Noble-Abel Stiffened Gas equation of state calibration

About

Noble-Abel Stiffened Gas (NASG) equations of state (EOS) calibration for compressible diphasic flow under mechanical equilibrium. Calibration of SG EOS parameters is done for a liquid in the presence of its vapor. The EOS parameters are determined from experimental saturation curves.

Reference

Le Métayer, O., & Saurel, R. (2016). The noble-abel stiffened-gas equation of state. Physics of Fluids, 28(4), 046102.

How to use

General remarks

0. Setup

This tool is fully compatible under Unix systems, however it is necessary to have the following utilities :

• Make
• Gnuplot

To install them through a package manager you can use the apt command :

$ sudo apt install pkg-name

With pkg-name the name of the package that you want to install.

1. Compilation & Run

The compilation is done with a Makefile. Under Unix systems it reads :

$ make 

To run the calibration tool you just need to type the following :

$ ./exe

If you want to delete all .o files from the compilation you can run :

$ make clean

In case you want to remove the executable exe:

$ make mrproper

To delete all the result files you can do :

$ make resClean

2. General

To run a Noble-Abel Stiffened Gas calibration you must provide two files located at the following path NASG-EOS_Calibration/input/:

• refState.txt wich contains data of the liquid reference state, the pressure p₀ (Pa), the density ρ₀ (kg/m³) and the sound speed c₀ (m/s).
• expData.txt which contains experimental saturation data at the temperature range of study. The first line of this file is not read, there are 7 rows to fill (each one separated by a blank or a tab) as follows:

T (K)	Psat (Pa)	vG (m3/kg)	vL (m3/kg)	hG (J/kg)	hL (J/kg)	Lv (J/kg)
T1	Psat1	vG1	vL1	hG1	hL1	Lv1
...	...	...	...	...	...	...
TN	PsatN	vGN	vLN	hGN	hLN	LvN

Remark: the decimal separator must be a dot.

3. Results and plot

Once the NASG parameters are calibrated you will get their values in the shell environnement.

Theoritical curves can be found in the folder NASG-EOS_Calibration/res/. If you want to plot theses curves and compare with the experimental ones you will have to go to the folder NASG-EOS_Calibration/res/ and run the script ./runPlot.sh. It might be possible that you don't have the rights to lauch these scripts, thus you will have to do a quick chmod +x runPlot.sh

Script runPlot.sh display a preview of all curves in Gnuplot GUI and create in the same time plot files in eps format in the repository NASG-EOS_Calibration/res/.

4. Library of test cases

Under the folder NASG-EOS_Calibration/input/lib/ you can find test cases for validation. The test cases are:

• Liquid/vapor dodecane in the temperature range T ∈ [300-500 K]. Experimental data are from J. R. Simões-Moreira, “Adiabatic evaporation waves” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, 1994.
• Liquid water and steam in the temperature range T ∈ [300-500 K]. Experimental data are extracted from NIST website.
• Liquid/vapor oxygen in the temperature range T ∈ [60-100 K]. Experimental data are available at the NIST website.

In case of a new calibration, useful experimental data can be found in the NIST website.