Applicability of Quasisteady and Axisymmetric Turbulence Models in Water Hammer

Two of the existing turbulence water hammer models, namely the two-layer and the five-layer eddy viscosity models, are implemented and analyzed and the accuracy of their quasi-steady and axisymmetric assumptions evaluated. In addition, a dimensionless parameter P (ratio of the time scale of radial diffusion of shear to the time scale of wave propagation) for assessing the accuracy of quasi-steady turbulence modeling in water hammer problems is developed and applied. It is found that the results of both models are in reasonable agreement, confirming that the turbulence modeling of water hammer flows is insensitive to the magnitude and distribution of the eddy viscosity within the pipe core. Comparison of model results with available data shows that the quasi-steady assumption becomes more accurate as the dimensionless parameter P increases. Furthermore, the analysis shows that the quasi-steady assumption is highly accurate as long as the simulation time is below the diffusion time scale and that this assumption causes an almost linear increase in the difference between model results and data with time. The accuracy of the flow axisymmetry assumption is evaluated by applying both models to a water hammer problem where flow asymmetry has been observed experimentally. It is found that the difference between models and data grows exponentially and reaches 100% after six wave periods.