New Method to Calculate Friction Velocity in Smooth Channel Flows Using Direct Numerical Simulation Data

Abstract

In this paper, we leverage the direct numerical simulation (DNS) data for closed-channel flow for a range of friction Reynolds number (Reτ∼180–5,000) to develop a new one-point friction velocity method (OPFVM) to calculate friction velocity U* in terms of free-surface velocity Um, flow depth h, and kinematic viscosity ν. In contrast to prevalent methods that require several cumbersome near boundary measurements to obtain friction velocity, the OPFVM relies on a single easy-to-measure free-surface velocity measurement. The formulation is used to obtain friction velocity for a closed-channel flow (CCF) DNS regime with Reτ=10,049 and on four open-channel flow (OCF) DNS regimes with Reτ∼180–2,000. The same formulation was then experimentally verified in our laboratory. To avoid being prescriptive, a sensitivity analysis was performed to determine the permissible variation in Um to restrict the error in estimated U* to 2%. The relationship between the depth-averaged velocity Ub and the maximum free-stream velocity Um is also explored using the DNS data sets and an approximate relationship between Ub and Um is proposed. With advances in remote-sensing technology that enables free-stream velocity measurements, this method extends the potential to measure even the friction velocity remotely. Measuring friction velocity U* is difficult in both laboratory and field settings for engineers and scientists. The proposed new method overcomes this challenge to estimate the friction velocity U* by measuring the velocity Um close to the free surface, flow depth h, and temperature (for viscosity). Because near-surface measurement of velocity is not difficult, this method greatly simplifies the measurement of U* with better accuracy than other prevalent methods in practice. In addition, direct numerical simulation (DNS) data has been used to estimate the average velocity Ub using the measured free-stream velocity Um, which further enables measurement of discharge using a single-point measurement of velocity near the free surface in smooth channels.