On the methodology of modeling the conditions of formation of condensation trails of aircraft


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This study examines the task of identifying the conditions of formation of aircraft condensation trails (ACT) during the interaction of the exhaust jet of a turbofan engine (TFE) with the environment. The method of numerical solution of the equations of gas dynamics (Reynolds equations) is applied, taking into account the nozzle shape of the considered TFEs. The calculations take into account geometric and gas-dynamic parameters that affect key processes for various types of the TFEs considered, including the bypass ratio, characteristics of internal and external flows, water vapor emissions, and others. The results obtained are necessary for the development of a criterion for the formation of stable ACT based on the degree of supersaturation of water vapor in the engine jet. The analysis of
examples of the formations of ACT is carried out, based on data from the real flight tests.

aircraft engine, axisymmetric nozzle, aircraft condensation trail, heat transfer, jet gas dynamics

DOI: http://doi.org/10.33257/PhChGD.26.3.1183


Volume 26, issue 3, 2025 year


О методике моделирования условий образования конденсационных следов самолетов

В данном исследовании рассматривается задача определения условий образования конденсационных следов самолетов (КСС) при взаимодействии выхлопной струи турбореактивного двигателя (ТРДД) с окружающей средой. Применяется метод численного решения уравнений газовой динамики (уравнения Рейнольдса) с учетом формы сопла рассматриваемых ТРДД. В расчетах учитываются геометрические и газодинамические параметры, определяющие ключевые процессы для различных типов ТРДД, включая степень двухконтурности, характеристики внутреннего и внешнего потоков, эмиссия водяного пара и другие. Полученные результаты необходимы для разработки критерия образования устойчивых КСС, основанного на степени перенасыщения водяного пара в струе двигателя. Проведен анализ примеров образований КСС, опираясь на данные натурных летных испытаний.

авиационный двигатель, осесимметричное сопло, конденсационный след самолета, теплообмен, газодинамика струи

DOI: http://doi.org/10.33257/PhChGD.26.3.1183


Volume 26, issue 3, 2025 year



1. Annex № 16 to the Convention on International Civil Aviation, Environmental protection. Aircraft Engine Emissions, ICAO, 2023, vol. 2, no. 5.
2. ICAO Engine Exhaust Emissions Databank, ICAO Doc. № 9646-AN/943, First Edition, 1995, (Implementation of Issue №30, 23 July 2023), URL: https://www.easa.europa.eu/en/domains/environment/icao-aircraft-engine-emissions-databank
3. Ivanova A.R., The impact of aviation on the environment and measures to mitigate negative impacts, Proceedings of the Hydrometeorological Center of Russia, 2017, no. 365, pp. 5-14.
4. Dedesh V.T., Grigoriev M.A., Zamyatin A.N., Zhelannikov A.I., Calculation assessment of formation, existence and destruction of aircraft condensation trails with account of interaction with wake vortices, Int. Conference on Environmental Science and Biological Engineering (ESBE), 2014, Beijing, pp. 17-23.
5. Lee D.S., Fahey D.W., Skowron A., Allen M.R., Burkhardt U., Chen Q. et al., The contribution of global aviation to anthropogenic climate forcing for 2000 to 2018, Atmos. Environ, 2021, vol. 1, 244 p.
6. Abramovich G.N., Theory of turbulent jets, Moscow, Science Publishing House, 1984. 10 p.
7. Schumann U., Busen R., Plohr M., Experimental test of the influence of propulsion efficiency on contrail formation, Journal of Aircraft, 2000, vol. 37, no. 6, pp. 1083-1087.
8. Schumann U. A., Contrail Cirrus Prediction Model, Geoscientific Model Development, 2012, vol. 5, no. 3, pp. 543–580.
9. Huang J. A., Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice,
J. Applied Meteorology and Climatology, 2018, vol. 57, no. 6, pp. 1265-1272.
10. Wilcox D.C., Turbulence Modeling for CFD, DCW Industries, 2006, pp. 34-43.
11. Dedesh V.T., Kiose S.N., Vid V.I., Kagarmanov R.L., Voronich I.V., Pavlova E.G., Tenishev R.H., Rumyantseva G.P., Stepanova S.Y., Patent RU 2532995 C1 dated 11/20/2014, The copyright holder is OJSC "LII named after M.M. Gromov".
12. Stasenko A.L., Physical mechanics of multiphase flows, Moscow, MIPT, 2005, 118 p.
13. Popovicheva O.B., Starik A.M., Aviation soot aerosols: physico-chemical properties and effects of atmospheric emissions (review), News of the Russian Academy of Sciences. Physics of the Atmosphere and Ocean, 2007, vol. 43, no. 2, pp. 147-164.
14. Schumann U., Formation, properties and climatic effects of contrails, Comptes Rendus. Physique, 2005, vol. 6, no. 4-5, pp. 549-565.
15. Schneider E., Czech H., Popovicheva O. et al., Mass spectrometric analysis of unprecedented high levels of carbonaceous aerosol particles long-range transported from wildfires in the Siberian Arctic, Atmos. Chem. Phys., 2024, no. 24, pp. 553–576.