Trans. JSASS Aerospace Tech. Japan Vol. 8, No. ists27, pp. Pa_47-Pa_56, 2010

Original Paper

Modeling LiH Combustion in Solid Fuelled Scramjet Engine

1) 1) By Domenico SIMONE and Claudio BRUNO

1)Department of Mechanics and Aeronautics, University of Rome “La Sapienza”, Rome, Italy

(Received July 17th, 2009)

Lithium Hydride is a hydrogen-rich compound with potential application as fuel, thanks to its high density and low molecular weight. It reacts exothermically with many substances and contains H2, suggesting its use where a much higher density (compared to that of LH2) would be beneficial. In this work LiH (solid at STP) has thus investigated as potential candidate for solid fuelled scramjets (SFSCRJ). Its thermochemical properties and issues associated to its combustion in a hot supersonic stream have been investigated; results show clearly that Li, released by thermal decomposition, plays a key role in the LiH performance. In fact, above the auto-ignition point liquid Li combustion with air increases local temperature and promotes LiH decomposition. To understand quantitatively these effects, a simplified physical model describing LiH “vaporization” and combustion was built and used in simulations of a notional SCRJ chamber by means of a CFD code. Results are intriguing: an intense and stable flame zone is predicted to be present over and downstream of the grain and high temperatures (of order 2900 K) are obtainable. Moreover, specific impulse and thrust density predicted at a flight Mach = 7 are also interesting, being 10,000 m/s and 200-300 m/s, respectively.

Key Words: Solid Fuel, Scramjet

1. Introduction surface exposed to air) the amount of hydrogen delivered (and liquid lithium) increases, and the reaction may Lithium Hydride is a hydrogen-rich compound with become explosive. Before the theoretical boiling point potential application as fuel, thanks to its high density (~ (1100 K at 1 atmosphere) the decomposition can be 0.88 g/cm3) and low molecular weight (MW = 7.9). 1-4) considered complete. Produced by reacting Li and H2 at moderate temperature The use of lithium hydride as fuel for aerospace (about 570 K at 1 bar), LiH is a ionic solid: it contains Li+ applications was investigated for the first time in 1958 in a and hydrogen anion H- (14.3 % in mass) and behaves as a research program devoted to asses specific impulse gains strongly reducing agent. LiH reacts also very fast with with new propellants for nuclear rockets. Lithium many oxidizers, halogenated hydrocarbons and acids; and hydride, beryllium hydride and boron hydride were 7) its combustion products contain light molecules with the investigated. With lithium hydride, the condensation of further advantage of the absence of solid particulate or lithium (released by decomposition) within the rocket gums. nozzle was estimated capable of releasing several times the LiH reacts slowly at STP with air oxygen; it burns energy that would be available from hydrogen expansion spontaneously on contact with air starting at 470 K; starting from the same initial reactor temperature. Due to however, finely dispersed particles form explosive the lower melting temperature of lithium (450 K) with mixtures especially in presence of moisture.5) However respect to lithium hydride (950 K), researchers focused data concerning the LiH reactivity with air at high their attention on the former, analyzing in particular its temperature ( T> 1200 K) rate are scarce or nonexistent. behaviour during nozzle expansion. Researchers pointed This lack is probably due to its ability to decompose out that the lack of data concerning the combustion endothermically releasing gaseous hydrogen; in fact LiH products (such as Li2O or LiO2) at high temperature was liquefies at 950 K: while the others alkaline hydrides critical to their study. After this work few citations of LiH 8) decompose at the melting point, liquid lithium hydride is as fuel can be found in the open literature. stable in a narrow range of temperatures ( 950 < T < 1100 Therefore the first phase of this investigation was K). Increasing the temperature from the melting point up to characterized by an extended campaign of thermodynamic the boiling point, the amount of hydrogen released by simulations, conceived to analyze the LiH propulsion thermal decomposition increases, producing a mixture of potential; results have been used to determine which Li and LiH. Also data concerning the LiH decomposition reactions should be considered in our solid-fuelled SCRJ rate are scarce or nonexistent; it is known that hydrogen (SFSCRJ) combustion chamber model. diffuses from LiH also at STP conditions;6) at the ignition Finally, we will show results obtained with a simplified point (470 K in dry air; that is 20 K over the melting point model of an ideal scramjet, flying along a constant of lithium) the amount of hydrogen leaving a LiH particle dynamic pressure trajectory, and developed to investigate is so significant that the liquid lithium formed on the LiH the effect of LiH decomposition and of liquid Li surface can ignite, heating the hydrogen and promoting its vaporization on performance and combustion products. combustion near the surface. Increasing the number of LiH particles present in a volume (that is increasing the LiH

Copyright© 2010 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved.

Pa_47 Trans. JSASS Aerospace Tech. Japan Vol. 8, No. ists27 (2010)

2. Reactions with High Temperature Air is favored. However, the most important consideration concerns LiH decomposition. Despite the decreased Simulations were initially performed to study the temperature, LiH still decomposes yielding gaseous H2 and behavior of LiH with air at conditions similar to those Li; only at very low oxygen concentration, when encountered in a notional SFSCRJ combustion chamber. combustion temperature is above 1600 K, a significant By using the NASA CEA2 code, equilibrium calculations amount of liquid Li with traces of gaseous LiH are present have been performed for inlet air temperature ranging from in the combustion chamber. 1000 K up to 1800 K, and pressure ranging from 0.5 up to The decomposition of LiH is an equilibrium process: 5 atmospheres.9) Results suggested that the LiH-oxygen reactions dominate in atmospheric environments, while the LiH-nitrogen reactions are relatively unimportant except Increasing temperature increases the rates of both when oxygen concentration is very low (not the case with forward and backward reactions. However, the increase in SCRJ, except perhaps near the end of the combustion the forward reaction is much greater than the increase in chamber). Thus, when simulating the behavior of liquid the reverse reaction, so that the overall effect of increasing LiH in presence of air, independently of its temperature we temperature is to shift the equilibrium in the forward concluded that reactions with nitrogen and their products direction. In a closed container, the forward reaction is can be excluded. constrained by the increasing vapor pressure of the gaseous This assumption is confirmed by exploring equilibrium hydrogen produced; in a vented container, or burning the composition in the combustion chamber as a function of hydrogen, decomposition will continues indefinitely, since LiH/air molar concentration and initial air temperature and escaping hydrogen will not build up sufficient vapor pressure. Figures 1 and 2 show that, at 1400 K initial air pressure to maintain equilibrium. However, steady temperature and at 1 atmosphere in high-oxygen decomposition brings about an increase in the environment LiH reacts exothermically producing gaseous concentration of Li atoms on the surface, with an LiOH, Li2O and small traces of LiO and water vapor; the accompanying acceleration of the reverse reaction (that is absence of nitrogen compounds (except for very high air proportional to the square of the concentrations of lithium concentration) confirms that nitrogen reactions are atoms on the surface), therefore lowering the equilibrium practically negligible. hydrogen pressure. The overall effect is an increase in the 3.E-01 equilibrium temperature, enhancing the cooling ability of LiOH H2 LiH. 3.E-01 Li However, in the case of a combustion chamber of a 2.E-01 Li2O(L) scramjet, the situation is slightly different: in fact, at high Li2O(cr) 2.E-01 ambient temperature and in high speed flow, liquid Li vaporization and/or dragging by the turbulent flow may 1.E-01 O2 Li(L) increase the forward reaction rate, enabling the 5.E-02 decomposition to proceed as fast as thermal fluxes allow. Equilibrium molar fraction Rate constants for hydrogen-atom transfers involving 0.E+00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 lithium have been computed by Mayer in the temperature 10,11) mol LiH / mol air range 900 K – 1200 K. Another important contribute to the understanding of issues associated with the thermal -2 Fig. 1. Equilibrium composition: molar fractions >10 decomposition is given by two experimental works of (Tair =1400 K; p =1 atm). 12,13) Modisette , which investigated LiH as a high temperature internal coolant for hypersonic missiles. As 4.E-02 stated in these works, lithium hydride exposed to a Mach 2 H2O 3.E-02 flow at 2000 K can absorb up to 7 kJ per gram of lithium 3.E-02 hydride decomposed. Li2O 2.E-02 To assess the propulsion potential of LiH in a scramjet accounting for the impact of LiH decomposition on overall 2.E-02 Li2 performance it was assumed that, heated by the convective 1.E-02 LiH and radiative thermal fluxes, the grain surface melts and NO 5.E-03 Equilibrium molar fraction LiH decomposes. To investigate the effect of a partial or LiO H 0.E+00 complete decomposition a parametric analysis was 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 performed by defining the parameter α marking the extent mol LiH / mol air of liquid LiH decomposition, and that varies from α=0

Fig. 2. Equilibrium composition: molar fraction < 10-2 (liquid LiH only) up to α=1, (LiH completely decomposed). (Tair =1400 K; p =1 atm). Decomposition of LiH releases gaseous hydrogen in the airstream; turbulent friction drags liquid Li forming over When the LiH concentration is increased, LiOH the grain surface and injects it too in the hot air, where it decreases and LiO disappears, because the formation of vaporizes near the surface and reacts; some of the liquid Li liquid Li2O, due to the decreased combustion temperature, vaporizes directly on the surface. To investigate the effect

Pa_48 D. SIMONE and C. BRUNO : Modeling LiH Combustion in Solid Fuelled Scramjet Engine

of an incomplete vaporization, a similar parameter β This fact suggests that thermal decomposition is a key (varying from β=0, i.e. only liquid Li, up to β=1, i.e. only factor in assessing LiH propulsion potential, in that it gaseous Li) was defined. allows the presence of free lithium (liquid or vaporized) in Finally the nozzle entrance conditions were calculated the combustion chamber. In fact, as confirmed by figure 5, assuming constant pressure in the combustion chamber and the reactivity of lithium in the presence of oxygen plays an frictionless flow. important role for oxygen-rich mixtures (Φ < 1): lithium Combustion of LiH with air was simulated using reacts forming Li O and LiO , releasing energy and NASA’s CEA2 code by varying the equivalence ratio Φ 2 2 from 0.2 to 6. Performance was then compared with that of increasing combustion chamber temperature: these are higher than burning H2, and grow with growing β. CH4/Air and H2/Air mixtures at the same conditions. Assuming Li released by thermal decomposition to vaporize completely (that is, β = 1), specific thrust 3100 obtained increases increasing LiH decomposition (α); in β = 1 fact, as shown in figure 3, when LiH is completely 2600 β = 0.5 decomposed, specific thrust is higher than that obtained 2100 using H2; even for α = 0.25 specific thrust is still CH4 β = 0 H2 interesting, being higher than that obtained with liquid Tc, [K] 1600 methane, another fuel being considered for SCRJ operation. 1100

3000 600 0123456 2500 Equivalence ratio Φ 2000 α = 1 H2 Fig. 5. Combustion temperature as a function of β (α = 1). 1500 α = 0.25 , [N/(kg/s)]

Ψ 1000 These results thus confirm that LiH thermal CH4 decomposition plays a fundamental role on its potential 500 performance: in fact, when decomposed, it behaves as a 0 powerful bi-fuel system by releasing gaseous hydrogen and 0123456 highly reactive Li. From this viewpoint LiH could act as Equivalence ratio Φ dense and safe hydrogen “carrier”. In turn, lithium

Fig. 3. Specific thrust as a function of α (β = 1). reactions with O2 increase locally the temperature, contributing to promote LiH decomposition. This feature is confirmed observing that partially decomposed LiH yields combustion temperatures of the 3. Lithium Properties same order of those of liquid hydrogen, while temperature reached in the presence of complete decomposition are up Until 1970 there was a serious lack of data on physical to 500 K higher and chemical properties of Li, including its reactions with The effect of β (liquid Li degree of vaporization) on various materials. Successively it was extensively performance is shown in the following figures 4,5. Here, investigated as coolant and breeding material for controlled assuming LiH completely decomposed on the surface thermonuclear reactors because of its low melting point, (α = 1), we have accounted for the amount of Li vaporized high boiling point, low vapor pressure, low density, high β. β heat capacity, high thermal conductivity and low viscosity by varying As expected, decreasing the specific thrust 14) also decreases; however performance appears to be less (Table 1). sensitive to the fraction of lithium vaporized than to that of LiH decomposed. Table 1. Lithium properties.

2500

H2 2000 β = 1 β = 0.5

1500 β = 0

[N/(kg/s)] CH4

� 1000 Ψ

500

0 0123456

Equivalence ratio Φ

Fig. 4. Specific thrust as a function of β (α = 1).

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Unfortunately for applications to fusion reactors to 1200 K were calculated and compared; the temperature technology, liquid lithium reacts strongly in the presence of upper limit was selected because the Li3N melting point air, releasing about 4 times more energy per unit mass than (that coincides also with the decomposition point) is 1123 liquid sodium (also considered a potential candidate for K. Results are in Table2. these applications). Many experimental investigations and theoretical studies were performed, aimed at understanding Table 2. Comparison between the reactions forming Li3N and Li2O. liquid lithium and its behaviour in terms of adiabatic flame temperature, pressure increase in closed containment vessels, reaction rates in presence of dry and moist air, reactivity with containment materials end reaction products toxicity. 15) In this context software tools were developed to model accurately liquid lithium combustion; among them are the LITFIRE and MELCOR codes, that are well documented in the open literature and present an intriguing approach to Li-air reactions analysis. On the basis of experiments at HELD in 1978, MIT researchers performed a theoretical analysis of lithium combustion in air based on thermochemical considerations and limited to the range of temperatures from 500 K to From Table 2 the lithium-oxygen reaction is 1100.15) After observing the reaction products, they significantly more exothermic than lithium-nitrogen. restricted the reaction in air of greatest interest to the Hence, one would assume that moving toward equilibrium, following group: reaction with oxygen would be preferred over nitrogen. Furthermore, the change in Gibbs free energy is greater 2Li(l,g) + 0.5 O2 → Li2O(s,g) for the reaction involving oxygen than that of nitrogen, ΔH°(298) = -142 kcal/mol; ΔG°(298) = -133.9 kcal/mol indicating that the forward reaction with oxygen is carried to greater completion than with nitrogen. While the heat of 2Li(l,g) + O2 → Li2O2(s,g) Li3N is fairly constant over the temperature range ΔH°(298) = -151.9 kcal/mol; ΔG°(298) = -133.1 kcal/mol examined, the Gibbs free energy changes significantly, increasing to positive values with temperature. In fact, at Li(l,g) + OH → LiOH(s,g) 298 K ΔG is -154 kJ/mol, becoming -59.02 kJ/mol at 800 ΔH°(298) = -166.5 kcal/mol; ΔG°(298) = -105 kcal/mol K and still higher +32 kJ/mol at 1500 K. This would indicate that the forward reaction of lithium with nitrogen 3Li (l,g)+ 0.5 N2 → Li3N2(s) is very slow at elevated temperatures. ΔH°(298) = -47 kcal/mol; ΔG°(298) = -37 kcal/mol On the other hand, examining the lithium-oxygen o reactions, the ΔG T of Li2O is = -151 kJ/mol at 298 K, -493 kJ/mol at 800 K, and -398 kJ/mol at 1500 K. Hence, where ΔHo is the standard enthalpy of reaction and ΔGo is the main forward lithium-oxygen reaction is still very the change in Gibbs free energy. Negative ΔHo indicate important at elevated temperatures. These observations exothermic reactions. imply that liquid lithium-nitrogen reaction is important at Then using the TRAN72 code (an old version of the combustion temperature < 900 K, becoming unimportant NASA CEA code) they simulated combustion with the at > 1100 K. same initial conditions (room temperature and 1 atm) and This analysis may be assessed by comparing our 16) different reactant concentrations; in this way they considerations with experimental data by Kazimi . investigated the contribution of the various reactants to the In fact, as stated by Kazimi, even though less exothermic total energy release and thus the peak flame temperature. then that between lithium and oxygen, the lithium-nitrogen These data are important to assess which species became reaction gives a significant contribution to the temperature airborne or vaporized or formed aerosols, and to assess increase at low ambient temperatures (this was undesirable which reactions were dominant. for the applications examined by the MIT researchers, as Results showed that the equilibrium temperature is quite could not be used in lithium fires); at the same time this insensitive to the reactants considered other than nitrogen reaction could thermally promote Li – oxygen kinetics and and oxygen (f.i., CO2); furthermore, results indicated that sustain LiH grain ignition when temperatures in the at small O2 concentration the fraction of nitrogen combustion chamber are still low. Thus this reaction participating to the reactions is very small. To explain this must be included in the set of reactions of interest for our observation, as suggested by MIT researchers, we can do problem. some thermochemical considerations based on the reaction This analysis suggests that the lithium-oxygen reactions r o dominates in atmospheric air, while the lithium-nitrogen enthalpy ΔH T and Gibbs free energy, ΔG T: in fact they are useful to assess whether, in a group of reactions, there are reactions are relatively unimportant except at T < 1000 K one o more reactions favoured by thermodynamics. and at very low oxygen concentration. Increasing the As an example, the heat of formation and the changes in temperature up to 1100 K - 1200 K, independently of the oxygen concentration, lithium-nitrogen becomes Gibbs free energy for Li3N(s) and Li2O(s) from 298 K up

Pa_50 D. SIMONE and C. BRUNO : Modeling LiH Combustion in Solid Fuelled Scramjet Engine

unimportant. Above this range solid Li N liquefies and 3 0.9 decomposes. As a consequence, at temperatures higher 0.8 Li than 1100 K we can neglect reactions with nitrogen and 0.7 O their products. 0.6 2 To confirm these assumptions, we extended our analysis 0.5 to temperature higher than 1100 K. Thus to assess the 0.4 0.3

effects of relative mole fraction of lithium-air and Molar fraction lithium-nitrogen mixtures as well as the lithium initial 0.2 Li2O LiO O 0.1 temperature on the final equilibrium temperature, CEA2 Li2 Li2O2 calculations have been done for lithium at p 1 atm and 0.0 012345678910111213 temperature 1200 K to 2000 K. Results shown the only mol Li / mol O effect of injecting lithium into a hot stream of nitrogen is to 2 lower the mixture temperature. Thus hereinafter we Fig. 8. Li/O2 combustion products – (1 atm; 2200 K). investigated lithium-air combustion using only oxygen as oxidizer. 0.16 Both hydrogen and lithium (freed from the LiH surface) Li2O react exothermically with the hot air stream. To highlight 0.14 the importance of lithium combustion, we compared the 0.12 LiO 0.10 combustion of lithium and of hydrogen in oxygen O assuming both fuels injected at an initial temperature from 0.08 1800 K to 2600 K in an oxygen stream at 1400 K, and at 0.06 Molar fraction pressure from 0.5 to 5 atm (that is the same condition 0.04 0.02 expected in the scramjet combustion chamber). Results are Li2O2 Li2 shown in figures 6-9. 0.00 012345678910111213 mol Li / mol O2

3400 Fig. 9. Li/O2 combustion products – detail.

3350

3300 These figures show the light and extremely reactive

3250 lithium atoms freed from the LiH surface burning in T = 1800 K oxygen and producing a mixture of oxide, peroxide and 3200 T = 2200 K T = 2600 K super oxide, respectively: 3150

3100 Li + O2 Æ Li2O + Li2O2 + LiO2 + LiO 3050 Combustion Temperature, K 3000 0 2 4 6 8 10 12 14 16 All that has some interesting similarities with the mixture produced (at chemical equilibrium) by the reaction mol Li / mol O2 between hydrogen and oxygen, that is: Fig. 6. Li/oxygen combustion temperatures (1 atm). H2 + O2 Æ H2O + H2O2 + HO2 + OH

3400 where each of the hydrogen oxides has a homologous in 3200 the lithium oxide mixture; this similarities suggests an analogy may exist also in the kinetics of the two fuels. 3000 T = 1800 K Note that the CEA2 database does not include, at the T = 2200 K 2800 T = 2600 K moment, lithium superoxide. While this significantly limits assessing Li/O2 chemical kinetics (see later), it is not 2600 significant when we considering products equilibrium

Combustion Temperature, K composition. 2400 012345678910111213 4. Products Analysis and Reaction Rates mol H2 / mol O2

Fig. 7. H2/O2 Combustion temperatures (1 atm). As shown by results obtained above, the main reaction products of LiH/O2 and Li/O2 reactions are respectively As shown in figures 6 and 7, Li combustion lithium hydroxide (LiOH) and lithium oxide (Li2O). While temperatures are slightly higher and with a broader peak solid Li2O is very stable in a wide range of temperature than those obtained burning hydrogen at the same initial (melting point: 1800 K, when decomposes); LiOH(s) conditions. Figures 8 and 9 show the Li-oxygen decomposes very close to its melting point (1200 K), that is, combustion products equilibrium composition. a temperature lower than the ones considered. Finally, Li2O

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decomposes at the boiling point, yielding oxygen, liquid Table 3. Thermodynamic comparison between LiO/Li and H2/O2 lithium and a little LiO.17) reactions. Few data are available about Li/O2 reactions at high temperature, and about gaseous Li2O properties; most are related to research on termolecular reactions of alkali 18,19) metals atoms with O2 and OH. In particular Plane, investigating the hydrogen concentration in the afterburning region of a Li flame, has shown that the termolecular reaction:

Li + O2 + N2 → LiO2 + N2 plays an important role in lithium/oxygen combustion. In As shown, the Li - LiO reaction is more exothermic than fact, demonstrating experimentally the termolecular H2 – O2. One would therefore assume that, in establishing behaviour, he has obtained a data fit for the absolute rate equilibrium, the former reaction would be preferred over constant in the temperature range 276 – 1100 K; then he the latter. Furthermore, the change in Gibbs free energy is extrapolated the rate to higher flame temperatures (1500 – of the same order for both reactions, with the H2 – O2 2500 K) by means of a fit to the Troe formalism: reaction slightly favourite with respect to Li - LiO reaction at higher temperatures (when Li2O decomposes), indicating 18 6 2 −2.03 −1704 []J / mol / RT (1) k = 2.25 x 10⎣⎦⎡⎤cm / mol s () T / 298 e that both forward reactions are carried to completion with comparable rates.

In the light of these last considerations (and due also to Reaction (1), involves the association of two neutral the lack of other reaction rate constants in the open fragments to form LiO2, which is known to exist as an ion - literature) it appears reasonable to assume equation (1) as pair Li+ O ; however, despite the strength of the Li-O 2 reaction rate for the lithium-oxygen combustion under bond, this ionic pair is highly unstable, the reason of its examination. instability being exactly its ionic nature. In fact, the Notice that Li reacts also with radicals produced by the covalent bond between the two oxygen atoms of the H /O combustion (OH, O H); despite the very high peroxide ion is relatively weak; bringing a positive ion 2 2 2 reaction enthalpies, these reactions may be neglected, as close to the peroxide ion, peroxide electrons will be the radical concentration is small or the reaction gradually strongly attracted towards the positive ion. more constrained, at increasing temperatures, by This compound is then well on the way to forming a thermodynamics (just as in the case of the Li/OH reaction). simple oxide ion if the covalent bond breaks off, and works best if the positive ion is small and highly charged, that is, if it has a high charge density. Even though it is only singly 5. Physical Model + charged, Li , at the top of the Group I in the periodic system, is so small and therefore has such a high charge Based on thermochemical properties information density that any peroxide ion near it breaks up yielding an summarized above and on the flow conditions into the oxide and oxygen. Past Group I, sodium and potassium combustion chamber, we list below the LiH modeling assumptions, each justified by mean of an order of ions (f.i.) are bigger and they don't have a similar effect. 9) The highly reactive LiO, in turn, reacts in a lithium rich magnitude analysis. Accordingly, LiH grain “combustion” will be modeled and described by the environment forming Li2O: following steps:

Li + LiO → Li2O - The LiH grain surface liquefies due to the thermal All these association/dissociation reactions involving fluxes produced by combustion in the gas phase; during light alkali metal atoms have characteristic times of the liquefaction we assume the solid-liquid interface (or same order of magnitude; at high temperatures (1500 K < “wall”) to be always at the LiH liquefaction T < 2500 K; that is the same range expected in the scramjet temperature ( Tliq = 950 K at 1 atmosphere ). combustion chamber) they can be faster than hydrogen/oxygen reaction .19 This circumstance, suggested - Thanks to the high thermal diffusivity of liquid LiH, in the preceding section by the similarities between the the LiH droplets formed at the wall, and heated by the equilibrium composition of Li/O and H /O combustion thermal flux, reach the LiH decomposition temperature 2 2 2 = 1100 K). LiH decomposes “fast” (i.e., compared products, is confirmed from thermodynamics. In fact, the (Tdec with the combustor convective time and before reacting following Table 3 reports reaction enthalpy and Gibbs free with oxygen), its decomposition time being of order 10-6 energy we calculated using the CEA2 polynomial s;10,11) in fact, the LiH reaction rate with oxygen is coefficients, in the temperature range 800 – 3600 K. lower than its decomposition rate (at least by three orders of magnitude) and the oxygen concentration near the surface is too small to allow significant oxidation.19

Pa_52 D. SIMONE and C. BRUNO : Modeling LiH Combustion in Solid Fuelled Scramjet Engine

As stated previously, LiH does not react with air with the gaseous fuel pyrolyzed and released by the solid nitrogen in this temperature range. grain surface. Accounting for specific differences, it is thus reasonable to assume one among the well known models - Following decomposition, gaseous hydrogen leaves present in the open literature to predict surface regression. the droplet surface bubbling vigorously and contributing The most plausible (and used) model of hybrid to its breakup into smaller liquid Li droplets. 11,12) combustion was developed by Marxman and Gilbert in Hydrogen diffuses through the boundary layer, mixes 1963.20) In this model the grain regression rate r& is with air oxygen driven by the highly turbulent stream, governed by the local thermal flux at the surface: burns and releases heat. Some Li particles, possibly q& ρρ& == ρ =w (2) trapped inside hydrogen bubbles leaving the surface, s rv gg () vw H burn with oxygen and increase the heat released by v hydrogen combustion. where ρg is the density and νg the velocity of the gaseous 2 fuel leaving the surface; q&w (J/m s) is the heat flux at - Liquid Li droplets are sheared and dragged away from the wall while Hv (J/kg) is, in general, the total heat the surface and into the turbulent boundary layer. required to ‘gasify’ the solid fuel. In the case of a LiH grain, the surface temperature is that of the phase change - The light Li droplets are thus mixed with air and (LiH solid to liquid; 950 K), and H accounts for the heat hydrogen combustion products present in the boundary v necessary to vaporize and decompose LiH (Hv ~ 11 layer; in the hot core flow they vaporize, yielding highly MJ/kg). reactive gaseous Li; carried by the turbulent stream, Li The impact of fuel injection from the surface burns with air oxygen. When allowed by the local (“blowing”) on the convective heat flux, was assessed oxygen concentration, Li combustion occurs in accounting for its influence on the local BL velocity profile. proximity of the droplet surface, enhancing liquid Li The first theoretical analysis of blowing was made in 1942 vaporization. by H. Schlichting;21 successively, experimental as well as theoretical investigation have been performed by J. C. - Where combustion is well developed, the water Rotta,21 while the injection of a gas through a porous wall vapour concentration is so high that it can react with the into a compressible flow, up to Mach 3.6, was investigated liquid LiH surface; however the LiOH produced in this by L. C. Squire, showing that Rotta’s assumption were still way decomposes at these temperatures, yielding liquid valid and leading to satisfactory results. Using Rotta’s Li and OH. empirical formulation, it is possible to show that 9) at ‘high’ temperature and flow velocity (1450 K and 1400 m/s, To assess conservatively the effect of heat fluxes on the typical of the case under examination) and for regression surface, LiH liquefaction rate can be roughly estimated by rates of order 1 mm/s or less, the impact of blowing on neglecting the effect of combustion heat transfer, and wall velocity profiles and heat fluxes is negligible. This accounting only for the convective heat fluxes and shear assumption however does not account for the cooling stresses due to the air stream entering the chamber, effect due to the gas injection temperature; furthermore, assuming also that the heat absorbed locally by the Rotta’s model is strictly valid for a flat plate, and may not interface is the sum of the latent heat of liquefaction and be appropriate in a flameholder recirculation zone or in the heat required to increase the liquid LiH temperature regions with shock-boundary layer interaction. In these from 950 K to 1100 K (ΔH = 875 kJ/kg). Since the th -6 2 regions, the blowing effect will be investigated analyzing thermal diffusivity of liquid Li is D ≈ 10 m/s, the simulation results. characteristic heating time of a 1μm-deep liquid layer is -6 about 10 s; thus we can assume the liquefaction and 6. Numerical Simulations heating processes to happen in a single step, with a total local heat required of about 3400 kJ/kg. For instance, for a 2 In simulating combustion in a LiH fuelled SFSCRJ, we thermal flux qw ≈ 1 MW/m ,the local flowrate is mv ≈ 0.6 have investigated geometrical configurations and “flight” 3 -7 3 mm /s (the liquid LiH density ρl = 5 x 10 kg/mm ), conditions similar to those in Ref. 22; in particular we have corresponding to a local regression rate about 0.6 mm/s. selected the following combustor inlet conditions: -3 As the convective time is of order 10 s, the thickness of the liquid layer formed during one millisecond on the Table 4. Inlet conditions. surface is h ≈ 0.6μm. Notice that the surface regression l Static Total Flow rate is slightly lower than typical regression rates of solid Inlet Static Pressure Pressure velocity fuels. However in this “conservative” analysis the heat flux Mach Temperature K contribution due to gas phase reactions was neglected; in atm atm m/s reality this contribution will enhance strongly the 2 1550 1 7.8 1490 combustion performance by increasing the regression rate and thus the amount of gaseous fuel produced. The geometries considered in this analysis (hereinafter To complete the grain “combustion” model, A solid referred as “cylindrical” and “dump combustor”, fuelled scramjet has many similarities with hybrid rockets: respectively) are shown in Fig. 10. the oxidizer diffuses into the boundary layer and reacts

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convective time. The coupling between chemical kinetics and turbulence is modeled using the Eddy Dissipation Concept (EDC) model. 26) Thermodynamic properties have been calculated using the CEA2 database; in particular, Cp of individual species was calculated by fitting CEA2 data with 3rd order polynomials from 300 K to 6000 K, and successively implemented in the code. To model blowing, mass, momentum and energy sources were imposed at the first cell above the wall (assumed

impermeable and adiabatic). These source terms, SΦ , Fig. 10. Cylindrical (a; Dr=1) and Dump1 (b; Dr=1.2) combustors. appear in the generic steady state transport equation (4)

Similarly to Ref. 22 and 23, the LiH grain is located ⎡⎤ (4) div⎣⎦ρφVS− Γ=φ grad φ φ along the upper surface of the 2-D half-section, with an inlet height of 5 cm; the LiH grain, 60 cm long, starts 5 cm from the inlet entrance and ends at 40 cm from the where the first and second left-hand side term are combustor exit. These last 40 cm are assumed adiabatic. convection and diffusion, respectively, φ stands for the Γ The dump ratio Dr is defined as: transported variable and φ the appropriate diffusivity. These sources are directly linked to equations (2). Using Dr = Rc/Ri (3) (2) we define the gas mass flow rate as a function of the heat flux to the surface. The all-important heat flux is where Rc is the combustor internal radius and Ri is the inlet calculated as a function of the solution for the gas phase internal radius. A control line, (half radius line) located at field (velocity, density, pressure and temperature) above Rc/2, will be used to plot pressure and temperature along the surface. To accomplish this task, we have used in the the combustor. The dump “height” is Rc – Ri. UDFs the standard wall function model to describe the The Dump1 combustor differs from the cylindrical one for thermal boundary layer. the presence of a sudden expansion with dump height 1 cm. 7. Results The third dump configuration simulated (Dump05), differs from Dump1 only in the dump height (0.5 cm). 7.1. Cylindrical configuration (Dr =1) Simulations were carried on using the Fluent™ 6.2.16. code, FANS and an axisymmetric domain The numerical Figure 11 shows the static temperature contours of both technique is a finite volume approach with quadrilateral reacting and non-reacting cases. control volumes and structured Cartesian mesh. Even though blowing may lead to intrinsic instabilities,24) a steady state solution was sought using a coupled, implicit, second order upwind scheme. Turbulence was modeled using a standard k-ε model. 22-26) The boundary conditions at the interface between regressing grain and gas required detailed considerations and are presented in the following section. To simulate gas phase combustion a 6-species simplified mechanism was adopted involving the following reactions:

LiH decomposition: Fig. 11. Contours of static temperature (reacting and non reacting case). LiH → Li + ½ H2

One-step reaction for hydrogen combustion: An intense flame is present over the fuel grain, growing along the combustor. Due to gas phase combustion, the H2 + ½ O2 → H2O surface heat flux is up to three times that due only to convection from hot air stream entering the combustor (in and one-step reaction for Li oxidation: the non reacting case). The surface regresses at a rate comparable to that 22 2Li + ½ O2 → Li2O calculated by Jarymowycz and Kuo , (see Fig. 12) The total LiH mass flow rate injected into the chamber This mechanism does not account for backward for the cylinder geometry is 0.065 kg/s; that of inlet air is reactions, since their characteristic times are larger than 2.77 kg/s; thus this scramjet combustor is working at an

Pa_54 D. SIMONE and C. BRUNO : Modeling LiH Combustion in Solid Fuelled Scramjet Engine

air-to-fuel ratio A/F = 42.2. Assuming Mach 7 flight conditions as in Ref. 22, the Isp is 11,170 m/s and the 2900 specific thrust 264 m/s; these values are slightly lower than those calculated in Ref. 26 at the same A/F by means 2700 Cylin. 2500 of an ideal SCRJ model. Dump05 The temperature reached along the combustor peaks at Dump1 Tmax, [K] 2300 2950 K near the grain end (see Fig. 14). The sharp temperature increase for x > 65 (the final part of the grain) 2100 is connected to the end of the cooling effect due to the 1900 colder (950 K) LiH decomposition gases injected in the 5 15 25 35 45 55 65 75 85 95 reacting boundary layer. x - coordinate, [cm]

7.2 Dump combustor (Dump05, D = 1.1) Fig. 13. Comparison among maximum temperatures at each x r station.

Also in this case an intense flame is present over the fuel This effect may be explained: the larger step height (1 grain, growing from the recirculation zone near the sudden cm) allows more intense expansion and a larger chamber area increase up to the exit section. The grain surface volume, lowering air temperatures more than the Dump05 decomposes and regresses at roughly the same rate of that configuration. This behavior is confirmed by comparing calculated by Ben-Harosh and Gany,23) see Fig.12. the engine ideal performance summarized in Table 6. The LiH and air mass flow rates entering the combustor are 0.075 kg/s and 2.77 kg/s, respectively Table 5. Performance comparison. (A/F =37.05). Assuming conditions in Ref. 22, the SFSCRJ Specifc Thrust Isp Dr Isp is 9,620 m/s and the specific thrust 260 m/s; these [m/s] [m/s] values are again slightly lower than in Ref. 1 with the 1 264 11170 ideal SCRJ model. 1.1 260 9630 1.2 245 8160 7.3 Configuration Dump1 ( Dr = 1.2) and comparisons 8. Conclusions As in the case of Dr = 1. and 1.1, a flame develops along the combustor. The heat transfer is comparable to that for Supersonic combustion between solid LiH and air has the cylindrical geometry, but at least 1 MW/m2 lower than been investigated with the goal of predicting the in the dump05. As a consequence also regression rate performance of LiH at conditions similar to those expected (Fig.12) and the maximum temperature at each x station in a solid-fuelled scramjet. A preliminary thermochemical (Fig.13) are lower than those of the Dump05. analysis has identified the main species and reactions involved in the process, in particular, the presence of large amounts of hydrogen and Li produced by the thermal 1.2 decomposition of LiH. Result suggest that, at sufficiently 1 high temperature, the species energetically most 0.8 important, besides hydrogen, is liquid Li when reacting Cylin. with air. 0.6 Dump05 Dump1 To overcome the lack of data concerning Li/air 0.4 combustion, a parametric analysis has been carried on to 0.2 predict chemical equilibria. Results show that at Regression rate, [mm/s] rate, Regression

0 temperature higher than 1100 K Li does not react with air 5 15 25 35 45 55 65 nitrogen; it produces mainly gaseous Li2O, showing many x - coordinate, [cm] similarities, in terms of equilibrium composition, with H2/O2 oxidation. A second thermochemical analysis, has Fig. 12. Comparison among regression rates. compared the reactions potentially involved in Li combustion, concluding that as a first approximation, the reaction scheme can be simplified assuming one-step global reactions. Furthermore, these reaction rates may be plausibly described as proposed by Plane et Rajasekhar for the reaction forming Li superoxide. The physical model describing fuel blowing and decomposing from the grain surface has been developed by means of an order of magnitude analysis, showing that almost all liquid Li droplets produced by decomposing LiH (and dragged away by the turbulent stream), vaporize and burn before exiting the combustor, contributing in a significant manner to heating and performance. The model

Pa_55 Trans. JSASS Aerospace Tech. Japan Vol. 8, No. ists27 (2010)

for fuel blowing in the air stream from the decomposing Propellants for Hypergolic Applications, Swift Enterprises, LiH grain was implemented in the CFD code as a nonlinear Ltd., West Lafayette, Indiana, U.S.A. 9) Simone, D.: Analysis of LiH Combustion in Solid Fuelled boundary condition at the interface between the liquid Scramjet Engine, Ph.D. dissertation, Department of Mechanics surface and the reacting gas. Numerically, that translates to and Aeronautics, University of Rome “La Sapienza”, Rome, formulating mass, momentum, energy and species sources Italy, February 2008. located near the surface. This model predicts LiH 10) Mayer, S. W. and Schieler, L.: Computed Activation Energies regression rates that are comparable with those obtained by and Rate Constants for Forward and Reverse Transfers of Jarymowycz et al. and Ben-Arosh et al.22,23) Hydrogen Atoms, The Journal of Physical Chemistry, 72 No. 1, (1968). Despite the limitations due to the standard k-ε model, 11) Mayer, S. W., Schieler, L. and Johnston, H.: Computed and to the assumption made about the Li/O2 reaction rate, High-Temperature Rate Constant for Hidrogen-Atom Tranfers results are still intriguing. An intense flame zone is Involving Light Atoms”, The Journal of Chemical Physics, 45 predicted to be present over the decomposing surface and No. 1, July (1966). downstream of the grain in the cylindrical configuration; 12) Jerry, B. and Modisette, L.: Preliminary Investigation of Lithium Hydride as High-temperature Internal Coolant, NACA the flame does not extinguish, and high temperatures (of RM L57B12a, Washington, 1957. order 2900 K) are obtainable. Introducing a sudden cross 13) Jerry, B. and Modisette, L., “Investigation of Lithium Hydride section enlargement (a ‘dump’) downstream of the inlet and Magnesium as High-temperature Internal Coolants with section, mixing in the combustor is enhanced, increasing Several Skin Materials”, NACA RM L58B17, Washington, the heat released to the core flow. Ideal specific impulse 1958. 14) Davison, H. W.: Compilation of Thermophysical Properties of and thrust density predicted at a flight Mach = 7 are also Liquid Lithium, NASA Technical Note, NASA TN D-4650, interesting, being 10,000 m/s and 200-300 m/s, July 1968. respectively. However, an excessive dump ratio decreases 15) Dube, D. A. and Kazimi, M. S.: Analysis of design Strategies the core flow temperature (due to expansion waves) and for Mitigating the Consequences of Lithium Fire Within increases the combustor volume, while lowering combustor Containment of Controlled Thermonuclear Reactors”, Department of Nuclear Engineering, Massachusetts Institute of performance. Technology report MITNE-219, July 1978. To conclude from this preliminary investigation, LiH 16) Gil, T. K. and Kazimi, M. S.: The Kinetics of Lithium Reaction seems a good candidate for solid fuelled scramjet With Oxygen-Nitrogen Mixtures, Plasma Fusion Center and the applications, behaving as an high energy density bi-fuel Department of Nuclear Engineering, Massachusetts Institute of system but also as a safe and compact hydrogen carrier. Technology report PFC/RR-86-1, January 1986.

Notice that in the light of recent studies performed about 17) Hildenbrand, D. L., Hall, W. F. and Potter, N. D.: Thermodynamics of Vaporization of Lithium Oxide, Boric the use of simple and complex metal hydrides as hydrogen Oxide, and Lithium Metaborate, The Journal of Chemical storage systems for on-board applications, researchers have Physics, 39 No. 2, July (1963), pp. 296-301. focused the attention on the possibility of decreasing their 18) Patrick, R. and Golden, D. M.: Termolecular Reaction of Alkali decomposition temperature by reacting them with light Metal Atoms with O2 and OH, International Journal of elements or other hydrides. This feature, if confirmed, will Chemical Kinetics, 16 (1984), pp. 1567-1574. 19) Plane, J. M. C. and Rajasekhar, B.: A Study of the Reaction Li extend the operational range of LiH as fuel at ‘low’ + O2+ M (M = N2, He) over the Temperature Range 267 – temperatures (i.e., low with respect to those here 1100 K by Time Resolved Laser-Induced Fluorescence of Li 2 2 considered) enhancing in the same time its performance in (2 PJ -2 S1/2), J. Phys. Chem., 92 (1988), pp. 3884-3890. a SCRJ combustion chamber. 20) Carmicino, C.: Alcuni Aspetti della Balistica Interna di un Endoreattore a Propellenti Ibridi e del Comportamento di Ugelli a Spina troncata, Tesi di Dottorato di Ricerca in References Ingegneria Aerospaziale, XV Ciclo, Università di Napoli 1) Simone, D. and Bruno, C.: LiH as Fuel for Aerospace Federico II, 2002. Propulsion, Paper ISTS-a-38, 25th ISTS Conference, 21) Schlichting, H.: Boundary-layer Theory, McGraw-Hill, 1979. Kanazawa, Japan, June 3-8, 2007. 22) Jarymovycz, T. A., Yang, V. and Kuo, K. K.: Numerical study 2) Ju, Y. and Austin, J.: AIAA - The Year in Review, Aerospace of Solid-Fuel Combustion Under Supersonic Crossflows, America, p. 55, December 2006. Journal of Propulsion and Power, 8 No. 2,(1992), pp. 346-353. 3) Welch, F. H.: Lithium Hydride Properties, General Electric 23) Ben-Arosh, R., Natan, B., Spiegler, E. and Gany, A.: Fuel-Air Aircraft Nuclear Propulsion Department, DC 61-3-73, March Mixing In Solid Fuel Scramjet Combustor, International 14, 1961. Journal of Turbo and Jet Engines, 15 (1998), pp. 223-234. 4) Holley, C. E. Jr., Challenger, G. E. and Pavone, D.: The 24) Fournier, C., Michard, M. and Bataille, F.: Numerical preparation of Pure Lithium hydride, LA-1705, Los Alamos Simulations of a Confined Channel Flow Driven by Scientific Laboratory, New Mexico, 1955. Non-Isothermal Wall Injection, Progress in Computational 5) Brinza, V. N., Bavaitsev, I. V. and Papaev, S. T.: Investigation Fluid Dynamics, 6 Nos 1/2/3, (2006). of the Combustion Rate of Aerosuspensions of Lithium 25) Ben-Arosh, R., Natan, B., Spiegler, E. and Gany, A.: Hydride Powder, Journal of Combustion, Explosion and Shock Theoretical study of a Solid Fuel Scramjet Combustor, Acta Waves, 15 No. 1, (1979), pp. 100–101. Astronautica, 45 No. 3, (1999), pp. 155-166. 6) Kawano, H., Zhu, Y. and Tanaka, A.: Thermal desorption of 26) Ben-Yakar, A., Natan, B. and Gany, A.: Investigation of a Solid H2, H-and Electron by Temperature-Programmed Heating of Scramjet Combustor, Journal of Propulsion and Power, 14 No. Saline Hydrides in Vaccum,Thermochimica Acta, 344 (2000), 4, (1998), pp. 447-455. pp. 119-125. 27) Coen-Zur, A. and Natan, B.: Experimental Investigation of a 7) Clifton, D. G. and Sitney, L. R.: Theoretical Specific Impulses Supersonic Combustion Solid Fuel Ramjet, Journal of of Lithium-based Propellant Systems in Nuclear and Chemical Propulsion and Power, 14 No. 6, (1998), pp. 880-889. Rockets, LA-2276, Los Alamos Scientific Laboratory, New 28) NIST Chemistry WebBook http://webbook.nist.gov/chemistry/ Mexico, 1959. 8) Purpoint, T. L. and Rousek, J. J.: Novel Organometallic

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