Discharge coefﬁcient performance of Venturi, standard concentric oriﬁce plate, V-cone and wedge ﬂow meters at low Reynolds numbers
The relation between the Reynolds number and differential producer discharge coefﬁcient was obtained through solutions to the steady, Reynolds-averaged Navier–Stokes equations. Discharge coefﬁcients were also obtained experimentally for the purpose of validating the numerical results. The focus of the study was directed toward low Reynolds numbers commonly associated with pipeline transportation of viscous ﬂuids, however high Reynolds number were also considered. The study indicates that, at low Reynolds numbers, the discharge oefﬁcients decrease rapidly with decreasing Reynolds number for Venturi, V-cone, and wedge ﬂow meters. The oriﬁce plate meter did not follow the general trends of the other meters, but rather as the Reynolds number decreased, the discharge coefﬁcient increased to a maximum before sharply dropping off with further decrease in the Reynolds number. The results presented herein provide an improved understanding of differential ﬂow meters operating at low Reynolds numbers, and demonstrate the usefulness of computational ﬂuid dynamics in predicting discharge coefﬁcient trends at very low Reynolds numbers.