Assessment of a Shallow Water Model using a Linear Turbulence Model for Obstruction-Induced Discontinuous Flows
DOI:
https://doi.org/10.18321/ectj109Abstract
Assessment of the performance of a shallow water model with closure using a linear k-Оµ turbulence model is made for various obstruction-induced discontinuous flows. The monotone upwind scheme of conservative laws (MUSCL) - Hancock scheme is used, together with the Harten Lax van Leer (HLL) approximate Riemann solver in the discretization of the finite volume shallow water model. These kinds of models contribute to the improvement of optimized design of various processes in chemical engineering and technology. Two obstructed flow applications are presented, namely, single obstruction and multiple obstruction induced discontinuous flows; and the ability of the shallow water model with the k-Оµ based turbulence model to predict these applications are assessed. The simulation results of the shallow water model are compared with those found by direct numerical simulation (DNS) and experimental measurements in the literature.
References
2. Harten, A., Lax, P. D. & van Leer, B. (1983).On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25, No. 1, 35-61.
3. Horritt, M. (2004). Development and testing ofa simple 2D finite volume model of subcritical
shallow water flow. International Journal of Numerical Methods in Fluids, 44,1231-1255.
4. Jiang, C. B., Yang, C. & Liang, D. F. (2009). Computation of shallow wakes with the fractional step finite element method. Journal of Hydraulic Research, 47, No. 1, 127-136.
5. Kabir, M. A., Khan, M. M. K. & Bhuiyan, M.A. (2004). Flow phenomena in a channel with different shaped obstructions at the entrance. Fluid Dynamics Research, 35, 391-408.
6. Lai, J. S., Lin, G. F. & Guo, W. D. (2005). An upstream flux-splitting finite-volume scheme for 2D shallow water equations. International Journal of Numerical Methods in Fluids, 48, 1149-1174.
7. Launder, B. E. & Spalding, D. B. (1974). The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3, No. 2, 269-289.
8. Lee, T. S. (1998). Early stages of an impulsively started unsteady laminar flow past tapered trapezoidal cylinders. International Journal of Numerical Method in Fluids, 26, 1181-1203.
9. Mingham, C. G. & Causon, D. M. (2000). Calculation of unsteady bore diffraction using a high resolution finite volume method. Journal of Hydraulic Research, 38, No. 1, 49-56.
10. Osher, S. & Solomone, F. (1982). Upwind difference schemes for hyperbolic systems of conservation laws. Mathematics and Computers in Simulation, 38, 339 –374.
11. Pu, J. H. Efficient finite volume numerical modelling and experimental study of 2D shallow water free surface turbulent flows. PhD Dissertation, University of Bradford, Bradford, UK, 2008.
12. Pu, J. H., Hussain, K. & Tait, S. J. (2007). Simulation of turbulent free surface obstructed flow within channels. Proceedings in the 32nd Congress of IAHR – Harmonizing the Demands of Art and Nature in Hydraulics, Venice, Italy, Theme A1, pp. 1-8.
13. Rodi, W. Turbulence models and their application in hydraulics - a state of the art review. International Association for Hydraulic Research, Netherlands, 1980.
14. Roe, P. L. (1981). Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43, 357–372.
15. Sana, A., Ghumman, A. R. & Tanaka, H. (2009). Modeling of a rough-wall oscillatory boundary layer using two-equation turbulence models. Journal of Hydraulic Engineering, 135, No. 1, 60-65.
16. Sanders, B. F. (2001). High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and nonprismatic channels. Journal of Hydraulic Research, 39, No. 3, 321-330.
17. Stansby, P. K. (1997). Semi-implicit finite volume shallow-water flow and solute transport solver with k-ε turbulent model. International Journal of Numerical Methods in Fluids, 25, 285-313.
18. Toro, E. F. Riemann solvers and numerical methods for fluid dynamics – a practical introduction. 2nd Edition, Spring-Verlag Berlin Heidelberg, 1999.
19. Tseng, M. H. (1999). Explicit finite volume non-oscillatory schemes for 2D transient freesurface flows. International Journal of Numerical Method in Fluids, 30, 831-843.
20. Wissink, J. G. (1997). DNS of 2D turbulent flow around a square cylinder. International Journal for Numerical Methods in Fluids, 25, 51-62.
21. Younus, M. and Chaudhry, M. H. (1994). A depth-averaged k-ε turbulent model for the computation of free-surface flow. Journal of Hydraulic Research, 32, No. 3, 415-444.
Downloads
Published
How to Cite
Issue
Section
License
You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially.
Eurasian Chemico-Technological Journal applies a Creative Commons Attribution 4.0 International License to articles and other works we publish.
Subject to the acceptance of the Article for publication in the Eurasian Chemico-Technological Journal, the Author(s) agrees to grant Eurasian Chemico-Technological Journal permission to publish the unpublished and original Article and all associated supplemental material under the Creative Commons Attribution 4.0 International license (CC BY 4.0).
Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
