Burning rate convective

The convective gas flow around a burning particle affects its burning rate. It has been postulated that in the absence of convection, the burning rate is independent of pressure. Forced convection, on the other hand, is befleved to increase the burning rate. 

More recently, Zucrow et al. (Zl) have run experiments which show that in the region of low flow rates the burning rates of certain propellants actually decrease with increasing gas flow. As the gas flow rate increases, the burning rate is observed to go through a minimum and then increase with further increases in gas flow rate. The decrease in burning rate was attributed to undefined mass-transfer processes. Eventually, the convective heat-transfer processes overcome this effect to give results similar to those obtained by others. 

Some of the thermal and fluid factors affecting the burning rate are illustrated in Figure 9.1. Convective heat flux depends on the flow conditions and we see that both... 

The corresponding laminar natural convection burning rate on a vertical surface was... 

Figure 9.11 (a) Laminar burning rate of a vertical plate under natural convection by Kim, deRis... 

Turbulent convective burning of vertical plate. An approximate solution matched to data was given by Ahmad and Faeth [11]. The average burning rate mp for a distance x measured from the start of the plate is given by the formula below ... 

The introduction of Equation (9.71) for Equation (9.26e) makes this a new problem identical to what was done for the pure diffusion/convective modeling of the burning rate. Hence L is simply replaced by L,n to obtain the solution with radiative effects. Some rearranging of the stagnant layer case can be very illustrative. From Equations (9.61) and (9.42) we can write... 

This equation along with Equation (9.97) allows us to eliminate the convective flame heat flux to develop an equation for the flame temperature. This equation will still contain the burning rate in terms of the effective heat of gasification, Lm. From Equation (9.97), we define Lm as the modified heat of gasification by the following ... 

From your formula, compute the initial burning rate in g/s for pure convective burning. 

A burning pool of liquid or a volatile solid fuel will establish a stagnant film height due to the natural convection that ensues. From analogies to heat transfer without mass transfer, a first approximation to the liquid pool burning rate may be written as... 

If, indeed, Eqs. (6.171) and (6.172) adequately predict the burning rate of a droplet in laminar convective flow, the droplet will follow a d3/2 burning rate law for a given relative velocity between the gas and the droplet. In this case (3 will be a function of the relative velocity as well as B and other physical parameters of the system. This result should be compared to the d2 law [Eq. (6.172)] for droplet burning in quiescent atmospheres. In turbulent flow, droplets will appear to follow a burning rate law in which the power of the diameter is close to 1. 

Goldsmith (16) subjected suspended droplets to an upward stream of air. Effective evaporation constants obtained from a plot of the square of the droplet diameter vs. time are presented in Table VII. Forced convection produced burning rates as high as 36% above the corresponding natural convection values. 

Table VII. Effect of Forced Convection on Burning Rate (16) ...

This term varies significantly with the nature of the fuel. Liquid fuels are characterized by the presence of recirculation currents induced by buoyancy. These currents homogenize the temperature distributions, reducing in-depth conduction. Nevertheless, convective motion transfers heat to the interior of the pool leading to an additional term of in-depth convection. Convective heat transfer in polymer melts has a similar behavior and could potentially have an important effect on burning rates nevertheless, the impact of polymer melt rheology on the flammability of materials is still a matter of great controversy. 

Burning-rate corrections for free convection depend on the Grashof number. 

Equations (45) and (46) are only two of many formulas that have been used to describe erosive burning [8]. Most of the formulas that have been suggested are based on physical concepts of influences of crossflow on propellant burning. Among these concepts is the idea that high external velocities produce a turbulent boundary layer (see Chapter 12) on the propellant surface and thereby effectively increase the thermal diffusivity of the gas, which in turn increases the rate of heat transfer to the propellant and hence the burning rate [99]. The idea that turbulent convective heat transfer from the hot combustion products outside the boundary layer provides an additive contribution to the heat flux reaching the propellant surface and,... 

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