SPH simulations of water flow through a Venturi meter of rectangular cross-section: Comparison with experiments

Abstract

We present three-dimensional simulations of water flow through a horizon- tal, small-scale Venturi tube of rectangular cross-section at Reynolds numbers between 13272 and 33180, using the method of Smoothed Particle Hydrody- namics (SPH) for solving the conservation laws. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) model for tur- bulence. Comparison with experimental measurements is provided in terms of centerline streamwise velocity and pressure profiles along the extent of the Ven- turi meter and cross-sectional velocity profiles at given stations. The numerical results are in good agreement with the experimental data, with root-mean square errors from 4.3% to 7.1% and from 1.4% to 6.8% for the centerline streamwise velocity (in units of m s−1) and differential pressure (in psi) along the Venturi tube, respectively, and ≲ 5.5% for the cross-sectional velocity profiles (in m s−1) within the throat and divergent sections. These errors increase with increasing volumetric flow rates. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flowmeters at moderately high Reynolds numbers instead of using costly experimental tests.