Effects of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interaction Broadband Noise

Transcription

1 Effets of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interation Broadband Noise Hongbin Ju* GE Global Researh Center, One Researh Cirle, Niskayuna, NY. 09 A method is developed for prediting broadband noise due to the fan-wake interating with the downstream swept outlet-guide-vanes in turbofan jet engines. It is validated against the NASA Soure Diagnosti Test data. Sweep effets on the soure, on the response and on the unsteady lift oupling with the dut modes are disussed. The mehanisms of broadband noise redution due to vane sweep are studied, and a simple model to aount for sweep effets is proposed aordingly. Keywords: Turbofan engine noise, Fan broadband noise, Aeroaoustis. I. Introdution The interation of fan wakes with downstream Outlet-Guide-Vanes (OGV) is the major soure of tones and broadband noise (BBN) in high bypass-ratio turbofan engines. Veloity defiit in fan wakes is the soure of tone noise. Turbulene in the wakes is the soure of broadband noise. One tehnique to redue tone noise is to sweep the OGV leading edges in the flow diretion as shown in Fig.. The mehanisms of tone noise redution in a subsoni flow were examined by Glegg [. The dominant effet is the phase variation of the gust introdued by the sweep. Usually the spanwise wavenumber k of the veloity defiit in a fan wake is small. When the fan wake hits the swept OGV, k inreases and the effetive frequeny redues, resulting effiient soure anellation and attenuation of aousti waves. Seondary effets inlude the redued effetive inflow veloity, the introdution of the spanwise mean flow, and the redued inter-blade phase angle (IBPA). Effets of the blade sweep on supersoni propeller noise were disussed by Parry [. Tone noise redution due to vane sweep was verified numerially in [ and experimentally in the NASA Soure Diagnosti Test (SDT) [4. BBN benefit is also shown in the SDT data. However, sweep effets on BBN have not been studied as thoroughly as for tone noise. The mehanisms for BBN noise redution are expeted to be different from for tones sine vortiity waves in a turbulent flow have no dominant diretions. k no longer monotonially inreases with the sweep angle. The objetives of this paper are to develop a redued order model for prediting BBN from fan-wake / swept OGV interation, examine the sweep effets and mehanisms of noise redution, and propose a model to aount for these effets. The redued order model is useful for preliminary designs. It is based on the semi-analytial method for oblique gust/asade interation in [5, and the broadband model for radial OGV in [6. The NASA SDT data reported in [4 for low noise OGV is used to validate the method. Figure. Radial and swept OGVs. * Aerodynamis and Aoustis Laboratory, juh@ge.om, AIAA Senior Member

2 II. Broadband Model for Swept OGV in Annular Dut The derivations of the sweep geometry and the sound power spetrum density (PSD) will be given in a separate paper. The ensemble average of PSD from ut-on modes in the annular dut is: Wˆ ˆ. () m n m and n are the spinning and radial mode numbers respetively. The sound power for mode (m,n) is Ro ˆ Bk d ( M d ) u0 ( r) 0 ( r) * Real ( ) ˆ W (,, 4 ( ) E r os h K K m k a k M S d d d d R i j ( K, K m S r i r j, k os ) L L E W ( r r) e L max( L, R ), L min( L, R ) K m BS os r o r R, i o i[ ( rr) R : inner/outer dut radius, ( r) ik ( l l' ) / os e r r s drdk, L r : spanwise turbulene length sale, m K tan, B: vane ount, S : pith, : stagger angle, m E ( r) ( nx n ) m ( r) i' m ( r) nr, m( r) : eigenfuntion, r Cr ix f ( os msin / rk sin s ), k, k r) e R( ( x f, r), k, k, k r) h ˆ ( k R ( x, r), k, k, k ) is alulated using the -D equivalene method in [5. ( f r 0 dx f r) dr, (). () III. NASA Soure Diagnosti Test (SDT) Data Analysis The detail of the NASA SDT ampaign is reported in [4. Two rotors (R4 and M4) and three OGVs were tested. The baseline OGV has 54 radial vanes. The low vane ount (LVC) OGV is also radial but with only 6 vanes. The solidity is kept onstant, or the hord length is inreased, to maintain the aero performane when reduing the vane ount. Sweep is added to the LVC OGV to form the rd OGV in the test. Its leading edges are swept by 0 in the downstream flow diretion, intended to redue interation tones. It is alled the low noise (LN) OGV. The aero performane of the LN OGV is lower than the other two OGVs due to higher loading and veloity. The differenes of the aero performane are small among the three OGVs near the peak effiieny. They beome larger when the operation onditions are away from the peak effiieny. The proess to extrat interation BBN from the stage (rotor+stator) total noise and the fan self-noise was desribed in [6. It turns out that the only data valid for the sweep study is at the approah ondition. Fan self-noise is higher than the stage total noise in other operation onditions. The data for R4 rotor, the LVC OGV, and the LN OGV at the approah ondition will be used in our analysis. (a)without frequeny saling (b)with frequeny saling Figure. PSD of exhaust fan-ogv interation broadband noise. NASA SDT data at approah. Blak line: LVC radial OGV, red line: LN swept OGV. Figure (a) depits the PSD in the exhaust dut of the LN OGV ompared with that of the LVC OGV. It is louder at low frequeny and quieter at high frequeny. The overall power level (OAPWL) is db for the radial OGV, and db for the swept OGV. db noise redution is ahieved with the sweep. Examining the spetra in

3 Fig.(a), one may find that their shapes are similar with just a shift in the log sale plot. In the linear sale, the spetrum W ˆ '( f ') for the swept OGV an be obtained by saling the frequeny in the spetrum Wˆ ( f ) for the radial OGV: ˆ 0.09 W'( f ') W( f ), f ' 0 f 0. 8 f With this frequeny saling, the two spetra ollapse in Fig. (b).. (4) IV. Validation The proposed predition method Eq.() is validated against the SDT data. Figure (a) shows the predited PSD at the approah ondition. The noise benefit at high frequeny is about.db, ompared with db in the data, Fig. (a). The predited OAPWL redution with sweep is.db, ompared with db in the data. Similar trend is found in terms of the spetral shapes in the log sale plot: the spetrum for the swept OGV an be obtained by shifting the spetrum for the regular OGV to lower frequenies. With the same frequeny saling as in Eq.(4), the two predited spetra in Fig. (b) also ollapse. (a)without frequeny saling (b)with frequeny saling Figure. Predited PSD of exhaust fan-ogv interation broadband noise. SDT approah ondition. Blak line: LVC radial OGV, red line: LN swept OGV. V. Effets of Vane Sweep There are four major hanges due to the vane sweep. The first is about the geometry. The normal hord C is redued sine the hord C r at onstant radius is maintained for aero performane. The pith S and the stagger of the unwrapped linear asade are different from the radial vane asade. Seondly, the mean/turbulent flow is hanged. Mah number inreases near the tip due to the modifiation of the flow-path for loss ontrol. The normal veloity to the asade is smaller. TKE deays and the turbulene length sale inreases as the flowpath to the swept OGV is longer. Thirdly, the swept OGV responds to the gusts differently. Although the redued frequeny is unhanged, the spanwise mean flow is introdued and the phase gradient of the gust varies with sweep. The last hange is on the propagation. Dut modes are onsidered unhanged, but their oupling with the unsteady lift is different. These hanges are highlighted in Fig. 4 for the PSD formula Eqs.() and (). We will disuss eah of them individually. The approah of the study is to replae the parameters in eah term by their ounterparts in the radial OGV onfiguration and examine the differene of PSD. This approah is valid only when the interations between different effets are small. Figure 4. Terms/parameters affeted by sweep are highlighted in the PSD formula Eqs.() and ().

4 To separate the effet of the mean/turbulene flow from the others, the same mean flow and turbulene statistis (TKE & length sale) are applied for both the radial and the swept OGVs. The PSD at the approah ondition is shown in Fig. 5, ompared with Fig. (a). Figure 5. PSD preditions of exhaust broadband noise at the SDT approah ondition. The same mean flow & turbulene statistis are applied for the radial OGV (blak line) and the swept OGV (red line). A. Effets on Soure (Vortiity Waves) and Propagation (Dut Modes Coupling) The pith and the stagger angle are hanged after sweep. However, sine S os S os, the sweep has no effet on terms (-) and (-) in Fig. 4. Term () in Fig. 4 represents the spanwise phase variation as shown in Fig. 6(a). With sweep, the span is longer, giving more soure anellation and noise benefit at high frequeny. With s 0 in term () replaed by s 0, the PSD in Fig. 6(b) hanges from the blue line to the red line, indiating extra 0.67dB noise benefit due to the longer span. Assuming the noise redution due to the soure anellation is proportional to the span, the extra benefit from the swept OGV is 0log(os s ), in db. (5) It is -0.6dB for 0 0 sweep, whih is onsistent with 0.67dB in the predition shown in Fig. 6(b). To further test the linearity of noise redution (db) with the span, we replae the whole term () in Fig. 4 by, i.e., totally omitting the phase variation and the soure anellation in the whole span of the swept OGV. The result in Fig. 6(b) shows signifiant noise inrease. Sine the noise benefit of the soure anellation is about 0.6dB per " os 0 ~ 0.86, the estimated total noise benefit for the full span 6.45 of the swept OGV is 4.6dB, not too far from.db in the predition shown in Fig. 6(b). 0 (b) PSD with different spanwise phase variations. (a) Spanwise phase variation Blak line: radial OGV, blue: swept OGV, red s 0 in term () in Fig. 4, green: term () replaed by in Fig. 4. Figure 6. Effet of the spanwise phase variation. Item () in Fig. (4) is the effet of the phase variation with sweep in the irumferential diretion, Fig 7(a). Its effet on sound power is very small as shown in Fig. 7(b). Item (4) represents the effet of the spanwise phase differene between the two TE points shown in Fig. 8(a). Its effet on sound power is also small, Fig. 8(b). 4

5 (a) Cirumferential phase variation due to sweep (b) PSD of exhaust broadband noise at approah. Blak line: radial OGV, blue line: swept OGV, red line: item in Fig. 4 replaed by. Figure 7. Effet of irumferential phase variation due to sweep. (b) PSD of exhaust broadband noise at approah. (a) Spanwise phase differene between Blak line: radial OGV, blue line: swept OGV, the two TE points. red line: item 4 in Fig. 4 replaed by 0. Figure 8. Effet of spanwise phase differene at the trailing edges. B. Effets on Gust/Casade Interation The -D equivalene method [5 is employed to alulate the unsteady lift R ( x, r), k, k, k ), item (5) in ( f r Fig. 4, on blades subjet to oblique gusts. The effets of the five -D equivalent parameters are to be examined separately. The first is the Mah number Fig. 9 ompares the two spetra for M M, M, e k u 0 z. ( k / e ) M and for M replaed by M. They ollapse when the frequeny is saled with the Mah number. That means the effet of M is simply to sale the frequeny. The saling fator is the same as in the equal turbulene energy analysis, whih will be disussed later. Figure 9. PSD of exhaust broadband noise at approah. Mah number effet on response. Blak line: radial OGV, blue line: swept OGV, red line: M replaed by M. The seond parameter is the -D equivalent IBPA: ss m / B ( S/ C)sin [( / ) e. Sine ( S / C)sin ( S / Cr ) sin, the sweep has no effet on the response through IBPA. 5 Figure 0. PSD of exhaust broadband noise at approah. Effet of stagger angle and solidity on response. Blak line: radial OGV, blue line: swept OGV, red line: and S replaed by and S.

6 where The third and the fourth parameters are the stagger angle and the inverse solidity respetively: M tan (tan ) /, S / C ( S / C) sin os ( / ).. If they are replaed by and S, the noise penalty shown in Fig. 0 is negligible. / The last parameter is the redued frequeny e e k u0z / u0. Sine 0 Cr / 0 C / u u,, with effetive redued frequeny the effet of the sweep is to introdue spanwise mean flow u 0 z. When u 0z 0 is set in e, PSD shown in Fig. hanges very little. The reason is that gusts with k =0 make the most ontribution to the interation BBN. Figure. PSD of exhaust broadband noise at approah. Effet of spanwise mean flow on redued frequeny in response. Blak line: radial OGV, blue line: swept OGV, red line: u 0z 0 in e. Figure. OGV subjet to two vortiity waves. C. Noise Penalty from Two Vortiity Waves It is shown in Fig. 6 that the soure anellation is important for BBN even for a radial OGV. However, the BBN redution is not due to the introdution of k from vane sweep. This is the major differene between BBN and tone noise. Let s examine two vortiity wave vetors K and K ' in Fig. with the same magnitude K K'. They are normal to the radial OGV LE and the swept OGV LE respetively. For the K wave, k inreases with the sweep, whih supposedly gives noise benefit. However, for the K ' wave, k redues with sweep, ausing noise penalty. The ombined effet from the two waves is determined by how the benefit and the penalty ompete, whih an be assessed from the vortiity wave strength and the asade response. The strength of a vortiity wave with ( k, k, k) in an isotropi turbulene flow is determined by the Liepmann spetrum 6 ( k) ) ( ( k) ) ( w ( k, k, k). (6) [ ( k k k ) is the turbulene integration length sale. The two waves have the same turbulene energy. However, for the vortiity wave/single airfoil interation, the total turbulene energy generating sound is the integration of Eq.(6) over k : ( k, k ) ( k, k For the K wave interating with the radial OGV, K, ( k For the K wave interating with the swept OGV, ' K, ( k, k ) dk K, k w 4 w 0) 4 4( [ ( k k) ) 4( K) [ ( K) ( ( k.5 k).5 ) s )(.5 w ( os K) K os s, k K sin s ). 4 [ ( K). (7). (8)

7 One an show that Similarly for the K ' wave, K', ( k K w ( os s )( K), ' K, 4.5 [ ( K) 0. s )(.5 w ( os K) K os s, k K sin s ), 4 [ ( K) ' K', K', ( k ' K, k K ', w 0) 4 w 4 4( K) [ ( K) [ ( K).5 (os )( K) s.5, (9) As the sweep angle inreases, the noise-generating energy of the K wave redues; the noise-generating energy of the K ' wave energy inreases. The sound frequeny from the K ' wave/asade interation is ' Ku0 os s, whih is smaller than that from the K wave/asade interation Ku0. In the first order, the K ' wave/asade response is stronger than the K wave. Sine both the soure and the response are stronger for the K ' wave, the ombined effet of sweep from these two waves is noise penalty. The noise redution mehanism for tones does not apply to BBN. D. Mehanisms & Modeling It is shown in the last setion that the introdution of k with sweep for a -D wave on the radial OGV is ounterated by a -D wave on the swept OGV, and mostly the total noise from the two waves inrease with sweep. Here we will show that the ontributing vortiity waves are mainly the D waves in the respetive OGVs, i.e. K in Fig. for the radial OGV and K ' for the swept OGV. 0. (a) (b) Figure. Normalized turbulene spetrum. Figure (a) illustrates the normalized spetrum: ( k, k) 4( (0,0) [ ( k k) ) ( ( k k).5 ). (0) The maximum turbulene energy is around k 0. 5, at whih the maximum energy is at k 0 as shown in Fig. (b). Therefore the vortiity waves with maximum noise-generating energy are those with k 0 no matter it is on the radial OGV or the swept OGV. It has been shown in [6 that if the spanwise turbulene integral length sale is small, for lower order dut modes and away from the tip or hub, noise is mainly generated by D gusts ( k 0 ). Contributions from oblique gusts anel eah other. Therefore, from both the soure energy and the response, waves with k 0 are the main noise-ontributing waves. On the radial OGV it is the K wave in Fig.. The frequeny of the generated sound is Ku0. On the swept OGV, it is the K ' wave with frequeny ' Ku0 Ku0 os s. The turbulene energies for these two waves are the same aording to Eqs (8) and (9). Therefore at ' os () s 7

8 the main ontributing vortiity waves near the swept OGV leading edges have the same energy as those near the radial OGV LEs. We have already shown that sweep has little effet on response other than the frequeny saling. Therefore, the major mehanism of BBN benefit from sweep is the frequeny saling resulted from the equal turbulene energy assumption. The seondary effet is the soure aneling and the extra benefit shown in Eq.(5) from longer span. Other hanges, suh as stagger/pith, irumferential / radial phase differene, response, et., have minimal effet on the interation broadband noise. From these analyses, a simple model to aount for sweep effets is proposed. Assume the noise spetrum for the radial OGV is w () in db, then the noise spetrum for the swept OGV with sweep angle s is: w' ( ) w( /os s ) 0log(os s ), in db. () This model is applied on the test data and on the preditions in Fig. 4. In both ases the spetrum alulated from the model mathes the spetrum for the swept OGV very well. (a) Data (b) Preditions Figure 4. PSD with sweep effets alulated using the proposed simple model Eq.(). Blak line: radial OGV, blue line: swept OGV, red line: sweep effets alulated using the model Eq.(). VI. Conlusions A broadband noise predition method was developed for fan wake/swept OGV interation. It was validated against the NASA SDT data, and used to analyze sweep effets. It was found that the major noise-ontributing vortiity waves are those normal to the OGV leading edges. The major mehanism of BBN redution from sweep is the frequeny saling due to the equal energy of these waves. The seondary mehanism is the soure anellation over the longer span after sweep. A model was proposed to aount for the two sweep effets. Preditions based on this model math with the SDT data well. Aknowledgments The author would like to thank his olleagues at the GE Global Researh Center for their fruitful disussions: Drs. Umesh Paliath, Trevor Wood, Nikolai Pastouhenko, and Lawrene Cheung. Speial thanks are due to Dr. Muni Majjigi at the GE Aviation for his permission to publish this work. Referenes [ Glegg, S. A. L., The Response of a Swept Blade Row to a Three-Dimensional Gust, Journal of Sound and Vibration, 7(), 999: 9~64. [ Parry, A.B., The Effet of Blade Sweep on the Redution and Enhanement of Supersoni Propeller Noise, Journal of Fluid Mehanis, Vol. 9, June 995, pp [ Kozlov, A.V., Atassi, H.M., Logue, M.M., and Topol, D.A., Effet of Stator Vane Sweep on High Frequeny Fan Noise and Comparison with Experiment, AIAA [4 Woodward R.P., Hughes, C.E., Fan Noise Soure Diagnosti Test Far-Field Aousti Results, AIAA [5 Ju, H., Mani, R., A Semi-Analytial Method for Oblique Gust/Casade Interation, submitted to the AIAA Journal. [6 Ju, H., Mani, R., Vysohlid, M., and Sharma, A., Investigation of Fan-Wake / Outlet-Guide-Vane Interation Broadband Noise, AIAA Journal, (05), aessed Ot. 5, 0. doi: 8