1、.:NASA Technical Memo_a:,dum 81470_ ANIMPROVEDPREDICTIONMETHODil FORTHENOISEGENERATEDIN._ FLIGHTBYCIRCULARJETS l.: (NASA-_,_-alq701 AN I_P_OVBD _REDICT_ON Nd0-22048, ._ RETHOD CR _E _OISE GB_ERATED IN FLIGH_ BXCIRCULAR OET_ (_AS _ “_._.,._ _“ Ninety-ninth _,ieettng of the Acoustical Society of Ameri
2、ca i;,_: Atlanta, Georgia, April 21-25, 198,9 l_: “%. _.F=_1980013561Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_.: AN IMI_ROVEDPRED|CTION M_“FHOD FOR THI_ N_ISE“ GEN_RATED IN FLIGHT BY CIRCULAR JETSby Jm_cs R. Stone and Francis J. Montcgani Nat
3、ional Aerommtics and 8paco Admhtistrat/oflLewis Resear0h CenterCleveland, Ohio 44135I.ABSTRACTA son, t-empirical model for predicting the noise genor_lted by Jets ex-haust/rig from titular nozzles is presented and compared with small-scalestatic and simulated-flight data. The present method is an up
4、dated version of; thllt part of the original NASA Aircraft Noise Predlctibh 1)rogranl (1974) rela-ting to circular jet noise. The earlier method has been shown tO agree reason-ably well with experimental static and flight data for Jet velocities up to 520“ “ m/see. The poorer agreement at higher jet
5、 velocities appeared to be due pri-marily to the manner in whlvh supersonic convection effects wore formuhtted. The purely empirical supersonic convection formulation is replaced in the pre-.- sent method by one based on theoretical considerations. Other improvementsof an empirical nature have been
6、included based on model-jet/free-Jet simula- ted-flight tests. The effects of nozzle size, Jet velocity, jet temperature, andl_ flight arc included. INTRODUCTIONi. Accurate noise prediction methods are now required-in order to predictthe environmental impact of airport operations on tee surrounding
7、communi-ties, as well as for the realistic design of new aircraft and the development ofnoise reducing modifications to existing aircraft. The prediction method pre-: sented herein is an updated, more theoretically rinsed, version of that part ofthe original NASA Aircraft Noise Prediction Program pe
8、rtaining to circularnozzles (ref. 1). This paper deals only with the noise generated by the ex-hans! Jet mixing with the surrounding air and does not consider other noisesemanating from the engine such as narrow-band shock screech or internally-generated noises.i_:_i-._ _ “ . . . . . _ _:_.,_ - o ,
9、, _ - , “, ._, :,-*_ ,_ ,f , ._ . ._,_,_/:._- _ I I _ .-J_,-. “ .1980013561-TSA03Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“ “ 2,f“ “t: Al_mug_ the numereue aspects of.the mechanisms of Jet noise generationii are not fully understo_.the neoessi
10、ty of pred!ot_ng J_ aoiseIres-ledtothede_ ,_Zt“ ve!opment of empt_cea proeedures. The NASa interim _ediotlon method fo_Jet norse ref, 1) and an updated S0oisty_f ,4amznoive E_ineers (SA.E) metlmd-.- - (ref, 2) are in m_rrenr_use, The SA_ method shows reasonable alpmementwlth I_ : static experlment_
11、dee, for jet veloo/t_es ep to about 8/0 m/see., The-Ur, lksr NASA method (ref, I)-showsl _uonable agremnent._Vlth both _ and. data at Jet-velocltles up to about 520 m/seo, HOwever, at higher velocities-: and at locations near the Jet axis (kngles _eate_ than about 1_0 O with respect to the inlet) th
12、e noise is overprectloted. The poo=e_ _reement at hiSh. Jet vel-_“ ocities appeared to be due primarily tothe mannel in whioli supersonic oon-veotion effects were formulated, The htgltly empirical supersonic convectionformulstion _f reference 1 is replaced by one (ref. 3 based o_ theoretical“ con-sl
13、derations (_efs. 4 and 5). With these ohsages, the method presented hereinagreeg fairly well with the SAE method (ref. 2) under static conditions. Thesame relsflonsIttpe are then used to pl_edict the noise in fligltt, in-oo,_l_ast to the SAE method, which uses a pureLy em_-ical approach for _ effect
14、s.For mapersonio Jets not fully expandedto ambient p_essure, sh6ok/turbu-lent4 interaction noise must also be ootmldered. The purely empirical, shooknoise procedure of referenoe lie rel_ced hi the ourrent metiz3d by a semi-.: empix4cal model based largely on the theory of HarperBourne and Fisher:. (
15、ref. e). SYM_LS(All symbols are in SI unJ.Lsunless noted.),a areao speed of soundD nozzle diameterF functional relatio_ (eq. (i3)f 1/3-oe_ave-hend center f_equencyI acoustic lz_msityKI coefficient in equation (t)k ratio of conVection velocity to Jet velooityI charaeteristic lengthM Math number, V/c-
16、T,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I:_“- :!, ,_. r_ convection factor exponent.o:“ OASPL overatl sound pressure level, dB re 20 _/m 2.: OASPL t predicted OASPL uncorrected for refraction, dB re 20/_N/m 2:_ p- presstireI“ : Pref roferen
17、oe pressure, 20/JN/m l. p mean-square acoustl_ pressure fluctuation, IR source-to-observer distance S - effective Strouhal number (eq. (12)SPL 1/3-0otave-band sound pressure level, dBre 20 _N/m 2T total temperatureV velocity tX source position downstream of nozzle exit plane (ia turbulent length sca
18、le ratiop effective angle of attack (fig. 1), deg iA fl/ght level relative to static, dBp density0 polar .angle from inlet . e effective; F flightOISA international stm_ard atmosphere (288 K and 101. IIkN/m“)_. J folly-expanded jet,.,% “. -“ “ 1980013561-TSA05Provided by IHSNot for ResaleNo reproduc
19、tion or networking permitted without license from IHS-,-,-!- 4I_V“ s ,t, io_“ - SO source alterationm“ s shOck noi_e .“ :“ 90 parameter evaluated at O= 90 0 aircraft: FORMULATION OF PROCEDUREThe noise levels predicted are free-field _no reflections), far-fbeld andlossless (1. e., the eff_sc_ of atmo
20、spheric-absorption are not included). Thegeometric variables describing _ position of the observer relative to the en-gtne are shOwn schematically in figtwe 1. The Jet mixing noise and shocknolseare assumed to by symmetric about the Jet axis. The results of the predictionprocedure are expressed in t
21、erms of S_L spectz.a at each an_le of interest.(Acoustic power relations are not given explicitly, but power computations maybe nwtde by integrating the results numerically over all angles.)“The prediction is first developed for shock-free Jet mixing noise with noflight effects. Then, the effects of
22、 flight are considered, and static-to-flightincrements established. Finally, supersonic Jet shock noise effects (static andflight) are incorporated into the prediction procedure.Experimental aoise measurements are often made at a distance far enoughfrom the sources to be in the acoustic far field of
23、 each individual source, butnot far enough away to treat the entire Jet plume as a poi_lt source at the centerof the nozzle exit plane. When such is tlie case, comparisons between e._q_eri-mental data and prediction must take source locations into account. The meth-ods used to approximate these.sour
24、c_e location effects are given in appendl A.Static Jet Mixing NoiseLighthills theoretical studies (refs. 7 and 8) established that the ncoustic- 2intensity of a shock-free Jet varies with pV_lca5jl . If the characteristic dimen-sion m is taken to be the square root of the fully-cxp:mded Jet area Aj,
25、 the in-tensity I at a distnnce R from the source would be given at 0 = 90 by 1980013561-TSA06Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-L!i =xiI,.2_l 1where KI is an expetimentally determined coefflcleflt.In experiments, however, it is genelall
26、y the mead-square pressme fluc-tuation p-_ which is measured and not the intensity. This mean-square pres-sure fluctuation is given by IPaCa, so that /:“ The mean-sqUare pressure fluctuations are usually expressed in deotbels (dB)referred to a reference pressure Pref and physical propert/_ aro often
27、 re-ferred to t_ose for the Intez_lonal Standard Atmosphere (ISA). Consequently,an equivalent relation to equation, (2) can bewritten in dimensionless logarith-. ,_ mic terms:_ OAS,L=,O,oSP2red ,0 og P_f / ,0 tog%/: + 10 log (3)4I! Pls_OISA/I-Thus far in the present development, the characteristic d
28、ensity p has notbeen specified. Experimenf_tl lesults (e.g., ref. 9) indicate that at high Jetvelocities the noise increases with inoreasing Jet density (decrlasing Jet tem-perature), approaching a square-law relation, Icc p_. On the other hand, at_.- low Jet velocity the noise decreases with increa
29、sing Jet density, approachingJan inverse relation, I _ p_l. These effects Were incorporated into the earlierNASA prediction (ref. 1) _y using the ambient deflsity in equation (3) but addinga term 10 log(oj/Pa)W to the right-hand side, where pj is the fully-expanded=k-1980013561-TSA07Provided by IHSN
30、ot for ResaleNo reproduction or networking permitted without license from IHS-,-,-t _.L“, . , _ . .: , .: . , .d._ _ Jet density. l_he foUowing annly_ical expression-for w, developed in refer- :,“ . co-= -I 14)!;“ 0.6+%/it,“ This expression gives values-elmllir to those reco-_mended by the SAE pro-.
31、:_ cedure (ref. 2), as is show1_in figure 2. The agreement is nearly exact overI_: the range in which the SAE curve is based on experimental data. With this_-i formulation for w it was determined that tie Jet velocity exponent requiredadjustment to V.5 from 8.0 to agree with data.The effect of sourc
32、e ecmvection on the noise rad/ation has been deter-mined on theoretical _rounda to-introdace a directionaleffect on the noiselevel. Acoot_g _ Ffowcs Williams (ref. 4) the acoustic inte_i6y is. multi-_ plied by the factor, + Me cos 2 + _ where Me = kVj/c a. Inthe present formulatzon the value of k is
33、 taken to be 0.62 and n is taken toT, _.be 3, as suggested by Goldstein and Howes (ref. 5). The value used for a is. 0.2, essentially as determined by Larson, et el. (ref. I0). The resulting ex-:_ pression for OASPL uncorreoted for refraction (OASPL) is given by_: OASPL = 141 + I0 tog . + i0 loE|.-t
34、-|“ I0log(, ,oe+ I0“tog - - 15 log + Me cos 9.+ . (B): a/.Note that for aft ideal gas the term. (,a/PtS._2(Ca/CiSA_ 4, reduces simply to.Pa P_SA“) The earlier NASA prediction (ref. I) contained a more complicatedjet velocity effect to give the experimentally observed trends at high jet veloc-ity. Th
35、is term is no I,nger needed with the theoretically more correct hand-!_;:,. 1980013561-TSA08Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- ling of supersonic corivect|on. Corrections for the effects of refraction are in-: - - corporated in the spec
36、tral curves, as discussed in the following paragraph.i Spectral curves are shown in figure 3, where SPleOaSPL is plotted at10 increments as a function of the logarithm of the effective Strouhal number,_ S, where“, - fD/T.0.|._4(1“*0OS0)%Va/where O* iSan effective angle givenby O(Vj/catl, and D is th
37、eequivalent_ eDr_ diameter based on fully-expanded Jet area, i/_ These results are alsoi.“ given in table I for the convenience, of the user. Thesb curves were evolvedm,-“ ._ through improvements to a similar set of curves determined empirically in- reference 1. Integration of the spectral curves pr
38、oduces a difference betweeni_ _ the corrected (OASPL) and uncorrected (OASPL*) Overall sound pressure lev-els, as Indicated by the bottom row of table I. This difference is attributed torefracUon.In figure 4 the level of agreement between the present method and that ofthe SAE (ref. 2) over the range
39、 of the latter (-0.4 “_ log(Vj/ca) _ +0.4 and20 .0to 880 m/see.The revised So_.wty of Automotive Engineers _3AE)method is shown to agrcereasonably well with the present jet mixing noise prediction in terms of staticlevel, directivity, -rod spectra. Tne two methods agree within a 1.8-dB stan-. dard d
40、eviation in OASPL. IAmited comparisons with model-scale simulated-flight data presented herein show that the levels and spectra are predicted ac- 1curateiy. An earlier report showed that this method predicts static to flight Iincrements for full-scale jet mtx,ng noise to within a 1.5-dB standard dev
41、ia-tion in OASPL.“Fh_shock noise method is shown to give reasomtbly accurate predictionsstatically _mdin flight; but detailed statistical comparisons hwe not beenmade. i_IfAPPF;NDIX _, _IOI.IIiCE IX)CATION COItRECIIDNS“. Experimental noise meamwements are often made at a distance far enough away to
42、be in the far field of any individual noise source region but not fiLr: enough aw_ty to treat the entire exhaust plunlc :is a point source at the evlliel Lof Ihc nozzle exi! phmc. When this is Ihe ea_e. the prt_tielion for each :_OUleemust take into :ieeoulll the leeilion of tha! source. This apiaen
43、dix gives the“ methods used herein to approxinutte these source location t,ffeets. Tile gee-_“ ;_ .w .; ._ . ;,.“. _. _. _ . - . ._- :1980013561-TSB02Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,D.: ),“ 15metrlorelationsforn_se soarcesdownstreamo
44、fthenozzleexitaregivenino,flgt!_roAI. Therelationshipoftheaot4_al_ure(_-to-o_zserverdistance,R, toits apparent value, Ra, for a source at a distancer X, downstream of the exit:= p|ane is as follows:J_:“. R =,_+ X cos Sa)z + X2 sin z Oa (AllL The relationship of the actual angle, 0, to its apparent v
45、alue_ 8a, is thenJet Mixing NoiseThe relation for Jet mixing noise source location is based very loosely onthe data of reference 18. The approximate relation used is as follows:“ xj = + V (a31./ 90/_.“ This is an approximation to the source position where the peak frequency noiseat each angle is gen
46、erated. The variation of source position with frequency isnot given explicitly, but is included to some degree of approximation in the.= -. spectral shapes. Figure A2 shows the OASPL correction for distance and: angle corrections for jet mixing noise as a function of apparent ahgle, 0a, for)i“ vario
47、us values of Ra/D.Shock NOise|,:e relation used for shock/turbulence interaction noise source location“ has some foundation in tlie theory of Harper-Bourne and Fisher (ref. 6). Ref-_- erence O indicates that the first shock occurs at 1.31 D and that the: spacing between shocks is about 6 percent of
48、that distance. Furthcrmore, ref-“ erence 6 indicates that about eight shocksare significant in the noise generationc7,_: _.1980013561-TSBO3Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-it:“li ; 16,!i“- process. The approxlhlation _u_d here emphasizes the earlier, stronger- shocks and is given as follows:xs= I.SD,.I. REFERENCES“ 1.J. R. Ston%,“InterimP1“edletionMethod forJetNoise,“NASA TM_ X-71618 (1974),2. “Gas
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