Convective Heat Exchange and Friction in a Thin Laminar-to-Turbulent Boundary Layer on the Impermeable Lateral Surfaces of Blunted Cones Featuring a Low Aspect Ratio

Authors: Gorskiy V.V., Savvina A.G. Published: 06.09.2021
Published in issue: #3(138)/2021  

DOI: 10.18698/0236-3941-2021-3-25-37

Category: Aviation and Rocket-Space Engineering | Chapter: Aerodynamics and Heat Transfer Processes in Aircrafts  
Keywords: convective heat transfer, friction, impulse loss thickness, boundary layer

In order to provide a high-quality solution to the problem of computing convective heat transfer parameters in a laminar-to-turbulent boundary layer, it is necessary to numerically integrate differential equations describing that layer, completed by semi-empirical turbulent viscosity models, said models having been tested by comparing their output to the results of experimental investigations where the gas dynamics of a gas flow around a body is correctly simulated. Developing relatively simple yet adequately accurate computation methods becomes crucial for practical applications. To date, the effective length method, being simple yet apparently boasting an acceptable accuracy, has become the most widespread technique for solving this problem in aircraft design and aerospace technology. However, this statement is not correct for large Reynolds numbers on a hemisphere. Under these conditions, semi-empirical apparent turbulent viscosity models provide significantly better matches to experimental data. The paper analyses the feasibility of using a similar approach for the lateral surface of a blunted cone featuring a low aspect ratio. We describe a new efficient approach to solving this problem, demonstrating a high accuracy and maximum simplicity when used in practice. We check the results of systematic computations using our method against comparable data obtained via the most frequently cited approaches to solving this problem


[1] Zemlyanskiy B.A., ed. Konvektivnyy teploobmen letatel’nykh apparatov [Convective heat transfer of aircraft]. Moscow, FIZMATLIT Publ., 2014.

[2] Gorskiy V.V. Method of numerical solution of two-dimensional laminar-turbulence boundary layer equations on permeable wall of blunt rotation body. Kosmonavtika i raketostroenie, 2017, no. 3, pp. 90--98 (in Russ.).

[3] Uidkhopf Dzh.F., Kholl R. Measurement of heat transfer on the blunted cone at the attack angle in transient and bypass flow state. Raketnaya tekhnika i kosmonavtika, 1972, vol. 10, no. 10, pp. 71--79 (in Russ.).

[4] Widhopf G.F., Hall R. Laminar, transitional and turbulent heat transfer measurement on a yawed blunt conical nosetip. AIAA J., 1972, vol. 10, no. 10. DOI: https://doi.org/10.2514/3.50376

[5] Cebeci T., Smith A.M.O. Analysis of turbulent boundary layers. New York, Academic Press, 1974.

[6] Gorskiy V.V., Loktionova A.G. Modified algebraical Cebeci --- Smith turbulent viscosity model for the entire surface of a blunted cone. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2020, no. 4, pp. 28--41 (in Russ.).

[7] Hirschfelder J.O., Curtiss Ch.F., Bird R.B. Molecular theory of gases and liquids. Chapman and Hall, 1954.

[8] Gorskiy V.V., Fedorov S.N. An approach to calculation of the viscosity of dissociated gas mixtures formed from oxygen, nitrogen, and carbon. J. Eng. Phys. Thermophy., 2007, vol. 80, no. 5, pp. 948--953. DOI: https://doi.org/10.1007/s10891-007-0126-5

[9] Gorskiy V.V., Pugach M.A. Estimation of the effect of free-stream turbulence and solid particles on the laminar turbulent transition at hypersonic speeds. TsAGI Science Journal, 2016, vol. 47, no. 1, pp. 15--28. DOI: 10.1615/TsAGISciJ.2016017056

[10] Gorskiy V.V., Loktionova A.G. Heat exchange and friction in a thin air laminar-turbulent boundary layer over a hemisphere surface. Matematicheskoe modelirovanie i chislennye metody [Mathematical Modeling and Computational Methods], 2019, no. 2, pp. 51--67 (in Russ.).

[11] Gorskiy V.V., Loktionova A.G. Heat transfer and friction in a thin air laminar boundary layer over semi-sphere surface. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2020, no. 2, pp. 17--33 (in Russ.). DOI: https://doi.org/10.18698/0236-3941-2020-2-17-33

[12] Linnik Yu.V. Metod naimen’shikh kvadratov i osnovy matematiko-statisticheskoy teorii obrabotki nablyudeniy [Least squares method and fundamentals of mathematical-statistical observations processing theory]. Moscow, FIZMATGIZ Publ., 1958.

[13] Aoki M. Introduction to optimization techniques. Fundamentals and applications of nonlinear programming. New York, Macmillan, 1971.

[14] Avduevskiy V.S., Koshkin V.K., eds. Osnovy teploperedachi v aviatsionnoy i raketno-kosmicheskoy tekhnike [Foundations of heat transfer in aviation and rocket-space technics]. Moscow, Mashinostroenie Publ., 1975.