Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

Abstract

SUMMARYIn the present study, Runge-Kutta schemes are used to simulate unsteady ow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central di erence scheme. Secondorder dissipative terms are added in regions of high gradients while they are switched o in smooth ow regions using a total variation diminishing (TVD) switch. The method is applied to both oneand two-dimensional water hammer formulations. Both laminar and turbulent ow cases are simulated.Di erent turbulence models are tested including the Baldwin-Lomax and Cebeci-Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two-dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non-dimensional parameter is identiÿed that controls the damping of pressure transients in elastic pipes.

Turbulence modeling for two-dimensional water hammer simulations in the low Reynolds number range

“…Recently, Wahba [6] implemented the Baldwinn-Lomax turbulence model, commonly used in aerodynamic flow simulations, within the (2D) water hammer framework and good agreement with experimental data was reported. However, it was noted by Wahba [6] that the short duration of the experimentally recorded transient, only three cycles, may not provide definite conclusions about the effectiveness of the Baldwin-Lomax model in simulating the attenuation of turbulent fluid transients.…”

“…However, it was noted by Wahba [6] that the short duration of the experimentally recorded transient, only three cycles, may not provide definite conclusions about the effectiveness of the Baldwin-Lomax model in simulating the attenuation of turbulent fluid transients.…”

“…To overcome this shortcoming, (2D) water hammer models were developed and introduced in the literature [6][7][8][9][10][11]. In the (2D) model, the two-dimensional form of the axial momentum equation is retained where the local velocity is now a function of both the axial and radial directions together with being a function of time.…”

Investigation of Non-Newtonian Fluid Effects during Transient Flows in a Pipeline

“…Second order dissipative terms are added to eliminate numerical oscillations. These terms perform only in the high gradient region, and they are effectively switched off in smooth regions [7].…”

“…The velocity profiles and their gradients can be compared with the corresponding computations provided by [7] (Fig. 4).…”