Numerical investigation of field-scale geysers in a vertical shaft

Abstract

Geysers in dropshafts of stormsewer systems are consecutive eruptions of a mixture of gas and liquid that can attain heights of more than 30 m. The present study investigates the mechanisms and characteristics of these extreme events numerically using OpenFOAM toolbox. The numerical model is based on a compressible two-phase flow solver and was validated using laboratory tests that achieved large eruption heights. The results show that the aforementioned experimental geysers can be reasonably well simulated using two- and three-dimensional numerical models. Further studies are needed to verify the applicability of two-dimensional models for simulating geysers in actual stormsewer systems. Moreover, the results suggest that compressibility of air plays a critical role in the formation of geysers. Overall, the conducted numerical study provides insights into the characteristics of geyser eruptions and presents some criteria for performing efficient numerical simulations of these events.

Keywords:

• Air–water interface interactions
• flows in pipes
• geyser
• numerical validation
• OpenFOAM
• sewer hydraulics

Acknowledgments

The authors would like to thank the three anonymous reviewers for their constructive comments that improved the quality of this study. The first author also would like to thank Dr Rodolfo Ostilla Monico for providing insightful suggestion. We acknowledge the support from the Center for Advanced Computing and Data Science at the University of Houston for the use of the Sabine Cluster.

Notations

α	=	volume fraction of water phase (–)
${\alpha }_t$	=	thermal eddy diffusivity (kg m−1 s−1)
κ	=	curvature of interface (–)
μ	=	kinematic viscosity (m2 s−1)
${\rho }_0$	=	initial density of water (kg m−3)
${\rho }_a$	=	density of air (kg m−3)
${\rho }_w$	=	density of water (kg m−3)
σ	=	surface tension (N m−1)
$c_{v,w}$	=	specific heat capacity of water (J kg−1 K−1)
$c_{v,a}$	=	specific heat capacity of air (J kg−1 K−1)
$D_d$	=	diameter of all pipes (m)
$E_h$	=	error in computation of the geyser height (–)
$\mathit{g}$	=	gravitational acceleration (m s−2)
$h_d$	=	length of vertical shaft (m)
$h_g$	=	geyser height (m)
$h_{max}$	=	maximum cell length in a mesh (m)
k	=	turbulence kinetic energy (J kg−1)
K	=	specific kinetic energy (m2 s−2)
$L_d$	=	length of horizontal pipe at the downstream side of the vertical shaft (m)
$L_u$	=	length of horizontal pipe at the upstream side of the vertical shaft (m)
N	=	number of cells in a mesh (–)
p	=	pressure field (Pa)
$R_a$	=	gas constant (J kg−1 K−1)
$R_w$	=	vapour constant (J kg−1 K−1)
$t_p$	=	time shift of pressure graph (s)
$t_s$	=	computation time of simulation (min)
T	=	temperature field (K)
$\mathit{U}$	=	velocity field (m s−1)
${\mathit{U}}_{\mathit{c}}$	=	compression velocity (m s−1)
U	=	magnitude of the exit velocity (m s−1)
$U_{max}$	=	magnitude of the maximum exit velocity (m s−1)
V	=	volume of a cell (m3)
$V_a$	=	volume of the air tank (m3)
$\mathit{x}$	=	position vector (m)

Additional information

Funding

The authors gratefully acknowledge the financial support of the US Environmental Protection Agency (National Center For Environmental Assessment) under [grant number R8335187]. This manuscript has not been formally reviewed by EPA. The views expressed are solely those of the authors. EPA does not endorse any products or commercial services mentioned.