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

Abstract

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.

Unsteady shock wave dynamics

“…Some experimental and numerical studies have been carried out using a variablegeometry second throat to investigate the effects of downstream periodic pressure perturbations on shocks (see for example Sajben & Kroutil 1981;Ott, Bolcs & Fransson 1995;Handa, Masuda & Matsuo 2003;Bur et al 2006). All have reported that the amplitude of shock oscillation decreases with increasing perturbation frequency, although the reasons for this are not discussed in detail.…”

Time‐linearized time‐harmonic 3‐D Navier–Stokes shock‐capturing schemes

“…For this configuration, the shock-wave position and the post-shock pressure-recovery cannot be predicted by 2-D computations [82][83][84]. Indeed, because of the relatively small width of the nozzle and the rather thick sidewall boundary-layers, only 3-D viscous computations can correctly predict this flow, where the shock-wave position is dominated by the corner-flow/shock-wave Table III in Chassaing et al [72]).…”

“…The time-linearized time-harmonic method is evaluated through comparison with measurements [81,82] and with previous time-nonlinear computations [72,83] in a 3-D nozzle experimentally and computationally investigated by Ott et al [82] (Figure 1). The facility, with a width of 40 mm, was equipped with nozzle liners giving a converging-diverging section.…”

“…Neglecting the nonlinear interactions between harmonics, the time-linearized computational procedure consists of running three separate computations, one for each of the first three harmonics (Equation (19)): with measurements [81,82] (Figures 1-3). The present time-linearized scheme is obtained by the linearization of the previously used time-nonlinear method [72], the only difference being that the RSM-transport equations were not linearized, but were replaced by the frozen-turbulence-scales assumption instead (cf.…”

“…Unsteady pressures were measured by unsteady pressure transducers located on the side-wall, at its intersection with the y-symmetry plane of the nozzle, and placed 5 mm apart, in the shock wave neighbourhood. Experimental conditions are [81][82][83] …”