces cage slip by up to 75 percent of its fully flooded value. This conclusion is consistent with existing experimental evidence.
A Study of the Growth Mechanism of Lenticular Carbides in Cyclically Stressed 52100 Steel
Authors: Borgese S.
Published: November 2010

The deformation bands which form in cyclically stressed AISI 52100 steel inner rings (during rolling contact) are studied by transmission electron microscopy. These deformation bands are regions where the temper carbides have dissolved and a well-developed cell structure has formed. Many of the deformation bands are bordered by lenticular-shaped carbides which form after prolonged cyclic stressing. The deformation bands were tempered in the electron microscope and most were found to be free of excess carbon since no precipitation of carbides occurred at normal tempering temperatures. In one specimen there was profuse precipitation of carbides at the cell walls indicating that an excess of free carbon had segregated around dislocations. It is concluded the regions free of excess carbon are due to the nucleation and growth of a lenticular carbide while no lenticular carbide formed at the deformation band which was supersaturated with carbon.
Influence of Flexibly Mounted Rolling Element Bearings on Rotor Response: Part I—Linear Analysis
Authors: Gunter E. J.
Published: November 2010

The paper evaluates the influence of damped, linear flexibly mounted rolling-element bearings on dynamic rotor unbalance response. The system analyzed is treated as a general four degree of freedom unbalanced rotor mounted on damped flexible supports and includes rotor gyroscopic effects. The rotor equations of motion are solved for synchronous precession over a wide range of speeds for various support conditions. Rotor performance curves on bearing amplitude, forces transmitted, phase angles as a function of speed for various values of support damping are computer plotted to illustrate rotor and bearing performance over a wide range of speed and operating parameters. Results indicate that forces transmitted to the bearings by the rotor synchronous unbalance response can be dramatically reduced by proper design of the bearing support characteristics.
Elastohydrodynamic Lubrication of a Spinning Ball in a Nonconforming Groove
Authors: Allen C. W. , Townsend D. P. , Zaretsky E. V.
Published: November 2010

An elastohydrodynamic solution for the spinning torque of a ball spinning without rolling in a non-conforming groove is presented. The solution is compared with experimental results using a synthetic paraffinic oil as the lubricant. A modified pressure-viscosity relation is proposed. The theory predicts increase in torque with stress and spinning speed and decreasing conformity. Good agreement was obtained between theoretical predictions and experimental results.
A Wear Equation for Bonded Solid Lubricant Films: Estimating Film
Wear Life
Authors: Finkin E. F.
Published: November 2010

A review of the literature establishes that the wear of bonded solid lubricant films for conditions of low average contact stress (say 10,000 psi and below), obeys an equation of the form V = KPL, where V is the wear volume, P is the normal load, L is the total sliding distance, and K is a constant. The limits on allowable bonded film thickness are examined, in the light of this equation, and it is shown that for low contact stress situations optimum film thickness is on the order of 10−3 in., rather than the popularly believed value of 10−4 in. This latter figure is the unfortunate consequence of applying data obtained at very high contact stress to contact conditions which are fundamentally different. Practical aspects of using this equation are explored by the development of specialized expressions which allow a design engineer or engineering analyst to estimate film wear life in terms of hours of operation or number of operating cycles. To aid in this purpose, wear coefficients for common solid lubricant-binder combinations are tabulated. A series of examples show how these expressions can be applied to typical situations. Equations are derived for the contact stress, area of contact, and average contact stress, for solid lubricant film covered surfaces under cylindrical or spherical contact. The use of these equations should replace the use of the Hertz contact equations in analyzing solid lubricated contact conditions.
Elastohydrodynamic Squeeze Films Between Two Cylinders in Normal
Approach
Authors: Herrebrugh K.
Published: November 2010

In this approach the fundamental hydrodynamic and elasticity equations that govern the problem are reduced to one single integral equation. Although the resulting integral equation in the present problem is at first sight similar in form to the one governing the steady rolling problem, on closer consideration it appears that the former constitutes a different type of equation, which is mainly characterized by the existence of a bifurcation point not occurring in the equation for steady rolling. By proper treatment of this complication, solutions also in the range of conditions where deformation may be expected to be large are obtained.
Steady-State Experiments on Rotating Externally Pressurized
Air-Lubricated Journal Bearings
Authors: Cunningham R. E. , Fleming D. P. , Anderson W. J.
Published: November 2010

Experimental load, stiffness and attitude angle data for a pair of 2 1/2-in-dia, 3 3/4-in-long externally pressurized air journal bearings are compared with two small eccentricity perturbation theories. Results show that load capacity is generally less than predicted by either theory, however, agreement with the small eccentricity pressure perturbation theory is better than with the linearized PH theory. Self-acting effects from journal rotation are greatest at the higher eccentricity ratios and lower supply pressures. Attitude angles vary with shaft speed as predicted by theory but are generally larger in magnitude. Measured air mass flow through the bearings agreed well with calculated values. Results were obtained for speeds up to 25,000 rpm and radial loads varied up to 20.2 psi.
An Investigation of the Squeeze Film Between Rotating Annuli
Authors: Allen C. W. , McKillop A. A.
Published: November 2010

The squeeze film between two plane annuli is examined theoretically and experimentally. The theoretical analysis considers the inertia due to the “centrifugal effect” but neglects all other inertia terms. The experimental investigation is by means of a free-falling spinning rotor which is decelerated by the squeeze film. Fluids examined are kerosene, SAE 10 oil, and a low melting point liquid metal. Good agreement between the predicted and actual decay rates is obtained for kerosene but that for the oil and liquid metal is only fair. The theoretical and experimental values of film thickness are in good agreement. The results for the liquid metal suggest the possibility of a thin air film between the rotor and the liquid metal.
Optimum Stiffness of Externally Pressurized Thrust Bearings in Turbulent Regime
Authors: Shen F. A.
Published: November 2010

The requirements for the optimum stiffness and the corresponding stiffness values of several types of externally pressurized, incompressible fluid-film thrust bearings under a turbulent Couette flow condition have been established. Study results indicate that the dimensionless optimum stiffness of the thrust bearing using any of the several types of geometrically restrictive compensators such as capillary and orifice, decreases with increasing Reynolds number. At high Reynolds numbers, the effect of varying Reynolds number on the stiffness becomes quite small. In contrast to the aforementioned restrictive compensation, the dimensionless stiffness of a constant-flow bearing design increases strongly with increasing Reynolds number. At Reynolds number of 106, the dimensionless stiffness varies approximately according to Re0.8.
The Analysis of Thermal Effects in a Full Journal Bearing
Authors: McCallion H. , Yousif F. , Lloyd T.
Published: November 2010

By means of numerical techniques, the behavior of a journal bearing of finite length running under steady load, including thermal effects, is investigated with reference to the two simpler models: the “isothermal” and the “adiabatic” cases. Different bearing operating parameters are obtained, which in the latter case are evaluated from the pressure and temperature distributions obtained from the simultaneous solution of the Reynolds and Energy equations. A simplified method, which uncouples the Reynolds and the Energy equations in the oil by neglecting all the pressure terms in the energy equation, is discussed and compared with the more exact numerical method of solving the two equations simultaneously. The case of heat being conducted through metal surfaces is described, with the assumption of zero net heat flow to the journal. In order to shorten the calculations, the uncoupling technique investigated in the adiabatic case is again used and the results obtained are compared with experimental findings.
Squeeze-Film Behavior for Porous Annular Disks
Authors: Wu Hai
Published: November 2010

An analysis is made of the squeeze-film behavior between two annular disks when one disk has a porous facing. The problem is solved analytically. Results are presented for pressure distribution, load-carrying capacity, and film thickness as functions of time.
The Dynamic Characteristics of a Turborotor Simulator Supported on Gas-Lubricated Foil Bearings—Part 2: Operation With Heating and Thermal Gradients
Authors: Licht L.
Published: November 2010

A high-speed rotor, supported by gas-lubricated foil bearings, is free from self-excited whirl and displays no loss of load capacity when vibrated at frequency equal half the rotational speed [1]. It is demonstrated here that in addition to tolerance of geometrical imperfections, misalignment, and foreign particles [3, 4], the foil bearing performs well at elevated temperatures and accommodates appreciable temperature gradients. The foil bearing is endowed with superior wipe-wear characteristics, and the flexibility of the foil accounts not only for the stability of the foil bearing but also for its forgiveness with respect to distortion, contamination, and contact.
Conditions for the Rupture of a Lubricating Film—Part II: New Boundary Conditions for Reynolds Equation
Authors: Coyne J. C. , Elrod H. G.
Published: November 2010

The pressure and flow conditions upstream of the rupture point of a lubricating film are analyzed with the theoretical model derived in Part I. The boundary conditions on the pressure and pressure gradient for use with Reynolds’ equation are developed as functions of a dimensionless parameter involving viscosity, speed, and surface tension. The load-carrying capacity which results from the use of these new boundary conditions does not differ appreciably from that of other boundary conditions in current use, except when the bearing load is extremely light, or when surface tension is large compared with the product of speed and viscosity. A simple experiment was conducted using a cylindrical lens bearing on a rotating oil-lubricated glass plate. Measurements of the bearing load and the location of the film attachment to the lens were in good agreement with the theory.
Dynamically-Loaded Journal Bearings: Numerical Application of the Mobility Method
Authors: Booker J. F.
Published: November 2010

For dynamically loaded journal bearings the classic analysis problem is prediction of the motion of a journal center under arbitrary loading. In most cases its speed and simplicity makes the mobility method seem the logical solution procedure. This paper reviews the method and details its numerical application, including particular examples for reciprocating machinery.
Air Bearings for High-Speed Mirrors Rotating in a Vacuum
Authors: Siryj B. W.
Published: November 2010

Current laser technology employs several types of scanners. A scanner consists of a high-speed rotating mirror attached to, or part of, a shaft. Supported on bearings and driven by a turbine or an electric motor, the scanner is used to deflect a light beam onto a recording medium. Rotor speeds of 120,000 r/min are common. If a mirror is rotated in air at such speeds turbulence will degrade the recording spot profile. The spot degradation is not apparent, however, if the mirror is rotated in a vacuum of 15 torr or less. This work has experimentally demonstrated the feasibility of rotating a 2-in. OD pyramidal mirror in a vacuum at 120,000 r/min. The mirror was fastened to an air turbine-driven rotor which in turn was supported on porous wall, carbon-graphite air bearings. The air bearings were supported by rubber O-rings to increase the operational stability range of the rotor. The mirror was located in a cavity whose pressure was maintained at 3.0 torr. A noncontacting dynamic face seal was used to isolate the air bearing area from the mirror cavity. Good correlation was obtained between the predicted and measured optimum journal load carrying capability. Static and dynamic methods were employed in determining the inversion point of the rotor. In the static approach the rotor was struck with a sharp radial blow, and the damped natural frequency of the system was recorded. This natural frequency coincides with the inversion point. In the dynamic analysis the inversion point manifested itself at a speed at which the orbiting amplitude of the rotor was maximum. The static approach predicted inversion at a speed of 48,000 rpm and was confirmed by dynamic testing which indicated a maximum rotor orbit at 50,000 rpm. Attitude tests conducted at speeds ranging from 0–120,000 r/min showed that the bearings and rotor constantly shifted in opposite directions as the speed was increased; however, the shift locations did repeat as the rotor was cycled between zero and maximum speed. It was noticed that throughout the entire speed range the eccentricity of the rotor was always in phase with that of the rubber O-ring supported bearings. At 120,000 r/min, the rotor orbit diameter was 15 microin., which is much less than that which would be encountered in the vicinity of the half-frequency whirl speed if the bearings were rigidly mounted.
Optical Analysis of Ball Bearing Starvation
Authors: Wedeven L. D. , Evans D. , Cameron A.
Published: November 2010

Elastohydrodynamic oil film measurements for rolling point contact under starvation conditions are obtained using optical interferometry. The experimental measurements present a reasonably clear picture of the starvation phenomenon and are shown to agree with theoretical predictions. Starvation inhibits the generation of pressure and, therefore, reduces film thickness. It also causes the overall pressure, stress, and elastic deformation to become more Hertzian. Additional experiments using interferometry illustrate: the cavitation pattern, lubricant entrapment, grease lubrication, ball spin, and edge effects in line contact.
Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact
Authors: Gohar R.
Published: November 2010

The effect of material properties upon the film thickness in elastohydrodynamic point contact is demonstrated with a rolling ball and plate machine. A 220 fold range of Young’s modulus is employed and a maximum Hertzian pressure of 5 × 105 lb f/in2 is reached. The oil film, which is measured by interferometry, shows no significant alteration at such high pressures, and is also fairly insensitive to the choice of bounding materials. Using a technique similar to that employed by Crook, the rolling friction between a tungsten carbide and a glass plate is found and compared with theory. The effect of spin is investigated and found to be slight.
Random Process Model of Rough Surfaces
Authors: Nayak P. Ranganath
Published: November 2010

Rough surfaces are modeled as two-dimensional, isotropic, Gaussian random processes, and analyzed with the techniques of random process theory. Such surface statistics as the distribution of summit heights, the density of summits, the mean surface gradient, and the mean curvature of summits are related to the power spectral density of a profile of the surface. A detailed comparison is made of the statistics of the surface and those of the profile, and serious differences are found in the distributions of heights of maxima and in the mean gradients. Techniques for analyzing profiles of random surfaces to obtain the parameters necessary for the analysis of the surface are discussed. Extensions of the theory to nonisotropic Gaussian surfaces are indicated.
Passively and Actively Controlled Externally Pressurized Oil-Film Bearings
Authors: Morsi S. A.
Published: November 2010

The first section of this paper is concerned with the description of a hydrostatic bearing when compensated by passive orifice or capillary type restrictor. In the second section a survey of the various types of active restrictors is outlined. Active restrictors considered include the constant flow valve, integral control valve, diaphragm controlled restrictor, and the tapered spool controller. A comparison of the film stiffness and power requirements for actively and passively compensated hydrostatic bearings is given in the third section of this paper, with the particular aim to facilitate, for the designer, the choice of the most suitable restrictor for any particular application.
Lubrication of Porous Journal Bearings
Authors: Cusano C.
Published: November 2010

An analytical solution for the performance characteristics of finite porous journal bearings is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for design variables of 0.0001, 0.001, 0.01, and 0.1. The load capacity obtained by using the finite bearing theory is compared to the load capacity obtained by using the short-bearing approximation and the infinite-bearing approximation.
Application of Finite Element Methods to Lubrication: An Engineering Approach
Authors: Booker J. F. , Huebner K. H.
Published: November 2010

The finite element method of lubrication analysis is presented for the novice from a viewpoint closely analogous to that of the familiar direct stiffness method of structural analysis. The lubricant film is seen as a system of component elements interconnected at nodal points where flows are summed and pressures (but not necessarily thicknesses, viscosities, or densities) are equated. System properties are deduced from component properties and connections. Detailed equations needed for solution of practical problems are given in Appendices and their use is illustrated in Examples.
A Bulk-Flow Theory for Turbulence in Lubricant Films
Authors: Hirs G. G.
Published: November 2010

The purpose of this study on the turbulent lubricant film is: 1 To give a brief outline of a new theory called bulk-flow theory; 2 To investigate to what extent results of theories based on law of wall and mixing length concept agree with the newly developed theory; 3 To provide a theoretical basis for the design of bearings lubricated by fluids of low kinematic viscosity.
The Rate of Change of Film Thickness in the Elastohydrodynamic Squeeze Film Process
Authors: Conway H. D.
Published: November 2010

When analyzing the problem of calculating the pressures developed during the normal approach of two bodies through an oil film, it is usual to assume that the rate of change of film thickness does not vary along the film at any given time. The ranges of validity of this assumption are estimated for the case of thin elastic layer indented through an oil film by a rigid cylindrical roller.
Gas Turbine Engine Mainshaft Roller Bearing-System Analysis
Authors: Rumbarger J. H. , Filetti E. G. , Gubernick D.
Published: November 2010

An interdisciplinary systems analysis is presented for high-speed gas turbine engine mainshaft roller bearings which will enable the designer to meet the demands for ever higher rotative speeds and operating temperatures. The latest elastohydrodynamic experimental traction data are included. Analytical results cite a need for better definition of the rolling friction portion of the total traction. A fluid mechanics model for the detailed analysis of fluid drags is developed based upon a turbulent vortex-dominated flow and includes the effect of lubricant flow through the bearing. A complete thermal analysis including dynamic and thermal effects upon bearing dimensions and resulting clearances is also included. Heat transfer coefficients are given in detail. Shaft power loss and cage slip predictions as a function of load, speed, and lubricant supply correlate well with available experimental data.
Inlet Shear Heating in Elastohydrodynamic Lubrication
Authors: Greenwood J. A. , Kauzlarich J. J.
Published: November 2010

In EHL, the oil film thickness of rollers is controlled by the rate at which the oil is drawn into the conjunction of the disks by the moving surfaces of the rollers. The theory often assumes isothermal conditions in the inlet although it can be shown that the maximum shear rate often exceeds 106 sec−1, even in pure rolling. A theoretical analysis is presented for the oil temperature rise in the inlet of rollers, and the result is applied to predict the consequent film thickness. It is found that thermal effects on film thickness are only negligible at low rolling speeds. A comparison with experiment supports the conclusion that the thinning of the film thickness below that predicted by isothermal theory is substantially explained by inlet shear heating of the lubricant.