The lubrication and heat transfer designs of bearing chamber depend on an understanding of oil/air two-phase flow. As initial and boundary conditions, the characteristics of ligament and droplet generation by oil film on rotating parts have significant influence on the feasibility of oil/air two-phase flow analysis. An integrated model to predict the oil film flow, ligament number, and droplet Sauter mean diameter (SMD) of a rotating disk, which is an abstraction of the droplet generation sources in a bearing chamber, is developed based on the oil film force balance analysis and wave theory. The oil film thickness and velocity, ligaments number, and droplet SMD are calculated as functions of the rotating disk radius, rotational speed and oil volume flow rate and oil properties. The theoretical results show that the oil film thickness and SMD are decreased with an increasing rotational speed, while the radial, transverse velocities, and ligament number are increased. The oil film thickness, radial velocity, and SMD are increased with an increasing oil flow rate, but the transverse velocity and ligament number are decreased. A test facility is built for the investigation into the ligament number of a rotating disk, and the measurement of ligament number is carried out by means of a high speed photography.
Bearing chamber is an important component of aeroengine and it gives a guarantee of shaft running reliably. To address the demands of modern aero engines development tendency, for example, higher compressor pressure ratio, operating temperature, and shaft speed, the need to promote the performance of bearing chamber becomes more obvious, while the sufficient lubrication and cooling designs of bearing chamber relate to the understanding of oil/air two-phase flow which includes air, oil droplets, and oil film. Therefore, special efforts have been made to carry out the research on that in recent years.
Several researchers have conducted the theoretical and experimental investigations onto the oil/air two-phase flow in bearing chamber. Their works focused on the characteristic of oil droplets which are atomized by rotating parts [
In the scope of oil droplet characteristics in bearing chamber, some experimental works have been carried out. Wittig et al. [
However, little theoretical work about the oil droplet which is atomized by rotating parts in the bearing chamber could be found, and the experiments which are suitable for various conditions are extremely time and finance consuming. Therefore, it is necessary to investigate the droplet generation characteristics in the bearing chamber. In this paper, firstly, a rotating disk structure which is an abstraction of droplet generation sources in the bearing chamber is determined. And then the centrifugal force which exerts on the oil film flowing on a rotating disk is proposed. With the force balance and Newton fluid behavior, the oil film thickness and velocity are calculated. Secondly, when the oil film reaches the rotating disk edge, the oil film wave characteristic is discussed and the gas pressure, surface tension force, inertia force, and viscous shear force which act on the wavy film are determined. With that the equation which involves wave growth rate is derived. The wave growth rate can evaluate the oil film disintegration. Solving the equation, the ligament number and oil droplet Sauter mean diameter (SMD) are obtained lastly. A test facility for the investigation into the droplet generation characteristics of a rotating disk is built. The measurement of ligament number is carried out by means of a high speed photography. The comparison of theoretical and experimental results supports the reliability of the proposed method. The work may be helpful to improve the research system of oil/air two-phase flow in the bearing chamber.
The droplet generation process in an aeroengine bearing chamber is shown in Figure
Droplet generation and oil/air two-phase flow in a bearing chamber.
As mentioned in [
An abstraction of the droplet generation sources in a bearing chamber.
A simplified structure for investigation into the droplet generation characteristics in the bearing chamber is determined in Section
Calculation scheme for the theoretical model.
In Figure
Oil film control element and forces on its surfaces.
Oil film control element
Forces on the control element
Prior to the proposition of oil film velocity and thickness analysis model, some reasonable assumptions have been made as follows. (1) The oil film flowing on the rotating disk is continuous, and its velocity and thickness distributions are axisymmetric (i.e., not vary in transverse direction). (2) Due to the extremely thin thickness, the pressure in film is considered constant and equal to that in environment. (3) Compared to the centrifugal force, the gravitational force is neglected. (4) The other inertial forces are omitted except for centrifugal force. (5) The oil is a Newtonian fluid with a constant viscosity and incompressible, (6) The oil has no relative movement at the interface between oil film and rotating disk.
Because of the coordinate system
The components of the centrifugal force
Substituting (
The radial component of centrifugal force
As shown in Figure
Using (
Equation (
The integration constant
For a Newtonian fluid, the relation between viscous shear stress and velocity gradient is generally known as
Using (
Equation (
The integration constant
For a steady and incompressible flow, the total volume flow rate of the oil film at radial position
Substituting (
From (
In much the same way as the derivation of that in radial direction, the oil film viscous shear stress
The elemental radial viscous shear stress
Substituting (
Equation (
At the free surface of the oil film, the transverse viscous shear stress
Similarly, with the constitutive equation for a Newtonian fluid, one obtains the relation between transverse viscous shear stress
Equation (
Obviously, the integration constant
The absolute transverse velocity of the oil film
The oil film flowing on the rotating disk will become unstable due to the aerodynamic interaction between the oil film and its surrounding gas. The oil film instability is described by a wavelike motion. Generally speaking, the oil film wave amplitude is lower before spreading to the edge of the rotating disk. However, when the oil film flowing over or just off the edge, its velocity is very high and the wave amplitude will be increased strongly. Until the wave amplitude reaches a critical point, the film is disintegrated. At this point, the tears appear and the fragments of film whose lengths are equal to one wavelength are broken. Then, the surface tension forces these fragments to turn into lots of ligaments around the edge of rotating disk. Figure
Schematic diagram of the oil film wave structure around rotating disk.
In Figure
Dombrowski et al. [
Section of the wavy oil film and the forces.
Section of the wavy oil film
Forces on the wavy oil film section
In addition, the gas surrounding the film will also be disturbed due to the interaction by wavy film. The displacement in
At the position of
The calculation of the forces are as follows.
Thus, the resultant gas pressure force in
After canceling out the term of
Lastly, the net viscous shear force on the oil film section
For the two interfaces of the oil film which are parallel to each other,
Equilibrium states of the oil film section in Figure
Substituting (
For a sine wave, substituting the wave motion equation (
From (
The transverse velocity
In recent years, many researchers have carried out the gas flow analysis in a bearing chamber [
The wave film will disintegrate at its most unstable state and the fragments which are caused by disintegration rapidly contract into lots of ligaments under the action of surface tension. Based on the classical Rayleigh-Weber theory, the disturbance with maximum growth rate
Equations (
The ligament diameter
The geometry and operating parameters which are adopted in the theoretical analysis are shown in Table
Geometry and operating parameters.
Rotating disk radius |
45 | 60 | 75 |
Rotational speed |
4000 | 6000 | 8000 |
Oil volume flow rate |
75 | 150 | 225 |
Oil density |
903.5 | 953.5 | 1003.5 |
Oil dynamic viscosity |
0.0351 | 0.0276 | 0.0201 |
To illustrate the validity of the assumptions which are mentioned in Section
Computational domain of oil film on a rotating disk.
The oil film flowing on the rotating disk is calculated using the commercial CFD package CFX. Under the conditions of
Comparison of data by (
Figure
Influence of rotational speed on oil film thickness.
Figure
Influence of rotational speed on oil film average velocities.
Figures
Influence of oil volume flow rate on oil film thickness.
Influence of oil volume flow rate on oil film velocity.
Figures
Variation in ligament number and droplet SMD with rotational speed.
Variation in ligament number and droplet SMD with rotating disk radius.
Figure
Variation in ligament number and droplet SMD with oil flow rate.
As shown in Figure
Variation in ligaments number and droplets SMD with oil properties.
Oil density
Oil dynamic viscosity
The test facility structure of rotating disk ligament number analysis is shown in Figure
Rotating disk ligament number analysis test facility. 1: power; 2: air circuit breaker; 3: inverter; 4: variable frequency motor; 5: diaphragm coupling; 6: rotational disk; 7: photography lights; 8: high speed camera; 9: computer; 10: thermometer; 11: pressure gage 12: flow control valve; 13: volumetric flow meter; 14: pressure reducing valve; 15: check valve; 16: stop valve; 17: relief valve; 18: oil pump; 19: motor; 20: level gauge; 21: filter; 22: oil heater; 23: oil reservoir; 24: thermocouple; 25: temperature controller.
Structure diagram
Physical map
The rotational disk diameter is 150 mm. The stationary housing inner diameter and width are 350 and 159 mm. The high speed camera is Phantom v4.3 which is produced by Vision Research Company, and the detailed information about the camera is shown in [
Properties comparison of L-HM 32 hydraulic oil and Mobil Jet 2 lubricant oil.
L-HM 32 | Mobil Jet 2 | |
---|---|---|
Kinematic viscosity (mm2/s) | ||
40°C | 30.69 | 27.6 |
100°C | 5.28 | 5.1 |
|
||
Density (kg/m3) | 874.8 | 1003.5 |
The experimental objectives of this paper, namely, the quantitative characterization of ligament, required applying technique for ligament visualization. In this paper, the high speed camera is used to obtain a detailed documentation of the oil ligament around the rotating disk edge. The high speed camera is linked to a computer and the oil ligaments are monitored on a screen. And then it is recorded on a hard disk and examined in detail using picture processing software Cine Viewer Application which is attached to the high speed camera. As shown in Figure
Measuring techniques of oil ligaments.
Under the operating parameters, rotating disk radius
Comparison of theoretical and experimental ligament.
It is a pity that, because the test facility vibrates obviously at high shaft speed, the shaft speeds of experimental analysis are lower than those of bearing chamber. As a supplement, with the help of others’ experimental data [
Comparison of theoretical and experimental oil droplet SMD.
|
|
|
|
|
---|---|---|---|---|
Experimental data [ |
Theoretical data | |||
100 | 5000 | 103 | 212.0 | 201.2 |
55 | 8500 | 60 | 121.2 | 109.8 |
65 | 3450 | 50 | 228.4 | 212.1 |
The present investigation focused on the characterization of oil film on a rotating disk, as well as ligament number and droplet SMD, which are generated by integration of oil film. From the calculation, it is observed that with increasing rotational speeds, the oil film thickness is decreased, while the radial and transverse velocities are increased; the rotating disk radius has no effect on the oil film thickness and velocity; with increasing oil flow rates, the thickness and radial velocity are increased, but the transverse velocity is decreased; with increasing disk rotational speeds and radiuses, the ligament numbers are increased, while with the increasing oil flow rates and viscosities the ligaments numbers are decreased; the oil density has less effect on the ligament number; with increasing rotational speeds, disk radiuses, and oil densities, the oil droplet SMD is decreased, while with increasing oil flow rates and viscosities the ligaments numbers are increased.
A test facility is also built, and the ligament numbers are measured under different conditions. The comparisons between theoretical and experimental ligament number, as well as oil droplet SMD, show that the theoretical method is reliable. The work of the present paper may contribute to understanding the oil droplet generation in a bearing chamber. However, the oil droplet generation in bearing chamber was strongly affected by more factors. Additional and more advanced approaches are necessary to further improve the theoretical model.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (Grant no. 51275411).