Multilayer Depth-Averaged Flow Model with Implicit Interfaces
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 10
Abstract
Using a depth-averaged model to obtain the velocity and pressure distributions in the vertical direction is difficult. A multilayer model is an option that can be used to improve on the depth-averaged model. However, the unknown flow depth needs to be predicted first and then divided into layers as an input for the multilayer model. An improved multilayer model is proposed here by introducing an implicit layer dividing interfaces that are associated with the flow velocity and pressure distribution. The formulation of interfaces also applies to boundary faces: Free surface and channel beds. Therefore, each flow layer behaves like that in the classical depth-averaged model. Subsequently the governing equations are also simplified due to the vanishing terms related to interfacial flow exchanges. This improved model has been satisfactorily applied to steady flow simulations in three cases: Flow over a slope transition from mild to steep, from steep to mild, and over a trapezoidal weir. The results demonstrate the efficiency and validity of the proposed models to simulate open channel flows with bed slope changes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was supported in part by the Natural Science and Engineering Research Council of Canada.NRC
References
Chaudhry, H. M. (1993). Open-channel flows, Prentice-Hall, Englewood Cliffs, N.J.
Chio, S.-U. (1998). “Layer-averaged modeling of two-dimensional turbidity currents with a dissipative Galerkin finite element method. Part I: Formulation and application example.” J. Hydraul. Res., IAHR, 36(3), 339–363.
Cramer, M. S. (2004). “Navier-Stokes equations: Physical boundary conditions.” ⟨http://www.navier-stokes.net/nsbc.htm⟩ (Sept. 30, 2005).
Dressler, R. F. (1978). “New nonlinear shallow flow equations with curvature.” J. Hydraul. Res., IAHR, 16(3), 205–222.
French, R. H. (1985). Open-channel hydraulics, McGraw-Hill, New York.
Ghamry, H. K., and Steffler, P. M. (2002). “Effect of applying different distribution shapes for velocities and pressure on simulation of curved open channels.” J. Hydraul. Eng., 128(11), 969–982.
Hager, W. H. (1985). “Equations for plane, moderately curved open channel flows.” J. Hydraul. Eng., 111(3), 541–546.
Hager, W. H., and Hutter, K. (1984). “Approximate treatment of plane channel flow.” Acta Mech., 51, 31–48.
HydroQual Inc. (2003). A primer for ECOMSED Version 1.3, user’s manual, Mahwah, N.J.
Jameson, A., Schmidt, W., and Turkel, E. (1981). “Numerical solution of the euler equations by finite methods using Runge-Kutta time stepping schemes.” Proc., AIAA 14th Fluid and Plasma Dynamics Conf., Palo Alto, Calif.
Jin, Y. C., and Steffler, P. M. (1993). “Predicting flow in curved open channels by depth-averaged method.” J. Hydraul. Eng., 119(1), 109–124.
Khan, A. A., and Steffler, P. M. (1996). “Vertically averaged and moment equations model for flow over curved beds.” J. Hydraul. Eng., 122(1), 3–9.
Lai, C. J., and Yen, C. W. (1993). “Turbulence free surface flow simulation using a multilayer model.” Int. J. Numer. Methods Fluids, 16(11), 1007–1025.
Le Méhauté, B. (1976). An introduction to hydrodynamics and water waves, Springer, N.Y.
Lynett, P. J., and Liu, P. L. F. (2004). “Linear analysis of the multi-layer model.” Coastal Eng., 51(5–6), 439–454.
Matthew, G. D. (1991). “High order, one-dimensional equations of potential flow in open channels.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 91, 187–201.
Montes, J. S. (1994). “Potential-flow solution to 2D transition from mild to steep slope.” J. Hydraul. Eng., 120(5), 601–621.
Montes, J. S. (1995). “Response to ‘Discussion on potential-flow solution to 2D transition from mild to steep slope.’” J. Hydraul. Eng., 121(9), 681–682.
Nezu, I., and Rodi, W. (1986). “Open-channel flow measurements with laser Doppler anemometer.” J. Hydraul. Eng., 112(5), 335–355.
Reggio, M., Hess, A., and Ilinca, K. (2002). “3D multiple-level simulation of free surface flows.” J. Hydraul. Res., IAHR, 40(4), 413–423.
Stansby, P. K., and Zhou, J. G. (1998). “Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems.” Int. J. Numer. Methods Fluids, 28(3), 541–563.
Steffler, P. M., and Jin, Y. C. (1993). “Depth-averaged and moment equations for moderately shallow free surface flow.” J. Hydraul. Res., 31(1), 5–17.
Wai, W. H., Lu, Q., and Li, Y. S. (1996). “Multi-layer modeling of three-dimensional hydrodynamic transport processes.” J. Hydraul. Res., 34(5), 677–693.
Xia, C., and Jin, Y. C. (2006). “Multilayer averaged and moment equations for one-dimensional open-channel flows.” J. Hydraul. Eng., 132(8), 839–849.
Ye, J., and McCorquodale, J. A. (1997). “Depth-averaged hydrodynamic model in curvilinear collocated grid.” J. Hydraul. Eng., 123(5), 380–388.
Zarrati, A. R., and Jin, Y. C. (2004). “Development of a generalized multi-layer model for 3D simulation of free surface flows.” Int. J. Numer. Methods Fluids, 46, 1049–1067.
Zarrati, A. R., Jin, Y. C., Shanehsaz-zadeh, A., and Ahadi, F. (2004). “Potential flow solution for a free surface past a sudden slope change.” Can. J. Civ. Eng., 31(5), 553–560.
Zerihun, Y. T. (2004). “A one-dimensional Boussinesq-type momentum model for steady rapidly varied open channel flows.” Ph.D. thesis, Univ. of Melbourne, Melbourne, Australia.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 10 • October 2007
Pages: 1145 - 1154
Copyright
© 2007 ASCE.
History
Received: Oct 26, 2005
Accepted: Apr 10, 2007
Published online: Oct 1, 2007
Published in print: Oct 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.