Numerical Integration Method for Three-Dimensional Equations of Laminar-to-Turbulent Boundary Layer on a Spherically Blunted Circular Cone Featuring a Low Aspect Ratio

Authors: Gorskiy V.V. Published: 12.09.2022
Published in issue: #3(142)/2022  

DOI: 10.18698/0236-3941-2022-3-4-17

Category: Aviation and Rocket-Space Engineering | Chapter: Aerodynamics and Heat Transfer Processes in Aircrafts  
Keywords: numerical method, boundary layer, laminar-to-turbulent flow, heat transfer


At present, the Navier --- Stokes equations are the most popular tool used to study three-dimensional heat transfer and friction. This approach significantly improves the investigation quality in the case of geometrically complex bodies, which confirms the validity of using this involved computational procedure in practice. In the case of simple geometries widely used in engineering to design refractory structural elements of high-energy devices, however, the Navier --- Stokes equations are inferior to the equations of the laminar-to-turbulent boundary layer in a number of aspects. There are no published accounts regarding experimental data on heat transfer in the blunted regions of refractory structural elements shaped as blunted cones at extremely high Reynolds numbers. Employing the boundary layer equations made solving this problem possible. Using the Navier --- Stokes equations to solve problems in which the body surface changes over time results in considerable issues. At the same time, not enough attention is paid to methodology for rigorously solving the three-dimensional equations of the laminar-to-turbulent boundary layer; in this regard, developing a modern method for solving the problem under consideration is of certain interest

Please cite this article in English as:

Gorskiy V.V. Numerical integration method for three-dimensional equations of laminar-to-turbulent boundary layer on a spherically blunted circular cone featuring a low aspect ratio. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2022, no. 3 (142), pp. 4--17 (in Russ.). DOI: https://doi.org/10.18698/0236-3941-2022-3-4-17


[1] Vaglio-Laurin R. Laminar heat transfer on three-dimensional blunt nosed bodies in hypersonic flow. ARS J., 1959, no. 2, pp. 123--129. DOI: https://doi.org/10.2514/8.4698

[2] Avduevskiy V.S. Calculation of 3-dimensional laminar boundary layer on spreading lines. Izv. AN SSSR. Mekhanika i mashinostroenie, 1962, no. 1, pp. 123--130 (in Russ.).

[3] Bashkin V.A. Design ratios and programs for numerical equations integration of spatial boundary layer on cone bodies. Trudy TsAGI, 1968, no. 106, pp. 97--118 (in Russ.).

[4] Dorodnitsyn A.A. On a method for solving equations of laminar boundary layer. PMTF, 1960, no. 3, pp. 111--118 (in Russ.).

[5] Bashkin V.A., Kolina N.P. Calculation of friction resistance and heat transfer on spherical blunt circular cones in supersonic flows. Trudy TsAGI, 1968, no. 106, pp. 119--181 (in Russ.).

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

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

[8] Shevelev Yu.D. Trekhmernye zadachi teorii laminarnogo pogranichnogo sloya [Three-dimensional of laminar boundary layer theory]. Moscow, Nauka Publ., 1977.

[9] Aleksin V.A. Modelirovanie turbulentnykh szhimaemykh pristennykh techeniy [Modelling of turbulent compressible flows]. V kn.: Giperzvukovaya aerodinamika i teplomassoobmen spuskaemykh kosmicheskikh apparatov i planetnykh zondov [In: Hypersonic aerodynamics and heat transfer of descent space vehicles and planetary probes]. Moscow, FIZMATLIT Publ., 2011, pp. 458--487 (in Russ.).

[10] Gorskiy V.V. Teoreticheskie osnovy rascheta ablyatsionnoy teplovoy zashchity [Theoretical foundations of calculating ablative heat protection]. Moscow, Nauchnyy mir Publ., 2015.

[11] Samarskiy A.A. Vvedenie v teoriyu raznostnykh skhem [Introduction into theory of difference chemes]. Moscow, Nauka Publ., 1971.

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

[13] 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 [Cosmonautics and Rocket Engineering], 2017, no. 3, pp. 90--98 (in Russ.).

[14] 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 (133), pp. 28--41 (in Russ.). DOI: http://dx.doi.org/10.18698/0236-3941-2020-4-28-41

[15] 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.).

[16] 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

[17] Shirakhi S.A., Trumen K.R. Comparison of algebraic turbulence models at the example of calculation using parabolized Navier --- Stokes equation of supersonic flow past a cone with spherical nosetip. Aerokosmicheskaya tekhnika, 1990, no. 10, pp. 69--81 (in Russ.).