SPH modelling of depth‐limited turbulent open channel flows over rough boundaries

Summary A numerical model based on the smoothed particle hydrodynamics method is developed to simulate depth‐limited turbulent open channel flows over hydraulically rough beds. The 2D Lagrangian form of the Navier–Stokes equations is solved, in which a drag‐based formulation is used based on an effective roughness zone near the bed to account for the roughness effect of bed spheres and an improved sub‐particle‐scale model is applied to account for the effect of turbulence. The sub‐particle‐scale model is constructed based on the mixing‐length assumption rather than the standard Smagorinsky approach to compute the eddy‐viscosity. A robust in/out‐flow boundary technique is also proposed to achieve stable uniform flow conditions at the inlet and outlet boundaries where the flow characteristics are unknown. The model is applied to simulate uniform open channel flows over a rough bed composed of regular spheres and validated by experimental velocity data. To investigate the influence of the bed roughness on different flow conditions, data from 12 experimental tests with different bed slopes and uniform water depths are simulated, and a good agreement has been observed between the model and experimental results of the streamwise velocity and turbulent shear stress. This shows that both the roughness effect and flow turbulence should be addressed in order to simulate the correct mechanisms of turbulent flow over a rough bed boundary and that the presented smoothed particle hydrodynamics model accomplishes this successfully. © 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd

[1]  E. R. V. Driest.  On Turbulent Flow Near a Wall , 1956 .

[2]  Dominique Laurence,et al.  Unified semi‐analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method , 2013 .

[3]  J. Monaghan.  On the problem of penetration in particle methods , 1989 .

[4]  James J. Feng,et al.  Pressure boundary conditions for computing incompressible flows with SPH , 2011, J. Comput. Phys..

[5]  Hitoshi Gotoh,et al.  SPH-LES Model for Numerical Investigation of Wave Interaction with Partially Immersed Breakwater , 2004 .

[6]  Abbas Khayyer,et al.  Modified Moving Particle Semi-implicit methods for the prediction of 2D wave impact pressure , 2009 .

[7]  Soon Keat Tan,et al.  Scaling of Velocity Profiles for Depth-Limited Open Channel Flows over Simulated Rigid Vegetation , 2012 .

[8]  Benedict D. Rogers,et al.  Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions , 2013, Comput. Phys. Commun..

[9]  Christophe Kassiotis,et al.  Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH , 2014, J. Comput. Phys..

[10]  Hong-Ming Kao,et al.  Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics , 2011 .

[11]  J. Smith,et al.  Velocity distribution and bed roughness in high‐gradient streams , 1991 .

[12]  Tsang-Jung Chang,et al.  SPH Modeling of One-Dimensional Nonrectangular and Nonprismatic Channel Flows with Open Boundaries , 2013 .

[13]  R. L. Shreve,et al.  Forces on stationary particles in near‐bed turbulent flows , 2007 .

[14]  Brian P. Bledsoe,et al.  Representing the bed roughness of coarse‐grained streams in computational fluid dynamics , 2006 .

[15]  Damien Violeau,et al.  Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview , 2007 .

[16]  Neil L. Coleman,et al.  VELOCITY PROFILES WITH SUSPENDED SEDIMENT , 1981 .

[17]  Ming-Jyh Chern,et al.  Effect of Corrugated Bed on Hydraulic Jump Characteristic Using SPH Method , 2013 .

[18]  Andrew Nichols.  Free surface dynamics in shallow turbulent flows , 2013 .

[19]  Hitoshi Gotoh,et al.  Turbulence particle models for tracking free surfaces , 2005 .

[20]  J. Monaghan,et al.  A refined particle method for astrophysical problems , 1985 .

[21]  Hitoshi Gotoh,et al.  LAGRANGIAN SIMULATION OF BREAKING WAVES USING PARTICLE METHOD , 1999 .

[22]  Yang Moon Koh,et al.  Turbulent Flow near a Wall , 1991 .

[23]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[24]  Seiichi Koshizuka,et al.  Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method , 2013 .

[25]  Hitoshi Gotoh,et al.  Simulating Coupled Motion of Progressive Wave and Floating Curtain Wall by SPH-LES Model , 2004 .

[26]  Yee-Chung Jin,et al.  Flow over sills by the MPS mesh-free particle method , 2011 .

[27]  Soon Keat Tan,et al.  Incompressible SPH simulation of open channel flow over smooth bed , 2015 .

[28]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[29]  V. C. Patel,et al.  Prediction of turbulent flow over rough surfaces using a force field in large eddy simulation , 2003 .

[30]  R. Pletcher,et al.  Prediction of Rough-Wall Skin Friction and Heat Transfer , 1982 .

[31]  C. Zeng,et al.  Modeling flows over gravel beds by a drag force method and a modified S–A turbulence closure , 2012 .

[32]  S. J. Lind,et al.  Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves , 2012, J. Comput. Phys..

[33]  Andreas Dittrich,et al.  Velocity Distribution in the Roughness Layer of Rough-Bed Flows , 2004 .

[34]  Dominique Laurence,et al.  DNS and LES of 3-D wall-bounded turbulence using Smoothed Particle Hydrodynamics , 2015 .

[35]  Yee-Chung Jin,et al.  A mesh-free method boundary condition technique in open channel flow simulation , 2013 .

[36]  W. Rodi,et al.  Open‐channel Flow Measurements with a Laser Doppler Anemometer , 1986 .

[37]  Salvatore Marrone,et al.  SPH modeling of plane jets into water bodies through an inflow/outflow algorithm , 2015 .

[38]  Hitoshi Gotoh,et al.  On particle-based simulation of a dam break over a wet bed , 2010 .

[39]  J. C. Rotta,et al.  Turbulent boundary layers in incompressible flow , 1962 .

[40]  Hitoshi Gotoh,et al.  Enhancement of stability and accuracy of the moving particle semi-implicit method , 2011, J. Comput. Phys..

[41]  Abbas Khayyer,et al.  Space potential particles to enhance the stability of projection-based particle methods , 2015 .

[42]  Taro Arikawa,et al.  On enhancement of Incompressible SPH method for simulation of violent sloshing flows , 2014 .

[43]  D. Coles.  The law of the wake in the turbulent boundary layer , 1956, Journal of Fluid Mechanics.

[44]  Salvatore Marrone,et al.  Simulating 2D open-channel flows through an SPH model , 2012 .

[45]  Stefano Sibilla,et al.  3D SPH modelling of hydraulic jump in a very large channel , 2013 .

[46]  Andrew P. Nicholas,et al.  Computational fluid dynamics modelling of boundary roughness in gravel‐bed rivers: an investigation of the effects of random variability in bed elevation , 2001 .

[47]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[48]  Luis Garrote,et al.  Smoothed particle hydrodynamics model applied to hydraulic structures: a hydraulic jump test case , 2010 .

[49]  Hong-Ming Kao,et al.  A new approach to model weakly nonhydrostatic shallow water flows in open channels with smoothed particle hydrodynamics , 2014 .

[50]  Songdong Shao,et al.  Potential Application of Mesh-Free SPH Method in Turbulent River Flows , 2016 .

[51]  T. Cebeci,et al.  Calculation of incompressible rough-wall boundary-layer flows , 1978 .

[52]  Hitoshi Gotoh,et al.  Sub-particle-scale turbulence model for the MPS method , 2001 .

[53]  B. K. Hodge,et al.  Prediction of Turbulent Rough-Wall Skin Friction Using a Discrete Element Approach , 1985 .