INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2004; 46:735–765 Published online 10 September 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/d.762 Numerical simulation of dense gas ows on unstructured grids with an implicit high resolution upwind Euler solver P. Colonna 1; ∗; † and S. Rebay 2 1 Faculty of Design; Engineering and Production; Energy Technology Section; Delft University of Technology; Mekelweg 2; 2628 CD Delft; The Netherlands 2 Dip. di Ingegneria Meccanica; Universit a di Brescia; via Branze 38; 25123 Brescia; Italy SUMMARY The study of the dense gas ows which occur in many technological applications demands for uid dynamic simulation tools incorporating complex thermodynamic models that are not usually available in commercial software. Moreover, the software mentioned can be used to study very interesting phenom- ena that usually go under the name of ‘non-classical gasdynamics’, which are theoretically predicted for high molecular weight uids in the superheated region, close to saturation. This paper presents the numerical methods and models implemented in a computer code named zFlow which is capable of simu- lating inviscid dense gas ows in complex geometries. A detailed description of the space discretization method used to approximate the Euler equations on unstructured grids and for general equations of state, and a summary of the thermodynamic functions required by the mentioned formulation are also given. The performance of the code is demonstrated by presenting two applications, the calculation of the transonic ow around an airfoil computed with both the ideal gas and a complex equation of state and the simulation of the non-classical phenomena occurring in a supersonic ow between two staggered sinusoidal blades. Non-classical eects are simulated in a supersonic ow of a siloxane using a Peng–Robinson-type equation of state. Siloxanes are a class of substances used as working uids in organic Rankine cycles turbines. Copyright ? 2004 John Wiley & Sons, Ltd. KEY WORDS: Euler solver; unstructured grid; high resolution upwind space discretization; implicit time integration; dense gas; real gas; equations of state; non-classical gasdynamics; BZT uids; siloxanes; organic Rankine cycle 1. INTRODUCTION In the numerical simulation of gaseous ows the polytropic ideal gas thermodynamic model is usually employed because of its simplicity and the corresponding low computational cost. This is an acceptable approximation in many cases, but there are applications in which the ∗ Correspondence to: P. Colonna, Faculty of Design, Engineering and Production, Energy Technology Section, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands. † E-mail: P.Colonna@WbMT.TUDelft.nl Received 10 December 2003 Copyright ? 2004 John Wiley & Sons, Ltd. Revised 2 June 2004