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

Abstract

Results on flows in a draft tube of a constant-head, constant-specific speed, model Francis turbine are presented based on computational fluid dynamics (CFD) simulations and theoretical analysis. A three-dimensional, unsteady, Navier–Stokes solver with the detached-eddy simulation (DES) model and the realizable k–ϵ (RKE) model is used to analyze the vortex rope formed at different discharge coefficients. The dominant amplitude of the pressure fluctuations at a fixed point in the draft tube increases by 13 times, and the length of the rope increases by 3.4 times when the operating point of the turbine shifts from a discharge coefficient of 0.37 to 0.34. A perturbation analysis based on a steady, axisymmetric, inviscid, incompressible model for the mean flow is performed to obtain a Sturm–Liouville (SL) system, the solutions of which are oscillatory if the discharge coefficient is greater than 0.3635, and nonoscillatory otherwise.

State of the Art in Designing Fish-Friendly Turbines: Concepts and Performance Indicators

“…Then, at the vicinity of the stator blades, and especially the runner, pressure drops rapidly, much faster than the pressure rise. Gauge pressure can drop even below zero (vacuum), near the suction side of the blades [47,48], or the spiraling vortex tube, also known as vortex rope in the relevant literature, emanating from the turbine hub [40,49]; indeed, the latter is well known to induce strong low-frequency vibrations to the whole turbine, which potentially threaten the integrity of the whole installation [50][51][52][53]. In any case, as the trajectory of a passing fish reaches the tailrace, pressure recovers gradually to near atmospheric conditions.…”

Experimental study of a Francis turbine under variable-speed and discharge conditions

“…To investigate the presence of synchronous component (axial), further analysis was carried out. Details about the synchronous and asynchronous components of vortex rope can be found in literature [49][50][51][52]…”

Investigation of Flow-Induced Instabilities in a Francis Turbine Operating in Non-Cavitating and Cavitating Part-Load Conditions

“…Minakov et al [19] used DES to study the RVR in the draft tube at different guide vane openings, and found that changing the guide vane opening leads to a different swirl number and discharge coefficient, which leads to different behavior of the RVR. Rajan and Cimbala [20] studied the flow in a simplified draft tube using the DES approach for different discharge coefficients. It was shown that the level of pressure fluctuations increases substantially when the RVR is formed in the draft tube.…”