4.1. OPM Measurement
Figure 3a illustrates the results of the OPM measurements, displaying the average OPM values obtained from the three repeated measurements for Cases 1 to 4.
Figure 3b is the three repeated measurements OPM’s standard deviation by bar. Deviation, despite variations in the overall OPM levels and due to factors, such as material type and position, resulted in similar patterns when examining the tendencies across the three experiments conducted for each case. This consistency may have been influenced by the surface temperature of the frying pan for each case, as shown in
Figure 4, as well as the relative humidity specific to each case, as depicted in
Figure 5.
Figure 4b and
Figure 5b represent the standard deviation of all experiments per case.
A notable common pattern was observed in the experimental results. The first pattern was characterized by a point of inflection where the temperature slightly decreased, and the relative humidity slightly increased after adding the material at the initial preheating temperature of 180 ± 20 °C. This occurrence can be attributed to the generation of fine smoke, including water vapor, when the ice attached to the frozen material comes into contact with the hot surface of the frying pan.
The second pattern also displayed a point of inflection when the material was flipped over after being left in the pan for 8.00 min. The peak time was observed to be approximately 8.33 ± 0.33 min. The reason for this pattern is that the temperature of the pan increased beyond the initial preheating level after 8.00 min. Flipping the material at this moment resulted in a higher OPM due to the instantaneous release of water vapor, as the condensed moisture on the surface of the uncarbonized material, which was at a relatively low temperature, came into contact with the hot pan surface.
The third observed pattern revealed similarities between the rising trends during the initial material addition (referred to as the first buildup) and when the material was flipped over (referred to as the second buildup). The experimental results indicated that the first buildup began at around 2.00 ± 1.00 min and continued until the moment of flipping over the material. Subsequently, the second buildup started at approximately 10.00 ± 1.00 min, which was approximately 2.00 ± 1.00 min after flipping over the material, and persisted until the end. These findings suggest that the moisture within the material rapidly dissipated within the initial 2.00 ± 1.00 min. Consequently, in experiments involving frozen cooked products, the actual burning of the material takes place in earnest after the surface, and interior moisture of the material evaporates within approximately 2.00 ± 1.00 min. Moreover, the minimum required time for one side to be burnt is 8.00 min.
4.2. Estimation of the Activation Time of the Photoelectric Smoke Detector
The three repeated experiments showed that the ASD was activated when the OPM reached and sustained around 15%/m for approximately 0.08 min. As the CSDs operates through light scattering, it does not provide numerical OPM values. Therefore, in this case, the OPM value of the adjacent ASD at the time of activation was used as a reference. When the CSD was activated, the OPM value of the neighboring ASD ranged from 5 to 12%/m. These results enabled us to determine that the CSD activates at an average OPM value of 8.5%/m. To estimate the activation times of the CSD and ASD, the average activation time of the photoelectric smoke detector for each case and position, as well as the OPM change rate of the photoelectric smoke detectors, were examined.
Table 4 presents the activation times of the photoelectric smoke detectors at each position for each case. Overall, the CSDs tended to activate earlier than the ASDs. Among the detectors that were activated over time, only two CSDs were activated between 0.00 and 0.33 min upon adding the material, while four CSDs were activated at 7.00 ± 1.00 min during the first buildup process. During the turning over of the material, between 8.00 and 8.67 min, three CSDs and four ASDs were activated. At 14.00 ± 2.00 min during the second buildup process, most of the photoelectric smoke detectors were activated, including 15 CSDs and 13 ASDs. After 16.00 min, 8.00 min after the material flip, the remaining seven ASDs were activated.
The results suggest that unwanted fire alarms may occur when a rapid fluctuation in the amount of water vapor exists due to temperature differences between the pan and the material, such as during the addition and flipping of the material. Additionally, unwanted fire alarms can occur when a sufficient amount of cooking by-products, capable of activating the photoelectric smoke detectors, accumulate after approximately 8.00 ± 1.00 min from the time of material addition or flipping, which initiates the buildup process. Note that, these results, which involve artificial interventions, were excluded when considering the OPM gradient of the photoelectric smoke detectors, as the photoelectric smoke detectors were determined to be activated by water vapor rather than cooking by-products.
The experiments showed that the six photoelectric smoke detectors did not activate sequentially. For a photoelectric smoke detector to activate, cooking by-products need to enter the internal chamber of the photoelectric smoke detector and cause light scattering, triggering a signal. The smoke generated during the cooking scenario has a lower temperature than the actual fire, resulting in lower thermal buoyancy and a relatively small updraft. Consequently, the inflow of smoke exhibited irregular characteristics, regardless of the location.
The ASD located at point 2, as shown in
Figure 6a, exhibited similar behavior to the average ASD of all points depicted in
Figure 6b.
Figure 6c shows all of the experiment’s standard deviation case by case. This implies that the overall smoke generation throughout the mock-up space is comparable to the ASD value measured at point 2. Consequently, based on the average results of the OPM gradient of the smoke detectors and their activation times, an equation for the activation time of the smoke detectors was derived.
To minimize errors when calculating the overall gradient, the OPM gradient was determined separately for the first and second half of the experiments.
Table 5 presents the OPM gradients of the smoke detectors. By analyzing the OPM gradient during the period from the first buildup until the moment of material flipping (referred to as the first half), and from the second buildup until the occurrence of maximum OPM (referred to as the second half), the gradient for the entire experiment was predicted.
Two minutes after the ingredients were added and 2 min after flipping them over, the moisture within the material rapidly dissipated. Therefore, the onset of the gradient for the first and second halves occurred at 2.00 and 10.00 min, respectively. The gradients for the first half were 0.804%/m·min for Case 1, 0.948%/m·min for Case 2, 0.558%/m·min for Case 3, and 0.840%/m·min for Case 4. The gradients for the second half were 2.052%/m·min for Case 1, 2.772%/m·min for Case 2, 2.526%/m·min for Case 3, and 1.914%/m·min for Case 4. These findings indicate that the gradients in the second half were higher than those in the first half. This could be attributed to the rapid increase in smoke, including cooking by-products during the second half, as the rise in temperature enhanced efficiency and carbonization with decreasing moisture in the material. The overall gradient can be expressed as the average sum of the gradients for the first and second halves, as derived earlier. Considering the relationship between the gradient and activation time measured in OPM for the smoke detectors, an equation was proposed to estimate the activation time at CSD 8.5%/m and ASD 15%/m.
Table 6 presents the estimation activation times of CSD and ASD. The formulas used to calculate the activation times of the photoelectric smoke detectors are shown below. These equations were derived to estimate the operating times of smoke detectors that activate in random order. The response level of the ASDs can be adjusted by modifying each parameter (gradient). Therefore, the equation was derived based on the gradient to provide a general representation of the operating sequence of the detectors. The activation time of the smoke detector is influenced by the resistance encountered at the entrance, which is known as entry lag. This entry lag can be expressed using the following equation:
where
is the detector’ s external optical density (OD) at the time of response,
is the internal OD required to enable the detector response, and
is the OD per unit length. Thus, Equation (1) was expressed by a gradient, as shown in Equation (2) [
5]. In addition to smoke characteristics and the detector’s operating mechanism, entry resistance, which is the ability to get the smoke into the chamber, affects the response of the unit. For spot-type photoelectric smoke detectors, entry resistance is caused by bug screens, chamber design, and the detector’s aerodynamic characteristics. In a scenario where the OD at the detector location increases with time, the OD inside the detector chamber will always be less than that outside the detector chamber. Similarly, if a detector is placed in a smoke stream having a constant OD, there will be a time delay before the OD inside the chamber approaches that which is outside the detector. If the time constant and rate of change of OD outside the detector are constant, this equation can be solved. Since we installed the same detector, this equation was applied. The relationship between the
OD (
) and OPM can be expressed as Equation (3), according to UL 217 Annex B.
Here,
represents the optical density during detector operation, as shown in Equation (4), while dt corresponds to the operating time of the detector minus the time before flipping the sample (2 min), since the amount detected before flipping is close to zero and there is no random intervention, as shown in Equation (5). To obtain the average value, Equation (6) is applied by separating the first half (before input) and the second half (after input) based on flipping, which can be expressed as shown in Equation (7). Furthermore, this can be expanded as Equation (8) to derive Equation (9).
where
is the time constant of the detector (time point when the detector is activated).
TimeSD represents the activation time of the photoelectric smoke detector. (TimeSD − 2) indicates the activation time of the photoelectric smoke detector starting 2 min after the beginning of the experiment. OGf refers to the gradient of the first half, OGs represents the gradient of the second half, and SDOPM denotes the OPM value required for the smoke detector activation. Assuming that the internal light sensitivity of the detectors is equal, given that the initial experiment conditions are identical, the anticipated SDOPM can be estimated by multiplying OPMGradient, derived from the experiment, by TimeSD.
The OPM value triggering photoelectric smoke detector activation was obtained by substituting 8.5%/m for CSD and 15%/m for ASD. The results indicated that the activation time for CSD was 7.95 min for Case 1, 6.57 min for Case 2, 7.00 min for Case 3, and 8.17 min for Case 4. In contrast, the activation time for ASD was 12.50 min for Case 1, 10.06 min for Case 2, 10.82 min for Case 3, and 12.89 min for Case 4.
4.3. Measurements and Gradient of Environmental Sensor
The gradients of OPM, PM, and carbon oxides were compared to assess the ES factors that can enhance the adaptability of photoelectric smoke detectors to unwanted fire alarms. The gradients were determined based on the average ES values at 6 points.
First, the gradient of PM measured using the ES was analyzed. PM1.0, PM2.5, and PM10.0, which have different particle diameters, exhibited variations depending on the scenario. Regardless of fire or unwanted fire alarms, PM10.0 showed an increasing trend, while PM1.0 demonstrated a decreasing trend as the visible smoke levels escalated. PM2.5 fell between these two values.
Figure 7a–c illustrate the gradients of PM1.0, PM2.5, and PM10.0, respectively. In all experiments, before flipping the samples, PM1.0, PM2.5, and PM10.0 exhibited higher values in that order. After flipping the samples, a significant amount of smoke was generated, resulting in higher values in the order of PM10.0, PM2.5, and PM1.0.
Figure 7d–f exhibit the standard deviation of PMs.
The sensor characteristics showed that PM1.0 increased due to moisture from the burnt material, as indicated by the corresponding increase in relative humidity. Notably, both PM1.0 and relative humidity rapidly increased between 0.00 and 2.00 min and between 8.00 and 10.00 min. However, they subsequently showed a rapid decrease. Moreover, PM2.5 displayed a slightly faster increase than the OPM gradient at the time of material addition. However, it tended to decrease during the second buildup, which involved carbonization. Therefore, applying PM2.5 as a characteristic factor for activating unwanted fire alarms in photoelectric smoke detectors is also impractical. In contrast, PM10.0 exhibited a pattern similar to the OPM gradient, suggesting that it could be employed as a characteristic factor for activating unwanted fire alarms in photoelectric smoke detectors.
Subsequently, the carbon oxides CO and CO
2 were examined as measured by the ES. While CO traditionally represents incomplete combustion products and CO
2 represents complete combustion products, both were measured in this study due to their potential occurrence during cooking. Although CO is typically measured in ppm and CO
2 in % concentration, both were measured in ppm for faster gradient measurement.
Figure 8a,c illustrate the time-dependent generation of CO and CO
2, respectively, and
Figure 8b,d exhibit the standard deviation of CO and CO
2. While the gradients of the carbon oxides slightly differed from the OPM gradient, both CO and CO
2 exhibited consistent increases. This suggests their suitability as characteristic factors for activating unwanted fire alarms in photoelectric smoke detectors. Consequently, using only one factor for verifying the respond characteristics and reducing unwanted fire alarms in photoelectric smoke detectors is challenging.
Table 7 lists environmental sensor gradients (EG) of the three identified characteristic factors applicable to unwanted fire alarms based on the experimental results discussed above. By applying these gradients, the
ESdata can be estimated.
These results differ from the slope values inferred using the unwanted fire alarm judgment area values proposed in previous studies, such as PM10.0 (295.7 μg/m³ min), CO (0.615 ppm/min), and CO
2 (23.35 ppm/min) [
15]. This difference is attributed to variations in the experimental environment, such as the height of the space and the presence of personnel intervention during sample insertion and turning.
By examining the gradients of PM10.0, CO, and CO
2 as characteristic factors for unwanted fire alarms, an equation was derived to estimate the environmental sensor data (
ESdata) at the time of photoelectric smoke detector activation. Based on these findings, Equation (11) illustrates the method for deriving the ES value, which exhibits a characteristic trend when the sensor activates in a cooking scenario.
where
ESdata is the environmental sensor data,
EGf is environmental sensor gradient of the first half and
EGs is environmental sensor gradient of the second half.
The activation time of the photoelectric smoke detectors, PM10.0, CO concentration, and CO
2 concentration values measured with ES, along with their standard deviations, are presented in
Table 8. The activation time of the CSD was 7.42 ± 0.76 min. Simultaneously, the PM10.0 value was 3707.85 ± 804.68 μg/m³, and the CO and CO
2 concentrations were 1.23 ± 0.34 ppm and 652.96 ± 42.97 ppm, respectively. The activation time of the ASD was determined to be 11.57 ± 1.35 min. Simultaneously, the PM10.0 value was 6542.09 ± 1421.03 μg/m³, and the CO and CO
2 concentrations were 2.16 ± 0.61 ppm and 1152.07 ± 87.99 ppm, respectively.
The applicability of PM10.0, CO, and CO
2 as sensors to supplement the unwanted fire alarms of photoelectric smoke detectors was examined by assessing the degree of data dispersion from the average. The coefficient of variation, obtained by dividing the standard deviation by the mean, was used to measure the degree of dispersion. PM10.0 and CO exhibited the same coefficients of variation (0.22 and 0.28, respectively) for both CSD and ASD, indicating their suitability as characteristic factors for unwanted fire alarm activations. The discrepancy in values compared to previous studies (PM10.0: 5914 μg/m³ and CO concentration: 12.3 ppm) is likely due to environmental differences, such as the shape and height of the space and the device installation method [
16]. However, CO
2 showed different coefficients of variation for CSD (0.07) and ASD (0.09), indicating that CO
2 is not suitable as a characteristic factor. This could be attributed to the influence of human intervention, as mentioned earlier. The coefficient of variation, representing the relative standard deviation, is a unitless measure that allows for comparing data sets with different units of measurement.
4.4. Discussion of Unwanted Fire Alarm Reduction Sensors and Limitations
The response characteristics of smoke detectors were investigated through experiments and analysis. This research suggests that unwanted fire alarms may occur when rapid fluctuations in the amount of vapor exist due to temperature differences between the pan and the sample, such as when adding or flipping the material. Additionally, the experiments revealed that six photoelectric smoke detectors did not operate sequentially. This is because the temperature is lower than that of an actual fire, resulting in low thermal buoyancy and relatively small updrafts. Since this factor interferes with improving reliability by understanding the characteristics of smoke detectors, we proposed equations that can estimate the activating time of smoke detector by considering the activation time.
Additionally, smoke detection characteristics were identified through various environmental sensors. The PM10.0 and CO sensors have been identified as effective in reducing unwanted fire alarms based on the findings. The activation times of 7.42 ± 0.76 min (CSD) and 11.57 ± 1.35 min (ASD) were inferred using equations and the photoelectric smoke detector gradient.
Using these research results, the location where unwanted fire alarms occur in a studio-type apartment due to cooking by-products can be predicted. Furthermore, the results can be used to install smoke detectors in the most suitable places to reduce unwanted fire alarms.
However, note that a slight discrepancy exists between Y.G. Choi’s study and the standards (ISO 7240-6, UL 268) in determining the gradient and the value of CO and PM10.0 as sensors to help reduce unwanted fire alarms. Although, this discrepancy is not unreasonable, as similar results have been observed [
16,
17,
18]. In particular, the value of CO obtained in this study is significantly lower than the gradient and value in a fire situation. Nevertheless, this value is still considered suitable value because it shows similarity to the gradient and value proposed in the cooking disturbance smoke alarm test of UL 268, which is an international standard. Although domestic and foreign research on this specific aspect is scarce, PM10.0 is considered effective because it falls within the particle size range (0.3–10.0 μm) of smoke that can be detected by a photoelectric smoke detector [
5].
Note that the gradient of each sensor may vary depending on the manufacturer and device; thus, additional verifications are necessary for future work. Additionally, the characteristics may be slightly different in spaces other than studio apartments. Therefore, further validation is needed for future work. We are conducting research in various spaces, such as stairs, and are considering a variety of materials that may occur in addition to the four scenarios.