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Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant...
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Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
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Validation of depth-averaged flow model using flat-bottomed benchmark problems.

Il Won Seo1, Young Do Kim2, Chang Geun Song3

  • 1Department of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744, Republic of Korea.

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Summary

A new shallow water flow code was developed and validated. It accurately simulates complex fluid dynamics, showing good mass conservation and agreement with analytical solutions for various benchmark problems.

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Area of Science:

  • Computational Fluid Dynamics (CFD)
  • Environmental Engineering
  • Hydraulic Engineering

Background:

  • Accurate simulation of shallow water flows is crucial for various engineering applications.
  • Existing models may face limitations in handling diverse flow conditions and complexities.
  • Development of robust and validated numerical codes is essential for reliable predictions.

Purpose of the Study:

  • To develop and rigorously test a novel shallow water flow code.
  • To validate the code's performance against established benchmark problems.
  • To provide a reliable tool for analyzing complex hydraulic phenomena.

Main Methods:

  • Implementation of a shallow water flow code using the nonconservative form of shallow water equations.
  • Application of the SU/PG weighting scheme and a fully implicit integration method.
  • Validation against four benchmark problems, including internal recirculating flow and supercritical flow with oblique hydraulic jumps.

Main Results:

  • Demonstrated accurate simulation of flow depth influenced by roughness and eddy viscosity.
  • Achieved a high mass conservation rate of 99.2% in a cylinder break test.
  • Vortex intensity trended towards theoretical values, and supercritical flow computations showed excellent agreement (within 0.2% error) with analytic solutions.

Conclusions:

  • The developed shallow water flow code is highly accurate and versatile across various flow conditions.
  • Benchmark test results provide valuable criteria for evaluating numerical methods in fluid dynamics.
  • The model offers a reliable approach for simulating complex shallow water phenomena.