Heat Fluxes Estimation in the Stagnation Point Neighborhood by the Modified Effective Length Method

Aeronautical and Space-Rocket Engineering


Аuthors

Minyushkin D. N.*, Braga A. V.**

Moscow Institute of Physics and Technology (National Research University), 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia

*e-mail: minyushkin.dn@yandex.ru
**e-mail: braga.av@phystech.edu

Abstract

Currently, methods for modeling the aircraft motion in the atmosphere are being actively developed. Tasks related to the full calculation of loads along the trajectory remain relevant, and methods for the trajectory optimizing and/or aircraft design, which require computing both power and thermal loads on the aircraft structure as a routine mass operation, are being actively elaborated. Solving the Navier-Stokes equations does not allow fulfilling these tasks in the format of a routine mass operation due to their high resource intensity. Thus, engineering methods that enable the heat fluxes estimation with relatively high computational speed are currently relevant. The effective length method is one of these methods.
The purpose of this work consists in modifying the effective length method to obtain smooth laminar heat fluxes in the spreading area.
The main idea of the work is a combination of the two approaches: integration along the streamline in the spreading area and application of engineering formulas outside the spreading area. The field integration in the spreading area is performed along the streamline built on a paraboloid, one of which properties consists in the presence of two symmetrical planes. Integration along the streamline follows the Buhl’s rule, which is of a high order of accuracy, which allows ensuring low computational error in the spreading area, i.e. the area where the effective length tends to zero. Besides, the paraboloid parameters are used to compute the surface curvature in the spreading area, enabling the velocity gradient computing, which is used further to determine the laminar heat flux. The article reflects mathematical formulation for laminar-turbulent transition modeling based on the local Reynolds number plotted along the momentum loss thickness of the laminar boundary layer.
The article demonstrates the results of the heat flux simulation on a sphere with a radius of R = 1m, a Mach number of 6, and pressure and temperature of 300 Pa and 250 K, respectively. A comparison with experimental data for laminar-turbulent transition on a sphere with a radius of R = 6.35cm, a Mach number of 5, and pressure and temperature of 4424 Pa and 73.6 K, respectively, is provided as well. These comparisons revealed close agreement for laminar heat fluxes and an overestimation of turbulent fluxes. The heat fluxes uprating is typical for the engineering effective length method and its application will not lead to errors in practical computations.
The article presents the results of the heat flux simulations on a complex-shaped body, namely the Juno meteoroid. Its surface contains concaves, cavities, and lacks a symmetric shape. The gas-dynamic computing was performed at an altitude of 70 km and a velocity of Mach 6. The simulation demonstrated the algorithm stability and ability to perform computations on bodies of various shapes.
The authors demonstrate the relative speed of the heat fluxes obtaining. The modified version of the program operates longer while separate processing of the spreading area, but this time remains incomparably small relative to the external flow-around problem solving.

Keywords:

convective heat flows, effective length method, spreading area, laminar-turbulent transition

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