Detailed analysis of the heat flux method for measuring burning velocities

Abstract

The heat flux method for determining the adiabatic burning velocity of gaseous mixtures of fuel and oxidizer and also producing well-defined reference flames is described in detail. Practical aspects of the heat flux method are discussed, especially the construction of the burner and attachment of thermocouples. An analysis is given of possible uncertainties and ways of correcting shortcomings. Conclusions from this analysis are applied to a typical measurement. The results are compared to other published results, including those from other often used methods, such as those with counter flow and closed vessels. For methane and air, a peak value of S_L = 37.2 ± 0.5 cm/s was found.

Introduction

The adiabatic burning velocity of a given mixture of fuel and oxidizer is a key parameter governing many properties of combustion, such as the shape and stabilization of a flame. Hence, much effort has been spent on measuring this parameter accurately for several mixtures, especially hydrocarbons because of their widespread use in domestic, as well as industrial burners. Problems arise because small disturbances of the flame appear to influence the burning velocity. This is the reason that early measurements showed considerable scatter, when plotted on one graph. Flame cooling, curvature, strain, and stretch appeared to be very complicated phenomena, which are now a field of investigation on their own [1]. To determine the adiabatic burning velocity, the flame should be as flat as possible: in the ideal case, one dimensional. However, flat flames are traditionally stabilized on a burner, which implies heat loss and therefore they do not represent an adiabatic state. Usually, some method of extrapolation is used to circumvent these problems: in the case of a stretched flame, experiments are performed at various stretch rates. Then, extrapolation to zero stretch rate yields the stretch-free burning velocity. In the case of a burner-stabilized flame, the flame can be tuned until it destabilizes, for example because the inlet velocity becomes higher than the adiabatic burning velocity. If the heat loss to the burner is measured, the same procedure can be followed: determine the heat loss as a function of the inlet velocity, and extrapolate the results to zero heat loss, which corresponds to the adiabatic state. As is generally known, extrapolations always have uncertainties. This holds especially for the burning velocities of stretched flames, where the modeling is necessarily simplified and relies heavily on experiments.

Due to stretch effects, the adiabatic burning velocity of methane/air was for a fairly long time reported to have its maximum at 42 cm/s [2], but more recent experiments have revealed that 37 cm/s is a much better burning velocity of a stretchless flame. In fact, when the old measurements are recalculated (extrapolated) using a more recent and insightfull stretch model, the results of the old measurements become lower and coincide with heat flux measurements, as shown by van Maaren [3]. This was later confirmed by Vagelopoulos et al. [1], who performed experiments with ultralow strain rates using a variation of the counterflow method. They used the transition of negative to positive stretch rate to find S_L by interpolation.

The counterflow method, described by Law [2], and the closed vessel method, recently used by Gu et al. [4], are common methods to measure burning velocities. Both use some kind of extrapolation to find the stretchless burning velocity. A method not needing any extrapolation due to either stretch or heat loss effects and producing a flame, which can be investigated in a laboratory is the heat flux method, introduced by van Maaren [5]. In this paper, the method is described in detail and several improvements on the original design are presented to obtain more accurate results and ease the process of duplicating the burner. The construction of the burner head is improved, including the attachment of small thermocouple wires to the burner plate, resulting in more consistent measurements. Moreover, an analysis is made of remaining systematic errors in the thermocouple measurements, providing a simple way to correct for these errors.

After a short description of the heat flux method and its history in Section 2, the method is described extensively. The general set-up and construction of the burner are presented in Section 3. Thermocouple measurements and an analysis of the physics behind the observed systematic temperature deviations will be treated in Section 4. The accuracy of the gas flows will be estimated in Section 5. Finally, a typical measurement and result will be analysed in Section 6, and conclusions are drawn in Section 7.