Experimental and numerical investigation of interior flow-induced noise in pump as turbine

2.1. Interior noise test

A standard test facility for the interior noise measurement of the investigated PAT has been constructed in [22], as shown in Fig. 1. In the test facility, a feed pump was installed to supply high pressure fluid required for PAT energy recovery. The pressure energy of fluid was transformed to the mechanical energy of shaft by rotating impeller. An electric eddy current dynamometer was adopted to measure and consume energy generated by PAT and to regulate rotating speed. The inlet and outlet pressure were obtained using pressure transmitters. The discharge was measured by using a turbine flow meter. At four times diameter of inlet pipe and draft tube, ST70 hydrophones were installed to measure the interior noise generated by PAT, with a sampling frequency of 25.6 kHz. The average method in whole range was adopted to reduce random noise error. And Hanning window was used to reduce leakage error in frequency-domain due to time-domain truncation. Note that, because the PAT was connected with the pipeline system, it must try to eliminate the effect of other sound sources in the pipeline to ensure the measurement accuracy. At each working condition, each valve in the loop system remained fully open, so the effect of valve noise can be ignored. Due to the flush installation method of hydrophone, the noise can be measured reliably with minimum effect on the flow field in the pipe. A shortcoming of this method is the measurement will be affected by the boundary layer turbulence noise on the pipe walls. However, the existing studies have shown that the boundary layer turbulence noise is so small compared with pulsating noise [23], so the measured noise by hydrophone can be thought of as the noise generated by the PAT.

Fig. 1Sketch of the test installation

The PAT investigated in this study is a volute-type single-stage centrifugal pump operating in a turbine mode. Its design parameters in pump mode are as follow: flow rate $Q_d=$90 m³/h, head $H=$35 m, rotating speed $n=$1500 r/min and specific speed $n_s=$60. Table 1 lists its main geometric parameters in pump mode.

2.2. Experimental modal analysis

Experimental modal analysis was a kind of dynamic test based on the exciting force and the response of a system. Fig. 2 shows the sketch of modal test. The highest natural frequencies of the mounting systems were verified to be far less than 20 % of the first-order natural frequency of structure itself. The acceleration sensor and hammer were connected to the signal modulation system and SD380 dynamic analysis system, respectively. By it, the matrix of frequency response function can be obtained through measurable and controllable dynamic excitation over structure. Then, the modal parameters can be acquired by polynomial curve fitting method in frequency domain. By motivating each point with a single response measuring point fixed, the modal experiment was performed. The acquisition frequency was chosen equal to 5.12 kHz with a resolution of 6.4 Hz. The transient force window was imposed to improve the signal-to-noise ratio of excitation signal. And index window was imposed on response signal, to accelerate vibration attenuation and avoid the leakage of frequency response function.

Fig. 2Sketch of the modal test

a) Rotor

b) Casing

The measuring points should be distributed appropriately to distinguish each vibration. The factors that should be considered when choosing the location of measuring points are as follows: (1) the structure contour of the PAT should be reflected and the measuring points on the regular part of structure should be arranged symmetrically. (2) Measuring points should be arranged closely at main load-bearing parts. (3) The acceleration sensor should be placed away from the nodes of each vibration modal without losing modal. (4) More measuring points should be placed at some local area where there may be more modal. Finally, 164 and 306 measuring points are arranged at the main part of rotor and casing.

3.1. Acoustic simulation

With fluid as noise source in PAT, there are two main forms of dipole sources, that are rotating dipole source on the surfaces of the impeller and fixed dipole source on the casing wall. And, the flow-induced interior noise can be divided into two kinds: (1) the directly radiated interior noise due to dipole source, that is flow-borne noise. (2) the radiated interior noise due to structure vibration under the action of dipole source, that is flow-induced structure noise. The two forms of interior noise exist side by side. Based on LMS Virtual.Lab 12, the BEM and FEM/BEM vibroacoustic coupling method were adopted to solve flow-borne noise and flow-induced structure noise. Fig. 3 shows the calculation process. In terms of the flow-borne noise excited by casing source, firstly four cycles of pressure fluctuations on inner walls of casing were solved based on URANS. Then, the interior acoustic field was solved based on BEM method. While as for the flow-borne noise generated by impeller source, only the pressure fluctuations on the walls of rotating impeller in time-domain was extracted. During the noise calculation, when the size of impeller is far less than the wavelength, the sound field caused by pressure fluctuations on the impeller surface can well be characterized by the fan sound source. While when the impeller size is bigger, the discrete fan sound source is needed to be used to calculate the sound field. That is, the impeller is divided into n parts with the load and its location defined on each part. Here, the impeller was divided into 10 pieces. Concerning the flow-induced structure noise, the load is no longer macro pressure fluctuation, but sound pressure on the casing due to internal dipole source. The pressure fluctuations on casing walls were firstly transferred onto the meshes of solid walls. Then, the solution of vibration displacement under the excitation was performed based on the natural modal of structure. Finally, with the vibration displacement as boundary conditions, the flow-induced structure noise was solved by FEM/BEM method. To predict the combined effect of the two interior noises, a computing method was employed, which was still based on FEM/BEM method. The only difference was that the pressure fluctuation was interpolated on the casing surfaces of interior acoustic model, not structure. In this way, the flow-borne noise considering structure can be solved under sound pressure.

Fig. 3Calculation process of BEM and FEM/BEM

Fig. 4 gives a general view of the generated meshes for acoustic boundary element and structure finite element. As for BEM, the closed surface mesh with consistent size was required. 6 millimeters were chosen as the element size, which is less than 1/6 of the corresponding wavelength at the maximum calculated frequency ($f_{max}=$ 2000 Hz, sound velocity in water $c=$1500 m/s). When taking into account of the influence of structure, the modal responses of casing was analyzed by FEM. The casing structure consisted of pump body, cover, suspension, supporting feet, inlet pipe and draft tube. The inner walls of the whole flow field were used as field point for measuring main acoustic results. When mapping acoustic boundary element mesh with structure finite element mesh, the geometry interpolation method of Element Maximum Distance was adopted. Four closest nodes were interpolated from the elements whose distance was less than 10 mm. The coupling interfaces were shown in Fig. 4(c). To simulate the direct spread of noise in piping without reflection, the inlet pipe and draft tube of PAT were set to full absorption, and other surfaces were defined as total reflection, with the acoustic impedance $Z=$1.5×10⁶ kg/(m²·s), Monitoring points were set at inlet pipe and draft tube for studies of the propagation properties, at the same position of the experiment.

Fig. 4Mesh diagram for interior noise

a) Acoustic boundary element

b) Structure finite element

c) Coupled interface mesh

To make the load transfer more accurate from flow-field to acoustic field, the whole fluid domain, including volute, impeller, leakage chambers, inlet pipe and draft tube, was discretized with tetrahedral cells. By it, the fluid forces acting on all surfaces of impeller and volute were taken into account. Three sets of tetrahedral mesh were generated and chosen by a grid independence test. It was found when the total number of cells is increased up to 2600k, the obtained head of centrifugal pump in turbine mode becomes independent of mesh size. The unsteady pressure fluctuations on the walls were calculated by CFX. With multiple coordinate systems, the flow field in the impeller was calculated in a rotating coordinate system, while others were set in a steady coordinate system. The interfaces were used for data transfer among rotating and static parts. For an initial steady calculation, the frozen rotor/stator interface was used, and the transient rotor/stator interface was used for transient calculation. The inlet and outlet in turbine mode were set as static pressure, and mass flow, respectively. All surfaces were defined as no-slip walls. The roughness was set to 50 μm. The turbulence selected was k-ε model. For sufficiently distinguishing the unsteady information, the time step was set to 1.1111×10^-4 s, which means the impeller rotates about 1° in each time step [24].

3.2. Structural simulation

The modal responses of rotor and casing were analyzed by ANSYS. It was the preparation for vibration modal and radiated noise without understanding local characteristics and stress conditions. So, the modeling process only retained the structures with larger normally radiating area. The other tiny structures (i.e. bosses, transition fillets) were removed. Moreover, the holes on the structure surface, such as injection and drainage holes and cover surface, were filled. The type of 187 solid elements was used. The finite element models of rotor and casing included 338 569 elements, 69 716 nodes and 1 914 480 elements and 379 537 nodes, respectively. The impeller was made of ABS with a mass density of 1050 kg/m³, an elastic module of 1.25 GPa and Poisson ratio of 0.39. The shaft was made of steel 45 with a mass density of 7890 kg/m³, an elastic module of 209 GPa, and Poisson ratio of 0.269. Gray Cast HT200 was applied to the casing, whose density $\rho =$7200 kg/m³, elastic module $E=$148 GPa and Poisson ratio $\mu =$0.3.

Table 2 lists the comparison of free modal frequencies among calculation and experiment. And Fig. 5 gives some orders of vibration modals. Under the approximate vibration modals, the absolute value of frequency error is under 10 % and 8 %, and the average error is only 5.12 % and 4.60 %, respectively for the rotor and casing. For the rotor, the frequency at fourth modal is closest to the experiment, with an error of 1.12 %, while the fifth modal is most deviating from the experiment, with an error of 9.46 %. The first modal is characterized by swinging around $y$ axis as a whole. The outer edge of impeller deforms alternately with 90 degrees and 60 degrees, respectively for the fourth and fifth modal. For the casing, the minimum error is 1.31 % at third modal, and the largest error is 7.57 % at sixth modal. The suspension twists around $y$ axis at second modal. At third modal, the discharge flange swings on $x$-$y$ plane and the suction flange swings in an oblique 45° direction. At sixth modal, the left and right support foots swing around $y$ axis. All these indicate the modal calculated is in good agreement with that of the experiment, suggesting that the dynamic characteristics of actual structure can be perfectly reflected by the finite element model established.

In real work, the rotor system was directly connected to the dynamometer, the casing was fixed on the foundation by foundation screw, and the inlet and outlet of PAT were fixed at the corresponding pipeline. So, plane constraints were imposed at the bearing of rotor system. Six direction constraints were placed on the contact between the casing and foundation. The inlet pipe was confined up-down displacement, and the draft tube was confined the axial displacement. Table 3 lists the top seven constraint modal frequencies of rotor and casing. For the rotor system, the natural frequency under constraint is greater than APF (25Hz), avoiding the possibility of resonance. The flow-induced structure noise excited by the impeller rotating dipole source can be ignored.

Fig. 5Comparison of free vibration modal for the rotor and casing

a) Third order

b) Fourth order

c) Fifth order

d) Second order [22]

e) Third order [22]

f) Sixth order [22]

4.1. Comparison of flow-borne noise due to different dipole sources

The sound pressure spectrum curves obtained by BEM at monitoring points for design flow rate ($Q=$90 m³/h) were compared, as shown in Fig. 6. More obvious harmonic characteristic can be observed for sound pressure radiated from casing source. The impeller source shows stronger sound pressure within the frequency range of 300 Hz. While, the higher sound pressure has been obtained from impeller source during other frequencies, especially at inlet pipe.

Fig. 7 and 8 give a comparison of sound pressure distributions in interior noise due to impeller and casing dipole sources. For impeller source, the highest sound pressure inside the casing surface is 181dB at APF (25 Hz), and the sound pressure reduces gradually with the increase of frequency order. At APF, the highest sound pressure can be found on the surfaces of the cover and draft tube. While most of sound energy is concentrate on the walls of casing at BPF and its second harmonic. As for casing source, the sound pressure with highest pressure can be observed, which is 167 dB at BPF (150 Hz), and the smallest pressure has been obtained at APF. At APF, higher sound pressure is located on the surfaces of draft tube, and the smallest pressure is on the most surfaces of casing. At BPF and its second harmonic, most of sound energy is concentrate on the walls of casing and draft tube. Comparing Fig. 14 with 15, the impeller source can be considered the main source at APF. While at BPF and its harmonics, main source comes from the casing source.

Fig. 6Sound pressure spectrum curves due to dipole sources (Q= 90 m3/h)

a) Inlet pipe

b) Draft tube

Fig. 7Sound pressure in interior noise due to impeller dipole sources (Q= 90 m3/h)

a) APF

b) BPF

c) Second order BPF

Fig. 8Sound pressure in interior noise due to casing dipole sources (Q= 90 m3/h)

a) APF

b) BPF

c) Second order BPF

4.2. Comparison of flow-induced noise due to casing source

Fig. 9 shows a comparison of spectrum curves of flow-induced noise at draft tube for three typical flow rates. As it can be seen from the figure, the sound pressure of flow-borne noise due to casing source is highest at BPF, with a sound pressure level (SPL) of 156.4 dB. Several other obvious peak values occur at its harmonic frequencies. Within the range of 150 Hz, the SPLs at broadband noise show higher. From Fig. 9 and Table 3, we can see as for flow-induced structure noise, the highest SPL is 116.5 dB at second BPF, not BPF. This is mainly because the vibration response is easily induced when the frequency is close to the first order natural frequency of structure. There has been an increase in SPL above 1200 Hz. By contrast, the SPL of flow-induced structure noise under certain frequency is lower than that of flow-borne noise. The biggest decline is 55.0 dB at BPF, and the smallest decline of 0.6 dB appears at tenth BPF. It can be inferred that the flow-induced structure noise is not the main factor of interior noise in PAT. The flow-borne noise considering structure shows nearly the same trend of spectrum curve with flow-borne noise. What is different, however, is that there is a slight increase and decrease of SPL, respectively at second BPF and other discrete and broadband frequencies. The sound energy is decreased mainly due to the dissipation by casing vibration, while the sound pressure at the second BPF under resonance excitation is enhanced.

Fig. 9Sound pressure spectrum curves due tocasing source at draft tube

a) 80 m³/h

b) 90 m³/h

c) 110 m³/h

The sound pressure distribution on casing surface for flow-borne noise considering structure at BPF is shown in Fig. 10. It can be found there is a strong ability of noise radiation at the surface of tongue. Compared with the inlet pipe and tongue, the SPL at draft tube is larger. With increasing flow rate, the noise is radiated from a larger area of casing and draft tube with enhancing amplitude.

Fig. 10Sound pressure for flow-borne noise considering structure at BPF

a) 80 m³/h

b) 90 m³/h

c) 110 m³/h

4.3. Comparison of calculation and experiment

The numerical and experimental spectrum curves of different interior noises are demonstrated in Fig. 11 in terms of flow rate. The spectrum curves due to flow-borne noise considering structure generated by casing source show a similar trend with those of experiment, especially at a flow rate larger than 90 m³/h. Within the range below 450 Hz, larger differences at broadband exist, and the experimental value is higher than calculated value on the whole.

As shown in [22], at APF, the interior noise is dominated by impeller source, but with bigger difference with the experiment. The minimum error is 12.6 % at 90 m³/h and the maximum error is 15.9 % at 110 m³/h. At BPF and its harmonics, the interior noise is basically determined by casing source, with relatively smaller errors at optimal and large flow rates. At BPF and its harmonics under these flow rates, the biggest error of flow-borne noise from casing source is only 9.3 %, and the minimum error is –0.9 %. As for flow-borne noise considering structure due to casing, the maximum error is 5.9 %, the minimum error is 0.4 % and the average error is only 3.25 %. All these illustrate that the flow-borne noise considering structure due to casing source can reflect joint action of multiple sources with better accuracy. And, it is quantitatively feasible to predict interior flow-induced noise induced only by casing source through FEM/BEM.