Full Length ArticleFlame heights of line-source buoyant turbulent non-premixed jets with air entrainment constraint by two parallel side walls
Introduction
Flame height is one of the most basic parameters for non-premixed jets [1], [2], [3], [4], [5], [6]. The flame height of a non-premixed jet is dominated by air entrainment, which can be buoyancy-driven ( < 5) or momentum-driven [7], [8], [9]. Flame height increases with fuel exit velocity in the buoyancy-driven regime, meanwhile is independent of fuel exit velocity in the momentum-driven regime [7], [8]. The flame height in buoyancy-driven regime, which has wide applications in many fields [1], [2], [3], [4], [5], [6], has received focused attention in the past decades. Despite the flame flow property itself, the other two important factors affecting the air entrainment hence the flame height are the source dimensions and the boundary (ambient) conditions.
For the source dimension effect, extensive works have been reported for axi-symmetrical sources [7], [10], [11], [12]. The basic law is that the flame height increases with fuel exit velocity by a 2/5 power dependency for the axi-symmetrical sources. However, it is more practical to have a non-axi-symmetrical line-source [13], [14], [15], which can be resulted from the crack of fuel pipe. Hasemi [14], Yuan [15] studied flame height of line-sources. The basic law is that the flame height increases with fuel exit velocity by a 2/3 power dependency for the line-sources, which is due to the different evolution of flame envelope and hence air entrainment () from that of an axi-symmetrical sources . Moreover, Quintiere [16] proposed a unified formula to describe flame heights from axi-symmetric and rectangular sources based on scaling analysis. Later, Hu [17] proposed an explicit model for flame heights of rectangular-source jets.
For the boundary (ambient) conditions, extensive works are reported recently concerning the special condition of sub-atmospheric pressure (for example, Lhasa in Tibet, 64 kPa) [18], [19], [20]. The flame height is found to be higher than that in normal pressure, which is due to the decrease of air density with decrease of ambient pressure that it needs more flame entrainment surface area (hence flame height) to consume the fuel in relative lower ambient pressures. Another important issue is the wall boundary condition. In early years, Hasemi [21] and Zukoski [22] studied the flame height against a wall from line-source and square-source, respectively. Later, Poreh [23] and Hasemi [24] studied the flame height against a wall and in a corner. These works show that when the flame is against or near to a wall, the flame is higher than that of a free jet. This is due to the air entrainment from the wall side is constraint. However, there is another wall boundary condition, i.e. two parallel side walls at the two sides of the flame, for which few data and investigation has been reported in the past. This is similar to the piratical situation that a jet fire resulted from the gaseous fuel transportation pipe leakage between two adjacent buildings. There are in fact very near adjacent buildings in very dense urban area, especially in some old towns or villages in China. The flame height will increase dramatically if the side walls constraint effect shows up, which can happen as the fire is relative large or the side wall separation distance is relative small that not allowing for free entrainment of the flame. When the flame height increases, the adverse impact to the surrounding buildings will be more severe. Recently, a similar work has been done by Tao [25] employing a three-wall configuration (with two parallel walls and another perpendicular wall in the other direction) allowing air entrainment only from the opened side. An empirical coefficient is proposed to characterize the difference between the flame heights produced by 6 mm and 10 mm round nozzles in such a three-wall configuration and those of corresponding free jets in an open space.
In this paper, we endeavor to study the flame height of line-source buoyant turbulent non-premixed jets between by two parallel side walls, which has not been revealed in the past. It is known that the air entrainment is different at the two sides of a line-source jet. How the flame height changes due to air entrainment constraint by the two parallel side walls at various separation distances with the longer- or shorter side of the nozzle perpendicular to the side wall is not clear. This also helps to understand the un-symmetry nature of the entrainment of a line-source buoyant turbulent jet. The flame height evolution with separation distance of the side walls, as well as the critical distance that the flame height turns to be identical to that of a free jet are quantified in this work. Non-dimensional correlations are finally proposed to characterize these quantities.
Section snippets
Experimental
Fig. 1 depicts a schematic of the laboratory-scale experimental apparatus consisting of a flow supply system, a 4 m long pipe and a stainless nozzle. Two line-source nozzles are employed with dimensions of 2 mm (W) × 142.5 mm (L) and 2 mm (W) × 217 mm (L). Two kinds of nozzle orientations relative to the side walls are considered, i.e. with its shorter or longer side perpendicular to the side walls, as shown in Fig. 1(a) and (b), respectively. Propane is used as fuel with supply flow rate controlled by
Experimental results
Fig. 2 shows the typical flame photos with increasing side walls separation distance and with no side wall for (a) nozzle shorter side perpendicular to side walls and (b) nozzle longer side perpendicular to side walls. It can be clearly observed that when the nozzle shorter side is perpendicular to the side walls, the flame height first decreases with increase in side walls separation distance and then approaches the value of a free jet (infinite distance) when the side walls separation
Conclusions
This paper investigates the evolution of flame height produced by line-source buoyant turbulent non-premixed jets with air entrainment constraint by two parallel side walls at various separation distances. The line-source nozzles are arranged with two kinds of orientations relative to the side walls, i.e. with its longer or shorter side perpendicular to the side walls. Major findings include:
- (1)
The flame height changes little with side walls separation distance when the longer side of the
Acknowledgements
This work was supported jointly by Key project of National Natural Science Foundation of China (NSFC) under Grant No. 51636008, Excellent Young Scientist Fund of NSFC under Grant No. 51422606, the Newton Advanced Fellowship (NSFC: 51561130158; RS: NA140102), Key Research Program of Frontier Sciences, Chinese Academy of Science (CAS) under Grant No. QYZDB-SSW-JSC029, Fok Ying Tong Education Foundation under Grant No. 151056 and Fundamental Research Funds for the Central Universities under Grant
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