Abstract
A mixed numerical formulation, based on the method of characteristics (MOC) and finite difference method (FDM), is proposed for the computational simulations of hydraulic transients. To include the effects of unsteady friction, i.e. the contribution of unsteady behavior of wall shear stress, the numerical algorithm includes the Brunone friction model. The governing water hammer equations are discretized by MOC and the discretization of the local and convective acceleration term in the unsteady friction model is conducted by FDM. The procedure results in an explicit-implicit time marching scheme used for predicting the unknown values of piezometric head and discharge from the known initial conditions. The resulting system of equations is resolved in an iterative fashion. Due to its relatively low complexity, the obtained numerical algorithm is attractive for computational implementation. At the end of the paper a few illustrative numerical examples are presented, compared with available experimental data, and discussed.
Highlights
It is well known that a change in the velocity field will cause pressure disturbance propagation through the space occupied by the fluid
The implementation of such constitutive models in a onedimensional flow model was explored for different numerical methods such as: finite difference method (FDM), finite volume method, finite element method, wave plan method and method of characteristics (MOC)
In this paper the water-hammer phenomenon is approached by considering the Brunone unsteady friction model [5] and its specific numerical implementation in the equations obtained by MOC
Summary
It is well known that a change in the velocity field will cause pressure disturbance propagation through the space occupied by the fluid. The main reason of these disagreements was the inappropriate definition of the fiction factor that in such rapid events should account for unsteady behavior of wall shear stress. To include such effects, several constitutive models were suggested for quantifying the contribution of frictional forces [5, 6, 7]. In this paper the water-hammer phenomenon is approached by considering the Brunone unsteady friction model [5] and its specific numerical implementation in the equations obtained by MOC.
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