Synchronized smoldering combustion

A typical smoldering experiment with no synchronization is shown in fig. 2(a). The sample was heated from below, leading to slowly increasing temperatures, with highest values in the lower part of the sample throughout the external heating. A self-sustained smoldering fire was initiated, indicated by temperature increase above the imposed heater temperature in multiple measurement positions after the heater was switched off at 13 h. Approximately 120 experiments have been carried out with wood pellets in the geometry shown in fig. 1 without the cooling unit. All display disordered combustion with steady or intense consumption of fuel like in fig. 2(a), with no synchronization. Also for experiments with cooling unit in the sample center (see fig. 1) but without water, disordered combustion with no synchronization was observed, as for the experiment in fig. 2(a). There were conductive heat losses through the cooling unit, but without effects on the overall combustion pattern.

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With water flow through the cooling unit from the start of the external heating, the expected disordered combustion was not observed immediately after the heater was switched off. Instead, the system cooled down for 2–3 h, before the temperatures started pulsating (fig. 2(b) and (c). During a pulse, the temperatures increased in a synchronized manner throughout the sample, reaching typical temperature maximums of $300\text{--}500\ ^{\circ}\text{C}$, with pulse duration of 2–4 h. After reaching maximum temperatures, the entire fuel bed cooled down and remained so for several hours, before the temperatures in concert again increased towards a new pulse. Here lies the synchrony.

In the experiment displayed in fig. 2(b), there were 9 consecutive synchronized pulses, after which the system displayed a spontaneous transition from synchronization to disordered intense combustion at 42 h. In fig. 2(c), there were 4 pulses before a transition to disordered combustion at 24 h. During the pulsating period, hot regions traveled within the sample (horizontally and vertically) at median traveling speeds of 2.1 mm/min (see the supplemental material for video animations cited in the appendix). This was not observed during disordered combustion, and interestingly, the traveling speed resembles the median of 1.8 mm/min for smoldering fronts in horizontal fuel beds [11]. From the large number of performed experiments, the rare phenomenon of repetitive pulsations (shown in fig. 2(b) and (c) was observed in 7 out of a total of 14 experiments with strong cooling (pulsation period $17.5 \pm 5.5\ \text{h}$). In the remaining 7 experiments, there were one or two pulsations, followed by self-extinguishing, see fig. 2(d) (pulsating period $4.7 \pm 2.1\ \text{h}$). No active extinguishing measures were used other than the central cooling unit with water flow. The variation in experimental outcome, despite the same initial conditions reflects the stochastic nature of smoldering.

For the pulsating period, linear regression showed a significant (p < 0.05) increase in both maximum temperature and pulse frequency as the system approached disordered combustion, see fig. 2(b),(c). Including all pulsating experiments, the last pulse before disordered combustion had significantly higher temperatures and frequencies ($413 \pm 44\ ^{\circ}\text{C}$ and $0.53 \pm 0.2$ pulses per hour) compared with the pulsations followed by a new pulse ($367 \pm 55\ ^{\circ}\text{C}$ and $0.34 \pm 0.1$ pulses per hour). Significance is determined at p < 0.05 by a two-tailed Mann-Whitney U test [25]. This indicates an increasing activity in the system as it approaches disordered combustion. The systematic increase also indicates that for a given pulse, there is some degree of predictability of whether the pulse will lead to a disordered situation, or maintain its synchronized combustion. Self-extinguishment could not, however, be predicted based the temperature or frequency of a pulse. The temperatures lie in the same range as the first pulsations of the non-extinguished pulsations (although often in the lower end of the range, as in fig. 2(d)). No increase in frequency could be determined with significance due to too few pulsations before self-extinguishment.

Comparing pulsations with disordered combustion, the pulsations represent a low-intensity form of combustion: Mass loss rates were an order of magnitude lower for the pulsating period than for the disordered period (typical ranges 25–45 g/h vs. 140–600 g/h). The maximum temperatures were also lower, $379 \pm 55\ ^{\circ}\text{C}$ vs. $599 \pm 33\ ^{\circ}\text{C}$.

To further elucidate the transition from pulsating to disordered combustion, consider the stability criterion used for a quasi–two-dimensional smoldering front, in terms of the dimensionless quantity $Ar_{\mathrm{c}} = RT_{\mathrm{c}}/E$, where R is the gas constant, $T_{\mathrm{c}}$ is the combustion temperature and E is the activation energy, a material-specific property [21,26]. These fronts oscillate, in the sense that propagation velocity varies, over positive values, in an oscillatory way. The criterion gives a material-specific prediction for transition from oscillating ($Ar_{\mathrm{c}} < 0.03$) to non-oscillating smoldering ($Ar_{\mathrm{c}} > 0.03$), facilitated by a high combustion temperature. For our case, where we have measured the activation energy 91.4 kJ/mol [27], the corresponding $Ar_{\mathrm{c}} = 0.034 \pm 0.005$ for the pulsating period and $0.054 \pm 0.003$ during disordered combustion. Although dimensionality and geometry are different in our system, it is striking that our pulsation period gives an $Ar_{\mathrm{c}}$ value close to the one for the transition from oscillating to non-oscillating mode. The corresponding $Ar_{\mathrm{c}}$ value for the self-extinguished experiments was $0.032 \pm 0.004$.

The thermocouples located within the sample only covered the plane described in fig. 1, to minimize heat conduction along thermocouples and mounting rack. One may object that the pulsations could have occurred only locally near these measurement positions. There are three observations that support the notion of global pulsations. Firstly, based on mass loss and observed sample height during the pulsating period, calculations show that a significant share (> 40 vol%) of the sample has been involved in the combustion. Secondly, the thermocouples are placed in different locations (albeit in a plane) and they are all synchronized. Thirdly, further experiments were made with thermocouples mounted on an additional stainless-steel rack along the perpendicular plane to that shown in fig. 1. Synchronized temperature pulsations were observed also in these experiments, supporting the idea that the pulsations indeed involve the entire sample volume.

The only physical difference between the experiments with and without pulsations is the centrally located cooling unit. The cooling effect from this cooling unit (fig. 3(a)) was ${\sim}18\%$ of the total heat losses during the pulsating period. Cooling peaked at the maxima in the average temperature in the sample (indicated by the vertical gray lines in fig. 3) and at the heat production maxima (fig. 3(a)). The relatively low cooling power, 5–20 W, was sufficient to established a radial temperature gradient and a centrally located heat sink. The cooling power was in the same range as the 0–60 W heat production from combustion. As the sample temperatures increase, eventually the net heat losses from the sample cancel out the driving force, the heat production, causing the maximum-point turnaround of the pulsations. Other main contributors to the total heat loss were thermal radiation heat loss (${\sim}17\%$), heat losses through the insulated container wall (${\sim}8\%$), heat loss due to the buoyant smoke emission at the top of the sample (${\sim}17\%$) and heat loss through the bottom plate below the sample (${\sim}32\%$). Neither could have caused pulsations, since all set-up components but the cooling unit were also used for the experiments with no pulsations.

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The effect of heat losses on the maximum point turnaround can be illustrated by assuming adiabatic conditions. With no heat losses, the heat production in the sample,

$$\begin{equation} \dot{q}_{\mathrm{prod}} = H_{\mathrm{c}} \: m_{\mathrm{s}} \: A_A \: e^{-(E/R \: T_{i})}, \end{equation} \tag{ 1 }$$

equals the heat storage in the sample,

$$\begin{equation} \dot{q}_{\mathrm{storage}} = \frac{T_{i+1}-T_i}{t_{i+1}-t_i} \: C_{\mathrm{p}} \: m_{\mathrm{s}}, \end{equation} \tag{ 2 }$$

where $H_{\mathrm{c}}$ is the heat of combustion (6 kJ/g [11]), $m_{\mathrm{s}}$ the sample mass, A_A the pre-exponential factor, E the activation energy, R the gas constant, T_i the sample temperature at time t_i, $C_{\mathrm{p}}$ the specific-heat capacity. Using eqs. (1) and (2) recursively, curves as shown in fig. 4 can be built up for temperatures as a function of time. The very rapid increase is a consequence of the nonlinear driving term (heat generation) in eq. (1), combined with a linear "friction" term (heat storage) in eq. (2). The specific adiabatic curves in fig. 4 were obtained by fitting to part of the experimental pulse data by adjusting the unknown pre-exponential factor A_A and the $C_{\mathrm{p}}$ of the partially combusted wood pellets. The best fit for a constant $A_A= 80\ \text{s}^{-1}$ gives a $C_{\mathrm{p}}$ range of 1.0–4.5 J/gK, close to literature values in the range 1.2–2.8 J/gK for fresh wood, wood pellets and wooden products [28–30]. The spread in $C_{\mathrm{p}}$ values and the variation in the curve shape from pulse to pulse is not unreasonable in view of the noisy nature of smoldering. The temperature calculated for adiabatic conditions is 15% higher than the measured temperature after 75% of the temperature rise of the pulse, indicated by arrows in fig. 4. This is the point when the heat losses become prominent, and cause the temperature rise to decrease towards the pulse peak.

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Large heat losses compared to heat production could be expected to lead to complete extinguishment. For half of the 14 cases with strong cooling it did, but the remaining 7 displayed repetitive pulsations eventually leading to disordered combustion. To understand this surprising behavior, consider the mechanism causing the following minimum-point temperature turnaround. Different mechanisms act at pulsation peaks and troughs, as indicated by the differences in temperature slopes before and after a peak (curves resemble relaxation oscillations, see e.g. ref. [31]). The temperature slope leading up to a temperature peak follows the near-exponential curve given in fig. 4 from eqs. (1) and (2) while the declining temperature slope is less steep, as is expected for cooling [32]. The minimum-point temperature turnaround is most likely linked to the gradual subsidence and local collapses in the sample during the preceding pulsation peak combustion. A pellet grain consists of compacted wood dust, and will after enduring a significant mass loss become too brittle to retain its structural integrity, and disintegrate. Local collapses can give delivery of unburnt fuel to reaction zones, which can cause temperature turnaround in smoldering fuel beds [33]. Gradual compacting of the sample gives more insulated reaction zones with lower heat losses, which also promote combustion. However, compacting may also promote extinguishment, through lower oxygen supply to reaction zones. Combined with the relatively low temperatures of the pulsation troughs, which give lower reaction rates and reduced air convection, both promoting extinguishment, the system is at a balance point. In half the cases, the outcome is self-extinguishment, the other half results in gradual temperature build-up towards new temperature peaks.

It could have been expected that the heat production to heat loss ratio was significantly lower for the cases resulting in self-extinguishment, but this was not the case. The system is at a balance point, with only small variations and slightly lower ratios observed in the self-extinguished cases. Gradual increase in maximum temperatures and pulse frequencies as the pulsations progress also reflect this delicate balance. The cooling unit removes heat generated by smoldering processes, until the heat losses either overcome the heat production and the system self-extinguishes, or the pulsating combustion continues at the balance point until the combustion processes eventually overcome limitations by oxygen supply and heat losses, resulting in disordered combustion. We therefore propose that the synchronized pulsating behavior (fig. 2(b), (c)) is an intermediate state between the normal disordered smoldering process (fig. 2(a)), and the situation where cooling leads to self-extinguishment (fig. 2(d)). This is supported by experiments at a lower degree of cooling (to be reported elsewhere): only the strongest cooling resulted in self-extinguishment. Pulsations were not observed in any experiments without cooling.