Thermoelastohydrodynamic Analysis of Fixed Geometry Thrust Bearings Including Runner Deformation

A thermoelastohydrodynamic theory for the analysis of sector thrust bearings is presented. The analysis includes the generalized Reynolds equation and a fully elliptic three-dimensional energy equation in the film. In addition, full three-dimensional heat transfer is allowed in the pad while axisymmetric conduction is allowed in the runner. Three-dimensional elastic deformation due to mechanical and thermal loading is allowed in the pad while axisymmetric mechanical elasticity is allowed in the runner. The performance of a parallel tapered-land thrust bearing including runner deformation effects is analyzed as a function of different models. It is seen that mechanical deformation of the pad affects the operating characteristics only slightly while thermal deformation of the pad can cause large increases in operating temperature. The runner deformation effects can include a reduction of the maximum film temperature at slight deformation or a large increase in film temperature at the inner radius of the pad at larger deformations.     

Thermo-hydrodynamic analysis of the finite slider pad—Adiabatic conditions

Results are presented of a three-dimensional analysis of the fluid film under a square fixed-geometry inclined slider pad. The analysis is applied to adiabatic conditions as a first step in the investigation of transverse viscosity gradient effects for a wide range of operating conditions. The predicted performance is compared with that obtained on the assumption of viscosity constant through the film thickness. The effect of the transverse viscosity variation is shown to reduce or enhance pressure generation according to the magnitude of two characteristic non-dimensional groups. The results are also compared with performance predicted on the basis of constant viscosity theory using an “effective” viscosity derived from an overall film energy balance.     

卧式水电机组用径向滑动轴承热弹流特性分析

研究轴颈挠度和瓦块表面热弹变形对卧式水电机组径向滑动轴承静态润滑性能的影响。推导考虑轴颈挠度和轴瓦热弹变形后的油膜厚度表达式;用中心差分法结合ANSYS软件联立求解雷诺方程、能量方程、固体热传导方程、密度方程、黏度方程和轴瓦热弹变形等,得到径向滑动轴承的热弹流润滑(TEHD)特性,并与不计入轴颈挠度及轴瓦热弹变形的油膜动压润滑特性进行比较。结果表明:在考虑轴颈挠度和轴瓦瓦面热弹变形的影响后,油膜压力、温度、厚度沿着轴承宽度中心线的对称特性消失;油膜压力峰值增大,峰值点位置由轴向中心区偏移至出口区;油膜温度峰值增大,最高温度发生在出口区;润滑区内的最小油膜厚度大幅度减小,油膜最小厚度处于出口侧边界附近;轴承润滑流量减小,损耗略有增大;轴承稳态运行时,轴颈偏位角基本一致。     

Temperature distribution in the lubricant film of sliding bearings under intensive lubricant-wall heat transfer conditions

It is assumed that the existence of some discontinuities in the experimentally determined circumferential temperature distribution of journal bearings is determined by the lubricant-wall heat transfer and the local hydrodynamic flow conditions. From this hypothesis a simplified theoretical model is proposed which uses adequate boundary conditions and reveals the existence of these discontinuities.The theory is developed by assuming both constant viscosity and a mean viscosity, constant across the film thickness, but varying with its length.     

Simultaneous monitoring of oil film thickness and temperature in fluid film bearings

This paper reports on the application of an eddy current sensor with an active compensation for changes in sensor temperature to simultaneous monitoring oil film thickness and temperature in a tilting pad thrust bearing. Sensor design, calibration procedure, sensitivity and accuracy are described. Test equipment along with sensor mounting is also presented. Tests were run at different rotational speeds and bearing loads as well as different supplied oil flow rates to evaluate sensor performance in various operating conditions. During the tests film thickness and temperature were simultaneously measured. Temperatures were compared with data from thermocouples installed in the pads and thermistors mounted in the collar. Tests have shown that the sensor can successfully be used to reliably monitor the conditions within the bearing.     

The thermal behaviour of thin cylindrical shells—I. Heat transfer and harmonic analysis

The combined heat transfer and thermal stress analysis of thin cylindrical shells is considered in this and a subsequent paper. This paper presents two typical heat transfer models and the harmonic analysis which is used to represent the temperature distributions as double Fourier coefficients. These models are (i) a circular hot spot caused by a postulated loss of part of the internal refractory lining in a high temperature cylindrical reactor vessel and (ii) a heated “band” caused by solar heating on a horizontal storage vessel. In the case of the hot spot the inside and outside surface temperature distributions vary independently in the axial and circumferential directions, with linear transition through the thickness. In the simpler case of solar heating, the through-thickness temperature gradient is negligible and the temperature only varies around the circumference. The use of the double Fourier coeficients to obtain the displacements and stresses is described in Part II     

Rotordynamic modelling of a hydrodynamic pivoted-pad thrust bearing

The rotordynamic characteristics of a hydrodynamic pivoted-pad thrust bearing are investigated in this paper. Firstly, the rotordynamic coefficients of a single pad are defined in the case of small perturbation. The Reynolds equation and its perturbed forms are solved by using the boundary element method (BEM). An iterative procedure is proposed to determine the static positions of the thrust pads when the static tilt of the runner is considered by using the Newton–Raphson method. The characteristics of the thrust bearing are obtained by using an approach based on a coordinate transformation principle.     

The Coupling of Waviness and Heating in a Seal

Thermoviscous lubricant flow in seals and bearings is treated as a Couette flow, and a fully coupled perturbation flow, which results from waviness of the boundary, and which gives rise to uneven heat input into the solid boundaries. Differences in modes of heat transfer within the seal rings and out to the environment are separable, and determine the thermoviscous behavior of the film in a simple way. The temperature perturbation, or wave, in the film is an order of magnitude smaller than the perturbation of heat generation, justifying the assumption of isothermal and isoviscous flow.

Calculations show that materials such as C and SiC cannot be idealized as insulators when run against metals.     

Effects of thermal contact resistance on film growth rate in a horizontal MOCVD reactor

Effects of thermal contact resistance between heater and susceptor, susceptor and graphite board in a MOCVD reactor on temperature distribution and film growth rate were analyzed. One-dimensional thermal resistance model considering thermal contact resistance and heat transfer area was made up at first to find the temperature drop at the surface of graphite board. This one-dimensional model predicted the temperature drop of 18K at the board surface. Temperature distribution of a reactor wall from the three-dimensional computational fluid dynamics analysis including the gap at the wafer position showed the temperature drop of 20K. Film growth rates of InP and GaAs were predicted using computational fluid dynamics technique with chemical reaction model. Temperature distribution from the three-dimensional heat transfer calculation was used as a thermal boundary condition to the film growth rate simulations. Temperature drop due to the thermal contact resistance affected to the GaAs film growth a little but not to the InP film growth.     

Flow and heat transfer measurements of film injectant from a row of holes with compound angle orientations

An experiment has been conducted on the flow and heat transfer characteristics of film coolant injected from a row of five holes with compound angle orientations of 35° inclination angle and 45° orientation angle. The Reynolds number number based on the mainstream velocity and injection hole diameter 3.58 x10⁴. Three-dimensional velocity, film cooling effectiveness and heat transfer coefficient data are presented at three different mass flux ratios of 0.5, 1.0 and 2.0. Flow entrainment has been found between the vortices generated by adjacent injectants. The injectant with compound angle orientation entrains not only the mainstream boundary layer flow but also the adjacent injectant. Because of the flow entrainment, the injectant. With compound angle orientation is characterized by a single vortex while two bound vortices are usually observed in the case of simple angle injection. The strength of the secondary flow depends strongly on the mass flux ratio, which shows significant influence on the film cooling effectiveness and heat transfer coefficient.     

Conditions of crank existence for a particular case of the RSSR linkage

Necessary and sufficient conditions of motion transfer for a particular case of the RSSR linkage is further derived and simplified. This particular case is considered when the frame is coincided with input and output axes distance, which may also be called as “simply skewed form” of RSSR. The results show that the conditions of crank existence for this particular case can be represented in a way quite resembling the Grashof criterion applicable to planar four bar linkages, and thus are of very simple expression and geometric sense. (The term “simple” normally implies that overhand computation by “rigours” programming may not be needed.)     

A method of temperature monitoring in fluid film bearings

In the present paper a method to improve temperature monitoring of fluid film bearings is described. The method is tested in an industrial tilting pad thrust bearing. Test results for steady state and transient operating conditions are reported. Temperatures monitored by a thermocouple through the utilisation of the proposed method are compared to those measured by thermocouples in the pad backing and in the collar. The method is also tested on a PTFE-faced bearing. Test results show that the proposed method improves sensitivity to thermal transients in conventional babbitted bearings and provides adequate means of temperature monitoring in the PTFE-faced bearings.     

负压下热管管外降膜蒸发的换热特性研究

热管作为一种高效的传热方式,以其优良的传热性能在工业生产的不同领域中得到了广泛应用.根据流体边界层理论,研究了负压下热管管外降膜蒸发过程中速度边界层和热边界层的形成规律,给出了速度边界层和热边界层厚度的计算函数.在此基础上得到了该模型下热管管外降膜蒸发换热系数的计算方法,推导出相关的计算公式.分析了真空度、喷淋负荷以及传热温差等对热管管外降膜蒸发传热性能的影响,为热管在负压下管外降膜蒸发的工程应用和研究提供了指导.     

The free vibrations of a thin circular finite rotating cylinder

The natural frequencies of a finite circular thin cylinder are obtained by employing an exponential matrix expansion of the so-called “fundamental matrix”. It is shown that the method is general enough and able to handle any system of linear differential equations of constant coefficients together with arbitrary boundary conditions. Results are given for rotating cylinders with clamped and free edges. The vibration frequencies of a stationary finite cylinder, previously obtained by other methods of solution, are used as a check on the present method with the special case of zero spinning velocity.     

利用边界层理论确定弹性金属塑料瓦油膜能量方程的进油温度边界条件

针对推力轴承的基本结构,利用边界层理论确定弹性金属塑料瓦（EMP瓦）油膜能量方程的进油温度边界条件,结合“三峡推力轴承方案”中EMP瓦推力轴承数据,分析考虑热边界层对进油温度影响时,EMP瓦推力轴承润滑性能的变化情况。计算结果表明：考虑热边界层对进油温度的影响时,进油平均温度和最高油膜温度均有所升高,最大压力也有所增加,最小油膜厚度、流量及功耗都有所下降,说明热边界层对推力轴承的润滑性能产生了一定的影响。     

Simulation of wall film condensation with non-condensable gases using wall function approach in component thermal hydraulic analysis code CUPID

In the containment of nuclear power plants, wall film condensation occurs with non-condensable gases under accident conditions. With non-condensable gases, condensation heat transfer on the containment wall can be degraded significantly because of the accumulation of non-condensable gases near the condenser wall; therefore, an investigation into the wall condensation heat transfer is of great importance to nuclear reactor safety. In this study, wall film condensation with non-condensable gases was simulated using the CUPID code. To evaluate the heat and mass transfer coefficients, a wall function approach was adopted to save the computational cost. To validate the model, a COPAIN condensation experiment was simulated using CUPID. The calculation results were compared with the COPAIN experiment data and results from the commercial CFD code (STAR-CCM+) results, which used the resolved boundary layer approach. From the comparison, good agreements were obtained between the CUPID code and the other results.     

Surface tension-affected laminar film condensation problems

Following Nusselt [1] there were few developments in the theory of laminar film condensation until the advent of digital computers in the 1950s. Approximations used by Nusselt, namely neglect of inertia, convection and surface shear stress (for the free convection case) were then found to give very accurate results for the normal practical range of vapour-to-surface temperature difference. Subsequent developments treated the gas phase and dealt with superheated vapour, condensation in the presence of a non-condensing gas and condensation of mixtures. The temperature discontinuity at the vapour-liquid interface has been studied experimentally and theoretically since the 19^th century and more recently in the 1960s by experiments using liquid metals. In the present paper the focus is on the condensate film and, in particular, the role played by surface tension which is important for condensation on finned surfaces and in microchannels, owing to abrupt changes in curvature of the condensing surface. The way in surface tension affects condensation heat transfer and difficulties which arise are first illustrated by reference to condensation on a smooth horizontal tube, where the effect of surface tension on heat transfer is minimal. Practically more relevant cases of condensation in microchannels and on finned surfaces and are then discussed and recent results presented.     

Free boundary of lubricant film in ferrofluid journal bearings

The growing interest in ferrofluid bearings is caused by their excellent self-sealing ability. The understanding of behaviour of ferrofluid film boundary adjacent to ambient air is crucial for the proper design of the sealing unit of ferrofluid bearings. This paper is the first attempt to predict the shape of a ferrofluid free boundary in the presence of a static load and magnetic field. Analysis involves simultaneous integration of the Reynolds equation and the free boundary equation using perturbation technique with respect to shaft eccentricity. Magnetic field is shown to flatten ferrofluid free boundaries as well as to reduce cavitation region; both effects diminishing lubricant leakage.     

Stiffness and damping characteristics of finite width journal bearings with a non-newtonian film and their application to instability prediction

Starting from the most general fluid flow equation of the power law type expressing rate of shear in terms of powers of shear stress for non-Newtonian lubricants a modified form of Reynolds'equation is derived for dynamically loaded finite width journal bearings. The finite difference technique with successive over relaxation is used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution. From the equations of fluid film forces, the values of stiffness and damping coefficients are obtained for a linearised case. The shear thinning effect of non-Newtonian lubricants at higher shear rates is shown to decrease the stiffness and damping values. Finally, the stability limit for such a bearing is obtained for different values of the nonlinear factor.     

Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton–Raphson method

Thermoelastohydrodynamic lubrication (TEHD) analysis is presented to investigate the static performance of tilting-pad journal bearings. A completely numerical solution is obtained. The Newton–Raphson method is employed to predict the bearing characteristics of the hydrodynamic pressure, the eccentricity and the pad attitude angles simultaneously. For the temperature calculation, three-dimensional (3D) energy equations for the fluid under each pad and 3D heat transfer equations for the pads are solved using a sequential sweeping method. The elastic deformation and thermal expansion of each pad are calculated with the 20-node isoparametric finite element method. It is found that the Newton–Raphson method is a smart and efficient method. The results show that the elastic deformation due to the hydrodynamic pressure and the influence of the temperature elevation play an important role in the calculated bearing system.