Propulsive characteristics of metal fuel-rich pyrotechnics in hydro-reactive motors

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Propulsive characteristics of metal fuel-rich pyrotechnics in hydro-reactive motors

Hojat Ghassemi ∗, Hamidreza Farshi Fasih

School of Mechanical Engineering, Department of Aerospace Engineering, Iran University of Science and Technology, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 July 2011Received in revised form 2 July 2012Accepted 25 August 2012Available online xxxx

Keywords:Hydro-reactive propulsionMetal fuelsPropulsive characteristicsPyrotechnic compoundCombustion products

In this paper, the propulsive characteristics of metal fuels in a hydro-combustion chamber areinvestigated in a thermodynamic approach. Using chemical equilibrium calculations, the thermo-chemistry of common metal fuels and water is studied and focused on magnesium. Next, the combustiontemperatures and characteristic velocities of mixtures of magnesium and some important solid oxidizersare investigated. For the purpose of hydro-reactive propulsion, where it is necessary to use the water asthe main oxidizer, the hydro-reaction of some fuel-rich mixtures of magnesium and sodium nitrate isstudied. For such compounds, the maximum combustion temperature is estimated to be about 3100 K atdifferent mass fractions of water. More fuel-rich mixtures offer higher characteristic velocity. It reachesabout 1700 m/s for the compound with maximum magnesium value content. The characteristic velocityand combustion temperature decrease for high values of water mass fraction, while the specific impulseincreases with water monotonically beyond 500 s. The analysis of hydro-reaction products shows thatmagnesium oxide, hydrogen, and steam are the main species formed. The magnesium oxide presents inits condensed forms. However, for a high amount of water, the main product is steam.

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1. Introduction

Metal fuels have high volumetric and gravimetric combustionenthalpies and high volumetric energy release. The high volumetricand gravimetric combustion enthalpies indicate potential useful-ness of metals as fuels in energetic materials such as propellants,explosives, incendiaries, and pyrotechnics. For example, aluminum,magnesium, and boron are used in the composition of commonsolid propellants as a part of the fuel. In such applications, metalfuels in the form of powder are blended with common oxidizerswhich also are in the form of powder.

The combustion of metal fuels with water and other oxidiz-ers can be used in explosive and propulsion systems to produceexothermic reactions. The metal fuels, especially aluminum, areused to enhance the fuel in ramjets. In this case, the oxidizercomes from ambient air. Also, combustion of aluminum and mag-nesium in gaseous carbon dioxide is considered for various rocketengine applications such as CO2/metal propulsion on Mars [12].The combination of aluminum and water has been theoreticallyanalyzed to assess its performance potential for space propulsion[11].

It is possible to use the water as an accessible oxidizer in anaqueous environment. Therefore, metal fuel–water reactions can be

* Corresponding author at: Iran University Science and Technology (IUST), Nar-mak, 1684613114 Tehran, Iran. Tel.: +98 21 77491228; fax: +98 21 77240488.

E-mail addresses: [email protected] (H. Ghassemi),[email protected] (H. Farshi Fasih).

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used to produce propulsion as a hydro-reactive system. To improvethe quality of the burning process, some extra oxidizers can beintroduced to the metal powder to form a fuel-rich compound.

Using lithium and sodium to lower the boiling point in gas tur-bines of submarines was investigated more than 60 years ago [10].In this case, the reaction of liquid metals and water has been ex-plored for the purpose of gas generation and using the producedgas as working fluid in a gas turbine. Some specific applications ofmetal fuels indicate their potential in propulsion systems.

The effects of different phases of water as an oxidizer on theaqueous combustion characteristics of aluminum particulate mix-tures were studied in well-characterized environments [9]. It isshown that the maximum temperature of water–Al combustion islower than air–Al combustion (reaching 3000 K). Even this temper-ature guarantees the ability of such a system to generate excessivewater vapor by adding extra liquid water. This vapor can be usedto produce thrust via a nozzle or power by a proper gas turbine.

The combustion of magnesium and boron has been experimen-tally studied in a hot vapor atmosphere [15]. The results show thatstable exothermic oxidation is achieved and the combustion tem-perature reaches to 1370 K and 1070 K for magnesium and boron,respectively. The study also reveals that hydrogen is produced be-sides of magnesium oxide and water vapor.

An experimental investigation has been conducted to determinethe relative propulsive performance and viability of a novel solidpropellant comprised of aluminum and ice (ALICE) using funda-mental techniques [8]. This form of water and aluminum looks likea solid propellant in which the fuel and oxidizer are mixed to-gether. Burning rates, slag accumulation, thrust, and pressure have

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Table 1Thermo-physical specifications of metal fuels [1,5,14,15,17,19].

Metalfuel

Density(g/cm3)

Combustionheat (withoxygen)(kJ/g)

Combustionheat (withoxygen)(kJ/cm3)

Combustionheat (withwater)(kJ/g)

Combustionheat (withwater)(kJ/cm3)

Meltingpoint ofmetal (K)

Boilingpoint ofmetal (K)

Meltingpoint ofmetaloxide (K)

Boilingpoint ofmetaloxide (K)

Al 2.7 63 170 18 49 932 2740 2318 3800Mg 1.75 24 42 15 26 923 1363 3075 3350B 2.4 58 139 25 60 2300 3950 723 2550Li 0.534 20 11 24 13 459 1615 1700 3200Na 0.968 18 17 21 20 371 1156 1405 2223

been experimentally obtained. It is found that ALICE propellantssuccessfully ignited and fired in a lab-scale rocket motor. Also, thecombustion efficiency was around 70%, while the specific impulseefficiency was 64%.

The potential of the aluminum–water and magnesium–waterreactions has been investigated as a propulsion system for under-water thrusters [13]. The effects of pressure and oxidizer fuel ratioon the specific impulse in such a system have been studied. Theexperiments revealed the slug accumulation in aluminum–watercombustion is larger than magnesium–water combustion. Also, thecombustion efficiency depends on the combustor length.

Preliminary experimental research on the performance ofhydro-reactive Al metal fuel and KClO4 has been conducted [4].Considering the chemical reaction process, the thermodynamiccharacteristics of hydro-reactive fuel-rich propellant were analyzed.The maximum temperature and characteristic velocity were ob-tained at water to fuel ratio equal to 1. Also, the specific impulsewas enhanced by increasing the amount of water in the wholerange of water to fuel ratio.

Experimental systems of hydro-reactive motors with magne-sium metal fuel have been introduced [2,3]. The experimental re-sults indicate the average content of metal fuel can combust stablyafter adding water. The combustion efficiency can be improved ef-fectively by changing the water fuel ratio and increasing the lengthof combustion chamber.

A hydro-reactive Mg/NaNO3 system has been experimentally in-vestigated [6]. The fuel-rich propellant was presented in a lab-scalehydro-reactive motor with ability of water flow rate control. Theresults show the hydro-reactive performance is improved by in-creasing the amount of water.

In spite of improvement in dominating the stated phenomena,few comprehensive thermodynamic studies are reported. Trying tounderstand the combustion of Mg/H2O systems leads to studyingthe thermo-chemistry of reaction between metal fuels and wa-ter. In this paper, the propulsive characteristics of metal fuels in ahydro-combustion chamber are investigated. The burning of metalswith water is not a sustainable process. Generally, to achieve stablecombustion, some mineral oxidizers are introduced to the metalin the form of a powder. The exothermic dissociation reactionsof the oxidizer provide an adequate condition for self-sustainablecombustion of metal in the water. Therefore, this combustion sys-tem is a ternary mixture of metal fuel, mineral oxidizer, and waterwhose reaction products result in propulsion. The main approach isto evaluate the thermodynamics of the combustion products. Thecombustion products and other specifications are calculated usingCEA code [7]. This study is presented in three main parts. First,the thermo-chemistry of common metal fuels reacting with oxygenand water is considered. A comparison of results is presented andmagnesium is selected for further studies. In the second part, thecombustion temperature and characteristic velocity of typical py-rotechnic compounds of magnesium and mineral salts as commonoxidizers are studied. Among different compounds, the mixture ofMg and NaNO3 is selected to study the hydro-reaction in the thirdpart. The combustion temperature, characteristic velocity, and spe-

cific impulse of such mixtures are investigated for different amountof water. Finally, the product compositions of such a system in dif-ferent conditions are presented.

2. Metal fuels and their specifications

Metal fuels have high volumetric and gravimetric combustionenthalpies and high volumetric energy release due to the high heatof reaction with oxygen. Aluminum, magnesium, boron, lithium,and sodium are renowned metals with wide applications in thearea of combustion and propulsion. Some thermo-physical specifi-cations of these metal fuels at the atmospheric pressure are pre-sented in Table 1. Also, the reaction heats of oxygen-combustionand hydro-reaction of the fuels are included.

The combustion behavior of metals is influenced by physi-cal properties as well as thermo-chemical characteristics. Amongmetal fuels, Al has maximum density, followed in order by B, Mg,Na, and Li. In a thermo-chemical point of view, reacting to oxy-gen, Al has maximum heat release (per mass) followed by B, Mg,Li and Na. In reaction with water, B shows maximum heat release(per mass) followed by Li, Na, Al and Mg.

Boron has high melting and boiling temperatures compared toother metal fuels. However, the melting point of boron oxide isvery low. High melting and boiling temperatures of boron are notfavorable characteristics for a hydro-reaction, where the averagetemperature is normally low. However, boron has a high heat ofcombustion among other metal fuels. Therefore, it has wide appli-cations in ram-rocket solid fuels, where the main oxidizer is air[18]. Lithium and sodium have the least energy per unit of vol-ume. Also, the melting points of these metals are very low and donot participate in solid phase reactions.

According to above discussion, aluminum and magnesium arethe best choices as metal fuels for reacting with water. In spite ofappreciable differences in oxygen-combustion heats of aluminumand magnesium, the hydro-reaction heat values of these metals arevery close.

2.1. The combustion of metal fuels

In order to assess the combustion behavior of metal fuels, thethermo-chemistry of metal–oxygen combustion is investigated. Inthis analysis, the ambient and combustion chamber pressures areassumed to be 0.1 MPa and 2 MPa, respectively. Also, the initialtemperature of all reactants is assumed 300 K. This initial tempera-ture and ambient pressure are kept constant in all calculations. Themoderate pressure of 2 MPa is an adequate choice for chamberslike air breathing combustor with ram compression from ambientconditions.

The stoichiometric mixture ratio, φs , is defined as the stoichio-metric mass ratio of metal fuels (M) to oxygen (O). It is tabulatedin Table 2 for the mentioned metals, according to the followingcomplete combustion scheme

aM + bO2 → MaO2b (1)


H. Ghassemi, H. Farshi Fasih / Aerospace Science and Technology ••• (••••) •••–••• 3

Table 2The stoichiometric equivalence ratio of metal fuels and oxygen.

Metal fuel Al Mg Na Li B

φS 1.12 1.52 2.87 0.87 0.45

Fig. 1. The oxygen-combustion temperature of metal fuels versus equivalence ratio.

The equivalence ratio is defined as the ratio of actual to stoichio-metric fuel/oxidizer mass ratio, as follows

φ∗ = φ/φS (2)

To calculate combustion parameters, the NASA’s CEA equilibriumcode is used. Using this code the combustion temperature andmole fractions of product species are calculated for specific reac-tants as well as a given combustion pressure and initial tempera-ture. In fact, the chemistry of such a system is not in an equilib-rium state. However, the equilibrium calculations give informationwhich is adequate for the purpose of a propulsive performanceanalysis. The combustion temperatures of several metal fuels andoxygen versus equivalence ratio are shown in Fig. 1. Boron showsmaximum combustion temperature around its stoichiometric ratio.The combustion temperature of aluminum is constant for a widerange of ratios. This behavior is mainly due to a phase change pro-cess of liquid alumina to vapor. For each metal fuel, the maximumcombustion temperature is obtained for the stoichiometric mix-ture. Also, the combustion temperatures of Al and Mg are morethan other fuels in almost the entire range of mass ratios.

The characteristic velocity is the parameter that explains thederivation of energy from fuel and existing energy after combus-tion. This energy is introduced in the form of velocity. The charac-teristic velocity can be written as

C∗ = √RT /Γ (3)

where T is the combustion temperature and R is the gas constantdefined as the ratio of the universal gas constant to molecularmass. The symbol Γ is a function of the specific heats ratio, γ ,as follows

Γ = √γ (2/γ + 1)(γ +1)/2(γ −1) (4)

Fig. 2 depicts the variations of characteristic velocity in terms ofφ∗ . For highly fuel-rich mixtures, it was not possible to calculatethe molecular mass, and subsequently, the characteristic velocityof the product gas. For such mixtures, the calculation was not pos-sible because the condensed phase is dominant in the products.The calculation of the molecular mass of products in the gas phaseencounters with difficulty. However, it is taken into account for allshown cases. Due to the significant effect of molecular mass andspecific heats ratio of the product gas, the characteristic velocitydoes not behave like combustion temperature. This behavior arises

Fig. 2. The characteristic velocity of oxygen-combustion products versus equivalenceratio.

Table 3The stoichiometric equivalence ratio of metal fuels and water.

Metal fuel Al Mg Na Li B

φS 1 1.33 1.2 0.77 0.4

since the characteristic velocity, according to Eqs. (3) and (4), isa function of combustion temperature T , molecular mass M (em-bedded in the gas constant R), and specific heats ratio γ . M and γof the product gas vary with the equivalence ratio. Therefore, thecharacteristic velocity is a function of equivalence ratio directly anddoes not need to behave the same as the combustion temperature.Finally, in Fig. 2 it is clear that oxygen-combustion of magnesiumproduces and keeps the highest characteristic velocity over a broadrange of equivalence ratios.

2.2. The water-combustion of metal fuels

The metal fuel combustion with water as an oxidizer producesexothermic reactions with high combustion enthalpy and high heatrelease. The reactions proceeding are presented according to thefollowing scheme

aM + bH2O → bH2 + MaOb (5)

For the water-combustion study, the stoichiometric ratio is definedas the mass ratio of fuel (M) to water. The stoichiometric ratiosare shown in Table 3 for the mentioned metal fuels. Sodium doesnot follow the above scheme. The complete reaction of water andsodium leads to NaOH instead of Na2O.

The combustion temperature of metal fuels with water versusequivalence ratio is shown in Fig. 3. Over a wide range of equiva-lence ratios, the combustion temperatures of aluminum and mag-nesium are higher than others. However, for fuel-lean combustion,lithium shows a temperature as high as aluminum and magnesium.The general trends of the water combustion temperature variationsare in agreement with those are presented in [15] for magnesiumand boron. Also, the theoretical combustion temperature of alu-minum with water is compared to the results reported in [9]. Itshows that the value and trend of temperature variation are almostthe same. The comparison between Figs. 1 and 3 shows the water-combustion temperatures of metal fuels are much lower than theoxygen-combustion temperatures.

Fig. 4 presents the variation of characteristic velocity in termsof φ∗ . In contrast to combustion temperature, the maximum char-acteristic velocity of water-combustion is greater than that ofoxygen-combustion for Al and Mg. This, mainly, is due to lowermolecular mass of the products.



According to the explanations of Fig. 1 to Fig. 4, Al, Mg, and Lihave higher combustion temperatures and characteristic velocitiesthan other metals. For the purpose of propulsion, the characteristicvelocity of the working gas is a suitable criterion which containsall affecting parameters. Additionally, the main focus is on the ox-idizer (water)-rich mixtures. In this range, Al, Mg, and Li are goodcandidates to react with water. Due to low density, lithium doesnot attract much interest. Using Al/H2O systems for the purpose ofspace propulsion is studied by Ingenito and Bruno [11]. For this ap-plication, aluminum is preferred due to higher density relative tomagnesium. In competition between magnesium and aluminum,the former has lower melting and boiling temperatures that aresuitable for sustainable combustion. Therefore, it makes magne-sium more attractive as a fuel in metal–water combustion system.Additionally, the primary experiments have shown the slug accu-mulation in a magnesium–water reaction is less than that of analuminum–water system [13]. In the next two sections, special fo-cus is placed on the Mg/H2O system as a potential hydro-reactivepropulsion device.

Fig. 3. The water-combustion temperature of metal fuels versus equivalence ratio.

Fig. 4. The characteristic velocity of water-combustion products versus equivalenceratio.

3. Thermo-chemistry of Mg-oxidizers pyrotechnic systems

The burning of magnesium as a fuel needs a suitable sub-stance as an oxidizer. A blend of magnesium and some mineralsalts forms a pyrotechnic compound. Nitrates and perchloratesare common oxidizers in solid propellants. The specifications ofsuch salts are presented in Table 4. Density, oxygen content, andheat of formation have great effects on oxidizer selection crite-rion. Additionally, melting and boiling temperatures of the oxidizerplay an essential role in the burning mechanisms of pyrotechnics.Among these oxidizers, because of high boiling temperature andheat of formation, lithium nitrates (LiNO3) and lithium perchlo-rates (LiClO4) are rarely used in the pyrotechnic compounds.

The combustion thermo-chemistry of magnesium and impor-tant oxidizers is investigated. In this study, different mixtures ofthe metal fuel and oxidizer are considered. The stoichiometricequivalence ratio φS is defined as the mass ratio of Mg to the oxi-dizer. The stoichiometric equivalence ratio and corresponding com-bustion temperature of Mg and different oxidizers are presented inTable 5. A constant pressure of 20 bar is defined to calculate thecombustion temperature.

The combustion temperature of magnesium and the stated ox-idizers versus equivalence ratio is illustrated in Fig. 5. The maxi-mum temperature for all compounds is obtained for equivalenceratios slightly more than 1. The temperatures show similar trendsfor all compounds. In the fuel-lean region, the temperature ismonotonically increasing with φ∗ . In the fuel-rich region, it de-creases in almost a monotone manner. However, the curves showthere are some breaking points where the slope of the temperaturedecreases. It is believed that formation of condensed phases due tolower combustion temperature causes the breaking points. Thesepoints are indicated by ovals. The first breaks B1 occur around3000 K, which is near the melting point of magnesium oxide inTable 1. Below this temperature, MgO exists in a solid phase. Thebreaking points occur at different equivalence ratios for differentoxidizers. It is due to difference between the heats of formationthat are presented in Table 4. It is believed the second breakingpoints B2 are due to the boiling point of magnesium. Above thistemperature, magnesium is present in a vapor or gas phase. Theboiling temperature of Mg in Table 1 is about 1400 K at 0.1 MPa,while the second break temperature is about 1900 K at 2.0 MPapressure. Additionally, Fig. 5 shows the combustion temperaturefor high values of φ∗ is nearly constant for all compounds. Thisfact is better shown in Fig. 6, where the combustion temperatureis shown versus Mg/oxidizer mass ratio. Clearly, in the fuel-richregion, the combustion temperature decreases severely around amass ratio of three. For Mg/oxidizer mass ratios more than 3, all

Table 5The stoichiometric equivalence ratio and combustion temperature.

Oxidizers NaNO3 KNO3 KClO4 NO3NH4 ClO4NH4

φS 0.72 0.61 0.71 0.31 0.52Combustion

temperature (K)3752 3765 3971 3412 3675

Table 4Specification of mineral oxidizers [10,16,17,19].

Oxidizer Density (kg/m3) Oxygen content (wt %) Melting point (K) Boiling point (K) Heat of formation (kJ/g)

NaNO3 2.17 47.06 581 653 −4.78KNO3 2.109 39.56 607 673 −4.88LiNO3 2.38 58.02 528 1146 −7.06NH4NO3 1.73 19.98 443 483 −4.57NH4ClO4 1.95 34.04 Decomposition before melting −2.48KClO4 2.52 46.19 798 873 −3.95LiClO4 2.43 60.15 509 703 −4.17



Fig. 5. The combustion temperature of Mg/oxidizers versus equivalence ratio.

Fig. 6. The combustion temperature of Mg/oxidizers versus Mg to oxidizer massratio.

systems show similar trends and almost the same values for com-bustion temperatures. The reason belongs to presence of a largeamount of unburned liquid magnesium.

Fig. 7 shows the characteristic velocity of the combustion prod-ucts of magnesium and different oxidizers versus equivalence ratio.This figure indicates similar trends of characteristic velocity for alloxidizers. The maximum characteristic velocity is obtained withinthe range of 1.3 < φ∗ < 2.7. In the fuel-lean region, the character-istic velocity is monotonically increasing with φ∗ . Also, this figureshows the characteristic velocity for high values of φ∗ is nearlyconstant for all compounds. This fact is better shown in Fig. 8. Inthis figure the characteristic velocity is shown versus Mg/oxidizermass ratio. Clearly, in fuel-rich region, the characteristic velocitydecreases severely for the mass ratios less than 3. For Mg/oxidizermass ratios more than 3, all systems show similar variations andsame values for characteristic velocity. It means the product gasof such compounds act similarly to produce the thrust. The samecombustion temperatures shown in Fig. 6 cause the constant char-acteristic velocity. For two oxidizers KNO3 and KClO4, the charac-teristic velocity cannot be calculated for mass ratios more than 5.7.

According to Figs. 5 and 6, all five oxidizers can be used as com-panions with Mg to form a primary pyrotechnic compound. Ac-cording to Figs. 7 and 8, it is obvious that ammonium perchlorate(ClO4NH4) and ammonium nitrate (NO3NH4) are favorable choicesas an oxidizer. However, for high equivalence ratios or high massratios, there is no significant advantage for the oxidizers. Therefore,criteria other than energetic properties may be applied to choosethe oxidizer. These criteria are density, availability, easy and safeprocessing, and environmental side effects. Hereafter, sodium ni-trate (NaNO3) is selected as the oxidizer. Such a combination haspreviously been used in conventional pyrotechnic compounds.

Fig. 7. The characteristic velocity of combustion products of Mg/oxidizers versusequivalence ratio.

Fig. 8. The characteristic velocity of combustion products of Mg/oxidizers versus Mgto oxidizer mass ratio.

4. Water-combustion of magnesium and sodium nitratecompounds

Magnesium, sodium nitrate, and water form a ternary systemwhich can be used for the purpose of gas generation and propul-sion in a hydro-reactive system. In such a system, magnesium andwater play roles of the fuel and oxidizer, respectively. Adding someamount of a mineral salt like sodium nitrate provides easy ignitionand stable combustion. In the beginning of ignition, it vaporizeseasily and introduces chemically active species. These species reactwith fuel component and lead to primary combustion. Thermo-chemistry of the binary system of Mg and NaNO3 has been studiedin the previous section. The effect of adding water to this binarysystem is investigated in the following section. A general schemefor this system may be presented as follows

aMg + bNaNO3 + cH2O → dMgO + eNaNO2 + f H2 + gH2O (6)

Five different blends of magnesium and sodium nitrate are se-lected. The selected mixtures are fuel-rich to provide appreciableoxidizing role for the water. The mass fractions of the selectedcompounds are presented in Table 6, and they are also indicatedby numbers in Figs. 6 and 8. Each compound is examined with adifferent amount of water. The mass fraction of water to sum ofwater and solid fuel masses introduces the amount of water whichis added in the ternary hydro-reactive system. This mass fractionis represented as a fraction of mass flow rates, ξ = mWater/mTotal .Therefore, an increase in ξ means an increase in the water added.

The combustion temperature of the hydro-reactive system ver-sus ξ is shown in Fig. 9 for different compounds. The pressureof the combustion chamber is assumed to be 2 MPa. It reveals



Table 6The mass fractions of the selected compounds.

Compound 1 2 3 4 5

Mg 0.85 0.80 0.75 0.70 0.65NaNO3 0.15 0.20 0.25 0.30 0.35mMg/mNaNO3 5.66 4.00 3.00 2.33 1.85

Fig. 9. The hydro-combustion temperature of different compounds versus ξ .

that the maximum combustion temperature for all compounds isconstant and equal to 3105 K, which is around the melting pointof magnesium oxide. Also, it depicts by decreasing the amount ofmagnesium in compound, approaching to the stoichiometric mix-ture, the combustion temperature is remaining constant in broaderregion of ξ . For instance, the constant maximum temperature isobtained in the regions of 0.27 � ξ � 0.4 and 0.1 � ξ � 0.35 forcompound 1 and 3, respectively. The solid curve in this figure is forcompound 1 which has extra magnesium. The curve is representa-tive for such characteristics and contains four different stages. Thefirst stage is constant temperature for ξ < 0.15, where the amountof oxidizers including the primary oxidizer (NaNO3) and water isnot sufficient to produce enough heat. In the second stage the suf-ficient amount of water causes to enhance the combustion leadingto the third stage with the constant temperature. Introducing extrawater causes decreasing temperature and the production of addi-tional water vapor in the fourth stage.

The characteristic velocities of the mentioned systems versus ξ

are shown in Fig. 10. This figure shows an increase in the amountof magnesium in the compounds leads to an increase the maxi-mum characteristic velocity. For a constant percentage of water inthe range of ξ > 0.3, superior characteristic velocity is available fora higher ratio of fuel to oxidizer. Also, the characteristic velocity in-creases with water up to ξ ≈ 0.4 and then decreases. Additionally,all compounds have same characteristic velocities, about 1600 m/s,for ξ ≈ 0.25.

The effect of combustion pressure on the temperature and char-acteristic velocity is investigated. Fig. 11 shows the temperatureand characteristic velocity in the system of water for compound3 for different pressures. It shows the stated parameters have nosensitivity to the pressure.

The ratio of specific heats for different compounds versus ξ isillustrated in Fig. 12. The figure shows different trends for differ-ent compounds when ξ < 0.3. While in the range of ξ > 0.3, thespecific heats ratios of all compounds behave similarly and canbe approximated by a single value. However, for the temperatureand characteristic velocity, the composition has no effects on thetrends.

The specific impulse is major criterion for evaluating of rocketperformance in a propulsion system. For a hydro-reactive propul-

Fig. 10. The characteristic velocity of hydro-combustion products for different com-pounds.

Fig. 11. The combustion temperature and characteristic velocity of different chamberpressure.

Fig. 12. The ratio of specific heats of hydro-combustion products.

sion system, it can be defined as follows

I S = F/g mFuel (7)

where, F is thrust which is produced by working gas, and mFuel isthe mass flow rate of the solid fuel. In conventional rocket systemsthe specific impulse is defined in terms of the mass consumptionrate of propellant which contains fuel and oxidizer (mPropellant =mFuel + mOxidizer). In hydro-reactive propulsion, like air-breathingpropulsion, the oxidizer is supplied from outside of the system.Therefore, only the mass flow rate of fuel is used in the definitionof specific impulse. Actually, mFuel represents the mass flow rateof the compound that may contain solid fuel (Mg) and some solidoxidizer (NaNO3).



Fig. 13. The specific impulse versus ξ for different chamber pressure.

Fig. 14. The specific impulse versus ξ for different compounds.

The well known thrust equation for a rocket is F = P C At C f ,where PC and At are the combustion chamber pressure andthe nozzle throat area, respectively. The working gas is a hydro-reaction product of solid fuel and water. Its mass flow rate atsteady state is mTotal = PC At/C∗ . Using these two expressions andthe definition of ξ (ξ = mWater/mTotal), the specific impulse can bepresented in terms of ξ as follows

Is = C∗C f /g(1 − ξ) (8)

where, C f is a thrust coefficient which for an adapted nozzle canbe calculated as follows

C f = Γ

√2γ /(γ − 1)

[1 − (Pe/P C )γ −1/γ

](9)

where, Pe is the nozzle exit pressure which is assumed to be 1 bar.The thrust coefficient, C f , is a function of PC and the specific heatsratio γ . Therefore, the specific impulse of a hydro-reactive propul-sion system is a function of chamber pressure and ξ via C f and C∗ .As a typical example, the specific impulse of compound 3 is shownin Fig. 13 for different combustion chamber pressures. The specificimpulse strongly increases as the amount of water is increased.However, for high values of ξ , the gas temperature decreases, theextra water would not evaporate, and more gas would not be pro-duced. Consequently, the specific impulse will be restricted.

Fig. 14 depicts the specific impulse of different compounds ver-sus ξ for a 2 MPa combustion chamber pressure. The specific im-pulses in different compounds are very close values and do notexceed from two lower and upper bounds which are shown in thefigure. Also, the specific impulses of all compounds are very closein the range of 0.25 � ξ � 0.35.

Fig. 15. Species mole fraction of combustion products for compound 3.

Fig. 16. Mole fraction of MgO and H2 versus ξ for compound 3.

5. Analysis of hydro-reaction products

As a propulsion device, it is desirable that the products of ahydro-reaction system appear in a gaseous state. However, highlymetal-loaded fuel produces solid phase products like metal ox-ides. Water as an oxidizer plays contradictory roles. On one hand,it plays as a chemical ingredient which affects the chemical re-actions. On the other hand, it plays as a diluting additive whichaffects the balance of concentration of other species. Whenever theconcentration of water is about its stoichiometric value or less, itschemical role is dominant. But, for high values of concentration,its main duty is reducing the products temperature via taking theheat of evaporation from the mixture.

In this section, an analysis of products of hydro-reaction is pre-sented for compound 3, as a typical fuel mixture. The chamberpressure is selected to be 2 MPa. However, the effects of fuelcomposition and chamber pressure can be investigated separately.Fig. 15 shows species mole fractions of dominant products thatare greater than 0.02. As this figure shows, MgO and H2 presentin whole range of ξ as the main products of oxidation of magne-sium by water. The presence of MgO is due to magnesium con-tent of fuel. It is mainly present in the solid phase. However, for0.2 < ξ < 0.4 it appears in liquid state. It is due to the high tem-perature of products in this range which allows MgO to be in asolid–liquid equilibrium. For larger ξ , water vapor becomes themain combustion product. This leads to two essential benefits froma propulsion point of view; increasing the specific impulse due tolow molecular weight of the steam, and decreasing temperature ofproducts. Fig. 16 shows mole fraction of these key species versus ξ .Decreasing concentrations of magnesium oxide and hydrogen athigh values of ξ depends on diluting effect of extra water.



Fig. 17. Mole fractions of gaseous and condense phases versus ξ for compound 3.

Fig. 18. Effect of pressure on species mole fraction for compound 3 and ξ = 0.32.

The presence of the condensed phase reduces the propulsionefficiency of the system. In Fig. 17 the mole fractions of gas phaseand condensed phase species versus ξ are shown separately. Itshows the variations of gas and condensed phases are in oppositemanners.

The effects of chamber pressure on the presence of differentspecies are investigated via examination of mole fractions of a se-lected compound and water mass fraction. Fig. 18 shows speciesmole fractions of the products for ξ = 0.32. The magnesium oxideand hydrogen are more sensitive to chamber pressure and otherproducts have almost constant mole fractions for different pres-sures.

6. Conclusion

• The thermo-physical specifications of metal fuels that havewide applications in the area of combustion and propul-sion are presented. To identify proper fuels for hydro-reactivepropulsion, the temperature and characteristic velocities ofmetal fuel combustion with water are investigated. Thisstudy remarks that the magnesium is a good candidate fora hydro-reactive system. Additionally, the combustion thermo-chemistry of magnesium and some important oxidizers are

studied. Special focus is placed on a fuel-rich mixture contain-ing magnesium and sodium nitrate, and different amount ofwater which form a ternary system.

• This system has a maximum characteristic velocity about1700 m/s and a maximum combustion temperature about3100 K, depending on the composition of the solid fuel. How-ever, the specific impulse of such a hydro-reactive system isincreasing monotonically, as the water content increases. Forhigh values of water mass fraction in the system, it can reacheven beyond 500 s.

• The analysis of the hydro-reaction products shows that mag-nesium oxide, hydrogen, and steam are the main species. Themagnesium oxide presents in its condensed forms. However, afor high amount of water, the main product is steam. It meansthe molecular weight of products approaches the molecu-lar weight of water vapor, which is a benefit of the hydro-reaction.

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Documents

Propulsive characteristics of metal fuel-rich pyrotechnics in hydro-reactive motors