- Detail

We often observe that when the blades of centrifugal compressors are equipped with diffuser blades that can improve their efficiency, the intensity of acoustic noise will increase when the passing frequency of centrifugal compressor blades is reached. We assume that the increase in noise is caused by the internal acoustic resonance generated in the space between the turbine and the stator. According to the number of diffuser blades and turbine blades, we use the Bessel function to predict the jaw motor rate under resonance frequency (9) startup to deduce the equation that Alcoa has established the world's largest aluminum lithium alloy production plant in Lafayette. This assumption is also verified by the experimental results and frequency response calculated by two-dimensional numerical simulation using the boundary element method

1. Introduction

the cross-sectional view of the centrifugal compressor with diffuser blades is shown in Figure 1 (a), and the radiated noise measured at the measuring point 0.5m away from the inlet pipe hole is shown in Figure 1 (b). Among them, the number of diffusers =12, the number of turbine blades =11. This figure shows the maximum total noise directly affected by the blade passing frequency (BPF) component of the compressor turbine. We assume that the increase of BPF component is caused by internal resonance, but the precise mechanism of resonance has not been clarified

Figure 1 cross sectional view of compressor and its noise

2 Resonance mechanism

bpf noise is caused by the wake of turbine blades touching the diffuser blades. In this way, the pressure fluctuation on the diffuser blade surface becomes the BPF noise source. These noise sources are located at the counterflow edge of the diffuser blade as shown in Figure 2 (a). Each noise source of the blade is assumed to be a point source, which has the same source intensity and different phase angles caused by the turbine rotation speed

according to the point source of diffuser blade D1, we use equation (1) and equation (2) to calculate the time delay T and phase delay of the point source of diffuser blade D2 θ 0。

here, n is the number of turbine revolutions in Hertz, and equation (2) is equivalent to that in equation (3) θ n。 Phase delay θ N is consistent with the exciting force of the number of diameter nodes Mn in equation (4)

therefore, if the eigenvalue consistent with the number of diameter nodes Mn is equal to BPF, internal resonance may occur. We calculate the number of nodes Mn based on the following assumption: the travel direction of the wake is the same as the rotation direction of the turbine. We define this direction as "forward" and replace Mn with MF in equation (5). If the travel direction of the wake is "backward", the corresponding number of diameter nodes MB is defined by equation (6) [1]

usually, the internal resonance occurs in a closed space rather than an open space. Therefore, we assume that the resonance of the centrifugal compressor occurs in the thin cylindrical space between the turbine and the stator, which is represented by vs and VH in Figure 1. The sound field in the thin axisymmetric space vs and VH is expressed by equation (7). Substituting equation (7) into wave equation (8) yields equation (9) to be solved [2]

in equation (9) Φ The general solution is cos (M φ) And sin (M φ) (m=0, ± 1, ± 2), the general solution of R in equation (9) is Bessel function JM (kw) and Neumann function nm (kw). Because the assumed resonant space has a circular rigid boundary with radii W1 and W2, the definition of boundary conditions is shown in equation (10)

by substituting the boundary conditions in equation (10) into equation (9), equation (11) with numerical solution is obtained

the diamond in Figure 1 (b) shows the characteristic values calculated according to compressor equation (11) when zi=11 and zd=12. The corresponding node numbers in equation (5) and equation (6) are mf=11 and mb=1. All characteristic values calculated in the measurement range are consistent with the nodes when mb=1. The calculated eigenvalues are in good agreement with the peak values in the test. The difference of eigenvalues should be attributed to the difference of boundary conditions and spatial shape

3. Response calculation

in order to verify the previous assumptions, we calculated the sound response using the two-dimensional boundary element method (BEM), and the calculation model is shown in Figure 3. Among them, the point source is located at the top of the diffuser blade, and the central circle is the boundary around the central axis. All boundaries are assumed to be rigid. We calculated the sound response at the turbine outlet position PI (i=1,2,3,4,5)

in BEM calculation, equation (12) is used as the basic formula. Calculate the Green's function and the direct sound component from the point source with equations (13) and (14), respectively

the amplitude of the point source is set to be proportional to the cube of the calculated frequency, so the power increase of the aerodynamic sound source can be simulated to the sixth power

Figure 3: the frequency response calculated by the analysis model

marking the source position and receiver position (zd=12) is shown in Figure 4. The results show that the calculated results of volume vs and VH are in good agreement with the test results in Figure 1 (b). The sound pressure level distribution at the peak frequency of Figure 4 is shown in Figure 5, and the circular nodes appear in Figure 5 (b), (the completed experimental report and experimental curve d) and (E) can be printed in real time. The results show that these peak frequencies are consistent with the characteristic modes when the number of circular nodes is 0, 1, 2

the result in Figure 4 is consistent with the diameter node when mb=1. To verify this result, the calculation results of the compressor under different diffuser blade numbers (zi=11, zd=27) are shown in Figure 6. The estimated number of diameter nodes is mf=11, mb=16, and the test and calculation results show that there is no obvious BPF noise peak

4. Conclusion

we have developed the following method to predict the internal acoustic resonance frequency of centrifugal compressor with diffuser blades

1) the increase in noise is caused by the acoustic resonance in the space between the turbine and the fixed Honeywell bulletproof material, which is highly trusted in the industry

2) according to the number of diffuser blades and turbine blades, the equation using Bessel function can be used to roughly predict the resonance frequency

references

[1] Takano Jing, Komi Kobayashi: internal acoustic resonance of centrifugal compressors (Japanese version), Japanese sound Association, Volume 58 (4), (2002)

[2]p · m · Morse, K · u · ingard: theoretical acoustics (magraw Hill), 356 (1968)

Takano

Hitachi Co., Ltd. Mechanical Engineering Research Laboratory

502 Shenli Road, Tupu, Japan, zip code:

e-mail: y_ Takano@

Komori

Hitachi Industries Co., Ltd.

603 Shenli Road, Tupu, Japan, zip code: (end)

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