Smoothing of density derivative

In this method, the discontinuous partial density derivatives are smoothed using a spline function between vapour qualities of ranging from 0 to x, x being a model parameter.

Such a method can only be implemented at the level of the equation of state, i.e. in the thermophysical properties database. Most fluid properties libraries are not open-source, which does not enable the implementation of such a method. However, the CoolProp library is open-source and its database comprises nearly as many fluids as the Refprop library. Its source code has therefore been modified to implement this method, which can be activated by a simple flag in when passing the working fluid name to the library.

The main drawback of this method is that the density function is still calculated with the original equation of state: the smoothed density derivative is not consistent with the density function provided by the EOS. This might cause a mass defect during the simulation.

In the following example, the working fluid R245fa isĀ  defined with density smoothing between vapor qualities 0 to 0.1. The |twophase_derivsmoothing_xend=0.1 flag indicates to CoolProp that smoothing must be activated and passes the smoothing range as argument.


Sylvain Quoilin, Ian Bell, Adriano Desideri, and Vincent Lemort. Methods to increase the robustness of finite-volume flow models in thermodynamic systems. To be published in Energies, 2014.

Ian H. Bell, Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. Pure- and Pseudo-Pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Industrial & Engineering Chemistry Research, 2014.