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A new mathematical method for quantifying flame trajectory length of inclined buoyant jet fires in crosswind

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Abstract

Outdoor gas pipeline leakage often results in inclined jet fires, often causes the domino incidents in industry and greatly threatens process safety and environment. In practical conditions, the presence of ambient wind and the behavior of gas leakage flame will become more complex and threatening. Massive attentions have been paid on gas leakage jet fire just oriented in vertical or horizontal directions, especially flame morphological scale characteristics. However, few studies have been conducted about the behavior of flames with different upward inclined angles. In this paper, the flame trajectory lengths of different upward inclined angles (0 ~ 90°) were studied with the combined effect of crossflow. Experiments are performed with 3 mm circular nozzle. Propane is used as the fuel in this study and the crosswind speed vary between 0 and 3.48 m s−1. A digital video camera is used to record the flame morphology. The experimental results display that the flame trajectory length increases with increasing inclined angle at low crosswind speeds (u∞ < 0.5 m s−1). As the crosswind speed increases, the flame length decreases with increasing inclined angle. Besides, for small inclination angle (0 ~ 45°) jet fire, the flame trajectory length increases with the increase in the crosswind speed, while in the case of flame inclination angle range of 45 ~ 90°, the flame trajectory length decreases with the increase in the crosswind speed. Then correlation models are developed to predict the flame horizontal length and vertical heights of upward inclined jet fires. And by observing the flame morphology, a mathematical analysis model based on circular approximation is established to predict the flame trajectory length of inclined buoyant jet fire in crosswind, which is useful in process industry. The present model is suitable to correlate all the data in this work, as well as those from previous works.

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Abbreviations

\(c_{\text p}\) :

Specific heat of air (J kg−1 K−1)

\(C\) :

Fitted coefficient

\(d\) :

Nozzle diameter (m)

\(Fr_{\infty }\) :

Air Froude number

\(Fr^{*}\) :

Modified Froude number

\(g\) :

Acceleration of gravity (m s−2)

\(l\) :

Radius of the circumference (m)

\(L_{\text f}\) :

Flame trajectory line length (m)

\(L_{\text x}\) :

Flame horizontal projection distance (m)

\(L_{\text y}\) :

Flame vertical height (m)

\(Q^{*}\) :

Dimensionless heat release rate

\(Q^{*}_{\text{mod}}\) :

Modified the dimensionless heat release rate

\(R\) :

Momentum ratio of fuel jet to crossflow

\(T_{\text f}\) :

Flame temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\(u_{\text j}\) :

Fuel velocity at the nozzle (m s−1)

\(u_{\infty }\) :

Crossair velocity (m s−1)

\(u_{\text t}\) :

Initial velocity of the flame (m s−1)

\(\theta_{0}\) :

Inclination angle relative to the horizontal

\(\beta\) :

Coefficient of thermal expansion of water

\(\rho_{\text j}\) :

Fuel density (kg m−3)

\(\rho_{\infty }\) :

Air density (kg m−3)

\(\alpha\) :

The half of the central angle

\(\varphi\) :

The arc cotangent of \(L_{y}\) and \(L_{x}\)

\(\phi\) :

The angle between \(u_{t}\) and \(u_{\infty }\)

\(\lambda\) :

Parameter defined in Eq. (11)

\(\sigma\) :

Parameter defined in Eq. (16)

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Acknowledgements

This work was supported jointly by the National Natural Science Foundation of China (NSFC) 51976051 and 51606057.

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Authors and Affiliations

  1. School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, 230009, Anhui, China

    Qiang Wang, Aquan Lu, Le Chang & Ben Wang

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  1. Qiang Wang
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  2. Aquan Lu
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Contributions

Qiang Wang was involved in conceptualization, resources, writing, reviewing and editing, supervision, project administration and funding acquisition. Aquan Lu was responsible for conceptualization, methodology, investigation, formal analysis, data curation, writing the original draft, validation and visualization. Le Chang took part in investigation, writing, reviewing and editing, visualization, and validation. Ben Wang participated in writing, reviewing and editing, visualization and validation.

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Correspondence to Qiang Wang.

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Wang, Q., Lu, A., Chang, L. et al. A new mathematical method for quantifying flame trajectory length of inclined buoyant jet fires in crosswind. J Therm Anal Calorim 147, 11363–11371 (2022). https://doi.org/10.1007/s10973-022-11348-x

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