Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

Abstract

Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

“…Turbulence model Particle stress Asano (1990), Li and Sawamoto (1995), and Dong and Zhang (2002) mixing length Bagnold Jenkins and Hanes (1998) mixing length kinetic theory Revil-Baudard and Chauchat (2013) mixing length granular rheology Li et al (2008) k − L Bagnold Bakhtyar et al (2009) k − ε Bagnold , Chauchat and Guillou (2008), and Amoudry et al (2008) k − ε kinetic theory Yu et al (2010) and Cheng et al (2017a) Amoudry (2014 and Bombardelli (2009, 2010) k − ω kinetic theory Lee et al (2016) k − ε granular rheology is modeled by the fluctuation energy of the particle phase (or granular temperature). Various models were developed to model the granular temperature.…”

“…In contrast to solving the transport of granular temperature, Jha and Bombardelli (2010) used a mixing length concept for the particle phase, and a simpler algebraic model for the granular temperature was used with success. More recently, the dense granular flow rheology initially proposed by GDRmidi (2004) for dry granular flows has been used for sediment transport applications in the laminar flow regime by Ouriemi et al (2009) and later to turbulent flow conditions by Revil-Baudard and Chauchat (2013), Chiodi et al (2014), and Lee et al (2016). Due to the complexity of the model formulation, most of the existing two-phase models are based on the Reynoldsaveraged approach and simplified into one-dimensional form (e.g., Hanes and Bowen, 1985;Jenkins and Hanes, 1998;Hsu et al, 2003;Revil-Baudard and Chauchat, 2013), with a few exceptions (two-dimensional models; Chauchat and Guillou, 2008;Bakhtyar et al, 2009;Amoudry and Liu, 2009).…”

“…At the bottom, the velocity of both phases are set to zero while a fixedFluxPressure condition is imposed for the pressure. As mentioned by Lee et al (2016), the fixedFluxPressure boundary condition must be used to avoid spurious oscillation on the wall normal pressure gradient close to the boundary. The granular rheology is turned on and an effective fluid viscosity model from Boyer et al (2011) is used.…”

“…These two layers are dynamically coupled using empirical sediment vertical fluxes: deposition and pick-up fluxes (Van Rijn, 1984), which are also parameterized based on the bed shear stress. The single-phase model has been widely used because of its simplicity and computational efficiency, and it has been integrated into meso-to large-scale models such as the Delft3D (Lesser et al, 2004;Hu et al, 2009), XBeach (Roelvink et al, 2009), and ROMS (Warner et al, 2008). Despite their ability to predict long-term regional morphology in littoral zones, there are several challenges to model sediment transport using such a single-phase methodology.…”

“…In addition, simple parameterization solely on the bed shear stress may be insufficient; for example, the role of pressure gradient in sediment transport has been identified for extreme events such as storms (Foster et al, 2006;Cheng et al, 2017a). Addressing these issues requires the development of comprehensive models that account for the variety of complex hydrodynamics and sediment transport processes on a regional-scale setting (e.g., Lesser et al, 2004;Roelvink et al, 2009). Because sediment transport occurs very close to the bed, effective parameterizations of sediment transport are needed.…”