# 1D System Transients Coupled with 3D Local Flow Details

[Rapport]

This work is a numerical study of the water flow in a square channel, during the closure of a gate. The flow is driven by a difference in surface elevation between an upstream and a downstream water tank. The case resembles, for example, the flow in hydro power water ways during a sudden closure of a turbine unit, in which it is of interest to quantify the amplitude and frequency of the following pressure waves. This work is a continuation of the senior SVC project aiming at studying 1D-3D coupling and system transients coupled to local flow unsteadiness. That project presented initial experimental and numerical studies under the same conditions as in the present work. The current objective is to address the numerical modeling of transients with special focus on detailed 3D processes interacting with the flow in an essentially 1D geometry. First the pressure oscillations observed during the easurement campaign when the gate is closed is analyzed. 3D simulations are performed using a computational domain that includes the upper and lower tank and its free surfaces. A flow rate is specified both at the inlet and outlet of the system, and the free surfaces dictates the pressure level in the system. A lot of time was spent dealing with a flow regulation valve below the upper tank that generated a pressure loss in the system, which was unfortunately not taken notice of in the original experimental study. The flow is assumed to be incompressible, and the time dependent Navier Stokes equations are solved in the system. The closing gate is modelled by cutting up the computational mesh. The results show that both the flow and the pressure behave as in the experiment. The pressure levels are similar as those in the experiment, since the loss generated by the regulating valve is taken into account. The oscillations observed in the experiments are not present in the numerical results, and it is suggested that these fluctuations observed in the measurement campaign are indeed pressure transients occurring due to the water hammer effect. Secondly, the upper tank and the pipe are modelled using a compressible 1D code based on the method of characteristics (MOC). A comparison with the experimental data shows that the correct unsteady behavior of the system is captured by the 1D approach if the losses and the gate characteristics are correctly accounted for, at the same time as the compressibility is adapted to the air contents of the water and flexibility of the structure. Finally, a coupled 1D-3D method is introduced, that combines the precision of the three-dimensional modelling in regions where the flow is complicated, and the simplicity and speed of the one-dimensional modelling for the pipe system. The simulations are time-resolved. The results obtained with the 1D-3D coupling method are in very good agreement with the experiments, and show that the method works.

Denna post skapades 2016-12-20.

CPL Pubid: 246394