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Research Papers: Flows in Complex Systems

# Detailed CFD Analysis of the Steady Flow in a Wells Turbine Under Incipient and Deep Stall Conditions

[+] Author and Article Information
M. Torresi

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, via Re David, 200, 70125 Bari, Italym.torresi@poliba.it

S. M. Camporeale

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, via Re David, 200, 70125 Bari, Italycamporeale@poliba.it

G. Pascazio1

Dipartimento di Ingegneria Meccanica e Gestionale, Centro di Eccellenza in Meccanica Computazionale, Politecnico di Bari, via Re David, 200, 70125 Bari, Italypascazio@poliba.it

1

Corresponding author.

J. Fluids Eng 131(7), 071103 (Jun 25, 2009) (17 pages) doi:10.1115/1.3155921 History: Received March 14, 2008; Revised May 06, 2009; Published June 25, 2009

## Abstract

This paper presents the results of the numerical simulations carried out to evaluate the performance of a high solidity Wells turbine designed for an oscillating water column wave energy conversion device. The Wells turbine has several favorable features (e.g., simplicity and high rotational speed) but is characterized by a relatively narrow operating range with high efficiency. The aim of this work is to investigate the flow-field through the turbine blades in order to offer a description of the complex flow mechanism that originates separation and, consequently, low efficiency at high flow-rates. Simulations have been performed by solving the Reynolds-averaged Navier–Stokes equations together with three turbulence models, namely, the Spalart–Allmaras, $k-ω$, and Reynolds-stress models. The capability of the three models to provide an accurate prediction of the complex flow through the Wells turbine has been assessed in two ways: the comparison of the computed results with the available experimental data and the analysis of the flow by means of the anisotropy invariant maps. Then, a detailed description of the flow at different flow-rates is provided, focusing on the interaction of the tip-leakage flow with the main stream and enlightening its role on the turbine performance.

## Figures

Figure 13

Distribution of the torque parameter γ [N] versus the blade-height fraction, r⋆

Figure 14

Gauge pressure (N/m2) distributions along the chord fraction at different r⋆ values obtained using the Reynolds-stress model for U⋆=0.238

Figure 1

High solidity Wells turbine

Figure 2

Velocity diagrams and forces acting on a cascade blade, where (1) and (2) refer to the upstream and downstream conditions, respectively

Figure 3

Wells turbine prototype

Figure 4

Turbine model geometry

Figure 5

Computational Grid A: discretization of the blade-tip surface and the leading- and trailing-edge regions

Figure 6

Computational grid: discretization of the blade and hub surfaces

Figure 7

Computational Grid A: partial view of the leading-edge

Figure 8

Computational Grid B: partial view of the leading-edge

Figure 9

Torque coefficient, T⋆

Figure 10

Nondimensional pressure drop, ΔPs⋆

Figure 11

Nondimensional stagnation pressure drop, ΔP⋆

Figure 12

Efficiency, η

Figure 15

Torque per unit area t (N/m) ((a)–(c)) and sum ts (N/m) of the pressure- and suction-side terms of t versus the chord fraction ((d)–(f))

Figure 16

Anisotropy invariant contours at midspan obtained using the Reynolds-stress model

Figure 17

Anisotropy invariant contours at R=0.15 m obtained using the Reynolds-stress model

Figure 18

Anisotropy invariant contours at midspan obtained using the k-ω model

Figure 19

Anisotropy invariant contours at R=0.15 m obtained using the k-ω model

Figure 20

Turbulent intensity contours at midspan obtained using the k-ω model (left) and the Reynolds-stress model (right)

Figure 21

Turbulent viscosity ratio contours at midspan obtained using the k-ω model (left) and the Reynolds-stress model (right)

Figure 22

ωx contours for U⋆=0.218

Figure 23

ωx contours for U⋆=0.238

Figure 24

ωx contours for U⋆=0.257

Figure 25

Figure 26

Figure 27

Particular of the ωx contours in the midchord plane

Figure 28

Figure 29

Figure 30

Gauge pressure (N/m2) distributions along the chord fraction at different R values obtained using the Reynolds-stress model

Figure 31

Tangential view of the pathlines for (a) U⋆=0.218 and (b) U⋆=0.238

Figure 32

Orthographic view of the pathlines for (a) U⋆=0.218 and (b) U⋆=0.238

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