Solving Innovative Problems of Thrust Vector Control Based on Euler's Scientific Legacy

Yuri A. Sazonov, Mikhail A. Mokhov, Inna V. Gryaznova, Victoria V. Voronova, Khoren A. Tumanyan, Egor I. Konyushkov


This study aims to develop an interdisciplinary approach to solving innovative thrust vector control problems. The methodology involves the development of a working hypothesis about the ejection process when using a controlled nozzle to deflect the thrust vector (velocity vector) in any direction within a complete geometric sphere. When developing the working hypothesis, a multilateral analysis of individual facts and scientific and technical information is performed using tools in the "big data" area, assessing opportunities to apply the "Foresight" methodology for predicting the development of fluidics. The authors propose new mathematical models to describe the thrust vector in the distribution of the mass flow rate of the fluid medium between flow channels. Patents for inventions support the novelty of scientific results that reveal new opportunities for more active development of fluidics as applied to simple and complex jet systems with low and extremely high energy density in flows. The proposed methodology rests on a modern computer base and is a logical continuation and development of well-known Euler’s works. The computer simulation of multiflow jet devices mainly focuses on power engineering, production, and processing of hydrocarbons. Some results of this research work, including patented design developments and calculation methods, also apply to developing robotics, unmanned vehicles, and programable jet systems. The authors attribute further development of the interdisciplinary approach for solving inventive problems to the use of different AI options.


Doi: 10.28991/CEJ-2023-09-11-017

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Fluid Dynamics; Interdisciplinary Research; Ejector; CFD; Nozzle Apparatus; Thrust Vector.


Sazonov, Y. A., Mokhov, M. A., Gryaznova, I. V., Voronova, V. V., Tumanyan, K. A., Frankov, M. A., & Balaka, N. N. (2021). Development and prototyping of jet systems for advanced turbomachinery with mesh rotor. Emerging Science Journal, 5(5), 775–801. doi:10.28991/esj-2021-01311.

Sazonov, Y. A., Mokhov, M. A., Gryaznova, I. V., Voronova, V. V., Tumanyan, K. A., Frankov, M. A., & Balaka, N. N. (2022). Designing Mesh Turbomachinery with the Development of Euler’s Ideas and Investigating Flow Distribution Characteristics. Civil Engineering Journal (Iran), 8(11), 2598–2627. doi:10.28991/CEJ-2022-08-11-017.

Holl, S. (2000). Parallax. Princeton Architectural Press, New York, United States.

Holl, S. (2020). Steven Holl: Inspiration and process in architecture. Princeton Architectural Press, New York, United States.

Sazonov, Y. A., Mokhov, M. A., Tumanyan, K. A., Frankov, M. A., & Balaka, N. N. (2020). Prototyping mesh turbine with the jet control system. Periódico Tchê Química, 17, 1160-1175. doi:10.52571/ptq.v17.n36.2020.1176_periodico36_pgs_1161_1175.pdf.

Dehghani, M., & Yazdanparast, Z. (2023). From distributed machine to distributed deep learning: a comprehensive survey. Journal of Big Data, 10(1), 158. doi:10.1186/s40537-023-00829-x.

Du, H., Thudumu, S., Giardina, A., Vasa, R., Mouzakis, K., Jiang, L., Chisholm, J., & Bista, S. (2023). Contextual topic discovery using unsupervised keyphrase extraction and hierarchical semantic graph model. Journal of Big Data, 10(1), 156. doi:10.1186/s40537-023-00833-1.

Darvishpoor, S., Darvishpour, A., Escarcega, M., & Hassanalian, M. (2023). Nature-Inspired Algorithms from Oceans to Space: A Comprehensive Review of Heuristic and Meta-Heuristic Optimization Algorithms and Their Potential Applications in Drones. Drones, 7(7), 427. doi:10.3390/drones7070427.

Morozov, A. V., Nazarov, E. A., & Pokotilo, S. A. (2022). The patent for invention No. 2777459 of the Russian Federation. Method of creating aerodynamic forces on an aircraft wing and a device for its implementation. Moscow, Russia.

Yao, Z., Kan, Z., & Li, D. (2023). Gust Response of Spanwise Morphing Wing by Simulation and Wind Tunnel Testing. Aerospace, 10(4), 328. doi:10.3390/aerospace10040328.

Rodríguez-Sevillano, Á. A., Casati-Calzada, M. J., Bardera-Mora, R., Nieto-Centenero, J., Matías-García, J. C., & Barroso-Barderas, E. (2023). Rapid Parametric CAx Tools for Modelling Morphing Wings of Micro Air Vehicles (MAVs). Aerospace, 10(5), 467. doi:10.3390/aerospace10050467.

Mahmood, F., Hashemi, S. M., & Alighanbari, H. (2023). Structural Dynamic Characterization of a Modular Morphing Wing Exploiting Finite Elements and Taguchi Methodology. Aerospace, 10(4), 376. doi:10.3390/aerospace10040376.

Friedmann, G. (1952). US Patent 2623474. Injection mixer. United States Patent Office, Alexandria, United States.

Wheatley, M. J. (1997). Apparatus for energy transfer. UK Patent Application, GB No: 2310005, London, United Kingdom.

Ringstad, K. E., Banasiak, K., Ervik, Å., & Hafner, A. (2022). Swirl-Bypass Nozzle for CO2 Two-Phase Ejectors: Numerical Design Exploration. Energies, 15(18), 6765. doi:10.3390/en15186765.

Jia, F., Yang, D., & Xie, J. (2021). Numerical investigation on the performance of two-throat nozzle ejectors with different mixing chamber structural parameters. Energies, 14(21), 6900. doi:10.3390/en14216900.

Jing, Q., Xu, W., Ye, W., & Li, Z. (2022). The Relationship between Contraction of the Ejector Mixing Chamber and Supersonic Jet Mixing Layer Development. Aerospace, 9(9), 469. doi:10.3390/aerospace9090469.

Zhang, Y., Dong, J., Song, S., Pan, X., He, N., & Lu, M. (2023). Numerical Investigation on the Effect of Section Width on the Performance of Air Ejector with Rectangular Section. Entropy, 25(1), 179. doi:10.3390/e25010179.

Yan, J., Shu, Y., Jiang, J., & Wen, H. (2023). Optimization of Two-Phase Ejector Mixing Chamber Length under Varied Liquid Volume Fraction. Entropy, 25(1), 7. doi:10.3390/e25010007.

Aidoun, Z., Ameur, K., Falsafioon, M., & Badache, M. (2019). Current advances in ejector modeling, experimentation and applications for refrigeration and heat pumps. Part 1: Single-phase ejectors. Inventions, 4(1), 15. doi:10.3390/inventions4010015.

Koirala, R., Ve, Q. L., Zhu, B., Inthavong, K., & Date, A. (2021). A review on process and practices in operation and design modification of ejectors. Fluids, 6(11), 409. doi:10.3390/fluids6110409.

Shank, K., & Tiari, S. (2023). A Review on Active Heat Transfer Enhancement Techniques within Latent Heat Thermal Energy Storage Systems. Energies, 16(10), 4165. doi:10.3390/en16104165.

Azarova, O. A. (2023). High Speed Flows. Fluids, 8(4), 109. doi:10.3390/fluids8040109.

Lee, J. H., Ryu, J. H., Lee, E. S., Han, H. S., & Choi, J. Y. (2023). Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications. Aerospace, 10(1), 27. doi:10.3390/aerospace10010027.

Wang, Y., & Wang, N. (2023). Influence of the Projectile Rotation on the Supersonic Fluidic Element. Aerospace, 10(1), 35. doi:10.3390/aerospace10010035.

Li, M., Lei, Z., Deng, H., Ouyang, X., Zhang, Y., Lu, X., Xu, G., & Zhu, J. (2023). Numerical Research on the Jet-Mixing Mechanism of Convergent Nozzle Excited by a Fluidic Oscillator and an Air Tab. Energies, 16(3), 1412. doi:10.3390/en16031412.

Resta, E., Marsilio, R., & Ferlauto, M. (2021). Thrust vectoring of a fixed axisymmetric supersonic nozzle using the shock-vector control method. Fluids, 6(12), 441. doi:10.3390/fluids6120441.

Ferlauto, M., Ferrero, A., Marsicovetere, M., & Marsilio, R. (2021). Differential throttling and fluidic thrust vectoring in a linear aerospike. International Journal of Turbomachinery, Propulsion and Power, 6(2), 8. doi:10.3390/ijtpp6020008.

Skaggs, B. D. (2000). US Patent #6,017,195. Fluid jet ejector and ejection method. United States Patent Office, Alexandria, United States.

Dodge, A. Y. (1995). U.S. Patent No. 3,188,976. Jet pump. United States Patent Office, Alexandria, United States.

Samuel, L. (1968). U.S. Patent No. 3,385,030. Process for scrubbing a gas stream containing particulate material. United States Patent Office, Alexandria, United States.

Bayles, W. H., & Nash, B. C. (1962). U.S. Patent No. 3,064,878: Method and apparatus for high performance evacuation system. United States Patent Office, Alexandria, United States.

Volker, M., & Sausner, A. (2018). U.S. Patent No. 10,072,674: Suction jet pump. United States Patent Office, Alexandria, United States.

Chanut, P. L. J. (1961). US Patent # 3013494. Guided missile. United States Patent Office, Alexandria, United States.

Sota Jr., C. G., Callis, G. J., & Masse, R. K. (2007). United States Patent 7155898. Thrust vector control system for a plug nozzle rocket engine. United States Patent Office, Alexandria, United States. (2018). Missile Control Systems. Available online: q0158.shtml (accessed on October 2023).

Sahbon, N., Jacewicz, M., Lichota, P., & Strzelecka, K. (2023). Path-Following Control for Thrust-Vectored Hypersonic Aircraft. Energies, 16(5), 2501. doi:10.3390/en16052501.

Bailey,J. M. (1982). US Patent #4355949. Control system and nozzle for impulse turbines. United States Patent Office, Alexandria, United States.

Hickerson, F. R. (1965). United States Patent 3192714. Variable thrust rocket engine incorporating thrust vector control. United States Patent Office, Alexandria, United States.

Kinsey, L. E., & Cavalleri, R. J. (2013). United States Patent 8387360. Integral thrust vector and roll control system. United States Patent Office, Alexandria, United States.

Plumpe Jr., W. H. (2003). United States Patent 6622472. Apparatus and method for thrust vector control. United States Patent Office, Alexandria, United States.

Cican, G., Frigioescu, T. F., Crunteanu, D. E., & Cristea, L. (2023). Micro Turbojet Engine Nozzle Ejector Impact on the Acoustic Emission, Thrust Force and Fuel Consumption Analysis. Aerospace, 10(2), 162. doi:10.3390/aerospace10020162.

Bhadran, A., Manathara, J. G., & Ramakrishna, P. A. (2022). Thrust Control of Lab-Scale Hybrid Rocket Motor with Wax-Aluminum Fuel and Air as Oxidizer. Aerospace, 9(9), 474. doi:10.3390/aerospace9090474.

Liu, B., Gao, Y., Gao, L., Zhang, J., Zhu, Y., Zang, X., & Zhao, J. (2022). Design and Experimental Study of a Turbojet VTOL Aircraft with One-Dimensional Thrust Vectoring Nozzles. Aerospace, 9(11), 678. doi:10.3390/aerospace9110678.

Zhang, X., Dang, H., & Li, B. (2023). Prediction of Aircraft Surface Noise in Supersonic Cruise State. Aerospace, 10(5), 439. doi:10.3390/aerospace10050439.

Yan, J., Hu, H., Gong, J., Kong, D., & Li, D. (2023). Exploring Radar Micro-Doppler Signatures for Recognition of Drone Types. Drones, 7(4), 280. doi:10.3390/drones7040280.

Xing, Y., Chen, W., Wang, X., Tong, F., & Qiao, W. (2023). Effect of Wavy Leading Edges on Airfoil Trailing-Edge Bluntness Noise. Aerospace, 10(4), 353. doi:10.3390/aerospace10040353.

Yang, Z., Zhang, J., & Shan, Y. (2023). Research on the Infrared Radiation Suppression of the High-Temperature Components of the Helicopter with an Integrated Infrared Suppressor. Aerospace, 10(4), 351. doi:10.3390/aerospace10040351.

Wang, C., Lu, H., Kong, X., Wang, S., Ren, D., & Huang, T. (2023). Effects of Pulsed Jet Intensities on the Performance of the S-Duct. Aerospace, 10(2), 184. doi:10.3390/aerospace10020184.

Ualiyeva, R. M., Kaverina, M. M., Ivanko, L. N., & Zhangazin, S. B. (2023). Assessment of Spring Wheat Varieties for Pest Resistance. OnLine Journal of Biological Sciences, 23(4), 489–503. doi:10.3844/ojbsci.2023.489.503.

Brethouwer, G. (2022). Turbulent flow in curved channels. Journal of Fluid Mechanics, 931, 21. doi:10.1017/jfm.2021.953.

Svorcan, J., Andrić, J., Čantrak, Đ., & Ivanov, T. (2022). Special Collection on advanced practices in aerospace and energy engineering. Advances in Mechanical Engineering, 14(10), 10. doi:10.1177/16878132221125578.

Abu Salem, K., Palaia, G., Chiarelli, M. R., & Bianchi, M. (2023). A Simulation Framework for Aircraft Take-Off Considering Ground Effect Aerodynamics in Conceptual Design. Aerospace, 10(5), 459. doi:10.3390/aerospace10050459.

Peciak, M., Skarka, W., Mateja, K., & Gude, M. (2023). Impact Analysis of Solar Cells on Vertical Take-Off and Landing (VTOL) Fixed-Wing UAV. Aerospace, 10(3), 247. doi:10.3390/aerospace10030247.

Drikakis, D., & Sofos, F. (2023). Can Artificial Intelligence Accelerate Fluid Mechanics Research? Fluids, 8(7), 212. doi:10.3390/fluids8070212.

Mitridis, D., Kapsalis, S., Terzis, D., & Panagiotou, P. (2023). An Evaluation of Fixed-Wing Unmanned Aerial Vehicle Trends and Correlations with Respect to NATO Classification, Region, EIS Date and Operational Specifications. Aerospace, 10(4), 382. doi:10.3390/aerospace10040382.

Shahzad, M. M., Saeed, Z., Akhtar, A., Munawar, H., Yousaf, M. H., Baloach, N. K., & Hussain, F. (2023). A Review of Swarm Robotics in a NutShell. Drones, 7(4), 269. doi:10.3390/drones7040269.

Pesci, A., Teza, G., & Fabris, M. (2023). Editorial of Special Issue “Unconventional Drone-Based Surveying.” Drones, 7(3), 175. doi:10.3390/drones7030175.

Dinelli, C., Racette, J., Escarcega, M., Lotero, S., Gordon, J., Montoya, J., Dunaway, C., Androulakis, V., Khaniani, H., Shao, S., Roghanchi, P., & Hassanalian, M. (2023). Configurations and Applications of Multi-Agent Hybrid Drone/Unmanned Ground Vehicle for Underground Environments: A Review. Drones, 7(2), 136. doi:10.3390/drones7020136.

Sazonov, Y. A. (2012). Fundamentals of calculation and design of pump-ejector installations. SUE “Oil and Gas Publishing House” of Gubkin University: Moscow, Russia.

Petrovich, G. P. (2002). Philosophy of technology and creativity of P. K. Engelmeyer: Historical and philosophical analysis. PhD Thesis, Ural State Economic University Press, Yekaterinburg, Russia.

Altshuller, G. S. (2011). To find an idea: An introduction to TRIZ - the theory of inventive problem solving. Alpina Publisher, Moscow, Russia.

Kurdyumov, S. P., & Knyazeva, E. N. (2021). Future and its horizons: synergetic methodology in forecasting. Synergetics and Scientific Forecasting, Moscow, Russia. (In Russian).

Raskin, N.M. (1958). Euler’s Questions of Technique. Leonhard Euler. Collection of articles in honor of the 250th anniversary of the birth, presented to the Academy of Sciences of the USSR, 499–556, Publishing House of the Academy of Sciences of the USSR, Moscow, Russia.

Ackeret, J. (1944). Investigation of a water turbine built according to Euler's proposals (1754). Swiss Construction Newspaper, 123/124. Available online: (accessed on July 2023).

Izadi, M., Seiti, H., & Jafarian, M. (2022). Foresight: a new approach based on the Z-number cognitive map. European Journal of Futures Research, 10(1), 1-14. doi:10.1186/s40309-022-00188-5.

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DOI: 10.28991/CEJ-2023-09-11-017


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Copyright (c) 2023 Yuri Apollonievich Sazonov, Mikhail Albertovich Mokhov, Inna Vladimirovna Gryaznova, Victoria Vasilyevna Voronova, Khoren Arturovich Tumanyan, Egor Ilyich Konyushkov

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