PARÂMETROS RELEVANTES NA FORMAÇÃO DA INVERSÃO DE CHAMAS

ENC-2020-XXXX

RELEVANT PARAMETERS ON THE FORMATION OF TULIP FLAMES

Júlia Caletti Silveira

Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite, 425.

Julia.caletti@hotmail.com

Andrés A. Mendiburu Zevallos

Universidade Federal Rio Grande do Sul, Rua Sarmento Leite, 425

andresmendiburu@ufrgs.br

Abstract. The objective of this work is to study the relevant parameters that can correlate to the distance of the onset of the formation of tulip flames inside a duct. For this, data were collected from articles involving experiments on tulip flames to relate the dimensionless parameters df/dh (ratio of the distance at which a flame becomes flat to the diameter of the tube) and SL/C0,S (ratio of laminar flame speed to the speed of sound of the reactants). The laminar flame speed and the speed of sound of reactants were calculated using the Cantera software. It was observed in the first part of the study that the best correlation is obtained when the aspect ratio (AR) is kept constant and the type of fuel is not greatly different, the data for mixtures of H2+CH4 correlate better than the data for mixtures of H2+CO. In the second part of the study it is observed by keeping constant the AR and the fuel type and letting the equivalence ratio to vary rather widely, the correlation coefficients show betters results and the R² ranged from 0,62 to 0,78. Comparing the experimental data with the available premixed flame acceleration theory the results show that a relative error below 25% is obtained for most of the data when the theory is used to determine df/dh.

Keywords: premixed flames, tulip flames, flame propagation, closed tubes, half-open tubes

1. INTRODUCTION

1. Theory and Literature Review

In the process of accelerating flames in tubes and ducts, the phenomenon of “tulip flame” is extensively investigated and is attributed as a combustion instability (Matalon and McGreevy, 1995). The tulip flame can often be observed during the propagation of premixed flames inside closed ducts and its shape is concave in relation to the mixture of unburnt mixture.

The prediction of the appearance of the tulip flame phenomenon is important and it is still very much studied. One of the first experimental works investigating the phenomenon was carried out by Ellis (1928) and revealed that a tulip flame forms only after the flame has traveled a certain distance from the ignition source. It was also observed that the tulip flames develop in tubes with aspect ratios greater than two. More recent studies have studied the different parameters that are related to the phenomenon for different types of fuels. Mendiburu et al. (2019) performed experiments with ethanol-air mixtures and demonstrated that the ratio of the distance at which the flame becomes flat to the hydraulic diameter of the tube (df/dh) is a measurable parameter that characterizes the appearance of the tulip flame. Progress has also been made in understanding the mechanism of flame acceleration and tulip flame formation in closed tubes, such as the theory developed by Valiev et al. (2013) and the experimental work by Ponizy et al. (2014), respectively.

The appearance of this phenomenon is associated with several factors, such as, aspect ratio (AR), mixture equivalence ratio (ER), type of fuel and tube boundary conditions, among others (Guénoche, 1964). Mendiburu et al. (2019) showed that for ethanol-air mixtures there is a correlation between the ratio of the distance at which a flame becomes flat to the tube diameter (df/dh) and the ratio of laminar flame speed to the speed of sound of the reactants (SL/C0,S). The objective of the present work is to assess the possibilities to predict the ratio df/dh through empirical correlations and through the available theory. This objective will be attained by the two following steps:

1. Evaluation of the effect of parameters such as AR, ER, type of fuel and tube boundary on the correlation between df/dh and SL/C0,S.
2. Determination of the ratio df/dh by means of the theory developed by Valiev et al. (2013) and comparison with experimental data available in the literature.

1. METHODOLOGY

The experimental data of the distance at which the flame becomes flat will be obtained from published experimental articles related to the tulip flame phenomenon. Data of the tube geometry, boundary conditions and air-fuel mixture were collected. In most articles the value of df was not directly measured. However, it is common to find graphs showing the distance of the flame front to the ignition source as a function of time and also direct photographs or schlieren images showing the instant at which the flame becomes flat. Therefore, by means of the GetData Graph software (GetData Graph, 2020) this kind of published information can be used to extract the desired df value. The laminar flame speed (SL) and the speed of sound of the reactants (C0,S) were determined by using the Cantera software (Cantera, 2020). Thus, by selecting several articles and keeping some variables constant, correlations were obtained between the values of df/dh and SL/C0,S. Therefore, this part of the study is divided in two sub-sections:

• Evaluation of correlations when AR is constant or varies within a small interval. Letting the type of fuel and the ER to vary freely.
• Evaluation of the correlation when the type of fuel is kept constant. Letting the AR and ER to vary freely.

The experimental data was obtained from the experimental work by Xiao et al. (2012), Xiao et al. (2013a), Xiao et al. (2013b), Hariharan and Wichman (2014), Ponizy et al. (2014), Xiao et al. (2014), Yu et al. (2015), Zheng et al. (2016), Jin et al. (2017), Yu et al. (2018a), Yu et al. (2018b), Yang et al. (2019a), Yang et al. (2019b), Zheng et al. (2019).

The second part of the study consist in comparing the distance at which the flame becomes flat with theoretical values. The axial distance travelled by the most advanced point of the flame until the moment the flame touches the side walls of the tube, ξtip, was considered as the theoretical value of df. The theory described by Valiev et al. (2013) was applied.

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