Estimating the number of transducers for flow rate measurement using the UVP method downstream of double elbows

• Flow rate errors were less than 2% when using the optimal number of transducers.
• The flow metering position was 1 diameter downstream of double elbows.
• The transducer number was determined using FFT and the sampling theorem.
• Circumferential velocity profiles on the pipe cross-section were used for FFT.

This study proposes a new method that determines the number of transducers for accurate flow rate measurements using the ultrasonic velocity profile (UVP) method downstream of double elbows. Because the UVP method can measure velocity profiles over a pipe diameter and integrate them to obtain the flow rate, it is also expected to obtain an accurate flow rate using multiple transducers under asymmetric flow conditions formed downstream of elbows. The new estimation method employs the wavenumber of velocity profile fluctuation along a circle on a pipe cross-section, obtained by fast Fourier transform (FFT). The number of transducers was determined as twice the wavenumber at the foot of maximum Fourier amplitude, on the basis of the sampling theorem. The method was evaluated by a preliminary experiment and numerical simulations using computational fluid dynamics (CFD). The experimental and simulated velocity profiles were located at three times the pipe diameter (3D) and 1D downstream of the second elbow, respectively. Reynolds numbers for the experiment and simulations were set at 4×104 and 5×106, respectively. Using the number of transducers estimated by FFT, the standard deviations of flow rate errors were less than 1% or 2%, verifying the efficacy of the new method.