Abstract
To estimate and model explosion pressure rise in closed volumes, industrial applications require a simple method. Ideal gas model is capable to assume pressure rise values to 10% above to initial pressure. However, most of the explosion venting devices opens higher than this pressure range.
Extension of ideal gas model was carried out in this paper. Authors made some experimental studies in 20 L explosion sphere at ambient temperature and atmospheric initial pressure, with propane-air mixtures at different concentrations between 2.8 and 6.3 vol%. They measured pressure values inside the chamber during explosion and recorded at 9,600 Hz. Based on experimental studies, authors extended ideal gas model application range to 1.5 barg.
1 Introduction
Dust and gas explosions or flame spread occur in everyday life [1] and a wide range in industrial segments from wood industry to food or chemical applications and mining. Dust safety science report of Cloney [2] summarized 28 dust explosions, 51 fire incidents and 8 fatalities worldwide, between January and June of 2021. Prevention of serious damages [3] based on four pillars: explosion-proof construction, avoidance of spread, suppression, and venting.
As it can be seen in Fig. 1, during explosion in closed vessels, the pressure rises quickly to maximum explosion overpressure
Effect of venting protection to explosion pressure rise
Citation: Pollack Periodica 17, 3; 10.1556/606.2022.00603
The maximum pressure values and deflagration indexes can be used to design proper venting protection for vessels and enclosures. Explosion venting devices, when pressure inside the vessel reaches their static activation pressure, become open in their full area and reduce the pressure inside the vessel, below the resistance of protected equipment, as it can be seen in Fig. 1.
Extensive experimental and theoretical studies are available to determine explosion characteristics in case of both unvented and vented cases; however their reliability varies according to scale of investigated chamber, and applied fuel. Some of the correlations have been included to international standards.
Explosion modeling work can be classified into three main categories:
- ‒ empirical correlations, such as model of Huzayyin et al. [4], or work of Razus et al. [5];
- ‒ phenomenological models, like Frolov model [6] or ideal gas model; and
- ‒ CFD models, like EXSIM code or FLACS. CFD models can give satisfactory accurate solution, however they are not led to the solution as fast as industrial calculations need.
On the contrary, the first two models give more simple correlations to predict explosion characteristics than the CFD models, they typically approach maximum rate of pressure rise and deflagration index. Mokhtar et al. [7] investigated the most widespread vented models against experimental studies. They found, e.g., in case of propane-air mixtures, that the errors of reduced explosion overpressures estimated according to EN 14994 standard [8], NFPA 68 standard [9], Bradley and Mitcheson method [10] and Molkov method [11] approximate to measurement results by a wide margin between 0.0068 and 52.258 relative error. Lautkaski [12] studied vented explosion models and vented ones with duct. Author revealed that in case of different fuels – natural gas, methane, and propane –similarly significant relative errors have been found against measured maximum explosion overpressures. Investigated correlations had been interpreted into NFPA 68 and VDI 3673 standards [9, 13].
It is clear, that most of the mathematical models, which are typically used to calculate vented explosions are very imprecise, but many of these equations have been incorporated into international standards of explosion protection.
To make applicable methods more precise besides keeping them as simple as possible, authors in this paper investigated propane deflagrations in closed vessel, since it is a widely used explosive gas in industrial processes. Authors carried out some experimental studies in a 20-L explosion sphere at ambient temperature and atmospheric initial pressure. Based on their experimental studies, they extended ideal gas model application range to 1.5 barg.
A further aim of their research is to develop such correlations for the maximum explosion pressure in case of vented and unvented explosions, for most common gas mixtures in industry, which can describe processes with more proper accuracy than currently used relationships.
2 Ideal gas model
2.1 Original form of ideal gas model
Ideal gas model is one of the phenomenological models of gas explosion. The model assumes a fully premixed air-fuel mixture in a closed volume before combustion occurs. Ignition source assumed infinitesimally small with proper amount energy to start self-sustaining deflagration, and at significant distance from the walls.
2.2 Extended form of ideal gas model
From the conditions of ideal gas model can be seen, - as mentioned above - Eq. (10) only valid if the pressure is 10% above the initial pressure during explosion, i.e., approximately during laminar phase of the flame propagation [14]. Aim of this research was to establish the formal extension of the model up to 1.5 barg, in case of atmospheric initial state (to 150% above initial pressure).
3 Measurements
Some experimental studies were made with closed vessel to validate the extended model. Authors made the test sphere with propane-air mixtures at different concentrations between 2.8 and 6.3 vol%.
3.1 Experimental set-up
Main parts of Kühner test chamber were designed according to the principles of standard EN 14034-2:2006 +A1:2011 [16]. The test chamber is a 20-L hollow sphere with double stainless steel wall, which serves as water-cooled jacket to transfer the heat and to thermostatically control the test temperatures. The explosion pressure inside the vessel is recorded with three independent pressure transducers of 9,600 Hz. The process control and data acquisition unit operated on the computer with data collection function.
Propane-air mixtures with 2.8–6.3 vol% were used in experiments. Air was applied from the environment for more realistic measurements. For testing, the gas in proper concentration is dispersed into the vacuumed chamber via gas filling nozzle. The ignition source is located in the center of the sphere. For gases, it is an electric spark, with computer-regulated 10 J energy.
3.2 Experimental process
Experimental studies were performed at atmospheric pressure (1 barg) and ambient temperature (298 K). To increase the reliability of the measurements, a filling chamber was designed and produced with 0.6 L volume, including all fittings. Its function was to fill the required amount of propane to the 20-L chamber. The desired propane amount was checked by a pressure transducer placed in the filling chamber, also at a frequency of 9,600 Hz.
Scheme of complete measurement setup with the gas filling chamber is shown in Fig. 2. At the Fig. 1 means gas filling chamber, 2 means Kühner explosion chamber. P1 shows pressure transducer connected to the filling chamber and P2 shows pressure transducer connected to explosion chamber. Both were P6A type, made by Hottinger Brüel & Kjaer GmbH. The chamber originally is equipped with, and ignition process was controlled automatically by K1 and K2 are Kistler piezoelectric pressure transducers.
The different stages of the closed chamber measurements are illustrated in Fig. 3. Solid line shows the characteristic curve of the pressure values recorded in the 20-L chamber, while the dashed line shows the characteristic curve of the pressure values recorded in the filling chamber.
In stage 1, the filling chamber and the explosion chamber were simultaneously vacuumed to a predefined value. At the end of vacuuming, the connection between the two chambers was eliminated by closing the ball valve between them.
In stage 2, propane was loaded into the filling chamber, also up to a predetermined overpressure, in order to reach the proper amount in the mixture. Proper loading pressures of propane determine the composition of explosive mixture in the chamber.
After propane loading, the ball valve between the two chambers was opened again, and part of the propane gas flowed into the explosion chamber in stage 3. At the end of this process, small amount of propane remains in the filling chamber, and the pressure is slightly less than ambient pressure. In order to eliminate the vacuum and flush the filling chamber, the missing air volume was provided from the ambient air by passing it through the filling chamber. At the end of the section, all openings on the explosion chamber were closed. . The filling method of the chamber and the resulting high degree of turbulence provides homogenous gas mixture in the chamber.
In stage 4, ignition was performed after a software-controlled delay of 60 ms, which ensures dissipation of turbulence before ignition, however gas components do not separate at this time. Pressure values in the chamber during the explosion were recorded. After the explosion occurred, the whole system was thoroughly ventilated to remove residual gases and combustion products.
3.3 Measurement results
As mentioned before, the tests were performed with propane-air mixture. The compositions of the mixtures were 2.8, 3.8, 4.8, 5.8 and 6.3 vol% propane in air. Typical explosion values (maximum explosion overpressure and deflagration index) from the tests are summarized in Table 1. For each concentration, at least five different measurements were developed, discarding the smallest and largest of these, and averaging the others. Furthermore, as it can be seen from the description of the measurement, the pressure values in the explosion chamber were recorded by three independent pressure transmitters, so that the characteristic values for a single concentration is the average of at least nine different measurements.
Measured explosion characteristics
Propane amount [vol%] | Maximum explosion overpressure |
Deviation of measured |
Deflagration index |
Deviation of measured |
2.8 | 5.46 | +1.4%, −2.18% | 21 | +3.04%, −6.08% |
3.8 | 7.36 | +1.72%, +0.04% | 85 | +8.59%, −6.05% |
4.8 | 7.91 | +1.46%, −2.54% | 111 | +1.38%, −2.27% |
5.8 | 7.15 | +1.21%, −1.26% | 49 | +8.44%, −9.17% |
6.3 | 6.54 | +3.44%, −2.46% | 23 | +22.83%, −18.50% |
The averages of measured maximum explosion pressure values compared to the literature data (Razus et al. [5], NFPA 68 [9], Cashdollar et al. [17]) are illustrated in Fig. 4. The measured values correlate with the literature, with an average deviation under 3.5% (see Table 1).
The measured deflagration indexes were compared the literature data (Huzayyin et al. [4]) is illustrated in Fig. 5. Since the initial turbulence has an extreme influence on the instantaneous flame velocity and on the rate of explosion pressure rise, this may explain significant deviation in measured values (see Table 1) and high discrepancy with the literature - although any information in the source cannot be found.
Based on literature and measured data of maximum explosion overpressure, and rate of pressure rise, extended ideal gas model can be established.
4 Extension of ideal gas model
Original ideal gas model was adequate until the pressure rise reaches maximum 10% above to initial absolute pressure. However, most of the explosion venting devices opens when the pressure is 10% above of operating pressure. Therefore, extension of ideal gas model was carried to 150% above the initial atmospheric pressure to cover activation pressures of venting devices, too. To extend the model, authors defined an
The values of
Values of ε correction factor related to propane amount
Citation: Pollack Periodica 17, 3; 10.1556/606.2022.00603
Coefficient in the approximation function, Eq. (12) is
Measured and modeled pressure values according to original and modified ideal gas model, in case of 4.8 vol% propane-air mixture
Citation: Pollack Periodica 17, 3; 10.1556/606.2022.00603
5 Conclusions
In this research, authors studied ideal gas model for 20-L volume closed vessel. They developed new, more accurate gas filling system for test chamber, and carried out closed vessel explosion measurements in wide range of propane amount. Based on these experiments, authors extended ideal gas model to wider range of explosion pressure rise.
Application range of former ideal gas model were extended from
These studies can be used to predict explosion pressure values inside closed vessel related to time and initial propane content. Development of the new model will be continued with vented explosion cases and developing a vented model for propane explosions.
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