New Method to Calculate Friction Velocity in Smooth Channel Flows Using Direct Numerical Simulation Data
Publication: Journal of Hydraulic Engineering
Volume 150, Issue 4
Abstract
In this paper, we leverage the direct numerical simulation (DNS) data for closed-channel flow for a range of friction Reynolds number () to develop a new one-point friction velocity method (OPFVM) to calculate friction velocity in terms of free-surface velocity , flow depth , and kinematic viscosity . 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 and on four open-channel flow (OCF) DNS regimes with . 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 to restrict the error in estimated to 2%. The relationship between the depth-averaged velocity and the maximum free-stream velocity is also explored using the DNS data sets and an approximate relationship between and 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.
Practical Applications
Measuring friction velocity is difficult in both laboratory and field settings for engineers and scientists. The proposed new method overcomes this challenge to estimate the friction velocity by measuring the velocity 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 with better accuracy than other prevalent methods in practice. In addition, direct numerical simulation (DNS) data has been used to estimate the average velocity using the measured free-stream velocity , which further enables measurement of discharge using a single-point measurement of velocity near the free surface in smooth channels.
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Data Availability Statement
The data for experimental profiles entitled LDA can be obtained from the corresponding author upon reasonable request. The DNS data sets used during the study were provided by a third party. Direct requests for DNS data sets may be made to the provider as indicated in the Acknowledgments.
Acknowledgments
We are grateful to the John Hopkins Turbulence Center (https://turbulence.pha.jhu.edu/), the TU datalib repository (https://tudatalib.ulb.tu-darmstadt.de/handle/tudatalib/2990), and the Texas repository (https://dataverse.tdl.org/dataverse/tocf/) for making available the DNS data sets used in this study. We thank the reviewers for their constructive comments and recommendations.
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Received: Apr 21, 2023
Accepted: Jan 26, 2024
Published online: Apr 26, 2024
Published in print: Jul 1, 2024
Discussion open until: Sep 26, 2024
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