Laminar burning rates

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

Figure 3.12 Computed 1D laminar burning rates versus pressure for H2/air mixtures with = 0.30 and 0.20 and fresh reactant temperatures 7 =673 and 773 K. Adapted from Ghermay et al. (2011) (with permission).

The fact that the fuel/air ratio is spatially constant in HCSI engines, at least within a reasonably close approximation, allows substantial simplifications in combustion models. The burn rate or fuel consumption rate dm /dt is expressed as a function of flame surface area the density of the unburnt fuel/air mixture Pu, the laminar burning velocity Sl, and the fluctuations of velocities, i.e., E as a measure of turbulence, u. ... 

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

In Figure 9.14 we see a more classical demonstration of the range of burning rate behavior of a pool fire. Below a diameter of 25 cm the burning rate is laminar with hc cx D 1 4 afterwards it is turbulent as hc oc D° or D1 5 at most. However, with... 

Figure 9.15 Regimes of the steady burning rate for methanol D < 25 cm laminar, D > 25 cm turbulent, D > 100 cm radiation saturated [16, 17]...

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. 

Experimental evidence from a porous sphere burning rate measurement in a low Reynolds number laminar flow condition confirms that the mass burning rate per unit area can be represented by... 

The opposed-flow geometry has some important differences, as well as benefits, compared with the burner-stabilized flat flame (e.g., Fig. 1.1). One is that the strain field can be varied by controlling the flow rate, ranging from an essentially strain-free situation to a flame extinction. As discussed subsequently, this flow configuration can be used experimentally for the accurate measurement of laminar burning velocities [238,438,448]. 

For a given set of flow parameters, the strained flame speed is taken as the fluid velocity at the minimum in the profile just upstream of the flame. Law and collaborators developed an analysis that uses a series of variously strained flames to predict strain-free laminar burning velocities [238,438,448]. As the strain rate is decreased, the strained flame speed decreases and the flame itself moves farther from the symmetry plane. There is an approximately linear relationship between the strained flame speed and the strain rate. Thus, after measuring the velocity profiles (e.g., by laser-dopler velocimetry) for a number of different strain rates, the strain-free burning velocity can be determined by extrapolating the burning velocity to zero strain. 

In addition to the low-strain limit, which can be used to determine laminar burning velocities, the opposed-flow configuration can also be used to determine high-strain-rate extinction limits. As the inlet velocities increase, the flame is pushed closer to the symmetry plane and the maximum flame temperature decreases. There is a flow rate beyond which a flame can no longer be sustained (i.e., it is extinguished). Figure 17.11 illustrates extinction behavior for premixed methane-air flames of varying stoichiometries. 

A similar flat flame technique—one that does not require a heat loss correction—is the so-called opposed jet system. This approach to measuring flame speeds was introduced to determine the effect of flame stretch on the measured laminar flame velocity. The concept of stretch was introduced in attempts to understand the effects of turbulence on the mass burning rate of premixed systems. (This subject is considered in more detail in Section 4.E.) The technique uses two... 

A laminar flame propagates through a combustible mixture in a horizontal tube 3 cm in diameter. The tube is open at both ends. Due to buoyancy effects, the flame tilts at a 45° angle to the normal and is planar. Assume the tilt is a straight flame front. The normal laminar flame speed for the combustible mixture is 40 cm/s. If the unbumed gas mixture has a density of 0.0015 gm/cm, what is the mass burning rate of the mixture in grams per second under this laminar flow condition ... 

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