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.

1.
Adamson, T. C., and Liou, M. S., 1977, “Unsteady Motion of Shock Waves in Two Dimensional Transonic Channel Flows,” Report No. UM-014534-F, Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI.
2.
Adamson, T. C., and Liou, M. S., 1978, “Unsteady Motion of Shock Waves in Two Dimensional Transonic Channel Flows,” Report No. UM-015411-F, Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI.
3.
Anderson, W. K., Thomas, J. L., and Rumsey, C. L., 1985, “Extension of Applications of Flux-Vector Splitting to Unsteady Calculations on Dynamic Meshes,” AIAA Paper No. 85-0122.
4.
Anderson, W. K., Thomas, J. L., and van Leer, B., 1987, “A Comparison of Finite Volume Flow With Shock Waves,” AIAA Paper No. 87-1152.
5.
Araki, T., Okamoto, Y., Ohtomo, F., and Arinobu, M., 1981, “Self-Excited Flow Oscillation in the Low Pressure Steam Turbine Cascade,” Communication de L’ITA/EPFL, No. 10, pp. 171–186.
6.
Bo¨lcs
A.
,
Fransson
T. H.
, and
Platzer
M. F.
,
1989
a, “
Numerical Simulation of Inviscid Transonic Flow Through Nozzles With Fluctuating Back Pressure
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
111
, pp.
169
190
.
7.
Bo¨lcs, A., Fransson, T. H., and Schla¨fli, D., 1989b, “Time-Dependent Measurements on Vibrating Annular Turbine Cascades Under Various Steady-State Conditions,” Unsteady Aerodynamic Phenomena in Turbomachines, AGARD Conference Proceedings No. 468, pp. 19.1–19.14, Luxembourg, Aug. 28–30.
8.
Bo¨lcs, A., Fransson, T. H., and Ko¨rba¨cher, H., 1991, “Time-Dependent Pressure Fluctuations on an Oscillating Turbine Cascade at Transonic Off-Design Flow Conditions,” Proceedings of the 6th International Conference on Aeroelasticity in Turbomachines, Sept. 10–15, Notre Dame, IN.
9.
Buffum, D. H., and Fleeter, S., 1989, “Experimental Investigation of Transonic Oscillating Cascade Aerodynamics,” AIAA Paper No. 89-0321.
10.
Buffum
D. H.
, and
Fleeter
S.
,
1990
, “
Oscillating Cascade Aerodynamics by an Experimental Influence Coefficient Technique
,”
Journal of Propulsion
, Vol.
6
, No.
5
, pp.
612
620
.
11.
Buffum
D. H.
, and
Fleeter
S.
,
1993
, “
Wind Tunnel Wall Effects in a Linear Oscillating Cascade
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
115
, pp.
147
156
.
12.
Carstens, V., 1991, “Transonic Unsteady Aerodynamics and Aeroelasticity,” presented at the 73rd Meeting of the AGARD Structures and Materials Panel, San Diego, CA, Oct. 7–11.
13.
Edwards, J. A., 1987, “Surface Pressure Distributions in an Unsteady Shock/Boundary Layer Interaction,” Thesis, Wolfson College, Cambridge, United Kingdom.
14.
Ezzat, A., Fransson, T. H., and Jolles, F., 1989, “Self-started Blade Vibrations in an Annular Turbine Cascade Operating at Transonic and Supersonic Mach Numbers,” ASME IGTI-Vol. 4, G. K. Serovy, T. H. Fransson, and J. Fabri, eds.
15.
Fransson, T. H., 1992, “Analysis of Experimental Time-Dependent Blade Surface Pressures From an Oscillating Turbine Cascade Using the Influence-Coefficient Technique,” Journal of Physics III, France, Apr., pp. 575–594.
16.
Gerolymos
G. A.
,
1993
a, “
Advances in the Numerical Integration of the 3-D Euler Equations in Vibrating Cascades
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
115
, pp.
781
790
.
17.
Gerolymos
G. A.
,
1993
b, “
Coupled 3-D Aeroelastic Stability Analysis of Bladed Disks
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
115
, pp.
791
799
.
18.
Hanamura
Y.
, and
Yamaguchi
K.
,
1988
, “
An Experimental Investigation on the Flutter of the Cascade of Turbomachinery in the Transonic Flow
,”
Journal of the Faculty of Engineering
, The University of Tokyo (B), Vol.
XXXIX
, No.
3
, pp.
311
338
.
19.
Inger, G. R., 1981, “Application of a Shock-Turbulent Boundary-Layer Interaction Theory in Transonic Flowfield Analysis,” in: Transonic Aerodynamics, Vol. 81, D. Nixon, ed., AIAA, ISBN 0-915928-65-5.
20.
Liang
S. M.
,
Tsai
C. J.
, and
Ho
C. K.
,
1992
, “
Numerical Investigation of Unsteady Transonic Nozzle Flows
,”
AIAA Journal
, Vol.
30
, No.
2
, pp.
566
568
.
21.
Ott, P., 1992, “Oszillierender senkrechter Verdichtungsstoß in einer ebenen Du¨se,” Communication du Laboratoire de Thermique Applique´e et de Turbomachines, No. 18, EPF-Lausanne.
22.
Ott, P., Bo¨lcs, A., and Fransson, T. H., 1992, “Experimental Study of an Oscillating Normal Shock Wave in a Nozzle,” Proceedings of the 11th Symposium on Measuring Techniques in Transonic and Supersonic Flows in Cascades and Turbomachines, Sept. 14–15, Mu¨nchen, Federal Republic of Germany.
23.
Sze´che´nyi, E., Cafarelli, I., Notin, C., and Girault, J. P., 1984, “A Straight Cascade Wind-Tunnel Study of Fan Blade Flutter in Started Supersonic Flow,” Proceedings of the Third International Symposium on Unsteady Aerodynamics of Turbomachines and Propellers, Cambridge, United Kingdom, Sept., pp. 447–458.
24.
Sze´che´nyi, E., 1985, “Fan Blade-Single Blade Instability or Blade to Blade Coupling?” ASME Paper No. 85-GT-216.
25.
Usab
W. J.
, and
Verdon
J. M.
,
1991
, “
Advances in the Numerical Analysis of Linearized Unsteady Cascade Flows
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
113
, pp.
633
643
.
26.
Verdon, J. M., 1989, “The Unsteady Aerodynamic Response to Arbitrary Modes of Blade Motion,” Journal of Fluids and Structures, No. 3, pp. 255–274.
27.
Whitehead
D. S.
, and
Newton
S. G.
,
1985
, “
A Finite Element Method for the Solution of Two-Dimensional Transonic Flows in Cascades
,”
International Journal for Numerical Methods in Fluids
, Vol.
5
, pp.
115
132
.
28.
Whitehead
D. S.
,
1990
, “
A Finite Element Solution of Unsteady Two-Dimensional Flow in Cascades
,”
International Journal for Numerical Methods in Fluids
, Vol.
10
, pp.
10
34
.
This content is only available via PDF.
You do not currently have access to this content.