1 Cav03-GS-19-001 Fifth International Symposium on Cavitation (CAV2003) Osaka, Japan, November 1-4, 2003 EFFECTS OF SPEED OF SOUND VARIATION ON UNSTEADY CAVITATING FLOWS BY USING A BAROTROPIC MODEL Ciro Pascarella CIRA (Centro Italiano Ricerche Aerospaziali) Via Maiorise, 81043 Capua (CE) Italy e-mail: c.pascarella@cira.it Vito Salvatore CIRA (Centro Italiano Ricerche Aerospaziali) Via Maiorise, 81043 Capua (CE) Italy e-mail: v.salvatore@cira.it Alessandro Ciucci European Space Agency 8-10 rue Mario Nikis 75738 Paris Cedex 15 France e-mail: a.ciucci@hq.esa.fr ABSTRACT Barotropic models despite their attractiveness, due to their simplicity and their clear physical meaning, need to be appropriately set by defining a key parameter that is the value of minimum speed of sound (SoS) for the liquid-vapor mixture. The different value of SoS setting can significatively affect the flow field resulting from numerical simulation especially in terms of unsteady modeling. This paper, hence, is addressed to investigate the influence of the minimum speed of sound of the mixture on the simulation of unsteady cavitating flow by using a barotropic model. In particular, results for four cases of cavitating flow around a NACA0015 airfoil at 8 o angle of attack are reported, and a barotropic relationship is implemented to take into account the liquid-vapor phase change. The variations of the flow dynamic response and the variations of the main flow features associated with different values of minimum speed of sound are reported and discussed. Results show that the minimum speed of sound of the mixture plays a very important role in the numerical simulation of cavitating flow revealing that a sudden change of flow field response occurs when a threshold value of minimum speed of sound is reached. INTRODUCTION The difficulty in the numerical modeling of cavitating flows using both an one-fluid (homogeneous) approach (Delannoy and Keuny, 1998, Kubota et al., 1992, Avva and Singhai, 1995, Chen and Heister, 1994(a), Pascarella et al., 2000,2001 and Salvatore et al. 2001) and a two-phase approach (Chen and Heister, 1994(b), De Jong and Sabnis, 1991) is well known. This paper deals with a numerical method belonging to the first family and, in particular, reports a work on the simulation of unsteady homogeneous cavitating flows in thermal equilibrium conditions. A cavitating fluid often corresponds to a complicated situation from a numerical point of view; in fact, both incompressible zones (pure phases) and regions where the flow may become highly supersonic (liquid-vapor mixtures) are present in the flow field and need to be resolved. The numerical stiffness of the phenomenon is further increased both from the high density ratio between the two phases (for water at 293 K the density ratio is equal to 1.7 10 -5 ) and from the strong shock discontinuity occurring at re-condensation. This singular behavior is due to the huge variation of speed of sound as the flow goes from a pure phase to a mixture. For instance, in the same hypothesis indicated above, the speed of sound is equal to about 1500 m/s for the liquid phase, 400 m/s for vapor phase and 3.2 m/s for a liquid-vapor mixture corresponding to a value of void fraction equal to 0.5 (Jacobsen, 1964). Moreover, the latter value of minimum speed of sound is calculated in thermal equilibrium conditions and neglecting both the exchange of mass between the two phases and the surface tension effects. Indeed, the calculation of minimum speed of sound can vary largely depending on the hypothesis that one assumes. For example, using the steam tables (Rivkin, 1988) and assuming cavitation as an isenthalpic transformation (Avva, 1995), the minimum speed of sound at 293 K is approximately equal to 0.004 m/s. In addition, the speed of sound is a parameter that can be easily defined only when the thermodynamics of phase change is very fast or very slow (frozen - equilibrium) with respect to the characteristic time of the phenomenon (Brennen, 1995). For all