Experimental and Numerical Study of the Time-Dependent Pressure Response of a Shock Wave Oscillating in a Nozzle

Investigations of flutter in transonic turbine cascades have shown that the movement of unsteady normal shocks has an important effect on the excitation of blades. In order to predict this phenomenon correctly, detailed studies concerning the response of unsteady blade pressures versus different parameters of an oscillating shock wave should be performed, if possible isolated from other flow effects in cascades. In the present investigation the correlation between an oscillating normal shock wave and the response of wall mounted time-dependent pressure transducers was studied experimentally in a nozzle with fluctuating back pressure. Excitation frequencies between 0 Hz and 180 Hz were investigated. For the measurements, various measuring techniques were employed. The determination of the unsteady shock position was made by a line scan camera using the Schlieren flow visualization technique. This allowed the simultaneous use of unsteady pressure transducers to evaluate the behavior of the pressure under the moving shock. A numerical code, based on the fully unsteady Euler equations in conservative form, was developed to simulate the behavior of the shock and the pressures. The main results of this work were: • The boundary layer over an unsteady pressure transducer has a quasi-steady behavior with respect to the phase lag. The pressure amplitude depends on the frequency of the back pressure. • For the geometry investigated the shock amplitude decreased with increasing excitation frequency. • The pressure transducer sensed the arriving shock before the shock had reached the position of the pressure transducer. • The computed unsteady phenomena agree well with the results of the measurements. INTRODUCTION Unsteady flow effects in turbomachines can be the source of various excitations that can lead to different vibrations, such as forced vibration and flutter. Turbomachine blade vibrations are known to appear over a large flight envelope for compressors in jet engines and on the last stages of industrial turbines. Main vibration problems appear in the transonic flow domain (Bölcs et al, 1989b; Ezzat et al, 1989; Usab and Verdon, 1990; Verdon, 1989; Araki et al, 1981; Széchényi et al, 1984, 1985; Buffum and Fleeter 1989, 1990, 1991; Hanamura, 1988; Fransson, 1992 to mention just a few) and it has been noted both theoretically and experimentally that oscillating normal shock waves can introduce large unsteady local loads on the vibrating blades [Verdon, 1989; Bölcs et al, 1991]. Because of the small blade dimensions usually employed for cascade experiments in the transonic flow domain it is extremely difficult to obtain accurate information about the exact position of the shock wave, how much it fluctuates, its harmonic and non-harmonic content, as well as the correlation between the "freestream" (outside the boundary layer) shock position and the time-dependent pressure responses on the blades. Numerical predictions are presently performed for both the forced vibration and the flutter problem. In these, emphasis is sometimes put on the sharp shock capture [Carstens, 1991] or shock fitting [Verdon, 1989], whereas other results indicate that less sharp shock capture gives smaller local unsteady loads but over a more spread out region [Whitehead et al, 1985, 1990; Gerolymos, 1992a,b], and that the total chordwise load agrees with global experimental data. For the correct interpretation of both experimental data and numerical predictions of the unsteady transonic flow around vibrating cascaded airfoils it is important to determine the correlation between the: