Session 12 : Monopropellant Thrusters

Transcription

1 Session 12 : Monoroellant Thrusters Electrothermal augmentation of chemical rockets was the first form of electric roulsion alied in sace vehicles. In its original imlementation, resistojets were used to imrove the erformance of regular hydrazine (N 2 H 4 ) thrusters in geostationary satellites. The motivation for this imortant alication is relevant to the develoment of electric roulsion and will be discussed in detail in this lecture. We start by reviewing the fundamentals of hydrazine monoroellant roulsion. Hydrazine was first isolated by Curtius in 1887, and in 1907 a suitable synthetic method was develoed by Raschig. Anhydrous hydrazine is a clear, colorless, hygroscoic 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 roerties. Although otential data show hydrazine to be a owerful oxidizing agent in acidic solutions, reactions with many reducing agents are so slow that only the most owerful ones reduce it quantitatively to ammonium ion. Hydrazine will react with carbon dioxide and oxygen in air. When hydrazine is exosed on a large surface to air, such as on rags, it may ignite sontaneously due to the evolution of heat caused by oxidation with atmosheric oxygen. A film of hydrazine in contact with metallic oxides and other oxidizing agents may ignite. Hydrazine is an endothermic comound and will decomose sontaneously in a similar way to hydrogen eroxide. The reaction of hydrazine with the oxides of coer, manganese, iron, silver, mercury, molybdenum, lead or chromium may be articularly violent. The sontaneous or artificially induced decomosition of hydrazine does not follow the reaction N 2 H 4 N 2 + 2H 2, but a more exothermic one such as 2N 2 H 4 2NH 3 + N 2 + H 2. When catalyzed either by an oxide or by a hot latinum surface, N 2 H 4 decomoses. Since at low temeratures ammonia, NH 3, is stable, the referred end roducts would be NH 3 + N 2 : 4 1 N 2 H 4 NH 3 + N 2 (1) However, this is a very exothermic reaction, and the equilibration temerature (T ) would be 1650 K, at which temerature NH 3 is not stable anymore. Hence, the final equilibrium comosition would contain very little NH 3, due to, 4 2 NH 3 N 2 + 2H 2 (2) and would be at an intermediate T, since the latter reaction is endothermic. In ractice reaction (1) is very fast (less than 1 msec) if catalyzed, while (2) is slow. Hence, for small decomosition chambers and high flow rates, when the residence time ρv/ ṁ is short, reaction (2) roceeds only artially, the extent being controllable by the design conditions. The final comosition and overall reaction assuming a fraction x of NH 3 decomoses is, 4 1 N 2 H 4 (1 x)nh 3 + (1 + 2x)N 2 + 2xH 2 (3) For an adiabatic combustion (no heat loss, no heating), we must have (starting from liquid N 2 H 4 at 298 K), 1

2 4 1 h N 2H4 ( J, 298K) = (1 x)h NH 3 + (1 + 2x)h N 2 + 2xh H 2 (4) The resective molar enthalies (kcal/mol) can be fitted by, h NH 3 (T ) = θ θ 2 h N 2 (T ) = θ θ 2 (5) h H 2 (T ) = θ θ 2 T where θ =. These exressions are valid in the range 0.3 < θ < 4. The secific heat 1000K dh is c (cal/mol K) =. dθ The value of the enthaly of liquid hydrazine at standard conditions can be found from tables, h N 2H4 (J, 298K) = 12 kcal/mol. We can now solve for the temerature at various arbitrary values of x, x x 2 ( x) θ = x Results from Eq. (6) are shown in the table below: (6) x (fraction of NH 3 decomosed) T (K) adiabatic temerature U to this oint, the ammonia decomosition fraction has been considered as a free arameter. In ractice, it will deend on residence time and oerating conditions, in articular the chamber ressure. If we assume that residence time is long enough to allow for infinite time for the decomosition reaction, hydrazine roducts would reach an equilibrium with some ammonia left (deending on ressure). From the law of mass action, the roducts must satisfy, NH 3 1/2 3/2 N2 H2 = K (T ) (7) where the equilibrium constant is aroximated by (ressures in atm), and in terms of artial ressures we have, K (T ) e 6289 T in atm 1 (8) Writing the reaction in terms of artial molar densities, = NH 3 + N 2 + H 2 (9) 2

3 we imose secies conservation, nn 2 H 4 n NH 3 NH 3 + n N 2 N 2 + n H 2 H 2 (10) for H 4n = 3n NH 3 + 2n H 2 for N 2n = n NH 3 + 2n N 2 (11) or in terms of the artial ressures, since = nkt, 3 NH H 2 2 = (12) NH N 2 Eqs. (7-9) and (12) constitute a system of four equations and four unknowns, i.e., the artial ressures and temerature. We solve this system by defining the ammonia mole fraction, After some maniulation, these equations can be written as, We also write the mol fraction Eq. (13) in terms of x, or, solving for x in terms of y, NH 3 y = (13) NH 3 1 y = H 2 2 5y = 1 (14) 3 4 y/ K (T ) = 1/2 3/2 ( N 2 /) ( H 2 /) 4 (1 x) 3 4(1 x) y = 4 = (15) (1 x) + 1 (1 + 2x) + 2x 5 + 4x 1 5y/4 x = (16) 1 + y Given some ressure and an initial guess for the temerature T, we find y and x. At this oint we need to verify that the temerature used in this calculation is consistent with the energy balance in Eq. (4). In all likelihood the temerature from Eq. (4) will not coincide with the initial guess, so we need to erform a few iterations of this rocess. In ractice, selecting the adiabatic temerature from the energy balance as initial guess for each iteration suffices to guarantee quick convergence. The following table shows some results using this rocedure as a function of ressure. 3

4 (atm) y = NH3 T (K) In all these cases we observe that ammonia is near to comlete decomosition if allowed to reach equilibrium conditions. If this result is not desirable in a thruster, then the only additional knob to control decomosition is residence time, so in many instances the geometry of the thruster is essential to determine the erformance. Now, for roulsion uroses, the imortant thing is not the adiabatic temerature, but the I s. This deends also on the molecular weight of the gas; since the gas gets lighter as NH 3 decomoses, this comensates for the lower T, and I s is very insensitive to x, for x < 0.4. F mu e + e A e u e e A e c I s = = = + (17) mg mg g 0 A t g where the characteristic velocity is defined as usual, γ+1 2( γ 0At R/M T 0 2 1) c = = with Γ(γ) = ( ) γ ṁ Γ(γ) γ + 1 Assuming frozen flow, and a ressure ratio e / 0, the exit velocity is, u e = The molecular mass is obtained with a weighted average, M = [ γ ( ) ] 1 2γ R γ e T 0 1 (18) γ 1 M 0 M 4 (1 x) + M 1 NH3 (1 + 2x) + M 2x 3 N2 3 H (1 x) + 1 = (19) (1 + 2x) + 2x 5 + 4x A similar rocedure can be used to comute the weighted average for the secific heat, and from here the ratio of secific heats γ = γ(x). The area ratio is, 4

5 +1 1 ( ) γ 1 γ 1 1/2 A γ 2 ( 2(γ 1) ) [ e γ ( ) ] e γ e = 1 (20) A t 2 γ The following age contains the results from these calculations for a ressure ratio e / 0 = , corresonding to an area ratio of about A e /A t = 50. As a ractical matter, one wants T 0 as low as ossible if the erformance is accetable. A very common choice is x = 0.4 for a secific imulse of about 250 sec. 5

6 Figure removed due to coyright restrictions. Please see Figure 6.8 from Schmidt, Eckart W. Hydrazine and its Derivatives. Wiley-Interscience,

7 MIT OenCourseWare htt://ocw.mit.edu Sace Proulsion Sring 2015 For information about citing these materials or our Terms of Use, visit: htt://ocw.mit.edu/terms.