Abstract
This research aims to develop high-fidelity turbulent simulation capabilities for aeromechanics problems of the turbomachinery and investigate the very challenging Non-Synchronous Vibration (NSV) phenomenon of high-speed axial compressors. So far, most of the turbulence simulation of turbomachinery aeromechanic problems utilizes Reynolds Averaged Navier-Stokes (RANS) methodology. The motivation of this dissertation is to advance the turbulence modeling to hybrid methods of Large Eddy Simulation (LES) and RANS, which is rarely implemented. The hybrid models developed for NSV in this dissertation include: 1) The Scale Adaptive Simulation (SAS) model based on the Spalart-Allmaras (SA) model; 2) Improved Delayed Detached Eddy Simulation (IDDES) based on the Shear Stress Transportation (SST) model. A two-equation Shear Stress Transport (SST) turbulence model is implemented along with its Detached Eddy Simulation based family of hybrid models. A non-conservative Finite Element Method based interpolation boundary condition is developed to study the effect of casing treatment on the compressor stall margin and performance parameters. A Roe finite difference and a low diffusion E-CUSP scheme as an approximate Riemann solver are adopted to handle high-speed flows involving transonic and supersonic flow with the SST based model.
The Favre-filtered compressible Navier-Stokes equations are solved in a fully coupled manner using the implicit unfactored Gauss-Seidel line iteration scheme. High order accurate third-order Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) and (third- and fifth-order) Weighted Essentially Non-Oscillatory methods are used for the inviscid flux. A conservative central differencing (second- and fourth-order) scheme for the viscous flux is employed. For the unsteady simulation, an implicit dual time-stepping scheme is used. The Fluid-Structure Interaction (FSI) simulation solves decoupled modal equations in a fully coupled manner similar to the implicit flow solver. The modal equations representing the motion of structure are solved simultaneously with the flow solver to capture non-linear interaction between the flow and vibrating structure.
The FEM based interpolation boundary condition is validated with the mixed-type compressor casing treatment. The predicted characteristic speed line agrees well with the experiment. The compressor with a recirculating type casing treatment extends the stall margin dramatically over the solid wall casing without the efficiency penalty at the design speed.
The SST turbulence model implementation is validated with a variety of flow problems to demonstrate the solver's stability and accuracy. The validation cases include: 1) The zero pressure gradient subsonic flat plate for the law of wall. The predicted nondimensional velocity is in close congruence with the law of wall. 2) For the transonic RAE 2822 airfoil, the aerodynamic performance and the coefficient of pressure agree well with the experiment. 3) For the swept-back Onera M6 wing at the high Reynolds number transonic flow, the predicted coefficient of pressure at various wing span shows an excellent agreement with the experiment. 4) The transonic axial compressor Rotor 67 is simulated for the characteristic speed line at the design speed. The predicted speed line, radial profiles at the design and near stall point are in close agreement with the experiment. The predicted shock structure in the flow passage matches with the experimental flow structure.
The extensive validation of the Scale Adaptive Simulation based on the SA and the Improved Delayed Detached Eddy Simulation based on the SST model includes: 1) the subsonic flat plate, 2) the massive flow separation for the NACA 0012 post-stall flow and 3) the wall-mounted NASA hump. For the zero pressure gradient subsonic flat plate case, the implemented hybrid models do not exhibit the Mean Stress Depletion with an ambiguous grid. For the massive flow separation of NACA 0012 airfoil post-stall flow, an unsteady simulation with the SA and SST overpredicts the aerodynamic performance at a high angle of attacks. The hybrid models predict aerodynamic performance in close harmony with the experimental measurements. The predicted small scale eddy structure represents the realistic turbulent flow structures in contrast to the URANS prediction. For the wall-mounted hump, the separation size is overpredicted with the steady and unsteady SST model whereas the SST-IDDES improves the separation bubble size prediction.
The SA based hybrid turbulence models are used to investigate the NSV mechanism of a high-speed axial compressor using the rigid and flexible blades. The numerical simulations are carried out using the one-seventh sector reduced-order model to reduce the computational efforts. For the rigid blade simulations, the predicted NSV frequency of rotor blades is 2522.75 Hz with the SAS, 2457 Hz with the IDDES and 2381.4 Hz with the URANS respectively in comparison to 2600 Hz measured in the experiment. The radial vortices or tornado-like vortices, formed near the rotor blade leading edge suction side, cause the NSV. These vortices travel in the rotor's counter-rotating direction and their associated frequency matches the non-synchronous vibration frequency at the simulated rotor speed in the current work. The trajectory of these vortices induces the torsional coupling force of 1T mode. The Fluid Structural Interaction (FSI) simulation with vibrating blades using the SA-DDES captures the NSV frequency very accurately on the suction side of the rotor blade. The tip vortex trajectory shows the blade vibration on the pressure side is affected not only by the adjacent blade only but also by other blades. The frequency analysis of the tip leading edge displacement shows the 1F mode dominant against the 1T dominant mode observed in the experiment. Therefore, the current simulation does not show the lock-in mechanism between the aerodynamic and structural mode of vibrations.
Overall, the high-fidelity hybrid models developed in this dissertation for fan/compressor aeroelastic problems exemplify the robustness and accuracy to advance state of the art. Future work to improve accuracy and reducing computational efforts are discussed at the end of this thesis.