Numerical modelling of one- and two-dimensional water hammer problems using a modified wave propagation algorithm and turbulence model

ABSTRACT

In this paper a modified Godunov-type wave propagation method is presented for modelling one- and two-dimensional water hammer problems. The proposed numerical solver is well-balanced and treats the friction terms within the flux-differencing of the finite volume computational cells. To investigate the effect of turbulence behaviour during the water hammer process, a ${\overline{v}}^2-\overline{f}$ turbulence model that provides precise prediction for the near wall-region is utilized. First, the one-dimensional water hammer problem without the friction term is considered and the obtained results are compared with the analytical solution. Then, the suitability of the proposed scheme is investigated for two-dimensional transient problems for a range of Reynolds numbers and the results are validated with experimental data. It is found that the proposed numerical solver with a new choice of turbulence model produces satisfactory agreement with the exact solution and available experiment data for the given ranges of Reynolds numbers.

Keywords:

• Flux-wave approach
• unsteady pipe flow
• ${\overline{v}}^2-\overline{f}$ turbulence model
• water hammer problem
• weave propagation algorithm