THE DYNAMIC CHARACTERISTICS OF TAPERED FLUID LINES WITH VISCOE-LASTIC PIPE WALLS (TRANSFER MATRIX AND FREQUENCY RESPONSE)
Keywords:
fluid power systems, tapered fluid lines, transfer matrix equation, viscoelastic pipe wall, frequency responseAbstract
For convenience in investigating the dynamic responses of a liquid-filled tapered line with a viscoelastic pipe wall, a transfer matrix equation, relating pressure to volumetric flow, is derived. In this derivation, it was assumed that the rate of divergence (or convergence) of the line is comparatively small. The fluid line model employed in the analysis is one of an unsteady viscous flow; that is, the frequency-dependent effect of viscosity is taken into consideration. The visco-elastic pipe wall model is a modified version of the Voigt mechanical model, and it is distributed along the pipeline. The frequency response curves are calculated from the matrix, and the accuracy of the curves is evaluated by comparing them with the response curves obtained without assuming the small taper angle. The results verify that the transfer ma-trix is accurate enough for practical applications.
Downloads
References
Belardinelli, E. and Cavalcanti, S. 1992. Theoretical analysis of pressure pulse propagation in arterial vessels. Comput. Biol. Med., pp. 1337-1349.
Goodson, R. E. and Leonard, R. G. 1972. A Survey of Modeling Techniques for Fluid Transmission Line Transients. Journal of Basic Engineering, Trans. ASME, Ser. D, Vol. 94, No. 2, pp. 474-482.
McDonald, D. A. 1960. Blood flow in arteries. Edward Arnold.
Misra, J. C. and Singh, S. I. 1987. A Study on the Non-linear Flow of Blood Through Arteries. Bull. of Mechanical Biology, Vol. 49, No. 3, pp. 257-277.
Muto, T., Kinoshita, Y. and Yoneda, R. 1981. Dy-namic Response of Tapered Fluid Lines (1st Report, Transfer Matrix and Frequency Response). Bull. of JSME, Vol. 24, No. 191, pp. 809-815.
Muto, T., Yamada, H. and Kato, H. 1996 A Fast and Convenient Method for Simulating Transient Re-sponse of Fluid Lines with Viscoelastic Pipe Walls. 12. Aachener Fluidtechnisches Kolloquium, Band 2, pp. 257-268
Nakano, K. and Yoshimoto, M. 1970. The Dynamic Characteristics of a Hydraulic Pipe Line with a Vis-coelastic Pipe Wall. Trans. of the SICE (in Japa-nese), Vol. 6, No. 3, pp. 201-209.
Oldenburger, R. and Goodson, R. E. 1964. Simplifi-cation of Hydraulic Line Dynamics by Use of Infi-nite Products. Journal of Basic Engineering, Trans. ASME, Ser. D, Vol. 86, pp. 1-10.
Pontrelli, G. 2000. Blood Flow through a Circular Pipe with an Impulsive Pressure Gradient. Mathematical Models and Methods in Applied Sciences, Vol. 10, No. 2, pp.187-202.
Rouleau, W. T. and Young, F. J. 1965. Distortion of Short Pulses in Tapered Tube Pulse Transformers. Part I-Inviscid Liquid. Trans. ASME, Ser. D, Vol. 87, No. 2, pp. 465-470.
Tahmeen, M., Muto, T. and Yamada, H. 2001. Simu-lation of Dynamic Responses of Tapered Fluid Lines. JSME Int. Journal, Ser. B, Vol. 44, No. 2.
Ursino, M. and Artioli, E. 1992. High Frequency Pressure Propagation in Viscoelastic Tubes: A New Experimental Approach. Bio-Medical Materials and Engineering, Vol. 2, pp. 19-31.
Womersley, J. R. 1957. An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mam-malian Arteries. McGregor and Midwest Corp. Dayton, Ohio.
