13/10/2016
J. Chauchat, Z. Cheng and T.-J. Hsu
The open source two-phase sediment transport model sedFoam (Cheng and Hsu, 2014) is used to test different constitutive laws for the modeling of interparticle stresses under sheet-flow conditions. The numerical model is first validated on Revil-Baudard et al (2015) data and on Sumer et al. (1996) data using both the kinetic theory of granular flows as adopted by Hsu et al. (2004) and the mu(I) dense granular flow rheology as proposed by Revil-Baudard and Chauchat (2013). Different turbulence models are tested that allows to further understand the complex momentum balance between Reynolds stress and interparticle stress under sheet flow conditions. For steady, unidirectional and uniform sheet flows, the first conclusion is that the turbulence model, once calibrated on detailed measurements does not influence much the results in terms of velocity and concentration profiles. Using the mu(I) rheology with the mixing length or the k-epsilon model leads to almost the same results. However, the kinetic theory as proposed in Hsu et al. (2004) seems to lack the dense granular flow behaviour at the transition between the immobile bed and the dense sediment moving layer. The granular behaviour in this layer is however well described by the mu(I) rheology (Capart and Fraccarolo, 2011). A possible way to improve the kinetic theory results would to be to implement a combined mu(I)/kinetic theory in the model in a similar way as Armanini et al. (2014) proposed.
Considering sheet flow in oscillatory flows, it has been observed that kinetic theory is not relevant for fine sands for which collisions are almost inefficient. The two-phase flow model validated for unidirectional sheet flows has been used to reproduce O’Donoghue and Wright (2004) data for sheet flows under sinusoidal waves for Coarse, Medium and Fine sands. The mu(I) rheology results are very similar to the one obtained using the kinetic theory. Based on these results it seems that the reasons for the poor predictions of oscillatory sheet flows with fine sand is not due to the particle stress closure but it is most probably due to the RANS turbulence model. LES simulations should give some more insight into to this hypothesis.
References
A. Armanini, M. Larcher, E. Nucci, and M. Dumbser. Submerged granular channel flows driven by gravity. Advances in Water Resources, 63:1 – 10, 2014.
H. Capart and L. Fraccarollo. Transport layer structure in intense bed-load. Geophysical Research Letters, 38(20), 2011.
Cheng, Z. and T.-J. Hsu. A multi-dimensional two-phase eulerian model for sediment transport- twophaseeulersedfoam. Research report CACR-14-08, Center for Applied Coastal Research - University of Delaware, august 2014.
Hsu, T.-J., Jenkins, J.T., and Liu, P. L.-F, (2004) On two-phase sediment transport : sheet flow of massive particles. Proc. Roy. Soc. Lond. (A), 460(2048), 2223-2250.
O’Donoghue, T. and S. Wright. Concentrations in oscillatory sheet flow for well sorted and graded sands. Coastal Engineering, 50(3):117 – 138, 2004.
Revil-Baudard, T., Chauchat, J., Hurther, D. & Barraud, P.-A. 2015 Investigation of sheet-flow processes based on novel acoustic high-resolution velocity and concentration measurements. Journal of Fluid Mechanics 767, 1-30.
Revil-Baudard, T. and J. Chauchat. A two-phase model for sheet flow regime based on dense granular flow rheology. Journal of Geophysical Research : Oceans, 118(2):619–634, 2013.
Sumer, B. M., A. Kozakiewicz, J. F. e, and R. Deigaard. Velocity and concentration profiles in sheet-flow layer of movable bed. Journal of Hydraulic Engineering, 122(10):549–558, 1996.