DETECTION AND ANALYSIS OF AZIMUTHAL ROTATING MODES IN A CENTRIFUGAL IMPELLER SUMMARY INTRODUCTION BACKGROUND

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1 DETECTION AND ANALYSIS OF AZIMUTHAL ROTATING MODES IN A CENTRIFUGAL IMPELLER Daniel WOLFRAM, Thomas CAROLUS University of Siegen, Institute of Fluid- and Thermodynamics, D Siegen, GERMANY SUMMARY Despite of low circumferential Mach numbers centrifugal fans may show distinctive tonal components in their sound spectra. Objective of the described experimental investigation is to identify possible azimuthal disturbances (modes), which rotate with a different circumferential velocity as compared to the impeller. The forces due to the interaction of such modes with the blades may act as acoustic dipole sources. Based on a technique published by Mongeau et al., Bent and Tetu (Pennsylvania State University, 1993) two stationary hot wire probes with a specified angular distance apart are applied at both, the inlet and the discharge of the impeller. The local unsteady flow velocities are measured synchronously. A correlation analysis of the signals from each pair of hot wires allows the identification of modes due to the unsteady flow field, in particular the determination of their order and convection velocity. INTRODUCTION The continued efforts by fan manufactures into low noise fans are indicative of the need to reduce even second order aeroacoustic mechanisms. Centrifugal fans sometimes show not only tones due to the well-known blade-casing tongue-interaction at blade passing frequency (BPF), but also at shaft rotating frequency (SRF), between 60 % and 70 % of BPF and at much higher frequencies. In many cases the underlying mechanisms are not fully understood. This, however, is a prerequisite for further noise reduction measures. Azimuthal flow disturbances in the impeller's in- or outlet region may be a reason for tonal noise. When they interact with the fan blades they may set up periodic fluctuating forces on the blade surfaces, which act as acoustic dipole sources. Objective of this study is to investigate whether such modes exist and to measure their parameters in order to determine possible interaction frequencies. BACKGROUND The basic hypothesis in this work is that rotating instabilities in terms of azimuthal wave patterns (modes) of flow velocity are existing at the intake and/or discharge of centrifugal fans. These modes may then interfere with the basic flow pattern which is associated with the flow through the Fan Noise 2007 Lyon (France) September 2007

2 Fan Noise impeller with its discrete blade channels. The basic flow is always fixed to the rotating impeller. Since the rotational speed of the impeller n Imp and the circumferential velocity of the wave pattern - referred to as rotational speed n Mod below - generally differ from each other, interactions appear each time a wave peak meets a leading or trailing blade edge. This may yield periodic fluctuating forces on the blade surfaces acting as acoustic dipole sources. It is important to keep in mind that at low circumferential Mach numbers the basic flow itself is not responsible for tonal noise generation (Roger, [1]). Three parameters of possible modes are of interest: the wave order m, i.e. the number of peaks along the circumference, the rotational (convection) speed of the wave pattern n Mod and the interaction frequency f Int as a result of both. Eventually the interaction frequency could comply with the acoustic frequency of tonal components. The technique employed here to measure and analyse such rotating instabilities was described by Mongeau et al. [2], Bent [3, 4] and Tetu [5]. We briefly illustrate important ideas employing a thought experiment. Figure 1 (left) shows a 5 th order azimuthal mode rotating with n Mod at the discharge region of a centrifugal impeller. The simplified basic flow at the impeller discharge has a pattern of 6 th order, since the impeller has z = 6 blades; it rotates with n Imp. Rotating instability Basic flow Superposition y ψ x n Imp n Mod Figure 1: Mode interaction at the discharge of a centrifugal impeller (schematically); left: basic flow and azimuthal mode; right: superposition and data acquisition points x and y (random noise added) The rotational speeds are chosen as n Imp = 1500 rpm and n Mod = 1000 rpm. Figure 1 (right) shows a snapshot of the pattern upon superposition. (A slight random noise is added to make it looking more realistic.) The depicted superposed velocity pattern varies at each time instance because of the nonequal rotational speed of mode and basic flow. Now, the time signals of the flow velocity c are acquired synchronously by two probes at the data acquisition points x and y, being a known angular distance ψ apart (here chosen as 45 degrees). The two time signals show a phase shift due to the probes separation angle and the rotation of the pattern. A portion of both signals is shown in Figure 2. A time period of 40 ms is equal to 1 revolution of the impeller at 1500 rpm.

3 Fan Noise x y c [m/s] t [ms] Figure 2: Signals at x and y in the time domain A first step of the data analysis is the transformation of both velocity signals from the time into the frequency domain. Figure 3 exemplarily shows the power spectral density G xx (f) from x(t) vs. the Strouhal number f f Sr = = BPF n z. (1) Both, G xx (f) and the almost identical spectrum G yy (f) from y(t), show sharp peaks at integer Strouhal numbers corresponding to BPF and its integer multiples, which are expected due to the 6 channel basic flow pattern rotating with n Imp. These peaks are not analysed in detail here. In addition distinctive peaks appear at Sr = (83.25 Hz). To allow inferences of flow disturbances moving relative to the impeller peaks have to appear in both spectra at the same frequency non-equal to SRF as a necessary constraint. The coherence function C xy Imp Gxy ( f) ( f) = G ( f) G ( f) xx is used to quantify the linear dependence of both signals x and y, Figure 4 (G xy (f) is the cross power spectral density). Coherence varies from 0 to 1 corresponding to no or complete linear dependence. High coherence is the main indicator of the existence of rotating modes. E.g., at Sr = the coherence C xy = 1 thus we encounter at this Strouhal number (or frequency) a rotating mode. yy 2 (2) G xx [db/hz] (c ref = 1 m/s) Sr [-] Figure 3: Test signal G xx in the frequency domain

4 Fan Noise C xy [-] Sr [-] Figure 4: Coherence between signals x and y In a second step based on coherence criterion phase data are used to analyse the phase shift between both signals at similar frequency and Strouhal number, respectively, Figure 5: ζ xy Im = arctan Re { Gxy} { Gxy} (3) ζ xy [deg] Sr [-] Figure 5: Phase between test signals x and y: overview (left); detail (right) Phase data are obtained from the ratio of imaginary and real part of cross power spectral density of both input signals. In this example ζ xy is found as -135 degrees for Sr = Because the phase boundaries are +/-180 degrees the real phase shift may be larger by an integer multiple of 360 degrees as compared to the calculated one. For each phase angle both, the mode order ζ m = (4) ψ and the rotational speed Sr z nmod = n Imp (5) m can now be calculated. In (4) ψ is the angle between both probes. Possible combinations of phase angle, order and rotational speed for the mode detected at Sr = are given in Table 1. Among others a mode of order 5 rotating at 16.6 rps (1000 rpm) with signal phase shift of 225 degrees is

5 Fan Noise detected - exactly as set before (Figure 1). Upon detecting the mode parameters the final step is to determine the frequency of interactions between the detected mode and the blades f Int. It is derived from the number of independent interactions per relative rotation of mode and impeller N Int (m,z) multiplied with the magnitude of difference between their rotational speeds, normalized with BPF according to the Strouhal number: f Int fint * = = BPF N ( m, z) n n Int Imp Mod BPF (6) Since simultaneous mode/blade interactions may only affect the level but not the stimulated frequency they are considered as one. In this example N Int (m,z) = m z = 30. Possible stimulated frequencies are shown in Table 1. The 5 th order mode rotating with n Mod = 1000 rpm (0.66 n Imp ) leads to an interaction frequency of f Int = 250 Hz or f Int * = It is worth to point out that the interaction frequency is totally different from the signature of this mode in the velocity spectra (83.25 Hz or Sr = 0.555, Figure 3). Table 1: Results of test signal analysis and possible mode parameters Sr [-] C xy [-] ζ xy [deg] m [-] n Mod [s -1 ] f Int * [-] Unfortunately in any case the method described yields additional interaction frequencies even if there is no interaction. However, it easily can be shown that in case of a 6-bladed impeller with its corresponding 60 degrees blade spacing and the probes located 45 degrees apart the artificial interaction frequency is always f Int * = 4 - independent of other parameters. Two aspects of this analysis are worth to be pointed out. (i) Although a large value of the coherence of both measured signals is the basic criterion to decide on the existence of a mode, there is no welldefined limit separating coherent from incoherent signals. The sensitivity of the chosen coherence value on the mode detection will be addressed later. (ii) According to Table 1 the determination of the mode's parameters based on phase information is ambivalent: Although the test signal comprises one rotating structure only, the analysis yields several possible combinations of mode order and rotational speed. To reduce the ambivalence it would be expedient to acquire velocity data synchronously with even more than two probes. Here we consider an additional 3 rd probe at a point z, Figure 6. The acquisition point z is located at an angular distance ψ yz apart from y (here chosen as 30 degrees) and thus ψ xy + ψ yz apart from x. This enhancement permits the evaluation of eqs. (1) to (6) not only for the signal pair x/y but for y/z and x/z as well. If all three evaluations yield the same mode, its physical existence is more certain than before.

6 Fan Noise z ψ yz y ψ xy x Figure 6: Data acquisition points x, y and z at the discharge of a centrifugal impeller The results of such a 3 point-data analysis of the test signal discussed above are shown in Table 2. All parameters and conditions stay unchanged. Although each analysis of every signal pair suggests several modes, only order m = 5 linked with the rotational speed n Mod = 16.6 rps = 1000 rpm is detected consistently (grey rows in Table 2) and thus identified as an existing mode. Table 2: Results of 3 point-data analysis and possible mode parameters Sr [-] C [-] ζ [deg] m [-] n Mod [s -1 ] f Int * [-] signal pair x/y (ψ xy = 45 degrees) signal pair y/z (ψ yz = 30 degrees) signal pair y/z (ψ yx + ψ yz = 75 degrees)

7 Fan Noise TESTED IMPELLER AND EXPERIMENTAL FACILITY The centrifugal impeller investigated consists of 6 backswept blades with two-dimensional curvature. Characteristic geometric dimensions are the outer diameter d 2 = 355 mm and the outlet width b 2 = mm. The point of best total to static efficiency (design point) corresponds to the non-dimensional flow rate φ r = Q/(π d 2 ² b 2 n Imp ) = 0.15, with the volumetric flow rate Q. The impeller exhausts directly into the free atmosphere without any casing. Via an inlet nozzle the impeller is sucking air from a large plenum. The total to static pressure rise is the pressure differential between plenum and atmosphere. The flow rate is measured at the plenum s inlet. Operating points are set by a throttle. Losses due to friction within the system are compensated with an auxiliary fan. The impeller is driven by an AC motor with frequency converter ensuring constant speed. Two stationary 1-D hot wire probes with a specified angular distance apart are employed at both, the inlet and the discharge. Data acquisition is carried out with the Streamline system by Dantec Dynamics. The sampling frequency is 20 khz. The hot wire probes are calibrated up to flow velocities of 40 m/s in a low turbulence stream of a calibration wind tunnel. The orientation of the wire in the probe is along the leading or trailing edge, respectively. Two different supports are necessary for measurements at the inlet and the discharge to traverse the sensors. At the impeller discharge the probes are mounted ψ = 45 degrees apart on a circular arc, Figure 7 (top). By means of a threaded spindle the arc and therewith both sensors can be traversed axially between hub and shroud. The radial distance between the hot wire sensors and the passing blade trailing edges are r = 4 mm. Two single sensor cylindrical hot wire probes are used (TSI model 1210-T1.5 with support model 1155). Hot wire measurements in the intake region are much more demanding. Probes and probe supports in the suction may cause upstream perturbations, which cause a flow disturbance not existent in the impeller without instrumentation. Therefore the hot wire probes are inserted from the hub into the impeller via a hollow shaft, Figure 7 (bottom). The probes are mounted on a stationary vee-support with ψ = 45 degrees spacing, as in case of the discharge assembly. The distance between leading edges and sensors is r = 4 mm. The probes are traversed in axial direction between hub and shroud. Single sensor miniature wire probes with offset prongs and the sensor perpendicular to probe axis are used (Dantec Dynamics model 55P15). Due to the probes with its electric cables in the hollow shaft a belt transmission is used to drive the fan via the electric AC motor.

8 Fan Noise Impeller Hot wire probes ψ r Flow AC drive Circular arc and spindle Plenum Nozzle Impeller Belt transmission Flow AC drive ψ Spindle r Support with hot wire probes Figure 7: Experimental Facility (schematically): Measurements at outlet - top view and axial sectional drawing (top); measurements at inlet - meridian and axial sectional drawings (bottom) RESULTS The impeller was working at its design point with 1500 rpm. The probes are placed in a plane close to the shroud at the inlet and discharge. Analysis based on the 2 point-data acquisition is done according to eq. (1) to (6). Figure 8 compares the results, i.e. the possible interaction frequencies f Int *, for inlet and discharge. The critical coherence level, which decides whether the measured signals are coherent or incoherent, is varied from 0.1 to 0.5.

9 Fan Noise In any case the data analysis confirms the existence of rotating modes both at inlet and discharge. The results at the intake and discharge are similar. Different from the thought model with a single frequency mode the measurements yield more possible interaction frequencies. This leads to the conclusion that the real disturbance consists of more than one sinusoidal mode. Each analysis also shows the expected artificial interaction frequency mentioned above at f Int * = 4. An increased coherence value C xy,crit results in a decreased number of possibly detected modes. In case of a low limit C xy,crit = 0.1 modes are detected, which cause interactions in almost the entire range of frequencies investigated up to Sr = 5. If C xy,crit set to 0.3, the number of modes is significantly reduced, now mainly corresponding to integer Strouhal-numbers Sr = 1, 3 and 5, i.e. at BPF and some integer multiples of BPF. Nearly the same patterns can be observed at intake and discharge. Increasing the coherence to C xy,crit = 0.5 only the modes at Sr = 4 and 5 remain in the graph, where the mode at Sr = 4 is believed to be an artifact, see the discussion above. inlet discharge Cxy,crit = 0.5 Cxy,crit = 0.3 Cxy,crit = f Int * [-] f Int * [-] Figure 8: Experimental results during variation of coherence criterion: Possible stimulated frequencies due to mode/ blade interaction at the in- and outlet at design point at n Imp = 1500 rpm

10 Fan Noise SUMMARY AND CONCLUSIONS Objective of this investigation was to analyse, whether azimuthal rotating disturbances in terms of wave patterns, so-called modes, exist at the inlet and/or discharge region of a centrifugal impeller. If so their parameters had to be determined in order to find possible frequencies of interaction between mode and blades. Synchronous velocity measurements with two stationary hot wires and an appropriate correlation analysis revealed that rotating modes do exist at both the inlet as well as the discharge of a test impeller. In general there is more than one sinusoidal mode found to interfere at the same time with the impeller-fixed basic flow. Possible mode orders, rotational speeds and hence interaction frequencies had been obtained. The influence of the set coherence value on the modes detected had been pointed out. In a next step acoustic spectra will be measured and correlated with the than 3 point modal analysis. If the interaction frequencies correspond to tonal components in the sound spectrum, the rotating disturbances can most likely be confirmed as an essential part of the tone generating mechanism. Of further interest is how the modes are distributed in the inlet and discharge region and how they depend on the operating point, i.e. on the mean flow field. This eventually could lead to the detection of the flow mechanics behind the disturbances. ACKNOWLEDGEMENT This investigation was funded by the German Federal Ministry of Economics and Technology (BMWi) via the consortium for industrial research "Otto von Guericke" (AiF) under grant 14611N/1 within a research project of the German research association for ventilation and drying technology (FLT). The authors would like to thank for this support. REFERENCES [1] M. Roger - Noise in Turbomachines. Lecture Series , von Karman Institute for Fluid Dynamics, Belgium, 2000 [2] L. Mongeau, D. E. Thompson, D. K. McLaughlin - Sound Generation by Rotating Stall in Centrifugal Turbomachines. Journal of Sound and Vibration 163(1), p. 1-30, 1993 [3] P. H. Bent - Experiments on the Aerodynamic Generation of Noise in Centrifugal Turbomachinery. Ph.D. Thesis. The Pennsylvania State University, 1993 [4] P. H. Bent, D. K. McLaughlin, D. E. Thompson - Identification of Non-Tonal Noise Sources in Centrifugal Turbomachinery. ASME Symposium on Flow Noise Modeling, Measurement and Control. New Orleans, 1993 [5] L. G. Tetu - Experiments on the Aeroacoustics of Centrifugal Turbomachinery. Master Thesis. The Pennsylvania State University, 1993