Lecture # 12: Shock Waves and De Laval Nozzle

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1 ArE 311L & ArE343L Lctur Nots Lctur # 1: Shock Wavs and D Laval Nozzl Dr. Hui H Hu Dpartmnt of Arospac Enginring Iowa Stat Univrsity Ams, Iowa 50011, U.S.A

ArE311L Lab#3: rssur Masurmnts in a d Laval Nozzl Tank

Distanc downstram of throat (inchs) Ara (Sq. inchs) 1-4.

15 0.497 7 0.30 0.518 8 0.45 0.539 9 0.60 0.560 10 0.

2 ArE311L Lab#3: rssur Masurmnts in a d Laval Nozzl Tank with comprssd air Tst sction Tap No. Distanc downstram of throat (inchs) Ara (Sq. inchs)

3 1st, nd and 3 rd critic conditions st critic condition 0 incrasing 1st critic condition 0 incrasing 3st critic condition

ArE311L Lab#4: rssur Masurmnts in a d Laval Nozzl 1. Undr-xpandd xpandd flow. 3rd critical 3. Ovr-xpandd xpandd flow with obliqu shocks 4. nd critical 5. Normal shock xisting insid th nozzl 6.

4 ArE311L Lab#4: rssur Masurmnts in a d Laval Nozzl 1. Undr-xpandd xpandd flow. 3rd critical 3. Ovr-xpandd xpandd flow with obliqu shocks 4. nd critical 5. Normal shock xisting insid th nozzl 6. 1st critical Rquird lots: lots of th masurd prssur (static and total prssur) as a function of distanc along th nozzl axis for th cass, 4, 5 and 6. lots of th thortically prdictd prssur (static and total prssur) as a function of distanc along th nozzl axis for th cass, 4, 5 and 6. lots with th masurd and prdictd valus of th wall prssur distribution on th sam graphs for th cass, 4, 5 and 6 for comparison. lots of th thortically prdictd and masurd Mach numbr as a function of distanc along th nozzl axis for th cass, 4, 5 and 6.

5 1st, nd and 3 rd critic conditions nd critical shock is at nozzl xit Flow clos to 3 rd critical Ovr-xpandd xpandd flow with shock btwn nozzl xit and throat Undr- xpandd flow Ovr- xpandd flow 1 st critical shock is almost at th nozzl throat.

6 rdiction of th rssur Distribution within a D Laval Nozzl by using Numrical Approach Throat, A* or A t T1 M<1 M>1 Shock A S T1 1 T M<1 A = atm = atm Using th ara ratio, th Mach numbr at any point up to th shock can b dtrmind: A * A = γ γ γ 1 + M M γ + 1 Aftr finding Mach numbr at front of shock, calculat Mach numbr aftr shock using: M γ 1 1+ M1 = γ 1 γ M1 Thn, calculat th A * γ 1 A = M As 1+ M γ + 1 ( ) γ + 1 γ 1 which allows us calculat th rmaining Mach numbr distribution A * A = γ γ γ 1 + M M γ + 1

7 rdiction of th rssur Distribution within a D Laval Nozzl by using Numrical Approach Throat, A* or A t T1 Shock A S 1 T1 T M<1 M>1 M<1 T A = atm = atm a.for 3rd Critical

8 rdiction of th rssur Distribution within a D Laval Nozzl by using Shock Tabl Mthod Throat, A* or A t T1 M<1 M>1 Shock A S T T1 1 T M<1 A = atm = atm mthod #1, by using quations: If th shockwav is locatd at position of tab#1: Mthod #: by using Isntropic Flow proprtis tabl (Appndix-A A of Andrson s s txtbook)

9 rdiction of th rssur Distribution within a D Laval Nozzl by using Shock Tabl Mthod By using th normal shock tabls with M1 = 1.64 w find that M = (Appndix-B B of Andrson s s txtbook) Nxt, w find th sonic rfrnc ara bhind th shock using th ara-mach rlation. i.., M=0.686 (Appndix-A A of Andrson s s txtbook) Find sonic rfrnc bhind th shock using th ara-mach rlationship: i.., A*=0.557sq. Inchs If th shockwav is locatd at position of tab#1:

10 rdiction of th rssur Distribution within a D Laval Nozzl by using Shock Tabl Mthod With th xit prssur to b sa- lvl standard prssur. W now calculat th total prssur bhind th shock using this valu of xit prssur and th prssur ratio at th xit: t 1 t = = 14.7 = Our last major task is to find th total prssur ahad of th shock, t1 = t1 1 t1 t 1 t

11 Som xampls of prvious studnt lab rports Thortical Data - Gaug rssur vs. osition Gaug rssur, psi Exprimntal 1-D Thory osition along Nozzl Axis, inchs 3rd Critical nd Critical Normal Shock 1st Critical rssur (SI) Gaug rssur, psi Exprimntal Rsults - rssur vs. Nozzl Location Nozzl location, inchs 5 Total rssur = SI Distanc from Troat (in) Undr-Expandd Flow Approximatly nd Critical Normal Shock

In this lecture... Subsonic and supersonic nozzles Working of these nozzles Performance parameters for nozzles

In this lecture... Subsonic and supersonic nozzles Working of these nozzles Performance parameters for nozzles Lct-30 Lct-30 In this lctur... Subsonic and suprsonic nozzls Working of ths nozzls rformanc paramtrs for nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay Lct-30 Variation of fluid