title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð° Ð³Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ Â«Ð¤Ð¾ÑÐ¼ÑÐ»Ð° Ð¡ÑÑÐ´ÐµÐ½ÑÂ»
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 optimization of the rear wing of the Â«Formula StudentÂ» racing car
Creators: name: Ð¡ÐµÐ¼ÐµÐ½ÑÑÐ°, ÐÐ»ÐµÐºÑÐµÐ¹
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: 2024
Subjects: Ð·Ð°Ð´Ð½ÐµÐµ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð¾ Ð³Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ°
Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾-ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½ÑÐ¹ Ð¿ÐµÑÐµÑ Ð¾Ð´
rear wing of a racing car
numerical optimization
Reynolds-averaged Navier-Stokes equations
laminar-turbulent transition

description: ÐÐ°Ð´Ð½ÐµÐµ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð¾ Ð³Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ ÑÐ²Ð»ÑÐµÑÑÑ Ð²Ð°Ð¶Ð½ÑÐ¼ ÐµÐ³Ð¾ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð¼, Ð¿Ð¾ÑÑÐ¾Ð¼Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ ÑÐ²Ð»ÑÑÑÑÑ Ð·Ð½Ð°ÑÐ¸Ð¼ÑÐ¼Ð¸ Ð·Ð°Ð´Ð°ÑÐ°Ð¼Ð¸ Ð¿ÑÐ¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð³Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð·Ð°Ð´Ð½ÐµÐ³Ð¾ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð° Ð³Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ Â«TreÂ» ÑÐµÑÐ¸Ð¸ Â«Ð¤Ð¾ÑÐ¼ÑÐ»Ð° Ð¡ÑÑÐ´ÐµÐ½ÑÂ» Ñ ÑÐµÐ»ÑÑ Ð¼Ð°ÐºÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ¾Ð·Ð´Ð°Ð²Ð°ÐµÐ¼Ð¾Ð¹ Ð¸Ð¼ Ð¿ÑÐ¸Ð¶Ð¸Ð¼Ð½Ð¾Ð¹ ÑÐ¸Ð»Ñ. ÐÐ¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¿ÑÑÐµÐ¼ Ð¿Ð¾Ð²Ð¾ÑÐ¾ÑÐ° Ð·Ð°Ð´Ð½ÐµÐ³Ð¾ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ° Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð°. Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð°, ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð½Ð° Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ, ÑÐ²Ð»ÑÐµÑÑÑ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµÐ¹, Ð¿Ð¾ÑÑÐ¾Ð¼Ñ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ ÑÐ¿ÑÐ¾ÑÐµÐ½Ð½Ð°Ñ Ð´Ð²ÑÐ¼ÐµÑÐ½Ð°Ñ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ° Ð² Ð¾ÑÑÑÐ²Ðµ Ð¾Ñ Ð°Ð²ÑÐ¾Ð¼Ð¾Ð±Ð¸Ð»Ñ. ÐÐµÑÐ¾Ð´Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ°ÑÑÐµÑÑ, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½ÑÐµ Ð² ÑÐ°Ð±Ð¾ÑÐµ, Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¸ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±Ð»Ð¾ÑÐ½Ð¾-ÑÑÑÑÐºÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ ÑÐµÑÐºÐ¸. ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐ°ÑÑÐµÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð² Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ Ð·Ð°Ð´Ð½ÐµÐ³Ð¾ Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð° Ð² Ð¿ÑÐµÐ´Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¸ Ð¿Ð¾Ð»Ð½Ð¾ÑÑÑÑ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÐµÐ³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ (Ð¼Ð¾Ð´ÐµÐ»Ñ k-Ï SST) Ð¸ Ñ ÑÑÐµÑÐ¾Ð¼ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾-ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° (ÐÐ¢Ð), Ð¿ÑÐµÐ´ÑÐºÐ°Ð·ÑÐ²Ð°ÐµÐ¼Ð¾Ð³Ð¾ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Î³-alg-SST. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¸, ÑÑÐ¾ Ð¿ÑÐ¸ Ð¿Ð¾Ð»Ð½Ð¾ÑÑÑÑ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ð¼ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ð¸ ÑÐµÑÐµÐ½Ð¸Ðµ ÑÐ²Ð»ÑÐµÑÑÑ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐ¼, Ð° Ð¿ÑÐ¸ ÑÑÐµÑÐµ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° â Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐ¼. Ð ÑÑÐ¾Ð¼ ÑÐµÑÐµÐ½Ð¸Ð¸ ÑÐ¾ÑÐ¼Ð¸ÑÑÑÑÑÑ Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐµ Ð»Ð¾ÐºÐ°Ð»ÑÐ½ÑÐµ Ð¾ÑÑÑÐ²Ð½ÑÐµ Ð·Ð¾Ð½Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÐÐ¢Ð, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½Ð¾Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½Ð° Ð²ÑÑ ÑÑÑÑÐºÑÑÑÑ Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð»Ð¸ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÐÐ¢Ð Ð½Ð° Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð½ÑÐµ Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð°, Ð¿ÑÐ¸ ÑÑÐ¾Ð¼ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ ÑÐ³Ð»Ð° Ð¿Ð¾Ð²Ð¾ÑÐ¾ÑÐ° Ð·Ð°Ð´Ð½ÐµÐ³Ð¾ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ° Ð°Ð½ÑÐ¸ÐºÑÑÐ»Ð° Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¾ Ð¼Ð¾Ð´ÐµÐ»ÑÐ¼Ð¸ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ Ð¾Ð´Ð¸Ð½Ð°ÐºÐ¾Ð²Ð¾ Ð¸ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ Ð¾ÐºÐ¾Ð»Ð¾ 48Â°.
description: The rear wing of a racing car is an important component, so the determination of the aerodynamic characteristics of the wing, as well as their optimization, are significant tasks during the development of a racing car. The paper involves the numerical optimization of the rear wing of the Â«Formula StudentÂ» racing car Â«TreÂ» with the aim of maximizing the downforce it creates. Optimization is carried out by rotating the rear element of the wing. Numerical optimization of a rear wing mounted on a car is a complex task, so this paper considers a simplified two-dimensional formulation isolated from the car. Methodological calculations carried out in the paper indicated the need to use a block-structured mesh. Various regimes of flow around the rear wing were calculated assuming a fully turbulent flow (k-Ï SST model) and taking into account the laminar-turbulent transition (LTT), predicted using the Î³-alg-SST model. The calculation results showed that the solution of the k-Ï SST model is steady, whereas considering the transition, the solution is unsteady. In this solution, unsteady local separation zones form in the LTT region, which have a global impact on the entire flow structure. The calculation results demonstrated a significant influence of the LTT on the predicted aerodynamic properties of the wing, while the optimal rotation angle of the rear element of the wing being predicted similarly by both models at around 48Â°.