A JTA A _ A98-35064 AIAA 98-3188 FUEL REGRESSION RATE ENHANCEMENT STUDIES IN HTPB/GOX HYBRID ROCKET MOTORS Philmon George and S. Krishnan Department of Aerospace Engineering Indian Institute of Technology Madras Chennai - 600 036, INDIA P. M. Varkey and M. Ravindran Vikram Sarabhai Space Centre Thiruvananthapuram - 695 022, INDIA and Lalitha Ramachandran Liquid Propulsion System Centre Thiruvananthapuram - 695 547, INDIA 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit July 13-15,1998/Cleveland, OH For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
AIAA 98-3188FUEL REGRESSION RATE ENHANCEMENT STUDIES IN HTPB/GOX
HYBRID ROCKET MOTORSPhilmon George* and S. Krishnant
Indian Institute of Technology Madras, Chennai - 600 036, INDIAP. M. Varkey* and M. Ravindran*
Vikram Sarabhai Space Centre, Thiruvananthapuram - 695 022, INDIAand
Lalitha Ramachandran*Liquid Propulsion System Centre, Thiruvananthapuram - 695 547, INDIA
AbstractThe results of a systematic experimental
investigation on the methods of enhancing theregression rate in hydroxyl terminated polybutadiene(HTPB) fuel used in HTPB/gaseous oxygen hybridmotor are presented. The effects of the addition ofammonium perchlorate (AP) or aluminum in the fuel,the variation of oxidizer-fuel ratio, and the variation ofcharacteristic dimensions of fuel grain are presented.While the addition of AP and/or Al, and the reductionof grain port diameter enhance the regression rate, theeffect due to the latter is the most significant one.Furthermore, the regression rate increases along theaxis and it becomes essentially constant in the portregion corresponding to a fuel rich composition. Thepossible physical processes for all these behaviors arediscussed. The experimentally obtained exponents ofthe variables namely, oxidizer mass flux and portdiameter, are found to be significantly different fromthose of the widely accepted Marxman equation for theregression rate. The similarity between the fuelregression rate equation used in solid fuel ramjet andthat obtained in hybrid motor is brought out.
A,B
*cCdD
G
LLemrhPr
Nomenclature= nozzle throat area, m2
= mass transfer number= characteristic velocity, m/s= coefficient of discharge= spatially averaged instantaneous port
diameter, m= total mass flux, kg/m2s= spatially averaged instantaneous oxidizer
mass flux, kg/m2s= fuel grain length, m= Lewis number= mass, kg= mass flow rate, kg/s= Prandtl number
regression rate, m/sf = spatially and temporally averaged
regression rate, m/sR = gas constant of oxygenT = oxygen temperature, KAt = time increment, sx = axial distance, mO = oxidizer-fuel ratiop = fuel density, kg/m3
y = specific heat ratio of oxygenT| = combustion efficiencyp. = viscosity, kg/ms
Subscriptc = aft combustion-chambereff = effectivef -fueli = igniter, instanto = oxidizers = sonic nozzlet = total
IntroductionThe dependence of solid fuel regression rate on
various operating conditions is one of the mostimportant design aspect in the study of hybrid motors.
Marxman and co-workers1"3 developed a turbulentboundary layer regression rate model based on the heattransfer mechanism. They assumed that the regressionrate was controlled by the heat transfer mechanism tothe fuel from the flame front that existed within theturbulent boundary layer. They used the Reynoldsanalogy and the approximation that Le = Pr = 1. Theimportant result of this model study is that theregression rate is 1) a strong function of the total mass
Research Scholar, Department of Aerospace EngineeringProfessor, Department of Aerospace Engineering. Associate Fellow AIAA
1American Institute of Aeronautics and Astronautics
-,0.8Nflux (r oc G ), 2) independent of the pressures atmotor operating conditions (the combustion beingdiffusion limited at high pressures), 3) a weak inversefunction of the axial distance (f oc x~°'2), and 4) a weakfunction of the properties of fuel and oxidizer (heat ofreaction and heat of gasification, f oc B°'23). The firsttwo points of this result were validated by the spatiallyand temporally averaged regression rate ( r ) resultsobtained by them (weighing the grains or measuringthe grain-dimensions before and after the tests). Theyexperimented with polymethylmethacrylate (PMMA),polyurethane (PU) and polybutadiene-acrylic-nitrile(PBAN) as fuels and gaseous oxygen as oxidizer.1'4 Aqualitative argument for the satisfaction of third pointwas presented from their experimental results.However, their experimental program did not addressthe validation of the fourth point. Furthermore at lowerpressures (< 1.0 MPa) they observed experimentallythe pressure dependence on regression rate: rdecreased as pressure was decreased. This observationcould not be "captured" by their basic heat transfermodel. They later argued that at lower pressures theregression rate could be dominated by the gas phasechemical kinetics rather man the heat transfermechanism. The basic theoretical and experimentalresults are summarized by Marxman and Wooldridge.The design aspects of hybrid motors from their studiesare summarized in Ref. 5.
The complete modeling of hybrid motorcombustion is quite complicated due to variousphysical and chemical processes. The model has toconsider in a fuel grain passage a reacting flow createdby the two distinctly different fluids: one, the mostly-vaporized-oxidizer entering the fore end of the fuelgrain passage and the other, the fuel vapor blowingfrom the passage-wall. The boundary layer growingfrom the fore end of the passage contains the diffusionflame front within. Fuel is vaporized as a result of theheat transferred from the flame front to the fuelsurface. The fuel vapor convects towards the flamefront while the oxidizer from the free stream diffusesinto the boundary layer also towards the flame frontfrom the opposite direction. Furthermore, at motoroperating conditions characterized by high Reynoldsnumber a finite flux of unreacted oxidizer to the fuelwall could exist through the mechanism of bulkturbulent eddy transport across the flame. The flamefront is established at a location within the boundarylayer determined by the stoichiometric conditionsunder which combustion can occur. The thickness ofthe flame is determined by the reaction rate at whichthe oxidation can occur. This rate is mainly dependenton pressure and typically follows an Arrheniusrelationship. However, this is unimportant for thelocation of the flame front as diffusion rate is lowerthan reaction rate. The primary mechanism of heattransfer to the fuel surface is by convection andradiation. There is a strong coupling between theconvective heat transfer and the rate of fuelvaporization ("blowing" rate) since the blowingdecreases the convective heat transfer to the fuel
surface. There is also an indirect coupling between theconvective and radiative heat transfers because thelatter tends to increase the blowing rate which in turntends to decrease the convective heat transfer. At thefore end of the grain the free stream consists of pureoxidizer at a low temperature. Along the fuel grainpassage the oxidizer concentration decreases and thetemperature increases. With the two zones on eitherside of the flame front, vitiated by the combustionproducts, the combustion, though stoichiometric, isoccurring drawing the increasingly "diluted" oxidizerand fuel-vapor along the grain. Since the oxidizerconcentration reduces along the passage, the diffusionflame within the boundary layer moves away from thefuel surface. In the limit, if all the available oxidizer isconsumed at a location along the grain passage,theoretically no flame can exist downstream of thislocation. However, the heat transfer to the fuel surfacewill continue from the hot combustion productscausing the continuance of fuel vaporization. In theabsence of any combustion downstream of the location,the blowing fuel vapor will only cool the passage flow.
Smoot and Price made significant contributions tothe data on hybrid fuel regression rate essentially atlow pressure conditions (< 1.2 MPa). Theydemonstrated the dependence of regression rate onoxidizer mass flux as well as pressure. Butyl rubber,PU, and butyl rubber with lithium hydride were thefuels and the mixtures of fluorine-oxygen and fluorine-nitrogen were the oxidizers. The measurements atdifferent pressures (0.24 - 1.2 MPa) and differentoxidizer mass fluxes (10 < G0 < 120 kg/m2s) showedthat 1) at low oxidizer mass fluxes (< 25 kg/m2s) r isG0 dependent (f oc G°'8) but pressure independent; 2)at high oxidizer mass fluxes (> 70 kg/m2s) it is G0
independent but pressure dependent ( f increases withp); and 3) at intermediate oxidizer mass fluxes,however, f is G0 as well as pressure dependent. Theyattributed the pressure dependence to the rate limitingchemical kinetic processes, possibly heterogeneous innature. Therefore the classical turbulent boundary layerregression rate model based on heat transfermechanism was extended to include the effects ofcondensed phase surface products. Agreement wasgood for low oxidizer mass fluxes but the extendedmodel did not account for the observed pressuredependence for intermediate as well as high G0's.
Muzzy,9 after discounting the possibility of ratelimiting heterogeneous chemical kinetic processes atgas-solid interface, considered the influence ofchemical kinetic processes in gas phase that cannot beneglected for the conditions of low pressures and/orhigh total mass fluxes. He showed throughcalculations that, at low pressure conditions, theregression rate was not that strong a function of totalmass flux and was dependent also on pressure (r ocG°'4 p°'5). Additionally, through experiments, heshowed that the regression rate was essentiallyindependent of the temperatures of the fuel grain andthe oxidizer. Kumar (Ramohalli) and Stickler10
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developed a theory based on the differences in polymerdegradation behaviors in inert and non-inertenvironments to account for the pressure dependenthybrid combustion. They argued that, under allconditions, a finite flux of unreacted oxidizer gas tofuel wall could exist through the mechanism of bulkturbulent eddy transport across the flame front. Theyconcluded that the observed pressure dependence onregression rate at low pressure/high mass fluxconditions could be due to the fuel wall oxidative(catalytic) depolymerization, which aids thermaldegradation in producing vaporizable fragments.
Paul et al." conducted experiments on rubber/oxygen + nitrogen system and found that the exponenton B is 0.5 instead of 0.23 the value theoreticallyobtained by Marxman and coworkers.1"3 Hence they,after accounting for the density variation across theboundary layer, estimated the "blocking effects" — theeffects of transpiration on skin friction factor and heattransfer coefficient — and demonstrated that theregression rate was a strong function of B. Paul et al.experimentally obtained the fuel regression rates hi ahypergolic combination (difurfurylidene cyclo-hexanone/red fuming nitric acid) for different massfluxes and pressures. The regression rate was found tobe pressure independent above 1.0 MPa. Theregression rate was calculated based on the curve fit ofthe integrated regression rate expression [ f = a G0
n orf = a G" x""1 (x the axial distance)]. They found thatthe exponent n of the regression rate law was about 0.5or a little lower and not 0.8 even though the flowthrough the port was turbulent. They argued that thelower n value was possibly due to the heterogeneoussurface reaction between the liquid oxidizer and thehypergolic fuel component. But later Paul13 found thatthe exponent n was less than 0.8 (i.e., n = 0.6) also in anon-hypergolic system of natural rubber/gaseousoxygen.
The growing interest in hybrid rocket propulsionhas initiated many research programs in recentyears.14"20 Strand et al.14 studied the solid fuelregression rate in a hybrid combustion model of rigorhigher than that of the classical turbulent boundarylayer regression rate model of 60's. They confirmedthe turbulent boundary layer heat transfer to be the ratelimiting process for hybrid fuel decomposition andcombustion for motor operating pressures. Strand etal.14"1 also experimentally obtained oxidizer mass fluxexponent n in the range of 0.56 (for 3 < G0 < 14kg/m2s) to 1 (for 7< G0 < 70 kg/m2s) for ? in ahydroxyl terminated polybutadiene (HTPB)/gaseousoxygen (GOX) system. Lewin et al. 7 through theirexperimental study in HTPB/GOX hybrid motorsshowed that the ballistically calculated spatiallyaveraged instantaneous regression rate (f) was G0
dependent and pressure independent over a G0 range of11 - 400 kg/m2s and pressure range of 0.8 to 2.3 MPa.They found that the exponent n of the regression ratelaw f = a G0" vary with fuel grain length and it was0.46 for longer fuel grains (203 mm) and 0.625 forshorter grains (89 mm). Kuo and co-workers18 from
their experimental study on HTPB/GOX twodimensional hybrid motors (Go < 338 kg/m2s; 1.3 < p <9.0 MPa) concluded that 1) the solid fuel surfacetemperature was around 950-1000 K and 2) theinstantaneous regression rate (f) increasedcontinuously in the axial direction. The latterobservation was argued to be due to the increased totalmass flux. Their instantaneous regression rate data ofsolid fuel over different locations of fuel slab throughthe real-time X-ray radiography as well as ultrasonicpulse-echo techniques are the valuable inputs forhybrid motor combustor modeling and design.
Thus we see that in hybrid motors the solid fuelregression rate, a very important design parameter, isdependent on operating variables such as mass flux,pressure, properties of fuel and oxidizer, and fuel graingeometry. The classical turbulent boundary layerregression rate model based on heat transfermechanism more or less explains the solid fuelregression rate behavior at high pressures relevant tomotor operating conditions. Accepting this basis forfuel regression rate behavior, subsequent modelstudies ' with enhanced rigor have confirmed theabove dependence. Though many experimental studieshave confirmed the regression rate to be mass fluxdependent and pressure independent, the mass fluxexponent obtained through the real time measurementsas well as the ballistic calculations using pressure-timedata point to a value significantly less than 0.8. Theeffect of the properties of fuel and oxidizer (affectingmass transfer number B) has been considered by Paulet al." experimentally as well as theoretically andshown to be higher than the originally calculated value(B0'23). No systematic experimental study has so farbeen reported on the effect of fuel grain geometry.Experimental data at motor operating mass fluxconditions are lacking.
For hybrid motors, most of the presently projectedfuel and oxidizer combinations in their basic form havefuel regression rate around 1.5 mm/s or less undermotor operating conditions. This low regression rate ofsolid fuel is the basic problem which degrades theapplication of hybrid motors. Addressing this issuemany studies have been conducted in recent years.Korting et al. conducted experimental study withPMMA and polyethylene as fuels, and oxygen andoxygen-nitrogen mixtures as oxidizers. One of theirimportant observations was that a rearward facing stepcould have a noticeable effect on combustion behavior— increasing the regression rate by changing theprofile of the burned fuel grain. Strand et al.'4supported the inclusion of particulate additives(aluminum and/or coal) in solid fuel as an approach toenhance fuel regression rate. Lewin et al. by theirexperimental study in a HTPB/GOX hybrid motorshowed that the fuel grains of shorter length (89 mm)had a higher regression rate than that of longer length(203 mm). Ramaholli et al.20 claimed a 30% increasein regression rate of HTPB fuels with the use of a"chemical bond-breaking catalyst".
In view of the above literature survey the presentstudy, with a primary goal of finding methods of
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regression rate enhancement, reports the results of asystematic investigation conducted at high mass fluxconditions. HTPB/GOX propellant combination wasadopted for the study as it is of current interest in largebooster applications. The effects of the addition ofammonium perchlorate or aluminum powder in fuelcomposition, the oxidizer-fuel ratio, and thecharacteristic dimension of fuel grain on fuelregression rate are presented. The effect of thecharacteristic dimension of fuel grain is found to be themost significant one for the enhancement of regressionrate.
Experimental ProcedureTest Facility
A high pressure hybrid motor test facility is used.The oxygen supply is from a bank of cylinders kept at amaximum pressure of 15.0 MPa. A ball valve is usedto initiate and terminate the flow of oxygen and a sonicnozzle in the line maintains a desired constant massflow rate. Nitrogen is used as a purge gas to terminatecombustion after the desired burning time. Thepressure maintained upstream of sonic nozzle is alwayskept higher than two times the maximum combustionchamber pressure, so that the oxidizer mass flow rate isconstant during the entire test. Oxygen supply tomotor (mounted on a thrust stand) is through two 20mm flexible Teflon hoses. The high pressure (4.0MPa) axisymmetric hybrid motor assembly, Fig. 1,consists of an injector, a pyrogen igniter, a pre-combustion chamber, a combustion chamber with afuel grain and an aft mixing chamber, and a nozzleassembly with interchangeable nozzles. The diameterand length of the pre-combustion chamber are 75 and50 mm respectively. The hybrid combustion chamberis a thick steel cylinder of outer diameter = 88.9 mmand inner diameter = 58.4 mm; combustion chambersof two different lengths (380 and 580 mm) areavailable.
The nozzle used for the first two tests were made oflow density graphite (density = 1600 kg/m3). Asexcessive throat erosion was experienced during thesetests, the low density graphite nozzles were replacedwith heavy copper-nozzles. These copper-nozzlescould withstand a maximum firing duration of 8s forunmetallized fuel grains. When metallized fuel grainswere used, the copper-nozzles started melting around3s. Hence for these grains high density graphite(density = 1800 kg/m3) nozzles were used; for these theerosion rate on radius was around 0.09 mm/s. For thefirst eight tests the igniters of 3s duration were used.As the successful ignition could be obtained within Is,in subsequent tests the "strong" igniters of 3s weresuccessfully replaced with Is ones.
Fuel SpecimenThe solid fuel composition was mainly of HTPB.
A small amount of carbon black (C) was mixed withthe fuel. Trimethelol propane (TMP) was also added toimprove the mechanical property of the grain; forcuring toluene di-isocyanate (TDI) was used. Thepreparation of fuel grain was as follows. The pre-mix
containing HTPB, C, and TMP was thoroughly mixedfor 10 minutes. Then on adding TDI the blend wasmixed for a further 10 minutes. The percentage masscomposition of the base fuel was HTPB:C:TMP:TDI =81.68:0.82:4.08:13.42. The mixture was then pouredinto the mold of cylindrical fuel grain and cured, firstfor three days at room temperature and then for fourdays at 60°C. Four different fuel compositions werestudied in the present investigation, Table 1. The basefuel composition with or without the additives (APand/or aluminum) was maintained same as above. Theparticle size [Z(ri j df)/Z(nid,3) ] of the aluminumpowder was 28 um and that of ammonium perchloratewas 98 um. The details of grain geometry are alsogiven in Table. 1. The mechanical properties of thesegrains are given in Table 2.
Before fixing the fuel grain into the combustionchamber, the chamber inner wall was lined with twolayers of 2 mm thick nitrile rubber based insulator.Then the cured grain was bonded to the liner usingepoxy. For initial tests, however, silica phenolic linerswere used; because of the problems faced in theirfabrication they were replaced with nitrile rubber basedones.
PRE COMBUSTIONCHAMBER! COMBUSTION CHAMBER
Fig. 1 Hybrid motor assembly
Test SchedulesThe parameters varied for this study are also
detailed in Table 1. Forty three tests, including thirtythree successful ones (fifteen successful sets), werecarried out for the present study. A repeatable test wastaken as successful. Initially three repeatable tests weretaken for a successful set. When the confidence levelimproved, two successful tests were taken to beadequate.
Each test run included the following steps. Bysuitable setting of the oxygen ball valve opening,constant supply pressure of GOX was maintainedupstream of the sonic nozzle. After the flow becamesteady the igniter train was initiated. After the desiredbum time in quick successions oxygen supply was cutoff and nitrogen purge was opened to extinguishcombustion. The test measurements were the thrustand the pressures: upstream and downstream of sonicnozzle, at aft combustion-chamber, and at pyrogenigniter. All the signals from strain gauge type thrust-and pressure-transducers were recorded using a data
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1.87 1.97 2.11 2.18 where T = -fy\ \r+rate is given by,
Elongation % 89
Stress at 50% 1.26elongation(MPa)
HardnessShore A
62
89
1.43
65
89
1.47
62
90
70
(1)
. The igniter mass flow
(2)
Here, C^ and Cdi are the experimentally calibratedvalues. The total mass flow rate through the hybridmotor nozzle is given by,
acquisition system. The sampling rate was 200samples/s. The other pre- and post-test measurementswere the fuel density, the oxygen temperature(atmospheric temperature), the initial and final nozzlethroat diameters, and the initial and final fuel grainmasses and dimensions. For each test the desiredoxygen mass flow rate could be obtained by choosingan appropriate sonic nozzle throat and its upstreampressure. All the tests were conducted with an initialoxidizer mass flux of around 500 kg/m2s.
Data ReductionWith respect to time, the measured values of the
thrust and the pressures at sonic nozzle upstream (ps),igniter chamber (pj, and aft combustion-chamber (pc)are available. As the flow Mach numbers at the abovepoints of pressure measurements are very low (< 0.1),the values are taken as the stagnation ones. The
t = P,,At/Ceff (3)
where Cefr is the effective characteristic velocity of thetotal combustion products of igniter and hybridcombustion chamber and it is given by,21
Ceff = •
0 + 1
O + lrhj + rtto -
The fuel mass flow rate is given by,
rhf = iht — I riio + til; I
(4)
(5)
At each time step rib and rhi are calculated from Eqs.(1) and (2). To calculate ballistically the spatiallyaveraged instantaneous regression rate, port diameter,
5American Institute of Aeronautics and Astronautics
22
and oxidizer mass fluxes the following scheme isadopted.Step 1. Assume a value for r\.Step 2. Assume a value for <!>. At the instant t; for themeasured pCii and the assumed value of O calculateusing the complex chemical equilibrium code CEC71.Calculate Ceff from Eq. (4).Step 3. Calculate rht using Eq. (3). Calculateusing Eq. (5). <X> = m0/m f i .Step 4. Is <D = 3> ? If not go to Step 2.Step 5.
f,- =•n Dj Lp (6)
Step.6. Under quasi steady state assumption thespatially averaged port diameter at the next time step isgiven by,
Step 7.
m' = m'f,i f,i At
(7)
(8)
Step 8. Calculate till extinguishment. The integratedtotal fuel mass consumed, m'f is compared with themeasured one, mf, i.e. the one obtained by weighingthe fuel before and after the test. Is m'f = mf ? If not goto Step 1.Step 9. The total mass flux and the oxidizer mass fluxare calculated by dividing the respective mass flowrates by the corresponding port area.
The disadvantage of this method is that thecalculation assumes a constant combustion efficiencythrough out dach test. The values of the convergedcombustion efficiencies obtained for the present studyvaried between 0.89 to 0.93. A logical variation incombustion efficiency could be observed betweenmetallized grain and unmetallized ones — themetallized one had a combustion efficiency of 0.89 andthe unmetallized one had a higher combustionefficiency around 0.93. The efficiency variationbetween a set of repeatable tests was mostly 1% butalways within 2%. The calculated spatially averagedport diameter at the extinguishment and the measuredspatially averaged port diameter of the burnt grainvaried within 2%.
Results and DiscussionAs a typical test-output, the combined pressure- and
thrust-time record of test No. 43 is shown in Fig. 2.During the igniter operation, evidently due to thesignificant igniter mass flow contribution to the totalflow, the chamber pressure is about 0.2 MPa higherthan the equilibrium chamber-pressure.
Fig. 2 Pressure- and thrust-time trace of hybridmotor testing
Oxidizer Mass Flux and Composition EffectOur tests for HTPB and AP grains were run at a
constant pressure of 2.0 MPa using copper-nozzles. Butthe test for Al grains could be run only under reducingpressure conditions (2.0 to 1.2 MPa) because of theerosion in the high-density graphite-nozzle used. Thespatially averaged instantaneous regression ratesversus oxidizer mass fluxes for the HTPB- and Al-grains (Table 1) are shown in Fig. 3. The oxidizermass flux exponent n in the regression rate equation r= a G0" is 0.53 for HTPB grain and 0.93 for Al gram.For the same grain dimensions Fig. 4 shows theregression rates of HTPB- and AP-grains. The oxidizermass flux exponent n is 0.71 for AP grain. While theseresults in Figs. 3 and 4 are for the grain dimension of250*12 mm, the trend is repeatable for the other graindimension of 400*20 mm as given in Table 3.
The enhancement of regression rate due toaluminum addition has been known for long time. At1.6 MPa, in the range of oxygen mass flux 80 - 30kg/m2s, Wooldridge et al.4 found that the regression
——— HTPB grain (Test Nos. 6, 8, and 12)4 — —Al grain (Test Nos. 2.4 and 34)
/MtoEE<D
!o'
0.4
Strand et al. HTPB fuelStrand et al.u HTPB+AI+C fuel
40 100
oxidizer mass flux, kg/m2s500
Fig. 3 Regression rates of HTPB and Al grains.Grain length*initial port diameter = 250*12 mm
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I0313
=O'
D)0)
0.4
- HTPB grain (Test Nos. 6, 8, and 12)• AP grain (Test Nos. 13 and 41)
40 100oxidizer mass flux, kg/m2s
500
Fig. 4 Regression rates of HTPB and AP grains.Grain length*initial port diameter = 250*12 mm
rate of PBAN and PU grains could be enhanced by26% by the addition of 20% aluminum. At 1.3 and 1.5MPa pressure conditions, in the range of oxygen flux5 0 - 1 0 kg/m2s, Strand et al.14 by modeling- andexperimental-studies found that the regression rate ofHTPB grains could be enhanced by 17% by theaddition of aluminum. Their HTPB grains containedparticulates of 40% aluminum and 30% carbon. On themechanism of regression rate enhancement byaluminum addition they argued that the augmentedradiative heat transfer was the cause. They furtherdemonstrated theoretically as well as experimentallythat, the radiation being pressure dependent, theregression rate enhancement due to aluminum additionshould also be pressure dependent. Their results for theHTPB (1.3 - 1.5 MPa) and the particulated HTPBgrains (1.5 MPa) are also shown in Fig. 3. Theirresults for the HTPB grains are comparable to theresults of the present study. But their regression rate ofthe particulated grain is significantly higher than thepresent result. The most likely reasons could be two:one, the higher paniculate content and the other, thehigher pressure; both because of higher radiative heattransfer component would lead to higher regressionrate. Again, for the reason of radiative heat transferbeing pressure dependent, the actual G0 exponent at afixed pressure of 2 MPa is expected to be less than thevalue of 0.93 found hi the present study for a reducingpressure conditions from 2 to 1.2 MPa.
The differential thermal analyzer (DTA) traces forthe samples of the HTPB grain and the AP grain withpurges of oxygen and of nitrogen at one atmosphericpressure are given in Fig. 5. With nitrogen purge anexothermic peak is observed around 200°C for theHTPB grain; but in the case of the AP grain the peak isfound delayed around 280°C with a higherexothermicity. With oxygen purge a similar peak butof higher exothermicity is observed around the same200°C for the HTPB grain; furthermore comparably inthe case of the AP grain a similar delayed peak but ofsubstantially enhanced exothermicity is found around240°C. These DTA observations have correspondingrecords in the experiments of thermogravimetricanalyzer (TGA). In fact, with oxygen purge one couldhear the sound of an explosion at 240°C in the case ofTGA experiment for the sample of the AP grain
When we compare the exothermicity at lowtemperatures (200 - 300°C) for the sample of the APgrain with nitrogen purge and that with oxygen purge,exothermicity with the latter is substantially enhanced.The fact that the AP content in the AP grain is only7.55% apart, suspecting that this enhancedexothermicity could be because of the reaction betweenthe evolved ammonia from AP and the oxygen, a DTA-experiment with oxygen purge for AP crystal wasconducted. With inert purge at one atmosphericpressure AP crystal is known to change its crystallinelattice from orthorombic to cubic at 240°C with a sharpendothermic peak; and to decompose very rapidly andexplode at 460°C.23 Interestingly the DTA trace withoxygen purge for AP obtained in the present study isnot different from the DTA trace with nitrogen purge.Furthermore, absence of any appreciable enhancementin the exothermicity between the samples of HTPB-and AP-grains under the nitrogen purge discounts thepossibility of heterogeneous/gas phase reaction amongfuel/fuel-vapor, perchloric acid, and ammonia. Then,the reason for the substantially.enhanced exothermicitywith oxygen purge in the samples of the AP graincould be the following. In the presence of the APdecomposed products namely, ammonia and perchloricacid, the thermally decomposed fuel vapor and thepurge oxygen are able to react more violently at lowtemperatures due to significantly different gas phasekinetics.
Table 3 Regression rate equations
HTPB grainAl grainAP grain
Grain I
(250* 12 mm)
8.7*10'5G0°'53
1.4*10-5G0°-93
3.8 * 10'5 G00'71
Grain II
(400*20 mm)
7.7 * 10'5 G0°'53
1.3* 10'5G0°'89
2.8 * 1Q-5 G0°'72
Grains I and II
5.35*10-5G0°-4D-°3
—
1.96*10-5G0°-6D-°-3
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—— HTPS-Oj•— HTP3-N2—— HTP9+AP-02• — HTPS+AP-Ni
100 200 300 400 500 600temperature °C
700 300
Fig. 5 DTA traces of the samples of HTPB- and AP-grains in oxygen and nitrogen atmosphere.
While this is the situation for thermal analysisexperiments the application of these results for hybridmotor operating conditions should be considered. Inthe grain port the decomposed fuel vapor and the APdecomposition products from the fuel surface convecttowards the flame front, which is expected to be at adistance of about 10% of the port radius under fullydeveloped turbulent flow conditions.24 As the flamefront temperature is not going to be significantlydifferent by the addition of small quantity of AP, if anyregression rate enhancement is to take place by theaddition of AP there should be a supplementary heatsource other than the flame front. This is possible onlywhen oxygen is available closer to the fuel surface inwhich region the decomposed fuel vapor and the APdecomposition products are convecting towards theflame front. Conceivably, a finite flux of oxygen tofuel surface could exist through the mechanism of bulkturbulent eddy transport across the flame front athigher mass flux conditions.10 Therefore the additionof AP is able to enhance the regression rate at highmass flux conditions but not under low mass fluxconditions as shown in Fig. 4. However, the exactphysical and chemical processes under which thesubstantially enhanced exothermicity occurs for thesamples of AP grain with oxygen purge cannot beexpected to happen under rocket operating conditionsbecause here the heating rates are about four order ofmagnitude and the pressures are more than one order ofmagnitude higher than those in thermal analyzers.
rates versus oxidizer mass fluxes for the AP grains at2.0 and 3.0 MPa are shown in Fig. 6. These resultsindicate that the pressure does not have much effect onregression rate. Similar results are obtained for theHTPB grain at 2.0 and 3.0 MPa. These results areagreement with the results of earlier studies ofMarxman et al.3 and Paul et al.'' at high pressures (>1.0 MPa).
Fig. 6 Regression rates of AP grains at 2.0 and 3.0MPa pressure. Grain length*initial port diameter =400*20 mm.
Length EffectInitially for a few tests the port entry was sharp (not
well rounded). In these cases a locally high regressionrate was observed at a few millimeters downstream ofthe port entry. This was rationalized to be due to aseparation and reattachment of the entry flow. Withthe flame front established at the vicinity of thereattachment point the local regression at that point washigh. Subsequently all the fuel grains were given wellrounded port entries. From the measurements of webthickness after each test, the local port diameter isfound to increase along the axis. This is because theregression rate is a function of local mass flux and thelocal mass flux increases along the axis. In Fig. 7, theratio of the local port diameter to the entry portdiameter for HTPB grains of initial port diameter = 20mm and three different lengths (250, 400 and 545 mm)are presented. It can be seen that for 545 mm grain, theincrease in local port diameter diminishes towards theaft end of the grain indicating a reduced regression rateafter 400 mm.
The variations of oxidizer-fuel ratio with respect totime for the above HTPB grains are shown in Fig. 8.Here it is seen that the grains of 400*20 mm operatecloser to the stoichiometric oxidizer-fuel ratio (2.95).But the grains of 250*20 mm operate at a fuel leancondition and the grains of 545*20 mm operate at afuel rich condition. At a fuel rich condition,theoretically, the stoichiometric diffusion flame can beexpected to be present only up to the grain lengthwhere the oxygen is available. Thereafter the hotcombustion gases would flow in the absence of the
. diffusion flame but with the continued addition ofvaporized fuel from grain. This fuel addition couldreduce the core gas temperature resulting in reducedtemperature difference between core gas and wall.However the mass flux would continue to increasealong the axis. Therefore, the reduced regression ratefor 545*20 mm grain after 400 mm could be due to the
8I•-.sf'tiitft or A eronautics and Astronautics
net reduction in heat transfer under the above twoopposing situations.
1.4
I f 1-2
I «•O 0)
ra "O
8.1.0
• 250 mm (Test Nos. 17 & 19)•400 mm (Test Nos. 14 & 32)•545 mm (Test Nos. 42 & 43)
0 100 200 300 400 500 600axial distance, mm
Fig. 7 Ratio of the local port diameter to the entryport diameter for HTPB grains. Initial portdiameter = 20 mm
Diameter EffectThe regression rates of HTPB grains with two
different initial port diameters are shown in Fig. 9. Thevalues of a and n in the regression rate equation r = aG0
n are given in Table 3. At a given oxidizer mass fluxthe grain with the lower initial port diameter (12 mm)regresses faster than the one with the larger portdiameter (20 mm). The regression rates obtainedagainst the oxidizer mass fluxes have the portdiameters varying from 12- to 40-mm. From thepresent data, hi order to distinguish the effect of portdiameter as well as G0 on r equations are obtained forHTPB- and AP-grains and given in Table 3. Theobtained equation for HTPB grain and the experimentaldata are presented in Fig. 10.
Marxman and co-workers by their turbulentboundary layer regression rate model based on heattransfer mechanism obtained the well known regressionrate mass flux equation. This Marxman equation underthe conditions of negligible radiant heat transfer, highoperating pressures, and fixed oxidizer-fuelcombination can be written as
Here G is the local mass flux given by
(9)
(10)
where 8* is the boundary-layer displacement thicknessgiven by,4'5
Jo.21D(x/xA)°-8
[0.2 IDX < X A = 5 DX > X A
8"
6'O
2
I4'<5N
I 2-
o-
° 250 mm grain (Test Nos. 1 8 & 20)• 400 mm grain (Test Nos. 14 & 32)° 545 mm grain (Test Nos. 42 & 43)
Oo0o0° °0 o°o0o°°°°0o
O 0 °
•
.*— '*— «*"***
1 2 4 6time, s
Fig. 8 Oxidizer-fuel ratio with respect to time forHTPB grains. Initial port diameter = 20 mm
032111It)inEO)0}
0.4
———— 12 mm (Test Nos. 6, 8, & 12)— — 20 mm (Test Nos. 14 & 32)
- - - -Marxman Eq. for 250*12 mm- — -Marxman Eq. for 400'20 mm
40 100oxidizer mass flux, kg/m s
500
Fig. 9 Regression rates of HTPB grains. Grainlength*initial port diameter = 1) 250*12 and 400*20mm.
U)
EE
as<DO)<U
0.4
Initial port diameter -12 mm(Test Nos. 6, 8, & 12)
Initial port diameter-20 mm(Test Nos. 14 & 321
1.5°'4 -° 3
Fig. 10 Regression rate dependence on oxidizermass flux and port diameter for HTPB grains.
American Institute of Aeronautics and Astronautics
Some times it is wrongly argued that the Marxmanequation does not account for the effect of D onregression rate. But if two grains of different portdiameters are considered with the same oxidizer massflux at the port entry, the one with a smaller diameterwill have a higher gradient of total mass flux along theaxis and hence will have a higher spatially averagedregression rate. Therefore the Marxman equationpredicts that the regression rate will decrease with thedecrease in mass flux, the increase in port diameter,and the increase in axial distance. The first twopredictions are in qualitative agreement with theexperimental observations. But hi the case of the third,most of the experimental studies including the presentstudy show an increase18 or constant regression ratealong the axis. With reference to the regression ratedependence on the mass flux and the port diameter thevalues of the exponents in the regression rate equationdo not agree with many experimental findings. Severalinvestigators for the purpose of engineering evaluationsplotted the experimental regression rate as a function ofoxidizer mass flux. The exponents obtained were lessthan 0.8 and near 0.5. As early as 1965 Marxman andWooldridge3 responded to this observation by statingthat the correlations based on the total mass flux, G,would lead to an exponent = 0.8 whereas those basedon oxidizer mass flux, G0, would only lead an exponent= 0.5. But this argument seems to be not valid. Theinitial regression rate experimentally obtained in thepresent study for 12 mm HTPB grain at 500 kg/m2soxidizer mass flux is taken as reference. The regressionrates with respect to time for varying G0 werecalculated through the conventional "incrementalanalysis"25 using the Eq. (9) for initial port diameters of12- and 20- mm and are shown in Fig. 10. Here thevalue of n for G0 is more than 0.8! Furthermore theprediction for the diameter effect is only qualitative.
A large number of studies on combustion chamberconfiguration similar to that of hybrid motor have beenconducted in recent years for solid fuel ramjet
76-78(SFRJ). Although the combustion processes inSFRJ are similar to those of hybrid motors the majordifferences are two. First, the SFRJ employs air otherthan a pure oxidizer; and second, it has a suddenexpansion of gaseous inlet flow. Due to this suddenexpansion three distinct flow fields exist: 1)recirculation zone, 2) reattachment region, and 3) zonedownstream of reattachment. The zone downstream ofreattachment hi SFRJ is similar to the fully developedturbulent boundary layer region in a hybrid motor. ForSFRJs with large L/D ratios, the spatially averagedinstantaneous regression rate will be controlled by theheat transfer mechanism to the fuel from the flamefront that exists within the fully developed turbulentboundary layer region. In such cases it is a commonpractice to get experimentally the spatially averagedinstantaneous regression rate as a function of air massflux and port diameter. And their exponents are foundto be around 0.4 to 0.6 and -0.25 to -0.4 respectively.26
Also in hybrid motors similar exponents are obtained,Table 3.
inEe<B
ao
'351-
0.4
* ———— AP + Al grain (Test Nos. 39 & 40)0 — — HTPB grain (Test Nos. 14 & 32)
40 100
oxidizer mass flux, kg/m2s500
Fig. 11 Regression rates of HTPB grains with initialport diameter = 20 mm and AP + Al grains withinitial port diameter = 12 mm.
Combined Regression Rate EnhancementThe primary motivation of the present study is to
find through a systematic investigation the methods forthe regression rate enhancement. Therefore thecombined effect of the addition of ammoniumperchlorate and aluminum in the fuel, and the portdiameter are shown hi Fig. 11. It is seen that theregression at the oxidizer mass flux of 300 kg/m2s canbe enhanced by more than 100% and this can be stillhigher at higher mass flux conditions.
Conclusions1. The addition of AP and/or Al in HTPB fuel, and
the reduction of grain port diameter enhance thefuel regression rate in HTPB/GOX hybrid motors.The effect due to the latter is the most significantone.
2. The addition of AP is able to enhance theregression rate at high mass flux conditions.Conceivably, this is because of an additional heatsource available near the fuel surface. This heatsource results from the reaction of the fuel-vapor,the AP decomposition products, and the finite fluxof oxygen to fuel surface, existing through themechanism of bulk turbulent eddy transport acrossthe flame front at higher mass flux conditions.
3. With reference to the conventional theory theregression rate decreases along the axis and itdepends on the mass flux G°'8. The presentexperimental results indicate that the regressionrate increases along the axis; and the exponent ofthe mass flux is significantly less than 0.8.
4. Similarity exists between the fuel regression rateequation used in a solid fuel ramjet and thatobtained in a hybrid motor. The present studypoints out to an equation for HTPB fuels in hybridmotors as r" = 5.58 * 10'5 G0
0'4 D'03.
AcknowledgmentsThe study reported forms a part of the research
sponsored by the Space Technology Cell formed by the
10American Institute of Aeronautics and Astronautics
Indian Space Research Organization at the IndianInstitute of Technology (Madras). The first two authorshad many discussions with Dr. S. R. Chakravarthywhile writing this paper.
References1. Marxman, G.A., Wooldridge, C. E., and Muzzy, R.
J., ''Fundamentals of Hybrid Boundary LayerCombustion," Heterogeneous Combustion, editedby Wolfhard, H. Q., Glassman, I., and Green, Jr.L., Vol. 15, Progress in Astronautics andAeronautics, Academic Press, New York, 1964,pp. 485-522.
2. Marxman, G.A., "Boundary Layer Combustion inPropulsion," Proceedings of the EleventhSymposium (International) on Combustion, TheCombustion Institute. Pittsburg, Pennsylvania,1967. pp. 269-289.
3. Marxman, G.A., and Wooldridge, C.E., "Researchon the Combustion Mechanism of HybridRockets," Advances in Tactical Rocket Propulsion,edited by Penner, S. S., AGARD ConferenceProceedings No. 1, 1968, pp. 421-477.
4. Wooldridge, C. E., Marxman, G. A., and Kier, R.J., "Investigation of Combustion Instability inHybrid Rockets," NASA CR-66812.
5. Wooldridge, C. E., and Muzzy, R. J., "InternalBallistic Considerations in Hybrid Rocket Design,"J. Spacecraft and Rockets, Vol. 4, No. 2, 1967, pp.255-262.
6. Smoot, L. D. and Price, C. F., "Regression Ratesof Nonmetallized Hybrid Fuel Systems," AIAAJournal, Vol. 3, No. 8, 1965, pp. 1408-1413.
7. Smoot, L. D. and Price, C. F., "Regression Ratesof Metallized Hybrid Fuel Systems," AIAAJournal, Vol. 4, No. 5, 1966, pp. 910-915.
8. Smoot, L. D. and Price, C, F., "PressureDependence of Hybrid Fuel Regression Rates,"AIAA Journal, Vol. 5, No. 1, 1967, pp. 102-106.
9. Muzzy, R. J., "Applied Hybrid CombustionTheory," AIAA Paper No. 72-1143.
10. Kumar, R. and Stickler, D. ., "Polymer-Degradation Theory of Pressure-Sensitive HybridCombustion," Proceedings of the ThirteenthSymposium (International) on Combustion, TheCombustion Institute, Pittsburg, Pennsylvania,1971, pp. 1059-1077.
11. Paul, P. J., Mukunda, H. S., and Jain, V.K.,"Regression Rates in Boundary LayerCombustion," Proceedings of the NineteenthSymposium (International) on Combustion, TheCombustion Institute, Pittsburg, Pennsylvania,1982, pp. 717-729.
12. Paul, P. J., Mukunda, H.S., Narahari, H. K.,Venkataraman, R., and Jain, V.K., "RegressionRate Studies in Hypergolic System," CombustionScience and Technology, Vol. 26, No. 1, 1981, pp.17-24.
13. Paul, P. J., "Regression Rate and Low FrequencyInstability Studies in Hybrid Rocket Engines," Ph.D. Thesis, Indian Institute of Science, Bangalore,India. 1982.
14. Strand, L. D., Ray, R. L., and Cohen, N. S.,"Hybrid Rocket Combustion Study," AIAA PaperNo. 93-2412.
15. Strand, L. D., Jones, M. D., Ray, R. L., and Cohen,N. S., "Characterization of Hybrid Rocket InternalHeat Flux and HTPB Fuel Pyrolysis," AIAA PaperNo. 94-2876.
17. Lewin, A., Dennis, J., Conley, B., and Suzuki, D.,"Experimental Determination of PerformanceParameters for a Polybutadiene/ Oxygen HybridRocket," AIAA Paper No. 92-3590.
18. Chiaverini, M. J., Harting, G. C., Lu, Y., Kuo, K.K., Serin, N., and Johnson, D. K., "FuelDecomposition and Boundary-Layer CombustionProcesses of Hybrid Rocket Motors," AIAA PaperNo. 95-2686.
19. Korting, P. A. O. G., Schoyer, H. F. R., andTimnat, Y. M., "Advanced Hybrid Rocket MotorExperiments," Acta Astronautica, Vol. 15, No. 2,1987, pp. 91-104.
20. Ramohalli, K., Bates, R., Jones, M., Wygle, B.,and Yi, J., "Some Recent Results from a Programin Hybrids at the University of Arizona," AIAAPaper No. 95-2945.
21. Adams, D. M., "Igniter Performance in Solid-Propellant Rocket Motors," Jl. Spacecraft andRockets, Vol. 4, No. 8, 1967, pp. 1024-1029.
22. Gordan, S. and McBride, B. J., "ComputerProgram for Calculation of Complex ChemicalEquilibrium Compositions, Rocket Performance,Incident and Reflected Shocks, and Chapman-Jauguet Detonations," NASA SP-273, 1971.
23. Waesche, R. H. W., Wenograd, J., and Feinaner, L.R., "Investigations of Solid PropellantDecomposition Characteristics and Their Relationto the Observed Burning Rates," ICRPG/AIAAHnd Solid Propulsion Conference, PreprintVolume, June 6-8 1967.
24. Schulte, G., Pein, R., and Hogl, A., "Temperatureand Concentration Measurements in a Solid FuelRamjet Combustion Chamber," Jl. Propulsion andPower, Vol. 3, No. 2, 1987, pp. 114-120.
25. Miller, W. H. and Barrington, D. K., "A Review ofContemporary Solid Rocket Motor PerformancePrediction Techniques," Jl. Spacecraft andRockets, Vol. 7, No. 3, 1970, pp. 225-237.
26. Krishnan, S. and Philmon George, "Solid FuelRamjet Combustor Design," Progress inAerospace Sciences, 1998 (in press).
27. Schulte, G., "Fuel Regression and FlameStabilization Studies of Solid Fuel Ramjets," Jl.Propulsion and Power, Vol. 2, No. 4, 1986, pp.301-304.
28. Zvuloni, R., Gany, A., and Ley, Y., "GeometricEffects on the Combustion in Solid Fuel Ramjets,"Jl. Propulsion and Power, Vol. 5, No.l, 1989, pp.32-37.
11American Institute of Aeronautics and Astronautics
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