Research Papers: Techniques and Procedures

A Polytropic Approximation of Compressible Flow in Pipes With Friction

[+] Author and Article Information
William M. Kirkland

Research Reactors Division,
Oak Ridge National Laboratory,
Oak Ridge, TN 37831
e-mail: kirklandwm@ornl.gov

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 24, 2019; final manuscript received May 4, 2019; published online June 7, 2019. Assoc. Editor: Oleg Schilling.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Fluids Eng 141(12), 121404 (Jun 07, 2019) (7 pages) Paper No: FE-19-1056; doi: 10.1115/1.4043717 History: Received January 24, 2019; Revised May 04, 2019

This paper demonstrates the usefulness of treating subsonic Fanno flow (adiabatic flow, with friction, of a perfect gas in a constant-area pipe) as a polytropic process. It is shown that the polytropic model allows an explicit equation for mass flow rate to be developed. The concept of the energy transfer ratio is used to develop a close approximation to the polytropic index. Explicit equations for mass flow rate and net expansion factor in terms of upstream properties and pressure ratio are developed for Fanno and isothermal flows. An approximation for choked flow is also presented. The deviation of the results of this polytropic approximation from the values obtained from a traditional gas dynamics analysis of subsonic Fanno flow is quantified and discussed, and a typical design engineering problem is analyzed using the new method.

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Grahic Jump Location
Fig. 1

Comparison of full Eq. (24) and simplified linear Eq. (25) for the polytropic index c

Grahic Jump Location
Fig. 2

Calculated net expansion factor Y for γ = 1.3

Grahic Jump Location
Fig. 3

Calculated net expansion factor Y for γ = 1.4

Grahic Jump Location
Fig. 4

Calculated net expansion factor Y for γ = 1.67

Grahic Jump Location
Fig. 5

Comparison of choking pressure to best-fit approximation, Eq. (34)



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