EXPERIMENTAL AND NUMERICAL STUDY OF NONLINEAR INTERACTIONS IN TWO-DIMENSIONAL TRANSONIC NOZZLE FLOW

Olivier Bron1,2, Pascal Ferrand1, and Torsten H. Fransson2

bron@energy. kth. se, Pascal. Ferrand@ec-lyon. fr, fransson@energykth. se

1L. M.F. A., Ecole Centrale, Lyon, France

2

Heat and Power Technology, Royal Institute of Technology, Stockholm, Sweden

Abstract A prerequisite for aeroelastic stability prediction in turbomachines is the un­derstanding of the flictuating aerodynamic forces acting on the blades. Un­steady transonic fbws are complex because of mutual interactions between trav­elling pressure waves, outlet disturbances, shock motion, and fluctuating turbu­lent boundary layers. Complex phenomena appear in the shock/boundary layer region and produce phase lags and high time harmonics, which can give a signif­icant contribution to the overall unsteady lift and moment, and therefore affect flutter boundaries, cause large local stresses, or even severely damage the turbo­machine.

This paper is concerned with the understanding of phenomena associated with travelling waves in non-uniform transonic flows and how they affect the unsteady pressure distribution on the surface as well as the far field radiated sound. In similitude with turbomachines potential interaction, the emphasis was put on the unsteady interaction of upstream propagating acoustic waves with an oscillating shock in a 2D nozzle ft>w. Both numerical and experimental studies are carried out and compared with each other. Results showed that the unsteady pressure distribution results from the superposition of upstream and downstream propa­gating pressure waves, which are partly reflected or absorbed by the oscillating shock. Beside, the phase angle shift underneath the shock location was found to linearly increase with the perturbation frequency, which can be critical regarding aeroelastic stability since it might have a significant impact on the phase angle of the overall aerodynamic force acting on the blade and shift the aerodynamic damping from stable to exciting.

Keywords: Unsteady flrw, shock motion, Shock Boundary Layer Interaction, Nozzle ft>w

463

K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 463-481. © 2006 Springer. Printed in the Netherlands.

Introduction

Transonic fbws about streamlined bodies are strongly affected, particularly near the shock location, by unsteady excitations. Experimental and computa­tional studies [1,2] have shown that the unsteady pressure distribution along the surface of an airfoil or a cascade blade in unsteady transonic flow exhibits a significant bulge near the shock location. Tijdeman and Seebass [3] reported that the unsteady pressure bulge and its phase variation resulted from non­linear interaction between the mean and unsteady flows. This non-linear in­teraction causes a shift in the shock location, which produces the observed large bulge in the unsteady pressure distribution. Studies [4] on choked flutter have shown that, in unsteady transonic flows around a single airfoil, the shock motion, and thus the pressure distribution along the surface, can be critical re­garding to the self-exciting oscillations of the airfoil. It was also shown that the mean flow gradients are of high importance regarding the time response of the unsteady pressure distribution on the airfoil surface. Beside, numeri­cal computations [5] pointed out that the exact location of the transition point could strongly affect the prediction of stall flutter. Further studies [6] sug­gested that this sharp rise in the unsteady pressure distribution was due to the near sonic condition, and that the near-sonic velocity acts as a barrier they identified as acoustic blockage preventing acoustic disturbances from propa­gating upstream in a similar way to the shock in transonic ft>ws. A transonic convergent-divergent nozzle experimentally investigated by Ott et al [7] was thereafter used as a model to investigate the non-linear acoustic blockage. An­alytical and numerical computations [8, 9, 10, 11] were then carried out to analyze and quantify the upstream and downstream propagation of acoustic disturbances in the nozzle.

Similarly, in order to focus the present analysis on essential features, the investigation has been carried out in a simple geometry such as a 2D conver­gent divergent nozzle. Special influences of leading and trailing edges, and interblade row region interactions are therefore avoided.