A Low Reynolds Number Discharge Coefficient Equation for Critical Flow Venturis and the Effects of Inlet Radius

摘要

The discharge coefficient, Cd, for a Critical Flow Venturi Nozzle (CFVN) corrects the theoretical mass flow to the actual mass flow at measured inlet conditions. The theoretical mass flow is calculated using 1-D isentropic theory and does not account for the subsonic boundary layer along the CFVN wall. For a precisely known throat area, Cd must be less than unity due to this boundary layer. Theory predicts that the geometry of the inlet to a CFVN will affect the boundary layer and therefore effect the Cd. This effect on Cd becomes more significant for smaller CFVNs which are operated at lower Reynolds Numbers. The international standard, ISO 9300, for toroidal CFVNs allows inlet curvature to vary from 1.8 to 2.2 times the throat diameter, d, but limits the use of the Empirical Cd-Reynolds Number equation to Reynolds Numbers above 21000. Low Reynold's Number calibration data for hundreds of small CFVNs with 2d inlet curvature will be used to generate an Empirical Cd-Reynolds Number equation. This paper will also present the results of testing multiple CFVNs with varying inlet curvature at low Reynolds Numbers. These results will be used to examine the specific Cd sensitivity to this geometric component and determine if more stringent inlet curvature requirements are necessary for low Reynolds number CFVN applications. The Empirical Cd-Reynolds Number equation, along with additional inlet curvature guidelines will be presented as a method for calculating actual mass flow through a CFVN when the Reynolds Number is below the minimum value at which the ISO 9300 equation can be applied.