The Geared Turbofan technology is one of the most promising engine configurations to significantly reduce the specific fuel consumption. In this architecture, a power epicyclical gearbox is interposed between the fan and the low pressure spool. Thanks to the gearbox, fan and low pressure spool can turn at different speed, leading to higher engine bypass ratio. Therefore the gearbox efficiency becomes a key parameter for such technology. Further improvement of efficiency can be achieved developing a physical understanding of fluid dynamic losses within the transmission system. These losses are mainly related to viscous effects and they are directly connected to the lubrication method. In this work, the oil injection losses have been studied by means of CFD simulations. A numerical study of a single oil jet impinging on a single high speed gear has been carried out using the VOF method. The aim of this analysis is to evaluate the resistant torque due to the oil jet lubrication, correlating the torque data with the oil-gear interaction phases. URANS calculations have been performed using an adaptive meshing approach, as a way of significantly reducing the simulation costs. A global sensitivity analysis of adopted models has been carried out and a numerical setup has been defined.
To reduce the environmental and climate impact from air traffic, the aeroengine industry and research community have been striving towards alternative engine configurations, with the aim of a significant reduction of specific fuel consumption. It is widely acknowledged that a SFC reduction can be achieved by increasing the engine bypass ratio. This is a key parameter to effectively improve propulsion efficiency, as well as reducing jet noise and engine emissions [
The Geared Turbofan (GTF) technology is one of the most promising engine configurations to increase bypass ratio. In this engine, a power epicyclical gearbox is interposed between the fan and the low pressure spool. Thanks to the power gearbox, fan and low pressure spool can turn at different speed. This brings some advantages: firstly, the fan speed can be reduced, leading to lower acoustic emissions; secondly, the speed of the low pressure spool can be sensibly increased, resulting in a more compact and efficient core engine.
The SFC is directly affected by the transmission efficiency of the gearbox and indirectly by the weight and the size of the cooling system. Therefore the gearbox efficiency becomes a key technology to achieve the benefits introduced by the GTF architecture. Although gearbox efficiency is higher than 99%, power losses can be equally important in high power application like this. Further improvement of efficiency can be achieved developing a physical understanding of losses within the transmission system.
Sources of power losses in a gearbox can be classified into two groups [
For very high speed (pitch velocity above 100 m/s) and high power gearboxes, typical of aeronautical applications, the lubrication is provided using nozzles to create small oil jets that feed oil into the meshing zone. It is essential that the gear teeth are properly lubricated and that enough oil gets into the tooth spaces for sufficient cooling, to ensure gearbox reliability. A good understanding of the oil jet behaviour inside the gearbox is therefore desirable, to minimize lubrication losses and reduce the oil volume involved.
Akin et al. [
It should be noted that the experimental visualization of this kind of multiphase flow is difficult due to the high speeds of the gears; thus, computational fluid dynamics (CFD) simulations can provide a more in-depth understanding of the oil-gear interaction phenomena. Arisawa et al. [
The aim of the present work is to study the oil injection losses by means of CFD simulations. In order to reach a deeper knowledge of this loss, a comprehensive numerical study of a single oil jet impinging radially on a single spur gear has been carried out using the VOF method. The main objective of this work is to predict the resistant torque due to a high speed spur gear subject to oil jet lubrication, while the oil recirculation losses are not considered. Full unsteady simulations with moving meshes were carried out. The main challenges regarding this analysis are large three-dimensional domain that leads to high computational cost, two-phase transient simulation, high speed free surface flow, and stationary and rotating domains. The VOF method, described by Hirt and Nichols [
The aim of this work is to study the forces exchanged between a high speed spur gear and the lubricating jet. To reach this goal, a representative geometry was defined (Figure
Sketch of reference geometry.
The gear rotates at typical velocities of a high speed transmission. The lubricating jet is introduced by a cylindrical duct set up on the casing surface. The oil is directed towards the rotor axis, impinging on the gear face center. No outlet has been defined because as only few tooth passages were simulated, the lubricant volume injected is negligible with respect to the volume of air in the system.
The geometrical dimensions are summarized in Table
Dimensionless geometrical parameters.
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126.7 | 158.3 | 105 | 45.8 | 3.3 | 6.7 | 1 | 38 |
The expected average resistance torque produced by the oil jet lubrication can be estimated calculating the oil momentum variation during the interaction with the tooth. With reference to Figure
Sketch of 0D-Model.
The simple model provides a resistant torque equal to
The operating conditions used in the simulations are representative of aeroengine cruise conditions: subatmospheric pressure condition, temperature that was matched with the typical operating value within gearbox systems, the ratio between the pitch line and the oil jet velocities that was fixed to 4.
The choice of such conditions takes effect on the oil jet behaviour. The lubricant has to cross a rotating air flow before to impact on the gear teeth. As it will be shown in Section
To a first approximation, the problem can be treated as an injection of liquid into a high speed crossflow (see Figure
Sketch of liquid jet in the air crossflow.
As the oil jet hits the high speed gear teeth, a fast momentum transfer occurs. To identify the order of magnitude of the different phenomena involved, a dimensionless groups analysis has been carried out. The useful dimensionless groups for this multiphase system are listed below:
In order to carry out a global sensitivity analysis of grid adaptation strategy and model parameters, a simplified geometry has been defined. Subsequently, the resulting numerical setup has been adopted for the reference geometry’s simulation. Two simplifications have been used: symmetry boundary conditions, simplified geometry.
The symmetry boundary condition has been used, exploiting the geometrical symmetry of the problem with respect to the oil jet axis. This condition leads to a considerable reduction of the computational cost, as only one half of the geometry has to be simulated. Preventing the flow from crossing the boundary, symmetry condition introduces an approximation in the URANS simulation, in fact the velocity components of the lubricant jet aligned with rotational axis are neglected. The impact on the resistant torque calculation due to this boundary condition will be evaluated in this work. The simplified geometry has been obtained by cutting the reference geometry with two radial planes passing through the gear teeth, as represented in Figure
Simplified geometry definition.
A sketch of the simplified computational domain is reported in Figure velocity components: 0, 0, oil volume fraction: 1, turbulence equations: a low intensity and a length scale equal to
Simplified computational domain.
Computational domain of reference geometry.
The reference pressure value was fixed at a point located on the symmetry plane highlighted in Figures
The computational domain has been subdivided into two domains: a rotating domain that encompasses the gear and the flow surrounding it and a stationary domain for the flow outside the gear region. The flow field within the rotor zone has been solved using the rotating reference frame equations, whereas the stationary zone uses the stationary frame equations. The sliding mesh model has been adopted in this paper to treat the stator-rotor interface. It is a mesh motion method wherein the rotor domain slides rigidly downwards along the stationary domain. Additionally, the rotor and stator zones are connected with each other through nonconformal interfaces; as the mesh motion is updated in time, the nonconformal interfaces are likewise updated to reflect the new positions of each zone.
The commercial code ANSYS ICEM-CFD has been used to generate the hexahedral meshes. The characteristics of the grids employed for the simulations are reported in Table
Main features of the computational grids before VOF calculation.
Geometry | Max size | Min size | Initial nodes |
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Simplified |
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Reference |
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Computational grid of simplified geometry.
The solution adaptive mesh feature implemented in ANSYS Fluent has been used with the aim to confine mesh refinements to specific regions, minimizing the simulation efforts. The initial meshes used in this work contain sufficient cells to represent the shape of the body and to capture the essential features of the aerodynamic flow field. The mesh regions to be adapted during VOF simulations are Liquid-Air Interface (LAI). Near wall region (NWR).
The refinement of LAI region has been obtained by means of the gradient adaptation function, selecting the cells at the air-oil interface based on the normalized gradient of the volume fraction (
A hybrid adaptation function has been created to refine the NWR; combining the boundary adaptation and the isovalue adaptation functions, native functions of the code, the cells close to the gear tooth surface are refined only if the lubricant is present, in order to reproduce the strong velocity gradients and high shear stresses due to the liquid-solid interactions. A visualization of the adaptation strategies is reported in Figure
Mesh adaptation strategies.
The hanging node adaptation process [
A sensitivity analysis of the results to the LOR parameter has been assessed for both strategies of refinement.
The commercial code ANSYS Fluent v14 has been used to solve the 3D unsteady RANS equations. A segregated solver with SIMPLEC scheme as velocity-pressure coupling algorithm was selected, in conjunction with a first-order backward difference scheme for time discretization, and an explicit scheme for the VOF equation with implicit body forces. The flow system was treated as isothermal, considering air and oil as incompressible fluids (Mach number < 0.3). The pressure field was discretized using PRESTO scheme. A second-order upwind scheme was used for the discretization of the velocity field. The compressive interface scheme was used for the volume fraction: this is a high resolution differencing scheme that produces an interface that is almost as sharp as the geometric reconstruction scheme [
Turbulence was modelled by means of
The simulations have been carried out with fixed time step, by maintaining a global courant number lower than 1. A typical resistant torque curve derived by the simulations is depicted in Figure
Dimensionless resistant torque curve resulting from calculation.
As regards computational efforts, the simulation of a simplified geometry with 4 levels of refinement for the NWR requires approximately 168 hours using 2 CPUs with Intel Xeon Processor E5-2630 with 8 cores or the equivalent of about 2700 CPU hours.
Before starting the VOF simulations, the air flow distribution inside the system is computed. Unsteady single-phase calculations were run, imposing a wall condition at the lubricant inlet instead of the velocity-inlet condition. When the resisting torque reached an asymptotic value, the calculation was stopped.
In Figure
Contour plot of
In high speed transmissions, the resistant torque due to windage effects becomes very intensive, as reported in the works of Dawson [
The windage torques resulting from the single-phase simulations of simplified and reference geometries are reported in Table
Dimensionless windage torques relating to single-phase simulations.
Geometry | Simplified | Reference |
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0.02 | 0.06 |
An extensive sensitivity study has been conducted, evaluating the effect of the computational parameters listed below: LOR parameter for LAI, LOR parameter for NWR, geometry simplification (symmetry condition).
A better description of the lubricant-gear interactions will be reported in the next section of this paper, while the main effects of modelling parameters on the resistant torque computations are now presented. The simulations that were carried out are reported in Table
Sensitivity analysis: test matrix.
Run | BC symmetry | LOR LAI | LOR NWR |
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1 | Yes | 3 | — | 2.6 | 0.995 |
2 | Yes | 3 | 3 | 2.6 | 0.995 |
3 | Yes | 3 | 4 | 4.2 | 0.885 |
4 | Yes | 3 | 5 | 8.9 | 0.883 |
5 | No | 3 | 4 | 7.9 | 0.874 |
Dimensionless averaged torques.
The maximum and minimum values of
The level of refinement for the near wall region is the parameter that mainly affects the resistant torque. Run 1 has no near wall refinement and run 2 has LOR equal to 3. In both of these cases there is very little variation in average torque compared to
Dimensionless resistant torques during the second impact: run 1 versus run 3.
Run 1: contour plot of velocity on the liquid surface.
Run 3: contour plot of velocity on the liquid surface.
The results of run 1 and run 3 related to the second impact were compared in terms of torque trend (Figure
From the data analysis, the liquid-gear interaction can be subdivided into four phases, summarized in Table
Liquid-gear interaction phases.
Phase | Description | Dimensionless time interval |
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a | Oil jet hits the tooth face | 0.20–0.22 |
b | Oil jet on the front zone of gear top land crest | 0.22–0.25 |
c | Oil jet on the rear zone of gear top land crest | 0.25–0.30 |
d | Oil film motion on the tooth surface | 0.30–0.40 |
Average dimensionless torques related to the oil-gear interaction phases during the second impact: runs 1 and 3.
Phase | a | b | c | d | Overall |
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9.3 | 15.3 | 25.4 | 50.0 | 100 |
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Run 1 | 3.85 | 2.53 | 0.67 | 0.14 | 0.985 |
Run 3 | 4.29 | 2.71 | 0.20 | 0.04 | 0.884 |
The average torque for run 3 is 11.4% greater than run 1 value for the phase a and about 70% lower for phases c and d; this last difference is the main factor leading to the overall average torque overestimation of run 1; in fact phases c and d represent together 75.4% of the overall oil-gear interaction time. The torque differences recorded during phases c and d have been investigated comparing the oil flow field for these periods. As shown in Figure
This behaviour can be explained by studying the contour plots of the volume fraction field on the symmetry plane, reported in Figure
Contour plot of oil volume fraction at the symmetry plane: runs 1, 2, 3, and 4.
To assess the effect of symmetry boundary condition on the torque calculation, in run 5 a new mesh was adopted. It was generated redoubling the grid used for the other runs with respect to the symmetry plane. The symmetry plane boundary condition does not significantly affect the results; in fact the average resistant torque for run 3 is 1.14% greater than run 4 value.
Two simulations of the reference geometry have been carried out, exploiting the numerical setup obtained by sensitivity analysis. The simulation parameters are reported in Table
Modelling parameters adopted in the reference geometry simulations.
Run | BC symmetry | LOR LAI | LOR NWR |
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Averaged torque |
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3D-1 | Yes | 3 | 4 | 2.3 | 0.899 |
3D-2 | Yes | 4 | 4 | 3.9 | 0.865 |
During the sensitivity analysis, the effects of the level of refinement for LAI on the resistant torque were not evaluated. This sensitivity has been assessed in the present section, comparing the average resistant torques arising from the simulations, as summarized in Table
A visualization of the resistant torque curve is depicted in Figure
Dimensionless resistant torque curve for run 3D-2.
A better description of the lubricant-gear interactions can be achieved focusing on the second impact: the resistant torque trend and the corresponding cumulative torque curve are depicted in Figures
Second impact data related to run 3D-2: dimensionless resistant torque.
Second impact data related to run 3D-2: cumulative torque curve normalized.
Run 3D-2: isosurface of oil volume fraction = 0.1.
Dimensionless time = 0.22
Dimensionless time = 0.23
Dimensionless time = 0.26
Dimensionless time = 0.36
The oil jet hits the tooth flank (point 1): the momentum transfer occurs in a very short time, leading to the resistant torque peak. At this time the tooth has transferred to the liquid thirty percent of the total momentum exchanged. On the tooth flank, the jet forms a thin oil film that gets down with high velocity toward the gear axis.
When the oil jet is passing over the gear top land, the lubricant does not impinge on the gear but forms a liquid film that flies over the tooth (Figures
In order to analyse the relative contribution of pressure and shear forces to the resistant torque calculation, the normalized cumulative torque curves, resulting from both forces, are reported in Figure
Second impact data related to run 3D-2: normalized cumulative torque curves resulting from pressure and shear forces.
A comprehensive numerical study of a single oil jet impinging radially on a single high speed gear has been carried out using VOF method. The adapting mesh feature, implemented in the commercial code ANSYS Fluent, has been used, developing hybrid adaptation functions to confine the adaptation to specific domain regions.
A global sensitivity analysis of grid adaptation strategy and model parameters was carried out. The level of refinement adopted for the near wall region is the parameter that mainly affects the simulation results, while the effect of other computational parameters is less significant. Thus a robust numerical setup has been defined.
This study has allowed the evaluation of the resistant torque due to oil jet cooling, developing more in-depth understanding of the oil-gear interaction phenomena. In particular, a good agreement between the average torque derived by a simple calculation based on the oil’s momentum variation and the computational torque has been revealed. CFD results showed how the oil jet does not impinge on the gear top land but forms a suspended oil film that breaks up into ligaments and small droplets. This amount of oil is not involved in the gear lubrication process and the total oil mass that exchanges momentum with the gear decreases, resulting in a reduction of the average torque with respect to the 0D-Model value.
Finally, it has been proved that the mechanism which mainly contributes to the resistant torque is the pressure distribution on the tooth flank resulting from the oil jet impact, while the shear forces contribution is negligible.
Dimensionless oil jet injection angle
Diameter
Force
Froude number
Length
Angular velocity
Radius
Reynold number
Torque
Velocity
Liquid jet Weber number
Crossflow Weber number
Liquid column breakup distance
Liquid column breakup height
Number of gear teeth.
Average property
Casing property
Tooth face
Axial Gap
Impact
Pitch property
Jet property
Shaft property
Tangential value
Zero value.
Computational fluid dynamics
Liquid-Air Interface
Level of refinement
Near wall region
Unsteady Reynolds Averaged Navier Stokes
Volume of Fluid.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank GE Avio srl for the publication permission.