Velocity Distribution Inversion Method Based on the RANS Equations Using Microwave Doppler Radar

Abstract

Microwave Doppler radar has been used to make non-contact river flow measurements and offers a high resolution and a wide range. However, discharge estimation with microwave Doppler radar is challenging due to the inability to measure flow velocity below the river surface based on the Doppler shift. To address this problem, a velocity distribution inversion method based on the Reynolds-Averaged Navier-Stokes (RANS) equations is proposed. A classical two-region model which divides the flow into the inner region and the outer region is applied. Velocity at the inner-outer boundary is estimated using surface velocity and the log law is used to estimate velocity distribution of the inner region. Taking velocities at the surface and the inner-outer boundary as boundary conditions, the velocity distribution in the outer region is derived by solving the RANS equations. Discharge is calculated by combining the proposed method with the velocity-area method. The results illustrated that the velocity distribution obtained by the proposed method and measured by an acoustic instrument are in reasonable agreement. Discharge estimated using the obtained velocity distribution has an error less than 10%. The work indicates the potential of microwave Doppler radar to retrieve the river cross section velocity distribution and estimate discharge.