Discrete Noise Sources in a Centrifugal Pump Operating at Partial Load
Raúl Barrio Perotti Jorge L. Parrondo José González Pérez Francisco Castro Ruiz Miguel Ángel Rodríguez Beneite
Proceedings of the International Institute of Acoustics and Vibration th XII International Congress on Sound and Vibration. Págs. 1849-1856.
Lisboa (Portugal). Julio, 2005.
© 2005 International Institute of Acoustics and Vibration.
Twelfth International Congress on Sound and Vibration
DISCRETE NOISE SOURCES IN A CENTRIFUGAL PUMP OPERATING AT PARTIAL LOAD Raúl Barrio Perotti (1), Jorge Luis Parrondo Gayo (1), José González Pérez (1), Francisco Castro Ruiz(2), Miguel Ángel Rodríguez Beneite (2) (1)
Departamento de Energía, Universidad de Oviedo. Campus de Viesques s/n, 33203 Gijón (Spain). E-mail:
[email protected]
(2)
Departamento de Ingeniería Energética y Fluidomecánica, Universidad de Valladolid. ETSII, Paseo del Cauce s/n, 47011 Valladolid (Spain)
Abstract Centrifugal pumps present different mechanisms for broadband and discrete noise production. Particularly relevant is the discrete noise generated at the rotation frequency and, over all, at the blade-passing frequency. The latter is associated to the fluid-dynamic rotor-stator interaction. The object of this work was the identification of the acoustic emission properties for one particular pump, with a specific velocity of 0.72, based on the comparison of experimental data of pressure fluctuations and the predictions from a simple acoustic model for the pump. The analysis was focused on the effects of the impeller-volute interaction as a function of the circulating flow-rate.
INTRODUCTION
During the operation of fluid turbo-machinery, fluid-dynamic perturbations are produced that can lead to vibration and noise emission. In the case of centrifugal pumps, a rotating impeller with passing channels delimited by a number of curved blades, transfers energy to the fluid by forcing it to circulate through the machine from the axial to the radial direction. Around the impeller a spiral shape casing called the volute, collects the fluid coming out from the impeller and directs it towards the pump outlet. Typical fluid-dynamic excitations in these machines are associated to the rotation frequency, to the blade-passing frequency and to broadband phenomena like turbulence. Excitation at the blade-passing frequency (f BP) is usually dominant, especially when the pump operates at off-design conditions.
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The f BP excitation is a consequence of: i) the flow pulsations in the volute that follow the passage of the rotating blades (jet-wake pattern), and ii) the intermittent interaction of those disturbances and the volute at the tongue region. The magnitude of this interaction, capable of generating acoustic pressure waves, is very dependent on the pump operating point [1] and on the geometry of the tongue region [2]. Since the vibration and noise levels induced by the phenomenon may become excessive under certain conditions, a low f BP excitation constitutes a design objective, and there is interest in knowledge of the phenomenon and in prediction tools. This paper is a continuation of the previously presented work in Parrondo et al. [3, 4] to characterize the effect of the fluid-dynamic blade-tongue interaction on the sound produced at f BP. In this case, a new centrifugal pump with a non-dimensional specific speed of 0.72 was used for the study, and new improvements were performed in the calculation program to achieve a better correspondence between the data obtained with the program and the results from the experiments. TEST PUMP AND EXPERIMENTAL RESULTS
The pump used in the experiments was a conventional single suction centrifugal pump model ENORM 125/250, whose main characteristics are resumed in Table 1. This pump extracted and returned the water from a cilyndrical tank in a closed-loop circuit (see Figures 1 and 2). Table 1 - Main characteristics of the test pump
Impeller outlet diameter (Ф2) 290 mm Rotation speed (ω) (maintained constant) Number of blades (z) 6 Specific speedω(s) 3 Nominal flow-rate (Q N) 205 m /h Blade-passing frequency (f BP) Nominal head (H N) 22 m R 2/R T (impeller radius / tonge-tip radius)
169.6 rad/s 0.72 162 Hz 0.87
The purpose of the experiments was to obtain pressure fluctuations at the impeller exit as a function of the flow-rate. In the hydraulic circuit, valves V 1 and V3 were always opened and flow was regulated using valve V2. A magnetic rate meter mounted in the circuit (downstream the pump, named C), was used to check the flow-rate. To get pressure fluctuations the pump was instrumented with piezoelectric transducers distributed every 10º around the front size of the volute as seen in Figure 1. The pressure 1 - Test pump with location of signals were amplified, captured with a Figure transducers multi-channel data acquisition board, digitized and then FFT processed to obtain the spectra of the pressure amplitude and the relative phase delay along the volute for each flow-rate. Tests were conducted for
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Figure 2 - Scheme of the hydraulic circuit
5 flow-rates, ranging from 0 to 100% of the nominal flow-rate. Figure 3 shows performance curves and pressure fluctuation signals along the impeller for the different flow-rates. As can be seen there the main peaks are produced near the tongue from 0 to 60º approximately ( φ=0º at the tongue-tip) and, as the pump had two anti pre-rotating blades in the suction duct just before impeller inlet, the main pressure wave of the blade-tongue interaction is modulated with a blade-anti prerotating blade interaction pressure wave. These experimental results (peak amplitude and phase at f BP) are used as inputs in the calculation program developed to characterize this blade-tongue interaction by means of some ideal sound sources positioned in the volute of the pump.
Figure 3 - Performance curves and pressure fluctuations around the impeller
ACOUSTIC MODEL
The acoustic model used in this paper is based on the one described in [3, 4]. The model considers that the interaction between the rotating jet-wake pattern behind the blades and the volute tongue can be simulated by means of a number of ideal point sources, each located at some position in the volute. These sources are assumed to radiate plane waves at f BP towards both the positive and negative directions (see Figure 4). Successive sound circulations along the volute are affected by: i) divergence, ii) sound emission through the impeller channels towards the inlet of the pump, iii) partial reflection at the tongue edge for waves traveling in the negative direction due to the abrupt increment in cross-section, iv) sound emission through the outlet pipe for waves arriving at the exit of the volute and v) entrance through the
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pump exit of the sound reflected at the outlet ducts. Unlike the preceding model, the reflection of sound waves from the outlet duct was taken into account.
Figure 4 - Pump with one ideal acoustic source F radiating sound along the volute, with detail of the 3-port acoustic system scheme for the tongue region
When the sound radiated by the source F towards the negative direction reaches the tongue, it encounters an abrupt increment in volute cross-section. In such situation, part of the incident sound energy is transmitted through the gap, and the rest is reflected back from the tongue edge. The new circulations of the sound transmitted in the negative direction and of the sound reflected back towards the positive direction, can be simulated by two new virtual sound sources located at the tongue edge. On the other hand, when the sound from the positive direction reaches the tongue, most of the sound energy will be directed towards the pump outlet and some fraction will continue for a new circulation along the positive direction. This recirculation can be simulated by means of a new acoustic virtual source located at the tongue edge radiating only towards the positive direction. On the contrary, part of the sound energy that had been directed towards the pump outlet could be reflected due to a change in the direction of the duct or the presence of a singularity (as a valve), and re-emitted back to the pump. When this sound reaches the tongue edge at the outlet side, it encounters an increment in volute cross-section that produces the same transmission-reflection process as the one described in the preceding paragraph. In this case, part of the sound is reflected again towards the outlet duct and the rest is reintroduced through the pump in the negative direction. This process can be simulated again by means of two new acoustic sources located at the tongue edge outlet side, the first emitting positive sound waves towards the pump outlet and the second emitting negative sound waves towards the pump. This process can be considered as a 3-port acoustic system like the one of Figure 4. The relationship between incident and emitted sound waves is given by:
⎡ Pae ⎤ ⎡R aa T ba Tca ⎤ ⎡ Pai ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Pe= P be =M·Pi= Tab R bb Tcb ⋅ P bi ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ Pce ⎥⎦ ⎢⎣ Tac T bc R cc ⎥⎦ ⎢⎣ Pci ⎥⎦
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(1)
The first matrix Pe represents the emitted sound in each of the ports whereas the last matrix Pi represents the incident sound. The matrix M, called scattering matrix, is formed by the reflection and transmission coefficients in each port, R ii and Tij respectively, whose values are basically dependent on the geometry (transversal port sections Sa, S b and Sc) and on the specific acoustic impedance of the flowing fluid. Some difficulties were encountered to evaluate the effect of the lateral gaps between impeller and stator in the effective sections at each port. For such reason, the elements of the scattering matrix were related from energy balances to two of them, R aa and R cc, which were considered as two new variables for fitting by means of the calculation program. With all these considerations, the resulting pressure field at f BP due to N ideal sound sources (both primary and secondary) can be modeled as:
⎡ ⎛ Sϕ ⎞ α − j(ω⋅t − k ϕ−ϕ −β ) ⎤ F F ⎥ + PB ⋅ e − j(ω⋅t −zϕ ) p(ϕ, t ) = ∑ ⎢PF ⎜⎜ ⎟⎟ ⋅ e ⎥⎦ F =1 ⎢ ⎣ ⎝ S F ⎠ N
(2)
where PF and βF are the pressure amplitude and phase delay of the font F, ω=2πf BP, j= − 1 , SF and Sφ are the volute cross-sections at angular positions φF and φ respectively, k is the angular wave number and exponent α quantifies the sound lost through the impeller channels towards the impeller inlet. For more discussion on this model see [3, 4]. CALCULATION PROGRAM
A special calculation algorithm was developed to compute the sound pressure field at f BP in the volute of the centrifugal pump based on the application of Equation (2). The algorithm assumes the presence of two primary point sources and, starting from an initial set of values, a predictor-corrector algorithm is used to reduce the sum of square errors between the model predictions and the experimental data. The degree of correspondence achieved, formed by the amplitude and phase delay at M positions, was evaluated by means of the determination coefficient R 2 defined as: 2 2 M ⎛ M ⎞ R = 1 − ⎜⎜ ∑ (PRi − PR (ϕ i )) + ∑ (PIi − PI (ϕ i )) ⎟⎟ i =1 ⎝ i=1 ⎠ 2
2 2 M ⎛ M ⎞ ⎜ ∑ (PRi − PR ) + ∑ (PIi − PI ) ⎟ (3) ⎜ i=1 ⎟ i =1 ⎝ ⎠
where PRi and PIi are the real and imaginary parts of the pressure amplitude measured at position φi, PR (φi) and PI(φi) are the real and imaginary parts of the amplitude calculated from Equation (2) and PR and PI are the arithmetic averages (real and imaginary parts) of the M experimental data. Taking into account that Equation (2) assumes notorious simplifications, and that the model does not consider the presence of the two anti pre-rotating blades in the suction duct, an R 2 coefficient of about 0.8 may be considered satisfactory.
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RESULTS FOR THE TEST PUMP
The described algorithm was applied to the pump of Table 1. Experimental data obtained suggested to consider two independent primary sound sources in the volute for the acoustic model simulations. Their pressure amplitude (p1, p2), peripheral position ( φ1, φ2) and time phase delay ( β1, β2), plus the blade pressure amplitude PB and the two coefficients R aa and R cc were estimated for each of the 5 flow-rates as well as the determination coefficient R 2. Figure 5 shows the results of these simulations. As can be seen there, the two sound sources are located near the tongue, one at each side (first and fourth quadrants) in a quite constant position. The pressure amplitude of the source located in the first quadrant results to be about 4 times greater than that of the one located in the fourth quadrant, due to the strong flux-tongue interactions that occur in this zone where the gap is smaller, and the time phase delay between the two sources is kept between 150170º. All these facts indicate that the two sound sources behave like a dipole radiating harmonic sound at f BP. This agrees with the results previously obtained in [3, 4] for other pumps and radial gaps. On the other hand, the order of the pressure magnitude of the sound sources is about 8 times greater in the case of the first source or 2 times greater in the case of the second one than that of the blade amplitude fluctuation PB, except for the nominal flow-rate, where the P B magnitude increases abruptly. This unexpected result was attributed to the occurrence of severe cavitation at the pump inlet for high flow-rates. Results obtained for the two coefficients R aa and R cc are practically independent Figure 5 - Parameters of sound of the flow-rate, with values of about 0.8 for R aa and sources, reflection and 0.3 for R cc. These values keep good relationship determination coefficients, as with the volute cross-section values for each port. unction of flow-rate Finally, the spatial distributions of the normalized zero-to-peak pressure amplitude (real and imaginary parts) along with the corresponding experimental data for the two sources considered are shown in Figure 6. As seen in the figure, there is good agreement between data, showing 6 maxima and minima resulting from the combination of hydraulic and acoustic disturbances.
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REAL PART
IMAGINARY PART
)
2 2
U ρ 5 . 0 ( / A p
Angular position (º) Figure 6 - Comparison of the experimental (dots) and theoretical (continuous line) pressure fluctuations at f BP for the different flow-rates
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CONCLUSIONS
A simple acoustic model was considered to simulate and quantify the effects of the fluid-dynamic blade-tongue interactions, at the blade-passing frequency excitation, in centrifugal pumps with volute casing by means of some ideal sources radiating plane waves along the volute. The properties of these sound sources were established for each pump and flow-rate after fitting the available experimental data of pressure fluctuations by a least-square error procedure. The model presented is an extension of the one described in [3, 4], and takes into account the sound emission through the outlet duct and partial reflections in it that can produce some reintroduction of the sound waves into the pump again. This tongue region was simulated as a 3-port acoustic system characterized by a scattering matrix with 9 elements. This methodology has been applied to a conventional centrifugal pump with an impeller of 290 mm in diameter (gap-radius ratio of 15%) and 5 flow-rates ranging from 0 to 100% of the nominal flow-rate. The obtained results show that the effect of the bladetongue interaction can be reasonably simulated by means of two ideal sound sources situated in the first and fourth quadrants that behave like a dipole. ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support of the Ministerio de Ciencia y Tecnología (Spain) under Project MCT-02-DPI04266-C0202 and the Fundación para el Fomento en Asturias de la Investigación Científica Aplicada y la Tecnología (FICYT). REFERENCES
[1] J. Parrondo, J. González, J. Fernández, “The effect of the operating point on the pressure fluctuations at the blade passage frequency in the volute of a centrifugal pump”, ASME J. Fluids Engineering, 124 (3), 784-790 (2002). [2] R. Dong, S. Chu, J. Katz, “Effect of modification to tongue and impeller geometry on unsteady flow, pressure fluctuations and noise in a centrifugal pump”, ASME J. Turbomachinery, 119, 506-515 (1997). [3] J. Parrondo. J. Pérez, J. Fernández, J. González, “A simple acoustic model to simulate the blade-passing frequency sound pressure generated in the volute of centrifugal pumps”, Forum Acusticum Sevilla 2002 (3rd European Congress on Acoustics), paper ENV-Gen-011 (2002). [4] J. Parrondo, J. González, O. Fernández, P. González, J. Pérez, “Characterization of blade-passing frequency sound sources in a centrifugal pump from pressure fluctuation measurements”, Tenth International Congress on Sound and Vibration, Stockholm (Sweden) 2003.
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