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Drag of a strongly heated sphere at small Reynolds numbers

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Abstract

Using an asymptotic small-perturbation method, the flow around a strongly heated sphere at small Reynolds numbers Re ≪ 1 is considered with account for thermal stresses in the gas in the higher-order approximations, beyond the Stokes one. It is assumed that the value of the Prandtl number Pr is arbitrary and the temperature dependence of the viscosity is described by a power law with an arbitrary exponent. In the O(Re2) and O(Re3 ln(Re)) approximations, the drag force of a heated sphere is found over a wide range of the ratios of sphere’s temperature to the gas free-stream temperature T W /T ∞. The limits of applicability of the first (in Re) approximation are investigated, including the negative-drag effect, attributable to the action of the thermal stresses. The results are compared with numerical calculations of the flow around a hot sphere. The limits of applicability of the approximations found are examined. Similar results are obtained for the standard Navier-Stokes equations in which the thermal stresses are neglected.

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Authors
  1. V. Yu. Aleksandrov
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Original Russian Text © V.Yu. Aleksandrov, 2011, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2011, Vol. 46, No. 5, pp. 142–156.

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Aleksandrov, V.Y. Drag of a strongly heated sphere at small Reynolds numbers. Fluid Dyn 46, 794–808 (2011). https://doi.org/10.1134/S0015462811050139

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