Development of universal mathematical model and computer program for online modeling of valved and valveless pulse jet engines

Olexander Khrulev, Valeriy Muntyan

Abstract


In connection with the appearance of new projects of unmanned aerial vehicles (UAVs) with a pulse jet engine, modeling their parameters and characteristics becomes relevant. However, despite a large number of research works and developed theoretical models of the working process, no calculation programs suitable for wide practical use and modeling of a pulse jet engine have been created for many years. Therefore, the subject of this work was valved and valveless pulse jet engines, and the goal of the work is to create a mathematical model and a real online program for modeling the working cycle of a pulse jet engine, available to a wide range of users. Therefore, it was necessary to solve the following problems: develop a mathematical model of processes in the combustion chamber, intake system, and resonance tube of a pulse jet engine, develop and debug an engine modeling program, place it on a special website, and model known engines to verify the model. Research methods. The model is based on the thermodynamic model of the process of volumetric combustion and gas exchange in the combustion chamber, on the method of "piston" analogy for non-stationary gas and air flow in the resonance pipe of the pulse jet engine and in the valveless engine’s intake pipe. The model includes a mathematical description of the dynamics of the valve petal movement and the non-stationary process of heat exchange with the walls. Results. The first developed special online program Pulsejet-Sim, built on a special data structure with division into server and client parts, provides the implementation of the model. The program is implemented as a web-oriented software service that does not require downloading to the user’s computer compared to traditional desktop packages and programs. This allows instant calculations using server resources and secure data storage in the cloud. Conclusions. With the help of the developed program, preliminary mathematical modeling of known pulse jet engines has been performed, which has shown satisfactory qualitative and quantitative agreement between the modeling results (error less than 10%) and the available experimental data on the main parameters. Previously unknown characteristics of pulse jet engines, including the indicator diagram, were obtained.

Keywords


UAV; pulse jet engine; pulsejet; valved; valveless; piston analogy model; indicator diagram

References


Schmidt, P. On the history of the development of the Schmidtrohr. A History of German Guided Missiles Development ; ed. by Th.Benecke and A.W.Quick. First Guided Missiles Seminar. Munich Germany, April, 1956 / Brunswick, Germany, 1957,pp. 375-399.

Gosslau, F. Development of the V-1 pulse jet. A History of German Guided Missiles Development ; ed. by Th.Benecke and A.W.Quick. First Guided Missiles Seminar. Munich Germany, April, 1956 / Brunswick, Germany, 1957,pp. 400-418.

Diedrich, G. The Aero-Resonator Power Plant of the V-l Flying Bomb. Project SQUID. Princeton, New Jersey, 1948. 46 p.

Sánchez, A.A. Design, construction and testing of a Pulsejet engine (versão final após defesa). Dissertação para obtenção do Grau de Mestre em Engenharia Aeronáutica (2º ciclo de estudos). Covilhã, 2022. 87 p.

Manganiello, E.J., Valerino, M.F., Breisch, J. H. Endurance tests of a 22-inch-diameter pulse-jet engine with a neoprene-coated valve grid. NACA Memorandum Report E5J03. Aircraft Engine Research Laboratory, Cleveland, Ohio, 1945. 15 p.

Prisacariu, V. Performance analysis of military flying wing UAV with pulse jet engine. Review of the Air Force Academy, 2022, no.2 (46), pp. 36-47. doi: 10.19062/1842-9238.2022.20.2.4

XKD5G-1 Target Drone. National Air and Space Museum. Steven F. Udvar-Hazy Center in Chantilly, VA. Available at: https://airandspace.si.edu/collection-objects/drone-target-xkd5g-1/nasm_A19660166000 (accessed 05.05.2025)

Lockwood, R.M. Hiller Pulse Reactor Lift Engine. Final Report. Advanced research. Report No. ARD 308. Bureau of Naval Weapons. Propulsion Dept. Contract NOw 61-0226-c. 1963. 230 p.

Mittal, V. The Novel Pulse Jet Engine Powering The Ukrainian Trembita Missile. Forbes, Jan 13, 2025. Available at: https://www.forbes.com/sites/vikrammittal/2025/01/13/the-novel-pulse-jet-engine-powering-the-ukrainian-trembita-missile/ (accessed 05.05.2025)

Newdick, T. Pulsejet Drone Flies, Could Have Big Impact On Cost Of Future Weapons. The War Zone, Mar 6, 2024. Available at: https://www.twz.com/news-features/pulsejet-drone-flies-could-have-big-impact-on-cost-of-future-weapons (accessed 05.05.2025)

Wave Engine Corp. Available at: https://wave-engine.com/ (accessed 05.05.2025)

Trembita (cruise missile). Available at: https://en.wikipedia.org/wiki/Trembita_(cruise_missile) (accessed 05.05.2025)

Shultz-Grunow, F. Gas-Dynamic Investigations of the Pulse-Jet Tube. Parts I and II. National Advisory Committee for Aeronautics. Technical Memorandum No. 1131. Technical High School, Aachen, Germany. NACA, Washington, 1947. 112 p.

Method of characteristics. Available at: https://en.wikipedia.org/wiki/Method_of_characteristics (accessed 05.05.2025)

Khrulev, A. Determination of gas parameters in resonant pipes and channels of engines with a periodic workflow using the piston analogy method. Eastern-European Journal of Enterprise Technologies, 2023, no. 5 (7 (125)), pp. 50–59. doi: 10.15587/1729-4061.2023.288520

Anand, V., Jodele, J., Shaw, V., Russell, A., Prisell, E., Lyrsell, O., & Gutmark, E. Visualization of Valved Pulsejet Combustors and Evidence of Compression Ignition. Flow, Turbulence and Combustion, 2020, no. 106 (3), pp. 901–924. doi: 10.1007/s10494-020-00203-4.

Schetinkov, E. S. Physics of Gas Combustion. Publishing House "Nauka", Moscow, 1965. 744 p. (in Russian).

Anand, V., Jodele, J., Prisell, E., Lyrsell, O., Gutmark, & E. Dynamic Features of Internal and External Flowfields of Pulsejet Engines. AIAA Journal, 2020, no. 58 (10), pp. 4204–4211. doi: 10.2514/1.j059685.

Meng, X., de Jong, W., & Kudra, T. A state-of-the-art review of pulse combustion: Principles, modeling, applications and R&D issues. Renewable and Sustainable Energy Reviews, 2015. 42 p. doi: 10.1016/j.rser.2015.10.110.

Van Heerbeek, P. A. Mathematical Modelling of a Pulse Combustor of the Helmholtz-type. Delft, 2008. 146 p. Available at: https://diamhomes.ewi.tudelft.nl/~kvuik/numanal/heerbeek_afst.pdf (accessed 05.05.2025)

Mohsen, K. K., & Hussain, Z. H. Numerical Comparison between Two Tailpipe Shapes of Valved Pulsejet Engine. INTCSET 2020. IOP Conf. Series: Materials Science and Engineering, 2021. 13 p. doi: 10.1088/1757-899X/1094/1/012001.

Agarwal, A., Pitso, I. Modelling & numerical exploration of pulsejet engine using eddy dissipation combustion model. Materials Today: Proceedings. Materials Today: Proceedings, 2020,vol, 27, pp. 1341–1349. doi: 10.1016/j.matpr.2020.02.620.

Gonzalez, I., Naseri, A., Rigola, J., Perez-Segarra, C.D., & Oliva, A. A fluid-structure interaction solver for the fluid flow through reed type valves. 10th International Conference on Compressors and their Systems. IOP Conf. Series: Materials Science and Engineering, 2017, vol. 232. 11 p. doi: 10.1088/1757-899X/232/ 1/012032.

Migalin, K. V., Ambrozhevich, A. V., Sereda, V. A., Larkov, S. N., Boychuk, I. P., Kartashev, A. S., & Silevich, V. Yu. Pulsejet air-breathing engines: monograph. Under the gen. ed. of K.V. Migalin. Tolyatti, TSU Publ. House, 2014. 296 p. (in Russian)

The Jet Engines. Fifth Edition. Rolls-Royce plc, Birmingham, 1996. 278 p.

Ahmadian, S. Computational Approach in Sizing of Pulsejet Engine. Emirates University, January 2014. 25 p. Available at: https://www.researchgate.net/publication/284511823 (accessed 05.05.2025)

Simpson, B. The Enthusiast's Guide to Pulsejet Engines. 2004. 106 p. Available at: https://www.academia.edu/28974608/Pjbookrev2a (accessed 05.05.2025)

Pearson, R. J., Bassett, M. D., Fleming, N. P., & Rodemann, T. Lotus Engineering Software – An Approach to Model-Based Design. The 2002 North American ADAMS Conference in Scottsdale. Arizona. 2002. Available at: https://ru.scribd.com/document/215011237/Lotus-Paper (accessed 05.05.2025)

GasTurb 14. Design and Off-Design Performance of Gas Turbines. GasTurb GmbH, 2023. 379 p. Available at: https://gasturb.com/Downloads/Manuals/GasTurb14.pdf (accessed 05.05.2025)

Khrulev, O. Analysis of possibility of using commercial micro turbojet engines for high-speed small-sized operational-tactical UAVs. Aviacijno-kosmicna tehnika i tehnologia – Aerospace technic and technology, 2023, no. 4sup2 (190), pp. 5-18. doi: 10.32620/aktt.2023.4sup2.01.

Anand, V., Jodele, J., Zakh, A., Geller, A., Prisell, E., & Lyrsell, O., Gutmark, E. Revisiting the Argus pulsejet engine of V-1 buzz bombs: An experimental investigation of the first mass-produced pressure gain combustion device. Experimental Thermal and Fluid Science, December 2019, vol. 109, article no. 109910. doi: 10.1016/j.expthermflusci.2019.109910.

Cavcar, M. The International Standard Atmosphere (ISA). 7 p. Available at: http://fisicaatmo.at.fcen.uba.ar/practicas/ISAweb.pdf (accessed 05.05.2025)

Khrulev, A. Modeling Work-Flow of the “Cylinder-Piston” Type Devices Using a Universal Thermodinamic Model. Evolutions Mech Eng. EME.000618, 2024, no. 5(4). 8 p. doi: 10.31031/EME.2024.05.000618.

Idelchik, I. E. Handbook of hydraulic resistance. Coefficients of local resistance and of friction. New York: Israel Program for Scientific Translations Ltd., 1966. 517 p.

Kravchenko, O., Khrulev, A., Gerlici, J., Saraiev, O., & Danets, S. Technical condition assessment and modelling of reed valves in vehicle engine intake systems. Communications. Mechanical Engineering in Transport, 2024, vol. 27 (1), pp. B41-B52 doi: 10.26552/com.C.2025.006.

Khrulev, A, Saraiev, O, Saraieva, I, &Vorobiov, O. Modeling of thermodynamic processes in internal combustion engine cylinder during cranking in compression measurement tests. Combustion Engines. 2024, vol. 198(1), pp. 3-14. doi: 10.19206/CE-187380.

Babu, V. Fundamentals of Gas Dynamics (2nd Edition). Chichester, John Wiley & Sons Ltd, 2015. 262 p.

Pisarenko, G.S., Kvitka, O. L., & Umansky, E. C. Streight of Materials. 2 ed. Kyiv, Vyscha Shk., 2004. 655 p. (in Ukrainian).

Khrulev, A. Mathematical modeling of reed valve operation in engines with periodic workflow. Integration of science as a mechanism of effective development: Proceeding of the 11th International scientific and practical conference, November 28 - December 01, 2023, Helsinki, Finland/ International Science Group, Helsinki, 2023, pp. 389-395.

Rohsenow, W. M., Hartnett, J. P., & Cho, Y. I. Handbook of Heat Transfer. Third Edition. New York, McGraw-Hill, 1998. 1500 p.

Janna, W. S. Engineering Heat Transfer. Third Edition. New-York, CRC Press, 2009. 980 p.

Lienhard-IV, J. H., & Lienhard-V, J.H. A Heat Transfer Textbook. Third Edition. Cambridge, MA, Phlogiston Press, 2008. 750 p.

Khrulev, A. E., & Saraev, O. V. The method of expert assessment of the technical condition of an automobile engine after overheating. Automobile transport, 2021, vol. 48, pp. 5-16. doi: 10.30977/AT.2219-8342.2021.48.0.5.

Biringen, S., & Chow, C. An Introduction to Computational Fluid Mechanics by Example. John Wiley & Sons, 2011. 310 p. doi: 10.1002/9780470549162.

Hoerner, S.F. Fluid-Dynamic Drag. Practical Information on Aerodynamic Drag and Hydrodynamic Resistance: theoretical, experimental and statistical information. Library on Congress Catalog Card Number 64-19666, 1992. 455 p.

Pulsejet-Sim:Pulsejet Engine Workflow Simulation Program. Available at: https://pulsejet-sim.com (accessed 05.05.2025)

Manganiello, E. J., Michael, F. Valerlino, M. F., & Essig, R. H. Sea-Level Performance Tests of a 22-inch -Diameter Pulse-Jet Engine at Various Simulated Ram Pressures. Aircraft Engine Research Laboratory. Cleveland, Ohio. Memorandum Report E5J02, NACA, Washington, 1945. 39 p.

Valerino, M. F., Essig, R. H., & Hughes, R. F. The Effect of Increase in Combustion-Air Inlet Temperature from 80° to 130° F on the Sea-Level Performance of a 22-inch-Diameter Pulse-Jet Engine. Aircraft Engine Research Laboratory. Cleveland, Ohio. Memorandum Report E6G01, NACA, Washington, 1946. 19 p.

Litke, P. J., Schauer, F. R., Paxson, D. E., Bradley, R. P., Hoke J. L. Assessment of the Performance of a Pulsejet and Comparison with a Pulsed-Detonation Engine. 43rd AIAA Aerospace Sciences Meeting and Exhibit. January 10-13, 2005, Reno, Nevada, 10 p. doi: 10.2514/6.2005-228.

Khalatov, A. A., Nemchin, A. F., Kobzar, S. G, Kuzmin, A. V., & Borisov, I. I. Pulse Detonation Engines: Current State and Results of Studies. Part 1: Current State ; ed. Khalatov A.A. Dnipro: LIRA, 2024. 88 p.




DOI: https://doi.org/10.32620/aktt.2025.4sup2.01