Numerical modelling of the water surface movement with macroscopic particles of dam break flow for various obstacles

ABSTRACT

In this paper, the movement of the water surface with macroscopic particles during a dam break flow using the volume of fluid (VOF) methods, the discrete phase model (DPM) and macroscopic particle model (MPM) models were numerically simulated. To solve this equation system numerically, the PISO numerical algorithm was chosen. The accuracy of the 3D model and the selected numerical scheme were tested using some laboratory measurements on the destruction of the dam break problem. In the test problem, the values were matched with measurement values and simulation data of other authors. Furthermore, two problems were also considered, the first problem is dam break flow with macroscopic particles, and the second problem – water movement with macroscopic particles, through a heterogeneous terrain and a dam that has a hole. With the help of the problems, the flooding zones and the time of flooding evacuating people from dangerous areas were determined.

Keywords:

• Dam break modelling
• DPM and MPM models
• flooding zones
• macroscopic particle interaction
• PISO algorithm
• VOF method

Acknowledgements

This work is supported by the grant from the Ministry of Education and Science of the Republic of Kazakhstan (AP09058406, AP05132770).

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Notation

$\mu$	=	fluid viscosity (Pa s)
$\rho$	=	fluid density (kg m-3)
g	=	gravity acceleration (m s-2)
$u_{pi}$	=	particle velocity (m s-1)
$\mathit{F}$	=	additional acceleration (force/unit of mass of the particle)
${\tau }_r$	=	relaxation time of the droplet or particle (s)
$\mathit{u}$	=	phase velocity of the fluid (m s-1)
${\rho }_p$	=	particle density (kg m-3)
$d_p$	=	particle diameter (m)
Re	=	Reynolds number (-)
$I_p$	=	moment of inertia (kg m2)
${\mathit{\omega }}_{\mathit{p}}$	=	angular velocity of the particle (s-1)
${\rho }_f$	=	liquid density (kg m-3)
$d_p$	=	particle diameter (m)
$C_{\omega }$	=	coefficient of resistance to rotation (-)
$\mathit{T}$	=	moment applied to the particle in the liquid region (kg m2)
$m_f$	=	fluid mass (kg)
${\mathit{V}}_{\mathit{f}}$	=	fluid velocity (m s-1)
${\mathit{V}}_{\mathit{p}}$	=	particle velocity (m s-1)
${\mathit{r}}_{\mathit{p}}$	=	radius vector from the center of the liquid cell to the center of the particle (m)
${\alpha }_p$	=	volume fraction of the particle (-)
r	=	particle radius (m)
J	=	impulse force (N s)
n	=	unit vector in the normal direction (-)

Additional information

Funding

This work is supported by the grant from the Ministry of Education and Science of the Republic of Kazakhstan [AP05132770].