Open Access. © 2021 A. N. Gutkowski and Z. Cebulski, published by Sciendo. This work is licensed under the Creative Commons Attribution 4.0 License Mechanics and Mechanical Engineering 2021; 25 (1):32ś38 Research Article Artur N. Gutkowski* and Zbigniew Cebulski Analysis of Flame Propagation in Small Adiabatic Tubes Characterized by Diferent Degrees of the End Opening https://doi.org/10.2478/mme-2021-0005 Received Sep 3, 2020; accepted Nov 21, 2020 Abstract: In the present work, we study numerically freely propagating fame in the stoichiometric propane-air mix- ture. The adiabatic small tubes with one end fully open and the second one characterized by diferent degrees of opening are examined. The degree of opening of the tubes was equal to: 0% (completely closed), 25%, 50%, 75% and 100% (fully opened) of the tube cross-sectional area. Sev- eral mechanisms, such as thermal expansion of the burned gas that can leave the tube freely (fully opened left end of the tube), frictional forces and movement of the unburned mixture generated by a pressure gradient, occur simulta- neously during fame propagation. As a result, a nearly- exponential dependence of fame propagation speed as a function of time is observed. For fully open right end (100%), normalized fame speed reaches about 75ś80 at the end of the tubes. By partially closing the right end, this efect is delayed and reduced ś for 25% of the opening nor- malized fame speed is about 20 for all tube diameters. Keywords: Premixed fame, small tubes, fame propagation speed, fame shape 1 Introduction The study of the premixed fames propagating through the channels has a long history. The channel geometry and boundary conditions on the fame behaviour during its propagation was analysed frst in [1, 2]. We can specify four typical confgurations of fames propagating in the channels, which are schematically shown in the Figure 1. *Corresponding Author: Artur N. Gutkowski: Lodz University of Technology, Institute of Turbomachinery, Łódź, Poland; Email: artur.gutkowski@p.lodz.pl Zbigniew Cebulski: Lodz University of Technology, Institute of Turbomachinery, Łódź, Poland; Email: zbigniew.cebulski@p.lodz.pl The frst confguration (Figure 1a) can be called a sta- tionary fame. In this case, there is an inlet in which a pre- mixed mixture with a certain velocity u u (volume rate) is delivered, and an outlet where burned gas is evacuated (with velocity u b ). A fame is stabilized at some position in the tube. The second confguration (Figure 1b), we can call a moving fame. In this case, the ignition of the mixture is located at the open end of the tube and a fame propagates towards a close end, with fame propagation speed S f in mixture, which is at rest (u u = 0). The third confguration (Figure 1c) is similar to the previous one, it means that one end of the tube is open and another one is closed but a mixture is ignited at the closed end of the tube, therefore, u b = 0. This confguration is very often used for turbulent fames and defagration to detonation transition analysis. The last one (Figure 1d) is a channel opened at both ends. The fame propagation in small channels has also been analysed numerically, for example, in the papers [3, 4]. The fame propagation mechanism in a tube with adiabatic and isothermal (cold) wall can be found in the paper [5], and for fames propagating between parallel plane walls in the work [6]. It was stated in these works that for tubes with Figure 1: Typical confgurations of flames propagating in channels.