Explosion Flame Research Articles

Experimental study on gas and coal dust explosive overpressure and flame dynamic characteristics in an engineering-level test roadway

The continuous development of coal science and technology has made gas and coal dust explosion disasters an important factor that restricts efficient and intelligent coal mining, which seriously threatens the safe production process of coal mines. To explore the gas and coal dust explosive overpressure and flame propagation characteristics in an actual roadway, the dynamic characteristics of gas and coal dust mixed explosion propagation and evolution laws of explosion flames were investigated using an integrated explosion test system and a high-speed image acquisition system in an engineering-level test roadway with a length of about 700 m and a cross-sectional area of 7.2 m2. Experimental results showed that the peak overpressure measured at each measuring point during the propagation process of explosion shock wave in the roadway did not rise or fall monotonously but fluctuated. The power of explosion shock wave was significantly strengthened by adding coal dust, while the flame propagation speed sharply increased in a certain zone, which generally showed a first increasing and then declining trend. In addition, the flame was blue white after the gas in the roadway was ignited, developed in an irregular shape, and ignited the surrounding combustible gas soon, which further ignited the coal dust under the combined action of pressure wave and flame front. In this case, the flame was deep yellow on the whole. The gas and coal dust explosion flame propagated along the longitudinal section above the roadway, and the flame propagated at an accelerated speed on the transverse section due to the disturbance of obstacles. The study results will provide an important theoretical basis for the R&D of technical active explosion suppression equipment in coal mines and the improvement in their installation technologies.

Suppression effect of nanocomposite inhibitor on Methane-Coal dust explosion flame propagation

To enrich the methane–coal dust explosion inhibition theory at different methane concentrations, the influence of the potassium oxalate-montmorillonite (OA-Mt) nanocomposite inhibitor on the flame propagation characteristics of 5%, 7% and 9% methane–coal dust explosion was studied experimentally and its explosion inhibition mechanism was revealed. Results showed that the optimum K2C2O4 loading concentration for explosion flame inhibition was 80%. The flame brightness was weakened, the flame instantaneous peak velocity vm was decreased, and the flame average velocity inhibition ratio φ was enhanced, proving that OA-Mt could be adopted as an excellent inhibitor for the methane–coal dust explosion. Additionally, OA-Mt had the most significant inhibition on 7% methane–coal explosion. Finally, an inhibition physical model of OA-Mt on methane–coal dust flame zones was established and the suppression mechanism was discussed. The physical-dominated inhibition effect in the flame preheating zone and the chemical-dominated inhibition effect in the combustion reaction zone co-mitigated the methane–coal flame propagation.

Research on the Explosion Venting Effect and Influencing Factors of Gas Explosion in Urban Shallow Pipe Trenches

ABSTRACT In this study, two groups of gas explosion venting tests were conducted based on a large-scale pipe trench test system (30 m length), and the numerical model of pipe trench was established through the FLACS software, which was verified by the corresponding experimental data, and then the explosion process and load distribution characteristics of the gas explosion in pipe trenches were further analyzed by varying the number, location, and size of the top vent and the size of the end opening. The results showed that the explosion flame and overpressure time-history oscillate significantly without top vents, and the peak impulse decreases while the peak pressure first increases and then decreases axially along the pipe trench, mainly attributed to the relative positions of the precursor and flame wave. The top vents can significantly block the flame propagation and weaken the oscillation phenomenon, but the attenuation of the peak overpressure is mainly limited to the upstream of the vents, so it is necessary to set multiple consecutive top vents to effectively reduce the overall explosive load. The overall peak stress and peak impulse can be attenuated by 12% and 57% respectively with 3 top vents, but the downstream peak stress even tends to increase with only one top vent. In addition, the explosion venting effect of top vents can be ignored with the small size (0.2 m × 0.2 m), the explosion venting effect of the end opening is also limited to a small range (12 m) upstream of it.

Effect of sludge-based suppression materials on the explosive flame characteristics of aluminium dust

A study was conducted to investigate the inhibitory effect of sludge-based phosphate-containing composite powder explosion suppressants (MPP/AMS) on aluminium dust explosion and combustion. The experiment compared the inhibition characteristics of ordinary sewage sludge particles, high-temperature alkali-modified sludge particles, phosphate-containing particles, and phosphate-modified sludge particles. The study utilized a flame propagation experimental device and an explosion pressure testing device for comprehensive research. The experimental recording devices revealed that sludge-based composite powder explosion suppressants effectively inhibit aluminium powder explosion and combustion. Thermodynamic analysis of the rapid oxidation stage was performed using the Coats Redfern (C-R) method, and validation was conducted using the Flynn Wall Ozawa (FWO) and Kissinger Akahira Sunose (KAS) methods. The results theoretically explain that sludge-based composite powder explosion suppressants can effectively suppress aluminium powder explosions and exhibit a blocking effect. Surface morphology and material element characterization experiments were conducted before and after the explosion, combined with pyrolysis characteristics. The analysis demonstrated that the inhibition mechanism of sludge-based composite powder explosion suppressants on aluminium powder explosion primarily involves two aspects: physical inhibition (MPP coating inhibition, porous adsorption isolation) and chemical inhibition (decomposition heat absorption, product oxidation). The theoretical findings provide evidence of the superior inhibitory effects of sludge-based composite powder explosion suppressants, offering new insights for the resource utilization of sludge waste and the development of novel explosion suppression materials.

Experimental Study on the Isolation Effect of an Active Flame-Proof Device on a Gas Explosion in an Underground Coal Mine

Passive explosion-isolation facilities in underground coal mines, such as explosion-proof water troughs and bags, face challenges aligned with current trends in intelligent and unmanned technologies, due to restricted applicability and structural features. Grounded in the propagation laws and disaster mechanisms of gas explosions, the device in this paper enables accurate identification of explosion flames and pressure information. Utilizing a high-speed processor for rapid logical processing enables judgments within 1 ms. Graded activation of the operating mechanism is enabled by the device. The tunnel flame-proof device’s flame-extinguishing agent has a continuous action time of 6075 ms. Experiments on the active flame-proof effect of a 100 m3 gas explosion were conducted using a cross-sectional 7.2 m2 large-tunnel test system. With a dosage of 5.6 kg/m2, the powder flame-extinguishing agent completely extinguished the explosion flame within a 20 m range behind the explosion isolator. Numerical calculations unveiled the gas-phase chemical suppression mechanism of the powder flame-extinguishing agent NH4H2PO4 in suppressing methane explosions. Building upon these findings, application technology for active flame-proofing was developed, offering technical support for intelligent prevention and control of gas explosions in underground coal mines.

Investigation of the effects of N2 and CO2 on the overpressure hazards, flame behaviors and reaction kinetics of LPG/air explosions

ABSTRACT To research the influence of inert gases on the explosion behaviors of LPG/air mixtures, LPG explosion tests suppressed by CO2 and N2 were conducted in a spherical chamber and the chemical reaction kinetic properties were analyzed. The results show that CO2 has a better inhibitory effect than N2, especially when the added amount is small. With the increasing volume fraction of inert gases, the LPG explosion flame propagation speed continuously decreases, and the phenomenon of flame uplift and wrinkling deformation occurs. The explosion pressure of LPG/CO2(N2)/air mixture and the average flame propagation speed in the initial stage follow an exponential function with an offset. The laminar flame structure of 4% LPG is similar to its mixtures with N2 and CO2. After adding inert gases, the maximum temperature of the LPG laminar flame decreases significantly, and the flame thickness increases. The key elementary reactions affecting the N2(CO2)/LPG/air explosions are given. The research results have important implications for suppression of LPG explosions.

Numerical Simulation of Gas Explosion with Non-uniform Concentration Distribution by Using OpenFOAM.

Gas explosions in coal mines have occurred occasionally, which may cause casualties and economic losses. In the actual mine roadway, the gas concentration distribution is uneven because the gas density is lower than that of air. Gas explosion characteristics of uneven gas distribution with the concentration gradient in mine roadways were analyzed by using the open-source computational fluid dynamic code OpenFOAM. The flame and pressure characteristics were calculated, and the flame and shock wave propagation laws of the non-uniform gas-air mixture explosion with different concentration gradients were analyzed and compared with the uniform gas-air mixture gas. The results show that when the overall gas concentration is the same, the flame velocity and the pressure growth rate of the uniform gas explosion are lower than those of the non-uniform, but the pressure peaks of both are similar. At the same time, when the initial volume concentration is 10%, the non-uniform gas explosion has the highest flame propagation velocity and peak value. The peak explosion pressure of different concentration gradients is proportional to the initial concentration. The above studies clarified the characteristics of gas-air mixture explosions with concentration gradients and provided theoretical support for the prevention and control of gas explosion disasters.

Effect of N2 and CO2 on the Explosion Properties of High Equivalence Ratios of Hydrogen.

The explosion characteristics of premixed gases under different equivalence ratios (1.0-3.0) and inert gas addition (5-20%) are experimentally investigated, and sensitivity analysis of the radical reactions is carried out using the USC Mech II model to analyze the molar fraction of radicals. The results show that at high equivalence ratios, inert gas has little effect on flame stability. The addition of an inert gas reduces the tensile rate in the early stage of flame growth. At high equivalence ratios, CO2 inhibits explosive flame propagation twice as effectively as N2. Due to the large heat capacity and chemical kinetic effects, CO2 has a stronger inhibitory effect on the explosion pressure than N2, and the inhibition efficiency on the explosion strength is nearly twice that high. To further analyze the effect of different inert gas addition ratios on chemical kinetics, sensitivity analysis, and molar fraction simulations were performed. The thermal and chemical kinetic effects of CO2 cause later generation of H and OH radicals and the partial chain reaction involving CO2 causes a lower peak of H radicals than the peak of H radicals generated under an N2 atmosphere. However, CO2 is a direct reactant and the third body to produce a small chemical kinetic effect.

Characteristics of Methane Explosion and Dynamic Response of Rock Mass in an H-Type Roadway with Different Ignition Sources.

Methane explosion is an undesired incident in the coal mining industry. Its high pressure wave can cause damage to the rock mass. This study numerically investigated the flame and wave transport characteristics of methane explosion with ignition sources at three different locations, and the corresponding dynamic response of the rock masses was discussed. The results showed that the flame propagation time is shortest when the ignition position is located at the center of the H-type roadway structure and the maximum overpressure decreases as the ignition position deviates from the center of the H-type roadway structure. When the ignition point is located at the center of the H-type roadway structure, the smallest total deformation of rock mass shows up with the highest maximum overpressure. In contrast, the largest total deformation appears when the ignition point is most away from the center due to the asymmetric distribution of the gas pressure exerted on both sidewalls of the rock masses. This work may provide insights into the understanding of deflagration propagation and the dynamic evolution of stresses under complex conditions.

Numerical simulation study of the mechanism of hydrogen explosion inhibition by fine water mist containing NaOH

The effect of NaOH-containing fine water mist on hydrogen explosion flames is investigated utilizing numerical simulations using a multi-step model of the chemical reaction mechanism. The suppression effect of hydrogen explosion fine water mist in different pipes is studied. The chemical agent NaOH is introduced into the water mist, and the inhibition mechanism is studied from a microscopic perspective. The results show that the addition of fine water mist can effectively reduce the flame temperature and that the fine water mist completely evaporates and absorbs heat in the preheating zone. The addition of NaOH can improve the inhibition effect of ultra-fine water mist on hydrogen explosion, which is the result of the joint action of physical inhibition and chemical inhibition. The mole fraction curve shows that NaOH delays the reaction process of hydrogen explosion by trapping high-energy free radicals.

Establishment of a model for NaHCO3 inhibition of coal dust explosions and molecular dynamics experimental study

To establish a targeted explosion inhibition model for NaHCO3-Coal dust and explore the inhibition mechanism, experiments on the explosion inhibition of NaHCO3/coal premixed dust were conducted. Utilizing a 20L spherical combustion chamber, five sets of experiments with different particle sizes and concentrations of NaHCO3 were carried out to inhibit coal dust explosions. The explosion characteristics of coal dust and the evolution of the explosion flame under the coupled inhibition effect of NaHCO3 were measured. Energy-dispersive X-ray spectroscopy (EDS) and simultaneous thermal analysis were employed to analyze the changes in the elemental composition and thermal decomposition characteristics of substances before and after the explosion, revealing the molecular dynamics behavior in a high-temperature system. Experimental results indicate that, in the five orthogonal explosion inhibition experiments, an increase in the inhibitor concentration and a decrease in particle size lead to a significant coupled inhibition effect. Based on the experimental data, a targeted explosion inhibition model for NaHCO3-Coal dust was constructed, with a fitting goodness of 0.95. During the explosion inhibition process, NaHCO3 undergoes endothermic decomposition, leading to a reduction in the mass loss rate and heat release rate of coal dust. The carbon (C) content decreases, and the oxygen (O) content increases in the explosion residue, indicating the indirect involvement of C elements in the form of gaseous molecules (CO and CO2) in the explosion inhibition process. This reduces the oxygen concentration in the reaction system, achieving the inhibition of coal dust explosions.

Study on Gasoline–Air Mixture Explosion Overpressure Characteristics and Flame Propagation Behaviors in an Annular Cylindrical Confined Space with a Circular Arch

Gasoline–air mixture explosions mostly occur in buried tank rooms, which are annular cylindrical confined spaces with circular arches. In this paper, explosion experiments at different gasoline–air mixture volume fractions are carried out in an annular cylindrical steel bench with a circular arch curvature radius of 900 mm and an annular half-perimeter to radial width ratio of 12π. The results show that the development process of explosion overpressure is clearly divided into four stages after first-order differentiation treatment. Compared with other types of confined spaces, 1.70% is still the most dangerous gasoline–air mixture volume fraction. However, this type of confined space has a larger inner surface area in the same volume condition, which will inevitably increase the heat absorption rate, reduce the chemical reaction rate, and slow down the flame propagation speed. Meanwhile, this spatial structure will inevitably make the explosion flames collide, which will promote positive feedback coupling between explosion flames and pressure waves, making the explosion more violent and dangerous. These results can provide theoretical and technical support for the explosion prevention design of buried tank rooms.

Explosion characteristics and reaction mechanism of nano-aluminum/methanol fuel spray in a square closed vessel

Nano-aluminum/methanol fuel has broad application prospects in the field of ship and automobile energy, but disasters caused by its spray explosion tend to be ignored. In this study, a 16.2-L visualization sealed chamber was employed to assess the impact of varying aluminum powder blending ratios (from 2 wt% to 15 wt%) on the flame morphology, flame speed, and explosion overpressure of nano-aluminum/methanol fuel spray explosions. The results show that, compared with pure methanol, the spray explosion flame of nano-aluminum/methanol fuel is more continuous and brighter. Within the microscopic flame structure, the agglomeration and combustion of aluminum particles become more evident as the mass fraction of nano-aluminum powder increases. When the aluminum powder mass fraction surpasses 8 wt%, the flame's instantaneous velocity showcases oscillatory propagation patterns similar to those observed in dust explosions. The Pmax and (dP/dt)max of the nano-aluminum/methanol fuel spray explosion initially increase, then decrease with the rise in nano-aluminum powder mass fraction, peaking at 4 wt%. Compared to pure methanol, the enhancements in Pmax and (dP/dt)max are over 23.1 % and 73.3 %, respectively. By integrating the TG analysis of reactants with the SEM analysis of explosion residues, a combustion mechanism for the single droplet explosion of the nano-aluminum/methanol fuel was established. Numerical simulations suggest that nano-aluminum augments the generation rate and quantity of O free radicals via elemental reactions R2 (Al + O2 <=> AlO + O), R4 (AlO + O2 <=> AlO2 + O), and R8 (AlO2 <=> AlO + O). This amplifies combustion reactivity, expedites fuel consumption, and bolsters flame propagation. The research provides empirical evidence supporting the safe application of nano-aluminum/methanol fuels.

Experimental study on the effect of initial accumulation pattern on gas explosion and explosion suppression in a real roadway

In real roadways, gas is prone to accumulate, which in turn can lead to explosive hazards. The state of gas accumulation has a significant impact on the degree of disaster caused by gas explosive hazards. In this study, gas explosion propagation in complex situations was investigated in the actual roadway. The mechanism of explosion suppression was explored from the perspective of kinetic analysis of chemical reactions. It is found that the peaks of explosion pressure occur in the gas accumulation zone. The length of explosion flame is 3–5 times larger than that of the initial gas accumulation zone. As the initial accumulation volume increases, the flame propagation velocity (FPV), maximum explosion pressure (MEP) and flame zone length all increase. ABC Powder can effectively suppress explosion flames of gas with different gas accumulation patterns. A prediction model of gas explosion wave energy in the roadway is proposed. The explosion wave energy increases with increasing overpressure ratio. The explosion wave energy decays significantly after 80 m because of explosion suppression. The explosion suppression of ABC powder is a synergistic effect of surface cooling, dilution, physical isolation and chemical mechanisms. The free radical ions generated by the pyrolysis of ABC powder destroy the structure of the flame and make the reaction more difficult, which corresponds to an increase in the critical flame temperature and makes the gas phase dilution effect easier to achieve.

Explosion and explosion suppression of gas/deposited coal dust in a realistic environment

Gas/deposited coal dust explosions are always one of the major accidents in coal mines. In this paper, gas/deposited coal dust explosion and explosion suppression experiments are conducted in a large tunnel to clarify the propagation law of gas/deposited coal dust explosion and the effect of ultra-fine dry powder on it in a real environment, and the evaluation method for the explosion wave energy in the roadway is also listed, which provides new ideas for the analysis of explosion accidents in the roadway. The results show that the pressure propagation velocity is always faster than the flame propagation velocity and the initial state of gas accumulation mainly influences the initial explosion propagation process. The increasing concentration of coal dust increases the flame propagation velocity. The maximum explosion (without explosion suppression) is achieved in the 100–120 m range. After the initial accumulation of gas has exploded, the explosion wave energy gradually increases, but the growth rate is slow. After 40 m, as the amount of deposited coal dust raised to participate in the explosion reaction increases, the growth rate of the explosion wave energy accelerates, and after 80 m, the explosion wave energy increases sharply, and then decreases as the fuel is consumed. The growth rate of the explosion wave energy is greatest in the 80–100 position interval. The explosion suppressing powder forms an inert cloud barrier in the cross section of the roadway. This barrier prevents the coal dust from continuing to move to the rear of the roadway, creating a region of high coal dust concentration in front of the barrier, resulting in an early maximum of explosion pressure and flame propagation velocity in this region. When the explosion flame passes through the explosion-suppressing cloud barrier, it is suppressed by a combination of surface cooling, gas-phase inerting and dilution, chemical synergy and physical isolation mechanisms.

Study on the inhibition mechanism of green suppressants zinc borate and zinc silicate for oil shale based on flame propagation experiment and thermodynamic analysis

The Green materials zinc borate (ZB) and zinc silicate (ZS) were adopted as suppressants. Hartmann tube was used to study the flame inhibition effect of oil shale explosion. It showed that the flame front length became shorter and the propagation velocity and acceleration gradually decreased by increasing suppressants. When 30 wt% ZB was added, the complete inhibition of oil shale explosion flame could be achieved, while the flame inhibition effect of ZS was relatively weak. Flynn-Wall-Ozawa and Starink methods were used to study the activation energy of oil shale, which showed that the activation energy increased significantly after adding the suppressant. By characterization tests, the microstructure changes of oil shale before and after the explosion were analyzed, and the mechanism of the explosion inhibition difference between two suppressants was revealed. ZS played a physical inhibiting role by absorbing heat, reducing temperature and diluting the concentration of combustible gases. While ZB not only had the physical inhibition role of absorbing heat and diluting the concentration of gases, but also had a covering physical inhibition role. Simultaneously, ZB also had the chemical effect. It played a highly effective physical and chemical synergistic inhibition role in the deflagration of oil shale.

Effect of metal coating on physicochemical properties of ceramic foam for flame suppression application

Combustible dust may result in a catastrophic dust explosion with much larger accident consequences than gas explosions. In this study, porous materials are explored as a promising solution for mitigating explosions. This study focussed on the investigation of aluminium powder explosion in the influence of ceramic foam, with and without coating with non-precious nickel nanopowders. The microscopic properties and structural characteristics of the ceramic foam were analyzed using X-ray spectroscopy, X-ray diffractometry, and scanning electron microscopy. The findings revealed that the nickel-coated ceramic foams are non-uniform and almost spherical in shape, with obvious agglomerations of metallic-silica present on the strut structure. Compared to non-coated ceramic, it can be said that nickel-coated ceramic foams demonstrate a significant reduction in maximum overpressure by approximately 10%. This suggests that the interconnected micro-network structure of the nickel-ceramic walls aids in quenching the flame of the aluminium dust explosion and hence, suppressing the overpressure.

Inhibition characteristics research of aluminum alloy polishing dust explosion through addition of ultrafine Al(OH)3 inerting agent

Investigations into the deactivation of explosion sensitivity and reduction of flame propagation for aluminium alloy polishing wastes were carried out by the addition of ultrafine Al(OH)3 inerting agent. Meanwhile, high-purity aluminium powders with similar mean diameters were also used as a comparative study. The explosion propagation characteristics of high-purity aluminium dust and aluminium alloy polishing waste dust under different inerting ratios (ε) were tested and investigated using a standardised Hartmann tester and a developed experimental platform. The results show that the minimum ignition energy of high-purity aluminium powder is between 40 and 45 mJ, and the minimum ignition energy of aluminium alloy polishing waste is between 500 and 550 mJ, which is one order of magnitude higher than that of high-purity aluminium powder. The lower explosion limit concentration of aluminium alloy polishing waste dust is 150 g/m3, which is 53.33% of that of high-purity aluminium powder. According to the analysis of the SEM image, the main reason is that the spherical particles of high-purity aluminium dust have a folded surface and good dispersion. Compared with the smooth fibre surface of aluminium alloy polishing waste dust, the former is easier to contact with air and the contact area is larger. Therefore, in engineering practice, it is not appropriate to use high-purity aluminium dust-related explosion parameters as the basis for the risk assessment of combustion and explosion at aluminium alloy polishing work sites. In addition, as the dust concentration decreases, the combustion intensity of high-purity aluminium dust and aluminium alloy polishing waste dust also decreases, and the flame propagation appears to be a discontinuous phenomenon. The peak flame propagation velocity of aluminium alloy polishing waste is 7.368 m/s at a concentration of 300 g/m3, which is 56.85% of that of high-purity aluminium powder. As the inerting ratio increases, the propagation velocity of the explosion flame slows down. When the inerting ratio reaches 30%, the minimum ignition energy of aluminium alloy polishing waste is inerted to 1 J, and self-sustained flame propagation cannot be formed. The results show that the ultra-fine Al(OH)3 powder has a significant inerting effect and is a realistic possibility in the production of aluminium alloy polishing.

Influences of concentration gradients and ignition positions on unconfined inhomogeneous hydrogen explosion

This work aims at investigating the inhomogeneous hydrogen cloud explosion in unconfined spaces. The influences of concentration gradient and ignition position on the explosion were studied. Different initial inhomogeneous hydrogen clouds with vertical concentration gradients were prepared by controlling the injection rate and ignition time. Results show that the explosion flame at the equivalent concentration zone has higher temperature, faster propagation and more intense combustion reaction. With the decrease of the concentration gradient, the flame is faster and higher in temperature. The max explosion temperature increases from 905.9 °C to 1000.8 °C. The shapes of flame and temperature field in the gas cloud change from mushroom-shaped to ellipsoidal and then to spherical. The maximum overpressure (Pmax), maximum rise rate of overpressure ((dP/dt)max) and positive impulse (I) increase significantly with the decrease of concentration gradient. While ignited with different ignition positions, the flame propagation from the equivalent concentration zone to the flammability limit zone is inhibited by the concentration gradient. Central ignition induces the most intense and shortest explosion process and causes the highest temperature. Generally, central ignition induces larger Pmax and I in the vicinity of the cloud. Non-central ignition extends the impact areas of explosion.

Effects of Flame Arrester Core with Different Thicknesses on Hydrogen/Methane/Air Explosion with Low Hydrogen Ratio

ABSTRACT In order to study the flame retardant performance of corrugated flame arrester core on the explosion characteristics of 9.5% hydrogen/methane/air premixed gas, a self-built experimental platform was used to study the explosive characteristics and propagation rules and the impact of varying thicknesses and different volumes of hydrogen. The results indicated that the corrugated flame arrester core on the explosion flame of premixed gas was observed with two scenarios, quenching and penetration. The flame is dominated by reverse vortex flow after quenching, reversing the axial direction of flame propagation. However, the flame penetration leads to more intense burning reactions as φ increases. And the increase in thickness changes the flame structure forms a spherical flame to a mushroom-shaped flame and finally form a turbulent flame. The velocity of flame decreased significantly when L = 60 mm with φ = 10% and 20% respectively. The quenching effect is more obvious in P2 with hydrogen added, and its better performance with increasing thickness, with 9.76% and 3.70% decrease when L = 40 mm with φ = 10% and 20%, respectively, and with 57.05% and 48.55% decrease when L = 60 mm with φ = 10% and 20%, respectively.