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: (1) 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. (2) For the geometry investigated the shock amplitude decreased with increasing excitation frequency. (3) The pressure transducer sensed the arriving shock before the shock had reached the position of the pressure transducer. (4) The computed unsteady phenomena agree well with the results of the measurements.

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]. Table III in Chassaing et al [72]).…”

“…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. for the Ott et al [82] nozzle (grid A [72]; notice that the plot-ranges are automatic and that measurements were not available for f = 10 Hz). Therefore, eventual differences between the time-nonlinear and the time-linearized results can be attributed to either the linearization itself, or to the fact that the turbulence transport equations were not linearized.…”

Experimental and Numerical Study of Oscillating Transonic Shock Waves in Ducts

“…Computational simulations of unsteady compressible internal flows are relatively common [2][3][4], although the vast majority of these use simplifying assumptions to reduce the complexity of a problem and make it easier to solve. For example, often a flow is assumed to be symmetrical and primarily two-dimensional (or at least quasi-twodimensional) so that only a section of the real flow is computed (e.g., half or quarter of a channel) and boundary conditions such as sidewalls are simplified by assuming they are inviscid or that the flow is periodic in the spanwise direction.…”

“…The maximum shock speed observed in experiments was 9 ms 1 , which implies that the shock could potentially move a streamwise distance of up to 1.1 mm during an exposure. Hence, it is estimated that shock position in a [7], b) Ott et al [2], and c) Edwards and Squire [6].…”

“…A number of experimental and numerical studies [2,3,[5][6][7][8] have implemented a variable geometry second throat to investigate the effects of downstream periodic pressure perturbations on shocks both experimentally and numerically. The authors of these studies found that the amplitude of shock motion decreased with increasing frequency (see Fig.…”