HYDRAULIC TRANSIENTS IN PENSTOCKS: COMPARISON OF RESULTS OF THE SOLUTION USING RUNGE-KUTTA AND METHOD OF CHARACTERISTICS APPLIED IN THE HYDRAULIC CIRCUIT OF THE TURBINES OF THE ITAIPU POWERPLANT
João Maria Marra1; Liliana Madalena Gramani2; Christian Wendt dos Santos3; Eloy Kavisky2
1 ITAIPU; 2 UFPR; 3 Unioeste
doi:10.20906/CPS/COB-2015-2490
Resumo
The disruption of elements of hydraulic turbines circuit in hydroelectric plants is an event with serious consequences and the project seeks a sizing to ensure the non-occurrence of this failure. The phenomena that submit these elements to extraordinary effort can have a static nature, as the overpressure due to a hydraulic transient caused by a rapid change in the flow rate of the flow, or by dynamic nature phenomena, such as those caused by resonances or hydraulic instability during normal operation of the turbine. The estimate of the pressure coming from a hydraulic transient in the penstock of a hydraulic turbine, despite the satisfactory results presented from the inelastic method of Alliévi (1925), evolved with the graphical method of Schnyder- Bergeron (1950), reaching the method of characteristics (1960), widely used in the estimation of extreme values of overpressure and underpressure in the penstock due its reasonable ease of implementation and good adherence of results. By the 70's comes the finite volume method developed by Maccormack and Paullay in the solution of transient Euler equations in 2D problems. This tool has a high capacity to solve nonlinear problems, such as convective acceleration of the Navier-Stokes equations. Posteriorly authors as Jaeger (1977), Fox (1989) and Streeter (1993) suggest using impedance method. The phenomena of dynamic nature in hydraulic circuits are subject of study to the authors of this work. However, this paper seeks to apply two methods to calculate the known phenomenon of water hammer, the traditional method of characteristics and the Runge-Kutta method for the discrete solution of the governing equations, without the simplifications used in the method of characteristics. It is intended with the use of the solution by Runge-Kutta preserve the dynamic response of the hydraulic system and verifies its influence in the estimation of extremes overpressure and underpressures and the dynamics of the pressure response in the hydraulic system, determine the eigenp
Palavras-chave: water hammer; penstock; turbine; hydraulic transient; numerical simulation