Research Papers

Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

[+] Author and Article Information
Dilip Prasad

Pratt and Whitney,
East Hartford, CT 06108
e-mail: dilip.prasad@pw.utc.com

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 11, 2018; final manuscript received August 28, 2018; published online October 15, 2018. Editor: Kenneth Hall.

J. Turbomach 140(12), 121004 (Oct 15, 2018) (10 pages) Paper No: TURBO-18-1197; doi: 10.1115/1.4041375 History: Received August 11, 2018; Revised August 28, 2018

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

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Fig. 1

Notional meridional section of engine, illustrating the stations used in the present study (adapted from Ref. [2])

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Fig. 2

Variation of fan speed parameter, λ with flow parameter, Φ. Both models and data indicate that λ is independent of Φ.

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Fig. 3

Circumferentially averaged profiles of (a) axial velocity and (b) stagnation temperature at rotor exit (station RE), scaled by a¯T,2A and T¯T,2A, respectively, based on the previous simulations [2]. The dependence of the profiles on the flow parameter, Φ, is evident.

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Fig. 4

Radial profiles of the normalized, circumferentially averaged (a) axial and tangential velocity and (b) stagnation enthalpy change at rotor exit, obtained from the numerical simulations of [2]. The symbols correspond to those of Fig. 3. The collapse of the profiles demonstrates the underlying self-similarity. Results of the asymptotic theory (– – –) and the model of [2] (–⋅–⋅) display good agreement with the simulations.

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Fig. 5

Nondimensional radial profiles at vane inlet: (a) velocity, (b) absolute flow angle, (c) stagnation temperature, and (d) stagnation pressure. The profiles show that flow self-similarity continues to hold downstream of the rotor.

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Fig. 6

Schematic illustration of the vane-to-vane flow in the stator. The large negative incidence results in the formation of an extended separation zone.

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Fig. 7

Illustration of the wake blockage at vane exit for Φ = 0.194 (left), Φ = 0.246 (center), and Φ = 0.313 (right). Contours of the normalized velocity, |v|/max|v|, are employed to visualize the blockage, which is observed to be essentially invariant with Φ.

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Fig. 8

Spanwise variation of the wake blockage at vane exit, indicating the invariance of this quantity with flow parameter, Φ. The symbols correspond to those of Fig. 3.

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Fig. 9

Spanwise profiles of the unblocked circumferentially averaged absolute flow angle, α14′, illustrating invariance with the flow parameter, Φ. The symbols correspond to those of Fig. 3.

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Fig. 10

Spanwise profiles of the unblocked circumferentially averaged velocity, c14′, normalized by the vane inlet area-averaged velocity, c¯VI (——), and by the unblocked vane exit area-averaged velocity, c¯14′ (– – –). The symbols correspond to those of Fig. 3. The normalization based on c¯14′ is seen to collapse the profiles.

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Fig. 11

Flow parameter dependence of (a) bypass duct Mach numbers, (b) nondimensional stagnation pressure losses, and (c) nondimensional fan rotational speed. The lines represent results obtained using the present the models. The symbols in (b) denote simulation results, while those in (c) correspond to test data.

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Fig. 12

Flowchart illustrating a procedure to estimate the fan speed parameter and component loss coefficients



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