Rocket Theories Continued

Transcription

1 38

2 Rocke Theories Coninued and Nozzle heory fundamenals

3 Various Liquid Proellans and heir yical Characerisics Pro Ox/F Thrus I s P c C F V * raio Vac SL Vac SL Vac (kn) (kn) s s bar m/s Lox/LH Lox/LH small big Lox/Ker big Lox/Ker small 3

4 Solid Rocke Performance Parameers Proellan weigh flow rae, W A b ρ G r G where, A G Area of grain burning surface b r Burning rae (linear) ; ρ G Densiy of he grain Burning rae of a roellan grain may be given as n b r is in cm/sec b r a where Combusion chamber ressure, and, a and n are burn or combusion indexes for he grain alernaely b x + y n r 0<n<08, always n<0 X and Y are burn consans 4

5 Now : Proeller mass burn mass increase in he comb chamber + gas flow in nozzle W A b ρ G r G d d g ρ v + AP R T g + ( ) where A is he nozzle hroa area Now if mass variaion inside he combusion chamber is considered zero hen, d d v ρ 0 ( ) + g g 5

6 Hence, + + n A g G P g P g A ρg r RT g + ρg a RT g + g g g Simlified exression A G A P n or, P n A G A This exression means ha if n is large, variaion of burning surface A G will have large effecs on he chamber ressure and on he roellan burning rae Thus, n should be low 6

7 Burning rae and Erosion : n Simlified reduced order model br ap and is no fully reresenaive of various hysical facors Burning Rae f (Chemical comosiion, geomerical shae, iniial emeraure, fabricaion rocess, radiaion, gas velociy on he surfaces, burning ime) The combined effec of all hese facors involving hysical and chemical ineracions need o be aken ino aoun Erosive burning is he erm used o indicae ha he burning rae of a solid roellan is affeced by he flow of high velociy gases arallel o he burning surface I is more ronounced a he beginning 7

8 Following general oins are relevan o he solid roellan grain design and rocke erformance: The combusion ressure is no uniform along he lengh of he chamber wih he fases burning rae near he fron end Because of various ressure losses, acual chamber ressure a he nozzle enry is less han he heoreically comued value The ressure and burning rae a any of one saion will vary wih ime of burning as crosssecional area increases 8

9 Burning characerisics of Solid Grain Pressure or Thrus Regressive burning : During which, hrus, CC ressure and surface area decrease mos of he ime Neural Progressive burning : During his Thrus, CC ressure and Burning surface area increase mos of he ime Neural Burning : Thrus, CC Pressure and Burning surface area remain arox consan Time 9

10 Solid Proellan grains 0

11 Rocke Nozzles Mos rocke nozzles oerae wih ressure raios above 5 or 30, or uo 00, and hence, all are convergen divergen yes Thus he condiion a he nozzle hroa is criical a all imes of he oeraion of he nozzle Since his criicaliy decides he mass flow hrough he nozzle and hence he hrus roduced, he geomery of he nozzle mus be such as o romoe required amoun of mass flow hrough he nozzle a all oeraing condiions The nozzles are generally fixed geomery ye There are some nozzles which can be swiveled o roduce change in direcion of he hrus roduced

12 Tyical nozzle flow characerisics

13 Rocke Nozzles The effec of underexansion is reducion in he exhaus velociy and herefore lowering of exi kineic energy and lowering of hrus roducion Overexansion roduces searaion inside he nozzle, as he flow comlees he exansion rocess when i is sill inside he nozzle, and ofen exeriences a searaion hereafer The direcion of hrus roduced is no alered by he flow searaion in he nozzle, if he flow searaes symmerically over he cross secion around he nozzle surface Searaion ours when he ambien ressure is 5 o 35 imes he nozzle inside wall ressure 3

14 Rocke Nozzles A nozzle, is ofen designed for full exansion a a high aliude, and is likely o give higher han he ideal hrus a sea level (where ambien ressure is high) The characerisic velociy V * of he rocke, (lec-37), is indeenden of he nozzle shae and is deendan on he fuel and oxidizer characerisics, combusion chamber design and he hermodynamic arameers afer combusion However, he definiion imlicily assumes fully exanded ideal nozzle flow 4

15 Rocke Nozzles Mos nozzles are of circular cross secion, bu of various shaes Diameer of he subsonic ar of nozzle is governed by (i) volume for combusion (liquid rocke), (ii) size of he grain (solid roellan rocke), (iii) size and arrangemens of injecors (liquid roellan) The sloe of he convergen nozzle is no imoran The lengh and he shae of he nozzle is rimarily decided by he hroa area and he exi area and he velociy variaion wihin i Thus he design of a rocke nozzle essenially means deermining he lengh and shae of he divergen ar of he nozzle 5

16 Rocke Nozzles The selecion of a suiable divergence shae (configuraion and angle of divergence) is made wih following crieria: i) Large divergence angles make he nozzle shor hence give low fricion loss ii) Small exi diameer gives low aerodynamic drag of he vehicle, bu increases nozzle lengh & surface area and hence weigh of he rocke 6

17 Rocke Nozzles iii) Large divergence angle near he nozzle exi roduces radial comonen of he flow, which is a no a hrus roducing flow comonen and is, hus, a loss iv) Large divergence may also roduce searaion and relaed loses near he exi v) Long nozzle (wih low divergence angle) is difficul o incororae in he rocke body 7

18 Rocke Nozzles From Isenroic flow equaions : Pressure raio across he convergen ar of he nozzle is Temeraure raio across he convergen ar of he nozzle 3 x e + + 8

19 Rocke Nozzles Velociy anywhere in he convergen nozzle V x c ( T 03 T x ) + V R( T03 T x ) + V R T 03 P P x 03 + V 9

20 Mass Flow, Velociy a he hroa T R R T V + R T A V A m ρ + + Rocke Nozzles 0

21 Rocke Nozzles In he divergen ar of he nozzle Area Raio A Vxν + + x + Ax V νx + Velociy raio V V x + x

22 Rocke Nozzles Thrus Co-efficien Thrus e a e e A A F ) ( e a e e F A A C e a e e A V V A F ) ( + ρ

23 Rocke Nozzles 3

24 Saurn Rocke Launch 4