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COMPUTATION OF RAPIDLY VARIED FLOW
Mountain streams, rivers during high floods, spillway chutes, conveyance channels, sewer systems, and outlet works are all examples of natural and man-made open channels with rapidly varied flows. In contrast to gradually varying flows, the analysis of these flows encounters a number of challenges, including the formation of roll waves, air entrainment, and cavitation. In addition, if the Froude number exceeds its critical value, instabilities might occur, resulting in roll waves or slug flow. Standing waves and large surface disturbances, often known as shocks or standing waves, are key aspects of rapidly varied flows that must be taken into account during analysis and design.
To compute supercritical flow in channel expansions, including the effects of bottom slope and friction, numerical integration of the steady, two- dimensional, shallow-water equations is only suitable for gradually varied flows and cannot be used to compute flows with shocks or standing hydraulic jumps. To overcome these limitations, researchers tried using the Shock-Tracking techniques but the scheme didn’t clearly handle the discontinuities. Others tried to use the Method of Characteristics - based procedures, however, it can not compute oblique jumps and requires many interpolations which may seriously affect the accuracy of the solution, and other utilized the Shock- Capturing finite-difference methods.
In this chapter, numerical modeling of rapidly varied flows is discussed based mainly on the papers published by the author with Jimenez, Gharangik, and Bhallamudi. Three different formulations are presented. In the first, a steady form of the shallow water equations is numerically integrated which is valid only for supercritical flows. In the second formulation, the unsteady gradually varied equations are solved with time until the solution converges to a steady state. And, in the third formulation, the Boussinesq equations are solved by an explicit scheme which is second-order accurate in time and fourth-order in space. For illustration purposes, the formation of hydraulic jump in a rectangular channel is simulated.
COMPUTATION OF RAPIDLY VARIED FLOW
Mountain streams, rivers during high floods, spillway chutes, conveyance channels, sewer systems, and outlet works are all examples of natural and man-made open channels with rapidly varied flows. In contrast to gradually varying flows, the analysis of these flows encounters a number of challenges, including the formation of roll waves, air entrainment, and cavitation. In addition, if the Froude number exceeds its critical value, instabilities might occur, resulting in roll waves or slug flow. Standing waves and large surface disturbances, often known as shocks or standing waves, are key aspects of rapidly varied flows that must be taken into account during analysis and design.
To compute supercritical flow in channel expansions, including the effects of bottom slope and friction, numerical integration of the steady, two- dimensional, shallow-water equations is only suitable for gradually varied flows and cannot be used to compute flows with shocks or standing hydraulic jumps. To overcome these limitations, researchers tried using the Shock-Tracking techniques but the scheme didn’t clearly handle the discontinuities. Others tried to use the Method of Characteristics - based procedures, however, it can not compute oblique jumps and requires many interpolations which may seriously affect the accuracy of the solution, and other utilized the Shock- Capturing finite-difference methods.
In this chapter, numerical modeling of rapidly varied flows is discussed based mainly on the papers published by the author with Jimenez, Gharangik, and Bhallamudi. Three different formulations are presented. In the first, a steady form of the shallow water equations is numerically integrated which is valid only for supercritical flows. In the second formulation, the unsteady gradually varied equations are solved with time until the solution converges to a steady state. And, in the third formulation, the Boussinesq equations are solved by an explicit scheme which is second-order accurate in time and fourth-order in space. For illustration purposes, the formation of hydraulic jump in a rectangular channel is simulated.
COMPUTATION OF RAPIDLY VARIED FLOW
Chaudhry, M. Hanif (author)
Open-Channel Flow ; Chapter: 8 ; 251-281
2022-01-01
31 pages
Article/Chapter (Book)
Electronic Resource
English
Computation of Rapidly Varied Flow
| Springer Verlag | 2008
| Springer Verlag | 2008
| Springer Verlag | 2022
COMPUTATION OF GRADUALLY VARIED FLOW
| Springer Verlag | 2022
Computation Of Gradually Varied Flow
| Springer Verlag | 2008