Aerospace Technic and Technology

Analysis of the thermodynamic and thermophysical properties of combustion products (CP) in the liquid rocket engine (LRE) chamber shows that their dissociation degree depends on temperature T, gas expansion degree ε, etc. Practically, CP’s are always chemically active working fluid, therefore the number of moles N of the products varies along the length of the LRE chamber in the entire reaction mixture. The local values of the parameters T and N depend on the specific physical conditions. Therefore, the distribution of local numbers of moles of the components of the gas mixture and its heat capacities can be represented as dependencies N~f(T) and c~g(T). For this purpose based on the numerical values of the moles and the heat capacities of the gas mixture components in the main sections of the LRE chamber are formed as corresponding empirical functions through interpolation. Analysis of changes in moles and weight fractions of gaseous and condensed СP’s components shows that, depending on the specific conditions (α, Km, pc, ε), the number of moles of one group of individual substances increases, while these parameters of the other group decrease. These changes are alternating in nature and lead to the formation of new centers -sources of chemical and thermal energy along the length of the LRE nozzle. Thus, for different conditions (α, Km, pc, ε), the design of the LRE chamber should be carried out taking into account the nature of the change in N, cp, cv, and γ. Therefore, from energy conversion, the number of moles of the i-th CP component can be represented as a function Ni = f(Ti) or Ni = f(x,y). Numerical studies show that, based on the Ni values in the main sections of the LRE chamber with a given length, it is possible to form linear or nonlinear empirical functions in the form Ni= f(x) by interpolation. Depending on the specific tasks, one of the interpolation functions can be taken into account in the formulas for calculating the specific heats of CP. In this case, to form the refined geometry of the LRE chamber, the thermo-gas-dynamic calculation is repeated taking into account new indicated dependencies. Consequently, the system of equations for the thermodynamic calculation of an LRE is solved taking into account new functions. This approach allows forming the optimal contour of the LRE chamber at the preliminary stage of engine design and improving the results of gas-dynamic calculation and profiling of the nozzle using a modified method of characteristics. In the framework of the presented studies, to obtain an optimal geometry for the LRE nozzle, are compared values of the velocities, which obtained using the solutions of the direct and inverse problems. Thus, the correct consideration of changes in the basic parameters along the nozzle length allows us to organize the correct operation of the LRE chamber by changing the thermal properties of CP along the nozzle length in all flight conditions of the flight vehicle. This circumstance requires some improvement of the principles and schemes of regulation systems of the LRE operation, which leads to the conduct of extensive researches in this direction.

liquid-propellant rocket engine; combustion chamber; nozzle; combustion products; thermo-gas-dynamic calculation

Alemasov, V. E., Dregalin, A. F., Tishin, A. P. Teorija raketnyh dvigatelej: uchebnoe posobie [Theory of Rocket Engines: A Textbook for High Schools]. Moscow, Mashinostroenie Publ., 1969. 464 p. (In Russian).

Babkin, A. I., Dorofeyev, A. A., Loskutnikova, G. T., Filimonov, L. A., Chernukhin, V. A. Raschet parametrov i kharakteristik kamery dvigatelya: uchebnoye posobiye po kursu "Teoriya dvigateley" [Calculation of parameters and characteristics of the RE camera: textbook for “Engines theory” course]. Moscow, MSTU named after N. E. Bauman Publ., 1990. 56 p.

Alemasov, V. Ye., Dregalin, A. F., Tishin, A. P., Khudyakov, V. A., Kostin, V. N. Termodinamicheskiye i teplofizicheskiye svoystva produktov sgoraniya: spravochnik [Thermodynamic and thermophysical properties of combustion products: reference book]. Scientific editor of Academician V. P. Glushko, T.1-10, Moscow, Academy of Sciences of USSR, VINITI, 1971-1976 yy.

Gurtovoy, A. A., Ivanov, A. V., Skomorokhov, G. I., Shmatov, D. P. Raschet i konstruirovaniye agregatov ZHRD: ucheb. posobiye [Calculation and design of LRE aggregates: education texbook]. Voronezh, VGTU Publ., 2016. 166 p.

Vasil'yev, A. P., Kudryavtsev, V. M., Kuznetsov, V. A., Kurpatenkov V. D., Obel'nitskiy A. M., Polyayev V. M., Poluyan, B. YA. Osnovy teorii i rascheta zhidko-stnykh raketnykh dvigateley: uchebnik dlya VUZov [Fundamentals of the theory and calculation of liquidrocket engines: textbook for high schools]. Editor V. M. Kudryavtsev, 3th edition, Moscow, High School Publ., 1983. 703 p.

Belov, G. V., Trusov, B. G. Termodinamicheskoye modelirovaniye khimicheski reagiruyushchikh sistem: uchebnoye posobiye [Thermodynamic modeling of chemically reacting systems: textbook]. MSTU named after N. E. Bauman Publ., 2013. 96 p.

Gurvich, L. V., Veyts, I. V., Medvedev, V. A. i dr. Termodinamicheskiye svoystva individual'nykh veshchestv: spravochnoye izdaniye [Thermodynamic properties of individual substances: reference book]. In 4 vol., Moscow, Science Publ., 1978-1982 yy.

Bulygin, Yu. A., Kretinin, A. V., Rachuk, V. S., Faleyev, S. V. Raschet teplovogo sostoyaniya kamery zhidkostnogo raketnogo dvigatelya: ucheb. posobiye [Calculation of the thermal state of the liquid rocket engine chamber: education textbook]. Voronezh, VGTU Publ., 1997. 90 p.

McBride, B. J., Zehe, M. J., Gordon, S. Coefficients for Calculating Thermodynamic Properties of Individual Species, NASA TP-2002-211556, NASA Glenn Research Center, Cleveland, Ohio, USA, 2002. 291 p.

Cantwell, B. J. AA283 course, Aircraft and Rocket Propulsion. Available at: https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283 Course_Notes/ (аccessed 25.03.2019)

Gordon, S., McBride, B. J. Computer Program for Complex Chemical Equilibrium Compositions and Applications I. Analysis. NASA RP 1311, vol. 1, 1994. 61 p.

Hill, P., Peterson, C. Mechanics and Thermodynamics of Propulsion. Addison-Wesley Publishing Company, 2nd Edition, 1992. 755 p.

Brykov, N. A., Volkov, K. N., Yemel'yanov, V. N., Teterina, I. V. Techeniya ideal'nogo i real'nogo gaza v kanalakh peremennogo secheniya s nestatsionarnym lokalizovannym podvodom energii [Ideal and real gas flows in variable cross-section channels with non-stationary localized energy supply]. Calculation methods and programming, 2017, vol. 18, Issue 1, pp. 20-40. Available at: http://num-meth.srcc. msu.ru/zhurnal/ tom_2017/v18r103.html (аccessed 10.05.2019) (In Russian).

Colonno, M. R., Van der Weide, E., Alonso, J. J. The Optimum Vacuum Nozzle: an MDO Approach. Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2008-911, Reno, Nevada, 7-10 Jan. 2008. 18 p.

Fu, L., Zhang, S., Zheng, Y. Design and Verification of Minimum Length Nozzles with Specific/Variable Heat Ratio Based on Method of Characteristics. International Journal of Computational Methods, 2016, vol. 13, no. 6. 13 p.

Kestin, J. Influence of Variable Specific Heats on the High-speed Flow of Air. A.R.C. Technical Report, C.P., London, Polish University College, no. 33 (13.176), 1950. 23 p.

Kyprianidis, K. G., Sethi, V., Ogaji, S. O. T., Pilidis, P., Singh, R., Kalfas, A. I. Thermo-fluid modelling for gas turbines-part 1: Theoretical foundation and uncertainty analysis. Proceedings of ASME TURBO EXPO 2009, GT2009-60092, Power for Land, Sea and Air, Orlando, FL, USA, June 8-12, 2009. 15 p.

Rizkalla, O., Chinitz, W. and Erdos, J. I. Calculated Chemical and Vibrational Non equilibrium Effects in Hypersonic Nozzles. Journal of propulsion and power, 1990, pp. 50-57.

Zebbiche, T. Stagnation temperature effect on the supersonic axisymmetric minimum length nozzle design with application for air. Elsevier, Advances in Space Research, vol. 48, Is. 10, 2011, pp. 1656–1675.

Anderson, J. J. Modern Compressible Flow: With Historical Perspective. New York, McGraw-Hill Book Company Publ., 1982. 466 p.

Pashayev, A., Abdullayev, P. and Samedov, A. Sıvı yakıtlı roket motorunun itme odasının geliştirilmiş tasarım yöntemi [Improved design method for the liquid propellant rocket engine propulsion chamber]. SAVTEK 2016, 9. Savunma Teknolojileri Kongresinin bildiri kitabı [Proc. of the 9th National Congress of Defense Technologies, SAVTEK 2018], METU, Ankara, 27-29 June, 2018. 11 p. (in Turkish)

Abdullayev, P. SH., Samedov, A. S. K voprosu profilirovaniya reaktivnogo sopla ZHRD [To the question of profiling of the LPRE nozzle]. Herald of aeroenginebuilding, Zaporozh'ye, MotorSich, no. 2, 2018, pp. 113-118.

Abdulla, N. Implementation of variable specific heat ratio in liquid rocket nozzle design using method of characteristics. Proceedings of the IV International Scientific and Practical Conference “Creative Potential of Young People in the Solving of Aerospace Problems, February Readings-2019”, National Aviation Academy, Baku, Azerbaijan, February 27-28, 2019, pp. 28–31.