SPHysics simulation of laboratory shallow free surface turbulent flows over a rough bed

Abstract

In this paper, the smoothed particle hydrodynamics method is used to simulate experimental shallow free surface turbulent flows over a rough bed made of regularly packed uniform spheres. The numerical program is based on the open source code SPHysics and significant improvement is made in the turbulence modelling and rough bed treatment within the code. A modified sub-particle-scale eddy viscosity model is proposed to simulate the effect of turbulence transfer mechanisms in the highly-sheared free surface flow, and a drag force term is introduced into the momentum equation as a source term to account for the existence of the bed roughness. To validate the numerical model, a laboratory experiment is carried out to study shallow, turbulent flow behaviour under different flow conditions. The SPH simulations are then compared with the flow velocity, shear stress and turbulent intensity profiles measured via acoustic doppler velocimeters. Several issues with regard to the rough bed hydraulics are investigated, including the study of water surface behaviour and its interaction with the bulk flow.

A Meshless WCSPH Boundary Treatment for Open-Channel Flow over Small-Scale Rough Bed

“…In the original SPS turbulence model, the eddy viscosity coefficient is taken as v t � (C s Δl) 2 |S|, where C s denotes the Smagorinsky constants with a range of 0.1∼0.2 and |S| denotes the local strain rate and can be calculated as |S| � (2S ij S ij ) 1/2 . In this study, the eddy viscosity coefficient is modified with reference to mixed length theory [36] and can be expressed as follows:…”

“…Recently, De Padova et al [35] investigated undular hydraulic jumps over small-scale rough bed for bed roughness of 0.02H, where H denotes the water depth. e SPH mixing-length turbulence model exhibits satisfactory performance for simulating hydraulic jump as long as strong turbulent rollers are not present and is applicable for openchannel flow simulation [25,36]. Overall, there have been insufficient studies of the open-channel flow over rough bed using SPH methods.…”

3D SPH Simulation of Dynamic Water Surface and Its Interaction with Underlying Flow Structure for Turbulent Open Channel Flows Over Rough Beds

“…The comparison of the water surface level showed that the SPH results obtained by either way of de¯ning the roughness terrain agreed better with the experimental data than the FV model. More recently, Kazemi et al [2017] and Gabreil et al [2018] treated the bed roughness by including drag force term into the momentum equation to simulate 2D turbulent open channel°ows over¯xed beds. Their results of velocity and shear stress show a good macth with the measured data.…”

“…In this case, improvements to the 3D SPH turbulence modeling will be made to address the shear stress, and new treatments of rough beds will be developed to account for the form drag forces due to roughness elements. In this study, the improvements made by Gabreil et al [2018] will be extended by taking into account the in°uence of the 3D°ow near the bed and the side walls of the channel. The improved model will then be used to examine the dynamic behavior of the water surface and its interactions with the underlying°ow structures underneath.…”

“…Implementation of 3D SPH numerical model would allow for more information on the underlying°ow structure and water surface pattern to be disclosed, and hence a better understanding on the linkages between the underlying°ow and free surface pattern throughout the°ow cross-section could be addressed. This section aims to modify the recent 2D SPH code (Gabreil et al [2018]) and make it suitable for 3D free surface°ows. Therefore the code will be signi¯cantly improved by including a suitable 3D turbulence model to simulate the turbulence transfer mechanisms found over the cross-sectional area of a free surface channel°ow.…”