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Compressible and Two-Phase Flow with Applications Including Pressure Relief System Sizing


J. Wagner and R. Whiteley (Oklahoma State University)


This SACHE product introduces mass, momentum, and energy balances for fluid flow in pipes and orifices. A brief review of incompressible fluid flow reinforces fundamentals and illustrates problem-solving techniques using spreadsheets to introduce concepts of compressible flow in pipes and orifices. These materials can be used in several courses; e.g., fluid mechanics, heat transfer, and senior design courses.

The differential momentum balance for real gases is used to describe vapor flow in pipes including limitations of sonic velocity (choked flow) on mass flow rates (illustrated with examples). The material on two-phase flow is limited to friction losses and slip. Friction factor and void fraction correlations based on both separated flow and homogeneous flow models are presented (illustrated with examples of flashing and non-flashing systems). Important for sizing emergency relief systems, flashing liquid flows modeled as non-equilibrium flow in short pipes and nozzles are discussed along with the effect of sub-cooled liquid at the relief inlet.

The Pipe Flow.xls and Pipe Flow 3-Point.xls applications each contain over three thousand lines of Visual Basic(c) code to solve the mass, momentum, and energy balances for single-phase liquid, single-phase vapor, or vapor-liquid two-phase flow in pipes of constant diameter. Users can select the type of flow problem (calculate flow, inlet pressure, or outlet pressure) and correlations for two-phase friction factor and void-fraction. Both applications accommodate single and multi-component systems.

Pipe Flow 3-Point.xls fits property expansion models to user input results for three adiabatic flash calculations. These models are used to calculate the physical and transport properties and vapor quality required for the numerical integration of the differential momentum balance.

Pipe Flow.xls uses Chemstations’ Chemcad(c) process simulator as a VBA server to perform flash calculations and to calculate the physical and transport properties, as well as the vapor and liquid phase compositions.

Nozzle Flow.xls and Nozzle Flow 3-Point.xls are Visual Basic(c) applications for sizing or rating relief valves or flow through orifices. Nozzle Flow 3-Point.xls uses property expansion models based on the results of user input isentropic flash calculations, while Nozzle Flow.xls uses Chemcad(c) to directly perform flash calculations.

This SACHE product is a companion to several previously published SACHE products by Darby (2005), Grossel and Louvar (2006), Parvin and Sterling (2003), and Wagner (2004).

This product was updated January 2011, and an errata from the first printing is available.

Student access: All files are available to students logged into the site.

Suggested courses that can use this product

  • Fluid Flow
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