Simulating Heat Flows Supplied to the Surface of a Blunt Convex Rotation Body in the Supersonic Gas Flow

Abstract

The paper presents analytical dependencies making it possible to determine the laminar relative heat flow supplied to the surface of a blunt rotation body flown around by the supersonic gas flow. Since solving the corresponding Navier --- Stokes or boundary layer equations requires serious time effort, obtaining such dependencies becomes an important tool in preliminary estimation of the heat flow significant parameters. The currently existing approximate formulas were obtained primarily for the spherical bluntness. In the case of studying the gas flow around ellipsoids, paraboloids and other convex surfaces, the local spheres rule is applied, when the heat flow on the body is accepted to be the same as on the sphere with the angles of the flow meeting the body surface and the sphere under consideration coincide. This approach often produces an error unacceptable in the engineering calculations. This is because formulas for the sphere were obtained based on a large number of simplifications. The obtained dependence is not limited to the spherical noses and was obtained for the case of a cold wall and large values of the Reynolds number. By comparing with the numerical solutions, the paper shows that the obtained dependence perfectly describes relative heat flow to the wall. The data obtained makes it possible to assess the heat flow values that are critical for a product at the early design stages

Please cite this article in English as:

Kotenev V.P., Resh V.G., Sysenko V.A. Simulating heat flows supplied to the surface of a blunt convex rotation body in the supersonic gas flow. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2024, no. 2 (149), pp. 109--120 (in Russ.). EDN: SPXFBV

References

[1] Dimitrienko Yu.A., Koryakov M.N., Zakharov A.A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Matematicheskoe modelirovanie i chislennye metody [Mathematical Modeling and Computational Methods], 2015, no. 4, pp. 75--91 (in Russ.).

[2] Berger K., Greene F., Kimmel R., et al. Aerothermodynamic testing and boundary-layer trip sizing of the HIFire flight 1 vehicle. JSR, 2009, vol. 46, no. 2, pp. 473--480. DOI: https://doi.org/10.2514/1.43927

[3] Toro E.F. Riemann solvers and numerical methods for fluid dynamics. Heidelberg, Springer, 2009.

[4] Zemlyanskiy B.A., ed. Konvektivnyy teploobmen letatelnykh apparatov [Convective heat transfer of aircraft]. Moscow, FIZMATLIT Publ., 2014.

[5] Gross A., Fasel H.F. High-order-accurate numerical method for complex flows. AAIA J., 2008, vol. 46, no. 1, pp. 204--214. DOI: https://doi.org/10.2514/1.22742

[6] Gorskiy V.V., ed. Matematicheskoe modelirovanie teplovykh i gazodinamicheskikh protsessov pri proektirovanii letatelnykh apparatov [Mathematical modeling of heat and gas dynamic processes in aircraft design]. Moscow, BMSTU Publ., 2011.

[7] Belotserkovskiy O.M., Andrushchenko V.A., Shevelev Yu.D. Dinamika prostranstvennykh vikhrevykh techeniy v neodnorodnoy atmosphere [Dynamic of spatial turbulence flow in nonuniform atmosphere]. Moscow, Yanus-K Publ., 2000.

[8] Anderson D.E., Tannehill J.C., Pletcher R.H. Computational fluid mechanics and heat transfer.‎ Washington, Hemisphere, 1984.

[9] Shirakhi S.A., Trumen K.R. Comparison of algebraic turbulence models using parabolized Navier --- Stokes equations for supersonic flow of cone with spherical head. Aerokosmicheskaya tekhnika, 1990, no. 10, pp. 69--81 (in Russ.).

[10] 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 (131), pp. 17--33 (in Russ.). DOI: http://dx.doi.org/10.18698/0236-3941-2020-2-17-33

[11] Pokrovskiy A.N., Frolov L.G. Approximate relationships for the determination of the pressure on the surface of a sphere or cylinder with an arbitrary Mach number in the free stream. Fluid Dyn., 1985, vol. 20, no. 2, pp. 329--332. DOI: https://doi.org/10.1007/BF01091054

[12] Kotenev V.P. Accurate dependence for determining the pressure distribution on a sphere at an arbitrary Mach number of a supersonic incoming flow. Matematicheskoe modelirovanie [Mathematical Modeling], 2014, vol. 26, no. 9, pp. 141--148 (in Russ.). EDN: TFRUWV

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

[14] Kotenev V.P., Sysenko V.A. Heat transfer modeling on the surface of a sphere in a gas flow. Matematicheskoe modelirovanie i chislennye metody [Mathematical Modeling and Computational Methods], 2023, no. 2, pp. 90--99 (in Russ.). EDN: HWBWIL