Inverse Computation Scheme of Turbomachinery Blade Shapes Applied to Axial Hydro-Turbine Runners

CATEGORY: TURBOMACHINERY
EngOpt 2012 – 3rd International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 01 - 05 July 2012.
Inverse Computation Scheme of Turbomachinery Blade Shapes Applied to Axial Hydro-Turbine Runners
Marcos Antonio Rodrigues dos Santos, Nelson Manzanares Filho, Waldir de Oliveira, Luis Guilherme Cunha Santos
ars.marcos@unifei.edu.br
nelson@unifei.edu.br
waldir@unifei.edu.br
lgcunhas@gmail.com
UNIFEI – Federal University of Itajubá, Itajubá-MG, Brazil
Abstract
Proposes an inverse scheme for computing the mean through flow surface of turbomachinery. The flow is considered inviscid and incompressible with the blades supposed infinitely thin. The computational domain consists of a meridional projection extending from the upstream section to the downstream section. Averaging the continuity and momentum equations leads to an equivalent elliptical differential equation for the streamfunction
which is complemented by (i) the conservation of hydraulic torque condition along streamlines for the bladeless regions and (ii) the mean flow tangency condition for the bade region. The blade region may be treated in direct mode solving for the streamfunction and hydraulic torque with a prescribed blade shape. For design purposes one adopts here an inverse approach by solving for the streamfunction and blade shape with a given hydraulic torque distribution. The streamfunction equation is solved iteratively by a differential quadrature method with Successive Over-Relaxation (SOR) using a non-orthogonal mesh. The projections of the blade leading and trailing edges coincide with mesh knots. An application is made for designing the conceptual mean runner blade surface of an axial flow hydro-turbine.
Introduction
With the progress of Computational Fluid Dynamics (CFD), the analysis of complex flow that develops inside the axial hydroturbine can be solved by using the Navier-Stokes or the Euler equations. Despite the increasing use of CFD techniques for the design and analysis of individual components or complete turbines, several flow types related with the boundary layer separation, vortex formation, interaction between the flows, cavitation, among others, in general can arise even at the point of the project.
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