Reduced Pressure Effect On The Flame Length Of Elevated N-Heptane Fires In An Aircraft Cargo Compartment

ABSTRACT

This paper investigates the influence of reduced pressure on flame characteristics of elevated n-heptane fires in an aircraft cargo compartment, including the flame height driven by the weak plume and flame extension length driven by the strong plume, in order to provide theoretical support to the fire detection and surface material design. A series of elevated n-heptane pool fire experiments were carried out in a full-size simulated aircraft cargo compartment at different atmospheric pressures (70 kPa, 80 kPa, 90 kPa, 100 kPa). Results show that the experimental data of flame height and flame extension length at normal pressure agree well with Heskestad and Quintiere & Grove models, however, which cannot predict these flame characteristics of elevated fires. As the fire source elevates gradually, the flame height and flame extension length increase. Then modified flame height and flame extension length models at normal pressure were established by considering the elevated height effect. Furthermore, due to reduced pressure effect on the air entrainment into the fire plume, the flame height and flame extension length increase with the decreasing pressure. New flame height and flame extension length correlations applicable to the reduced pressure conditions were proposed by introducing a reduced pressure coefficient and modified nondimensional heat release rates.

KEYWORDS:

• Reduced pressure
• flame height
• flame extension length
• aircraft cargo compartment fires
• elevated fires

Acknowledgments

This study was supported by National Natural Science Foundation of China under Grant No. 51806156, 52076199 and 51706212; Hubei Provincial Key Research and Development Program under Grant No. 2020BCB072; Project of Natural Science Foundation of Hubei Province under Grant No. 2018CFB226 and Project of Hubei Provincial Department of Education under Grant No. B2018007.

Disclosure statement

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Highlights

• Effect of elevated height on flame height and extension length at low pressures.

• Modified correlations to predict flame height at reduced pressure.

• Modified correlations of flame extension length fit for reduced pressure.

Nomenclature

C₁constant related to entrainment coefficient in Eq. (4a)(4a) ${\dot{Q}}_{mod}^{\ast }=Cf(Lf/D{)}^{1/2}[1+2C_1(L_f/D){]}^2$(4a)

C_fcorrelation constants in Eq.(4a)(4a) ${\dot{Q}}_{mod}^{\ast }=Cf(Lf/D{)}^{1/2}[1+2C_1(L_f/D){]}^2$(4a)

c_pspecific heat of air at constant pressure (J/kg K)

C_Pthe coefficient of flame height under different pressures in Eq. (7)(7) $\frac{r_f}{D}=0.502{\left(\frac{L_f-H}{D}\right)}^{0.96}$(7)

Dburner diameter (m)

ggravitational acceleration (m/s²)

G_rthe Grashof number

hthe elevated height (m)

Hthe distance between burner and ceiling (m)

Kthe coefficient of flame height at different elevated heights in Eq. (2)(2) $K=1.276+0.083h$(2)

ldimensionless length (m)

$l_x$; $l_y$dimensions of the flame cross-section at impingement in x- (y-) direction (m)

Llength of rectangular-source burner (m)

L_fthe free flame height (m)

Pambient air pressure (kPa)

$\dot{Q}$ heat release rate of fire source (kW)

non-dimensional heat release rate defined in Eq. (4b(4b) ${\dot{Q}}_{mod}^{{ }^{\ast }}=\dot{Q}/({\rho }_{\mathrm{\infty }}{c}_p{T}_{\mathrm{\infty }}\sqrt{g}{D}^{\frac{5}{2}})$(4b) ${\dot{Q}}_{\mathrm{m}\mathrm{o}\mathrm{d}}^{\ast }$

${\dot{Q}}_H^{\ast }$non-dimensional heat release rate defined in Eq. (11b(11) $\frac{{C{ }^{\mathrm{\prime }}}_f}{C_f}=\frac{\lambda { }^{\mathrm{\prime }}}{\lambda }=(\frac{n{ }^{\mathrm{\prime }}}{n}{)}^{-3/2}\left\{\begin{array}{cc}\frac{0.0041}{0.0059}=0.695& P=70\mathrm{k}\mathrm{P}\mathrm{a}\\ \frac{0.00406}{0.0059}=0.688& P=80\mathrm{k}\mathrm{P}\mathrm{a}\\ \frac{0.00393}{0.0059}=0.666& P=90\mathrm{k}\mathrm{P}\mathrm{a}\\ \frac{0.00376}{0.0059}=0.637& P=100\mathrm{k}\mathrm{P}\mathrm{a}\end{array}\right.$(11) )

${\dot{Q}}_H^{\ast }$ non-dimensional heat release rate defined in Eq. (13b)(13) $r_f/H_{}fcn(V_{fu}\dot{Q}/V_f)$(13)

r_fflame radial extension length beneath ceiling (m)

$\mathrm{\Delta }T$the temperature difference

$T_{\mathrm{\infty }}$the ambient temperature

vthe viscosity of the convection fluid

V_fvolume of a free flame (m³)

V_fuflame volume portion intercepted by the ceiling (m³)

Wwidth of the rectangular-source burner (m)

Greek symbols

ΔDifference

$\alpha$entrainment coefficient

${\rho }_{\mathrm{\infty }}$ambient air density (kg/m³)

$\beta$the inverse of the film (mean) temperature

$\mathrm{\Delta }{H}_c/s$heat of combustion per unit mass of air

${\chi }_{\mathrm{r}}$flame radiation fraction

$\mathrm{\Psi }$dimensionless parameter

$\lambda$a constant related to fraction of stoichiometric air entrained for combustion

$\gamma$the coefficient of flame height under different pressure in Figure (10)

$\zeta$the coefficient of flame height under different pressures in Eq. (17)

Subscript

ccombustion

fflame

Pconstant pressure

$\mathrm{\infty }$ambient

Additional information

Funding

This work was supported by National Natural Science Foundation of China [No. 51806156, No. 52076199, No. 51706212]; Hubei Provincial Key Research and Development Program [No. 2020BCB072]; Natural Science Foundation of Hubei Province [No. 2018CFB226].