A Polytropic Approximation of Compressible Flow in Pipes With Friction

Kirkland, William M.

doi:10.1115/1.4043717

Title: A Polytropic Approximation of Compressible Flow in Pipes With Friction

Abstract

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. Here, 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.

Authors:

^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Fri Jun 07 00:00:00 EDT 2019

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1524879

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Fluids Engineering

Additional Journal Information:: Journal Volume: 141; Journal Issue: 12; Journal ID: ISSN 0098-2202

Publisher:: ASME

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING

Citation Formats


                    Kirkland, William M. A Polytropic Approximation of Compressible Flow in Pipes With Friction.  United States: N. p., 2019. 
Web.  doi:10.1115/1.4043717.

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                    Kirkland, William M. A Polytropic Approximation of Compressible Flow in Pipes With Friction.  United States.  https://doi.org/10.1115/1.4043717

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                    Kirkland, William M. Fri .  
"A Polytropic Approximation of Compressible Flow in Pipes With Friction".  United States.  https://doi.org/10.1115/1.4043717.  https://www.osti.gov/servlets/purl/1524879.

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@article{osti_1524879,

  title        = {A Polytropic Approximation of Compressible Flow in Pipes With Friction},

  author       = {Kirkland, William M.},

  abstractNote = {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. Here, 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.},

  doi          = {10.1115/1.4043717},

  journal      = {Journal of Fluids Engineering},

  number       = 12,

  volume       = 141,

  place        = {United States},

  year         = {Fri Jun 07 00:00:00 EDT 2019},

  month        = {Fri Jun 07 00:00:00 EDT 2019}

}

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https://doi.org/10.1115/1.4043717

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Works referenced in this record:

Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio
journal, January 2012

Christians, Joseph
International Journal of Mechanical Engineering Education, Vol. 40, Issue 1
DOI: 10.7227/IJMEE.40.1.9

Estimating sonic gas flow rates in pipelines
journal, March 2005

Keith, Jason M.; Crowl, Daniel A.
Journal of Loss Prevention in the Process Industries, Vol. 18, Issue 2
DOI: 10.1016/j.jlp.2004.12.004

Flow Analysis and Assessment of Loss Models in the Symmetric Volute of a Turbo-Blower
journal, January 2012

Kim, Semi; Park, Junyoung; Choi, Bumseok
Journal of Fluids Engineering, Vol. 134, Issue 1
DOI: 10.1115/1.4005670

A flow rate equation for subsonic Fanno flow
journal, March 2013

Urata, Eizo
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 227, Issue 12
DOI: 10.1177/0954406213480295

Single Phase Compressible Steady Flow in Pipes
journal, January 2010

Hullender, David; Woods, Robert; Huang, Yi-Wei
Journal of Fluids Engineering, Vol. 132, Issue 1
DOI: 10.1115/1.4000742

A Novel Adiabatic Pipe Flow Equation for Ideal Gases
journal, January 2012

Seob Kim, Jung; Radheshyam Singh, Navneet
Journal of Fluids Engineering, Vol. 134, Issue 1
DOI: 10.1115/1.4005679

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Similar Records

Title: A Polytropic Approximation of Compressible Flow in Pipes With Friction

Abstract

Citation Formats

Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio journal, January 2012

Estimating sonic gas flow rates in pipelines journal, March 2005

Flow Analysis and Assessment of Loss Models in the Symmetric Volute of a Turbo-Blower journal, January 2012

A flow rate equation for subsonic Fanno flow journal, March 2013

Single Phase Compressible Steady Flow in Pipes journal, January 2010

A Novel Adiabatic Pipe Flow Equation for Ideal Gases journal, January 2012

Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio
journal, January 2012

Estimating sonic gas flow rates in pipelines
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journal, January 2012

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journal, March 2013

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journal, January 2010

A Novel Adiabatic Pipe Flow Equation for Ideal Gases
journal, January 2012