### Abstract

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier–Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.

Original language | English |
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Pages (from-to) | 8166-8178 |

Number of pages | 13 |

Journal | Applied Mathematics and Computation |

Volume | 217 |

Issue number | 21 |

Early online date | 21 Mar 2011 |

DOIs | |

Publication status | Published - 1 Jul 2011 |

Externally published | Yes |

### Keywords

- Finite volume modeling
- Reynolds-averaged Navier–Stokes (RANS) equations
- Standard k − ε model
- Design of experiments
- Gravity settlers
- Numerical simulation

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## Cite this

Del Coz Díaz, J. J., García Nieto, P. J., Castro-Fresno, D., & Menéndez Rodríguez, P. (2011). Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM.

*Applied Mathematics and Computation*,*217*(21), 8166-8178. https://doi.org/10.1016/j.amc.2011.03.044