EFFECT OF HEAT SUPPLY TO A NARROW BAND OF THE BOUNDARY LAYER ON ITS STABILITY
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EFFECT OF HEAT SUPPLY TO A NARROW BAND OF THE BOUNDARY LAYER ON ITS STABILITY S. A. Gaponov∗
UDC 532.526
Abstract: Stability of a subsonic boundary layer with heat supply into its narrow band is studied. The maximum length of the stable boundary layer in the case of heat supply is found to be approximately three times smaller as compared to the case of a thermally insulated wall without heat supply. The frequency range of disturbances and their growth rates are approximately doubled. In contrast to the case without heat supply, three-dimensional disturbances are the most rapidly growing disturbances. In the case of a heated wall, the growth rate of disturbances decreases after heat supply into the boundary layer, which may lead to an increase in the length of the laminar region of the boundary layer. Keywords: boundary layer, stability, heat supply, flame, self-similar, disturbances. DOI: 10.1134/S0021894420050016
INTRODUCTION Heat supply to a narrow band of the boundary layer can be considered as an approximate model of the diffusion flame formed in the case of fuel injection through a porous wall with a nearby flow of the oxidizer. Many investigations of diffusion combustion in the boundary layer are based on solving the Emmons problem [1]. The problem of laminar diffusion combustion was considered in much detail [2]. The problem of stability of laminar diffusion combustion is less studied. The first investigations of stability of laminar flows in the presence of the diffusion flame were performed for the fuel–oxidizer mixing layer or with jet injection of the fuel into the oxidizer. The problem of stability was studied in the inviscid approximation, and viscosity in stability equations was neglected [3]. Direct numerical simulations have been used since the 1980s in addition to approximate methods [4, 5]. Stability of the boundary layer with combustion of the fuel injected through a permeable surface and burning in the oxidizer layer has not been studied until now. The complexity of solving the problem in the presence of the flame is caused by the necessity of taking into account the gas composition. It is known, however, that flow stability is mainly determined by the distributions of the streamwise velocity and density. In the presence of the flame, the density mainly depends on temperature, which can be modeled by concentrated heat sources. Thus, the temperature distribution in the diffusion flame is modeled in the present study by a heat source in the boundary layer. The study is performed for a subsonic flow past a flat plate with the Mach number M 1.
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia; ∗ [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 5, pp. 5–13, September–October, 2020. Original article submitted May 18, 2020; revision submitted May 18, 2020; accepted for publication May 25, 2020. ∗ Corresponding author. c 2020 by Pleiades Publishing, Ltd. 0021-8944/20/6105-0685
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