title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð¿Ð¾ Ð³Ð¾ÑÑÑÐµÐ¹ Ð³Ð°Ð·Ð¾Ð²Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸
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: Numerical modeling of laminar flame propagation through a combustible gas mixture
Creators: name: ÐÑÐ´Ð¸Ð»Ð¸Ð½Ð°, ÐÐ»ÑÐ³Ð°
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: 2021
Subjects: ÐÐ»Ð°Ð¼Ñ
ÐÐ¾ÑÐµÐ½Ð¸Ðµ
Ð¢ÐµÐ¿Ð»Ð¾Ð²Ð¾Ðµ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ðµ
ÐÐ°Ð·Ð¾Ð²ÑÐµ ÑÐ¼ÐµÑÐ¸
ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑÐ¾Ð»ÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸
ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÑÑÐ±ÐºÐ°
thickened flame model
cylindrical tube

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð² Ð·Ð°ÑÐ°Ð½ÐµÐµ Ð¿Ð¾Ð´Ð³Ð¾ÑÐ¾Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸. ÐÑÐ»Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð¼ÐµÑÐ¾Ð´Ñ TFM (Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑÐ¾Ð»ÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸), Ð¸ Ð¼ÐµÑÐ¾Ð´ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð°Ð´Ð°Ð¿ÑÐ°ÑÐ¸Ð¸ ÑÐµÑÐºÐ¸. ÐÑÐ½Ð¾Ð²Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð·Ð°ÐºÐ»ÑÑÐ°ÑÑÑÑ Ð² Ð²ÑÑÐ°Ð±Ð¾ÑÐºÐµ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹, Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²Ð°ÑÑÐµÐ¹ ÑÐ¾Ð³Ð»Ð°ÑÐ¸Ðµ ÑÐ°ÑÑÑÑÐ½Ð¾Ð¹ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð¼ ÐºÐ°Ð½Ð°Ð»Ðµ, Ð·Ð°Ð¿Ð¾Ð»Ð½ÐµÐ½Ð½Ð¾Ð¼ ÑÐ¼ÐµÑÑÑ ÑÑÐ¸Ð»ÐµÐ½Ð° Ð¸ Ð²Ð¾Ð·Ð´ÑÑÐ°, Ñ Ð¾Ð¿ÑÐ±Ð»Ð¸ÐºÐ¾Ð²Ð°Ð½Ð½ÑÐ¼Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼Ð¸ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÑÐ½Ð½ÑÐµ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ: â ÐÐ½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¾Ð±Ð·Ð¾Ñ Ð¾Ð¿ÑÐ±Ð»Ð¸ÐºÐ¾Ð²Ð°Ð½Ð½ÑÑ ÑÐ°Ð±Ð¾Ñ Ð¿Ð¾ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð¿Ð¾ Ð³Ð°Ð·Ð¾Ð²Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸ (Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ: Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÑÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸ Ð½ÐµÐ´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐµÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ð¸; Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ, ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¸ Ð¿ÑÐ¸Ð¼ÐµÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ TFM; Ð¿ÑÐ¸Ð¼ÐµÑÑ ÑÑÑÑÐ¼ÐµÑÐ½ÑÑ ÑÐ°ÑÑÑÑÐ¾Ð²). â ÐÐ½Ð°Ð»Ð¸Ð· ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°ÑÑÑÑÐ¾Ð² Ðº ÑÐµÑÐ¾ÑÐ½Ð¾Ð¼Ñ ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ñ. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ TFM. ÐÐ²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð°Ð´Ð°Ð¿ÑÐ°ÑÐ¸Ñ ÑÐµÑÐºÐ¸. ÐÑÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹. â Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÑÑÑÑ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ansys Fluent. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð¾Ð¿ÑÐ±Ð»Ð¸ÐºÐ¾Ð²Ð°Ð½Ð½ÑÐ¼Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼Ð¸ ÑÐ°ÑÑÑÑÐ¾Ð² Ð¸ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð´Ð»Ñ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸. â ÐÐ½Ð°Ð»Ð¸Ð· ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÑÐ¾Ð½ÑÐ° Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸. Ð Ð¾Ð»Ñ ÑÐµÐ¿Ð»Ð¾Ð²Ð¾Ð³Ð¾ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ñ. â Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½ÑÑ Ð¸ Ð¼Ð½Ð¾Ð³Ð¾ÑÑÐ°Ð´Ð¸Ð¹Ð½ÑÑ ÑÐ¸Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð¾Ð². â ÐÑÑÐ°Ð±Ð¾ÑÐºÐ° ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸Ð¹ Ð¿Ð¾ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹ Ð¿ÑÐ¸ Ð½ÐµÐ´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐµÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ð¸. ÐÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÑ ÑÑÐµÑÐ¼ÐµÑÐ½ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð² Ð·Ð°ÑÐ°Ð½ÐµÐµ Ð¿Ð¾Ð´Ð³Ð¾ÑÐ¾Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð¼ Ð¿ÑÐ¸ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÐºÐ¾ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°. ÐÐ¾ Ð²Ð²ÐµÐ´ÐµÐ½Ð¸Ð¸ Ð¸Ð·Ð»Ð¾Ð¶ÐµÐ½Ð° Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð±Ð¾ÑÑ, ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÐµÐ»Ñ Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ. Ð Ð¿ÐµÑÐ²Ð¾Ð¹ Ð³Ð»Ð°Ð²Ðµ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¾Ð±Ð·Ð¾Ñ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð¼ Ð¿Ð»Ð°Ð¼ÐµÐ½Ð¸ Ð² Ð·Ð°ÑÐ°Ð½ÐµÐµ Ð¿Ð¾Ð´Ð³Ð¾ÑÐ¾Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸, Ð¿ÑÐ¸Ð¼ÐµÑÑ ÐµÐ³Ð¾ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. ÐÐ¾ Ð²ÑÐ¾ÑÐ¾Ð¹ Ð³Ð»Ð°Ð²Ðµ Ð´Ð°ÑÑÑÑ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸ Ð½ÐµÐ´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐµÑÐ¾ÑÐ½Ð¾Ð¼ ÑÐ°Ð·ÑÐµÑÐµÐ½Ð¸Ð¸. Ð ÑÑÐµÑÑÐµÐ¹ Ð³Ð»Ð°Ð²Ðµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð¿Ð°ÐºÐµÑÐ° ANSYS Fluent. Ð ÑÐµÑÐ²ÐµÑÑÐ¾Ð¹ Ð³Ð»Ð°Ð²Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ñ Ð¸ Ð¿ÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°Ð±Ð¾ÑÑ. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ð² ÑÐ¾ÑÑÐ°Ð²Ðµ Ð½Ð°ÑÑÐ½Ð¾Ð¹ Ð³ÑÑÐ¿Ð¿Ñ Â«ÐÐ¾ÑÑÑÐµÑÑÑ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð² Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾Ð¶Ð°ÑÐ°Â» ÐºÐ°ÑÐµÐ´ÑÑ Â«ÐÐ¸Ð´ÑÐ¾Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°, Ð³Ð¾ÑÐµÐ½Ð¸Ðµ Ð¸ ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½Â» ÐÐ½ÑÑÐ¸ÑÑÑÐ° Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð¾Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¸ Ð¸ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸ Ð¡ÐÐ±ÐÐ£. ÐÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÐµ ÑÐµÑÑÑÑÑ Ð¿ÑÐµÐ´Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÑÐ¿ÐµÑÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½ÑÐ¼ ÑÐµÐ½ÑÑÐ¾Ð¼ Â«ÐÐ¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹Â» (Ð¡ÐÐ±ÐÐ£).
description: This work is devoted to the numerical simulation of the propagation of a laminar flame in a pre-prepared mixture. Methods of TFM (Thickened Flame Model) and Dynamic Mesh Adaptation were used. The main results are in the development of a calculation technique that ensures the agreement of the calculated flame propagation velocity in a cylindrical channel filled with a mixture of ethylene and air with the published measurement results. The tasks solved in this work: - Analytical review of published works on numerical modeling of the propagation of a laminar flame through a gas mixture (including: approximate methods of numerical modeling with insufficient grid resolution; description, implementation and examples of the application of the TFM model; examples of three-dimensional calculations). - Analysis of the sensitivity of the calculation results to the grid resolution. Application of the TFM model. Automatic mesh adaptation. Development of calculation methods. - Numerical calculations of flame spread using Ansys Fluent. Comparison with published calculation results and experimental data for the laminar flame velocity. - Analysis of the stability of the flame front. The role of thermal radiation. - Comparison of global and multistage chemical mechanisms. - Development of recommendations for performing computations with insufficient grid resolution. The introduction describes the relevance of the work, formulates the goal and objectives of this work. The first chapter provides a review of the literature on laminar flame in a premixed mixture, examples of its numerical simulation. In the second chapter, a description of approximate methods of numerical simulation with insufficient grid resolution is given. The third chapter describes the ANSYS Fluent package. The fourth chapter shows and analyzes the main results of the work. The work was carried out as part of the scientific group "Combustibility of Materials and Fire Modeling" of the Department of "Hydroaerodynamics, Combustion and Heat Transfer" of the Institute of Applied Mathematics and Mechanics of SPbPU. Computing resources were provided by the Polytechnic Supercomputer Center.