Stability analysis of the flow past a low-pressure turbine blade

Abstract

Results are presented of BiGlobal linear stability analysis of incompressible flow over a row of T-106/300 aircraft Low Pressure Turbine (LPT) blades. In particular the three-dimensional stability of two-dimensional steady and periodic states is investigated for Reynolds numbers below 10,000, where the primary two-dimensional instability leading the flow through a Hopf-bifurcation from steady to periodic has been identified to be at a chord Reynolds number of Rec = 905 ± 1. Structured and unstructured meshes have been used while variation of the polynomial order of the numerical methods as well as extension of the domain under consideration has ensured numerical convergence. Furthermore, consistency between linear stability analysis and full Navier-Stokes solution is shown. The leading Floquet- and eigenvalues of the LPT flow are observed at a range of Reynolds and span-wise wavenumber parameters. They show that the instability depends on the imposed periodicity in the two-dimensional plane of the computational model. Neglecting subharmonic effects the flow undergoes a three-dimensional transition caused by three-dimensional long wavelength disturbances immediately after its two-dimensional instability. The associated unstable mode is related to the wake of the basic state. A second short wavelength stable mode has been identified to be associated to the separation bubble at the trailing edge. A pseudospectra analysis has also been performed showing sensitivity of the eigenvalue problem and the associated potential for transient growth due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulation (DNS) shows that three-dimensional transition is susceptible to the modes identified. Finally, a subsequent two-dimensional optimum growth analysis based on a newly developed method related to the computation of the singular values of the eigenvalue problem has been performed for flow past a cylinder and the LPT flow. Optimum modes that exhibit strong energy growth were identified and compared with the adjoint modes as found in the literature. The maximum energy associated to sensitivity regions is located around the separation bubble at the trailing edge of the blade as they grow downstream. Demonstrating the potential of the developed method based on singular values, the purely two-dimensional results as presented in this work serve as a basis for future three-dimensional analyses.