1. Pressurehastheoppositeeffectontheotherendofthemassfluxspectrum.Inthe low mass-flux regime, the effect of thermal radiation becomes important because the heat flux due to turbulent convection is relatively small. As the product of pressureandmotorinnerdiameter(pD)increases,theeffectofradiationbecomes more prominent at a given mass flux. The pD term gives a measure of the gas optical density as described by Incropera and Dewitt [52]. When pD is high, the gas emits thermal radiation more efficiently and the regression rate increases to highervaluesthanpredictedbyclassicaltheory.Marxman[9-11],Esteyetal.[13], Strandetal.[14],andChiaverinietal.[15,16]investigatedthisbehavior.Similar Pressure x Diameter
2. Wenowturnourattentiontothefuelregressionratebehaviorofvarioustypesof non-classicalhybridmotors,includingswirl-injectedhybrids,vortexhybrids,endburninghybrids,radial-flowhybrids,andhybridsemployingcryogenicsolidfuels or paraffin-based solid fuels. In most cases, these hybrids have been introduced fairlyrecently(circamid-1990s)withtheobjectiveofeitherincreasingfuelregressionratestoimproveoverallperformanceanddesignflexibilityorofdevelopinga uniquemotorgeometryforaparticularapplication.Wewillfirstexaminevarious typesofhybridsthatemployuniqueinjectionmethodsandgraingeometries,such asswirl-injectedhybridsandend-burninghybrids.Afterward,high-regressionrate solidfuelssuchasparaffin-basedfuelsandcryogenicsolidfuelswillbediscussed. For completeness, the regression rate behavior of metallized solid fuels will be reviewedbriefly,althoughinChapter 10thistopic is discussed in more detail. A. HybridMotorswith Unique Injectorsand Fuel Grain Geometries
3. Motivatedbythedesiretoincreasefuelregressionratesforobtainingvolumetricallyefficientfuelgraindesigns,Knuthetal.atOrbitalTechnologiesCorporation [ORBITEC] experimented during the mid-1990s with laboratory-scale vortex hybrids wherein the swirl oxidizer injector was located at the aft end of the fuel grain just upstream of the converging portion of the exit nozzle. Figure 20 is a schematicofoneoftheirtestmotors.Knuthetal.discoveredthatthisarrangement generatedapairofcoaxial,bidirectionvorticesinthecombustionport.Theouter vortex spiraled toward the head end of the motor across the fuel surface, mixing and burning with the pyrolyzed fuel. At the head end, the vortex flowed inward toward the motor axis and formed an inner vortex that spiralled downward and outthenozzle[53].Figure21showsavelocityvectorfieldinthemeridonalplane generated from numerical simulations of a 500-lbf thrust vortex hybrid burning GOX and HTPB using the Finite Difference Navier Stokes (FDNS) code [54]. The numerical simulation captured the salient features of the bidirectional vortex flowfield including the upward-flowing outer vortex and the downward-flowing inner vortex. Note that the swirl velocity is not apparent in this sectional view of thegrainchamber.Vortexhybridflowfieldcharacteristicsarefurtherdiscussedin Chapter6.