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Transient analysis for compressible fluid flow in transmission line by the method of characteristics

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Abstract

Transient analysis for compressible fluid flow has been conducted to evaluate the dynamic characteristics of the dead-ended or volume-terminated transmission lines following a sudden pressure change at its entrance. The two partial-differential equations, based on the conservation of mass, energy and momentum, were derived for the one-dimensional adiabatic compressible flow with friction and entrance head loss. The governing equations describing the present transient-state flow are hyperbolic, and the boundary conditions include a fixed volume termination at the exit and sinusoidal disturbance in the sudden pressure change at tube entrance. The method of characteristics is used to transform the partial differential equation into the particular total differential equations, which can be integrated along the characteristic lines. The present result shows good agreements with the existing results. The effects of tube length. tube diameter and end volume are evaluated on the responses of the pressure and on the damping factor.

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Abbreviations

A :

Cross section area of the pipe

c :

Acoustic velocity

C c :

Critical damping coefficient

C k :

Coefficient of entrance loss

D :

Pipe diameter

f :

Friction factor

g :

Acceleration of gravity

H :

Pressure head

k :

Fluid-elastic stiffness coefficient

L :

Pipe length

m :

Effective mass of fluid in the pipe

p :

Pressure

Q :

Flow rate

Re :

Reynolds number

t :

Time

T :

Period of oscillation

u :

Mean flow velocity

V q :

Fixed volume of the receiver

x :

Axial coordinate

ζ:

Damping factor

μ:

Viscosity of fluid

ρ:

Density of fluid

ω:

Circular frequency

+:

Nondimensional parameter

a :

Based on acoustic velocity

e :

Entrance

t :

Based on lumped acoustic element method

mean :

Mean value

res :

Sending reservoir

rt :

Receiver

s :

Static step input

References

  • Abbott, M. B., 1966, “An Introduction to the Method of Characteristics,”American Elsevier, New York.

    Google Scholar 

  • Bradner, M., 1949, “Pneumatic Transmission Lag,”Instruments, Vol. 22, pp. 618–625.

    Google Scholar 

  • Bulaty, T. and Niessner, 1985, “Calculation of 1-D Unsteady Flows in Pipe Systems of I. C. Engine,”Journal of Fluids Engineering, Vol. 107, pp. 407–412.

    Google Scholar 

  • Chaudhry, M. H., 1987, “Applied Hydraulic Transients,”Van Nostrand Reinhold, 2nd ed., New York.

  • Evangelisti, G, 1969, “Waterhammer Analysis by the Method of Characteristics,”L’Energia Electrica, Nos. 10-12, pp. 673–692, 759–770, 839–858.

    Google Scholar 

  • Holloway, M. B. and Chaudhry, M. H., 1985, “Stability and Accuracy of Waterhammer Analysis,”Advances in Water Resources, Vol. 8, pp. 121–128.

    Article  Google Scholar 

  • Iberall, A. S., 1950, “Attenuation of Oscillatory Pressures in Instrument Lines,”Journal of Research of the National Bureau of Standards, Research Paper RP2115, Vol. 45, pp. 85–108.

    Google Scholar 

  • Kinsler, L. E., Frey, A. S., Coppens, A. B. and Sanders, J. V., 1982, “Fundamentals of Acoustics,” John Wiley & Sons, 3rd ed., New York.

    Google Scholar 

  • Moise, J. C., 1954, “Pneumatic Transmission Lines,”Journal of the ISA, Vol. 1, pp. 35–40.

    Google Scholar 

  • Rohmann, C. P. and Grogan, E. C., 1957, “On the Dynamics of Pneumatic Transmission Lines,”Trans. ASME, Vol. 79, pp. 853–867.

    Google Scholar 

  • Sabersky, R. H, Acosta, A. J. and Hauptmann, E. G., 1971, “Fluid Flow,” Macmillan Co., 2nd ed., New York.

    Google Scholar 

  • Schuder, C. B. and Binder, R. C., 1959, “The Response of Pneumatic Transmission Lines to Step Inputs,”Journal of Basic Engineering, Vol. 81, pp. 578–584.

    Google Scholar 

  • Wiggert, D. C., Otwell, R. S. and Hatfield, F. J., 1985, “The Effect of Elbow Restraint on Pressure Transients,”Journal of Fluids Engineering, Vol. 107, pp. 403–406.

    Article  Google Scholar 

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Authors and Affiliations

  1. Korea Atomie Energy Research Institute, Korea

    Woo-Gun Sim

  2. Chungnam National University, Chungnam, Korea

    Jong-Ho Park

Authors
  1. Woo-Gun Sim
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  2. Jong-Ho Park
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Sim, WG., Park, JH. Transient analysis for compressible fluid flow in transmission line by the method of characteristics. KSME International Journal 11, 173–185 (1997). https://doi.org/10.1007/BF02944891

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  • DOI: https://doi.org/10.1007/BF02944891

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