title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÑÐµÐ» Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð²ÑÑÐ¾ÐºÐ¾ÑÐºÐ¾ÑÐ¾ÑÑÐ½ÑÐ¼ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð¼ Ð²ÑÐ·ÐºÐ¾Ð³Ð¾ Ð³Ð°Ð·Ð° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ¾Ð´Ð° Eilmer
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Numerical simulation of supersonic flow over axisymmetric bodies using the Eilmer code
Creators: name: ÐÑÐ°Ð´ÑÐ¸Ð¹, ÐÐ°Ð½Ð¸Ð¸Ð»
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: 2023
Subjects: Ð²ÑÑÐ¾ÐºÐ¾ÑÐºÐ¾ÑÐ¾ÑÑÐ½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ
ÑÐµÐ»Ð° Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÑÐµÐ¼ÑÐµ ÐºÐ¾Ð´Ñ
high-speed flows
axisymmetric bodies
numerical simulation
free software tools

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐµÑÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ð¹ Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ Ñ Ð¾ÑÐºÑÑÑÑÐ¼ Ð¸ÑÑÐ¾Ð´Ð½ÑÐ¼ ÐºÐ¾Ð´Ð¾Ð¼ Eilmer (ÐÐ²Ð¸Ð½ÑÐ»ÐµÐ½Ð´, ÐÐ²ÑÑÑÐ°Ð»Ð¸Ñ). ÐÐ°Ð´Ð°ÑÐ¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÑÐ±Ð¾Ñ Â«Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð¸ÑÐµÐ»ÑÐ½ÑÑÂ» Ð¼Ð¾Ð´ÐµÐ»ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¾Ð± Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ð¸ ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²ÑÐ¼ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð¼ ÑÐµÐ» Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð¹ ÑÐ¾ÑÐ¼Ñ. 2. ÐÐ±Ð·Ð¾Ñ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½ÑÑ Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ¾Ð², Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð½ÑÑ Ð·Ð°Ð´Ð°ÑÐµ ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÑÐµÐ» Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð¼ Ð³Ð°Ð·Ð°; Ð²ÑÐ±Ð¾Ñ Ð½Ð°Ð´ÐµÐ¶Ð½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ Ð²Ð°Ð»Ð¸Ð´Ð°ÑÐ¸Ð¸. 3. ÐÐ¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ° Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð´Ð»Ñ Â«Ð¿ÑÐ¾ÑÑÑÑÂ» ÑÐµÑÑÐ¾Ð²ÑÑ Ð·Ð°Ð´Ð°Ñ (ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð² ÐºÐ°Ð½Ð°Ð»Ðµ Ñ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½ÑÐ¼ ÐºÐ»Ð¸Ð½Ð¾Ð¼, Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½ÑÐ¹ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÐ¹ ÑÐ»Ð¾Ð¹) Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ¾Ð´Ð° Eilmer; ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð¿Ð¾ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-Ð¾Ð±ÑÑÐ¼Ð½Ð¾Ð¼Ñ Â«Ð½ÐµÑÑÑÑÐºÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¼ÑÂ» ÐºÐ¾Ð´Ñ SINF/Flag-S (Ð¡ÐÐ±ÐÐ£). 4. Ð Ð°ÑÑÐµÑÑ ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÑÑÐµÑ ÑÐµÐ» Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ: Ð·Ð°ÑÑÐ¿Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ ÐºÐ¾Ð½ÑÑÑ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°, Ð·Ð°ÑÑÐ¿Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ ÑÑÐµÑÐµ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð¸ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð½ÑÑÐ°. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°ÑÑÐµÑÐ° Â«Ð¿ÑÐ¾ÑÑÑÑÂ» ÑÐµÑÑÐ¾Ð²ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð¾ÑÐµÐ½ÐºÐ° ÐºÐ°ÑÐµÑÑÐ²Ð° ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ´Ð°ÑÐ½Ð¾-Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð¹ ÐºÐ°ÑÑÐ¸Ð½Ñ ÑÐµÑÐµÐ½Ð¸Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð²ÑÐ·ÐºÐ¸Ñ ÑÑÑÐµÐºÑÐ¾Ð² Ð² Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð¼ ÑÐ»Ð¾Ðµ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² ÑÐ¾ÑÐ¾ÑÐ¾ ÑÐ¾Ð³Ð»Ð°ÑÑÑÑÑÑ Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð° ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÑ ÑÐµÑÐµÐ½Ð¸Ñ Ðº Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾Ð¼Ñ ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ñ. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°ÑÑÐµÑÐ° ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÑÑÐµÑ ÑÐµÐ» Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ: Ð·Ð°ÑÑÐ¿Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ ÐºÐ¾Ð½ÑÑÑ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°, Ð·Ð°ÑÑÐ¿Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ ÑÑÐµÑÐµ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð¸ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð½ÑÑÐ°. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð° ÑÐ»Ð¾Ð¶Ð½Ð°Ñ ÑÑÑÑÐºÑÑÑÐ° ÑÐµÑÐµÐ½Ð¸Ñ, ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÑÑÐ°ÑÑÑ ÑÑÑÐµÐºÑÐ°Ð¼Ð¸ Ð²ÑÐ·ÐºÐ¾-Ð½ÐµÐ²ÑÐ·ÐºÐ¾Ð³Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ. ÐÐ»Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÐºÐ¾Ð½ÑÑÐ° Ð¸ ÑÑÐµÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ñ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐ¼Ð¸ Ð¸Ð· Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¾ÑÐµÐ½ÐºÐ°Ð¼Ð¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² ÑÐ²ÐµÑÑÐ·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð½ÑÑÐ°, Ð² ÑÐµÐ»Ð¾Ð¼, ÑÐ¾ÑÐ¾ÑÐ¾ ÑÐ¾Ð³Ð»Ð°ÑÑÑÑÑÑ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐ¼Ð¸ Ð¸Ð· Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸.
description: The given work is devoted to the solution of model problems of supersonic aerodynamics using the free software Eilmer. Research objectives: 1. Selection of "representative" model problems of supersonic flow over axisymmetric bodies 2. Review of literature sources devoted to the problem of supersonic laminar flow over axisymmetric bodies; selection of reliable experimental data for validation. 3. Definition and performing verification calculations for "simple" test problems (supersonic flow in a channel with a central wedge, laminar boundary layer) using the Eilmer code; comparison of the results with the data obtained using the finite-volume "unstructured" code SINF/Flag-S (SPbPU). 4. Calculations of supersonic laminar flow past three axisymmetric bodies: a cylinder blunted along a cone, a cylinder blunted along a sphere, and a double cone. The quality of the resolution of the shock-wave flow pattern and the viscous effects in the boundary layer was evaluated, based on the analysis of the results of calculation of "simple" test problems. It is shown that the calculation results are in good agreement with the analytical data. The sensitivity of the solution to the spatial resolution is investigated. An analysis is made of the results of calculating a supersonic laminar flow around three bodies of revolution: a cylinder blunted along the cone, a cylinder blunted along the sphere, and a double cone. The complex structure of the flow, characterized by the effects of viscous-inviscid interaction, has been studied. For the problem of flow past a cone and a sphere, the calculation results are compared with analytical data known from the literature. It is shown that the results of calculations of the supersonic flow around a double cone, in general, are in good agreement with experimental data known from the literature.