STUDY OF SHOCK MOVEMENT AND UNSTEADY PRESSURE ON 2D GENERIC MODEL

Davy Allegret-Bourdon

Chair of Heat and Power Technology

Royal Institute of Technology, Stockholm, Sweden

davy@energy. kth. se

Torsten H. Fransson

Chair ofHeat and Power Technology

Royal Institute of Technology, Stockholm, Sweden

fransson@energykth. se

Abstract A ffexible generic model has been developed at the Chair of Heat and Power Technology in order to perform ffitter experiments in a more fundamental fash­ion. It is made of engineered fexible material and oscillate in a controlled way at non-uniform amplitude and variable frequencies. Time-resolved measurements of the unsteady surface pressures, the instantaneous model geometry as well as unsteady Schlieren visualizations are performed in order to study the shock wave motion and the aerodynamic load acting over this ffexible generic bump. The model oscillates at reduced frequencies from 0.015 to 0.294 at transonic fow condition. The mode shapes of such a fexible bump strongly depends on the excitation frequency of the generic model. Schlieren pictures are obtained for an operating point characterized by an inlet Mach number of 0.63. More­over, the presented results demonstrate that the phase of shock wave movement towards bump local motion shows a decreasing trend for the third bending mode shapes at reduced frequency higher than k=0.074. At the pressure taps located after the shock wave formation, the phase of pressure fuctuations towards bump local motion presents the same decreasing trend.

Keywords: Fluid-structure interaction, Schlieren, Long line probe, shock wave movement,

Unsteady static pressure, first bending mode shape, Flexible generic model

409

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

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 409-421. © 2006 Springer. Printed in the Netherlands.

Nomenclature

cax	[mm]	Axial chord of the generic model
Cp	[-]	Unsteady pressure coefficient, Cp = —
D	[mm]	Test section width
E	[MPa]	Young modulus
f	[Hz]	Excitation frequency
H	[mm]	Test section channel height
У	[mm]	Local generic bump height
Ушах	[mm]	Maximum generic bump height
hbump	[-]	Bump bending amplitude, dimensionless with channel heigth
hshock	[-]	Shock wave amplitude, dimensionless with bump amplitude
k	[-]	Inlet reduced frequency based on the half chord, k = n. f. cax/vax
Miso 1	[-]	Inlet isentropic Mach number, MiSO 1 = ( () L1
Miso2	[-]	Outlet isentropic Mach number, Mtao2 = )
Ps	[kPa]	Local static pressure on the bump surface
P.1	[kPa]	Upstream static pressure
Ps2	[kPa]	Downstream static pressure
Pt	[kPa]	Upstream stagnation pressure
Q	[kg/s]	Mass ft>w
Re	[-]	Reynolds number
t	[s]	Instantaneous time
t	[-]	Time dimensionless with the excitation period, t’ = Jjr
T	[s]	Period of excitation
Tt	[K]	Stagnation temperature
vax	[m/s]	Axial ft>w velocity
x	[m]	Bump chord wise location
ДФЬитр	[Deg.]	Largest phase difference of bump motion for one mode shape
Фshock	[Deg.]	Phase lead of shock wave movement towards bump motion
фР	[Deg.]	Phase lead of pressure flictuation towards bump motion

1. Introduction

Structure oscillating phenomena occur in many industrial applications in the field of energy technology. Under certain conditions a curved shape located in an uniform fbw, such as a blade, an airfoil or the surface of a nozzle, can enter into a self-excited vibration known as flitter. Under flitter condition, aerody­namic loads can rapidly increase the amplitude of vibration of a structure until its failure.

Experiments on controlled vibrating models have been performed by sev­eral researchers to investigate such aerodynamic loads and observe the shock wave motion related to it. Kobayashi et al. [1994] studied this relationship on an annular blade row oscillating in torsional mode with interblade phase angle. They drew the conclusion that at an inlet Mach number of 1.19 the shock wave movement significantly changed between the reduced frequencies

of 0.102 and 0.136, and that after this range of reduced frequencies the un­steady force damps the blade oscillation. Fujimoto et al. [1997] studied this unsteady fliid structure interaction on a transonic compressor cascade oscillat­ing in a controlled pitching angle vibration. They noticed that although the am­plitude of the shock wave displacement did not change much within the range of this experiment, the phase lag relative to the blade oscillation increases up to almost 90r as the blade oscillation reduced frequency increases to 0.284. Later, Hirano et al. [2000] performed other experimental campaigns on this transonic compressor cascade oscillating in a controlled pitching angle vibration. They conclude that the shock wave movement has a large effect on the amplitude and the phase angle of unsteady pressures on the blade surfaces; the amplitude of unsteady pressure becomes large upstream of the shock wave but decreases rapidly downstream; the phase angle across the shock wave changes largely for the surfaces facing the fl»w passages adjacent to the oscillating blade, the amplitude of shock wave movement increases following the increase of the re­duced frequency, and the phase angle relative to the blade displacement lags almost linearly as the reduced frequency increases.

In such kind of experiments, a driving system is creating an artificial oscil­lation of the rigid structure, whose amplitude and frequency can be controlled. The compressor blade of Lehr and Bolcs [2000], for example, is made oscil­lating in a controlled plunging mode by a hydraulic excitation system. The high-speed pitching vibrator of Hirano et al. [2000] is able to reach a 500Hz frequency of a 2D mode shape controlled oscillation in a linear cascade. In most of the cases, the vibrating structures are designed in metal to be close to real applications. Thus, large amplitudes of vibration at high oscillation fre­quencies prompt the failure of the structures. Moreover, recent research has presented a 2D blade harmonically driven in a 3D mode shape controlled vi­bration such as in Queune et al. [2000].

To date, this kind of flitter experimental investigations have been limited to stiff models made of metal, which oscillate in a pitching mode. Rather than studying the complex geometry of a turbomachine and specific industrial applications, the here presented generic experiments are voluntarily not taking into account inertial effects, radial geometry, numerous blades or 3D aspect of the flow occurring in industrial applications. Thus a generic oscillating flexible model is studied in order to reach a better understanding of the physics of the flutter phenomenon under transonic operating conditions.