Small Combustion Chamber. Combustion chamber area ratio
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1 Lsses & Real Effecs in Nzzles Flw divergence Nnunifrmiy p lss due hea addiin Viscus effecs bundary layers-drag bundary layer-shck ineracins Hea lsses Nzzle ersin (hra) Transiens Muliphase flw Real gas prperies Nnequilibrium flw Lsses and Real Nzzle Effecs - Small Cmbusin Chamber Cmbusin chamber area rai cc A cc /A If cc < 3-4 hen Mach number in cmbusin chamber high and can resul in significan p lss (Rayleigh flw) <0 >0 dt ideal, cnsan area dp = M e.g., fr =., M=0.5 pressure lss is ~5% f emperaure increase Lwer p means lwer I sp and less ṁ p p Lsses and Real Nzzle Effecs -
2 Flw near wall slwer han freesream als hermal b.l. Bundary Layers subsnic b.l. Displacemen hickness ne effec is less area available freesream e.g., A effecive < A gem ṁ drp supersnic b.l. can esimae frm chked nzzle discharge cefficien Q T vel. shear y cmpressible heaing y Lsses and Real Nzzle Effecs - 3 Displacemen Thickness Esimae Chked nzzle discharge cefficien C D Lsses and Real Nzzle Effecs - 4 m m fr R C acual ideal R A effec A D R Tang and Fenn, AIAA J 6, 978, p C D 3.66 R R D C R = R Re = Re Reynlds N. a hra radius curvaure a hra.8 = Re Re R R
3 Displacemen Thickness Example Typical values H /O prducs a 000 psi, 000 K (340 F) ~ m /s, ~., R /R ~O(), R ~3 Re~O(0 7 ) C D small mass flwrae change <0.%R even if Re0 (p,r, ) hin B.L. a hra Lsses and Real Nzzle Effecs - 5 C D C D /R E+05.E+06.E+07.E+08.E+09 Re ' /R Bundary Layers Viscus Drag Viscus drag a walls lwers u (decreases p ) shear usually small effec n axial hrus unless very lng nzzle (usually << p) resul shwn fr runcaed bell nzzle frm Hill and Peersn L/D Lsses and Real Nzzle Effecs - 6 < -.5 % lss in, I sp 3
4 Bundary Layers Shck Ineracins shck Can lead unseadiness and flw separain p a infrmain can prpagae hrugh subsnic b.l. shck-induced b.l. separain frm Hill and Peersn Lsses and Real Nzzle Effecs - 7 Bundary Layers Shck Ineracins Can imprve c fr verexpanded bell nzzles by increasing pressure n nzzle walls frm Hill and Peersn Lsses and Real Nzzle Effecs - 8 p /p a 4
5 Hea Lsses and Ersin Hea lsses frm nzzle will end lwer u e, I sp less enhalpy available fr cnversin kineic energy Q u e h h e Ersin (hermal and chemical) ms significan near hra highes emperaure, harder cl will increase ṁ wih ime, als reduces Lsses and Real Nzzle Effecs - 9 Transien, Unseady Flw Significan ransiens (d/d 0) end lwer hrus f nzzle cmpared seady value unseady pressure and mass flw rae Can ccur during sar up, shu dwn hruser pulsing cmbusin insabiliies in c.c. Lsses and Real Nzzle Effecs - 0 5
6 Muliphase Flw Flw in nzzle includes cndensed phases (liquid r slid) alng wih gas Al O 3 in slid prpellans, s fr HC fuels cndensain a lw T fr sme prpellans Cndensed phases d n prvide expansin (heir densiy is ~cnsan) lwers I sp vs same mass f gas Larger lss if vlume fracin f paricles size f paricles Bu can increase ṁ. paricles lag gas, drag n gas. slwer give up heir hermal energy Lsses and Real Nzzle Effecs - 6
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