A One-Dimensional Model of Piloted Ignition - Science Direct

COMBUSTION A N D F L A M E 80:94-107 (1990)

94

A One-Dimensional Model of Piloted Ignition L. S. TZENG, ARVIND ATREYA, and INDREK S. WICHMAN Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226

In this article a model of piloted ignition is analyzed. The two-dimensional coupled solid and gas phase problem is simplified by assuming that the mass evolution rate from the combustible solid is a known function of time and by employing a plane rather than a point ignition source. Thus only a transient one-dimensional analysis of the gas phase is necessary. The equations are solved numerically using a fast scheme especially suitable for combustion problems. The pilot flame is modeled as a thin slab of gas that is periodically raised to the adiabatic flame temperature of the stoichiometric mixture. The effects of (1) ignition source location, (2) fuel mass evolution rate from the surface, and (3) surface temperature of the solid are investigated. An explanation is offered for the preignltion flashes often observed experimentally. A rational criterion for positioning of the pilot flame is proposed. The minimum fuel flow rate, by itself, is found insufficient for predicting the onset of piloted ignition; heat losses to the surface play an important role. Also, the conditions at extinction of a steady diffusion flame are found to be very similar to those for piloted ignition.

NOMENCLATURE A D 3) E

preexponential factor specific heat quenching distance diffusion coefficient Damkohler number, 3) = (Ap2Cph2 /)Qe -a~ activation energy

h Le

m

Cp dq

/3 /30 ~ 0

nondimensional activation energy,/3 =/3°or ° nondimensional activation energy, B° =

E/RTf

laminar flame thickness, 8 .-~ h/povoC. nondimensional temperature, 0 = (T -

Too)/(T f - T ~ )

boundary layer thickness Lewis number, Le = X/pCpD

X v

thermal conductivity stoichiometric coefficient

~

nondimensional position coordinate, ~

M q

mass flux, m = a v nondimensional mass flux, M = m C p h / k heat release

p

Q

nondimensional heat release, Q = q/Cp

Subscripts

=

x/h r

density nondimensional time, r = M/pCph 2

(T f - Too) R 5{ t T v x

Ideal gas constant nondimension.al reaction term, 5t = ~DYo YF exp[--fl(1 - - 0 ) / ( 1 - a°(1 - 0))] time temperature velocity position coordinate

f F i O S oo

Y

mass fraction

1. I N T R O D U C T I O N

Greek Symbols nondimensional factor, ot° = 1 - Too/Tf

ct°

0010-2180/90/$3.50

flame fuel ignition source oxygen surface ambient

The problem of piloted ignition of combustible materials under external heating is fundamental to Copyright (~) 1990 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 655 Avenue of the Americas, New York, NY 10010

A ONE-DIMENSIONAL MODEL OF PILOTED IGNITION E X T E R N A L

RAD

I AT

95 I ON

11111111 y#T UYF ,'~~ /

W/////////I///#/Y////////I////////I//IIII/IIIII/J WOOD Fig. 1. Pilotedignition of solids--the physicalproblem. fire science and technology because it addresses the process of fire initiation and growth. Its importance is underscored by the numerous investigations that have been conducted to date. References 1-4 serve as an excellent review of this previous work. The phenomenon of piloted ignition, however, remains rather poorly understood. This is evident from the numerous empirical ignition criteria that have been proposed in the literature such as critical surface temperature, critical fuel mass flux,

critical char depth, and critical mean solid temperature. Of these, critical fuel mass flux at ignition appears physically the most reasonable, but critical surface temperature has proved to be the most useful because it can be easily related to flame spread. The physical mechanism of piloted ignition is quite complex. The solid must first chemically decompose to inject fuel gases into the surrounding air. This produces a flammable mixture in the boundary layer, which is ignited by an ignition Sustained

480

460

o.

440

uJ r~ D p. ,,¢ nuJ o.

420

u.I IuJ O