DETECTION AND ANALYSIS OF AZIMUTHAL MODES IN A CENTRIFUGAL IMPELLER

Transcription

1 The 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, February 17-22, 28 ISROMAC DETECTION AND ANALYSIS OF AZIMUTHAL MODES IN A CENTRIFUGAL IMPELLER D. Wolfram, Th. Carolus Institute of Fluid- and Thermodynamics, University of Siegen, D-5768 Siegen, Germany, Fax: Phone: daniel.wolfram@uni-siegen.de Phone: thomas.carolus@uni-siegen.de ABSTRACT Despite of low circumferential Mach-numbers centrifugal fans may show distinctive tonal components in their sound spectra. Objective of the present investigation is the application of experimental methods which allow identifying possible flow disturbances seen by the rotating impeller as azimuthal modes rotating relative to the impeller. The forces due to the interaction of such modes with the blades may act as acoustic dipole sources. Two experimental techniques are employed: (i) According to Mongeau et al., Bent and Tetu (Pennsylvania State University, 1993) two stationary hot wire probes with a specified angular distance apart are placed either close to the intake or the discharge of the impeller. The local unsteady flow velocities from both sensors are measured synchronously. (ii) The rotor blades are instrumented with flash mounted miniature pressure sensors (microphones) distributed on the surfaces of all blades. Local unsteady pressure fluctuations from various sets of up to six pressure sensors are measured synchronously. A correlation analysis is applied to the signals allowing an identification of modes, in particular a detailed reconstruction and quantification of their circumferential order and their convection velocity. NOMENCLATURE BPF Hz Blade passing frequency b 1 m Spanwise blade length at leading edge b 2 m Spanwise blade length at trailing edge C m Blade chord length C - Coherence d 2 m Outer diameter of impeller f Hz Frequency f Int Hz Interaction frequency f Int * - Non-dimensional interaction frequency G db/hz Cross power spectral density G xx G yy db/hz Power spectral density of x db/hz Power spectral density of y m - Mode order N Int - Number of interactions per revolution n rpm Rotational speed of impeller n Mod rpm Rotational speed of mode Q m³/min Volume flow rate SRF Hz Shaft rotating frequency Sr - Strouhal-number x m/s; Pa Leading signal (velocity or pressure) y m/s; Pa Lagging signal (velocity or pressure) z - Number of impeller blades ζ deg Phase Ψ deg Angular distance of acquisition points φ r - Non-dimensional flow rate INTRODUCTION Centrifugal fans show not only broadband but also often tonal noise. In some cases the source mechanisms are not fully understood. This, however, is a prerequisite for further noise reduction measures. Numerous authors (e.g. Neise, 1975) were dealing with the well-known interaction of the blade channel flow with the volute, particularly in the tongue region. Extreme tones at blade passing frequency (BPF) may be excited. In case of radial fans without any volute type housing the identification of tonal noise mechanisms is much less straight forward. In general the circumferential Machnumber of the fans considered here is well below 1., say. The spatially non-uniform flow field built up by the flow through all the blade channels (i.e. the impeller's basic flow) rotates with the same low Mach-number and hence can not act as a significant source for tonal noise (see e.g. Roger, 2). Thus the mechanisms are of "second order": Azimuthal instabilities of the flow velocity in the impeller discharge region had been found to be a 1

2 possible source for tones at % and 7 % of BPF (Bent, 1993a). Tonal noise at BPF had been described by Staiger and Bader (22) as well as very recently by Visconti and Mazzarella (27). In general an interaction of stationary or rotating secondary flow structures with the rotating impeller blades are thought to generate the fluctuating forces on the blade surfaces and eventually to cause tonal noise. The origin of such flow structures, however, is not clear so far. Objective of this work is primarily to compile and apply experimental methods allowing the detection and, if existent, the quantification of secondary flow structures at the in- and outlet of a centrifugal fan impeller. For that the relevant secondary flow structures are considered as modes in either the stationary or rotating frame of reference. BACKGROUND The basic hypothesis in this study is that instabilities in terms of azimuthal wave patterns (modes) of flow velocity at the intake and/or the discharge of a centrifugal impeller exist. These modes - rotating or non-rotating - may interfere with the basic flow pattern which is associated with the flow through the discrete blade channels and hence with the number of impeller blades. Since the basic flow is fixed to the impeller it rotates with the same rotational speed as the impeller n. If the rotational speed of the modal wave pattern n Mod differs from n (including steady state modes in the stationary frame of reference as a special case), interactions appear, for instance when a wave peak hits a leading or trailing blade edge. This results in periodic fluctuating forces on the blades and thus acoustic dipole radiation. A possible azimuthal mode is characterized by three parameters: The rotational (convection) speed of the wave pattern n Mod, the mode order m, i.e. the number of lobes along the circumference, and subsequently the interaction frequency between mode and impeller blades f Int. Clearly, the interaction frequency corresponds to the frequency of the acoustic tone. Figure 1 shows schematically a 5 th order azimuthal mode rotating with n Mod at the discharge region of a centrifugal impeller. The simplified basic flow has a pattern of 6 th order since the impeller has six blades. It rotates with n. A similar picture could be drawn for the intake region. The technique analysing such rotating instabilities was described by Mongeau et al. (1993), Bent (1993a, 1993b) and Tetu (1993). At least two signals (x, y) from circumferential positions spaced a known angular distance Ψ apart have to be measured. In a first step of the data analysis the power spectral densities Gxx(f) and Gyy(f) as well as the cross power spectral density G(f) are estimated from the recorded time signals x(t) and y(t). The coherence function C G ( f) ( f) = G ( f) G ( f) xx yy is used to quantify the linear dependency of both signals. The coherence function varies from to 1 corresponding to no or full linear dependence. As an azimuthal mode is supposed to be a coherent structure a high value of the coherence function is a necessary condition for a rotating mode at a certain frequency. n n Mod Figure 1: A 5 th order mode interfering with 6 th order basic flow at the discharge region of a centrifugal impeller (schematically) At the frequencies corresponding to a high coherence the phase shift between both signals is calculated from the ratio of imaginary and real part of the cross power spectral density Im ζ = arctan Re 2 { G} { G} (1). (2) Because the phase is bounded at +/- degrees the actual phase shift may be larger by an integer multiple of 3 degrees. Now the mode order can be found by the ratio of the phase and the angular distance between the data acquisition points Ψ : Rotating instability Basic flow m = ζ (3) ψ The rotational speed of the mode depends on whether the probes are rotating with the impeller or non-rotating, i.e. fixed in the steady (absolute) frame of reference. For nonrotating data acquisition points the mode's rotational speed is 2

3 n Mod f Sr z = = n. (4a) m m If the data acquisition points are rotating with the impeller the rotational speed of the mode can be obtained from f Sr z nmod = n = n 1 m m. (4b) Here n Mod is assumed to be a fraction of n moving in the impeller's rotational direction. In (4a) and (4b) Sr is the Strouhal-number f f Sr = = BPF n z used as a non-dimensional frequency scaled with the blade passing frequency BPF, where z is the number of impeller blades. Based on these mode parameters the dimensionless interaction frequency can be derived from the number of independent interactions per relative revolution between the modal wave pattern and the impeller N Int (m,z) multiplied by their relative rotational speed f Int (, ) ( ) (5) f NInt m z n Int nmod * = =. (6) BPF BPF As the Strouhal-number he dimensionless interaction frequency is scaled with BPF. Since simultaneous modeblade-interactions are supposed to affect only the level but not the frequency they are considered as one. Thus only in case of asynchronous interactions is N Int = m z. EXPERIMENTAL FACILITY The investigated centrifugal impeller consists of 6 backward swept blades with two-dimensional curvature. Characteristic geometric dimensions are the outer diameter d 2 =.355 m, the spanwise length of the trailing edge b 2 =.11 m, of the leading edge b 1 =.116 m and the blade chord length C =.15 m. The ratio of inner and outer diameter is ν = 8. The point of best total to static efficiency (design point) corresponding to the nondimensional flow rate (note the special definition for centrifugal turbomachines) Q ϕr =.15, (7) 2 2 π d b n 2 2 where Q is the volume flow rate. The impeller is operated without any casing. Experimental facility for hot wire measurements Two slightly different facilities are necessary for the flow velocity measurements at the intake and the discharge, Figure 1 and 2. The impeller is taking in air from a large plenum via an inlet nozzle. The total to static pressure rise is the pressure difference between plenum and atmosphere. The flow rate is measured at the plenum s inlet. The fan operating point is the design point and 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 a constant speed n = 15 rpm. The two stationary 1-D hot wire probes are placed with an angular spacing Ψ = 45 deg apart at both, the intake and the discharge. The hot wires are mounted 5 mm in front the leading and 5 mm after the trailing edge, respectively. The wires are aligned with the blade edges. At the impeller discharge the probes are mounted on a stationary circular arc, Figure 2. By means of a threaded spindle the arc and therewith both sensors can be traversed in axial direction between hub and shroud. Two single sensor cylindrical hot wire probes are used (TSI model 121-T1.5 with support model 1155). To keep the flow disturbances possibly caused by probes and probe supports in the inlet region as low as possible the hot wire probes for the intake measurements are mounted on a stationary vee-support, which is inserted from the hub into the impeller via a hollow shaft, Figure 3. The probes are traversed in axial direction between hub and shroud by means of another spindle. Single sensor miniature wire probes with offset prongs and the sensor perpendicular to probe axis have been used (Dantec Dynamics model 55P15). The hollow shaft design requires a belt transmission to drive the fan via the electric AC motor. The sampling frequency is 2 khz. The hot wire probes are calibrated up to flow velocities of 4 m/s in a low turbulence calibration wind tunnel. Data acquisition is carried out with the Streamline system by Dantec Dynamics. Levels of velocity fluctuations (in db) are defined with reference to 1m/s. Experimental facility for blade pressure fluctuation measurements The facility used differs very much from the previous ones, Figure 4a. The impeller takes air via an inlet nozzle from a large plenum which is - for future acoustic measurements - an anechoic room. It exhausts into a large box with acoustically damped walls. A duct with anechoic termination is attached to this box. Again, the impeller is running at n = 15 rpm and operating at its design point controlled by a throttle downstream of the anechoic termination. The flow rate is measured by a hot film probe in the duct. Each impeller blade has been instrumented with seven flash mounted miniature microphones (Knowles Acoustics, type FG-3329-P7) to measure the 3

4 (a) AC drive (a) Throttle Anechoic termination eller Nozzle Plenum Hot wire probes ψ Inflow Circular arc and spindle Flow Duct Hot wire probe Anechoic room Slip ring transducer Box eller Figure 2: Experimental facility for velocity measurements at discharge: top view (a) and axial sectional drawing (a) Belt transmission eller Nozzle Plenum AC drive Support with hot wire probes Inflow Spindle Figure 3: Experimental facility for velocity measurements at intake: meridional (a) and axial sectional drawing ψ Hollow shaft 5 % b 1 5 % b 1 95 % b 1 Inflow Hub Shroud Microphones 5 % b 2 5 % b 2 95 % b 2 3 % C 5 % C 97 % C Figure 4: a) Experimental facility for blade pressure fluctuation measurements; b) Pressure side of impeller blade, instrumented with miniature microphones pressure fluctuations on the blade s pressure side, Figure 4b. Levels of surface pressure fluctuations (in db) are defined with reference to Pa.The angular distance between corresponding microphones Ψ equals exactly the blade spacing, i.e. deg. Signals from up to six microphones can be captured simultaneously. The sampling frequency is 25.6 khz. Each microphone is calibrated in situ. The signals are transferred to the stationary data acquisition system via a slip ring transducer (Schleifring with special low noise slip rings). 4

5 Sources of possible experimental errors are (i) the noise from the slip ring transducer, (ii) the electric contamination due to the AC net and (iii) the acceleration of the microphones due to the rotation of the impeller. These possible error sources had been checked in great detail and were found to be not existent or negligible. RESULTS Figures 5 and 6 show coherence and phase data from intake and discharge of both the flow velocity and the pressure. The pressure signals are taken from two adjacent blades at 3 % and 97 % of chord length C at midspan (5 % b 1, b 2 ). The hot wire probes were also placed at midspan. Since the focus within this investigation is mainly on low frequency tonal noise only Strouhal-numbers up to Sr 1 are of interest. Within the data processing the leading signal is called x, whereas y is the lagging signal. Obviously both the fluctuating flow velocity and blade pressure at the intake and discharge show a medium to high spatial coherence at distinguished frequencies. In general the coherence of the pressure fluctuations is higher than the coherence of flow velocity but the peaks are more broadband. Nevertheless, all distinguishable peaks are now considered to indicate possible modes. High coherence can be detected at integer multiples of Sr = 1/6 (=.17), i.e. at shaft rotating frequency SRF = BPF/z = 25 Hz. In the pressure analysis at intake and discharge these peaks emerge quite consistently at all integer multiples of SRF. By contrast, in the velocity analysis these peaks appear only at some integer multiples of SRF (Sr = 1/6, 2/6, 4/6, 5/6, 1 at intake and Sr = 2/6, 3/6, 4/6, 5/6, 1 at discharge). The corresponding phase plots derived from the blade pressure fluctuations look different from those based on (a) C ζ [deg] C ζ [deg] /6 2/6 3/6 4/6 5/6 1 1/6 2/6 3/6 4/6 5/6 1 (.17) (.33) Sr (7) (3) (.17) (.33) Sr (7) (3) Figure 5: Coherence and phase data of flow velocity at intake (a) and discharge (a) C ζ [deg] C ζ [deg] Figure 6: Coherence and phase data of blade pressure fluctuations at intake (a) and discharge 5

6 the flow velocity: The phase shift between the pressure signals show more or less clearly a constant slope for each interval from + to - deg. This implies a linear relation between phase and Strouhal-number and hence a constant ratio. Eq. (4b) for rotating sensors can be written as ζ n z ψ = = const, (8) Sr n n Mod where the phase and the angular sensor distance are substituted for the mode order according to eq. (3). Since the impeller s rotational speed, the angular sensor distance and the number of impeller blades are fixed the convection speed of flow structures has to remain constant in the range of linearity. Thus the flow may be shaped by a multitude of discrete structures of different frequencies rotating relative to the impeller with the same velocity. Within this broad-banded arrangement only those structures at frequencies coinciding with a high coherence seem to develop stable while the others arise and decay consistently. The phase shift between the velocity signals seems more diffuse without obvious structures. The results of the analysis following eqs. (3), (4) and (6) are compiled in Tables 1 and 2. The measuring method (stationary or rotating sensors) as well as the angular sensor spacing (45 and deg, respectively) had been taken into account. Referring to the ambivalence of the phase information only the lowest positive value of possible phase shifts is analysed. The mode order is always assumed to be integer. In the investigated frequency range approximately 1 Strouhal-numbers are identified to have distinctive peaks in the coherence function. The analysis yields mode orders between 1 and 9, i.e. coherent structures with up to 9 sinusoidal lobes along the circumference of the impeller intake or discharge. The derived rotational speed of the modes depends on the measurement method. From the velocity data - among others - modes are obtained which rotate exactly with the impeller rotational speed of 15 rpm - mostly at integer multiples of SRF. Thus, the corresponding coherent structures are fixed to the impeller without any relative rotation. They reflect the 6th order basic flow pattern rotating with the impeller as seen by the stationary hot wire probes. Moreover, modes are detected with rotational speeds varying from 135 to 147 rpm. By contrast, the analysis of the pressure data yields highly coherent structures which do not rotate at all: At integer multiples of SRF the rotational mode speed is zero. The flow structures are stationary in the absolute frame of reference. Furthermore, mode structures are detected which rotate quite slowly with 24 to 258 rpm. Table 1: Possible mode from flow velocity Sr C ζ [deg] m n Mod [rpm] f Int * Table 2: Possible mode from blade pressure fluctuations Sr C ζ [deg] m n Mod [rpm] f Int * intake intake discharge discharge

7 Possible dimensionless interaction frequencies based on velocity and pressure data analysis are shown in Figure 7 (compiled from Tables 1 and 2). The height of the lines indicates how often the analysis of the measured data yields an interaction event at the particular frequency. Interaction frequencies f Int * range from nearly zero up to 5, i.e. coherent structures detected in a frequency range up to Sr = 1 are able to cause interaction frequencies and thus tonal noise up to Sr = 5. The largest number of interactions is found to occur at f Int * = 1, corresponding to BPF. One has to keep in mind, however, that this result stems from the blade surface pressure data only. SUMMARY AND CONCLUSIONS Objective of this work was primarily to compile and apply experimental methods allowing the detection and quantification of secondary flow structures, so-called modes, at the in- and outlet of a centrifugal fan impeller. Time-synchronous measurement at two spatially separated stations either of the unsteady flow velocity or the blade pressure had been proven successful. A correlation analysis of the data leads to the conclusion that coherent structures exist at the intake as well as the discharge of the investigated impeller. They can be described in terms of several sinusoidal modes. number of occurrences pressure analysis velocity analysis f Int * Figure 7: Interaction frequencies due to mode-bladeinteraction and their number of occurrences in the evaluated data The correlation analysis of the flow velocity data from the stationary frame of reference allowed detecting coherent structures which rotate almost nearly or even exactly with the impeller rotational speed. Hence they do not interact with the impeller blades and can not act as a tonal noise source. By contrast, the evaluation of the surface pressure data from the rotating frame of reference unveiled the existence of structures which rotate quite slowly or are even stationary in the absolute frame of reference. They interact with the blade, and yield an interaction frequency predominantly at BPF. They are most probably the reason for tonal noise radiated by the centrifugal rotor even without volute. One has to keep in mind that the correlation technique shown here does not give any information about the amplitudes of the modal disturbances. It is possible that the amplitudes of the rotating and stationary modes are very different - an estimate will be carried out in the future. Eventually simultaneous noise measurements have to show which modes and interaction events are responsible for the acoustic signature of the fan rotor. ACKNOWLEDGEMENTS 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 (Bent, 1993a) Bent, P. H. - Experiments on the Aerodynamic Generation of Noise in Centrifugal Turbomachinery. Ph.D. Thesis. The Pennsylvania State University, 1993 (Bent, 1993b) Bent, P. H.; McLaughlin, D. K.; Thompson, D. E. - Identification of Non-Tonal Noise Sources in Centrifugal Turbomachinery. ASME Symposium on Flow Noise Modeling, Measurement and Control. New Orleans, 1993 (Mongeau, 1993) Mongeau, L.; Thompson, D. E.; McLaughlin, D. K. - Sound Generation by Rotating Stall in Centrifugal Turbomachines. Journal of Sound and Vibration 163(1), p. 1-3, 1993 (Neise, 1975) Neise, W. - Application of Similarity Laws to the Blade Passage Sound of Centrifugal Fans. Journal of Sound and Vibration 43(1), p , 1975 (Roger, 2) Roger, M. - Noise in Turbomachines. Lecture Series 2-2, von Karman Institute for Fluid Dynamics, Belgium, 2 (Staiger and Bader, 22) Staiger, M.; Bader, A. Neue Schaufelgeometrie für flüsternde Ventilatoren, KI Luftund Kältetechnik 22 (7), p , 22 (Tetu, 1993) Tetu L. G. - Experiments on the Aeroacoustics of Centrifugal Turbomachinery. Master Thesis. The Pennsylvania State University, 1993 (Visconti and Mazzarella, 27) Visconti, F. M.; Mazzarella, L. - Computational aeroacoustic simulation of a plug-fan prototype: capabilities, limits and perspectives of U-RANS approach. International Symposium Fan Noise, Lyon, 27 7