A multi-scale model for geared transmission aero-thermodynamics

Open Access
McIntyre, Sean Michael
Graduate Program:
Aerospace Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
November 30, 2015
Committee Members:
  • Robert Francis Kunz, Dissertation Advisor
  • Kenneth Steven Brentner, Committee Member
  • Philip John Morris, Committee Member
  • Jules Washington Lindau V, Committee Member
  • Daniel Connell Haworth, Committee Member
  • CFD
  • conjugate heat transfer
  • gearbox
  • multi-scale model
A multi-scale, multi-physics computational tool for the simulation of high-performance gearbox aero-thermodynamics was developed and applied to equilibrium and pathological loss-of-lubrication performance simulation. The physical processes at play in these systems include multiphase compressible flow of the air and lubricant within the gearbox, meshing kinematics and tribology, as well as heat transfer by conduction, and free and forced convection. These physics are coupled across their representative space and time scales in the computational framework developed in this dissertation. These scales span eight orders of magnitude, from the thermal response of the full gearbox O(10^0 m, 10^2 s), through effects at the tooth passage time scale O(10^-2 m, 10^-4 s), down to tribological effects on the meshing gear teeth O(10^-6 m, 10^-6 s). Direct numerical simulation of these coupled physics and scales is intractable. Accordingly, a scale-segregated simulation strategy was developed by partitioning and treating the contributing physical mechanisms as sub-problems, each with associated space and time scales, and appropriate coupling mechanisms. These are: 1. the long time scale thermal response of the system, 2. the multiphase (air, droplets, and film) aerodynamic flow and convective heat transfer within the gearbox, 3. the high-frequency, time-periodic thermal effects of gear tooth heating while in mesh and its subsequent cooling through the rest of rotation, 4. meshing effects including tribology and contact mechanics. The overarching goal of this dissertation was to develop software and analysis procedures for gearbox loss-of-lubrication performance. To accommodate these four physical effects and their coupling, each is treated in the CFD code as a sub problem. These physics modules are coupled algorithmically. Specifically, the high-frequency conduction analysis derives its local heat transfer coefficient and near-wall air temperature boundary conditions from a quasi-steady cyclic-symmetric simulation of the internal flow. This high-frequency conduction solution is coupled directly with a model for the meshing friction, developed by a collaborator, which was adapted for use in a finite-volume CFD code. The local surface heat flux on solid surfaces is calculated by time-averaging the heat flux in the high-frequency analysis. This serves as a fixed-flux boundary condition in the long time scale conduction module. The temperature distribution from this long time scale heat transfer calculation serves as a boundary condition for the internal convection simulation, and as the initial condition for the high-frequency heat transfer module. Using this multi-scale model, simulations were performed for equilibrium and loss-of-lubrication operation of the NASA Glenn Research Center test stand. Results were compared with experimental measurements. In addition to the multi-scale model itself, several other specific contributions were made. Eulerian models for droplets and wall-films were developed and implemented in the CFD code. A novel approach to retaining liquid film on the solid surfaces, and strategies for its mass exchange with droplets, were developed and verified. Models for interfacial transfer between droplets and wall-film were implemented, and include the effects of droplet deposition, splashing, bouncing, as well as film breakup. These models were validated against airfoil data. To mitigate the observed slow convergence of CFD simulations of the enclosed aerodynamic flows within gearboxes, Fourier stability analysis was applied to the SIMPLE-C fractional-step algorithm. From this, recommendations to accelerate the convergence rate through enhanced pressure-velocity coupling were made. These were shown to be effective. A fast-running finite-volume reduced-order-model of the gearbox aero-thermodynamics was developed, and coupled with the tribology model to investigate the sensitivity of loss-of-lubrication predictions to various model and physical parameters. This sensitivity study was instrumental in guiding efforts toward improving the accuracy of the multi-scale model without undue increase in computational cost. In addition, the reduced-order model is now used extensively by a collaborator in tribology model development and testing. Experimental measurements of high-speed gear windage in partially and fully-shrouded configurations were performed to supplement the paucity of available validation data. This measurement program provided measurements of windage loss for a gear of design-relevant size and operating speed, as well as guidance for increasing the accuracy of future measurements.