AN ANALYTIC THERMODYNAMIC MODEL FOR HYDRAULIC RESISTANCES BASED ON CFD FLOW PARAMETERS

Abstract

This article illustrates the development of an analytic lumped parameter thermo-hydraulic model for a wide range of hydraulic resistance geometries based on mass flow. The relevant flow parameters such as the contraction coefficient in case of laminar flow separation are derived from CFD simulations. Furthermore, the consideration of cavitation effects can be included. State of the art in lumped parameter simulations of hydraulic circuits utilise volume-flow based equations like the orifice equation, which is extended for a wide variety of geometries and flow conditions including the transition from laminar to turbulent flow by adjusting the discharge coefficient based on empirical equations or lookup tables. The same situation persists for laminar flow description. In this case the Hagen-Poiseuille equation is often used in conjunction with correction factors based on the Reynolds number to regard the transition of laminar to turbulent flow. However, in practical applications the use of different equations for various flow conditions and geometries is cumbersome. Furthermore, in the widely used volume based flow description, the absolute pressure dependency of mass flow due to density changes and critical flow at which cavitation occurs is not accounted for until now. Without consideration of these influences a mass conservative modelling and thus high model precision is not possible. The overall goal of the proposed model is to increase accuracy of hydraulic system simulation tools and to support usability by simplifying parameterisation on basis of dimensions available from data sheets. The results of this study are obtained analytically as well as empirically by means of CFD simulations. Moreover, a large number of performed simulations support the understanding of fundamental effects in hydraulic resistance flow.