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Research Papers

# Theoretical Analysis of the Aerodynamics of Low-Speed Fans in Free and Load-Controlled Windmilling Operation

[+] Author and Article Information
Nicolas Binder

ISAE-SUPAERO,
Université de Toulouse,
10, avenue Edouard Belin,
BP 54032,
Toulouse Cedex 4 31055, France
e-mail: nicolas.binder@isae.fr

Suk-Kee Courty-Audren

SAFRAN-TECHNOFAN,
10, place Marcel Dassault,
BP 30053,
Blagnac Cedex 31702, France

Sebastien Duplaa, Guillaume Dufour, Xavier Carbonneau

ISAE-SUPAERO,
Université de Toulouse,
10, avenue Edouard Belin,
BP 54032,
Toulouse Cedex 4 31055, France

This definition is equivalent to the usual traction coefficient found in the literature dedicated to propeller.

If there is an inlet to outlet variation of radius at hub or shroud because of a contraction of the meridional channel, the use of the rotor outlet radius is recommended (the inlet swirl is generally small, and the sine of this angle is considered at the inlet plane; the error of neglecting the meridional curvature is thus imputed on small quantities, which minimizes the global error).

In an inviscid process, it might be observed that $φ∧p<φ∧t$. But the model does not account for the contribution of losses to the pressure drop. Thus, it will be found that $φ∧p>φ∧t$. The different operating regimes can thus be identified: for $φ∧<φ∧t$ the usual fan mode, for $φ∧t<φ∧<φ∧p$ the stirrer mode, and for $φ∧>φ∧p$ the turbine mode.

This distortion is mainly due to viscous effect at the shroud, and to the presence of the hub cap.

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 19, 2014; final manuscript received April 1, 2015; published online May 12, 2015. Assoc. Editor: Michael Hathaway.

J. Turbomach 137(10), 101001 (Oct 01, 2015) (12 pages) Paper No: TURBO-14-1247; doi: 10.1115/1.4030308 History: Received September 19, 2014; Revised April 01, 2015; Online May 12, 2015

## Abstract

The present work is a contribution to understanding the windmilling operation of low-speed fans. Such an operating situation is described in the literature, but the context (mainly windmilling of aero-engines) often involves system dependence in the analysis. Most of the time, only regimes very close to the free-windmilling are considered. A wider range is analyzed in the present study, since the context is the examination of the energy recovery potential of fans. It aims at detailing the isolated contribution of the rotor, which is the only element exchanging energy with the flow. Other elements of the system (including the stator) can be considered as loss generators and be treated as such in an integrated approach. The evolution of the flow is described by the use of theoretical and experimental data. A theoretical model is derived to predict the operating trajectories of the rotor in two characteristic diagrams. A scenario is proposed, detailing the local evolution of the flow when a gradual progression toward free and load-controlled windmilling operation is imposed. An experimental campaign exerted on two low-speed fans aims at the analysis of both the local and global aspects of the performance, for validation. From a global point of view, the continuity of the operating trajectory is predicted and observed across the boundary between the quadrants of the diagrams. The flow coefficient value for the free-windmilling operation is fairly well predicted. From a local point of view, the local co-existence of compressor and turbine operating modes along the blade span is observed as previously reported. It is further demonstrated here that this configuration is not exclusive to free-windmilling operation and occurs inside a range that can be theoretically predicted. It is shown that for a given geometry, this local topology strongly depends on the value of the flow coefficient and is very sensitive to the inlet spanwise velocity distribution.

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## Figures

Fig. 1

Conventions and references: (a) triangle of velocities and (b) stations of a conventional stage

Fig. 2

Trajectories in the diagrams: (a) generic trends and (b) decomposition of the operating modes

Fig. 3

Possible local composition of velocities (without inlet swirl) along the span: (a) fan-like, (b) neutral, and (c) turbine-like

Fig. 5

Illustration of the experimental setup for the two fans: (a) fan 1 and (b) fan 2

Fig. 6

Experimental results for the two fans without preswirl, compared with the theoretical expectation: (a) fan 1 and (b) fan 2

Fig. 7

Experimental results for the fan 1 with preswirl, compared with the theoretical expectation

Fig. 8

Comparison between the theoretical prediction of φ∧p as a function of the inlet swirl and the experimental results for the two fans

Fig. 9

Analysis of fan 2. (a) Evolution of the pressure-drop coefficient as a function of the flow coefficient, for direct measurement and corrected data, compared with the theoretical expectation. (b) Estimation of the pressure loss coefficient, as a function of the reduced mass-flow.

Fig. 10

Overall pressure drop coefficient as a function of the flow coefficient for the fan 1, for two different IGV configurations

Fig. 11

Distribution along the blade span compared with expectation predicted from geometry, for φ∧p and φ∧l. (a) Local ψ-to-φ gradient. (b) Relative flow angle at the outlet of the rotor.

Fig. 12

Local prediction of the local enthalpy variation along the blade span; evolution of the neutral radius rp. (a) Increase of the flow coefficient for a uniform inlet velocity distribution. (b) Distortion of the inlet velocity distribution for φ∧ = φ∧p.

Fig. 13

Distribution of the dimensionless total enthalpy change along the blade span. The predicted and effective neutral radius positions are quoted. (a) φ∧ = φ∧p. (b) φ∧ = φ∧l.

Fig. 14

Spanwise evolution of the losses. (a) Contributions to the total pressure ratio at φ∧ = φ∧p. (b) Loss coefficients (main figure: ξ, subfigure: ∼ΔP*|losses).

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