An experimental investigation of the local heat transfer coefficient distribution during gas injection into the supersonic-flow portion of a Laval nozzle is discussed. The controlling dimensionless parameters of the investigated process are presented in terms of a generalized relation for the maximum value of the heat transfer coefficient in the nozzle cross section behind the injection hole. Data on the heat transfer coefficient variation along the nozzle length as a function of gas injection rate are also presented, along with the heat transfer coefficient distribution over a cross section of the nozzle

Bakirov, F. G.

Shaykhutdinov, Z. G.

English

NASA Technical Reports Server

HH2KEHEPHO-0H3HMECKHFI
1973 r. A\AH TOM XXIV, .Ns 5
536.244:533.6.011.5
<P. F. BaKupoe, 3. r. UlauxyrduHoe
OCOBEHHOCTH TEHJIOOBMEHA B OBJ1ACTH
B CBEPX3BVKOBOR BblCOKOTEMnEPATVPHblH HOTOK
uccjiedoeann pacnpedeAenue KO3tp(punu-
Ten.wodMBHa npu edyee zcaa e ceepxssyKoeyio <tacrb conAo
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npo^cca.
B noc^eziHee speMH peaKo Boapoc HHiepec HccJieflOBareJieH K
CBepxsByKOBbix TeneHMH c nonepeqHbiM BflyBOM BTOPHIHOFO rasa. B HSBCCT-
KHX pa6orax flocxaToqHO noapo6HO ocsemeHhi rasoflHHaMH^ecKHe Bonpocw
H npaKTHMeCKH nOAHOCTbK) OTCyTCTByiOT flaHHbie 06 HCCJieflOBaHHHX OC06eH-
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JIOM. HaMH cae.naHa nonuTKa BOcncuiHHTb STOT npo6eji.
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HOCTb MCTOaa 33K.1K)Ma.TaCb B 3KCnepHMCHTa^bHOM OnpeflCJlCHKH K03(j)(pHUH-
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noBepXHOCTbio CTCHKH, oMbiBaeMOH noiOKOM. HarpeB soHfla no speMenH (pHK-
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https://ntrs.nasa.gov/search.jsp?R=19850017451 2020-03-20T19:23:35+00:00Z
6.0U.5
terptii
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86CT-
OOCbl
6en-
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(1)
OcoSeHHocru rer..ioo6MeHa a o6Aacru edyea e ceepxsByKoeoii HOTOK 791
Moro notoKOM ropua. Floc-ieanec KOKTpojiHpyetCH cneuHaflbHoii TepMO-
napofi.
flpn npoaeflenHH SKcnepHMCHTOB B CTeHKy con.ia B 06.N3CTH Bflysa ra3a
3zae.nuBa.nocb 30 — 40 crep/KHeft — SOHSOB. FIoKaaaHHH TepMonap perHcrpH-
posa.THCb Ha ui.iefi(J)OBbix ocuHJi.norpa^ax H-700. TepMonapu saaejibiBajiHCb
iia oanoil noJioBHHe npeano.iaraeMofi SOHU BosMymeHHH teMeHHH. CHMMCT-
pumio HM. Ha apyrofi no.iOBHHe soHbi, H3Mep«^ocb nojie aaBJienHH, nosBOJiHio-
mee comacosaTb xapaKtepHCTHKH Teruioo6MeHa c OCOSCHHOCTHMH raaoaHHa-
MHMCCKOH KaprHHbi reqeHHH.
Hcc.aeaoBaHna npOBoaHJiHCb Ha CBepxaByKOBbix KOHHMCCKHX conjiax c
MHC.T3MH MI B CeHCHHH BflyBB, paBHUMH 2,75 H 3,36, KOTOpblC yCT3HaBJlHBa-
jincb Ha raaoreHeparopHOH ycraHOBKe. B xaiecTBe paGoMero rejia (K3K oc-'
HOBHOrO, T3K H BflyBaCMOrO) HCnO.1b3OBa.HHCb npOflVKTb] CFOpaHHH KCpOCHHa
B Bosziyxe c TeiunepaTypofi ropMo>KeHHH T\ =600-=- 1700 °K H HOJIHUM aaB-
jieHHeM PI =20-^-43 6ap. Fas BflyBa.ncn nepneHflHKy^apHo creHKe con.ia ne-
pea xpymoe OTBepctHe B creHKe con^a fluaMerpoM d2=4-4-12 MM. BTOPHMHUH
raa a.na Baysa oTSnpa.acH H3 KaMepu cropanHH rasoreHeparopa. HaMCHCHHe
pacxoaa BTOPHMHOFO rasa aocTHra.iocb sa cqe? H3MCHeHHH ^HaMerpoB oTBep-
cTHa aaVBa dz H nocraHOBKOH pacxo^Hbix uiaH6 B rpy6e noaeofla sayBaeMO-
ro rasa, MCM aocTHrajiacb HMHrauHH paajiHHHbix CXCM noflanH BtopHHHoro
rasa — apoccejinpoBaHHa aaB.aeHHH H HSMCHeHHH n.aomaflH ce^eHHH con^a
Bflysa. PaccTOHHHe or oTBepcxHji Bflysa rasa no cp-eaa con^ia Bbi6npayiocb
T3KHM o6p330M, MTOSbl KpHBOJIHHeHHblfl CK3HOK yn.aOTHCHHH, 06pa3yK>mHHCH
nepea BflysaeMOH crpyeft, He nonaaaJi H3 creHKy conjia H He B03HHKajia OT-
p3>KCHH3H yaapnan BOJina. MHC.IO PefmoJibaca Rei pasHH^ocb (l-r-8)-106 .
CymecTBeHHOe 3H3M6HHe a^H KOHeqHbix' pesyjibTaTOB HccjieflosaHMH HMe-
CT Bbi6op onpeaejiflioineH TeMneparypu T/, Koropsn npeflcraBJiaeT coSoft Me-
cTHyro reMneparypy npiicreHHoro C.IOH rasa B BO3MyweHHOH SOHC H aHa-ao-
rHHHa TCMnepaType BoccraHOBjieHHH Te B norpaHHqnoM CJioe. HasecTHO, WTO
3T3 Be.aHHHHa 33BHCHT OT CTeneHH flHCCOUH3UHH paSoqeFO T333, OTHOCHTe.Tb-
HOH HHTCHCHBHOCTH Ha.ayMCHHH, yCJIOBHH TenJI006MeHa H T. fl. B yCJIOBHHX
IlpOBeaeHHH 3KCnepHMeHTOB flHCCOUHaUHH r333 npaKTHMeCKH OTCVTCTBOBa.ia,
jiojin .ayqHCTbix Ten.aosbix OOTOKOB B o6meM ren^oBOM noroKe, nonsaaiouueM
Ha cxeHKy con.aa, cocraB.aH.aa npenegpeiKHMo Majiyio Be/iHMHHy. B STHX yc.ao-
,BHHX cooTBercTByiomHH pacieTHbiH aH3JJH3 noKasbiBaeT, HTO onpeae.aHK>m3H
TCMnepsrypa T/ npHMepno Ha 5 — 8% HHjKe T], T. e. 7/~ 0,92 -f- 0,95 T], MTO H
CblJIO npHHHTO B aS.nbHCHIUeM. HpH 3KCnepHMeHT3;ibHblX H3Mep6HHHX Tf 6bl-
.no mxiyqeHO TtIT\ = (0,93-=-0,95) ±0,08.
Ha pnc. 1 npeacTas^eHo rnnHMHoe pacnpeaejieHHe oTHocHiejibHoro KO-
~~ __ y
3(})(J)HUHeHTa renjiooSMCHa a = a/oo no fljiHHe conjis x= — —
P* = 32 6ap H OTHOiueHHfl reMneparyp TOPMOKCHUH T%lT\ =0,95 npn Tpex
3HaieHHHx OTHocHTe.ibHoro pacxoaa BayBaeMoro rasa. Ha pnc. 2 npHBeaeHO
pacripefle.neHHe a no ueHipaJibHOMy yr.iy q>i RJIH rex we ycjiOBHH B nonepei-
HOM ceneHHH con^a. •
HsMepeHHbie npn BUVBC rasa B coruio snaieHHa K03(})(})HUHeHTa Tenwioo6-
M6H3 a OTHCCeHfal K COOTBCTCTByHDUtHM JlOKajIbHUM 3H3HeHHHM OQ flJIH TOrO
/Ke-con.ia npn xex JKC napaiaerpax ocHOBHoro rasosoro noroKa, Koropue TaK-
>Ke 6biJiH no.nyMCHbi SKcnepHMeHtajibHUM nyreM npH OTcyrctsHH Baysa rssa.
BbiSop B KanecTBe ecrecTBCHHoro MacuiraGa OTHeceHHH AJIH <z HMCHHO H3-
MepeHHblX 3HaH6HHH Oo nOSBOJIHCT yMeHbUIHTb BO3MO)KHyK) CHCTeMaTHMC-
CKyK) norpeuiHOCTb npHHaioro Mexofls H3MepeHHH K03(})(})Hu,HeHTa renjioo6-
MCH3. HSMepCHHbie npH OTCytCTBHH BAyB3 r333 B COnJIO 3H3MeHHH
792 . r. BoKupoo, 3. r. lUauxyrduHOo
tHT3 Clo COnOCTaB.TH.1HCb C paCMCTHblMH flaHHbJMH, HO.'JVHeHHbJMH HO H3beCT-
i!biM iwemaaM pacweta KO3(j)<})HUHeHTa TenjiooSMena (no 4)opMV.ne n.nn O&IJH-
HofiuH.iHHiipHMecKofi TpvOu, Metoflu BapTua, ABflyeBCKoro. HeBJiesa H T. a.),
a npH 3TOM 6bj.no no.nyieHo yaoBjieTBopHTejibHoe cosnaaeHHe STHX aaHHbix.
Kax BHflHO us PHC. 1, 2, B o6jiacTH Bflysa npOHCxoflHT cymecTBCHHafl ne-
pecTpofth'a KapiHHbi ren^ooSMCHa, HHTCHCHBHOCTb ero yBWiHMHBaerca no
Bcefi nosepxHocTH con.aa, orpaHHneHHOH SOHOH BOSMyweHHH. RJIH oStHCHe-
HJia 3Toro xapaiaepHCTHKii Ten.noo6MCHa conocjaB^H.iHCb c aaHHbiMH n3Me-
pemiH no.iefi ^aB.ieHHH. no.nyMeiinbix B rex >Ke 3KcnepHMeHiax.
Flic. 1. H3.Meiieiine KO3(j)$nuHeH7a Ten.noo6M6Ha no a-inne con.ia npH BayBe SBVKOBOH rrpyii
iepes npymoe oiBepCTiie. rf2=10 MM; Mi=2,75; / — Gs=2,2%; 2—4,75; 3—7,5
PHC. 2. Pacnpeae-ieniie KO3<j)<}>imneHTa Ten.iooSMeHa B nonepeiHO.v ceqeHHH con.ia
jt,/d:=4,l fljis Mi=2,75 npii Bayse rasa: 1 — G2=2,2%; 2 — 4,74; 3 — 7,5. tp. zpad
CoBMecTHoe paccMorpeHHe nojiy^eHHUx peayjibtaioB c. npHB.ieMeHHeM
HSBecTHbix pa6or no (JmaimecKOMy BaaHMOfleHCTBuro noTOKOB npH Bflyse rasa
B CBepX3BVKOBOH HOTOK [3], [4] 'H flp. nCKaSblBaCT, HTO H3 JIHHHH OTpblBa
ipexMepHoro norpaHH^Horo CJIOH (JIHHHH s) KO34)(})HUHeHT Tenjioo6M6Ha
i!Meer MecTHbift MHHHMVM. STO xopouio cor^acyercH c peay^bTaxaMH [51,
r^e npea^araercH onpefle.i«Tb ro^Ky orpHBa norpaHHinoro CJIOH no
HOMy MHHHM) rMy K03(p4)HUHeHTa a- MaKCHMaJIbHbie 3HaH6HHH
amax nadsitonaioTca nepea BflysaeMofi crpyeS Ha JIHHHH pac-
a (CM. puc. 1). Xopoiuo corjiacyiOTCH no.nyHeHH^bie pesyjibiaTU c
TenjiepoBCKHMH (poxorpa(J3HflMH (CM.. nanpHMep, [3]). aaax cooTBCTCTByer
30He naaeHHa KpHBO.aHHeftHoro CKanua yn^OTneHHa Ha creHKy con^a. Heno-
cpeACTBCHHO nepea crpyefl K03(})4)HUHeHT TenjiooSMena pesno VMeHbmaeTCH,
MTO CBHSaHO C Ha.lHIHeM SflCCb 33CTOHHOH 30HU. CjieOy&T OTMCTHTb, MTO T6n-
noHsoJiHpoBaHHbifl CTepjKeHb, npHMeHHeMHH flJiH onpefleJieHHH jioKajibHoro
3HaHCHHH K03({)(J)HUHeHTa TenjioodMeHa, HM^er KoneqHbie pasMepu, ITO npH-
BOflHT K HCKOTOpOMy OCpeflH6HHK) 3H3ieHHH a, HOJiyiaeMblX npH H3Mep6HHHX.
FTosTOMy flJiH GoJiee TOIHOFO onpefleJieHHH amax SUJIH npHMeHenu cneuHa.ib-
HblC BCT3BKH B COH.10 BflyBa, B KOTOpblX OTBepCTHC RJIH BflyBa
C HCKOTOpUM 3KCUeHTpHCHT6TOM OTHOCHT6JIbHO 60KOBOH HOBepXHOCTH BCT3B-
Oco6enHOcru TenAOo6Mena e odjiacru edyea a cecpxseyKoeoii noroK 793
T.fl.),
HHblX.
an ne-
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KH, MTO n03BO.ail.10 HSMCHHTb nOJlOKCHHe OTBCpCTHH Bfl}'B3 B CT6HKC COIUia
OTHOCHTCvlbHO 3afle.n3HHbIX HenOflBHWHO Ten^OH3OflHpOB3HHblX CTep/KHCH Ha
BeJiHMHHy 3Toro SKCucHTpHCHTCTa. BospacracT KO3(p<pHUHeHT Ten.aooSMCHa
ii B 30He sa BaysaeMOH crpyefi. HHiepecHO, MTO Ha flJiHHe x = 8-=-10 a~oo,
T. e. 3(j)(j)eKT BosMymeHHH B CMbicJie Teanoo6MeHa npaKTHMecKH HCMesaeT, a
3TO FOBOpHT O6 ynOpHflOMCHHOCTH flBHWCHHH FlOTOKa B 3TOH 3OHC. Xap3KT6p
a no yrjiy 91 raKJKe noBTOpHer ocoSeHHOCTH raso-flHHaMHMecKofi
eVCHHH: MBKCHMyMU KO3(J)(j)HUHeHTa Ten^006MCHa COOTBCTCTByk)T
.IHHHHM pacreKaHHfl, a M M H H M Y M H pacnojiararoica Ha ^HHHHX creKaHHn Mac-
.IflHUX KapTHH TeMCHHH.
npOBeflCHHbie H3MH 3KCnepHM6HTa.abHUe HCCJlCflOB3HHH B^HHHHH paSJlHM-
HBIX napaMeipOB ocHOBHoro H BxopHHHoro noroKOB Ha HHTeHCHBHOCTb Ten.io-
o6MCHa B 30HC BO3MymCHHH nOKa33JIH, MTO OCHOBHOC B^HHHHC H3 O OK33UBa-
f* ' '
ei oTHOcHTejibHbifl pacxofl BflyBaeMoro rasa G2= ^-2- H MHCJioMaxa OCHOBHOPO
GI
noTOKa MI B ceweHHH Bflysa. ZlaB.neHHe Topiwo/KeHHa P2 BflVBaeMoro rasa
npn nocroHHHOM ero pacxoae, asBJieHHe Pi H reMnepsrypa 7"-] OCHOBHOFO
noroKa, npo(J)HjiH OCHOBHOFO H BTOPHMHOFO conjia npaKTHMecKH ne
IOT B^HHHHH H3 OTHOCHTC^bHyiO B6JIHHHHy K03(})4)HUHeHTa TenjI006M6Ha a. '
Ha pHC. 3 npHBOAHTCH 33BHCHMOCTb MaKCHMaJlbHOFO SHaqCHHH O OT OTr
HOCHTejibHoro pacxofls na Bays H qacjia Mi naGeraiomero noiOKa.
MTO OTHOcHTejibHbifl pacxofl BflysaeMoro rasa OKasuBaeT peiuaiomee
K3 «max- yBeJlHMCHHe MI T3K*e HBCKO^bKO yBEJIHHHBaeT M3KCHM3JIbHOe 3H3-
KO3(})(})HUHeHTa Ten.iooSMeHa. STO osnaMaeT, MTO CMemeHHe OTBepCTHH
B con^e 6JiH»;e K KpHTHwecKOMy ero ceneHHio npHBe^eT K HeKOTOpoMy
oTHocHTejibHoro K03(J)4)HUHeHTa Ten^ooSMena amax, oanaKo no
a6CGJIK)THOH BejlHMHHe OH npH'STOM yBeJlHMHT.CH, T3K K3K yBejIHHHTCH OflHO:-
BpeMCHHO K03(})(J)HUHeHT TenJIOoSMCHa Co-
BbiHB.ieHHH onpeA&nHromHx KpHTepHeB HCCJieflyeMoro npouecca BOC-
3H3.1H30M paSMepHOCTCH, KOTOpHH nOSBOJIHCT BblflBHTb 3TH 663-
p33Mepnbie napaMCTpu, HC npnGeraH K ypaBHCHHHM, onHCbisaioiUHM HCCJIC-
ayeMbiH npouecc<[6].
SanHineM Bee HesaBHCHMbie napaiueTpbi saaanH, xspSKTepnsyiomHe Moae-
wiHpyeMoe HB^eHHe, CMHTan HCKOMOH BCJIHMHHOH K03({)(pHUHeHT Tenjioo6M6Ha
a: xi, q)) — xoopaHHaTbi TOMKH B conjie; a»i,:pi., cPl, AI, r j i , R}, T\ — napaMCT-
PH ocHOBHoro rasoBoro noiOKa; w2, pz, cp, , K2, t\2, Ri, T2 — BTOPHMHOIO; D\ —
TCKymafi flHaiaeTp con^a; p — yroji Baysa; Tc? — reMnepaTypa CTBHKH; g —
ycKopeHHe CHJibi THjKecTH; yi — yroji pacTBOpa conjia; l\ — paccTOHHHe or
KpHTHMecKoro ceieHHH; FJ\ H /72 xapsKTepnsyiOT npo(J)H^b OCHOBHOFO H BTO-
pHHHoro conjia; d2 — flHaMeTp OTBCPCTHH RJIR Bflysa; /T H e — MacuiTaS H HH-
TCHCHBHOCTb TypSy.nCHTHOCTH; |J2 — K034)(j)HUHeHT p3CXOfl3 BTOpHMHOFO COn-
.na. . .
TaKHM o6pa30M, HMCCTCH cosoKynHOCTb 29 napaweTpoB, KOTOpsa onpeae-
Ten.noo6MeH B conjie B BOSMymeHHofl SOHC npH Bflyse rasa. OCHOBHUMK
epeHHH 6yayT: K.F, M, CBK, °K.
Opouecc paccMaTpHBaeM KaK KBasHCTauHOHspHbifi. npHMenaeM n-Teope-
My BaKHHreiaa. OSmee MHC.HO SespasMepnux KpHTepHes
r = n — m' = 29 — 4 = 25. (5)
Ms mix oana SespasMepnan BejiHMHHa a 6yaeT (^yHKUHefl 24 apyrnx fiespas-
MepHbix KpHrepHCB. EipOBeflH flajiee anajins pasMepnocTeH, corjiacno [6],
nojiyiaeM, MTO peuienHe 33fl3MH o Ten-nooSMene npn BTOPHMHOM Bflyse rssa
B COnJIO M05K6T HMCTb, H3npHMCp, CJieflyiOIHHH
XXI
794 0. r. BdKupoe. 3. r. lUauxyrduHoe
'• -Nu = f -2- , <PI. Re,". Re.- Pr1? Pr... Fr, M,, M,,, T,, P, *i, *2, 77^ /72,
TIpH fiojiee ofimefl nocraHOBKe 33A3MH B MHCJIO onpeAeJiHiomHX kpHrepHCB BOH-
eme Sh = ——, FAC TO — xapsjcrepHoe BpeMH./
Kan BHAHO, peujeHHe saAa^H B caMofi oSmeff nocranoBKe HMeer ipesBH-
jiOKHblH BHA. flqSTOMy A-1H CFO ynpOmCHMH HCOCXOAHMO npOaH3JlH3H-
pOBarfa ace 6e3pa3MepHMe BejiHHHHU c TOHKH speHHH HX BOSMOKHOPO B.THH-
HHH H3 HCKOMblfl pe3yJlbT3T, T. 6. K3K 6bl BUHBHTb K03^4)HUHeHTbI BJIHHHHH
•jinn Ka)KAoro H3 STHX napaMerpos. EciecTBeHHO, HTO BBHAy orcyTCTBHH
aHa.iHTHMecKoro peiiieHHH saAaiH OTBCT na STO MOJKCT Aaib SKcnepHMeHrajib-
HaH nposepKa B^HHHHH Ka>KAoro HS KpniepHeB H3 HccyieAyeMbift npouecc.
HTOFH npoBeaeHHbix 3KcnepHMeHTa.ibHbix HCCJieAOBaHHH no BUHB^CHHIO
BJIHHHHH 6e3p33MepHbIX DSpSMeipOB yp3BH6HHH (6) H3.tt A^IH yCJIOBHH, H3-
SjiiOAaromHxcH npn npOBeAeHHH SKcnepHMeHTOB (P = 90°, Mz=l H T. A - ) > a
T3K)Ke Hcno.ib30B3HHe npHBeACHHbix B JiHieparype 3KcnepHM6HT3JibHbix ASH-
IIUX O03BOJIHJIH HCKJlK)HHTb 6esp33MepHbie nSpaMBTpbl, OTHOCHTe^bHO KOTO-
pbix npoiiecc HB^«etcH npaKTHnecKH aBTOMOACJibHUM. TorAa KoneqHoe peuie-
HHC AJIH H31I1HX yC.aOBHH npHHHMaCT
SOT] (7)
a B BHAB a=«/ao, a He B BHAC MHCJia Nu CBHsano c TCM,
OTHOCHTejlbHaH HHTCHCHBHOCTb TenjIOOSMCHa UpSKTHieCKH aBTOMOACJIbHa OO
MHC.ny Rei B HccjieAOBaHHOM AHanasoHe ero H3MeH6HHH, a -Nu = f (Rei ) , H no-
3TOMy nepexoA K ot ecrecTBCH. KpoMe roro, a MO>KHO npeAcraBHTb H I
NT 'NUNu =
Nuft
g.1
= a.
KOMIUICKC coSoft oTHomeHHe pac-
BAyBseMoro raas K pacxOAy OCHOBHOTO rasa qepes eAKHHinyio
B cjiyqae 0=^=90° H Mj^ 1 pemeHHC 33A3HH AJIH cjiyqan, KorAa BAysae-
MHH raa orfiHpaercH HS Kawepu cropaHHH, MO«HO npeAcraBHTb B
- cos 9 1 , (9)
= ,- ; 6CT = — v^ ; x* ~ mjjo* [ — - -- cos P 1 ;
•PlWl TI \W2 ]
W
— -(I — cosp) 6bui paHee BBCAen B pafioiax B. C.
Oco6exHOCTu Ten/too6Mena e oO.iacru sdt/ec e ceepxseyKoeou IIOTOK 795
H.B. H. riaHMCHKo. OH oSoSiuaer BJIHHHHC fespasMepHux napaMerpos p1, k,,
w, IR T \ - ,. ••• • .
Heo6XOflHMO OTMCTHTb, MTO COBOKynHOCTb KpHTCpHeB, BXOAHIUHX B COOT-
iioiiieHHe (6), MOiKeT 6biTb: nojiyneHa H apyrma nyreM — Ha ocHose anajiHsa
ypSBHCHMH flJlH OCHOBHOFO H BTOpHMHOPO HOTOKOB Fa33. B 1HCJ10 3THX yp3B-
HCHHH BXOAHT ypaBHeHHe coxpaHeHHH cyMMapHoro pacxoaa rasa B conjie,
ypaBHCHHH coxpaHCHHa SHeprnH H HMnyjibcos, ypaBHCHHH COCTOSHHH
bcHOBHOFO H BTOpHHHOrO T330B H T. fl.
10
o —/
PHC. 3. SaBHCHMOcTb MaxcHMa-ibHoro K03(J)(J)nUHeHTa ren;ioo6MeHa' nepea
crpyefi or oTHOCHTCJibHoro pacxoaa BayBae.woro raaa: / — jWi=3,36; 2 — 2,75; 0=90°; C,
PHC. 4. O6o6meHHan 3HaMeHiin KO3<p<pimHeHTa
B nonepeMHOM ceieHHH con^a 33 OTBepciHeM aaysa
HecMOipa Ha anaHHTe^bHoe ynpomeHne peiueHHH saaawn B BHfle (7)
(B cmiHiHe or (6)) , npeacraBJieHHe peay^bTaiOB SKcnepHMeHrajibHux Hcc.ie-
AOB3HHH B 3TOH (pOpMC OK33ajIOCb 3aTpyflHHT6JlbHbIM B BHfl)' CJIOJKHOCTH
Bcero nonn a B coiuie B BOSMymeHHoA sone.
llO9TOMy 33BHCHMOCTH nOfloSHOrO pOfl3 yfl3JIOCb nO.lJ'HHTb H3 OCHOB6 pe-
syjibTaroB HccJieaoBaHHH jimiib AJIH Hexoropux xapaKTepnbix sHaqeHHH a B
BOSMyiUCHHOH 30H6, 3 HC fl^H BCCFO HO^H K03(})4)HUHeHTa TeiLnOOSMCHa.
Ha PHC. 3 npHBoaH^HCb HeKOTopwe pesyjibiarbi HCCJieaoBaHHfi aji£
CHMaJIbHOPO 3H3WCIB1H OTHOCHTCJIbHOro K03(p(})HUHeHTa TenJIOo6M6Ha
nepea ctpyeABflyBa fl^H M2= 1 H
6blTb annpOKCHMHpOB3HU 33BHCHMOCTbK)
= 90°. STH pesyjibiarbi Moryr
= 1 M?-35 [ . P^« . -- 0,19 I"'"5 .[ P,<?(*i)- IHJI. J .(10)
amax nepea crpyefl onpeflejiHercH cooTHouieHHew
' rf.
-=0,2-1-0,25, (H)
rae xm — KoopflHHara TOHKH c
796 0. r. EuKupoe, 3. r. LUauxyrduMOB
MaKCHMa.HbHUH KCOtJHpHUHCHT TenJIOoSMCHa B BOSMyiUCHHOH 30H6 B
npoHSBOJibHOM noncpeiHOM ceqeHHH conjia 3a oTsepcTHeM
ercfl no cooiHOiueHHio
-o.i (12)
pesyjibTarb! sKcnepHMeHTaflbHux HCC-ieflOBaHHH KHR x ^ 0, p =
= 90°, Mj = 1 (CM. PHC. 4). Sflecb ax = aja^^ a ox — MaKCHManbHHH no
BeflHHHHC OTHOCHTevlbHHH KOSlJxpHUHeHT Ten^OOSMCHa B npOH3BO;ibHOM CCMCHHH
corma 33 oreepcTHeM BAysa.
B COOTHOUjeHHHX (10) H (12) BCT OTCyTCTByCT, T3K K3K H3 flSHHOH CT3-
HCCJieflOBaHHH BJiHHHHC 3TOPO napsMeipa He Hsynajiocb.
33BHCHMOCTH MOFyT SblTb HCnO.1b30BaHbI npH Opr3HH33UHH
coneji, HMeiomiix CHcreMU BTOPHMHOFO Bflysa rasa
ynpaBJieHHfl BCKTOPOM THPH.
a — KosijxJ'HUHeHT Ten.noo6.MeHa; x — paccroHHHe OT oMbiDaeMoro HOTOKOM xopua
crep>KHH ao npousBo.ibHofi TOHKH B T&ne; xi — Koop^HHara TOMKII na nosepxHOCTH coiuia,
OTCiHTUBaeMaa no oCpaayioiuei'i OT nonepeiHOro ceieHHH, npoxoaamero qepea uenip
OTBepcTHH mix Bflyaa; (pi — ueHipa.ibHbifl yro.n Meway ofipasyromHMH noBepxHOCTH conJia,
npoxoflHuyiMH wepes uenrp OTBepcTHH Baysa H npOHSBO.ibHyio TOMKy; T — BpeMH; P— flas-
^enHe; T—reMneparypa; W — CKOpoctb; p — njiOTHocTb; cp—renjioeMKocTb npn nocro-
HHHOM aaB^eHHH; m — Macca; F — n.iomaab; G — ceKyHAHufi pacxoa rasa; a, 'f., r\ — KO-
3<J)(})HUHeHTbi re.vnepaTyponpoBoaHocTii , renjionpoBoaHOCTH H AHHaMimecKofi BSSKOCTH;
.£), d — flHainerp; / — naiwa; R H k — raaosan nocTosiHHan n noxasaTe-ib aaHaCaibi; p H
Y — ynvi B^VBa H yro.i pacraopa KOHHnecKoro coiua; r — o6mee MHC.IO 6espa3MepHbix KPH-
TepHea; n — oCwee HHCJIO napaMerpoB; m'—qncio HesauHCHMHx CAHHHU H3MepeHHa; Re,
Pr, -Nil, Bi, Fo, Fr, Sh, M — THCJia PefiHo;ib,aca npanflTJifl, Hyccevibra, BHO, <t>ypbe, *py-
.aa, Crpyxa-na, Maxa; HHaeKcu: 0 — HaqaJibHbie napaMerpu, napaMerpu npn OTC>TCTBHH
aaysa rasa B con.no; 1,2*, CT,— napaMerpu OCHOBHOPO noiOKa, BflysaeMOH ctpyn, ropMO-
s<eHHH, creHKii cooTBeTCTBeHHo; max — MaKCHMa^bHoe SHaneHHe; e, x — napametpbi BOC-
CTaHOB.16HHH H B HpOIISBOjlbHOM HOnepeHHOM CCqCHHH COIUia.
Nomenclature
a, heat transfer coefficient; x, dinstance from streamlined rod end face to any point of
body; x-t, coordinate of point on nozzle surface calculated along generatrix from cross-
section passing through centre of orifice for blowing; q>i, central angle betweengenerating
nozzle surfaces passing through- centre of orifice for blowing and any point; T, time; P,
pressure; T, temperature; w, velocity; p, density; Cp, heat capacity at constant pressure;
m, mass; F, area; G. gas flow rate per second; a, X, T), thermal diffusivity, thermal con-
ductivity and dynamic viscosity; D, d, diameter; /, length; R, k, gas constant and adiaba-
tic exponent; p\ Y, blowing angle and apex angle of conic nozzle; r, total number of
dimensionless criteria; n, total number of parameters; m', number of -independent measu-
ring units; Re, Pr, Nu, Bi, Fo, Fr, Sh, M, Reynolds, Praridtl', Nusselt, Biot, Fourier,
Froude, Struhal and Mach numbers; Symbols 0, initial parameters, parameters with no
gas injection into nozzle; 1, 2, *, CT, parameters of main strea, injected jet, stagnation
and of wall, respectively; max, maximum value; e, x, recovery parameters and those in
any cross-section of nozzle.
Figure Captions
Fig. 1. Variation of heat transfer coefficient along nozzle length with sonic jet injec-
tion through round hole.
Fig. 2. Distribution of heat transfer coefficient in nozzle cross-section Jr1/d2=4.1 for
MI =2.72 with "gas injection.
XX" i!
fl-
2)
10
IH
J-
OcodeHHOcru ren/ioo6MCHa e odAccru edyea e ceepxaoyKoeou norOK 797
Fig. 3. Maximum heat transfer coefficient before injected jet versus relative flow rate
of gas injected.
Fig. 4. Generalized relationship for maximum value of heat transfer coefficient in
nozzle cross-section behind injection hole.
Summary
Heat transfer coefficient when gas is blown into a nozzle has been studied experi-
mentally. To determine local values of a, the method of investigating unsteady-state heat
conduction in a semi-infinite rod described by relationships of types (1) and (2) has been
used. In Fig. 2 a typical picture of heat transfer distribution in a_disturbed region is
shown. In Fig. 3 experimentally is plotted the maximum value of amai versus process
parameters. This dependence may be presented as (10). The maximum value of a in
some section behind the blowing orifice is determined by (12) obtained by mathematical
treatment of experimental data.
JlMTepaiypa
1. U, ii p e .1 b M a H H. M., B a K H p o B <J>. f., LU a ft x y T A H H o B 3. F. H<lvK, 24,jfc 2, 1973.
2. Jl hi K o B A. B. «TeopHH Ten.ionpoDOjHocTii. M., iBtJcman uixo.na*, 1967.
3. r ji a r o a e B A. H. H ap. MSB." AH CCCP, M>KP, Xs 3, 1967.
4. B o H T e H K o fl. M. H ap. MSB. AH CCCP, MXF, N<> 1, 1966.
5. H H f l x e M fl. A. PaKCTHaa Texmina H KOCMoHasTiiKa (nepeaoa), 3, Ns 4, 1965.
6. P y x w a H A. A. BseaeHHe B reopmo noaoGim. M., «Bucman mno.na>, 1967.
[7.VIII 1972 r.] UHCTUTI/T UM.
e.


Characteristics of heat exchange in the region of injection into a supersonic high-temperature flow

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