Computational and Experimental studies on Aerospike Nozzles1. INTRODUCTION1.1 BackgroundSingleStagetoOrbit (SSTO) missionsdemandits engines tobeoperatedat varyingbackpressure conditions as it has to operate from ground to vacuum. Generally engines operating athigh combustion chamber pressures (more than 100bar) ith moderate area ratios (!" #0$%0)areusedfor this purpose& asthis ensures that theno''leflos full duringlift off andtheatmospheric flight. (onventional bell no''le ith fi)ed area ratio orks efficiently at a particular altitude here e)itpressure e)actly matches ith the back (ambient) pressure causing e)haust to perfectly e)pandedthereby ma)imi'ing efficiency and thrust. !t loer altitude here ambient pressure is higherthanthee)haust pressure& theambient air pushes thee)haust air inardhichcauses theseparation of flo from the boundary of no''le all thereby decreasing thrust and efficiency.Thisconditionisalsoknonasovere)pansion.!thigheraltitudehereambientpressureisloer than the e)it pressure hich is knon as undere)pansion. !mbient air causes e)haust toflo past the no''le e)it. Since the additional e)pansion occurs outside of the no''le& it does note)ert thrust on the no''le& so that thrust is lost. Figure 1: Overexpanded and Underexpandednozzle [1]IIST Thiruvananthapuram2011 Page 1Computational and Experimental studies on Aerospike NozzlesSince& both overe)pansion and undere)pansion reduce overall engine efficiency and thrust& forma)imi'ing thrust and efficiency& the concept of an ideal no''le has been contemplated*+,.-dealno''le increases its e)it area ratio such that e)it pressure e)actly matches ith ambient pressureasrocket ascends.Thusanideal no''leouldbeabletocontinuallyad.ust itsarearatiotoma)imi'e thrust at each altitude& knon as altitude compensation. /ractically it is not possible todesign a bell no''le hich changes its geometry during the flight. !ero0spike no''le is the otheroption here the flo is adapted to the ambient conditions at all altitudes& by virtue of the no''leconfiguration as this provides the altitude compensation at least in theory.The aero0spike no''le is a truncated spike (or plug no''le) that adapts to the ambient conditionsso that it ensures that the e)haust .et flos full during most part of the operational regimes byoptimal e)pansion at each altitude. !t high altitudes& the no''le flo leaving the truncated spikecreates aclosedake& calledanaerodynamicspike*+,. 1hentheakeis closed& thebasepressureandthecontributionofthebaseregiontotheaero0spikethrust areindependent ofaltitude and hich is desirable in altitude compensation.Figure 2: Schematic of flow in Aeropi!enozzle["]!t lo altitudes high ambient pressure forces the e)haustplume inard increasing the pressureonthe !erospikeno''lecontourandthethrust.!t designpressuretheflobecomescolumnshaped& much like a bell no''le. !s the rocket climbs to higher altitudes& the air pressure holdingthe e)haust against the spike decreases& but the pressure on top of the engine decreases at thesame time. 2oeverthe recirculation 'one keeps the pressure on the base up to fraction of 1 bar&IIST Thiruvananthapuram2011 Page 2Computational and Experimental studies on Aerospike Nozzlesapressurethat isnot balancedbythenearvacuumontopoftheengine3 thisdifferenceinpressuregivese)trathrust at altitude& contributingtothealtitudecompensatingeffect. Thisproduces an effect like that of a bell that gros larger as air pressure falls& providing altitudecompensation. Thus in theory at least& the aerospike no''le meets or e)ceeds the performance ofthe bell no''le at all operating pressures*4,.The altitudecompensation feature and thrust vectorcontrol is provided under minimum re5uirements for geometric variations and no gimbaling ofthe no''le and are the main discriminating features of the !erospikeengine.-t also fits ell intotrailing edge of a inged or lifting type vehicle and often has less engine and structural mass.2oever&thereali'ationofaerospikeno''lefacesmanyhurdlesduetoitsaerodynamicandstructural design considerations. To contain the e)treme heating loads on the annular throat andno''le& a combination of regenerative cooling& film cooling and dump cooling using hydrogenhas to be employed. !lso the thrust prediction remains a challenge as the no''le plume shapesvary ith the back pressure conditions here the conventional thrust e5uations fail to predict thethrust. /erformance validation is not yet done& although e)periments are being done around theorld.6)periments andstudies on!erospikeengineerestartedin7Sinearly1890but thrustachieved by !erospike engine as roughly e5ual to the bell no''le. -n 1880 !erospike engine isconsidered as potential engine for:!S!;selocity at e)it is found from Aach number and temperature at e)it by isentropic relationsUe= 2++1 )To[1( pe"o)+ 1+]Thrust for ideal no''le is ' = !c(ockedUe=t "0(2++1)+ +1+1 2 +2+1 [1( pe"o)+1+](alculation of thrust shos that thrust is not dependent upon total temperature& hoever the value of ratio of specific heat is dependent upon temperature& therefore calculation done ith considering total temperature =00 I for thrust calculation ill somehat less than the total temperature 0f =900 I.Thrust coefficient for ideal no''le is C'='"o

t=(2++1)+ +1+ 1 2+2+1 [1( pe"o)+1+]IIST Thiruvananthapuram2011 Page 12Computational and Experimental studies on Aerospike Nozzles(oefficient of thrust is calculated for an ideal no''le having chamber pressure e5ual to 90 bar forvarying e)it pressure ith change in time and tabulated for the comparison ith three no''les taken into consideration.,.iscous force by ambient fluid particle is ignored3 hoever it can be calculated by e)ternal flo simulation1. Force on inlet all can be calculate by multiplying surface area ith chamber pressurec(a!$e &fo&ce=60*105*0.1570797=942477.8,ewtons+. Forces on alls 4& %& 11& 14& +%& += can be computed by Fluent& and e can call it Fluid_Force.=. !mbient force can be ritten asJ!$ien tfo&ce=(-nleta&ea+Spikea&eaX+.asea&ea)"a!$ientThe area of spike on O0P plane is calculated by pro.ecting area of spike and from geometry it canbe calculated as&easpike X=/ *( 0. 47520.3722)=0.274075684 !2Therefore ambient force in