Trans. Japan Soc. Aero. Space Sci. Vol. 52, No. 177, pp. 180–187, 2009 Comprehensive Design Method for LOX/Liquid-Methane Regenerative Cooling Combustor with Coaxial Injector à By Nobuyuki YATSUYANAGI ÃFormerly, Kakuda Research Center, National Aerospace Laboratory, Kakuda, Japan (Received December 8th, 2008) A comprehensive design method for a LOX/Liquid-Methane (L-CH4) rocket engine combustor with a coaxial in- jector and the preliminary design of the regenerative cooling combustor with 100-kN thrust in vacuum at a combustion pressure of a 3.43 MPa are presented. Reasonable dimensions for the combustor that satisfy the targeted Cà efficiency of more than 98% and combustion stability are obtained. Key Words: LOX/Liquid-Methane Rocket Engine, LOX/LNG Rocket Engine, Coaxial Injector, Cà Efficiency, Combustion Stability Nomenclature n: nozzle section o: oxygen AðxÞ: surface area cpL: specific heat of LOX 1. Introduction CÃ: characteristic exhaust velocity Dc: chamber diameter Japan is now developing the GX rocket for launch a sat- DðxÞ: droplet diameter ellite mass of approximately 2 tons into a sun synchronous D32: Sauter mean diameter of LOX spray orbit at a height of 800 km. The first launch is scheduled f : frequency after 2011. The engine of the second stage will be a newly LÃ: characteristic chamber length developed LNG-fueled engine and development of an M: molecular weight LOX/LNG engine is now progressing. The merits of using N: number of injection elements LNG fuel is that the combustion of methane, the major com- NuðxÞ: Nusselt number ponent of LNG, with oxygen delivers the highest specific O=F: mixture ratio impulse among the hydrocarbon fuels and methane is much Pc: combustion pressure cheaper than hydrogen. Therefore, a LOX/LNG engine has Pcr: reference pressure (¼ 3:5 MPa) advantages next to a LOX/L-H2 engine. Worldwide, the 0 P ðtÞ: pressure perturbation Russian RD-190 LOX/L-CH4 engine is well known, and PL: vapor pressure of LOX Korea is developing the CHASE LOX/LNG engine. In Pr: Prandtl number Japan, NAL conducted fundamental research on the com- R: universal gas constant bustion and cooling characteristics of the LOX/L-CH4 com- T: temperature bustor in the 1990s and found they were similar to LOX/ t: time L-H2 combustion. In a regenerative cooling combustor tÃ: period of oscillation using LNG, the injected LNG is gasified, so a coaxial injec- V: velocity tor is used as in a LOX/L-H2 combustor. Therefore, when w0ðtÞ: mass release rate designing a LOX/LNG combustor, a similar design to that x: axial direction for a LOX/L-H2 combustor can be used, although it is nec- : latent heat of vaporization of LOX essary to clarify the design particularites for LOX/LNG Á: increment combustor. Alaskan LNG is composed of 99.81 weight % Subscript CH4, 0.07 weight % C2H6 and 0.12 weight % N2, so the fol- 1T: first tangential mode lowing assumes pure CH4 when calculating combustion b: breakup of LOX jet properties. The present study describes the LOX/L-CH4 c: combustion gas or cylindrical section engine as a representative LOX/LNG engine. Previous 1,2) f: fuel work, derived the optimum design for a L-H2 cooled i: injection regenerative combustor for a LOX/L-H2 engine, and NAL L: LOX has previously reported experimental studies on the com- bustion and cooling characteristics of the LOX/L-CH4 com- Ó 2009 The Japan Society for Aeronautical and Space Sciences bustor.3–5) This study develops a comprehensive design for a ÃPresent address: 989–1603, Miyagi, Japan Nov. 2009 N. YATSUYANAGI: Comprehensive Design Method for LOX/Liquid-Methane Regenerative Cooling Combustor 181 Table 1. Design conditions of LOX/L-CH combustor. 4 where, Kb is the burning rate of a LOX droplet with gaseous Unit Nominal condition methane. The numerical value of Kb was derived from the Thrust (Vacuum) kN 100 author’s previous experiment using a combustor with a 3) ¼  À5 Combustion pressure MPa 3.43 single element injector. The value of Kb 0:38 10 2 Mixture ratio — 3.2 (m /s) used in Eq. (1) corresponds to the condition of ¼ ¼ LOX mass flow rate kg/s 21.91 Pc 3:43 MPa and O/F 3:2, while the value of Kb for À5 2 the LOX/L-H2 combustion was 1:1  10 (m /s). Assum- L-CH4 flow rate kg/s 6.85 ing that a chemical equilibrium reaction occurs between these oxygen and injected methane at the given mixture LOX/L-CH4 regenerative cooling combustor with a ratio, the mass of the reacted propellants is calculated in coaxial injector and a preliminary design for an engine with the axial direction. Thus, the combustion gas is composed 100 kN of thrust in vacuum. These specifications were of reacted propellants, unreacted methane gas, and residual selected to meet the needs of the GX rocket, so this study LOX spray. The thermal conductivity of the LOX/L-CH4 will help in development and evaluation of that engine. combustion gas is explained below. To evaluate the local Table 1 shows the major specifications of the targeted heat transfer coefficient, hgðxÞ, shown by Eq. (2), a basic engine. In the assumed engine cycle, L-CH4 is injected equation for forced convection in a cylinder is used as in directly after being used as combustor coolant. Therefore, the previous study:2) the temperature of the injected methane depends on the heat h ðxÞ¼0:023k ReðxÞ0:8Pr0:4=D ðxÞ; ð2Þ absorbed through the combustion chamber wall, and the g t c injection temperature greatly affects the combustion pro- where, kt the thermal conductivity of the LOX/L-CH4 com- cesses. As the liquid/gas phase coaxial-type injector is also bustion gas is 0.15 W/(mÁK). Because the relation deduced 4) used for the LOX/L-CH4 injector, the author’s optimized by the NAL experiments was kt=ktðO2=H2Þ¼0:43, where 2) design for the LOX/L-H2 regenerative combustor is fun- the thermal conductivity for LOX/H2 combustion, damentally applicable, although the characteristic constant ktðO2=H2Þ was 0.35 W/(mÁK). Then local heat flux, qðxÞ, of the burning rate and that of the thermal conductivity and total heat load to the combustor, Qt, are calculated. should replace those for the LOX/L-H2 combustion to cal- The injection temperature of the methane, Tf,i, is calculated culate the combustion processes and the heat load. These from Qt, although Tf,i and Qt affect each other through the characteristic constants are derived from NAL experiments combustion processes. The calculation of combustion per- 3,4) on LOX/L-CH4 combustion. formance and heat load is conducted following the proce- dure shown in Fig. 1, based on the author’s previous study.2) 2. Calculation and Evaluation of Combustion Perform- 2.2. Verification of calculation of combustion per- ance and Combustion Stability formance To verify the validity of the present method for calculat- 2.1. Method for calculating combustion performance ing combustion performance and heat load, the results were The method of calculating combustion performance is assessed by comparison with experiments on the CHASE 6,7) basically similar to that used for LOX/L-H2 combustion engine. Table 2 lists the major specifications of the in the author’s former study,2) except for the characteristics CHASE engine. The dimensions of the injector element of LOX/L-CH4 combustion. So here, the discussion focuses are not available, so rational assumptions were made. The À5 2 on introduction of characteristic factors controlling combus- burning rate constant, Kb ¼ 1:0  10 (m /s) was used tion performance and heat load to the combustion chamber. based on experimental data by NAL3) under combustion These factors are the burning rate constant of the LOX spray conditions of Pc ¼ 7:2 MPa and O/F ¼ 3:0. In Fig. 2, the with methane and the thermal conductivity of the LOX/ calculated Cà efficiencies vs. the injection temperature of L-CH4 combustion gas. The calculation scheme is com- LNG are shown for comparison with experiments. Although posed of the atomization process for the LOX jet and the the experimental data are somewhat scattered, the tendency combustion process for the LOX spray with methane gas. of the calculation agrees with them. Figure 3 shows the heat To evaluate the atomization process of the LOX jet with flux distribution along the axial direction of the chamber gasified methane, the author’s atomization model1) is used. wall. Although there are some underestimations near the This model can calculate the local atomization rate of the injector face, the calculation tendency is generally satisfac- LOX jet and the size histogram of formed droplets in the tory. Reasonable agreement between the calculations and LOX spray, giving the initial combustion conditions. The the experiments suggest that the present calculation method reaction rate of the propellants is controlled by the burning is sufficiently accurate to be used for the LOX/L-CH4 case. rate of vaporized oxygen with methane gas. Equation (1) 2.3. Method of evaluating combustion stability expresses the relation for a single droplet of LOX, and then Here, the methods of evaluating low and high frequency integrates it over the whole LOX spray to obtain the reacted combustion instability are briefly introduced. For low fre- mass of the oxygen along the axial position of x: quency combustion instability, as in the previous study,2) the analytical model derived by Szuch8) was used. This ÁDðxÞ2=t ¼K NuðxÞ=2; ð1Þ b model is based on the fact that in a system with time delays 182 Trans.