New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Rocket Propulsion

by: Demond Hoppe

Rocket Propulsion AE 6450

Demond Hoppe

GPA 3.79

Narayanan Komerath

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Narayanan Komerath
Class Notes
25 ?




Popular in Course

Popular in Aerospace Engineering

This 0 page Class Notes was uploaded by Demond Hoppe on Monday November 2, 2015. The Class Notes belongs to AE 6450 at Georgia Institute of Technology - Main Campus taught by Narayanan Komerath in Fall. Since its upload, it has received 119 views. For similar materials see /class/234304/ae-6450-georgia-institute-of-technology-main-campus in Aerospace Engineering at Georgia Institute of Technology - Main Campus.


Reviews for Rocket Propulsion


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/02/15
AE6450 Fall 2004 Lecture 16 Airbreathing Propulsion for Orbital Missions Copyright 2003 Narayanan Komerath The Brayton Cycle The operation of ramjet and gas turbine quotjetquot engines can be expressed in its most basic form as a quotBrayton Cyclequot or quotGas Turbine Cyclequot There are four steps involved Step Thermodynamic Process 1 Compress the working Adiabatic Compression fluid air 2 Add heat to the fluid Constant Pressure Heat Addition 3 Extract work from fluid by Adiabatic Expansion allowing it to expand 4 Cool the fluid Constant Pressure Heat Extraction Copyright 2003 2 Narayanan Komerath Pressure Volume Note Step 4 occurs in the atmosphere after the engine has passed We don39t worry about it because we don 39t need to reuse the same air or pay to cool it Copyright 2003 Narayanan Komerath mvton Cycle Analysis Ramjet Engine 4 4 Diffuser Burner Nozzlegt Step 1 Step 2 Step 3 Net work output work done by the system in Step 3 minus the work put into the system in Step 1 Net heat input heat put in during Sep 2 assuming that we don39t pay to cool the air and cannot recover the heat that is lost in the exhaust gases Ideal Cycle Efficiency Net work output Net heat input Net work output per unit mass flow rate h h h h C D B A Copyright 2003 4 Narayanan Komerath hC hB 771hDhA Efficiency hC 43 Net heat input Dividing throughout by specific heat Cp Copyright 2003 Narayanan Komerath Thermal Efficiency and Pressure Ratio The process from A to B is isentropic as is C to D Also pressure is constant from B to C 71 i i y and TA PA 7 1 7 1 PD i TC PC PB 1 As the engine quotoverall pressure ratioquot increases efficiency rises towards 1 2 This means that to get high efficiency we must use a high pressure ratio These are extremely useful results Note P B A Efficiency heat added heat wasted heat added Thus to increase efficiency a Increase Tc the highest temperature in the engine b Bring TD down as close to TA as possible expand hrough the nozzle and extract the maximum work possible c Reduce TB take out heat from the compressor using heat transfer to the fuel this is considered in upersoniccombustion engines which use cryogenic Copyright 2003 Narayanan Komerath If TD ltTA you get efficiency gt 1 a perpetual motion machine Thus we see that in reality the exhaust temperature cannot be lower than the ambient temperature Efficiency is limited by the outside air temperature Copyright 2003 Narayanan Komerath Let us pause for a moment and consider what the exit Mach number will be Since stagnation pressure is constant throughout this ideal engine and the specific heats are assumed constant 7 1 amp y T4 Pa Obviously the exit Mach number will be equal to the ight Mach number E 39t eloc39t 39s we u4 M m and the flight velocity is ua Ma yRTa T Thrust per unit air mass flow rate 1 fue ua m Thrust Specific Fuel Consumption m f T SF C ma Copyright 2003 Narayanan Komerath Notes 1 As Mach number increases the ramjet pressure ratio increases The combustor walls must be stronger For the same reason highMach number flight at sealevel becomes difficult 2 As Mach number increases the temperature at the inlet to the combustor increases When this reaches the highest permissible combustor temperature no heat can be added so no thrust can be produced Thus this provides an absolute upper limit on the Mach number at which thrust can be produced Of course the vehicle may not be able to fly at this Mach number because we have not considered how much thrust is needed to overcome drag and accelerate to this Mach number Copyright 2003 Narayanan Komerath Ideal Ramjet Cycle This is essentially the Brayton cycle Here we quot quotl l l l l l llllllllllllllllllllllllllllllllllllllllllllHillllHllllHHilHlHlmHmlHlHlmHllllHlHlmHlllllllllllllllll l lllw have a flowing fluid so that it is not useful to W draw a pressurevolume diagram We will instead represent the engine processes on a Temperature Entropy T s diagram This is Diffuser Burner Nome the same as an EnthalpyEntropy diagram a Ramjet Engine a l D 9 a Mollier Chart if cp is constant Region Process ldeal Actual a to 1 No change supersonic flow no external compression or suction ahead of inlet 1 to 2 Adiabatic lsentropic Po drops due to compression P T increase To Po constant shocks and friction no work except s constant Entropy increases volumeechange A 2 to 3 Constant pressure AS gt 0 Po drops Heat addition To risesPo constant T re 3 to 4 Adiabatic Po drops slightly expansion No To Po constant T P drop s increases slightly work except AS gt AS ithatefevelrume rev Copyright 2003 10 Change39 Narayanan Komerath Temperature T Ts Diagram pa Entropy 5 Copyright 2003 11 Narayanan Komerath Ideal Ramjet Analysis Example Problem An ideal ramjet engine has an isentropic inlet which decelerates incoming air at a flight Mach number of 30 to a low Mach number without any losses Heat is then added by chemical reaction with a fuel whose heating value is 19000 Btu I lbm The altitude is 11000m The maximum temperature in the engine is limited to 2000K The heat addition occurs at constant pressure and at a low Mach number The nozzle is fully expanded and has an exit diameter of 1 meter Find the thrust and thrustspecific fuel consumption of the engine assuming constant specific heats Station 1 Here we have undisturbed air just before entering the inlet of the engine The stagnation temperature can be determined from the static temperature and the Mach number using the isentropic relation 7 1 Tog Ta1yTMa2and Pod Pal7TlMa271 76121 661 RHZRM Copyright 2003 12 Narayanan Komerath lsentropic diffuser from Station 1 to Station 2 Adiabatic and no work done except that of volume change T02 01 lsentropic reversible adiabatic therefore no losses P02 2 P01 ConstantPressure Heat Addition from Station 2 to Station 3 T is specified for a given thrust setting For maximum thrust this value is limited by 0 the limiting temperature of the combustor material P03 P02 To find the fuelair ratio needed to achieve this temperature we consider the enthalpy balance across the combustor Copyright 2003 13 Narayanan Komerath FuelAir Ratio Calculation Stagnation enthalpy of the air burned products leaving the combustor Stagnation enthalpy of the air entering the combustor sensible enthalpy of the fuel heat released by reaction We neglect the sensible enthalpy of the fuel since it is very small compared to the heat released by reaction ma fCpTE3 manY EB quR Solving for the fuelair ratio f 02 qR i CpTOZ T02 Copyright 2003 14 Narayanan Komerath Nozzle l t 39N f Stt39 3tStt39 4 sen ropIc ozze rom ann o alon T04 03 P04 P03 Fully expanded flow at the nozzle exit static pressure is the same as the ambient atmospheric pressure P4 Pa Relating temperature ratio and pressure ratio gt T4 Thrust per unit mass flow rate i1fueh uec 1 6uquot mah TSFCZL Tmah Copyright 2003 Narayanan Komerath Combustor Pressure Losses There are three main sources of stagnation pressure losses 1 Loss due to friction and flow separation boundary layers mixing devices flameholders 2 Shock losses due to deceleration of supersonic flows 3 Rayleigh Line losses due to heat addition at high Mach number In jet engine main combustors Type 1 losses are the most important because the Mach number is low In afterburners and subsonic combustion ramjets Types 1 and 3 are important All types are critically important in supersoniccombustion ramjets Copyright 2003 16 Narayanan Komerath RayleighLine Losses Adding heat to a flowing fluid drives the Mach number towards 10 Stagnation pressure loss is directly related to Mach number Thus in a constantarea duct with Station 1 denoting conditions upstream of heat addition and Station 2 the conditions downstream 2 7 1 2 h1nyH 1 2 M2 and T01 17M22 M1 17T 1M12 1 L 7 2 7 1 1 M amp 17M12 2 2 2 p01 17M2 171M12 2 The decrease in stagnation pressure due to heat addition can be large Copyright 2003 17 Narayanan Komerath Bussard Ramjet Fusl from Space http lwwwgrcnasagovVWVWPAOimag eslwarpwarp 1 2 9 if Copyright 2003 Naray anan Komerath Transatmospheric Airbreathing Engines Ref Czysz P Vandenkerckhove J Transatmospheric Launcher Sizing In Curran T Murthy SNB Ed Scramjet Propulsion AIAA Progress in the Aeronautical Sciences Vol 189 2000 Copyright 2003 Narayanan Komerath Sizing Trans atmospheric Launchers Obiectives 1 Quantitative sizing model to assess SSTO and TSTO characteristics 2 Assess potential of LOX collection for both SSTO and TSTO Approach Old Approach Begin by drawing constant wing area or constant weight concept aircraft Each component independently sized designed assembled Iterated to approximately same mission radiusrange Not very satisfactory for high performance aircraft New Sizing aircraft concepts to both mission distance and maneuver performance gt decisions now possible on equal performance aircraft of differing size and weight Size configuration to mission performance requirements iterate on system weight Significant difference between conventional aircraft and hypersonic launcher propellant volume Commercial aircraft passenger volume 80 Launcher propellant 80 Copyright 2003 20 Narayanan Komerath Mass ratio for mission is determined independently by trajectory analysis Volume of vehicle is iterated until volume available volume required and mass ratio required mass ratio Significant number of critical conditions at higher speeds Need to focus on cost of payload to orbit and long duration use Most significant gains possible from propulsion propellant capabilities Sizing emphasizes energy management and propulsion Fundamental equation for weight ratio to orbit WR WGTO WOE pr 21 prl 1rOFW nal WOE WOE WOE WOE OxidizerIfuel ratio rOF is averaged over the trajectory and Woxidizer que Copyright 2003 21 Narayanan Komerath Weight ratio can be minimized if OIF rate can be minimized Also WR exp lspe effective specific impulse V P V V 15 DWOE PP I PP S I PP tot IS I Spin WR1 pn Vtot Spln1395 p M Propulsion Index I AV ppp pfue1rOF exp D 1 p WR1 1r Amquot I 1 39 OF 9 Sln7 poxdizer Sp D Copyright 2003 Narayanan Komerath AV gspe i 22 Operational empty weight WOE is a product of 3 terms pp 8 Is determined by geometry pln ppp is determined by aerothermopropulsion system WR 1 Spln by size Copyright 2003 23 Narayanan Komerath Propulsion index is a product of two terms First is a function of propellant density and OIF Second is a function of propellant engine size excess thrust over drag and climb angle for given increment in velocity Magnitude of p is a function of maximum sustained speed Not much of propulsion type Larger the propulsion index smaller and lighter the vehicle for given speed Mean value of propulsion index is lp 1o75X10 0081M where M is maximum sustained Mach Number Scatter is Jr10from subsonic cruise fighter with supersonic dash to an SSTO vehicle Copyright 2003 24 Narayanan Komerath Fundamental Sizing Relationships Volume index T Kuchemann relates volume to platform area Kuchemann u is a volume parameter Fuels JPIKerosene 752 KgIm3 Subcooled liquid methane 464 KgIm3 Subcooled liquid hydrogen 746 KgIm3 For kerosene fueled low volumeIarea slender SST 003 I As fuel density decreases 1 increases to 0039 0147 High volumeIarea LHzLOX propellant combined cycle powered space launcher 1 018 to 020 Copyright 2003 25 Narayanan Komerath ppp Vpp 15 V Now W rs pp 15 Vtot pln Recall WEO WOE pay Wcrew Wdry Ppp Vpp 15 gt WEO WR 1E Tspln Wpay Worew 15 ppp IVppjfspln WR1 Vtot 1quot39ruse ruse useful payload ratio Copyright 2003 26 Narayanan Komerath Copyright 2003 Narayanan Komerath 27 Design variables related directly to dry weight Define structural fraction I39Str a gives the last of the set of fundamental equa ons 15 Wstr IOPP VPP rstr TS pln Swet WR 1 Vtot 1quot39ruse KW where Wstr OEWrstr KW wetSpln gt Directly relates geometry to materialstructure and propulsion parameters gt Better propulsion p gt more structure mass allowed for convergence Lower I p gt need structuresmaterials breakthrough Copyright 2003 28 Narayanan Komerath Correlating factors Kuchemann z VtOta t15 15 Spin 8 In 0667 US Industry t T total 0 Vtotal Vtotal 8 15 S 15 15 wet Kwspm 8 8wet KWSpIn 0 O667 V 23 V 23 total total S volumetric efficiency factor T shape efficiency factor Copyright 2003 29 Narayanan Komerath Note Blended Body designs LD 45 at Mach 12 with r 0104KW 264 BCDO 00574 Ref Froning H D Jr Leinang J L Impact of Aerospace Advancements on Capabilities of EarthtoOrbit Ships International Astronautical Federation Oct 1990 Copyright 2003 30 Narayanan Komerath Summary of Parameter Groups pppl WR 1 Wstr Swez V pp Size fineness ratio geometry Vtot Wstr OEW W pay r OEW pay Swet KW Spln I Propulsion concept propellant aerodynamics energy p Materials structural concepts manufacturing capability lsz r rstr Materials size fineness ratio geometry Approximately constant Size fineness ratio geometry Copyright 2003 31 Narayanan Komerath External Aerodynamics Correlations Empirical correlation parameter by Dwight Taylor 1993 15 0667 V S F tot wet S S pln pln L A Kuchemann max MMach Number A and B empirical 1959 Future SOA Used Here Slender Orbital Aircraft 4 3063 A 3 3 B 3 3 Copyright 2003 32 Narayanan Komerath AE6450 Fall 2004 Lecture 17 Performance Characteristics Of Airbreathing Engines Copyright 2003 Narayanan Komerath Aerodynamics Correlation 5 23063M3 D max M BCDO 005772 exp04076F Zerolift drag coefficient is a function of relative volume Relative wetted area and Mach Number Total drag can then be estimated using approach of Vinh CDSpIn CDO 1 BSpln Copyright 2003 34 Narayanan Komerath Different cases Acceleration CL O1CLLDmax 1 B 2075 Minimum fuelflow cruise CL O82CL LDmax 1 B 275 Glideat LDmax CLCLLDmax1B30 Copyright 2003 Narayanan Komerath Given a reference configuration and drag thrusttodrag along the Trajectory can be corrected for total volume T T IBCDO Tref E r 5 ref IBCDO 7 1 TDT SPETref W Tref ISPET WR WRgtrrereXp Thus from trajectory analysis the dragcorrected propulsion index I IS Opp p p WR 1 in density units Copyright 2003 36 Narayanan Komerath Propulsion Systems 3 broad categories of ab propulsion 1 Combination of individual engines operating separately perhaps including rocket engine 2 Individual engine usually rocket operating with an engine that can operate in more than one cycle mode or a combined cycle engine 3 Single combined cycle engine that operates in all of the cycle modes over entire flight trajectory Copyright 2003 37 Narayanan Komerath Altitude speed representation of performance boundaries 1 For a fixed entropy rise engine cycle entropy of nozzle exhaust gas increases with altitude 2 At high speed air kinetic energy gtgt Brayton cycle heat addition Rate of maximum combustion energy to kinetic energy per unit mass of air Qnet 2Q77Carnot KE U2 Carnot cycle loss due to unrecoverable loss of energy because the atmospheric temperature gt 0K Ucamot reasonable Energy available to overcome drag and provide acceleration is reduced by 4 every time the flight speed is doubled Speed where available energy drag energy maximum airbreathing speed 38 Copyright 2003 Narayanan Komerath From energy viewpoint practical airbreathing speed 14200 fps 433 kms Practical may be really 39 kms 12700 fps with potential to reach 427 kms with improvements in materials Altitude gt 120000 degrades operation due to increasing entropy Excess hydrogen can combine with dissociated air gt thrust upto 170000 ft Copyright 2003 39 Narayanan Komerath Major Sequence of propulsion cycles Figure Rocket derived air augmented 1 Rocket motor as primary ejector M lt 6 2 Ram rocket gt rocket operated fuel rich gt exces ue bm air M lt 6 Airbreathing rocket M6 diffuser static pressure T 1666K Copyright 2003 40 Narayanan Komerath Reduce temperature of air a Deeply cool airjust short of saturation Use turbo compressor to pump air gas into rocket chamber b Liquefy air and turbo pump liquid air into rocket chamber Disadvantage large nitrogen mass into combustion chamber gt increased thrust and propulsive 7 Copyright 2003 41 Narayanan Komerath a Deeply cooled rocket Expanded cycle rocket developed for HOTOL Hydrogen air heat exchanger in air inlet to capture inlet air kinetic energy gt controls air temperature and limits work of compressor gt compressed hydrogen air enters rocket combustion chamber gt turbo compressor gt drive expansion turbine Works for M lt 6 Copyright 2003 42 Narayanan Komerath LACE engine Liquid Air Cycle Engine Hzlair heat exchanger gt cool inlet air to near saturation gt pressurize to a few atmospheres liquefying heat exchanger gt turbopumps liquid air into rocket motor gt heat exchanger needed in combustion chamber gt airbreathing rocket M lt 6 Reduces Mass ratio to 5gt58 range 02 fuel to 3 Copyright 2003 43 Narayanan Komerath 3 Thermally Integrated Combined Cycle Propulsion Rocket ejector gt ramrocketramjet gt thermally integrated into a rocket propulsion system gt Integral rocket ejectors provide thrust and compression at low Mach Number gt Deeplycooled turbojet thermally integrated into expander rocket becomes analogous to rocket ejector ram rocket ramjet excellent lowspeed performance Copyright 2003 44 Narayanan Komerath 1 2 KLIN cycle Deeply cooled turbojet rocket Precooler on turbojet gt Takeoff to M 55 with rocket augmentation through transonic range Conventional cryogenic rocket for M gt 55 934 F But produces lowspeed thrust Mass ratio 55 to 6 Deeply cooled rocketramscramjet for HOTOL subsonic throughflow ramjet Ramjet above Mach 6 Weight ratios 3 to 4 9lt1 F Copyright 2003 45 Narayanan Komerath 3 LACE Rocket Ram Scramjet Thermal energy from air hydrogen combustion drives expansion turbine gt turbopump Cools inlet air to saturation using airH2 heat exchanger pressurizes gt liquefies gt turbopump gt rocket chamber H2 exiting turbo machinery goes into ramjet chamber Airbreathing rocket and ramjet operating in parallel for M lt 6 For M gt 6 ramjet converts to scramjet Rocket takes over at scramjet shutdown For airbreather operation to 12000to 14000 fts Mass ratio 3 to 4 2lt1 F ISp 4500 sec at Mach 3 to 6 Copyright 2003 46 Narayanan Komerath 4 Thermally Integrated Enriched Air Combined Cycle Liquidenriched air is separated into nearly pure LOX and oxygen poor nitrogen NZ gt ramjet equivalent to mixed flow bypass turbofan a ACESLACE Ejector RamScramjetrocket ACES Air Collection Enrichment System 90 LOX stored for rocket portion N2 reduces mass averaged velocity gt noise reduction Weight ratio lt 3 05 F ACES Deeplycooled Ejector RamScramjet Rocket Not yet developed as propulsion hardware Weight ratio lt 3 05 F Copyright 2003 47 Narayanan Komerath Cycle Comparison Combined cycle reduces gross weight by 2 to 45 times the W0 E compared to rocket Copyright 2003 48 Narayanan Komerath gt If weight ratio gt 43 best launcher is VTOHL If less HTOL may be ok For 6000 Nmz WIS maximum absolute speed must be gt 10000 fts for HTOL to be good Landing WIS 2200 Nm2 Fighter Bottom line with LACE 40 of oxidizer eliminated from launch weight Oblique Detonation Wave Engine ODWE can be one operating regime when internal drag becomes too large Copyright 2003 49 Narayanan Komerath AE6450 Fall 2004 Lecture 6 Monopropellant Thrusters Copyright 2003 Narayanan Komerath Monopropellant Thrusters Regulator valve Single propellant Tank Thruster Recall that monopropellant thrusters are used for many lowthrust applications low total impulse Types 1 Cold gas thrusters 2 Hydrazine catalyst 3 Hydrogen Peroxide catalyst 4 Resistojet electric These are relatively inexpensive thrusters but their performance is also relatively low Copyright 2003 Narayanan Komerath Cold Gas Thruster Candidate gases He lsp 180 sec vacuum large a NitrO en lsp 80 sec Reca 6 oc yRTO High gamma and low molecular weight help get a high exhaust velocity Other considerations include safety toxicity storage pressure thus tank weight required gas mass related to density Copyright 2003 Narayanan Komerath Cold Gas Thrusters contd Energy comes from high gas storage pressure expelled via a simple blowdown system Typical propellants pressurized include He and N2 Features Low thrust Low performance Simple and cheap No need for a heat addition system Nontoxic eg rendezvous with ISS Used primarily for attitude control Courtesy U Queensland HYSHOT Flight Program httpwwwmechuqeduauhvperhvshothvshot thruster39pg wwwmechugeduaul hyperlhyshot approx BOON of thrust w bottle pressure of21MPa could also turn valve on and off reliably in 1 ms Copyright 2003 4 Narayanan Komerath Cold Gas Thruster Example Initial tank pressure is 100 atmospheres 101 E7 Pa Initial temperature in the tank is 300K Tank volume is 02 m3 Nozzle expansion ratio is 20 Nozzle is a 15degree conical nozzle Throat area is 1 cm2 Thruster is operated in vacuum space Further assume an isothermal system so that with short impulses heat will leak into the tank from the rest of the satellite to maintain stagnation temperature of 300K Assume a pressure regulated system so that the nozzle upstream stagnation pressure is 10 atmospheres Thus the thrust level can be kept steady until the tank pressure falls to 10 atm Assume the flow below the regulator is isentropic Copyright 2003 5 Narayanan Komerath For N2 molecular weight is 2802 This gives R 296 Joules per Kg per Kelvin Specific heat ratio gamma is 14 fully diatomic at 300K a Determine the initial and final nitrogen mass in the tank m m 101E702 quot 296300 The final pressure in the tank is 101 E6 Pa Temperature is unchanged from 300K 2275Kg Residual mass is mf 2275Kg Copyright 2003 6 Narayanan Komerath b Determine the c and isentropic CF Assume constant To isothermal T 300 K V VRTO 14296X320 4352ms y1 y 2 2y 1 142j y1 24 To get CF we must first know PePo for e 20 6 1 12 2 For gamma 14 this gives 7 y 2 j er1 8 02588 8 12 02857 2 07143 U7 1 K K 1W J W m PC PC Copyright 2003 Narayanan Komerath Trial amp error solution From charts of this function guess pressure ratio of 0002 for e20 Gives a 2405 too high Change guess of pressure ratio to 0003 Gives a 1823 too low Linear interpolation at s 20 pressure ratio 00027 Exact solution 000262 Nozzle efficiency factor for divergence losses in the 15degree conical nozzle 221Cosa 039983 H 12 71 CF21 y Muse p 71 71 190 190 Vacuum Pa 0 Gives CF in vacuum 1662 Copyright 2003 8 Narayanan Komerath gtxlt c Fmd Isp Isp CF 2 27374560 0 d Assuming choked flow find the mass flow rate of propellant thrust and total impulse available in this system m ZLCFZMZM p Spg0 CFcilt 0 go 80 mp 20232kgs From Part a the mass used up is 20475 kg Therefore Burn time is 8825 seconds Thrust is 1679N and total impulse thrustburntime is 148kNs assuming that the tank stays at constant temperature Copyright 2003 Narayanan Komerath Real Cold Gas System not isothermal If the system is on for some time we can no longer assume that the tank temperature is constant isothermal As the gas is expelled its temperature will drop see Humble p 144145 As a result c decreases lsp decreases mass flow rate of propellant increases for the same thrust Copyright 2003 10 Narayanan Komerath Decompositionbased Monopropellant Systems Relative to coldgas systems monopropellant systems that release heat due to a catalytic reaction have higher performance and lsp and use liquid storage which means more compact and lower pressure hence lower tank weight Copyright 2003 11 Narayanan Komerath Candidate propellantsOnly Hydrogen Peroxide nPropyl Nitrate and Hydrazine thrusters have been flown Propyl nitrate used to start jet engines rejected due to shock sensitivity Hydrogen peroxide decomposes slowly causing tank pressure increase and propellant dilution Hydrazine is now the mono propellant of choice Hydrogen Peroxide H202 Usually expressed as a percentage of H202 in a solution with water by m 1 atm Boiling Average density kgm3 at Storage mass temp 77F temperature 95 326 2948F 1414 Room temp H202 98 334 2992F 1432 Room temp H202 Note Drugstore hydrogen peroxide is about 30 Copyright 2003 Narayanan Komerath Hydrogen Peroxide Decomposition H202 deteriorates with time as it naturally decomposes into H20 and 02 Hazel and Huang give a concentration decrease rate of 1 per year In the presence of a catalyst Humble p 242 2H202l quotH20l n 2H20g 02g Q Q 10848kJ of heat released exothermiC Where n is determined by the original concentration of H202 Higher concentrations give better performance due to higher temperatures and lower molecular weights in the exhaust products avoid vaporizing inert H20 This reaction is fairly complete in the presence of a catalyst Copyright 2003 13 Narayanan Komerath Early Catalysts for Hydrogen Peroxide Early catalysts where liquids were injected into H202 Potassium permanganate KMnO4 sodium permanganate German V2 gas generator application These systems worked but required complex injection valving timing etc to manage the reaction Copyright 2003 14 Narayanan Komerath More Recent Catalysts Later I quot a 39 r palladium Ul gtiIVEl r 39 39 anu me chamber H202 39 Catalyst Pack wire screens 5cm long with AD to allow 250kglmZs Cupynghua mm 15 Narzvanan Kumerath Performance of H202 thrusters The decomposition of H202 is relatively cool by rocket engine standards say 1000K to 1500K for the exhaust products depending on concentration 100 H202 gives a temperature of 1250K 1277K Although hot many metals retain their strength at these temperatures therefore H202 thrusters do not require active cooling radiation only At these temperatures the lsp of an H202 system is 140 sec to 190 sec Copyright 2003 16 Narayanan Komerath Hydrazine Monopropellant NZHA Very popular and widely used monopropellant Storable Highest performance of monopropellants e liqu Toxic Molecular weight 3205 Density 1010 kglm3 B 9 temperature 2354F Li uid storable at room temperature 39 Heater amp Catalyst Pack Mass flux 200kglmZs through catalyst Cupynghua mm 17 Narzvznan Kumerath Hydrazine Reactions For hydrazine there are 2 reactions one exothermic and one endothermic 3N2H4 a 4NH3 N2 33628KJ in the presence of catalyst But also 4NH3 a 2N2 6H 2 1844KJ absorbs heat This reaction absorbs heat and this reduces lsp With proper design of the catalyst bed we can limit the amount of ammonia that is dissociated according to the above equation say 50 range is from 30 to 80 Specific heat ratio gamma increases from 12 at 20 ammonia decomposition to 136 at 100 At 50 gamma is 125 The performance of this system is a direct function of the amount of ammonia decomposed in the above equation Copyright 2003 18 Narayanan Komerath Catalysts for N2H4 Mariner In the 60s nitrogen tetroxide slugs were used as a liquid igniter to raise the temperature of a monopropellant system so that the reaction would continue However this required a priori knowledge of the number of starts required Later catalysts current Currently beds of ceramic pellets coated with iridium Shell 405 pellets 1962 allow the NZH4 to decompose without an igniter Multiple restarts are also possible Copyright 2003 19 Narayanan Komerath Hydrazine Thruster Performance For steadystate operation with a hot catalyst bed Brown Hydrazine lsp 230s at sealevel c3952 fts Tf 1394K Range 220230s vacuum lsp Monopropellant thrusters are generally pulsed to provide attitude control Some short time is needed to heat the catalyst and hydrazine up as the thrust comes up Shown below is a qualitative thrust profile after a cold start Ignition delays may be 1020 ms at catalyst and propellant temperature of 40 to 70F delay down to 1ms at catalyst bed temperature of 500F Pressure rise time to 90 of steady state gt 15ms with tailoff time to 10 of steady state gt20ms 100 90 Thrust 10 ON Time OFF Copyright 2003 20 Narayanan Komerath Hydrazine Pulsed Thrust Profiles If the system is cold very short pulses or a long interval between pulses the lsp and thrust can fail to reach steadystate values 230 Steady state lsp lsp 107 ms pulse 14 ms pulse cold lsp 120 60degF exhaust 1 sec 10sec 1005ec Time Between Pulses Negative pulses OFF from steadystate ON are used for attitudecontrol eg Magellan during Venus orbit insertion Copyright 2003 21 Narayanan Komerath Catalyst Life Cold starts create pressure pulses in the catalyst bed that damage the pellets over time For this reason and performance reasons discussed above monopropellant hydrazine thrusters often have heaters to keep the system warm 475K 600K With heaters catalyst beds can last up to 500000 to 1 million pulse cycles Brown pg62 Voyager FLEETSATCM FLEETSATCOM 01lb thrusters maintained at 315C rated for 1 million cycles Voyager 200 C 400000 pulses Copyright 2003 22 Narayanan Komerath Monopropellant Thruster Weight Correlation Weighrabs 034567F055235 Note Above is for a thruster with a single valve least squares fit to data in the range Where thrust is between 1 and 150lb and weight up to 5b In addition the weight tends towards the weight of the valve at the low thrust limit Minimum valve weight is roughly 04lb Copyright 2003 23 Narayanan Komerath Electrothermal Monopropellant Thrusters This type of thruster uses electrical energy to heat a monopropellant working fluid or add additional heat to the decomposition temperature 1 Resistojet heat transfer through resistance element 2 Arcjet heat transfer through electrical arcing For a resistojet with hydrazine the lsp can be 300 sec For a resistojet with hydrogen Hz the lsp can approach 840 sec However power is high and TNVe is low power conversion 65 to 90 Copyright 2003 24 Narayanan Komerath Arcjets Arcjets are less efficient at converting power to lsp 20 to 30 but higher lsps are possible 500sec to 1500sec still low TNVe Variations include Microwave heated flow and coupling of magnetic fields to rotate the electrical discharge magnetoplasmadynamic MPD see Humble p 525 Copyright 2003 25 Narayanan Komerath Catalytic vs Electrothermal Hydrazine Thrusters Relative to traditional hydrazine monopropellant thrusters electrothermal thrusters Are capable of higher lsp Require additional spacecraft power Have higher weight lower TNVe Typicaly require a preconditioning period to heat up the elements Good for steady lowthrust burns Good when substantial spacecraft power is available for short periods Copyright 2003 26 Narayanan Komerath Electric thrusters Atlantic Research Co mgr Pawn mmnnia uwanclssmg um mm m k Hvdmzin 1th Elnunlhermnl Hvdmzim mm m A P a a Svsum mm Plasma Thrustev Hnlnhms m Cupyngme mm 27 NammnKumEm Xenon ion thruster Copyngm 2003 Naravanan Komerath AE645O Fd 2004 Lecture 9 Turbomachinery for Liquid Rocket Engines 2 pump analysis Copyright 2003 Narayanan Komerath Centrifugal Compressor Geometric Parameters U2 T C J she 2r1 Jk Copyright 2003 Narayanan Komerath Centrifugal Compressors Application regime 1 Where frontal area is not a major issue 2 Small engines flow passages for axial machines become too small secondary flow losses become large there 3 Low partscount minimize number of stages and blades 4 Multiphase flows Centrifugal compressors can achieve large stage pressure ratio because the pressure rise mechanism is not just recovery of momentum hence boundary layer separation is not a major fear Copyright 2003 3 Narayanan Komerath Relation Between Work and Turning Angles Conservation of Angular Momentum gives with 1 and 2 denoting compressor inlet and outlet T 92 rca1 m Torque per unit mass flow rate rate of change of angular momentum Work done on the fluid per unit time per unit mass flow rate by the rotor is UT WTUC 92 Cal 2 2 C C wzhoz h012h2 h1 quotFL L 2 2 c 2 62 2 1 12 h1UC 92 Uco1 Thus 2 2 Copyright 2003 4 Narayanan Komerath Relation Between Stagnation Temperature and Flow Turning Angle Absolute and relative velocities same system as for axial machines 66UW6 crzwr czzwz 2 2 2 2 6 cr 66 62 2 2 2 2 w w w6 wZ 1quot Energy equation applied to a streamline in a reference frame fixed to the rotor Copyright 2003 5 Narayanan Komerath Pressure rise in centrifugal compressors erz a w2 For changes along a streamline dh d 2 Using the state equation Tds dh dp 2 2 2 d 9 r dl TdS p 2 2 For isentropic flow dp 9272 dwz 2 2 In the case of axial compressors dr 0 along a streamline so that the first term is negligible Thus pressure rise can come only from velocity change In the case of centrifugal compressors pressure rise can come mostly from the first term Not limited by flow separation Copyright 2003 Narayanan Komerath Impeller Designs 0 Backwardleaning Forward39leaning Copyright 2003 Narayanan Komerath Stagnation temperature rise Assuming uniform angular momentum of the incoming fluid uniform swirl 2 Tog Tmy1e coincal T01 5 01 U2 U22 If the inflow is purely axial no swirl 2 T02T01 1 i Caz T 7 U 01 am 2 For all 3 impeller geometries forwardleaning radial and backwardleaning 662 2 U2 Wrz tan 62 Hence 2 Toz Tm 2 i W 1 1F2t Tm 7 U an 2 a01 2 Copyright 2003 8 Narayanan Komerath Centrifugal Pumps Variables J T Power P mU2AC62 2H 2r2 m Mass Flow Rate U2 Impeller Tip Speed l gtl b l4 A Increase in tangential component of absolute fluid velocity C492 through impeller Equal to tangential component of absolute fluid velocity at the impeller tip if there is no preswirl 11 APO 2 Dimensionless ressure variable PU2 p m Z erPUZ Dimensionless flow variable For an ideal pump W 1 tan 62 Copyright 2003 9 Narayanan Komerath Pressure Rise vs Flow Rate Characteristics For an ideal pump W 1 tan 62 Forward Leaning B2 ve Straight Radial 320 Backward Leaning B2 ve n397 27Z39r2pr2 Copyright 2003 10 Narayanan Komerath Nondimensional groupings Pump pressure rise Apo fQmpydesignD Pump efficiency 2 2 Agozzf msQ D design pg D 0ng 122 2 77p9 m 39 D design u p903 APO 09202 Can be shown that W OC and Copyright 2003 Narayanan Komerath mAPo pP rh Docm3 QeH p02 Pressure rise can also be written as W where H is the hydraulic head of the pump V f Redesign butindependent of Reynolds number for Up 9 turbulent flows pWL Regt1o6 Actual qr is less than ideal because 1 Fluid does not leave impeller at the blade angle 3 there is slip 2 This means that the work done is less than ideal 3 Frictional losses in rotor and stator especially if the flow is partially stalled Copyright 2003 12 Narayanan Komerath Turbines Types of high speed turbines include 1 Impulse turbine nozzle accelerates flow into rotor multistage 2 Pressurecompounded turbine more than 1 impulse good general purpose turbine for GG cycle with large pressure drop 3 Velocity compounded turbine nozzle then rotorstator fallback option for GG cycle if blades of pressure compounded turbine are too short lt 05cm 4 Reaction turbine no nozzle just nozzlestarter rows more common on low pressure drop turbines like stage combustion or expander cycle 50 50 reaction means 50 of pressure drop occurs in rotor and 50 in starter See Fig 536 and 538 from Humble Copyright 2003 13 Narayanan Komerath Performance calculations C0 isentropic spouting velocity maximum available velocity for expansion through the pressure ratio of the turbine y l C0 242CPTi 1 1 y t ralio units are ms if CP Ki 21000CP m T K deg 600K for expander and 1100K for GGSC P PlaU0 M 2 20 25 for GG and 23 for SCExpander Plurbine exil Copyright 2003 14 Narayanan Komerath Net Positive Suction Head How far the inlet pressure is above the vapor pressure About 10 20 is considered adequate to prevent significant cavitation problems P P NPSH w net positive suction head m ft gp Table 31 pp 696 Humble Copyright 2003 15 Narayanan Komerath Mean Pitch Line Velocity Um At various material temperatures the maximum mean pitch line velocity um is limited by turbine blade material properties Steel 450 ms Titanium 2200 ms eg Aluminium 2219 Titanium 6242 lnconel lN100 lnconel 718 Waspaloy etc see Fig 537 For a given material and Ti the um can be found See Fig 537 Humble Different turbine configurations have different efficiencies as a function of um C0 What is shown in the figure is Ideal efficiency real will be about 95 of these numbers for large turbines or 75 of these numbers for small turbines Copyright 2003 Narayanan Komerath shaft power Fluid power 7 1 1 y Pavail shaft UT 771 CpTi 1 t ratz39o J where CP 7 K degrees MT KgS through turbine P p w l ralzo P turbine exit Copyright 2003 17 Narayanan Komerath Example For a twostage 50 reaction turbine driving a stagedcombustion cycle pump with B ratio 2 m 10Kgs material IN100 7 1000K 7 125 CP 2 25 J 77 12gmmole mole K What are the C0777T and the turbine shaft power 125 1 C0 21000gmkg25Jng1000K be 125 12gmmole 7344ms spouting velocity From Fig 537 for lN100 um 450ms mean pitchline velocity SO um 450ms C0 7344ms Copyright 2003 18 Narayanan Komerath From Fig 539 7h ideal z 88 for 2 rotor reaction 88T95 836 knock down 3 25 P 2 8361 0Kgs1 0009mKg2152Jg 01000K 1125 P2254 MW to the shaft Note Humble also reviews various arrangements for the pumps and turbines and gives examples and reasons for favoring each Copyright 2003 19 Narayanan Komerath Successful Designs RocketDyne Mark 3 2500 produced or H1 pump below Both fuel and LOX pumps on the same shaft Each has Axial inducer single centrifugal stage pump on the same s aft Twostage axial turbine running at 49 times the pump speed This cutaway drawing of the turbopump for the H1 engine shows the backto back arrangement of oxidizer pump at left end and fuel pump at right end operating off a common turbine and gear box center The propellerlike inducer blades can be seen on the left end of the shaft historynaszgnv suznsipsupg Copyright 2003 20 araVanan Komerath A cutaway drawing of the Mark 10 turbopump for the F1 engine httphistorynasagov SP4206ch4htm Copyright 2003 21 Narayanan Komerath SSME Turbopumps LOX and LH2 inducers separated from respective pumps and driven by different turbines at very different speeds One centrifugal stage for LOX highest pressure Three centrifugal stages for LH2 No gear reduction unit 4 1 IIIquot I II SSME POWERHEAD C39OMPONENI ARRANGEMENT Cm IDEZER HIEURNH maH unsure oxmlm ma 50mm MIG WSWquot mm emanate enmm mnmam 5 mootum 7g httpelifritzmembersatlanticnetphotosssme3gif Copyright 2003 22 Narayanan Komerath Copyngm 2003 Naravanan Komerath Copyngm 2003 araVanan Komerath Pressure disiribuiion on nq32 impeller surface Picture from gnd ievei 2 krepsilnn rurbuienee made Whale gnd 1134592 eeJis 16 black The Laboratory of Applied Therrmdynarries HUT Finland pressure 70000605 61250605 52500605 43750905 35000605 m w s lw Copyright 2003 Narayanan Komerath 26 Pressure disiribuiion on nq32 impeller surface Picture from gnd ievei 2 krepsilnn rurbuienee made Whale gnd 1134592 eeJis 16 black The Laboratory of Applied Therrmdynarries HUT Finland pressure 70000605 61250605 52500605 43750905 35000605 m w s lw Copyright 2003 Narayanan Komerath 28 Combustion of Liquid Propellants Combustion efficiency approaches 995 unlike the 97 of jet engines High temperature very high reaction rate thorough mixing In small thrusters with few injectors efficiency might be only 95 Based on Sutton Sakheim et al AIAA 791301 Injection atomization amp ignition 39 Rapid combustion Streamtube combustion subsonic Transonic region Supersonic expansion HAHCWSUSIMMEHWHR 39 Copyright 2003 29 Narayanan Komerath Injection Liquid jets enter chamber at relatively low velocity partial evaporation interaction of jets amp highpressure gases Atomization lmpingement ofjets or sheets liquid fans formbreakup into droplets secondary breakup liquid mixing some liquid reaction oscillation of jets or fans vaporization reaction Vaporization Droplet gasification amp diffusion heat release Low gas velocity crossflow Radiant and conductive heating acceleration Vaporization influenced by pressure and temperature oscillations and acoustic waves Copyright 2003 Narayanan Komerath Rapid Reaction Zone Mixing amp reaction turbulent mixing chemical reaction interaction with turbulence As temperature rises density drops Spatial and temporal variations some tangential and radial flows Rapid chemical equilibrium Copyright 2003 31 Narayanan Komerath Expansion in Chamber Turbulence increasing axial gas velocity Formation of boundary layer acceleration Streamlined highaxialvelocity flow 200 600 ms Residence time in chamber 10 ms Energy release 370 MJm3s Copyright 2003 32 Narayanan Komerath Combustion Instability Fluctuations in heat release and pressure interact with natural frequencies of feed system vehicle structure and chamber acoustics periodic superimposed oscillations Under smooth combustion pressure fluctuations may be 5 of Pc Rough combustion random fluctuations Unstable Organized oscillations at welldefined intervals possibly growing Types 1 Lowfrequency chugging or feed system instability 10 400 Hz Linked with feed system if not entire vehicle 2 Intermediate Acoustic buzzing entropy waves 4001000Hz Linked with mechanical vibration injector manifold flow eddies OF fluctuations feed system resonances 3 High frequency gt1000Hz Combustion pressure waves chamber acoustic resonance Screaming screeching squealing Copyright 2003 33 Narayanan Komerath LowFrequency Instability Source Sutton text Due to pump cavitation gas trapped in propellant flow tank pressure control fluctuations vibration of enginefed system or coupling of structural amp feed system POGO Large launch vehicle longitudinal oscillation at 1050Hz Cure Energy Absorption devices in fuel lines perforated tank liners special tank supports Partiallygas filled pogo accumulator Pogo frequency changes as vehicle mass changes NASA KSC69PC413 o suppression in propellant lines Pogo induced pressure waves a f httpMmmclaviusorg mglp ogoabsorbergif Copyright 2003 34 Narayanan Komerath Buzzing Source Sutton text Seldom gt5 of Pc but may initiate high frequency instability Cause is coupling between combustion process and flow in propellant feed Acoustic resonance of combustion chamber with critical portion of Pump Prevalent in mediumsize engines 2000 to 25000 N Transverse modes dominate in large liquid rocket engines especially near the injector Combination of spinning and standing waves also occurs Copyright 2003 35 Narayanan Komerath Screech Screaming Energy content increases with frequency destructive Longitudinal Transverse tangential and radial Spinning or traveling Standing wave pattern fixed amplitude oscillates at given point Traveling wave amplitude fixed at given points wave travels rotation of whole vibrating svstem Flap in a Typical p 4 Li392735 i l Hr l tiarar 1251 lEl 3 1 1 Fr y agrant5 air xquot 3919 Jan1 eW if lLl tl 1 W MT3E1 m lat2 maxi 1 Ml ha 5 din E 1 a j grgmr39r 1quot 1 39 A I h 11 391 139 quot 5 viquot 39BiCaJ 34 varies Eta naner a T39f caquot 71 Wis1323 i a iu l Streaming In lm 139air i lath Tarzujun a Marin Copyright 2003 36 Narayanan Komerath Screech continued Energy for screech is believed to be predominantly from acoustically stimulated variations in droplet vaporization andor mixing and local detonations distinct boundary layer seems to disappear heat transfer rates increase by orders of magnitude Tangential modes are the most damaging heat transfer goes up by 4 to 10 times Popping as trigger Random highamplitude pressure disturbance with hypergolics with some characteristics of a detonation wave Irregular cavitation at the inducer impeller can trigger instabilities In jet engine exhaust flows screech is attributed to interaction between shear layer vortices and shock waves resulting in acoustic feedback outside a supersonic jet Copyright 2003 37 Narayanan Komerath Natural frequencies Frequency 1 kTR l MW is the universal gas constant I A where R T is local average absolute temperature a is local speed of sound I is wavelength Copyright 2003 38 Narayanan Komerath Rating Techniques Introduce shock waves into the system and study the response in time and frequency content Usually use prototype heavywalled chambers not flightweight chambers 1 2 9075 Nondirectional bombs six 250grain pellets of RDX or PETW encased in teflon nylon case Oriented explosive pulses from a pulse gun through the chamber sidewall varying amplitude Directed flows of inert gas through the sidewall Momentary operation at offmixtureratio Introduce slugs of inert gas Hard start Copyright 2003 39 Narayanan Komerath Control of Instabilities Longitudinal instability passive geometric control Thermoacoustic active control Helmhotz resonator enclosed volume with small tubular opening damping twice per cycle due to inflow and outflow jets Helmholtz resonators used at periphery of injector plate Corner forms a pressure antinode and velocity node Copyright 2003 40 Narayanan Komerath Amplitude psi Amplitude spectra of combustor pressure The instability shows a 03 psi 0 5 3 Open Imp peak at 530 Hz When controlled by a Mode nhased cuntml modelbased instability control method Adaptive phaseshift control and by an adaptive PhaseShifting D 4 method the peak is reduced to 02 l r psi l DeLaat J Chang 0 NASA GRC I In 03 02 11 httpwwwgrcnasagovNVWWRT200250005530deIaathtml gig I 0 20539 4W GDD Frequency Hz SDU 1 EDD 41 Other liquid rocket engine components Injector Various impingement patterns can be used to help mix the propellants and maximize combustion efficiency and minimize combustor length L like doublets unlike doublets triplets concentric tubes pintle ZZkN m 17 luucnmzm w Ncoolinl 5 E02 Ea Eli I N H2 H2 0 H2 02 o 02 z uwmawsm vARIous ankoszNuva N mums httplwwwhqnasagovof cepaoHistoryS P 4404p22jpg Copyright 2003 42 Narayanan Komerath AE6450 Fall 2004 Lecture 13 Electric Propulsion Copyright 2004 Narayanan Komerath Perspectives on Achievable Performance Hill amp Peterson Minimum energy expenditure in taking 1 kg of mass to Earth Orbit 9kWh Earth Escape 18kWh Chemical energy depends of mass of propellant used upper limit on energy per unit mass H202 37kWh per kg Upper limit on chemical propulsion specific impulse 500 5 Nuclear thermal energy transfer must come across some solid walls maximum propellant temperature is limited by maximum wall temperature Max specific impulse may be around 10005 Copyright 2004 Narayanan Komerath Electrical No upper limit identified on energy transfer per unit mass no upper limit on specific impulse Energy source can be solar or Energy from nuclear fuel which has extremely high energy density orders of magnitude gtgt chemical Ffuopellanl Eleclriu Velocity Charmin1 iiii i uf Tami mpulsa Elmmi wwwislandoneorgAPClectric00html Tme Courtesy RobertH Frisbee JPL Copyright 2004 3 Narayanan Komerath Several classes of electric propulsion 1 Electrothermal resistojets and arcjets N2H4 2 Electromagnetic steady MPD and unsteady pulsed plasma thrusters PPP stream of conducting fluid is accelerated by electromagnetic and pressure forces Most easily used in pulsed operation for short burst of thrust 3 Electrostatic ion propulsion Propellant consists of discrete particles accelerated by electrostatic forces Particles usually atoms are charged by electron bombardment Here we will concentrate on ion propulsion Fig 917 Humble Ion Propulsion Copyright 2004 4 Narayanan Komerath E emntherma Hvdim zine Thrusten39 Hydrazinla Arniets and Power Prunessing Unit Pulmd Plaama Thruster High PDWEI Ammuma wwwrocketcomepandsehtml Arniet and Feed System Copyright 2004 Narayanan Komerath Hanan In Engine wwwrocketcome andsehtml Functional Model Thruster FMT provided by the NASA Glenn Research Center The FMT is functionally equivalent to the 23 kW NSTAR ion thruster that flew on Deep Space 1 NSTAR was the first demonstration of ion thruster technology as primary propulsion on an interplanetary spacecraf Copyright 2004 6 Narayanan Komerath www nnnin Ilmirh 39 smaljpg Copyright 2004 3111 Propellants for lon Propulsion Various propellant types have been used We generally want a cheap easily ionized dense propellant with easily accelerated particles Xenon Argon Krypton Cesium 060 Carbon 60 Copyright 2004 Narayanan Komerath D51 ion propulsion system mswnni Mama 9 4Eki l m l Ian mm I 0 3 v us wwwmumrgscl snezmclusnasnn mu Cupyngm 2n n4 Namvanan Kummm I sac Chnmical Thrust N http wwwwrssc gpp uc a edudawn magesCR4845 gwf ctrussell ucla edu Resistojet Propellants THE39FIIIAL mm1m 0 mm mquot 539quotme ammonia biowastes Elam Amu u CourtesyDr RobertH Frisbee hydrazme hydrogen r Augmented hydrazine r 39 thruster augments catalytic decomposition fgx 39fgg lSID 300 lbeslbm Input power few hundred kilowatts 60 90 efficiency 30 better performance than cold gas thrusters LHEAT ElmM EH FDWEH SUPPL F wwwisandoneor APCEectricl02htm Technology issues materialpropellant compatibility at high temperatures heat transfer radiation losses Heat transfer to gas stream is complicated by the geometries and temperature ranges typical of resistojets Hydrazine resistojets used on several communication satellites Four TRW hydrazine thrusters on Ford Aerospace39s INTELSAT V satellites for station keeping Thrust of 022 to 049 Newtons and lsp 296 lbfslbm require 250 to 550 Watts of power lsp 336 lbfslbm and operational lifetimes gt 26 x 103 Ns demonstrated Copyrlght 2004 Narayanan Komerath Arcjets ode Insulator HopeHam Flm39uI Aquot 39 Tungsten I Camade I I Tho a tedTungstan Constriclor FIPIEJET www9roiectr hocoml rocketrocket3c2htm Copyright 2004 12 Narayanan Komerath Arcjet Thruster cums mm mm Full length 1022mm Electrode gap 00 mm Mam Maternal Tungst usterlarcjet thrusterjpg mp NWWW aero kyushuru ac jpmes Ludyarothrusterarqebmrustenp Thruster Performance Mass Flaw Rate 00 o m o I K mgsec N ran n Speci c Impulse sec 00 o m o 30 0 40 0 50 0 Speci c Power MIkg EkcEIcvwev um um unlh l z m Luneni swine 4 Arcjet Thruster Design Considerations for Satellites NASA preferred reliability practices PD h l WWWh sa ovof Operational Characteristics 1 High voltage mode Low voltage mode 10mgsec Nitrogen 10mgsec Nitrogen 10A 30V 10A 22V http lwww aerokyushuu ac jp 39nlstudyarc th rusterarcjet thrusterjpg Operational Characteri tics Copyright 2004 m Narayanan Komera Operational Characteristics a E i s Hydrazine Resistojets RCA SATCOM GStar and Spacenet communication satellites utilize hydrazine resistojets manufactured l by Olin Rocket Research quot9now Primex Aerospace wwwisandoneorgl APCElectricl02htm Copyright 2004 19 Narayanan Komerath pmszme mm 5 mun nzslsmn 333433 39AUGMENYAnuu ML quotEm mm MouNnNssmucmRE va man was suPPuRT 44m swam HEAY sxcmnazn emu 30m um sxcumuzn mum mm ans GENERAmn wuzuvznv was awe sum AUGMENYAYION new mam Figure 4 Augmcnled Can ylic Thvusler 20 httplwwwirsunistuttgartdeRESEARCHIELPROPIRESeak04b12gif Augmented Catalytic Thruster Schub N O8O36 Betriebsdruck bar 26562 Spez Impuls s 299 Min Impuls Bit mNs 8896 Gesamtirnpuls st 5249 Masse kg 0871 Ventil Leistung W 825 Ventil Heizerleistung W 154 Katalysebett Heizerleistung W 393 Resistojet Heizerleistung W 885610 Resistojet Spannung V 295245 DC Nomineller Betrieb 30 him Einzelbetrieb 370 h akkumuliert Abb 7 39 MR 5 02A Widerstandsbeheiztes T riebwerk der F irma Primex Aerospace wwwirsunistuttgartde IRESd res usahtm Copyright 2004 21 Narayanan Komerath Ion Thruster PERMANENT Exmm elon AND MAGNETS v1 1 AECELERATJHE GRIDS n a E H 7 V m a GAS I E E INLET I I a H CATHGD E a E i If I g nuscamera NEUTRAL21MB can ME EH ELECTED BEAM httpwww plasma inpe brLAPPortaLAPSiteFiguresIonThrustergif Copyright 2004 22 Narayanan Komerath NEUTRALIZING GATHBDE httplwwwplasmainpebrLAPPortaLAPSitdFiguresIonThrustergif Copyright 2004 Narayanan Komerath fluidipptgovpll sbarralionhtm Copyright 2004 Narayanan Komerath lon thrusters used for stationkeeping on geostationary satellites since 1997 Demonstrated ability to propel space probes encounter of NASA Deep Space1 spacecraft with comet Borrelly in September 2001 Ion thrusters unexpectedly performed the first electric propulsion aided orbit transfer of a satellite following failed orbital injection of ESA39s Artemis mission 2003 first use of a microwave ion thruster on Japanese MusesC spacecraft 24 Radiofrequency Ion Thruster Assembly RITA sp 3000 to 5000 s adjustable thrust from 15 to 135 operating life gt 20000 urs 85 less propellant than bipropellant thrusters A 4100 kg spacecra in GEO using conventional propellants over its 15 year life would save around 574 kg in propellant mass by using RITA mm 05 space eads netspAmagesRiTAjchematlcipg Copyright 2004 25 Nara39y39anan Komaam System Performance Components are Power Supply Power preparation and conditioning 1 2 Thrusters 2 Due Between the output supply and the jet exhaust pU62 pS 2 where W 77377PP77th 77T Copyright 2004 26 Narayanan Komerath Efficiencies 77 1 for solar arrays since they produce electricity directly 8 not this does not account for the 18 to 25 conversion efficiency of a solar array from solar radiation to electricity 77 O 1 O 3 for a nuclear device that must convert heat 8 39 39 energy to electricity with some type of Engine or mechanism thernoelectric Brayton engine Stirling engine 778 O for electrostatic power preparation 778 0 for steady arcjet systems depending on lsp and propellant Fig 941 8 from Humble Copyright 2004 27 Narayanan Komerath Also equations are available to estimate the thermal and power preparation efficiencies for various sp and propellants From Table 911 Humble For Argon A 2024 B 0307 Uppnth A B nlsp At a specific impulse of 2500 sec Argon the combined efficiency above is 378 Copyright 2004 28 Narayanan Komerath System Mass It appears that lsp and efficiency get better with more power When then would we not want a system with as much power as we can get POWER COSTS MASS Typically we use a linear relationship Mass BsPs where bs is specific mass For a typical solar array Bs 7 to 25 kgkW depending on cell efficiency and substrate type see Table 910 from Humble For a typical nuclear reactor remember Ps thermal power 3s 2 to 4 kgkW depending on shielding Note that we require space radiators to reject the heat dissipated by the power systems or reactor Space Radiator Bs 01 to 04 kgKW of waste heat Copyright 2004 29 Narayanan Komerath Note Humble also provides a way to estimate mass of the power preparation hardware and the thrusters for common systems 3pp 02 kgKW for arcjet compared to 20 kgKW for PPT For electrostatic we can combine the power preparation and thrusters Bpp Bthnpp ClspD From Table 911 For Argon C 4490 D 0781 Copyright 2004 30 Narayanan Komerath Masspp Massthrusters ClspD PS For Argon with Ps 10 KW and sp 2500 O781 9965kg So for a given system we can calculate the power system mass the radiator mass and the pp thruster mass Treating sp as an independent variable and knowing from the rocket equation Av MassRatio M msys mp mp0 2 egoSp Mf msys Copyright 2004 31 Narayanan Komerath As lsp increases Mass ratio decreases but if lsp increases Ps increases system mass decreases so payload mass decreases These are competing effects so there is usually an optimum lsp that results from the compromise Optimum lsp depends on many systemslevel design characteristics Fig 93 in Humble Copyright 2004 32 Narayanan Komerath AE6450 Fall 2004 Lecture 19 Detonation Wave Ramjets Copyright 2004 Narayanan Komerath TiHE SHERA JET u ehic e Hardy H quotmedicE lnr39t and Naule If fnir Flew llnlen Shanks ShackInduced Contbugtion Courtesy Prof Sislian httpcaiusutiasutorontocashcramjethtml Copyrigh 2004 Nara anan Komerath Detonation Wave Ramjets Sislian Jean P Detonation Wave Ramjets ln Scramjet Propulsion Progression Aeronautics and Astronautics Vol 189 2002 Detonation Flame front propagating with a shock at supersonic speeds Heat addition to a premixed combustible flow below its ignition temperature using shock wave If ignition occurs far enough downstream of shock shockinduced heat addition If ignition occurs close to the shock combustion process couples with the shock detonation wave Figure 1 detonation wave configurations Copyright 2004 3 Narayanan Komerath Advantages Very rapid heat addition Lower inlet losses Shorter engine gt lower overall weight gt lower combustor cooling load lssues Experimental data needed on stable detonations Mixing Avoiding preignition upstream and in boundary layer Avoiding boundary layer separation Getting realistic performance estimates SquotPP NT Copyright 2004 Narayanan Komerath Ram Accelerator Figure 2 Copyright 2004 Narayanan Komerath Experimental Evidence for Standing Detonation Wave Figure 4 Copyright 2004 Narayanan Komerath Operating Envelope of Standing Detonation Waves Figure Closed form solution can be obtained for detonation properties from the conservation equations for mass momentum energy Copyright 2004 7 Narayanan Komerath Detonation wave angle 3 related to wedge angle 6 1 7M1n2 iM1n2 12 271M1n25 6 B tan 1 2 M 71M1n2 1 1n Q Where M1 M1Sn 6 and Q CpT1 Copyright 2004 8 Narayanan Komerath For Q gt 0 the above has two nontrivial solutions ie For given M1T1Q and 8 there are two values of 6 satisfying the conservation equations When both solutions coincide 2 M1n2 1 2y1M1nZQ 0 Under this condition the normal Mach M2quot is 1 This is the ChapmanJougnet state This gives the minimum detonation wave angle 8 on each locus of states for given gt 0 gt minimum total pressure loss for given approach conditions See Figure 10 Copyright 2004 Narayanan Komerath Q gt Oanszn gt 1 weak underdriven oblique detonation 6 gt OandMZrl lt 1 weak overdriven oblique detonation 6 gt Oanszn 1 ChapmanJougnet State Near this 1 Minimum total pressure loss 2 Total pressure loss is insensitive to flow turning angle Copyright 2004 10 Narayanan Komerath Flow deflection angle for ChapmanJouguet state 17M1n 2 chz Cj tan1 C 2 2 M1 71 M1 1 no M1ncj Corresponds to minimum total pressure loss for given oncoming flow conditions Copyright 2004 11 Narayanan Komerath Figure 11 How 90 varies with M1 for stable oblique detonation for stoichiometric hydrogenair Copyright 2004 Narayanan Komerath FuelAir Mixing Process Fuel must be injected at a point where it is below the ignition temperature Injected fuel total temperature is usually gt 1000K so cannot inject normal or oblique to flow gt hence need parallel injection Parallel slot injection mixing length results Figure 17 Mixing length distance to achieve stoichiometric conditions Note that mixing lengths are of the order of 5 to 10 meters Why lower at higher M Copyright 2004 13 Narayanan Komerath Parallel slot injection mixing length results Figure 17 Assumed 1 Neglect initial boundary layer and wall boundary layer adjacent to mixing zone 2 Prandtl 1 Lewis 1 3 Turbulent shear stress from Prandtl mixing length incompressible data 4 Nondimensional velocity profile independent of distance from origin 5 lsobaric mixing 6 Mixing similarity parameter independent of distance from mixing origin Copyright 2004 14 Narayanan Komerath Performance Analysis ChapmanJougnet detonation normal Mach is proportional to the amount of heat released ie to fuelair equivalence ratio 1 and inversely proportional to the square root of static temperature ahead of detonation wave Thus for best performance T of the premixed gas must be allowed to reach its limiting ignition value Copyright 2004 15 Narayanan Komerath Velocity ratio across any ramjet y I 0 Ue 2 TPd pepo y 1 2 0 0 U0 V 1M0 7o de Po 1yjw02 Subscripts 0 e and pd denote oncoming exit and post detonation or post combustion flow parameters Superscript 0 stagnation value For fully expanded nozzle pe p0 ramjet thrust ThzmaUO f 1 f1m 0 ma 0 Ue ppd Maxumlzed when and are max for given f 0 Copyright 2004 16 Narayanan Komerath Oswatitsch criterion for Nshock inlet Minimum shock loss occurs for a given flight Mach number and number of oblique shocks N when the incoming Mach normal to each of the shocks is the same That is M1 M2n 2MNn ZMnS 0 T 0 Condition of max ppd for given M0 and A P00 T0 1J1 lt1 zfgtlt1 mgt39 Mn82 1 Wf f1F11Mnd Copyright 2004 17 Narayanan Komerath Where Mndz 1 FMnd4y1 F FMnd2 7 1 yF 1 1 Z f Mndz 1 y H yFMnd2 1Fy1 FMnd2 F is a dimensionless detonation wave classification parameter F 1 is ChapmanJougnet detonation 1 lt F lt 2 is overdriven detonation wave F 2 is shock wave Copyright 2004 18 Narayanan Komerath Also T 0 F2 F M 12 L2 1f3nMnS quotd 2 2 TO 7127 1M0 1mm f2nFMnSMnd C7 0 given quantity where q is heat added per unit mass CpTO 1 com P Here f3 Mns To 2M5 y 12y 1Mn82 n 712 Mns2 Copyright 2004 19 Narayanan Komerath Tcomlo is the temperature at the end of the compression and ahead of the detonation wave Maximum engine cycle static temperature at the discharge side of the detonation wave is 717FMnd2 1F71 FMnd2 T Tmax LdszMMns 12M 2 7 nd 7 0 7 0 f4nFMnSMnd These relations are used to study optimal detonation wave ramjets for given number n of equal strength inlet shocks Copyright 2004 20 Narayanan Komerath AE6450 Fall 2004 Lecture 10 Solid Rocket Engines 1 Copyright 2003 Narayanan Komerath Solid rocket motors Unlike liquid rocket engines the fuel and oxidizer are premixed in solid rocket The result is a rubbery solid that burns when heated Solid rockets are simpler and cost less than liquidfueled rockets have lower lsp than most liquids 285 sec are more dense gt higher density impulse plsp So packaging is easier Thrust is limited by nozzle size not by pump capacity Easy to get very high thrust for boosters Cannot be throttled or shut down during the flight unless predesigned to do so Copyright 2003 Narayanan Komerath Solid Propellant Ingredients Tables from Humble Copyright 2003 Narayanan Komerath Oxidizers Ammonium Perchlorate AP contains chlorine acid rain Ammonium Nitrate AN is more benign But inherently low burning rate and a phase change near 30 deg C Copyright 2003 Narayanan Komerath Applications Missiles acceleration storage Booster strap ons high thrust per size Apogee kick motors knownAV Copyright 2003 Narayanan Komerath StarGrained Solid Rocket Motor httpwwwnfsuitedklstargrain After l minute of burn Copyn39ght 2003 Narayanan Komerath General configuration TEM3644 is a 15000 lb thrust solid propellant motor developed for use as an upper stage It is an enlarged version of the TEM364 one of a series of solid propellant motors that powered the workhorse USAF Burner l and Burner llA upper stages to orbit scientific weather navigation and communications satellites The TEM3644 powered the upper stages of the USAF Atlas boosters used to launch the Global Positioning System GPS satellites It also was used as the second stage motor on USAF Thor vehicles that launched satellites of the Block 5D Defense Meteorological Satellite Program DMSP as well as the third stage motor on the Thor Delta launch vehicles wwwwpafbafmil museumenginesen962htm Copyright 2003 7 Narayanan Komerath Cutaway vtew of the Sottd Rocket Booster strowtrtg 30m Nozzle and Thrust Vector erket Mator propeHant and aft tiold punt control Sys em Flume 3 68 m 124 n Outs tele Diameter 4 Separation Motors 22050 lb thrust each SOHO Rocket Mutt Ait He d Jmm Sotld WOVENam Aft Sktrt and Launch Support BoosterExternal Tank Attachment thg Att Avionics and Sway Braces Dimenstons Length 14916 tt4546m Dtameter 1217 ft 3 70 m Mam Parachutes 3 4 Separatton Motors 22050 ll lhntsl each SRB Extcrnat Tank Thrust Attachment Dwguc Chme Rate Gyro Assemblies 3 1 A Forward Separation AVIOmCS Operationat quot 4 5km Flrglrt nslrumentatlon Recovery Frustum Avmntcs and Range Safety System Nose Fairing may mewrgrmw sm Copyright 2003 8 Naray anan Komerath Mtitude We Ham Switch 1 Flotation I39 r Iquot 11 31quot 1353 Frustom Locatinn ids quotquot quot Frustum Flange 33f ety SFlB Location aids System 1 Int 3 grated f a 51333 anv ard Skirt Forward I System Tunnel s quot lnterc nnn acting Cables Plate quot 4 Gyro 5 II Mt Attach Hing Assembly 39 lt r II x l 39quot Extemal TankSHE Integrated 5 Interface Electronic iiigquot Assembly 39 Aft t P f r 1 r r k d Aft Skirt 1 41 ll Separation Motors SolidFlnclcet BoosterExploded View STS SRB motors SRB motor propellant mixture ammonium perchlorate oxidizer 696 percent by weight aluminum fuel 16 percent iron oxide a catalyst 04 percent a polymer a binder that holds the mixture together 1204 percent and an epoxy curing agent 196 percent The propellant is an 11point star shaped perforation in the forward motor segment and a double truncated cone perforation in each of the aft segments and aft closure This configuration provides high thrust at ignition and then reduces the thrust by approximately a third 50 seconds after liftoff to prevent overstressing the vehicle during maximum dynamic pressure iftoffmsfcnisaqovl ShuttleAboutdetsrbhtml pupylight 2003 9 Narayanan Komerath The SRBs are used as matched pairs and each is made up of four solid rocket motor segments The pairs are matched by loading each of the four motor segments in pairs from the same batches of propellant ingredients to minimize any thrust imbalance The segmentedcasing design assures maximum flexibility in fabrication and ease of transportation and handling Each segment is shipped to the launch site on a heavy duty rail car with a specially built cover Copyright 2003 10 Narayanan Komerath The forward section of each booster contains avionics a sequencer forward separation motors a nose cone separation system drogue and main parachutes a recovery beacon a recovery light a parachute camera on selected flights and a range safety system Each SRB has two integrated electronic assemblies one forward and one aft After burnout the fonrvard assembly initiates the release of the nose cap and frustum and turns on the recovery aids The aft assembly mounted in the external tankSRB attach ring connects with the fonrvard assembly and the orbiter avionics systems for SRB ignition commands and nozzle thrust vector control Each integrated electronic assembly has a multiplexer demultiplexer which sends or receives more than one message signal or unit of information on a single communication channel Copyright 2003 11 Narayanan Komerath The nozzle expansion ratio of each booster beginning with the STS8 mission is 7 to79 The nozzle is gimbaled for thrust vector direction control Each SRB has its own redundant auxiliary power units and hydraulic pumps The allaxis gimbaling capability is 8 degrees Each nozzle has a carbon cloth liner that erodes and chars during firing The nozzle is a convergent divergent movable design in which an aft pivot point flexible bearing is the gimbal mechanism The cone shaped aft skirt reacts the aft loads between the SRB and the mobile launcher platform The four aft separation motors are mounted on the skirt The aft section contains avionics a thrust vector control system that consists of two auxiliary power units and hydraulic pumps hydraulic systems and a nozzle extension jettison system Eight booster separation motors four in the nose frustum and four in the aft skirt of each SRB thrust for 102 seconds at SRB separation from the external tank Each solid rocket separation motor is 311 inches long and 128 inches in diameter Copyright 2003 12 Narayanan Komerath 39 39 Solid rocket Explosion 3 Large fragments created wwwwstfnasagovll x lo i l FTestin htm Narayanan Komerath Inertial Upper Stage wwwaeroor IIcrosslinkl winter2003108html W Paul Dunn Copyright 2003 14 Narayanan Komerath Stinger ManPortable SA Missile Stinger Unofficial nameslslang na Function To provide ciosen surfaceetoeair Weapons forthe defense of forward com at areaS Vitai areas and instaiiations agains i iow aimude air attac 5 Date deployed 1987 ct mm Gapm iFFiNTBmoGATOR Contra orGenerai Dynamics iRayineon MECHANVSM Unltcos 8 000 iaimmremmn Length 5 H K Wings MAW Diame e 0 000m DEVICE Spe n Weight at launch 34 5 ibs iauncher W iSSiie 42 335M mmm GuidanceFireeandforgetpassiveinfiared see er Rangeap prox i r 8 km Englne Duai thrust Soiid fuei rocket motor wwwcombatindexcomll detaillmislstin erhtm Warhead High expiosive Copyright 2003 15 Naravanan Komerath Pintlecontrolled Solid Rocket Motor CFDRC wwwcfdrccoml researchpintlehtml 6inch diameter heavy wall system capable of producing a range of thrust of approximately 150 to 750 pounds thrust The motor uses ten pounds of cartridgeloaded propellant which for these tests was a 11 class minsmoke formulation that is a current production Army SRM propellant The motor was fired in both a fixed mode and a closedloop active control mode based on motor pressure If Flat 3d iii1 3 m cm in it Map rim1i F m an 39 tuaw1 p nmaw Heisman Pun fml h quot395 I I I L I If I I 1 quot I I I If Iquot J w II E l i I J i l l I I It I r E n II39 I l I III a l l I i E III l quot1 r a a I 4 1 Tm ms Copyright 2003 16 Narayanan Komerath SOLID ROCKET MOTOR DISPOSAL combines cryowashout of the propellant from the motor casing with a simple supercritical water oxidation reactor for environmentally safe disposal of the effluent Copyright 26619a wwwgacomlatg apssolid1html 17 Narayanan Komerath Solid Propellants Double Base molecules of fueloxidizer are mixed eg gun powder dissolved in nitroglycerine oxygen in both less common more explosive Composite Heterogeneous mixture of fuel oxidizer and binder plus some other additives more common Copyright 2003 18 Narayanan Komerath Fuels Powdered Aluminium STS Powdered Mg Binders HTPB e PBAN e RSRM most popular now The binder holds the entire formulation in a structurally sound propellant grain under temperature and pressure variations plus accelerations and vibration loads of flight Binders should have low density and energy of combustion plus structural integrity using minimal binder volume Solids Loading percentage the total propellant mass taken up by fuel oxidizer Usually gt 90 Binders are usually longchain polymers keep the propellant powders and crystals in a continuous matrix through polymerizing and crosslinking Copyright 2003 Narayanan Komerath Other Ingredients Fixers bonding agents improve bond between oxidizer and binder Curatives increase rate of polymerization Plasticizer improve physical properties at low temperatures Darkening agents reduce thermal radiation losses through translucent propellant HMX increases burning rate Can cause detonations too Copyright 2003 20 Narayanan Komerath Propellant Burning Rate 7 Re ress39on La St Robert s La r aPC 9 39 W W regression rate proportional to pressure to some n r nr nlnaPC A plateau type burning rate law is more common where n becomes close to zero over a range of pressure Note n has to be 5 1 for stability quot7 nlt1 Copyright 2003 21 Narayanan Komerath Grain cross sections to control burning End grain neutral lnternal Burning Tube progressive lnternalExternal Burning Tube neutral Rod and Tube neutral lnternal Burning Star neutral Dog Bone neutral Slots and Tube neutral Slotted Tube neutral Wagon Wheel neutral Multiple Perforations neutral Neutral thrust history generally gives the smallest inert mass since the maximum and average pressures on the structure are nearly the same with this Else use regressive thrust profiles Copyright 2003 22 Narayanan Komerath Simple Solid Rocket Analysis In a solid rocket motor the chamber pressure is related to the geometry and burn rate Therefore we must know something about the geometry to find Pc time and thusL thrust and lsp vs time web meXit Then from conservation of mass Slmple endburner desugn mburn mvoume meXit mass released from surface per unit time mass added to growing chamber volume mass exhausted Abtpprpcvcmem 2 Pp density of solid Po density of gas in bore mp propellant mass flow rate Copyright 2003 23 Narayanan Komerath T CFPCAt CFC Recall Sp z 90 90 mp 90 mp or Et meXl39t 3 3 3V PA SO AbtpprVcch EJ where r aPC St Robert s Law 4 Copyright 2003 24 Narayanan Komerath Let us first assume 1 0 in equilibrium at 2 3V 3 Ab t is constant end burner type design 4 r aPC n lt 1 and a n ppC do not change over time then Ab PC PC A t FCpp aPC Cpp Copyright 2003 25 Narayanan Komerath Ab PC aawcwpi 1m 1MPa 100cm 1106Pa steadystate lumpedparameter where PC a MPa cm s MPa m C a A K Mam i m 8 5 This is a steadystate approximation Pay particular attention to units in 5 if we are going to use Humble s table of a in Table 69 We can use equation 5 to estimate the size of an endburner for a desired Pc and performance Copyright 2003 26 Narayanan Komerath Example PC 4Mpa 6 target 0 1500ms Cfv 185 note f z12 for solids pp 1800Kgm3 r 4opC3 in cms Pc MPa If the desired TVac 500000N and Find AnAb T CfAtPC tb 100seC and Web SOOOOON 185At4 106Pa At 0676m2 IWeb rtb 4o4MPa393100sec IWeb 606290m 6063m Copyright 2003 27 Narayanan Komerath from 5 i 4MPa At 44MPa 31500ms18OOKgm3101 mjj a A Tb24435 So Ab244350676m2 t A Ab1651m2 and Db7b2 Db 2293m Lweb 132 Db If this geometry is unacceptable we can change Pc and resize For example a higher Pc will make a longer more slender solid rocket Copyright 2003 28 Narayanan Komerath Time varying Burn Area For a more general cross section tube stov Wagon Wheel etc we would expect the crosssectional area or the total exposed burn area to change with time Given the initial geometry dX dt 1 A 1m 1MPa E P b aC C HA pp1000m1106pa r aPC and Copyright 2003 29 Narayanan Komerath Time varying Burn Area In the units we have been using for each where typically assume a C p and n are constant 1 1 p But AbAt and Pc can change with time Let AbAbx and At befixed Then n dX 1m Ab x 1m 1MPa W a aC pp 6 dt 1000m A 100cm 110 Pa Copyright 2003 Narayanan Komerath n X t A X 1 IltdxX Xi Ia1i A ac di Xi 0 1000m A 100cm 110 Pa at xxf ttb for most complex shapes we will need to integrate the RHS numerically and Ab X may be a complex calculation over multiple regions For a simple shape Ab X 2 39XL where L bore length Copyright 2003 31 Narayanan Komerath AE6450 Fall 2004 Lecture 12 Hybrid Rocket Engines Copyright 2004 Narayanan Komerath Hybrid Rocket Motors Hybrid Rocket Motors Hybrid Rockets combine one liquid propellant with one solid propellant typically a solid fuel and a liquid oxidizer wwwukrocketmancomrocketrv hvbridscienceshtml Oxidizers LOX GOX common 39Hzoz N204 LF2 Can be combined with LOX Copyright 2004 2 Narayanan Komerath Hybrid Rocket Motors wwwpropulsionpolymerscoml imagesMarcusBilljpg Copyright 2004 3 Narayanan Komerath Hybrid Rockets Safer than liquids and premixed solids easy handling Can be throttle shut down lsp is between solids and liquids 300320 sec Bulk density is good better than liquid but not quite as good as a solid Do not have toxic exhaust like based solids Not as sensitive to exposed cracks like solids Low regression rate needs more port area to generate required thrust Burn is often incomplete due to complex port design shows combined fuel one left at the end of the burn lower effective mass fraction Copyright 2004 Narayanan Komerath Hybrid Rocket Motors Fuels HTBP Hydroxyterminated polybutadene rubbery HC binder from solid fuels Plexiglass Polymethylmethacrylate PMM Early coal wood rubber In some cases carbon black or aluminium powder can be added to the fuel grain to increase burning Copyright 2004 Narayanan Komerath Burn rate Regression rate There are several burn rate models but a good one is r G total mass flux 5 9 fueoxidizer S X distance down the port m a regression coefficient In theory n z 80 m z 20 az206610 5ms Copyright 2004 Narayanan Komerath However experimentally nz75 77 mz 14 16 Note This equation uses 6 X GO X G where both are a function of so the implicit solution is iterative to determine Gf Copyright 2004 Narayanan Komerath Burn rate depends on flow rate and downstream distance Here the key observations are r is proportional to Gx and thus G can be turned off burn rate decreases with length along L This is primarily due to the diffusion nature of the flame region As the boundary layer grows flame moves away from surface heating rate decreases As a result the regression is slightly longer at the injector end Copyright 2004 Narayanan Komerath Other Empirical Fits For Burn Rate Other burning rate equations exist and may be better in some cases eg r a GO Lm averaged method r average regression rate GO average oxidizer flux L port length This equation is simpler in that it depends on average values May be ok for performance predictions Show table 75 from Humble curve fits to AMROC data for various equations Copyright 2004 9 Narayanan Komerath Change in OF Ratio As the solid fuel is burned web is consumed the port area increases and thus Gox decreases 9 max As such decreases and F will increase over time mf This causes a shift in 7 C and Sp as the motor burns Over a given OF range the lsp might shift by a few Copyright 2004 10 Narayanan Komerath Typical Port Configurations In general two ports will have the same oxidizer flow rates if their hydraulic diameters are equal Objective maximize volumetric efficiency minimize sliver fraction keep mOX thus Gox the same in all ports Fig 717amp18 from Humble shows typical port configurations for hybrid rockets and the associated variations of volumetric efficiency and chamber lengthtodiameter ratio LD as a function of required fuel mass Circular Low 7kg and large size 7cylinder cluster high sliver fraction residuals Wagon Wheel with center port good compromise at larger size Note The wagon wheel design is more difficult to solve analytically but can be solved numerically Copyrlght 2004 11 Narayanan Komerath Port Configuration Using multiple ports holes on a hybrid system will allow us to have more surface area exposed to the oxidizer and thus generate more thrust for a given diameter Define Volumetric efficiency 77 VolumeOccupiedBySoidFue V9 Volumelnside CaseOfThe quot Grain Skew Fraction 1 mass of solid fuel used mass of solid fuel available Hydraulic diameter 4 CrossSectionaAreaOfAPort PerimeterOfAPon D Copyright 2004 12 Narayanan Komerath Note for a circular port 0 0 Copyright 2004 Narayanan Komerath Performance Analysis For a given propellant with I an aGoanm ms regression rate and a given grain geometry N ports For a given mox find GOX NXXP r aGOX A39Lm alternate versions of this are available por quotID eg llama but require iteration Dimensions known Dn and L given mf gs3N N number of ports mp mox mfue ignore gas added to chamber Copyright 2004 14 Narayanan Komerath Foragiven mOX find GOX 39 n m r aaox L alternate versions of this are available but require iteration 6399quot fGTota mf N numberof ports Dimensions known Dn and L given density of solid surface area of a single port assume identical here mp mOX mfue ignore gas added to chamber Copyright 2004 15 Narayanan Komerath Timestepping procedure O mox F Is I gt find 74C Tf n mfue from charts in Appendix B of Humble Since C CF 2 T CFPCAZ Sp 90 39 39 mprepgo mpreng P mpOpC C At Copyright 2004 16 Narayanan Komerath Given 8 find CF and thus thrust and lsp Note throat erosion can cause At to change over time For a small time step hold r constant and use Ar fAt to find new port cross section area Ap and surface area Sp Repeat until first web segment is nearly consumed or tb is reached Copyright 2004 17 Narayanan Komerath Example calculation from pp 433434 in Humble lsp vs time from table Thrust vs time from chart 7 port Wagon Wheel no burning in center port Copyright 2004 18 Narayanan Komerath Hybrid Motor Ballistics This derivation is from the text by Humble It is presented to illustrate the basis for the empirical expressions for burn rate Equation numbers are the same as those in Humble et al The burn rate of a solid fuel in a hybrid rocket motor also depends on oxidizer flow rate Thus fuel regression rate is rzaanm71 Here r is expressed in ms Note that its values are typically in mms or cms G total propellant in Kgm25 X distance down the point A n m are regression rate constants of the propellant Copyright 2004 19 Narayanan Komerath r is a functionf m r is also g X G increases with x A major difference from solid and liquid rockets hybrids burn in a diffusion flame as opposed to the premixed flames in the other types of rockets ln solid rockets OF is independent of x However in hybrids the OF ratio does vary with x Copyright 2004 20 Narayanan Komerath Interior Ballistics Model Turbulent diffusion flame Controlling factors rate of heat transfer to surface heat of decomposition of solid fuel G determines rate of heat generation and hence flow The flame occurs within the turbulent boundary layer Please refer to the figure showing the boundary layer and the flame zone inside the boundary layer Note that the axial velocity ie the velocity component directed along the axis of the port at the flame zone is thus lower than the velocity at the edge of the boundary layer Ub ltUe Copyright 2004 21 Narayanan Komerath The burning rate equation is Qw rhf Q heat flux transferred from flame to solid surface J mzs W m f mass flux rite of vaporized fuel perpendicular to surface K g m S hv heat content of unit mass of gasified fuel at surface minus heat content of solid at ambient temperature JKg includes 1 heat to warm solid to surface temperature 2 thermal changes such as depolymerization 3 heat of vaporization hv measured in labs Copyright 2004 22 Narayanan Komerath Heat transfer through boundary layer occurs by conduction which is proportional to the thermal gradient 8T k ah Z k oooooooo 703 Qw By Cp By k molecularturbulent boundary layer gas conductivity Jmsk T gas temperature at any point yx h Specific enthalpy of gas at any point y Jkg C p Specific heat of gas at constant pressure Jkg The form in terms of the enthalpy gradient ah Q k is useful when chemical recombination occurs in W the bounda la er ay W 3 Copyright 2004 23 Narayanan Komerath In terms of the Stanton CH Qw CHObUbAh axial massflux in flamezone Ah Total specific enthalpy difference between flame and wall Jkg Ob 1 gas density at flame kg m3 Ub Gas velocity at gas flame ms Copyright 2004 24 Narayanan Komerath CH can be determined from friction coefficient CF for which experimental data are available for turbulent flow over flat plate Assume 1 C u k oPrandtl Lewis 1 diffusivity of heat and molecular species are equal Reynolds analogy temperatureenthalpy profile through a boundary layer is d U proportional to d y Copyright 2004 25 Narayanan Komerath Note Nondimensional parameters source Hill amp Peterson Nusselt number for convective heat transfielr x 1 Nu L Rex C f hf k 2 Stanton CH 2 pCpU Heat transfer Film coefficient h 3 is such that o From this we can see that Q Tw Too AT and Copyright 2004 26 Narayanan Komerath Using Reynolds analogy Q Qw T shear stress at y Pascals U axial velocity at y Ti 76 81 a 75 8y By Copyright 2004 27 Narayanan Komerath Integrating equation 75 between the burning zone and the surface amp Tw 77 Ah U19 Divide by prb Compare with 74 CH Qw 7w 78 PbUbN prb2 Copyright 2004 28 Narayanan Komerath From definition of Cf I 1 1w EpeUeZCf 79 where 3906 freestream gas density kgm2 U 6 freestream ms Cf flow friction coefficient Copyright 2004 29 Narayanan Komerath From 78 C 2 CH 2 fp6 Ue2 710 2 prb For noncombusting boundary layer C CH0 711 Copyright 2004 30 Narayanan Komerath Here boundary layer is extended due to blowing from the surface due to fuel vaporizing Expecting blowing to have similar effects on heat and momentum transfer C C H f 7 12 CH0 Cfo Combine 72 74 712 713 Basic expression for burning rate in hybrid rocket 39 39 o2 CH U Ah mfzrpf C U e h HO b V Evaluate skin friction coefficient Cf from empirical law for turbulent boundary layers Empirical law for Pr 1 is C A CR6O392 C 03 empirical G R x 715 e u Copyright 2004 31 Narayanan Komerath With equation 715 for R6 03102608 CH Ah mfzrpfz 02 C U h 716 X H0 b V m f mass flux rate of fuel from solid surface kgmzs Iquot regression rate ms of solid fuel pf density of solid fuel viscosity of burned gas CH I Stanton with blowing CH0 3 Stanton without blowing Copyright 2004 32 Narayanan Komerath Combine Eqns 2 4 10 BZ fj 718 determined from propellant properties Maxman 1964 I 39V f in II B I quotin 7431 8 H135 U39EM39B u b l HBJ Lll o Copyright 2004 33 Narayanan Komerath In the range 5 a B lt 20 usual in hybrid systems 5 3 j393 I 139 H Ir 1i39ijji Final expression z in 1 39 39 quot U quotu39 quot J u v iiiri rJ iii3 i c J B quot i22 IE 1 I Cnntrast tn solid rocket r rig2kquot Copyright 2004 34 Narayanan Komerath Equatidn 2231 is l n m quot2113 I Dapandanda an axial length ii r in gi m725 fill oxidizer maaa flux in part kgir naj U f fuel flux added to part in frant of paint a kgi mga Copyright 2004 35 Narayanan Komerath Regression rate 726 l 39 m39quotU 1 xll where U is determined by integrating luelrmass addillon along the pm 727 DH hydraulic diameter m 4AIP A pnrlCSarea m2 P port permeier m Data shows lhai hybrid combusllon down the port provides fairly constant burn rates Wh 1 Boundary layer grows as x gt decreases heat ux balanced by Increase in G lie to adding fuel 2 Spurious higher local CS causes reduced local mass ux rgt levels out contours NamVanan mmmm AE6450 Fall 2004 Lecture 14 Electric Propulsion Copyright 2004 Narayanan Komerath The quotjetquot or exhaust power Pjet of any thruster is Pjet 12 gc lSp F Thus for a situation where we wish to fix the thrust at a constant value as specific impulse increases the jet power must also increase Jet power is in turn a function of the total quotbusquot electric power Fe and the overall efficiency h of converting electric power into jet power Djet 3e h The mass of the electric power system as well as power conditioning and thrusters is proportional to the total quotbusquot electric power leower a 3e where a is the overall system specific mass typically in kgkW electric Finally Mo Mb exp AV gc lsp The propellant mass Mp is simply the difference between M0 and Mb Mp M0 Mb Copyright 2004 Narayanan Komerath Designing Electric Propulsion Path A Power Source Based on Chosen Thruster and Mission Specify Mission Select Thruster Select Power Source Design Thermal Mgmt System Design Power Conditioning System Assess Performance Path B Power Source Based on What is Available from Spacecraft Specify Mission Select Power Source Select Thruster Design Power Conditioning Design Thermal Mgmt System System Assess Performance Copyright 2004 Narayanan Komerath ms Optimum Specific Impulse canal ThmsI msslun Thrust a Power nap Mp Mpmef x i hw ffF 9quot m 1 9 Mas x prm39 Power Supp Hp Prupei lannt I wwww quotan W 39iral39hua gl J II Speci c lmpwlse I513 Courtesy RobertH Frisbee JPL httpwwwislandoneorgAPCEIectricimpulsegif Copyright 2004 Narayanan Komerath System Analysis Thrust or Jet Power 1 mPUe Initial mass Required sourcepower PS j P 3 System Inert mass mmert Ps Specific mass of propulsion system KgNV a Specific power of propulsion system WKg Copyright 2004 Narayanan Komerath If thrust duration assuming constant thrust is T 39 P mp 7 BU 2m m Inert 2 77T7 mpay mf mineT where mf is final mass achieving AV AV AV 2 m U a e Ue 1e Ue 18 9 m 277739quot Copyright 2004 6 Narayanan Komerath Design goal maximize payload mass fraction Define W AV AV U0 U Ue U0 AV AV m 1 2 m 2 Copyright 2004 Narayanan Komerath Propulsion system mass per unit ofjet power Jetspecific mass jzgz 77T 0577T Optimal exhaust speed 239 Ueo 2k 8 Where k 1 Copyright 2004 Narayanan Komerath lf 6 is too high or the allowable thrust time is too low optimum speed may be less than that from chemical rockets May still use electric propulsion for missions with electric power supply Primary electric propulsion will not benefit from power system sharing until it is a large scale mission with many MW of power Possible uses gt stationkeeping no benefit to impulsive thrust gt lifting large structures low g continuous thrust AV 3 23AVImpusive gt Electric primary propulsion needs ISp gt 1000s to compete with modern chemical system Sp 450s Copyright 2004 Narayanan Komerath Electromagnetic Propulsion Electromagnetic force per unit volume on a gas carrying current in a magnetic field Fm j x B E magnetic induction field in gas Tesla Electric current density ln gas Am2 Nm3 F m Copyright 2004 10 Narayanan Komerath AE645O Fall 2004 Lecture 5 Nozzles In this lecture we will cover Types of nozzles Expansion Ratio criteria Nozzle heat transfer and materials issues Copyright 2003 Narayanan Komerath NOZZLES The function of the rocket nozzle is to convert the thermal energy in the propellant into kinetic energy as efficiently as possible in order to obtain high exhaust velocity along the desired direction The mass of a rocket nozzle is a large part of the engine mass Many of the failures encountered in rocket engines are also traceable to failures of the nozzle historical data suggest that 50 of solid rocket failures stemmed from nozzle problems The design of the nozzle must trade off 1 Nozzle size needed to get better performance against nozzle weight penalty 2 Complexity of the shape for shockfree performance vs cost of fabrication Copyright 2003 Narayanan Komerath Ts Diagram or hs Diagram for a nozzle Ideal QlcIo Entropy s i reactants at chamber pressure po f final mixture at combustion chamber stagnation conditions po To t throat conditions Mach 1 p T e exit conditions pe Te assuming fully expanded Copyright 2003 Narayanan Komerath Ts Diagram or hs Diagram for a nozzle with losses Losses show up as increases in entropy for each step usually accompanied by a loss of pressure At the exhaust note that exhaust temperature is higher than ideal when the final pressure is reached To Entropy s i reactants at chamber pressure p0i f final mixture at combustion chamber stagnation conditions po To t throat conditions Mach 1 p T e exit conditions pe Te assuming fully expanded Copyright 2003 4 Narayanan Komerath Recall Expressions for Thrust Coefficient 1 F 1y P0 where At is nozzle throat area and p0 is chamber pressure Nmz Thus at tyRY 2 171 For sonic conditions at the throat Oz 2 100 CF 1 and 7 lay 1 y lw 2 2TT 2 F Atpo7R j 1 amp pepoAe 7 1 71 P0 Copyright 2003 Narayanan Komerath Thrust Coefficient 2 Using isentropic flow relations all TtTO p0 H 2 ptR 71 2 02 71 002 y H 94 12 2 2 y 1 7 FZAtpOy pepaAe 7 1 71 P0 and Thrust Coefficient 1 12 1amp y M 71 71 190 poAt Depends entirely on nozzle characteristics The thrust coefficient is used to evaluate nozzle performance 71 y l F Copyright 2003 Narayanan Komerath Characteristic Velocity c Used to characterize the performance of propellants and combustion chambers inde endent of the nozzle characteristics 71 mp0Ar L m4 p0Arr VRTO 71 yRTO wherer is the quantity in brackets Note do V YRTO So m 1quot ao 0 pOAt Characteristic velocuty m Assuming steady quasi1dimensional perfect gas The condition for maximum thrust is ideal expansion nozzle exit static pressure being equal to the outside pressure In other words pe pa Copyright 2003 Narayanan Komerath Nozzle Types The subsonic portion of the nozzle is quite insensitive to shape the subsonic portion of the acceleration remains isentropic The divergent nozzle is where the decisions come into play Conical Nozzle Easier to manufacture for small thrusters Divergence losses Exit velocity is not all in the desired direction Bell Nozzle Complex shape Highest efficiency near axial flow at exhaust Large base drag during atmospheric flight after burnout Plug Nozzle or Aerospike Nozzle linear or annular X33 VentureStar 1960s concept Altitude compensating see Chang 330c Expansion Deflection Nozzle ED Shortest nozzle of the enclosed types Copyright 2003 8 Narayanan Komerath Conical Nozzle Easier to manufacture for small thrusters Divergence losses Exit velocity is not all in the desired direction 39V 221C0sa Note a can be as large as 12 to 18 degrees 7M 1 12 2 T CF1 2Li lamp y 609 pa 71 71 190 190 Here 7L is the thrust efficiency defined as ratio of actual to ideal thrust accounting for flow divergence a is the nozzle Area Ratio ratio of exit area to throat area Copyright 2003 9 Narayanan Komerath Geometric Representations of Nozzles Cone nozzle R Throat internal radius XN R15m0 R Radius of curvature of the nozzle contraction YN RT R11C050 N Transition point from circular contour to conical contour Located along at angle a downstream of throat L N Nozzle Length RrE1Rl 1 4 39 L Cosa N Re Exit radius TOW For a conical nozzle R1 151 is a typical choice Copyright 2003 10 Narayanan Komerath Bell Nozzle Complex shape Highest efficiency near axial flow at exhaust Large Base Drag during atmospheric flight after burnout A true bell nozzle is contoured to minimize the turning compression shock losses at the wall as the flow expands but still turning the flow towards an axial exhaust Note that the flow may still be under over or fullyexpanded at the exit and hence shocks I expansions may exist downstream ConvergentDivergent Nozzle Underexpande Hot Subso 111 c Copyright 2003 1 1 Narayanan Komerath Bell Nozzle An approximate shape can be formed from a parabola after GVR Rao y39 Px39QSx39T12 R1 15Rt Upstream of the throat R1 0382Rt Downstream of the throat Copyright 2003 12 Narayanan Komerath Parabolic Bell Nozzle Contour cont d Rao 1958 There are 4 unknowns in the rotated parabolic segment equation PQST and 4 boundary conditions 1 AtN X39N0 Y39N0 2 Ate X39eXeXNY39eYYN Or X39e Xe XN L XN Y39e Ye YN x2Rt YN 3 At N 6N is given Rao 1958 plots 2 At e 6 is given Rao 1958 plots see Humble p 225 Copyright 2003 13 Narayanan Komerath So y 1 Y39NzPX39NQSX39NT 2 2 and henc Q 1 2 Y39e PX39eQSX39eTA SX39eT Y39e PX39e Q and 3 N 2SX39NTA I S T a P an N 2Q 2r C 2Tcml9N P 4 Tan eP S 1 2SX39eTA 1 S SX39TA e 2TangeP D Copyright 2003 Narayanan Komerath from A B Equating B D leads after some manipulation to S 200 PgtltTaquot9N PgtltY39ePX39egt E TanQN T611168 Also squaring B SX39eTY39e PX39e Q2 Substituting for Q from C S 2 Y 39e PX 39e2Tcm9N P X39e TanQN Y39e F Eventually gives Y39e TanQN Y 39e T611166 2X39e Tan eTanQN 2Y39e X39e TanQN X39e T617168 P G Down to one unknown Copyright 2003 15 Narayanan Komerath Use eqn G to find P PX39eY39e6N68 Then either F or E to get S Then use C to get Q Then use A to get T in terms of the original XY axes 1 YYNPX XNQSXXNTE Recall Yve 2Y8 YN JERI Rt R11 Cos6N and X 39e Xe XN L RlSz39nQN where L is generally a fraction of that for a 15degree halfangle cone with the same R1 ie 0382Rt 1 Rr E1R1L081501 f 100 90 or 80 of a 15degree cone tan15 Lf Copyright 2003 16 Narayanan Komerath Comparison of bell and cone nozzles For the same a we would expect Abe gt Leone A bell nozzle while more complex to build will generally yield a more efficient exhaust than a cone in a shorter nozzle length Same nozzle efficiency factor can be reached with about 70 of the length of a cone nozzle Alternatively efficiency factor can be increased from about 98 for a cone to about 992 for a bell of the same length Copyright 2003 17 Narayanan Komerath


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.