Research Papers

A Theory on the Onset of Acoustic Resonance in a Multistage Compressor

[+] Author and Article Information
Xiaohua Liu

School of Aeronautics and Astronautics,
Shanghai Jiao Tong University,
No. 800 Dongchuan Road,
Shanghai 200240, China
e-mail: xiaohua-liu@sjtu.edu.cn

Tobias Willeke

Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universität Hannover,
Appelstraße 9,
Hannover 30167, Germany
e-mail: willeke@tfd.uni-hannover.de

Florian Herbst

Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universität Hannover,
Appelstraße 9,
Hannover 30167, Germany
e-mail: Herbst@tfd.uni-hannover.de

Jun Yang

School of Energy and Power Engineering,
University of Shanghai for
Science and Technology,
No. 516 JunGong Road,
Shanghai 200093, China
e-mail: yangjun@usst.edu.cn

Joerg Seume

Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universität Hannover,
Appelstraße 9,
Hannover 30167, Germany
e-mail: Seume@tfd.uni-hannover.de

1Corresponding author.

Manuscript received February 15, 2018; final manuscript received June 8, 2018; published online July 24, 2018. Assoc. Editor: Rakesh Srivastava.

J. Turbomach 140(8), 081003 (Jul 24, 2018) (12 pages) Paper No: TURBO-18-1032; doi: 10.1115/1.4040551 History: Received February 15, 2018; Revised June 08, 2018

A novel theoretical model of the internal flow field in multistage axial compressors based on an eigenvalue approach is developed, in order to predict the onset of acoustic resonance in aircraft engines. Using an example high-speed four-stage compressor, it is shown that one of the resultant frequencies is in excellent agreement with the experimental data in terms of acoustic resonance. On the basis of the computed natural frequency of the whole compression system and the measured spanwise distribution of static pressure, the location of the acoustic excitation source can be found in the third stage. Unsteady flow simulations of the full annulus of this stage reveal two criteria for acoustic excitation at the rotor-blade tip, reversed flow near the suction surface and flow impingement on the pressure surface. Additionally, a fast Fourier transform of the unsteady pressure field at the upper rotor-blade span verifies the existence of the computed unstable frequency of the oscillating tip leakage flow. Using this novel theory, which combines a theoretical calculation of flow-instability frequency of the global system with the computational simulation of a single stage, the onset mechanism and location of the excitation source of acoustic resonance in multistage turbomachinery can be explained at acceptable computational cost.

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Fig. 1

Sketch of the four-stage high-speed axial compressor test rig

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Fig. 2

Wall static pressure during slow throttling process from Ref. [6]

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Fig. 3

Measured acoustic pressure level of the resonance frequency 1487 Hz at an operating point close to stall [9]

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Fig. 4

Meridional section of multistage compressor with an arbitrary streamline (R: rotor; S: stator)

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Fig. 5

Sketch of the body force at discrete points (b1 to bn) along a streamline in a blade-to-blade passage

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Fig. 6

Uniform annular duct with uniform flow

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Fig. 7

Computed frequencies (minimum values of the solid line) compared with the analytical solution (dash dot line)

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Fig. 8

Block groups used in the single-passage steady CFD simulation

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Fig. 9

Computed performance line by steady-state CFD compared to experimental data

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Fig. 10

Computed reciprocal of condition number for the four-stage compressor at a reduced mass flow of 7.26 kg/s and 95% rotational speed

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Fig. 11

Block groups of S2-R3-S3 component

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Fig. 12

Reversed flow (negative axial velocity) of circumferential mode 3 in tip gap region at a reduced mass flow of 7.26 kg/s and 95% rotational speed

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Fig. 13

Contour of axial velocity on a section of 35% chord of R3: (a) complete range of axial velocity and (b) negative axial velocity

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Fig. 14

Relative streamlines and flow impingement on adjacent pressure surface at blade tip in an enlarged area (impinging areas A and B are indicated by black circle, and origin areas of impinging flow are marked as C and D) at a reduced mass flow of 7.26 kg/s and 95% rotational speed

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Fig. 15

Computed local speed of sound at blade tip marked by colored lines on the basis of steady CFD results and computed propagation speed of acoustic wave marked by dash dot line using Eq. (46)

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Fig. 16

Fast Fourier transformation analysis of computed unsteady static pressure at blade tip at a reduced mass flow of 7.26 kg/s and 95% rotational speed

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Fig. 17

Enlarged area for low frequency spectrum (dash dot line is the theoretically computed sound source frequency)



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