Calculation of Turbine Flow Meters by Computational Fluid Dynamics Methods

Using the Ansys Fluent 2020 R2 computational fluid dynamics suite, a method for calculating the three-dimensional velocity field in helicoid-type turbine flow meters is developed, based on the torque balance equation, i.e., the equality of the driving and retarding torques on the turbine, which is achieved at an equilibrium rotation speed for a given constant volumetric flow rate (which is fulfilled when the angular acceleration is equal to zero). At constant flow rate, when the rotor speed changes, the moment on the rotor blade is determined. The value of the speed is found at which the moment changes sign. The dependence of the torque on the number of revolutions is plotted on a graph and the true number of revolutions is determined at which the torque is zero for a given flow rate. The basis for the mathematical description of turbulent three-dimensional flow in flow meters is a system of differential equations of conservation of mass (continuity equation) and momentum and the standard k–ω turbulence model (based on the Wilcox model) with partial derivatives in cylindrical coordinates in a three-dimensional problem setting. The multiple reference frame method incorporated into the Ansys Fluent computing suite allows reducing the problem involving stationary and rotating elements to a stationary one. The numerical calculation is performed at various flow rates (from 354 to 1982 m3/h) and kinematic viscosity (from 0.2 to 140 cSt). The main characteristics of turbine flow meters are determined: the specific meter factor (or K-factor), and the Strouhal and Roschko numbers. The greatest discrepancy between the numerical calculation and the experimental data on the K-factor value is obtained at low flow rates and at the highest viscosity of 140 cSt (which is beyond the scope of application of the researched flow meter) and is no more than 5%.