Convective Heat Transfer in a Rotating Hollow Cylinder with an End Wall
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tive Heat Transfer in a Rotating Hollow Cylinder with an End Wall V. A. Arkhipova*, O. V. Matvienkoa,b, A. S. Zhukova, and N. N. Zolotoreva,c a
National Research Tomsk State University, Tomsk, 634050 Russia Tomsk State University of Architecture and Building, Tomsk, 634003, Russia c Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia *e-mail: [email protected] b
Received September 24, 2019; revised April 13, 2020; accepted April 16, 2020
Abstract—A method and calculation results are presented for the flow field and convective heat transfer in a hollow cylinder having an end wall and rotating about the axis of symmetry under variation of the angular velocity of rotation and cylinder height. Keywords: hollow cylinder, end wall, angular velocity of rotation, flow field, convective heat transfer, mathematical modeling. DOI: 10.1134/S1063785020070159
Rotating elements are widely used in gas turbines, aircraft engines, chemical engineering equipment, and industrial and laboratory devices. Rotation of elements leads to significant changes in conditions of their heat transfer [1]. In the particular, characteristics of ignition of condensed substance samples by multimode laser radiation are measured using the method of spatial averaging of the radiation intensity by rotating the cylindrical sample [2]. Rotation of a condensed substance sample is accompanied by the appearance of convective heat transfer between the irradiated end surface (disk) and immobile surrounding medium (air). The intensity of the transfer increases as the surface is heated by the laser radiation. Regularities in the convective heat transfer of rotating elements were considered in the literature in detail for a disk and a hollow cylinder without end walls [3–7]. This work presents results of calculation of the f low field and heat transfer in a hollow rotating cylinder with an end wall (Fig. 1). Let the surface of a rotating disk with radius R (of a cylinder with wall height h = 0) be uniformly heated to temperature Ts. The density of convective heat flow from the surface to an immobile medium is determined by the relationship (1) q = λ (Ts − T )Nu, R where T is the temperature of the surrounding medium and λ is the heat conduction coefficient of the medium.
The Nusselt number during the flow past the disk rotating with angular velocity ω (rad/s) is determined by the relationship [8]
Nu = 0.388 Reω Pr,
(2)
where Reω = ρωR2/μ is the rotational Reynolds number, Pr = μcp/λ is the Prandtl number, and ρ, μ, and cp are the density, dynamic viscosity coefficient, and specific heat capacity at constant pressure of the surrounding medium. The calculation results for q by formulas (1) and (2) depending on Ts and rotation frequency n = 30ω/π (rpm) for the thermal and physical characteristics of air λ = 0.0244 W/(m K), ρ = 1.205 kg/m3, Pr = 0.72, μ = 1.8 × 10–5 Pa s, cp = 1008 J/(kg K), and T = 293 K are presented in Table 1. Rotation of a hollow cylinder with a wall height h ≠ 0 has a significant
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