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u QH 'CwY jwit CH VvmQOv= QHD UQQ - IAUNresearch.iaun.ac.ir/pd/hojaji/pdfs/PaperM_5938.pdf · C}ty= xm Q}PBsm=QD C*wY uwO=t |@* v=H u=}QH QO CwY jwi=t C* H l} *Ot=aDt |UQQ@ |=Q@ "CU=

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Page 1: u QH 'CwY jwit CH VvmQOv= QHD UQQ - IAUNresearch.iaun.ac.ir/pd/hojaji/pdfs/PaperM_5938.pdf · C}ty= xm Q}PBsm=QD C*wY uwO=t |@* v=H u=}QH QO CwY jwi=t C* H l} *Ot=aDt |UQQ@ |=Q@ "CU=

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32

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"CU= nQR@ |x@=OQo u}= Q}F-=D CLD COWx@ lr=@ AJ CtU|xrY=i =@ w CH x@ l}ORv |x}L=v QO Qo}O |D}akwt QO lr=@ 'xt=O= QOQO lr=@ Qw[L C=QF= =D �A3 C}akwt� OW xO=O Q=Qk uQ=kD \N R= 5D |[Qa|Q}oxR=Ov= R= pY=L G}=Dv "OQ}o Q=Qk |UQQ@ OQwt u=} QH u=O}t |wQ Q@ Cr=L u}=QO u=} QH u=O}t xm OyO|t u=Wv �?12 pmW� lr=@ CUOu}}=B QO pm Q=Wi=@ xD@r= "CU= xOWv |U=U= C=Q}}eD VwNDUO u=OvJ p@k Cr=L Ovv=t Cr=L u}=CtU |x@=OQo xm OwW|t xOy=Wt hr=10 pmW w ?12 pmW j}kO |xU}=kt"CU= xOW QDsm =QDt |mOv= w hQLvt AJ hQ] x@ lr=@ Qw[L Crax@ CU=Qw Y = 4 |xOwOLt QO CU=Q CtU |x@=OQo |=B OQ x@ u=wD|t x]@=Q u}= QOxOy=Wt ?12 pmW QO QF= u}= &OQm xQ=W= hr=10 pmW QO 6 < Z < 10

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34

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?Yv C2 C}akwt QO lr=@ xm |r=L QO 'J C=QF= |UQQ@ |xt=O= QOCUO x@ G}=Dv |xU}=kt "OW |Q}oxR=Ov= u; CUOu}}=B pm Q=Wi u=O}t 'OWQ}}eD sOa seQ|ra xm OyO|t u=Wv �15 pmW =@ 16 pmW |xU}=kt� xOt;xm xJv; hqNQ@ u=} QH |rm Q=DN=U ^iL w �3 pwOH� =yx@=OQo uwQO CPt;min

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|Q}oxH}Dv "9CH l} Ot=aDt |x}rND R= |W=v |}x@=OQo u=O}t Q@ lr=@ l} C=QF= j}kLD u}= QO|x}rND pLt CUOu}}=B QO Q}PBsm =QD CwY uwO=t |@v=H u=} QH QO CwY jwi=tu=} QH QO xOWx}rND CH w O=R; u=} QH M=t OOa "CU= xDiQo Q=Qk |UQQ@ OQwt CH"CU= xOw@ 2 5 w 0 7 =@ Q@=Q@ ?}DQDx@ w C@=F xOt; CUO x@ G}=Dv |t=tD QO O=R;|x}rND pLt x@ C@Uv lr=@ C}akwt pt=W j}kLD u}= QO |UQQ@ OQwt |=yQDt=Q=B

"Ov=|@v=H u=} QH x@ CH |m}t=v}O Q=Wi C@Uv w CHO=ODt= QO lr=@ Qw[L C=QF= xm OvyO|t u=Wv =yV}=tR; u}= R= pY=L G}=Dv|x@=OQoCiH C} wkD CQwYx@ QDW}@ CH x@ l}ORv |L=wv QO w uQ=kD |xLiY"OwQ|t u}@ R= C=QF= u}= G} QODx@CH |x}rND pLt R= uDiQoxrY=i =@ wCU= u=NQJpN=OD ?Hwt |[Qa |xrY=i l} =@ CH x@ l}ORv |L=wv QO lr=@ Qw[Lu=O}t uwQO?r=e |=yx@=OQo R=|m} uDiQ u}@ R=?Hwt R}v|y=o w 'lr=@ w =yx@=OQo|U=U= C=Q}}eD |[Qa |xrY=i u}= 'CUOQwO |L=wv QO xm |r=L QO "OwW|t|xOwD uOW QDnQR@ w |oDiW; O=H}= CQwYx@ QDW}@ w OQ=Po|tv u=} QH u=O}t Q@V}=Ri= =@ xm OvyO|t u=Wv G}=Dv "OwW|t xOy=Wt lr=@ =@ Q}oQO |x@=OQo |RmQtG} QODx@ =yx@=OQo 'CUOQwO |L=wv QO |@v=H u=} QH x@ CH |m}t=v}O Q=Wi C@Uv|m}t=v}O Q=Wi |=yC@Uv |xty QO u}vJty "Ov=xOQm Pwiv |@v=H u=} QH uwQO x@"OwW|t xOy=Wt u=vJty lr=@ =@ Q}oQO |x@=OQo |oDiW; V}=Ri= 'V}=tR; OQwt

CWwv=B1. counter rotating vortex pair (CRVP)2. trisonic

�References� `@=vt1. Dormiex, M. and Marsaa-Poey, R. \Numerical assess-

ment of aerodynamic interactions on missiles with trans-verse jet control", Computational and Experimental As-sessment of Jets in Cross Flow, AGARD CP 534, pp.30.1-30.11 (1993).

2. Cassel, L.A., \Applying jet interaction technology", J.Spacecraft and Rockets, 40(4), pp. 523-537 (2003).

3. Srivastava, B., \Aerodynamic performance of supersonicmissile body- and wing tip-mounted lateral jets", J.Spacecraft and Rockets, 35(3), pp. 278-286 (1998).

4. Brandeis, J. and Gill, J. \Experimental investigation ofsuper- and hypersonic jet interaction on missile con�g-

urations", J. Spacecraft and Rockets, 35(3), pp. 296-302(1998).

5. Graham, M.J.; Weinacht, P. and Brandeis, J. \Numericalinvestigation of supersonic jet interaction for axisymmet-ric bodies", J. Spacecraft and Rockets, 37(5), pp. 675-683(2000).

6. Margason, R.J. \Fifty years of jet in cross ow research",Computational and Experimental Assessment of Jets inCross Flow, CP-534, AGARD, pp. 1.1-1.41 (1993).

7. Kelso, R.M.; Lim, T.T. and Perry, A.E. \An experimen-tal study of round jets in cross ow", J. of Fluid Mechan-ics, 306, pp. 111-144 (1996).

8. McCann, G.J. and Bowersox, R.D.W. \Experimental in-vestigation of supersonic gaseous injection into a super-sonic freestream", AIAA J., 34(2), pp. 317-323 (1996).

9. Santiago, J.G. and Dutton, J.C. \Velocity measurementsof a jet injected into a supersonic cross ow", J. ofPropulsion and Power, 13(2), pp. 264-273 (1997).

10. Beresh, S.J.; Hen ing, J.F. and Erven, R.J. \Stereo-scopic PIV for crossplane vorticity measurement of a su-

36

Page 9: u QH 'CwY jwit CH VvmQOv= QHD UQQ - IAUNresearch.iaun.ac.ir/pd/hojaji/pdfs/PaperM_5938.pdf · C}ty= xm Q}PBsm=QD C*wY uwO=t |@* v=H u=}QH QO CwY jwi=t C* H l} *Ot=aDt |UQQ@ |=Q@ "CU=

"""w|v=]

rU=[Q

OtLt'|

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tLt personic jet in subsonic compressible cross ow", AIAA,Paper 2004-2181 (2004).

11. Beresh, S.J.; Hen ing, J.F.; Erven, R.J. and Spillers,R.W. \Penetration of a transverse supersonic jet intoa subsonic compressible cross ow", AIAA J., 43(2), pp.379-389 (2005).

12. Arabzadeh, B. and Nikoukar M. \Applied probability &statistics", 3rd Edition, Azadeh Publications, (1994).

13. Chocinski, D.; Leblanc, R. and Hachemin J., \Experi-mental/computational investigation of supersonic jet insubsonic compressible cross ow", AIAA, Paper 97-0714(1997).

14. Taeibi-Rahni, M.; Soltani, M.R. and Hojaji, M. \Investi-gation of supersonic jet into high subsonic cross ow", InProceedings of the 7th Iranian Aerospace Society Con-ference, Sharif University of Technology, Tehran, Iran(2008).

15. Hojaji, M.; Soltani, M.R. and Taeibi-Rahni, M. \Newvisions in experimental investigations of a supersonicunder-expanded jet into a high subsonic cross ow",Proc. I Mech E, Part G: J. Aerospace Engineering, 224,(2010).

16. Payne, J.L.; Roy, C.J. and Beresh, S.J. \A comparison ofturbulence models for a supersonic jet in transonic cross ow", AIAA, Paper 2001-1048 (2001).

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