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

Girish K. Rajan, John Michael Cimbala

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5 Citations (Scopus)

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-? (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.

Original languageEnglish (US)
Article number021102
JournalJournal of Fluids Engineering, Transactions of the ASME
Volume139
Issue number2
DOIs
StatePublished - Feb 1 2017

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Francis turbines
Vortex flow
Discharge (fluid mechanics)
Computational fluid dynamics
Turbines
Computer simulation

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

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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-? (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.",
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