title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ RANS-Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð¹ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾Ð¹ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð¸, ÑÐ°Ð·Ð²Ð¸Ð²Ð°ÑÑÐµÐ¹ÑÑ Ñ Ð²Ð½ÐµÐ·Ð°Ð¿Ð½Ð¾ Ð½Ð°Ð³ÑÐµÐ²Ð°ÐµÐ¼Ð¾Ð¹ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ñ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÐ¼Ð¸ Ð²ÑÑÑÑÐ¿Ð°Ð¼Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Application of RANS-models of turbulence for the calculation of unsteady free convection, developing at a suddenly heated vertical plate with periodically distributed protuberances
Creators: name: Ð¢ÑÑÐ½Ð¾Ð²Ð°, Ð¡ÐµÑÐ°ÑÐ¸Ð¼Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÐ¹ ÑÐ»Ð¾Ð¹
ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð°Ñ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ñ
ÑÑÐ´Ñ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¾Ð²
ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½
Â«temporalÂ»-Ð¿Ð¾Ð´Ñ Ð¾Ð´
numerical simulation
boundary layer
natural convection
rows of cylinders
heat transfer
temporal approach

description: ÐÐ°ÑÑÐ¾ÑÑÐ°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¸ ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½Ð° Ð² ÐµÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾-ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð²Ð½Ð¾Ð¼ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð¼ ÑÐ»Ð¾Ðµ Ð½Ð° Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¸Ð·Ð¾ÑÐµÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ðµ, Ð²Ð¾Ð·Ð¼ÑÑÐ°ÐµÐ¼Ð¾Ð¼ ÑÐ¸ÑÑÐµÐ¼Ð¾Ð¹ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¸ ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð²ÑÑÑÑÐ¿Ð¾Ð², Ð¾ÑÐµÐ½ÐºÐµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð½Ð° ÑÐµÐ¿Ð»Ð¾Ð¾ÑÐ´Ð°ÑÑ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ Ð¿ÐµÑÐ¸Ð¾Ð´Ð° ÑÑÐ´Ð¾Ð² Ð²ÑÑÑÑÐ¿Ð¾Ð² Ð¸ Ð¿Ð¾Ð¸ÑÐºÑ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð²ÑÐ³Ð¾Ð´Ð½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ Ñ ÑÐ¾ÑÐºÐ¸ Ð·ÑÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½Ð°. ÐÐ¿ÐµÑÐ²ÑÐµ Ð´Ð°Ð½Ð½Ð°Ñ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ð° Ð¸ÑÑÐ»ÐµÐ´ÑÐµÑÑÑ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Â«temporalÂ»-Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°, ÑÑÑÑ ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ Ð·Ð°ÐºÐ»ÑÑÐ°ÐµÑÑÑ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð²Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð° Ð½Ðµ Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¾ ÑÐµÑÐµÐ½Ð¾ Ð½ÐµÑÐºÐ¾Ð»ÑÐºÐ¾ Ð·Ð°Ð´Ð°Ñ: 
1. Ð¢ÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ RANS-Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ Ð½Ð° Ð·Ð°Ð´Ð°ÑÐµ Ð¾ ÐµÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð¸ Ð²Ð´Ð¾Ð»Ñ Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ Ð½Ð°Ð³ÑÐµÑÐ¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ð±ÐµÐ· Ð¿ÑÐµÐ¿ÑÑÑÑÐ²Ð¸Ð¹, ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð¿ÑÑÐ¼Ð¾Ð³Ð¾ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. 
2. Ð Ð°ÑÑÐµÑ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð½Ð° Ð¿Ð»Ð°ÑÑÐ¸Ð½Ðµ Ñ Ð²ÑÑÑÑÐ¿Ð°Ð¼Ð¸, ÑÑÐ´Ñ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ñ Ð½Ð° Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ð¸ Ð´ÑÑÐ³ Ð¾Ñ Ð´ÑÑÐ³Ð°, ÑÑÐ¾Ð±Ñ ÑÐ»ÐµÐ´ Ð¾Ñ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ Ð¿ÑÐµÐ´ÑÐ´ÑÑÐµÐ³Ð¾ ÑÑÐ´Ð° Ð½Ðµ Ð´Ð¾ÑÑÐ¸Ð³Ð°Ð» ÑÐ»ÐµÐ´ÑÑÑÐµÐ³Ð¾. 
3. ÐÐ°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÐµÑÐ¸Ð¾Ð´Ð° ÑÑÐ´Ð¾Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¾Ð² Ñ ÑÐµÐ»ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÐµÐ³Ð¾ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð½Ð° ÑÐµÐ¿Ð»Ð¾Ð¾ÑÐ´Ð°ÑÑ, ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¸Ð½ÑÐµÐ³ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ¿Ð»Ð¾Ð²Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐ¾ÐºÐ° Ð½Ð° Ð¿Ð»Ð°ÑÑÐ¸Ð½Ð°Ñ Ñ Ð²ÑÑÑÑÐ¿Ð°Ð¼Ð¸ ÑÐ¾ ÑÐ»ÑÑÐ°ÐµÐ¼ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ð±ÐµÐ· Ð½Ð¸Ñ.
ÐÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ¸Ð¸ Ð½Ð° Ð¿Ð»Ð°ÑÑÐ¸Ð½Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¿ÑÐµÐ¿ÑÑÑÑÐ²Ð¸Ð¹ Ð¿ÑÐ¾ÑÐ¸Ð²Ð¾Ð¿Ð¾Ð»Ð¾Ð¶Ð½Ð¾ Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð´Ð²ÑÑ ÑÐ°ÐºÑÐ¾ÑÐ¾Ð², Ð²Ð»Ð¸ÑÑÑÐ¸Ñ Ð½Ð° ÑÐµÐ¿Ð»Ð¾Ð²Ð¾Ð¹ Ð¿Ð¾ÑÐ¾Ðº Ð¾Ñ ÑÑÐµÐ½ÐºÐ¸: Ñ Ð¾Ð´Ð½Ð¾Ð¹ ÑÑÐ¾ÑÐ¾Ð½Ñ, Ð²ÑÑÑÑÐ¿Ñ ÑÐ¾ÑÐ¼Ð¾Ð·ÑÑ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¸, ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾, Ð¾ÑÐ»Ð°Ð±Ð»ÑÑÑ ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½, Ð° Ñ Ð´ÑÑÐ³Ð¾Ð¹, Ð¾Ð½Ð¸ ÑÐ¿Ð¾ÑÐ¾Ð±ÑÑÐ²ÑÑÑ Ð²Ð¾Ð·Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ ÐºÑÑÐ¿Ð½Ð¾Ð¼Ð°ÑÑÑÐ°Ð±Ð½ÑÑ Ð²Ð¸ÑÑÐµÐ²ÑÑ ÑÑÑÑÐºÑÑÑ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸Ð½ÑÐµÐ½ÑÐ¸ÑÐ¸ÑÐ¸ÑÑÑÑ ÑÐµÐ¿Ð»Ð¾Ð¾ÑÐ´Ð°ÑÑ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿ÑÐ¸ Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ ÑÐ¾Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ð¸ Ð²ÑÑÐ¾ÑÑ Ð¿ÑÐµÐ¿ÑÑÑÑÐ²Ð¸Ð¹ Ð¸ ÑÐ¾Ð»ÑÐ¸Ð½Ñ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ Ð²ÑÐ¾ÑÐ¾Ð¹ ÑÐ°ÐºÑÐ¾Ñ Ð¿ÑÐµÐ²Ð°Ð»Ð¸ÑÑÐµÑ, Ð¸ Ð² ÑÐ°ÐºÐ¾Ð¼ ÑÐ»ÑÑÐ°Ðµ ÑÐµÑÐµÑÐºÐ¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð²ÑÑÑÑÐ¿Ð¾Ð² ÑÐµÐ»ÐµÑÐ¾Ð¾Ð±ÑÐ°Ð·Ð½Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð´Ð»Ñ Ð»ÑÑÑÐµÐ³Ð¾ Ð¾ÑÐ»Ð°Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÐµÐ¹.
description: This work is devoted to studying the flow and heat transfer in a naturally convective boundary layer on a vertical isothermal plate perturbed by a system of periodically arranged cylindrical ledges, assessing the effect of the period of rows on the heat transfer, and finding the most favorable conditions to heat transfer intensification. For the first time this problem is investigated using the âtemporalâ approach, the essence of which is to simulate the development of the flow not in space, but in time. Several tasks were solved:
1. Testing various RANS-models of turbulence in conditions of natural convection along an infinite heated plate without obstacles, comparing the results with direct numerical simulation data.
2. Calculation of 3-D flow on a plate with protrusions, the rows of which are located at an enough distance from each other so that the trace from the flow past the previous row does not reach the next.
3. Varying the period of the rows of cylinders in order to determine its effect on heat transfer, comparing the specific integral heat flux on the plates with projections with the case of the plate without them.
In the case of ledges on the plate, there is a struggle between two factors affecting the heat flux: on the one hand, the ledges inhibit the flow and, therefore, reduce heat transfer, and on the other, they contribute to the emergence of large-scale vortex structures that intensify heat transfer. It is shown that for a certain ratio of the height of cylinders and the thickness of the boundary layer the second factor prevails, and in this case, it is advisable to use system of cylindrical ledges for better cooling of the surfaces.