Shape optimization of the cone body for the improved performance of the V-cone flowmeter: A numerical study

Abstract

The present study has been carried out to optimize the shape of the cone body by providing a curved surface (the radius of curvature (R)) at the base of the cone element for improving the performance of the V-cone flowmeter using CFD. Radii of curvature of 20 mm (hemispherical, R/d = 0.5), 22 mm (R/d = 0.55) 25 mm (R/d = 0.625) and 27.62 mm (R/d = 0.6905) are taken in order to gradually reduce the arc length keeping the chord length constant. In addition a semi-elliptical based cone with 20 mm semi-major axis and10 mm semi-minor axis has also been investigated in the present study. The centre of the spheres and ellipse lie on the axis either in the frustum or cylindrical part of the cone. The equivalent diameter ratio (β) has been taken as 0.6 while three different fore-vertex angles (φ) namely 60°, 75° and 90° have been investigated. The Reynolds number has been varied in the range of 1 × 103 to 1 × 106. The results have been compared with the slant surface based cone. It is seen that introduction of a curved surface at the cone base has profound effect on the coefficient of discharge of the V-cone flowmeter. The coefficient of discharge is dependent on Reynolds number for the flowmeter with hemispherical and semi-elliptical based cone element. The coefficient of discharge is seen to be a weak function of Reynolds number for Re = 4000 and beyond for the other three curvatures. The cone flowmeter with a curved base cone of R/d equals to 0.55 has higher coefficient of discharge and smaller standard deviation compared to a device with an aft vertex cone.