Unsteady Numerical Simulation of Flow in Draft Tube of a Hydroturbine Operating Under Various Conditions Using a Partially Averaged Navier–Stokes Model

Abstract

The variable energy demand requires a great flexibility in operating a hydroturbine, which forces the machine to be operated far from its design point. One of the main components of a hydroturbine where undesirable flow phenomena occur under off-design conditions is the draft tube. Using computational fluid dynamics (CFD), the present paper studies the flow in the draft tube of a Francis turbine operating under various conditions. Specifically, four operating points with the same head and different flow rates corresponding to 70%, 91%, 99%, and 110% of the flow rate at the best efficiency point (BEP) are considered. Unsteady numerical simulations are performed using a recently developed partially averaged Navier–Stokes (PANS) turbulence model, and the results are compared to the available experimental data, as well as the numerical results of the traditionally used Reynolds-Averaged Navier–Stokes (RANS) models. Several parameters including the pressure recovery coefficient, mean velocity, and time-averaged and fluctuating wall pressure are investigated. It is shown that RANS and PANS both can predict the flow behavior close to the BEP operating condition. However, RANS results deviate considerably from the experimental data as the operating condition moves away from the BEP. The pressure recovery factor predicted by the RANS model shows more than 13% and 58% overprediction when the flow rate decreases to 91% and 70% of the flow rate at BEP, respectively. Predictions can be improved significantly using the present unsteady PANS simulations. Specifically, the pressure recovery factor is predicted by less than 4% and 6% deviation for these two operating conditions. A similar conclusion is reached from the analysis of the mean velocity and wall pressure data. Using unsteady PANS simulations, several transient features of the draft tube flow including the vortex rope and associated pressure fluctuations are successfully modeled. The formation of the vortex rope in partial load conditions results in severe pressure fluctuations exerting oscillatory forces on the draft tube. These pressure fluctuations are studied for several locations in the draft tube and the critical region with highest fluctuation amplitude is found to be the inner side of the elbow.

Effect of turbulence intensity of fluid medium interface layer on magnetic liquid seal in liquid environment

“…Firstly, the internal flow of the sealed liquid is approximated as a three-dimensional incompressible flow. The flow field should satisfy the mass and momentum conservation equations [15] . Mass conservation can be theoretically described as the equality of the mass of the fluid flowing out of the control body to that reduced by the density change in the control body in the same time interval.…”

Computational and Theoretical Analyses of the Precessing Vortex Rope in a Simplified Draft Tube of a Scaled Model of a Francis Turbine

“…They concluded that the DES model captures the structure of the vortex rope much better than the other models considered. Foroutan and Yavuzkurt [27] also tested the performances of a partially averaged Navier-Stokes (PANS) model and the traditional RANS model in simulating the flow in the draft tube of a Francis turbine for four different operating conditions. Based on their results, they concluded that though both the RANS and PANS models performed well in predicting the flow when the operating point of the turbine was close to the BEP, the results of the RANS model did not agree well with the experimental measurements, for conditions in which the operating point of the turbine was not close to the BEP.…”

“…Similarly, if u and e are the velocity vector and the real eigenvector of D, then the real eigen helicity is defined as h ¼ ðu Á eÞ (27) For a detailed description of visualization techniques for vortex ropes, see Refs. [37][38][39][40].…”

An Experimental Investigation of the Air Injection Effect on the Vortex Structure and Pulsation Characteristics in the Francis Turbine

“…This phenomenon was observed in experimental models of draft tubes [3,4]. Precession of the vortex rope is one of the mechanisms generating low-frequency flow pulsations in hydraulic turbines [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”