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Shock tube flows past partially opened diaphragms

Published online by Cambridge University Press:  25 April 2008

PAOLO GAETANI ,
ALBERTO GUARDONE  and
GIACOMO PERSICO
PAOLO GAETANI
Affiliation:
Dipartimento di Energetica, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
ALBERTO GUARDONE
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
GIACOMO PERSICO
Affiliation:
Dipartimento di Energetica, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
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Abstract

Unsteady compressible flows resulting from the incomplete burst of the shock tube diaphragm are investigated both experimentally and numerically for different initial pressure ratios and opening diameters. The intensity of the shock wave is found to be lower than that corresponding to a complete opening. A heuristic relation is proposed to compute the shock strength as a function of the relative area of the open portion of the diaphragm. Strong pressure oscillations past the shock front are also observed. These multi-dimensional disturbances are generated when the initially normal shock wave diffracts from the diaphragm edges and reflects on the shock tube walls, resulting in a complex unsteady flow field behind the leading shock wave. The limiting local frequency of the pressure oscillations is found to be very close to the ratio of acoustic wave speed in the perturbed region to the shock tube diameter. The power associated with these pressure oscillations decreases with increasing distance from the diaphragm since the diffracted and reflected shocks partially coalesce into a single normal shock front. A simple analytical model is devised to explain the reduction of the local frequency of the disturbances as the distance from the leading shock increases.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 267 - 286
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ainsworth, R. W. & Allen, J. L. 1990 Investigating the performance of miniature semi-conductor pressure transducers for use in fast response aerodynamic probes. In Proc. 10th Symp. Meas. Tech. Turbomachines.Google Scholar
Alpher, R. A. & White, D. R. 1958 Flow in shock tube with area change at the diaphragm section. J. Fluid Mech. 3, 457–470.CrossRefGoogle Scholar
Barkhudarov, E. M., Mdivnishvili, M. O., Sokolovp, I. V., Taktakishvili, M. I. & Terekhin, V. E. 1991 Mach reflection of a ring shock wave from the axis of symmetry. J. Fluid Mech. 226, 497–509.CrossRefGoogle Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298.CrossRefGoogle Scholar
Fergason, S. H., Guardone, A. & Argrow, B. M. 2003 Construction and validation of a dense gas shock tube. J. Thermophys. Heat Transer 17 (3), 326–333.CrossRefGoogle Scholar
Gaydon, A. G. & Hurle, I. R. 1963 The shock tube in high temperature chemical physics. Reinhold.Google Scholar
Glass, I. I. & Sislian, J. P. 1994 Nonstationary Flows and Shock Waves. Clarendon.CrossRefGoogle Scholar
Gossweiler, C., Humm, H. J. & Kupferschmied, P. 1990 The use of piezo resistive semi-conductor pressure transducer for fast-response probe measurements in turbomachinery. In Proc. 10th Symp. Meas. Tech. Turbomachines.Google Scholar
Guardone, A. 2007 Three-dimensional shock tube flows of dense gases. J. Fluid Mech. 583, 423–442.CrossRefGoogle Scholar
Guardone, A. & Vigevano, L. 2007 Finite element/volume solution to axisymmetric conservation laws. J. Comput. Phys. 224, 489–518.CrossRefGoogle Scholar
Hickman, R. S., Farrar, L. C. & Kyser, J. B. 1975 Behavior of burst diaphragms in shock tubes. Phys. Fluids 18 (10), 1249–1252.CrossRefGoogle Scholar
Mirels, H. 1963 Test time in low-pressure shock tubes. Phys. Fluids 6 (9), 1201–1214.CrossRefGoogle Scholar
Mirels, H. & Mullen, J. F. 1964 Small perturbation theory for shock-tube attenuation and nonuniformity. Phys. Fluids 7 (8), 1208–1218.CrossRefGoogle Scholar
Nettleton, M. A. 1973 Shock attenuation in a ‘gradual’ area expansion. J. Fluid Mech. 60, 209–223.CrossRefGoogle Scholar
Paniagua, G. & Dénos, R. 2002 Digital compensation of pressure sensors in time domain. Exps. Fluids 32, 417–424.CrossRefGoogle Scholar
Persico, G., Gaetani, P. & Guardone, A. 2005 Dynamic calibration of fast-response probes in low-pressure shock tubes. Meas. Sci. Technol. 16, 1751–1759.CrossRefGoogle Scholar
Petrie-Repar, P. & Jacobs, P. A. 1998 A computational study of shock speeds in high-performance shock tubes. Shock Waves 8, 79–91.CrossRefGoogle Scholar
Rothkopf, E. M. & Low, W. 1974 Diaphragm opening process in shock tubes. Phys. Fluids 17 (6), 1169–1173.CrossRefGoogle Scholar
Sun, M. & Takayama, K. 2003 Vorticity production in shock diffraction. J. Fluid Mech. 478, 237–256.CrossRefGoogle Scholar
White, D. R. 1958 Influence of diaphragm opening time on shock-tube flows. J. Fluid Mech. 4, 585–599.CrossRefGoogle Scholar