Analytical flutter investigation of a composite propfan model

Abstract

T h i s paper presents a t h e o r e t i c a l model and an a s s o c i a t e d computer program f o r p r e d i c t i n g subsonic bending-torsion f l u t t e r i n prcpfans. The model i s based on two-dimensional unsteady cascade s t r i p t h e o r y and three-dimensional steady and unsteady l i f t i n g s u r f a c e aerodynamic t h e o r y i n c o n j u n c t i o n w i t h a f i n i t e element s t r u c t u r a l model f o r t h e blade. The a n a l y t i c a l r e s u l t s compare w e l l w i t h p u b l i s h e d experimental data. A d d i t i o n a l param e t r i c s t u d i e s a r e a l s o presented i l l u s t r a t i n g t h e e f f e c t s on f l u t t e r speed o f steady a e r o e l a s t i c deformations, b l a d e s e t t i n g angle, r o t a t i o n a l speed, number o f blades, s t r u c t u r a l damping, and number o f modes. N; a l s o d i s t a n c e f r o m t h e a x i s o f r o t a t i o n b l a d e l e n g t h along t h e r e f e r e n c e 1 i n e t i m e v e c t o r o f b l a d e d e f l e c t i o n s a t g r i d p o i n t s 1 v e c t o r o f steady s t a t e d e f l e c t i o n s a t g r i d p o i n t s steady s t a t e d e f l e c t i o n s due t o c e n t r i f u g a l loads steady s t a t e d e f l e c t i o n s a f t e r t h e i -t h i t e r a t i o nf r e e stream v e l o c i t y r e 1 a t i v e v e l o c i t y modal m a t r i x expressed i n terms o f i n d i v i d u a l bending and t o r s i o n c o n t r i b u t i o n s about t h e r e f e r e n c e a x i s bending c o n t r i b u t i o n s o f m normal modes o f t h e r e f e r e n c e a x i sF values a t f l u t t e r p o i n t S u p e r s c r i p t s d i f f e r e n t i a t i o n w i t h r e s p e c t t o t irne T transpose I d i f f e r e n t i a t i o n w i t h r e s p e c t t o s p a t i a l c o o r d i n a t e INTRODUCTION

A review of propeller stall flutter

“…The structural modelling used by Reddy & Kaza [43] involved the derivation of the staticdisplacement and normal modes and frequencies from a non-linear finite element analysis which was then supplied to the standard modal equations of motion for a propeller blade [55]. The final equations were derived as:…”

Aircraft Propulsion Systems Technology and Design

“…113, which is an extension of the propfan work done in Ref. 112. Once again, the SR3C-X2 rotor was analyzed, together with a rotor designated the SR3C-3.…”

“…7.70 (taken from Ref. 112), which is a root locus plot of the complex eigenvalues, consisting of the real part \i (proportional to damping) and the imaginary part v (proportional to frequency). Thus, in this phase plane plot, the stable/unstable boundary is at \ JL = 0, with flutter occurring for a positive real part.…”

“…Both of these were tuned rotors, as in Ref. 112. In addition, a deliberately mistuned rotor, the SR3C-X2/SR3C-3, was analyzed.…”