Burning Rate of Wood Cribs with Controlled Airflow

Figure 4 shows the average peak burning rates for all crib designs as a function of the forced flow rate. The burning rates were normalized by the burning rate in unrestricted quiescent ambient conditions. The error bars indicate one standard deviation between replicate tests, which tended to increase with thinner sticks (and thus crib design number). This increased variability is possibly due to the increased numbers of sticks used per fuel bed, so variations in the dimensions and density of the sticks and how the beds were assembled compounded. More variability is also seen in most crib designs at 100 LPM, likely due to the somewhat marginal burning conditions. The average variability is 5.5% of the mean peak burning rate, and ranges from 0.63% to 23.12%. Given this mild variability, in general, the burning rates are seen to increase with the air flow rate. There are two main reasons for this increase. For ventilation-limited cribs, an increase in the ventilation improves the air–fuel ratio, increasing the heat released and heat feedback to the solid fuels (for example [14, 15, 23]). This holds when the ventilation is limited either because the cribs are densely packed or because of insufficient supplied airflow. Even if the cribs are not ventilation limited, increased airflow increases the char oxidation rate and therefore the mass loss rate of the solid fuel increases [25, 26].

There are some exceptions, however, to this increasing trend. For example, the apparent increasing trend for crib design #1 is very weak, as the measured peak burning rates are not statistically different from one another (p values > 0.05). An important note is even though they are not different from each other, the measured peak burning rates of crib design #1 at all flow rates except 400 LPM (which, for this crib design, had the largest experimental standard deviation of 5.4% of the mean) are statistically different from the unrestricted quiescent case.

An additional exception to the general monotonically increasing trend is the burning rate of crib design #4. For this case, the normalized burning rate decreased for flow rates above 600 LPM, indicating that the balance between heat release and heat losses had shifted. As the flow through the crib is increased, convective heat losses increase [27]. Additionally, the flames themselves get pushed upward, away from the solid fuel, likely reducing the heat feedback that contributes to the burning [23]. This non-monotonic behavior of the burning rate with flow rate was also observed by Harmathy in [25] and in previous work using a chimney to induce flow through the crib [23]. Unfortunately, there is no one parameter that seems to characterize this “turning point.” For example, crib #8 has a similar porosity (see Table 2), but its burning rates still increases with airflow in the range tested. The initial crib mass is another parameter that would be logical to suggest, but no relation with this parameter was found either. As seen from Table 2, crib designs #1, 5, 8, and 12 have similar initial masses, and crib design #7 weighs considerably less. The forced flow rate for crib #4 is about six times that naturally induced in normal ambient conditions (see discussion below in Sect. 3.2), but crib design #1 also had an equally low naturally induced flow with no clear decline in burning rate seen for the flows tested here. Crib design #1, however, is very dense (Table 1) so one could argue that its burning rate has more “potential” to increase with forced flow whereas crib design #4 is normally not ventilation limited. Crib design #4 is the shortest crib so the air inside the crib would likely have a lower temperature, providing more cooling to the stick surfaces, as well as the shortest residence time to participate in combustion. The non-dimensional heat release rate (Q*), a.k.a. Zukoski number, could also be considered. Similar to the square root of the Froude number, the Zukoski number is frequently defined as [28]:where \(\dot{Q}\) is the heat release rate (kW), \({\rho }_{\infty }\) is the density of the ambient air (kg/m³), c_p is the specific heat of the ambient air (kJ/kg-K), \({T}_{\infty }\) is the ambient air temperature (K), g is the acceleration due to gravity (m/s²), \(l\) is the crib length (m), \({\dot{m}}_{b}\) is the burning rate (g/s), and Δh_c is the heat of combustion (kJ/g). The heat of combustion is assumed to be 14.1 kJ/kg [29]. Since Q* is related to the Froude number, smaller values would suggest that the momentum of the fuel gases exiting the fuel surface is very slow in unrestricted quiescent conditions, and a forced airflow would easily overwhelm this buoyant fuel flow. Crib design #4 has the lowest Q* in unrestricted quiescent conditions (Table 2), but not drastically, so it is unclear what is driving this behavior without seeing at which flow rates the “turning points” occur for the other crib designs. Harmathy [25] saw this curvature explicitly for two of his crib designs (W-1–1 and W-1–2 is his notation). His Figure 5 is reproduced here in Figure 5. Unfortunately, a direct comparison to his data can’t really be made. In his setup, the cribs were placed on a screen directly on the liquid fuel ignition tray, effectively blocking off airflow from underneath the cribs. It was shown in [18] that placing the crib directly on the platform can reduce the burning rate by as much as 90% compared to when sufficient space is provided, such as was done in this work. Despite this, if one calculates the Q* for his cribs using Equations 2 and 3 (for unrestricted ambient conditions), it would appear that the turning point for his cribs occurs at higher flow rates as Q* increases (see Figure 5), suggesting that this parameter may indeed at least help explain this behavior.

In Figure 4, the burning rates have been normalized by the burning rates obtained in normal unrestricted quiescent conditions. Because the box is sealed with a finite and relatively limited initial supply of air that is likely largely consumed during ignition, normal entrainment of air into the fuel bed is suppressed during a large part of the burning duration. Consequently, when plotted as in Figure 4, the airflow that is naturally induced through the fuel bed can be inferred by finding the flowrate that corresponds to a normalized burning rate equal to one. Where necessary, linear interpolation was used when the match was achieved between two tested flow rates. For example, by re-examining Figure 4, we see that the normalized burning rate for crib design #6 is 1 (indicated by the horizonal blue line) when the flow is 400 LPM, thus the airflow induced in quiescent conditions is inferred to be 400 LPM. Similarly, using linear interpolation, the normalized burning rate for crib design #2 is 1 for a flow rate of 341 LPM. In some cases, this was not clearly achieved in the range of flow rates tested here. For example, crib design #1 appears to draw in less than 100 LPM of air into the fuel bed itself while burning in ambient conditions (at 100 LPM, the normalized burning rate was 1.10). On the other hand, crib designs #10 and 12 seem to pull in just over 1000 LPM into the fuel bed while burning in unrestricted quiescent conditions. At 1000 LPM, their normalized burning rates were 0.99 and 0.97, respectively. Unfortunately, testing at higher flows was limited by constraints on the house air supply, so the trends cannot be reliably extrapolated to confirm a more accurate estimate of the matched value. Because the normalized burning rates are very close to 1, a rough estimate of 1000 LPM seems like an acceptable first rough approximation. For flow rates less than 100 LPM, it was observed with crib design #8 that the outflow is so weak through the ventilation hole that there is a possibility that air can be pulled into the box from above. This results in much higher uncertainty of what the flow actually is through the fuel bed, so no further testing at lower flow rates was conducted. Table 2 shows the values of the estimated naturally entrained flow rate into the body of the crib while burning at the peak rate in unrestricted quiescent conditions. Note that these are estimates of the amount of air only within the fuel bed and do not include the air that would be entrained into the fire and smoke plumes.

Intuitively, this air flow rate that is naturally entrained through the fuel bed under normal unrestricted quiescent ambient conditions generally increases with the burning rate. Figure 6 shows this estimated entrained flow into the crib as a function of the burning rate predicted by Thomas [17] from Equation 2. As mentioned earlier, the Thomas correlation [17] provides a better prediction of the burning rate for a wider variety of cribs than the Heskestad correlation [16] in Equation 1 [18]. This is confirmed here in Figure 7 which demonstrates agreement of the Thomas correlation with the experimental data to within 22%. The linear regression in Figure 6 suggests that the air-to-fuel ratio within in fuel bed is approximately 1.11. However, Quintiere and McCaffrey in [30] estimate that the stoichiometric air-to-fuel ratio for wood cribs is 4.92. By comparing these air-to-fuel ratios (1.11/4.92 = 0.23), it would seem then that the majority (> 75%) of the air required to consume the pyrolyzed fuel is therefore entrained in the flame with only a small portion (< 25%) passing through the fuel bed.

The path that the entrained flow takes through the crib was shown in [24] to be a complex problem where the resistances to flow in the horizontal and vertical directions are strongly dependent on the crib structure. In particular, as the aspect ratio (stick length divided by the stick thickness, \(l\)/b) of the crib increased, more and more of the airflow was shown to originate from below the crib. In [24], it is argued that for aspect ratios of 20 or larger (\(l\)/b ≥ 20), such as for crib designs #3–12 tested here, limited airflow is likely through the sides. If inadequate space is provided below the crib, the burning rate will drop [18, 24], though it is unknown whether the entrained airflow through the horizontal sides of the crib will follow the same trend with the burning rate as reported here. It is possible that the suggested air–fuel ratio within the fuel bed is only applicable for cribs with unrestricted access to flow from underneath.

To define crib porosity as an air-to-fuel ratio, there have been at least two different methods of estimating the airflow through the crib. To develop his porosity factor, Heskestad estimated the air flow rate as A_vs^1/2 [16]. In [14] and [20], the volumetric buoyant airflow up through the crib vents was assumed to be related to A_vh^1/2. Figure 8 compares the experimentally determined air flow rates induced during unrestricted quiescent conditions to both relations from the literature. Interestingly, both relations correlated with the experimental values equally well and also as well as the predicted burning rate (Figure 6) (which is essentially A_ss/h^1/2), at least based on the r² value. In [16], Heskestad argues that A_vs^1/2 fits the data better than A_vh^1/2, however, this is not clearly seen here. Though the r² value is about the same, the data visually look more scattered when A_vh^1/2is used. However, if crib design #12 is omitted, which is the rightmost point in Figure 7 and likely had an induced air flow rate above the 1000 LPM assigned (see above discussion), the r² improves to 0.9711 for A_vs^1/2 but remains relatively unchanged at 0.9356 for A_vh^1/2 (orange lines in Figure 8). This suggests that A_vs^1/2 may indeed be a better term to use for the air flow rate as suggested by [16].

Figure 9 replots the normalized burning rate, this time against the air flow rate normalized by the estimated entrained air flow rate in unrestricted quiescent conditions from Table 2. Figure 9 demonstrates that the data collapse to a single curve when the forced flow is below the naturally entrained flow (normalized flow rates below 1). In these “under-ventilated” conditions, the burning rate is clearly controlled by access to air only, and the relative reduction in the burning rate does not depend significantly on the characteristics of the fuel bed. This is seen more clearly in Figure 10 which zooms into the “under-ventilated” region to take a closer look, demonstrating an exponential increase up to unrestricted quiescent conditions. However, for “over-ventilated” conditions, the data do not collapse to a single curve, indicating that the fuel bed’s response to increased ventilation isn’t as straightforward, and the characteristics of the crib influence the relative increase in burning rate in this regime.

To understand how the fuel bed’s characteristics might influence the burning behavior in the “over-ventilated” regime, Figure 11 plots the data in a similar manner as Harmathy [25]. In this figure, the dimensioned burning rate (\({\dot{m}}_{b}\), g/s) and air flow rate (\({\dot{m}}_{a}\), g/s) are scaled by the exposed surface area of the sticks (A_s, cm²) (Table 1) so that both are in terms of a mass flux. Plotted this way, each crib design that Harmathy tested followed its own curve (as in Figure 5). However, in manipulating the data, it was noted that there is a slight dependence on the stick thickness (b, cm) and the crib porosity (φ, cm) as defined by Heskestad (Equation 1) [16]. By including these slight dependences and scaling the burning rate by the additional non-dimensional parameter \({\left(b/\phi \right)}^{0.25}\), all of the data appear to generally collapse to a single curve:

In the literature [14‐16], the burning rate is frequently scaled by A_sb^−0.5, as this is the “idealized” burning rate expected from an individual stick. The dependence on the stick thickness isn’t quite as strong here though (exponent of 0.25 instead of 0.5). The inclusion of the porosity factor (φ) is logical as it accounts for the natural air-to-fuel ratio of a particular crib. Dense cribs with a smaller porosity have more potential to increase their burning rate with forced flow. It is important to note that the x-axis in Figure 11 includes only the total exposed surface area, not how that surface area is arranged, hence the need for a parameter that describes the compactness of the fuel bed in the y-axis.

Returning to this notion of air-to-fuel ratios, Heskestad [16] correlated the burning rate normalized by the “idealized” value for an individual stick (A_sb^−0.5) as a function of the air-to-fuel ratio (φ, where the fuel quantity is also given by A_sb^−0.5). To pursue a similar approach, the “idealized” value of the burning rate for both axes is taken instead as the predicted quiescent burning rate (Equation 2 with constants inserted: 0.00119A_ssh^−0.5). Figure 12 shows the mass loss rate relative to this “idealized” value as a function of the ratio of the “forced” air-to-fuel ratio (\({\dot{m}}_{a}\)/0.00119A_ssh^−0.5) to the quiescent air-to-fuel ratio (φ). The x-axis is therefore an “equivalence ratio” of sorts. The line of best fit in Figure 12 is a slightly better fit to the data when treated this way (r² improved to 0.7990):

Note the general similarity of the shape of the curves in Figures 9, 10, 11 and 12 and form of Equations 4 and 5 to that found in Gross [14], Block [15], and Heskestad [16] (for fit equation see [18]). This implies that there is a similar split into two regimes. When the airflow into the crib is small, the burning rate is controlled by the access to air. In this regime, the scaled burning rate (whether by A_s(b/φ)^−0.25 or the quiescent burning rate) increases dramatically with airflow. At some point, the scaled burning rate begins to level off at some new “idealized” burning rate with further increases in airflow, before decreasing at high flow levels. Logically, this new “idealized” burning rate under forced flow would be sensitive to some parameter characterizing the crib’s denseness (φ, s, or A_v) and a parameter related to ability of air to promote char oxidization (A_s).

It is important to note that these lines are likely to curve downward for higher air flow rates as in Harmathy [25], so that this curve is only applicable over a certain range of airflows. However, for most crib designs, it was not possible to test sufficiently high flow rates here to observe this curvature, so it is still unknown exactly where this curvature occurs and what best predicts it. This is thus not accounted for in the approaches considered above. As mentioned earlier, unfortunately, a direct comparison to the data of Harmathy [25] where this curvature does occur can’t really be made because his setup likely reduced the airflow underneath the crib which could have a major influence on the resulting burning rate.