On the question of computing convective heat transfer parameters in a laminar-to-turbulent boundary layer on an impermeable hemispherical surface

In order to qualitatively solve the problem of computing convective heat transfer parameters in a laminar-to-turbulent boundary layer, it is necessary to numerically integrate differential equations descrybing that layer, completed by semiempirical turbulent viscosity models. These must be validated using results of experimental investigations where the gas dynamics of a gas flow around a body is correctly simulated. In terms of practical applications, developing relatively simple yet highly accurate computation methods is important. At present, the most widely used method to solve this type of problems in aviation and aerospace engineering is the effective length method developed by V.S. Avduevskiy, Academician. The paper shows that significant errors characterise computations using this method and traditional turbulent viscosity models to determine parameters of those blunted components of aircraft that are subjected to the highest temperatures. We present a solution to this problem, based on constructing systematic numerical solutions to the equations describing the laminar-to-turbulent boundary layer and subsequently approximating them. We prove that this approach ensures both acceptable computation accuracy and solution simplicity

References

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

[2] Gorskiy V.V., Pugach M.A. Laminar-turbulent heat transfer on the surface of a hemisphere in hypersonic air flow. TsAGI Science Journal, 2014, vol. 45, no. 8, pp. 903--913. DOI: 10.1615/TsAGISciJ.2015013556

[3] Gorskiy V.V. Numerical solution technique of laminar turbulent boundary layer equations on penetratable wall of blunt rotation body. Kosmonavtika i raketostroenie, 2017, no. 3, pp. 90--98 (in Russ.).

[4] Uidkhopf Dzh.F., Kholl R. Heat transfer measurement on blunt cone at the angle of attack in transient and turbulent flow regimes. Raketnaya tekhnika i kosmonavtika, 1972, vol. 10, no. 10, pp. 71 (in Russ.).

[5] Widhopf G.F. Laminar, transitional and turbulent heat transfer measurement on a yawed blunt conical nosetip. AIAA Journal, 1972, vol. 10, no. 10, pp. 1318--1325. DOI: 10.2514/3.50376

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

[7] Lunev V.V. Method of massaverage quantities for the boundary layer in an outer flow with transverse nonuniformity. Fluid Dyn., 1967, vol. 2, no. 1, pp. 83--86. DOI: 10.1007/BF01024813

[8] Hirschfelder J.O., Curtiss C.F., Bird R.B. The molecular theory of gases and liquids. Wiley-Interscience, 1964.

[9] Gorskii 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: 10.1007/s10891-007-0126-5

[10] 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

[11] Linnik Yu.V. Metod naimen’shikh kvadratov i osnovy teorii obrabotki nablyudeniy [Least square method and fundamentals of observation analysis theory]. Moscow, Fizmatgiz Publ., 1958.

[12] Aoki M. Introduction to optimization techniques. Macmillan, 1971.