Characterization of Combustion in a Hybrid Rocket Motor Paraffin-Based

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1 44th July 2014, Tucson, Arizona ICES Characterization of Combustion in a Hybrid Rocket Motor Paraffin-Based Saulo A. Gómez 1, Shirley Pedreira 2 and Pedro Lacava 3 Instituto Tecnologico de Aeronáutica, São José dos Campos, Brasil, A hybrid rocket motor is an intermediate choice between solid and liquid propulsion systems. The use of paraffin as fuel increases the regression rate because of the formation of droplets originated from a process of hydrodynamic instability on the oxidant-fuel interface. Chamber pressure is measured in a laboratory test with a hybrid configuration that uses paraffin and gaseous oxygen. In addition, a numerical solution of the continuity equation is applied to the combustion chamber, using an algorithm that takes into account physical and thermo chemical properties of the propellants as well as the internal geometry of the motor. Finally, numerical and experimental results are compared. A c A i C d L P 0 R R g T 0 V a ṁ ox n r t δ 0 δ p δ ox γ Nomenclature = critical area of the nozzle = injection area = discharge coefficient = length of the fuel grain = chamber pressure = instantaneous radius of the fuel grain = constant for ideal gas model = flame temperature = instantaneous volume of chamber = constant of the burning rate = mass flow of the oxidant = exponent of the burning rate = burning rate = time = density of gas on the chamber = grain density = density of the oxidant = specific heat ratio I. Introduction N a hybrid propellant rocket, fuel and oxidant are stored separately in different phases, this concept of propulsion Iis shown in figure 1. According to Sutton & Biblarz, the most common hybrid configuration is solid fuel and the oxidant can be in liquid or gas form. Hybrid propulsion is restartable, due to oxidant supply can be regulated. In addition, it offers safe manufacture and operation. Hybrid propulsion is considered as an alternative way of chemical energy conversion stored in propellants into kinetic energy 1. This energy is applied in propulsive systems of manned platforms, maneuvering procedures and repositioning of micro satellites. It is a system of minimum environmental impact and lower cost than traditional systems based on liquid or solid propellants. 1 Master student, Propulsion Department, sagomezs@unal.edu.co. 2 PhD Student, Propulsion Department, shirley@ita.br. 3 Professor, Propulsion Department, placava@ita.br.

2 Oxidant propellant Combustion chamber Fuel propellant Figure 1. Hybrid rocket concept, adapted from Sutton. A composition paraffin-black carbon is used as fuel on the experimental rocket motor, whereas the selected oxidizer is gaseous oxygen. Particles of black carbon improve mechanical characteristics of the grain 4. Paraffin, C 20 H 42, is an alkane whose molecular mass is 282,6 g/mol. The stoichiometric reaction can be written as: C 20 H ,5O 2 20CO 2 +21H 2 O The percentage of black carbon is 4%. The grain is made according the process described by Santos, Mota e Lacava, In order to form the inner hole, ø i = 10mm, centrifugal action is used while solidification is occurred. Final dimensions of the cylindrical bar are: ø 32.8mm x 150.0mm Paraffin presents a regression rate that can reach three or four times other fuels for hybrid configurations, 6 since the liquid layer formed on the burning surface ensures high regression rate when convected into the flame front. II. Numerical Approach The mass balance equation in a hybrid rocket motor is presented by Sutton as: ( ) (1) a and n are empirical constants that depend on the propellant composition. Whereas ṁ ox is determined by the pressure difference between the supply tank and the chamber, the complete expression is: c is a constant, function of the properties of the combustion products: ( ) (2) ( ) (3) If the pressure function, P 0, is continuous and differentiable at the time interval A-B, Figure 2, an algorithm based on finite differences to solve P 0 can be implemented. The interval is divided in a finite number of sub-intervals with width Δt j each one. Figure 2. Numerical approach for the pressure chamber. 2

3 In order to value numerically Eq (1), it is discretized on the same way described in Gómez, An implicit equation for P 0 is resolved to obtain the transient comportment of the pressure chamber, due to V and R are function of P 0 and all other parameters of Eq (1) are known, which are indicated on the table 1 Table 1. Numerical Inputs T K R g γ 1.21 n 0.62 a 1.17 x 10-4 m 2n+1 s n-1 /kg n δ p 840 kg/m 3 L 0.15 m C d 0.7 A i 5.5x10-6 m 2 P i 3 MPa A c 31 x 10-6 m 2 The plot of P 0 evaluated with this discretization is presented in the figure 3. III. Experimental Results A test with the hybrid motor was conducted using 3 MPa as pressure of injection, a sketch of the experimental setup is shown on the figure 3. Figure 3. Experimental setting of the hybrid motor 5 3

4 Pressure Chamber, bar Numerical and experimental plots are presented on the figure Experimental Numerical Time, s Figure 4. Numerical and experimental results Both plots show a low variation during the combustion, with a difference of approx. 15% on the mean pressure. Nevertheless, the total time differs considerably, more than 50%. One reason of this high change is the short diameter of the chamber that limits the burning time. Consequently, uncertainties are more significant. The simulation can be improved if properties of the exhaust gas are measured directly, instead of use assumed values. IV. Conclusion The numerical approach based on finite differences is appropriate to predict the chamber pressure during the combustion process. These results can be used to anticipate the performance and the given power of a hybrid rocket motor. Although experimental results show acceptable agreement with the proposed model, more laboratory tests under different conditions should be conducted in order to verify the numerical implementation and the range where it is valid. The model would be improved if other phenomena like chemical reactions more complex, thermal and kinetic losses are included. In order to reach a longer time of combustion, diameter of grain can be increased, due to the chamber pressure not change considerably during the burning. In a solid propellant (fuel and oxidant are contained on the same grain) under radial burning, other effect is observed, the pressure is higher on the end of the combustion 3. Therefore, a superior stress is supported by the chamber wall and it grows with the time burning. References Books 1 Sutton, G.P. and Biblarz O., Rocket Propulsion Elements, 8 th ed., John Wiley and Sons, New York, Humble, R.W; Henry, G.N; Larson, W.J. Space Propulsion Analysis and Design, 2 nd ed., McGraw-Hill, Space Technology Series, United Spaces Department of Defense and the Aeronautics and Space Administration. 748p.. Proceedings 3 Gomez, S., Ceron, H., Murcia. Dynamic Model of the Internal Pressure in a Solid Propellant Rocket Motor. 22 nd International Congress of Mechanical Engineering COBEM2013. Ribeirao Preto, Brasil. 4 Lacava, P.T; Barros, T. M. Protótipo de Motor Foguete Movido a Propelente Híbrido XVI Meeting of Scientific Initiation and Graduate ITA - XVI ENCITA / 2010 Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil, October 20,

5 5 Santos, G.P; Pedreira, S.M; Lacava, P.T. Phisycal Property and Carbon Black Distribution Impact on Propulsion Efficiency of Paraffin-Based Fuel ASME, Proceedings of the International Mechanical Engineering Congress & Exposition, IMECE2012, November 9-15, 2012, Houston, Texas, USA, pp Reports, Theses, and Individual Papers 6 Karabeyoglu, M. A. Scale-up Tests of High Regression Rate Liquefying Hybrid Rocket Fuels. AIAA Stanford University Stanford, CA and NASA Ames Research Center Moffet Field, Mountain View, CA. June, Pp SALVADOR, C. A. V. Investigação Experimental de um Propulsor Híbrido para Satélites e Veículos Espaciais Usando Parafina e N2O4 como Propelentes Tese de Doutorado do Curso de Pós-graduação em Engenharia e Tecnologia Espaciais/Combustão e Propulsão. Instituto Nacional de Pesquisas Espaciais, S. José dos Campos, S. Paulo, 179p. 5