Ignition Phenomena

Abstract

Ignition is the mechanism leading to the onset of a vigorous combustion reaction and is characterized by a rapid increase of temperature. An understanding of ignition is important in a wide range of combustion processes, from designing practical combustion devices to preventing unwanted fires. Ignition of a combustible material is often classified in two ways: spontaneous ignition, also known as autoignition, occurs through the self heating of the reactants, whereas piloted ignition occurs with the assistance of an ignition source. Topics included in this chapter are: (1) the thermal theory of spontaneous ignition of a gas phase mixture, (2) piloted ignition of a gas phase mixture, and (3) ignition of condensed fuels.

Exercises

• 5.1 For spontaneous ignition (autoignition), how is the critical temperature defined? How is the critical pressure defined? Show the conditions and equations to solve for these two variables. Sketch a qualitative plot of critical temperature and pressure for spontaneous ignition.

• 5.2 Consider a spherical vessel (constant volume) having a radius of 10 cm. It contains a stoichiometric mixture of methane and air at 1 atm. The system is initially at temperature T _i . The heat losses to the surroundings per unit volume of the vessel are ${\dot{q}\prime \prime \prime _L} = \frac{A_S}{V}\tilde{h}\left( {T - {T_\infty }} \right)$, where T is the temperature, V is the volume of the vessel, A _S is its surface area, $\tilde{h}$ is the heat transfer coefficient (15 W/m²-K), and ${T_\infty }$ is the ambient temperature (300 K). The rate of heat generation per unit volume is ${\dot{q}\prime \prime \prime _G} = Q_c\hat{\dot{r}}$ where ${Q_c}$ is the heat of combustion (MJ/mol) and $\hat{\dot{r}}$ is the fuel consumption rate [mol/(m³-s)].

  • a. Calculate the heat of combustion of the mixture Q _c .

  • b. For $\tilde{h} = 15\,{\hbox{W/}}{{\hbox{m}}^2}{\hbox{ - K}}$, plot ${\dot{q}\prime \prime \prime _L}$ and ${\dot{q}\prime \prime \prime _G}$ as a function of the system’s initial temperature T _i for ${T_i} \geqslant 300\,{\hbox{K}}$. You do not have to calculate how the system evolves in time, focus only on its initial state.

  • c. For $\tilde{h}{ = 15}\,{\hbox{W/}}{{\hbox{m}}^2}{\hbox{ - K}}$, what is the lowest initial temperature at which the rate of heat production by combustion offsets the heat losses?

  • d. Calculate the autoignition temperature of the system (T _c ).

• 5.3 Plot the autoignition temperature versus the number of carbon atoms for those straight chain hydrocarbon fuels listed in Table 5.1. Discuss any trends.

• 5.4 Determine the ratio between the minimum ignition energy and the heat release for a 400 cc spark-ignition piston engine running with a stoichiometric isooctane-air mixture at ambient conditions.

• 5.5 In the chemical industry, a fitted equation called the Antoine equation with three parameters is often used as $\log P = A - \frac{B}{{T + C}}$ or $\ln P = A - \frac{B}{{T + C}}$, where A, B, and C are parameters fitted from data. Write a program to find the vapor pressure of a given chemical species at a specified temperature based on the following Antoine equation.

  $$ log(P) = A - B/(T + C), $$

  where log is the common (base 10) logarithm, the coefficients A, B, and C for a few select species are tabulated in Table 5.4 (values for other species are found in Appendix 7). P is expressed in mmHg, T is expressed in Celsius, and the valid temperature range (T _min  < T < T _max ) is also given.

  Table 5.4 Exercise 5.5: Antoine equation coefficients

  Note that it is inappropriate to use the Antoine equation when the temperature is outside the range given for the coefficients (A, B, and C), for pressures in excess of 1 MPa, or when the components differ in nature (for example a mixture of propanol/water).

• 5.6 A 2 cm thick plywood is subject to a uniform heat flux of 50 kW/m². Estimate the time it takes for the plywood to catch fire.