End burning velocity

Consider the ignition of a flammable mixture at the closed end of a horizontal circular tube of cross-sectional area A. The tube has a smaller opening at the other end of area A0. The process is depicted in the figure below. The flame velocity in the tube is designated as vf. It is distinct from the ideal burning velocity, Su, which is constant in this adiabatic case. The following assumptions apply ... 

The remainder of this chapter is devoted mainly to a mathematical amplification of the concepts introduced in this section. In particular, it will be seen that the burning velocity is an eigenvalue of the conservation equations. Many questionable aspects of the reasoning employed in this section will have been remedied before the end of this chapter. 

Fig. 31. Burning velocities of hydrogen + nitrogen + oxygen flames having. 02.u 0.0460 and T = 336 K, showing dependence on the initial mole fraction ratio Xhj,u/Xn2,u (after Dixon-Lewis et al. [158]). Line represents values calculated by Dixon-Lewisetal. and x, additional calculations using sets 1 and 3 of rate coefficients in Table 30 and +, additional calculations using set 2 of Table 30 (+ at each end). (By courtesy of The Royal Society.)...

A test procedure which has proved very useful was first described by Hatfield. The samples are cylinders 32 x 12-5 mm in diameter with a standard abraded finish which are supported on open-ended refractory boats in a tubular furnace. In the original test the atmosphere, which was produced by burning towns gas with a 50% excess of air, was passed over the specimens at a standard velocity after first preheating to test temperature over refractory packing in a separate furnace chamber. More latterly, natural gas has been used with suitable modification of air gas ratio to give... 

The combustion gas of an internal burning of a propellant flows along the port of the propellant If the nozzle attached to a rocket motor is removed, the pressure in the port becomes equal to atmospheric pressure and no sonic velocity is attained at the rear-end of the port. Then, no thrust is generated by the combustion of the propellant However, if the mass burning rate of the propellant is high enough to choke the flow at the rear-end of the port, the pressure in the port is increased and the flow reaches sonic velocity. The increased pressure in the port is converted into thrust. The thrust F is represented by... 

The air-intake used to induce air from the flight-altitude atmosphere plays an important role in determining the overall efficiency of ducted rockets. The air pressure built up by the shock wave determines the pressure in the ramburner. The temperature of the compressed air is also increased by the heating effect of the shock wave. The fuel-rich gaseous products formed in the gas generator burn with the pressurized and shock-wave heated air in the ramburner. The nozzle attached to the rear-end of the ramburner increases the flow velocity of the combustion products through an adiabatic expansion process. This adiabatic expansion process is equivalent to the expansion process of a rocket nozzle described in Section 1.2. 

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