To stay competitive within the gas turbine community, turbine aero designers strive to maximize the total work output of each turbine stage through a combination of airfoil design improvements and increased total pressure ratio. Although increasing the mass flow rate could achieve a higher power target, the resultant increase in turbine annulus would result in structural limitations due to longer blades which cause increased strain on the blade root as well as amplified flutter and rotor dynamic excitation. An alternative path to achieving higher power output is to maximize the loading of each turbine stage through increased pressure ratio, but this may lead to airfoil limit loading and high aerodynamic losses.
This research systematically develops a detailed methodology to simulate the prediction of airfoil limit loading as well as provides a thorough investigation into the factors that influence the limit loading condition. A computational baseline was established using data previously collected at the Pratt & Whitney Canada High-Speed Wind Tunnel at Carleton University near design conditions using the Reynolds-Averaged Naiver-Stokes shear stress transport k-ω turbulence model (SST) with γ transition. An adaptive mesh refinement algorithm was developed based on the normalized local cell gradients of total pressure, total temperature, density, turbulent kinetic energy, turbulent eddy viscosity and the specific dissipation rate of turbulence. An overall reduction in computational cost was determined as 50% per simulation. The SST turbulence model with Gamma transition was found to have superior predictive veracity compared to other eddy viscosity turbulence models for the limit loading condition.
Variation of turbine inflow conditions were analyzed for four different transonic turbine airfoils based on the potential flow conditions exhausted by an upstream combustor. Influence of inflow conditions was found to be minimal on the exit flow profile with the exception of the mass-flow averaged total pressure loss coefficients. Results show incidence variation to change the total pressure loss coefficient differently for each airfoil, whereas turbulence intensity and turbulent length scale predicted a drastic rise in loss with increased turbulence level for all airfoils considered. The geometric characteristics of each airfoil were also investigated for influence on the stages to limit loading. Similar to previous experimental work, the limit loading pressure ratio and the mass-flow averaged outlet flow angle were strongly correlated with the airfoil outlet metal angle. It was also determined that the airfoil stagger and trailing edge blockage ratio play a role in the determination of the sublimit loading range, although no definitive parameter could be isolated due to lack of specific geometric constraints.
Lastly, the effect of transient vortex shedding on the nature of the trailing edge shock system and subsequent influence on the stages towards limit loading were investigated. A detailed review of the boundary layer states at the trailing edge were performed showing that all of the modeling approaches predicted laminar boundary layer profiles along the pressure surface trailing edge and turbulent profiles along the suction surface. Each modeling strategy (unsteady Reynolds-Averaged Navier Stokes, Delayed Detached Eddy Simulation and turbulence model free) predicted separation along the suction surface during limit loading due to acoustic wave propagation caused by the shock-base pressure interaction, although with varying degrees of size and magnitude. Temporal evolution of the mass flow averaged total pressure loss coefficient downstream of the airfoil allowed for the dominant vortex shedding frequency to be determined and subsequent Strouhal number to be calculated. It was found that each transient modeling strategy predicted the vortex frequency differently. A formal documentation and review were made outlining the required simulation time step to achieve accurate temporal resolution as well as approximate vortex shedding period. Qualitative images of numerical Schlieren (normalized density gradient) contours were presented and reviewed showing large differences in the prediction of vortex shape, size, and subsequent shock influence. Although conclusions were made on modeling ability, without extensive experimental documentation no concrete justification can be made at this time, outlining the importance of an experimental investigation.