5. 522, Space Propulsic Prof. Manuel martinez-Sanchez Lecture 5: Chemical Thrusters for In-Space Propulsion HYDRAZINE Hydrazine was first isolated by Curtius in 1887, and in 1907 a suitable synthetic method was developed by Raschig. Anhydrous hydrazine is a clear, colorless hygroscopic liquid with an odor similar to that of ammonia. Anhydrous hydrazine is a trong reducing agent and a weak chemical base. Aqueous hydrazine shows both oxidizing and reducing properties. Although potential data show hydrazine to be a powerful oxidizing agent in acidic solutions reactions with many reducing agents are so slow that only the most powerful ones reduce it quantitatively to ammonium ion Hydrazine will react with carbon dioxide and oxygen in air. When hydrazine is exposed on a large surface to air, such as on rags, it may ignite spontaneously due to the evolution of heat caused by oxidation with atmospheric oxygen. A film of hydrazine in contact with metallic oxides and other oxidizing agents may ignite Hydrazine is an endothermic compound and will decompose spontaneously in a similar way to hydrogen peroxide. The reaction of hydrazine with the oxides of particularly violent. The spontaneous or artificially induced decomposition of y be copper, manganese, iron, silver, mercury molybdenum, lead or chromium m hydrazine does not follow the reaction N2H4= N2 +2H2, but a more exothermic one such as 2N,2H4 2NH3 +N2 +H2 SUMMARY AND CONTENTS PHYSICO-CHEMICAL METRIC VALUE ENGLISH REFERENCE FIGURE PROPERTIES N2H4 ecular Weight 32.04 1.5C 34.7F (6) Freezing Point Diagram (10) Critical Properties P =145 atm C(716F) d e =0.231 g/cc Density, liquid 10045g/c@25C 8482|b/ga@77F 14.38mm@25C 0018atm@7F(6) Surface Tension 62.32 dynes/cm@ 35 C 004270|b/ft@95F(9) 0.90 centipoise 25C 000605b/f-sec|(11,12) I Heat Flux at qu/ Pressure at Flux at qu/ mperature eat Flux at qu/vel 16.522, Space P pessan Lecture 5 Prof. Manuel martinez Page 1 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 1 of 12 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 5: Chemical Thrusters for In-Space Propulsion HYDRAZINE Hydrazine was first isolated by Curtius in 1887, and in 1907 a suitable synthetic method was developed by Raschig. Anhydrous hydrazine is a clear, colorless, hygroscopic liquid with an odor similar to that of ammonia. Anhydrous hydrazine is a strong reducing agent and a weak chemical base. Aqueous hydrazine shows both oxidizing and reducing properties. Although potential data show hydrazine to be a powerful oxidizing agent in acidic solutions, reactions with many reducing agents are so slow that only the most powerful ones reduce it quantitatively to ammonium ion. Hydrazine will react with carbon dioxide and oxygen in air. When hydrazine is exposed on a large surface to air, such as on rags, it may ignite spontaneously due to the evolution of heat caused by oxidation with atmospheric oxygen. A film of hydrazine in contact with metallic oxides and other oxidizing agents may ignite. Hydrazine is an endothermic compound and will decompose spontaneously in a similar way to hydrogen peroxide. The reaction of hydrazine with the oxides of copper, manganese, iron, silver, mercury, molybdenum, lead or chromium may be particularly violent. The spontaneous or artificially induced decomposition of hydrazine does not follow the reaction N2H4 = N2 +2H2, but a more exothermic one such as 2N2H4 = 2NH3 +N2 +H2. SUMMARY AND CONTENTS PHYSICO-CHEMICAL PROPERTIES METRIC VALUE ENGLISH REFERENCE FIGURE Molecular Formula N2H4 (1) Molecular Weight 32.04 (1) Freezing Point 1.5 CD 34.7 FD (6) Freezing Point Diagram with Additives 1 Boiling Point 113.5 CD 236.3 FD (10) 4 Critical Properties C P = 145 atm. c T = 380 C (716 F) D D dc = 0.231 g/cc (5) (5) (5) 3 3 3 Density, liquid 1.0045 g cc @ 25 CD 8.482 lb gal @ 77 FD 2, 3 Density, vapor and liquid (5) 3 Vapor Pressure 14.38 mm @ 25 CD 0.0189 @ 77 F atm D (6) 4 Surface Tension 66.67 dynes/cm @ 25 CD 62.32 dynes/cm @ 35 CD .004568 lb ft @ 77 FD .004270 lb ft @ 95 FD (7) (9) Viscosity, liquid 0.90 centipoise @ 25 CD .000605 lb ft -sec @ 77 FD (11, 12) 5 Heat Flux at qul / Pressure (8) 6 Heat Flux at qul / Temperature (8) 7 Heat Flux at qul / Velocity (8) 8
Heat of fusion 3.025 kcal/mole 15C 37.51Bt/b@34() 9.600 kcal/ mole 1135C 540Btu/b@236(3) Capacity (liquid) 23.62 cal/mole-C@25'C 737Btub@77(6 NH40)+O2=N2+2H00)1486 kcal/ mole@25 c 8346Bu/h7(20) Heats of Formation at 25C(77°F) N2+2H2=N2H4(g) N2+2H2 N2H4(liq) 22.750 kcal/mole 1278 Btu/ lb 11.999 kcal/mole N2+2H2+H20=N2H4.H2010300 kcal/mole 675 Btu/lb N2+2H2+ aq=N2H4 aq.140 kcal/mole 579 Btu/lb 457 Btu/lb Index of refraction D 1.4641825c(7F Dielectric Constant 51.7@25C(77F) (19) Electrical Conductivity 3×106ohm1@25c(77 (11) Flash Point(open cup) 52C 126°F (18) Explosive Limits(in air, 1 4. 7% lowe 100% upper B Materials: The following table gives an evaluation of the compatibility data that are available for numerous metals, plastics elastomers, and miscellaneous material: COMPARATIVE COMPATIBILITY OF VARTOUS MATERIALS WITH HYDRAZINE AND HYDRAZINE MIXTURES( Ref. 28)1 A-Material is acceptable for general service. B-Material is acceptable for limited service C-Material which must be avoided MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRAZINE HYDRATE HYDRAZINE NITRATE- MIXTURES e Al AAA B 24sT 40E ABBA B 52ST 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 2 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 2 of 12 Heat of Fusion 3.025 kcal/mole @ 1.5 CD 37.51 Btu lb @ 34.7D (6) Heat of Vaporization 9.600 kcal/mole @ 113.5 CD 54.0 Btu lb @ 236 FD (3) Heat Capacity (liquid) Temp. 23.62 cal/mole- C @ 25 C D D .737 Btu lb- F @ 77 F D D (6) 9 Heat of Combustion N2H4 (l)+O2=N2+2H2O (l) 148.6 kcal/mole @ 25 CD 8.346 Btu lb @ 77 FD (20) Heats of Formation at 25 C (77 F) D D N2+2H2 = N2H4 (g) N2+2H2 = N2H4 (liq) N2+2H2+H2O = N2H4.H2O N2+2H2+ aq = N2H4. aq 22.750 kcal/mole 11.999 kcal/mole 10.300 kcal/mole 8.140 kcal/mole 1278 Btu/lb 675 Btu/lb 579 Btu/lb 457 Btu/lb (20) (20) (20) (20) Index of Refraction, D 1.4644 @ 25 C (77 F) D D (9) Dielectric Constant 51.7 @ 25 C (77 F) D D (19) Electrical Conductivity -6 -1 3 10 ohm @ 25 C (77 F) × D D (11) Flash Point (open cup) 52 CD 126 FD (18) Explosive Limits (in air, 1 atm.) 4.7% lower 100% upper (18) (18) B. Materials: The following table gives an evaluation of the compatibility data that are available for numerous metals, plastics, elastomers, and miscellaneous material: COMPARATIVE COMPATIBILITY OF VARIOUS MATERIALS WITH HYDRAZINE AND HYDRAZINE MIXTURES (Ref. 28) A-Material is acceptable for general service. B-Material is acceptable for limited service. C-Material which must be avoided. MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRATE HYDRAZINEHYDRAZINE NITRATEWATER MIXTURES Metals Aluminum 2S A A B 2SO A A B 2SH A A B 3S A A B 3SH A A B 24ST A A A 40E B B B 43 B B B 52ST A A A
75sT MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRAZINE HYDRATE HYDRAZINE NITRATE ATER MIXTURES XA-545 Brass Cobalt BBBCCB Inconel InconelⅩ Lead Magnesium BBBCCBBCCOCCB CCC Molybdenum Nickel Nickel-chrome alloys Chromel-A, Nichrome BBC BBBC CCB Steel Stainless 303 304 CACC 316 321 329 410 416 BCACCCBCABCCB 430 430F BCACCCBCABCCBCCCBBA 440C Stellite Tantalum Titanium Zinc Plastics and elastomers 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 3 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 3 of 12 61ST A A A 75ST A A A MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRATE HYDRAZINEHYDRAZINE NITRATEWATER MIXTURES XA-545 B B B 716 B B B Brass B B B Cobalt C C C Copper C C C Inconel B B B Inconel X B B B Iron C C C Lead C C C Magnesium C C C Manganese C C C Molybdenum C C C Monel B B C Nickel B B C Nickel-chrome alloys (Chromel-A, Nichrome) B B C Silver B B B Steel Mild C C C Stainless 302 B B B 303 C C C 304 A A A 315 C C C 316 C C C 317 C C C 321 B B B 329 C C C 347 A A A 410 B B B 416 C C C 420F C C C 430 B B B 430F C C C 440A C C C 440C C C C W B B B Stellite B B B Tantalum A A A Tin C C C Titanium A A A Zinc C C C Plastics and Elastomers
Cellulose acetate ANHYDROUS HYDRAZINE HYDRAZINE- HYDRAZINE HYDRATE HYDRAZINE NITRATE ATER MIXTURES cellulose Furane resin BBBB Kel-F BBBBBC Lactoprene C Lucite Melamine formaldehyde Phenolic Polyester Polystyrene and BBBCAC BBBCAB polydichlorostyrene Polyvinyl chloride (Koroseal, vinylite, B Rubber Natural gum Synthetic B L Saran CBCBAB CBCBAB U.SRubber L7825 B M20995 B Veloform Miscellaneous Materials siestas Soft A Pyrex Graphite AAB Graphitar Pipe-joint compounds AABBB AN-C-53 ead-Tite BBBC R 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 4 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 4 of 12 Cellulose acetate C C C Diallyl phthalate C C C MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRATE HYDRAZINEHYDRAZINE NITRATEWATER MIXTURES Epon B B B Ethyl cellulose B B B Furane resin B B B Hycar B B B Kel-F B B B Lactopreme C C C Lucite B B B Melamine formaldehyde B B B Nylon B B B Phenolic B B B Polyester C C C Polyethylene A A A Polystyrene and polydichlorostyrene C C B Polyvinyl alcohol C C C Polyvinyl chloride (Koroseal, Vinylite, etc.) B B B Rubber Natural gum C C C Synthetic B B B Saran C C C Silastic B B B Teflon A A A Tygon B B B U.S. Rubber Plastic L7825 B B B M20995 B B B Veloform C C C Miscellaneous Materials Asbestos B B B Glass Soft A A A Pyrex A A A Graphite B B B Graphitar B Pipe-joint compounds AN-C-53 B B B Oxyseal B B B Thread-Tite B B B Rags C C C
Silicone lubricants DC-200 series MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRAZINE HYDRATE HYDRAZINE NITRATE ATER MIXTURES DC-550 DC-710 ug-cocK grease Solder BBBB Silver B B C. Equipment: The selection of materials of construction of equipment for use with hydrazine should be limited to those previously listed as acceptable for general service Hydrazine and hydrazine rockets (1)Properties. Hydrazine monopropellant rockets have become standard for NsSK and other on board maneuvering needs. This is because of the simplicity of a monopropellant rocket, storability of hydrazine over many years, and relatively good performance achievable. Also, the technology of hydrazine engines is well developed. There had been other monopropellants used or considered before(H2O2, nitromethane) but they are inferior either in safety or in performance Formula Clear, very similar to water in physical properties (p=1g/cm, freezes at 1.5'C, boils at 1135'C, surface tension 66.7 dyn/cm at25 C, viscosity =0.9 cp at 25C, specific heat 0. 72 cal/g Cat 25C). Other properties listed in the given table Chemically, however, N2H4 is very different from H2O. It will react with CO2 and O2 in air; if exposed to a large surface of air, as in wet rags, it may ignite; it may also ignite in contact with metallic oxides. Its combustion is very exothermic NH4+02→N2+210+149K%koe and so hydrazine is a good fuel for a bipropellant rocket(hydrazine o2 Variations are the monomethyl hydrazine(mmh) nh3 CH3 and the unsymmetric dimetyl hydrazine(UDMH, NH2(CH3)2), which are very similar but somewhat 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 5 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 5 of 12 Silicone lubricants DC-200 series B B B MATERIAL ANHYDROUS HYDRAZINE HYDRAZINE HYDRATE HYDRAZINEHYDRAZINE NITRATEWATER MIXTURES DC-550 B B B DC-710 B B B Plug-cock grease B B B Solder Lead-tin B B B Silver B B B Varnish B B B Wood C C C Wool C C C C. Equipment: The selection of materials of construction of equipment for use with hydrazine should be limited to those previously listed as acceptable for general service. Hydrazine and hydrazine rockets - (1) Properties. Hydrazine monopropellant rockets have become standard for NSSK and other onboard maneuvering needs. This is because of the simplicity of a monopropellant rocket, storability of hydrazine over many years, and relatively good performance achievable. Also, the technology of hydrazine engines is well developed. There had been other monopropellants used or considered before (H2O2, nitromethane) but they are inferior either in safety or in performance. Formula: N2H4 Clear, very similar to water in physical properties ( 3 ρ = 1 g cm , freezes at 1.5 CD , boils at 113.5 CD , surface tension = 66.7 dyn/cm at25 CD , viscosity = 0.9 cp at 25 CD , specific heat 0.72 cal/g C D at 25 CD ). Other properties listed in the given table. Chemically, however, N2H4 is very different from H2O. It will react with CO2 and O2 in air; if exposed to a large surface of air, as in wet rags, it may ignite; it may also ignite in contact with metallic oxides. Its combustion is very exothermic: 24 2 2 2 N H +O N 2H O+149 Kcal Mole → + and so hydrazine is a good fuel for a bipropellant rocket (Hydrazine + O2). Variations are the monomethyl hydrazine (MMH) NH3CH3 and the unsymmetric dimetyl hydrazine (UDMH, NH2(CH3)2), which are very similar but somewhat
inferior thermochemically, but have a wider liquid range. A popular bipropellant combination is A50 (50% hydrazine, 50% UDMH) These cannot be used as monoprop, because they poison the catalyst Hydrazine evolves NH3, and smells like it. Its vapors damage the eyes and the pulmonary tract. The liquid if pure, is fairly inert, but vapors form flammable mixtures in air for vapor pressures corresponding toT>40 C. the liquid decomposes exothermically if catalyzed by iron oxide, copper oxide or oxides of Pb, Mn, Mb, Ag, Hg or Cr. It is not sensitive to friction or impact Materials compatibility is an important consideration, especially for long term torage and for parts of thrusters with long life exposed to it Materials which are oK are aluminum stainless 304 or 347, titanium tantalum rhenium and platinum. also glass, Teflon and polyethylene plastics. to be avoided are copper cobalt, iron, lead, magnesium, manganese, molibdenum, mild steel, high Mo stainless(416, 303), most plastics(except as noted), wood, rags, paper. See table handed out Oils are oK for lubrication, but not if there is a catalytic bed, since it gets poisoned by the oil. Hydrazine is expensive($ 50-60/Ib for MMH, as of 1994) (2) Thermochemistry. When catalyzed either by an oxide or by a hot platinum surface, N2H4 decomposes. Since at low temperatures ammonia, NH3 is stable, the preferred end products would be NH3 +N2 3NH H3+N2 (a) However, this is a very exothermic reaction and the equilibration T would be 1650K at which temperature NH3 is not stable anymore. Hence, the final equilibrium composition would contain very little NH3, due to H3→N2+3H2 and would be at intermediate t since the latter reaction is endothermic. In practice reaction(a) is very fast(less than 1 msec) if catalyzed, while(b)is slow Hence for small decomposition chambers and high flow rates when the residence time Pas Van/m is short, reaction(b)proceeds only partially, the extent being controllable by the design conditions. The final composition and overal reaction assuming a fraction x of NH3 decomposes is N2H4→=NH3+N2 Form (1)+X(2); x=fraction of NH, that decomposes H3→5N2+2H2 NH4→(1-x)NH2+(1+2x)N2+2xH2 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 6 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 6 of 12 inferior thermochemically, but have a wider liquid range. A popular bipropellant combination is A50 (50% hydrazine, 50% UDMH). These cannot be used as monoprops, because they poison the catalyst. Hydrazine evolves NH3, and smells like it. Its vapors damage the eyes and the pulmonary tract. The liquid, if pure, is fairly inert, but vapors form flammable mixtures in air for vapor pressures corresponding to T > 40 CD . The liquid decomposes exothermically if catalyzed by iron oxide, copper oxide, or oxides of Pb, Mn, Mb, Ag, Hg or Cr. It is not sensitive to friction or impact. Materials compatibility is an important consideration, especially for long term storage and for parts of thrusters with long life exposed to it. Materials which are OK are aluminum, stainless 304 or 347, titanium, tantalum, rhenium and platinum. Also glass, Teflon and polyethylene plastics. To be avoided are copper, cobalt, iron, lead, magnesium, manganese, molibdenum, mild steel, high Mo stainless (416, 303), most plastics (except as noted), wood, rags, paper. See table handed out. Oils are OK for lubrication, but not if there is a catalytic bed, since it gets poisoned by the oil. Hydrazine is expensive ($ 50-60/lb for MMH, as of 1994). (2) Thermochemistry. When catalyzed either by an oxide or by a hot platinum surface, N2H4 decomposes. Since at low temperatures ammonia, NH3, is stable, the preferred end products would be NH3 +N2: 3N H 4NH N 24 3 2 → + (a) However, this is a very exothermic reaction, and the equilibration T would be 1650 K, D at which temperature NH3 is not stable anymore. Hence, the final equilibrium composition would contain very little NH3, due to 2NH N +3H 3 22 → (b) and would be at intermediate T, since the latter reaction is endothermic. In practice reaction (a) is very fast (less than 1 msec) if catalyzed, while (b) is slow. Hence, for small decomposition chambers and high flow rates, when the residence time ρgas ch V mi is short, reaction (b) proceeds only partially, the extent being controllable by the design conditions. The final composition and overall reaction assuming a fraction x of NH3 decomposes is 24 3 2 3 3 22 4 1 N H NH + N (1) 3 3 Form (1)+ x(2) ; x = fraction of NH that decomposes 4 2 NH N + 2H (2) 3 3 → → 24 3 2 2 ( ) ( ) 4 1 N H 1 - x NH + 1+ 2x N + 2xH 3 3 →
For an adiabatic combustion(no heat loss, no heating), we must have(starting from liquid N2H4 at 298K) h(,298)4(1×)hm(T)+31+2×)h2(T)+2xh(T)→ Equation for T The respective molar enthalpies can be fitted by h(T)=16.83+12.350+0.983020=7 mole 1000°K h2(T)=-2.83+7756+01830 h4(T)=1967+660+03670(300≤T≤4000K (Notice c,(cal/mole C))is o, with h in Kcal/mole) From the table given, hm((, 298 K)=12 Kcal/mole. We can now solve for T at various arbitrary values of x: √39.3-20.75×+845×2-(9.525+095×) 1.372-0.455X x(fraction of NH3 decomposed) 0 0.2040.60.81 T(K), adiabatic temperature 16591502134311821023863 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez age 7 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 7 of 12 For an adiabatic combustion (no heat loss, no heating), we must have (starting from liquid N2H4 at 298 KD ) ( ) ( ) () ( ) () () N H NH N H 24 3 2 2 4 1 h ,298 1-x h T 1+2x h T 2xh T Equation for T 3 3 A D = + +→ The respective molar enthalpies can be fitted by ( ) 3 2 cal NH K T h T = -16.83 +12.35 + 0.983 = mole 1000 K θ θθ D ( ) 2 2 h T = -2.83 + 7.75 + 0.183 N θ θ ( ) 2 2 h T = -1.967 + 6.6 + 0.367 H θ θ (300 T 4000 K ≤ ≤ ) D (Notice c cal mole C p ( ) D ) is dh dθ , with h in Kcal/mole) From the table given, ( ) N H2 4 h ,298 K 12 Kcal/mole = D A . We can now solve for T at various arbitrary values of x: ( ) 2 139.3 - 20.75x + 8.45x - 9.525 + 0.95x = 1.372 - 0.455x θ x (fraction of NH3 decomposed) 0 0.2 0.4 0.6 0.8 1 T( K), D adiabatic temperature 1659 1502 1343 1182 1023 863
Equillibrium Hydrazine Decomposition If we allowed "infinite" time for the reaction, hydrazine products would reach an equilibrium with little ammonia left(depending on pressure). The product, N2, H2, NH3, must then satisfy =K2(T); Kp=1.089×10°e(atm2) (Ps in atm) and the pressure is To conserve moles of H and N, starting from(arbitrarily )3 moles of N 2H4, we must H:3nk+2n2=3×4=12 dividing +2Pn2=2 nm+2n=3×2=6 (ammonia mole fraction) 2 Solv P PN, 16. 522, Space Propulsion Prof. Manuel martinez-Sanchez Page 8 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 8 of 12 Equilibrium Hydrazine Decomposition If we allowed “infinite” time for the reaction, hydrazine products would reach an equilibrium with little ammonia left (depending on pressure). The product, N2, H2, NH3, must then satisfy ( ) 3 2 2 NH 1 3 p 2 2 N H P =K T P P ; ( ) 6289 -6 T -1 K 1.089×10 e atm p (P’s in atm) and the pressure is NH N H 322 P=P +P +P To conserve moles of H and N, starting from (arbitrarily) 3 moles of N2H4, we must have × × 3 2 3 2 3 2 3 2 NH H NH H NH N NH N H : 3n + 2n = 3 4 = 12 3P + 2P dividing, = 2 N : n + 2n = 3 2 = 6 P + 2P Define NH3 P y = P (ammonia mole fraction). Then 2 2 H N 3y + 2P P = 2 y + 2P P and H N 2 2 P P y+ + =1 P P Solving, H2 P 2 5 = 1- y P3 4 N2 P 1 1 = 1- y P3 2
and substituting into the equilibrium law, y P 1(,1 3(3Pk (T)=K So, given P and t, we can solve this for But T itself must be consistent with energy conservation 4(1-x)hn(T)+1+2xh(T)+2xhn(T)=h there h, H, would be 12.0 Kcal/mol if we start from liquid hydrazine at 298K, or it could include the external heating energy due to an electrical heater, as in the case of an Electrothermally Augmented thruster(in fact, in this case the equilibrium assumption is realistic, given the long residence time in the heater, and the higher temperature Now x is the fraction of NH3 decomposed after the initial fast reaction NH4→3 Nh+ To relate it to y, which is the mole fraction of NH3 in the final products, we write 4(1-×) 1+2x 4-5V 4(1+ (notice for x=0 we have y y of the products is N2 while for x=l, y=o). So, to complete the computation we could iterate as follows (1) Given P, guess T 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 9 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 9 of 12 and substituting into the equilibrium law, 12 32 p y =K P 11 25 1- y 1- y 32 34 ( ) 12 32 12 32 p y y 12 = PK T K 1 5 3 3 1- y 1- y 2 4 ≡ So, given P and T, we can solve this for NH3 P y = P . But T itself must be consistent with energy conservation ( ) () () () NH N H N H 3 2 2 24 4 1+ 2x 1 - x h T + h T + 2xh T = h 3 3 where N H2 4 h would be 12.0 Kcal/mol if we start from liquid hydrazine at 298K, or it could include the external heating energy due to an electrical heater, as in the case of an Electrothermally Augmented thruster (in fact, in this case the equilibrium assumption is realistic, given the long residence time in the heater, and the higher temperature). Now x is the fraction of NH3 decomposed after the initial fast reaction 24 3 2 4 1 N H NH + N 3 3 → . To relate it to y, which is the mole fraction of NH3 in the final products, we write ( ) ( ) ( ) 4 1-x 4 1-x 3 y= = 4 1+ 2x 5 + 4x 1 - x + + 2x 3 3 or ( ) 4 - 5y x = 4 1+y (notice for x=0 we have 4 y = 5 , i.e. 1 5 of the products is N2 while for x=1, y=0). So, to complete the computation, we could iterate as follows: (1) Given P, guess T
(2) Compute Ke (T),K, (T, P),NH (T), hM, (T),hH T) (3) Solve 1 =k for y (4) Calculate x Calculate prods. =5(1-x)Nh+ +2xh and the error"hrods-h (6 Use this error to generate a new t guess go back to(2) Some results(with no external heating) P P(atm)y T(K) which, indeed, shows 0.00098 864.8 minimal NH3 present 0.0024 867.3 0.0046 871.3 0.0086 878.4 0.0185 895.5 100 0.0306 916.3 0.0479 945.0 For propulsion purposes, the important thing is not T, but Isp. This depends also on the molecular weight of the gas(and somewhat on y ) since the gas gets lighter as NH3 decomposes, this compensates for the lower T, and Isp is very insensitive to x for X<0.4. Assuming frozen flow(constant y, constant M),and a pressure ratio Pe/Po the exit velocity is R 17×(1-×)+28 1+2 T 3+2x.2 M P 1+2 +2X 96 M and the area ratio is 16. 522, Space Propulsion Lecture 5 Prof. Manuel martinez-Sanchez Page 10 of 12
16.522, Space Propulsion Lecture 5 Prof. Manuel Martinez-Sanchez Page 10 of 12 (2) Compute () ( ) ( ) ( ) ( ) p y NH N H 322 K T , K T, P , h T , h T , h T (3) Solve 1 3 y 2 2 y = K y 4 1- 1- y 2 5 for y (4) Calculate ( ) 4 - 5y x = 4 1+y (5) Calculate ( ) prods. NH N H 3 22 4 1+ 2x h = 1 - x h + h + 2xh 3 3 and the “error” prods. N H2 4 h -h (6) Use this error to generate a new T guess, go back to (2) Some results (with no external heating) which, indeed, shows minimal NH3 present For propulsion purposes, the important thing is not T, but Isp. This depends also on the molecular weight of the gas (and somewhat on γ ); since the gas gets lighter as NH3 decomposes, this compensates for the lower T, and Isp is very insensitive to x for x<0.4. ∼ Assuming frozen flow (constant γ , constant M), and a pressure ratio Pe/Po, the exit velocity is -1 e e 0 0 R P u = 2 T 1- -1M P γ γ γ γ ( ) ( ) 4 1+ 2x 17x 1 - x + 28 + 2x.2 M = 3 3 4 1+ 2x 1 - x + + 2x 3 3 96 M = 5 + 4x and the area ratio is P(atm) NH3 P y = P T(K) 2 0.00098 864.8 5 0.0024 867.3 10 0.0046 871.3 20 0.0086 878.4 50 0.0185 895.5 100 0.0306 916.3 200 0.0479 945.0