# Effects of Initial Fuel Temperature and Altitude on Flame Spread over Diesel Fuel

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3 Part II Fire atmospheric pressure and partial pressure of oxygen approximately equal to two-thirds of those in areas near sea level. Since the atmospheric humidity and temperature were almost the same at both altitudes, the effects of ambient temperature and humidity on flame spread in this experiment are assumed to be negligible. Location Table 1. Ambient conditions during low and high altitude experiments. Altitude (m) Atmospheric pressure (kpa) Partial pressure of oxygen (kpa) Relative humidity (%) Ambient temperature ( C) Tibetan Plateau Hefei Plain INTRINSIC REASONS FOR ALTITUDE EFFECTS ON FLAME SPREAD OVER LIQUIDS Altitude effects on flash point With an increase in altitude, environmental pressure and partial pressure of oxygen will reduce. These parameter variations may essentially influence ignition sensitivity of the combustible liquids. According to the Clausius Clapeyron relation [14], the saturated vapor pressure of liquid fuel ( P δ ) variation with fuel temperature (T) can be expressed as follows, dln P dt h δ vap m =, (1) 2 RT where R is the universal gas constant, and vaph is the latent heat of evaporation due to the phase m change, which is a constant for a given fuel type. Integration of Eq. (1) yields [15], vaphm 1 1 Pδ = P0exp. R T0 T The liquid temperature may reach its boiling point (T b) when the saturated vapor pressure is equal to the atmospheric pressure. On the other hand, as predicted by the barometric formula [16], the ambient pressure at an altitude of Z, P, is given by the following formula, Pz Z = P0 exp, H z where P 0 is the atmospheric pressure at sea level (101.3 kpa), and H = RT /( Mag) is called the scale height of the atmosphere, km. Combining Eqs. (2) and (3) yields the boiling point of liquid fuel at altitude Z, T bz 1 =, 1 Z R + T h H 0 vap m where T is the boiling point of the liquid fuel at altitude Z. Catoire and Naudet [17] developed an bz equation for the estimation of the flash point with a maximum absolute deviation of only 10 K, TFL = 1.48 T b vaphm n, (5) 435 (2) (3) (4)

4 Proceedings of the Eighth International Seminar on Fire and Explosion Hazards (ISFEH8) where vaph in kj/mol is the standard enthalpy of vaporization at K; and n is the total number m of carbon atoms in the molecule. T FL in K is the flash point temperature and T b in K is the normal boiling temperature. 1 Supposing that C1 T =, R C 2 h H =, so the flash point of a liquid fuel at altitude Z is predicted as, FL vap m C1+ C2 Z 0.8 vap T = h n m. (6) In this expression, C 1, C 2, vaph and n are all constant. Thus, under a certain initial temperature, m Eq. (6) predicts that the flash point of a liquid decreases with an increase in altitude. In fact, the flash point of the 0 # diesel fuel is measured as approximately 75 C in Hefei and 54.5 C in Lhasa. The fuel vapor is more easily volatilized from the liquid fuel at a high altitude than at a low altitude, so that the flame is expected to spread more rapidly in a higher altitude environment. Altitude effects on surface tension As discussed previously, flame spread across a liquid surface involves preheating by subsurface convection flow, which is driven primarily by variations in surface tension along the direction of spread over the pool. Therefore, investigating ambient pressure effects on the surface tension of a liquid is imperative to identify flame propagation behavior over a liquid fuel. According to Albertyʼs work, the relation between the surface tension and air pressure is written as follows [18]: d dp Γ RT P σ = 2, (7) where Γ 2 is designated as the amount of adsorbed molecules per unit surface. The surface of the condensed phase is assumed to be smooth, and adsorption hypothetically occurs only within a single molecular layer structure on the liquid surface. Based on both hypotheses, Langmuir [19] postulated that the amount of adsorbed molecules per unit surface could be predicted as follows: Γ 2 = Γ bp. (8) 1+ bp In this equation, Γ is the limiting adsorption at an extremely high gas pressure value, and b is a constant. The following is obtained by combining Eqs. (7) and (8): σ = σ0 Γ RT ln(1 + bp). (9) Eq. (9) indicates that the surface tension of a liquid decreases as gas pressure increases. Therefore, less air is absorbed into the liquid fuel in high-altitude areas than in low-altitude areas, which results in higher surface tension of the liquid fuel. A strong subsurface convection flow is then induced, which further increases flame spread rate. In summary, both the analyses of the flash point and surface tension of a liquid fuel predict that flames will spread more rapidly in a high-altitude environment. In the following discussion, flame spread rates under various initial fuel temperatures are measured in both Hefei (sea level) and Lhasa (high altitude). The flame speed rates of Hefei and Lhasa are then quantitatively compared. 436