Abstract
ABSTRACTThis paper presents a new macroscopic mesh-free particle method in which Darcy’s and Forchheimer’s terms are introduced into the governing equation to ensure the capacity of the particle method in simulating laminar and turbulent porous medium flows. A developed interfacial condition and inflow boundary condition are implemented in the macroscopic particle method to improve the stability of the Particle-based model. The comparisons of channel flow over and within porous bed among the present method, previous mesh-based method, and experimental data show that the macroscopic particle method is capable of simulating flows in both the clear flow region and porous flow region. Finally, two cases of flow over a rigid box and a cylinder lying on porous bed are simulated, and the numerical results are in good agreement with the measured data. The analysis and comparisons indicate that the newly developed particle-based method is reliable and has been successfully extended to macroscopic porous medium simulation.
Highlights
Most researchers have paid attention to channel flow over impermeable bed
The turbulence is not considered in Eq (2), similar approaches have been executed by Shao (2010), as indicated by Fu and Jin (2013) that in MPS simulation of steady state open channel flow, turbulence model will not significantly affect the simulation results; for the turbulent flow cases simulated in this study, the turbulent shear stress is calculated by a simple turbulence model (Fu & Jin, 2013; Nazari, Jin, & Shakibaeinia, 2012)
The interfacial condition used in numerical methods of channel flow over porous bed represents the effects from the porous flow region; some of the previous numerical studies introduced a slip velocity as the interfacial condition for simplicity, another widely used interfacial boundary condition is jump stress condition, which has been successfully utilized in mesh-based methods (Deresiewicz & Skalak, 1963; Ochoa-Tapia & Whitaker, 1995; Pedras & de Lemos, 2001; Vollmera, Ramos, Daebel, & Kuhn, 2002)
Summary
Most researchers have paid attention to channel flow over impermeable bed Coefficients such as Manning’s roughness coefficient n or roughness height ks (Yen, 1991; Zarrati, Tamai, & Jin, 2005) are required to represent the channel bed roughness in numerical studies (Delft3D WL & delft hydraulics, 2001; Fluent Inc, 1998). Tracking the free surface becomes troublesome, and the porous medium formula has to be adopted into the mesh-based form in these methods (Beavers & Joseph, 1967; Chan et al, 2007; Prinos et al, 2003; Silva & de Lemos, 2003). The developed particle-based macroscopic model will first be verified and applied to various kinds of channel flow over and within porous bed cases
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