Density Smoothing

The idea of this method is to smooth out (i.e. making it C1-continuous) the density for a range of vapour qualities and recalculating its partial derivatives in the smoothed area. In this situation, the density derivatives are continuous (but not smooth).

The density is smoothed using a spline function with respect to the enthalpy between the liquid saturation line and a constant vapor quality line, set as 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.

In the following example, the working fluid R245fa isĀ  defined with density smoothing between vapor qualities 0 to 0.1. The |rho_smoothing_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.

Smoothing of the density using a spline function