Semiempirical method of determining flow coefficients for pitot rake mass flow rate measurements

Flow coefficients applicable to area-weighted pitot rake mass flow rate measurements are presented for fully developed, turbulent flow in an annulus. A turbulent velocity profile is generated semiempirically for a given annulus hub-to-tip radius ratio and integrated numerically to determine the ideal mass flow rate. The calculated velocities at each probe location are then summed, and the flow rate as indicated by the rake is obtained. The flow coefficient to be used with the particular rake geometry is subsequently obtained by dividing the ideal flow rate by the rake-indicated flow rate. Flow coefficients ranged from 0.903 for one probe placed at a radius dividing two equal areas to 0.984 for a 10-probe area-weighted rake. Flow coefficients were not a strong function of annulus hub-to-tip radius ratio for rakes with three or more probes. The semiempirical method used to generate the turbulent velocity profiles is described in detail.