On the evolution of the shock waves systems created by the fan blades

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Abstract

Fan is one of the noise sources in a modern engine. The fan noise is especially noticeable during takeoff at high angular rotation speeds. In such operating modes, supersonic flow around the tips of the fan blades is realized, which leads to the formation of shock waves that propagate upstream until they exit of the engine channel. As a result, a specific noise is emitted into the front hemisphere, consisting of harmonics that are multiples of the fan rotation frequency. The paper analyzes the described effect based on a simple model of the propagation of a shock waves system. By using energy analysis, it is shown that the system of shock waves with equal amplitude decays faster than a system of shock waves with a spread in amplitude.

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About the authors

M. A. Yudin

FAU TsAGI, Research Moscow Complex TsAGI

Author for correspondence.
Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

V. F. Kopiev

FAU TsAGI, Research Moscow Complex TsAGI

Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

S. A. Chernyshev

FAU TsAGI, Research Moscow Complex TsAGI

Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

G. A. Faranosov

FAU TsAGI, Research Moscow Complex TsAGI

Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

M. A. Demyanov

FAU TsAGI, Research Moscow Complex TsAGI

Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

O. P. Bychkov

FAU TsAGI, Research Moscow Complex TsAGI

Email: mikleudin@ya.ru
Russian Federation, st. Radio 17, Moscow, 105005

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Supplementary files

Supplementary Files
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2. Fig. 1. Flow diagram near the tips of blades flown at supersonic speed M = Mₐ²+Mₐ² >1 , where Mₐ and Mτ are the axial and tangential Mach numbers, respectively.

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3. Fig. 2. Regular system of shock waves (λ) is the distance between shocks).

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4. Fig. 3. Schematic representation of the shock wave merging process.

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5. Fig. 4. Comparison of analytical and numerical solutions.

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6. Fig. 5. Evolution of the spectrum of a regular wave system (N is the harmonic number with frequency Nω₀, ω₀ = 2π/T, T is the fan rotation period).

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7. Fig. 6. Evolution of a system with one distinct jump.

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8. Fig. 7. Evolution of the spectrum of the system with one different jump, harmonics at the blade following frequency are highlighted in red.

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9. Fig. 8. Layout of adjacent profiles in the model grid. L is the profile chord. The dotted line shows the profile at the angle of attack α.

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10. Fig. 9. Scheme of the computational domain.

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11. Fig. 10. Results of calculating the pressure field for a regular grid of profiles: (a) — grid 1; (b) — grid 2; (c) — distribution of pressure disturbances along the propagation line for grid 1 (line 1), for grid 2 (line 2) and the amplitude of shock waves for a one-dimensional model (line 3).

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12. Fig. 11. Pressure field obtained as a result of calculating a two-dimensional irregular grid of profiles, and data analysis lines.

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13. Fig. 12. Comparison of numerical simulation data (curve 1) and calculations using a one-dimensional model (curve 2).

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