2022 Vol. 42, No. 2
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2022, 42(2): 022101.
doi: 10.11883/bzycj-2021-0065
Abstract:
The liquid hydrocarbon fuel droplets need to be broken up and vaporized before further participating in detonation combustion, resulting in a more complex phenomenon in liquid-hydrocarbon fueled rotating detonation combustors (RDCs). To explore the incomplete combustion phenomena in liquid hydrocarbon-fueled rotating detonation, the conservation element and solution element method (CE/SE method) was used to simulate a two-phase three-dimensional RDC fueled with a liquid gasoline/air mixture. The Euler-Euler model was used to establish the three-dimensional gas-liquid two-phase governing equations in the cylindrical coordinate system. The source terms were solved by the fourth-order Runge-Kutta method. The phase transition was described by the droplet stripping and evaporation model. Furthermore, the energy and momentum exchange between the two phases was considered. The internal energy of the components was calculated from the enthalpy values of the polynomial fitting and the temperature was solved by Newton iteration. The injection conditions of the gas and liquid phases were assigned by different back pressures. The reactant equivalence ratio can be obtained by the area ratio of the droplets and the gas flow. The effects of the injection pressure and the equivalence ratio on the structure and performance of the rotating detonation flow field were analyzed. When the total equivalent ratio is fixed to 1.00, the inhomogeneous distribution of the fuel in the combustor is enhanced with the increase of the fuel injection pressure, resulting in some local fuel-rich areas. The fuel fails to completely combust in the combustor, leading to a decrease of the specific impulse. With a constant injection pressure and a reduced equivalent ratio, there are still local fuel-rich areas, resulting in incomplete combustion and reduced specific impulse performance. The results show that the reactant injection scheme has a significant effect on the incomplete combustion of the gas-liquid two-phase rotating detonations.
The liquid hydrocarbon fuel droplets need to be broken up and vaporized before further participating in detonation combustion, resulting in a more complex phenomenon in liquid-hydrocarbon fueled rotating detonation combustors (RDCs). To explore the incomplete combustion phenomena in liquid hydrocarbon-fueled rotating detonation, the conservation element and solution element method (CE/SE method) was used to simulate a two-phase three-dimensional RDC fueled with a liquid gasoline/air mixture. The Euler-Euler model was used to establish the three-dimensional gas-liquid two-phase governing equations in the cylindrical coordinate system. The source terms were solved by the fourth-order Runge-Kutta method. The phase transition was described by the droplet stripping and evaporation model. Furthermore, the energy and momentum exchange between the two phases was considered. The internal energy of the components was calculated from the enthalpy values of the polynomial fitting and the temperature was solved by Newton iteration. The injection conditions of the gas and liquid phases were assigned by different back pressures. The reactant equivalence ratio can be obtained by the area ratio of the droplets and the gas flow. The effects of the injection pressure and the equivalence ratio on the structure and performance of the rotating detonation flow field were analyzed. When the total equivalent ratio is fixed to 1.00, the inhomogeneous distribution of the fuel in the combustor is enhanced with the increase of the fuel injection pressure, resulting in some local fuel-rich areas. The fuel fails to completely combust in the combustor, leading to a decrease of the specific impulse. With a constant injection pressure and a reduced equivalent ratio, there are still local fuel-rich areas, resulting in incomplete combustion and reduced specific impulse performance. The results show that the reactant injection scheme has a significant effect on the incomplete combustion of the gas-liquid two-phase rotating detonations.
2022, 42(2): 022201.
doi: 10.11883/bzycj-2021-0209
Abstract:
The determination of the blast loads acting on the inner wall of explosion containment eessels (ECVs) is the basis for the study of the dynamic response characteristics, the design of structure and the safety assessment of ECVs. In order to obtain the characteristics and distribution law of the blast loads acting on the inner wall of cylindrical explosive containment vessels when the central charge is exploded, a series of implosion loading tests were carried out on the self-developed combined cylindrical explosion containment vessel, with the blast loads acting on several typical positions of the inner wall of the vessel being measured, while by using ANSYS/LS-DYNA software, a simplified model of 1/8 of the vessel is established to numerically simulate the whole process of formation and propagation of the internal detonation field of the vessel. Through the analysis of the test results, the characteristics of the blast loading on the inner wall of the vessel and its distribution law are obtained, and the empirical calculation formulas for the peak pressure, positive pressure action time and specific impulse of the first pulse of blast loads acting on the inner wall of the cylindrical shell part of the vessel, and the empirical calculation formulas for the quasi-static pressure inside the vessel are fitted. By analyzing the numerical simulation results, the formation mechanism of the characteristics and distribution law of the blast loads on the inner wall of the vessel are clarified. The research results show that the Mach reflection waves generated from the inner wall of the ellipsoid end cap converge at the end cap pole, so that the peak pressure and the peak specific impulse of single pulse of the blast loading on the pole are always the biggest among all the measurement points, and the maximum peak pressure of the load can reach 2.79 times the maximum peak pressure that acting on the cylindrical shell, which should be paid a close attention.
The determination of the blast loads acting on the inner wall of explosion containment eessels (ECVs) is the basis for the study of the dynamic response characteristics, the design of structure and the safety assessment of ECVs. In order to obtain the characteristics and distribution law of the blast loads acting on the inner wall of cylindrical explosive containment vessels when the central charge is exploded, a series of implosion loading tests were carried out on the self-developed combined cylindrical explosion containment vessel, with the blast loads acting on several typical positions of the inner wall of the vessel being measured, while by using ANSYS/LS-DYNA software, a simplified model of 1/8 of the vessel is established to numerically simulate the whole process of formation and propagation of the internal detonation field of the vessel. Through the analysis of the test results, the characteristics of the blast loading on the inner wall of the vessel and its distribution law are obtained, and the empirical calculation formulas for the peak pressure, positive pressure action time and specific impulse of the first pulse of blast loads acting on the inner wall of the cylindrical shell part of the vessel, and the empirical calculation formulas for the quasi-static pressure inside the vessel are fitted. By analyzing the numerical simulation results, the formation mechanism of the characteristics and distribution law of the blast loads on the inner wall of the vessel are clarified. The research results show that the Mach reflection waves generated from the inner wall of the ellipsoid end cap converge at the end cap pole, so that the peak pressure and the peak specific impulse of single pulse of the blast loading on the pole are always the biggest among all the measurement points, and the maximum peak pressure of the load can reach 2.79 times the maximum peak pressure that acting on the cylindrical shell, which should be paid a close attention.
2022, 42(2): 023101.
doi: 10.11883/bzycj-2021-0147
Abstract:
As the most important part of concrete material, coarse aggregate has a very important influence on the mechanical properties and failure mode of concrete. In order to study the effect of the coarse aggregate average size on the dynamic mechanical properties of concrete, a series of SHPB experiments were carried out for concrete and mortar materials with different average particle sizes (6 mm, 12 mm and 24 mm) of coarse aggregate. A dual-pulse shaper was used in the tests for dynamic stress equilibrium and constant strain rate loading. Moreover, the dynamic stress equilibrium in the test specimen was checked, and it is considered that the test data are valid when the dynamic imbalance factor is less than 5%. The stress-strain curves of the specimens under different strain rates were obtained, and the dynamic increase factor (DIF) of each material was linearly fitted with the logarithm of the strain rate. The results indicate that the compressive strength of the mortar and the concrete has an obvious strain rate effect, the dynamic compressive strength increases gradually with the strain rate, and the stress-strain curves show a similar trend. Under the same dynamic strain rate condition, the dynamic compressive strength of the concrete with an average coarse aggregate size of 12 mm is the highest, which is quite different from the maximum compressive strength of the mortar under quasi-static conditions. The CEB and other models are inapplicable to the relationship between the DIF and the strain rate because they do not consider the effect of the coarse aggregate size found in this study. Therefore, the specimen’s dynamic DIF and the logarithm of strain rate are fitted by Bischoff's model in the paper. The strain rate strengthening coefficient of concretes with different coarse aggregate sizes is larger than that of the mortar. With the increase of the coarse aggregate dimensionless size, the strain rate strengthening factor of the concrete increases at first and then decreases.
As the most important part of concrete material, coarse aggregate has a very important influence on the mechanical properties and failure mode of concrete. In order to study the effect of the coarse aggregate average size on the dynamic mechanical properties of concrete, a series of SHPB experiments were carried out for concrete and mortar materials with different average particle sizes (6 mm, 12 mm and 24 mm) of coarse aggregate. A dual-pulse shaper was used in the tests for dynamic stress equilibrium and constant strain rate loading. Moreover, the dynamic stress equilibrium in the test specimen was checked, and it is considered that the test data are valid when the dynamic imbalance factor is less than 5%. The stress-strain curves of the specimens under different strain rates were obtained, and the dynamic increase factor (DIF) of each material was linearly fitted with the logarithm of the strain rate. The results indicate that the compressive strength of the mortar and the concrete has an obvious strain rate effect, the dynamic compressive strength increases gradually with the strain rate, and the stress-strain curves show a similar trend. Under the same dynamic strain rate condition, the dynamic compressive strength of the concrete with an average coarse aggregate size of 12 mm is the highest, which is quite different from the maximum compressive strength of the mortar under quasi-static conditions. The CEB and other models are inapplicable to the relationship between the DIF and the strain rate because they do not consider the effect of the coarse aggregate size found in this study. Therefore, the specimen’s dynamic DIF and the logarithm of strain rate are fitted by Bischoff's model in the paper. The strain rate strengthening coefficient of concretes with different coarse aggregate sizes is larger than that of the mortar. With the increase of the coarse aggregate dimensionless size, the strain rate strengthening factor of the concrete increases at first and then decreases.
2022, 42(2): 023102.
doi: 10.11883/bzycj-2021-0151
Abstract:
To investigate the mechanical behavior of concrete-filled steel tubular (CFST) columns under coupled fire and impact loads, a finite element (FE) model was established with ABAQUS software to describe the impact resistance of axial-loaded CFST columns under elevated temperatures. The commonly used ISO 834 standard fire and rigid-body impact were employed to model the fire and impact loads, respectively. In the model, the static implicit and dynamic explicit analysis were coupled by using “Restart” and “Import” commands and the strain-rate effect was taken into account. The numerical model was validated by comparing the impact force time history curves obtained from relevant tests at different temperatures. Based on the validated FE models, the impact responses of axial-loaded CFST columns under coupled fire and impact loads were analyzed. Then, the influences of the fire duration, concrete and steel strength, steel ratio and impact energy on the mechanical behavior were investigated, and some design suggestions were proposed. The platform impact force and the maximum mid-span deflection were employed to quantitatively analyze the impact resistance of the CFST columns. The results show that the CFST column presents a flexural failure mode when it is exposed to coupled fire and impact loads. With the increase of fire duration, the proportion of energy consumption of the steel tube reduces. The impact resistance of the column decreases obviously when it is subjected to fire for a duration of 15 min. Axial compression load has an adverse influence on the impact performance. When the axial-load level increases from 0 to 0.2, the platform value of the impact force reduces by 7.8% at a fire duration of 60 min. The concrete strength has a significant effect on the impact resistance. When the cubic compressive strength of the concrete increases from 30 MPa to 50 MPa, the impact resistance is improved by approximately 85% when the fire lasts for 90 min. The steel ratio and steel strength have marginal influences on the impact resistance of the CFST columns at elevated temperatures.
To investigate the mechanical behavior of concrete-filled steel tubular (CFST) columns under coupled fire and impact loads, a finite element (FE) model was established with ABAQUS software to describe the impact resistance of axial-loaded CFST columns under elevated temperatures. The commonly used ISO 834 standard fire and rigid-body impact were employed to model the fire and impact loads, respectively. In the model, the static implicit and dynamic explicit analysis were coupled by using “Restart” and “Import” commands and the strain-rate effect was taken into account. The numerical model was validated by comparing the impact force time history curves obtained from relevant tests at different temperatures. Based on the validated FE models, the impact responses of axial-loaded CFST columns under coupled fire and impact loads were analyzed. Then, the influences of the fire duration, concrete and steel strength, steel ratio and impact energy on the mechanical behavior were investigated, and some design suggestions were proposed. The platform impact force and the maximum mid-span deflection were employed to quantitatively analyze the impact resistance of the CFST columns. The results show that the CFST column presents a flexural failure mode when it is exposed to coupled fire and impact loads. With the increase of fire duration, the proportion of energy consumption of the steel tube reduces. The impact resistance of the column decreases obviously when it is subjected to fire for a duration of 15 min. Axial compression load has an adverse influence on the impact performance. When the axial-load level increases from 0 to 0.2, the platform value of the impact force reduces by 7.8% at a fire duration of 60 min. The concrete strength has a significant effect on the impact resistance. When the cubic compressive strength of the concrete increases from 30 MPa to 50 MPa, the impact resistance is improved by approximately 85% when the fire lasts for 90 min. The steel ratio and steel strength have marginal influences on the impact resistance of the CFST columns at elevated temperatures.
2022, 42(2): 023201.
doi: 10.11883/bzycj-2021-0036
Abstract:
In order to examine the effect of damping on the equivalent static load dynamic factor of the air blast loading, the solutions of the elastoplastic displacement and ductility ratio were derived by the structural equivalent single degree of freedom (SDOF) method for the air blast loading. According to the relationship between the duration of the air blast loading and the duration required for the structural members to complete elastic vibration, the members are divided into two types: rigid members and flexible members. Twenty typical calculation cases, including damping ratios from 0.000 1 to 0.1 and ductility ratios from 1 to 4, were completed and compared with the dynamic factor formula results of the current blast resistant design code. The results show as follow. A ductility ratio less than 0.000 1 can be regarded as a state without damping. The relative error of the dynamic factor between the calculation results with a damping ratio of 0.01 and without damping is less than 2.08%. This relative error is so small that the damping effect with a damping ratio less than 0.01 can be ignored. The dynamic factor with a damping ratio of 0.05 is about 9.92% lower than the one without damping. This relative error is so great that considering the damping ratio will have obvious economic benefits for the blast resistant design when its value is greater than 0.05. Based on the elastic design, the calculation results from the current blast resistant code formula are in good agreement with those from the derived formula in this paper, and the value of the dynamic factor calculated from the code is between the results of damping ratios of 0.01 and 0.05. Furthermore, the current air blast resistant design code formula is more suitable for flexible structure systems. When the code formula is applied to calculate the dynamic factor of rigid members, there will be a large calculation error, which is more unfavorable for members with small damping.
In order to examine the effect of damping on the equivalent static load dynamic factor of the air blast loading, the solutions of the elastoplastic displacement and ductility ratio were derived by the structural equivalent single degree of freedom (SDOF) method for the air blast loading. According to the relationship between the duration of the air blast loading and the duration required for the structural members to complete elastic vibration, the members are divided into two types: rigid members and flexible members. Twenty typical calculation cases, including damping ratios from 0.000 1 to 0.1 and ductility ratios from 1 to 4, were completed and compared with the dynamic factor formula results of the current blast resistant design code. The results show as follow. A ductility ratio less than 0.000 1 can be regarded as a state without damping. The relative error of the dynamic factor between the calculation results with a damping ratio of 0.01 and without damping is less than 2.08%. This relative error is so small that the damping effect with a damping ratio less than 0.01 can be ignored. The dynamic factor with a damping ratio of 0.05 is about 9.92% lower than the one without damping. This relative error is so great that considering the damping ratio will have obvious economic benefits for the blast resistant design when its value is greater than 0.05. Based on the elastic design, the calculation results from the current blast resistant code formula are in good agreement with those from the derived formula in this paper, and the value of the dynamic factor calculated from the code is between the results of damping ratios of 0.01 and 0.05. Furthermore, the current air blast resistant design code formula is more suitable for flexible structure systems. When the code formula is applied to calculate the dynamic factor of rigid members, there will be a large calculation error, which is more unfavorable for members with small damping.
2022, 42(2): 023301.
doi: 10.11883/bzycj-2021-0230
Abstract:
Impedance-graded-material enhanced Whipple shields have excellent protective performance. The purpose of this paper is to study the ballistic limit of Ti/Al/Mg shields, which is an improved impedance-graded-material enhanced Whipple shield. Hypervelocity impact experiments on Ti/Al/Mg, Al/Mg and 2A12 shields were performed using a two-stage light-gas gun at impact velocities of 3.0–8.0 km/s. The hypervelocity impact characteristics, the ballistic limit curve and shielding performance of the Ti/Al/Mg shields were studied. The reason of its excellent performance is explained by comparative analysis. As the impact velocity increases, the failure mode of the rear wall showed a detached spall or tearing damage instead of tiny perforations similar to an aluminum shield. The results show that a high-acoustic-impedance titanium alloy layer can generate higher shock pressures and induce a greater temperature increase, which is more effective for fragmenting an impacting projectile. The shock pressure and specific internal energy in the projectile increased by 23.0% and 30.7% compared to the aluminum on aluminum impact event at 8.0 km/s, respectively. The shielding capability of a Ti/Al/Mg shield is significantly greater than that of 2A12 and Al/Mg shields when the bumper has the same areal density. The critical projectile diameter of Ti/Al/Mg shields is 6.58 mm at ~8.0 km/s, which is an improvement of approximately 34.8 % compared to the 4.88 mm of aluminum shields. Finally, to explore the transition velocities of the ballistic limit curve of the Ti/Al/Mg shields, a theoretical analysis was conducted, which suggests that for an aluminum projectile impacting a Ti/Al/Mg bumper, this value might be ＜7.0 km/s. However, a transition point is not apparent in the experimental ballistic limit curve, and the critical projectile diameter increases with increasing velocity in the range of 3.0–8.0 km/s. It is different from the typical Whipple shield. Further hypervelocity impact tests and additional research needs to be conducted to study in detail the ballistic limit of the Ti/Al/Mg shields.
Impedance-graded-material enhanced Whipple shields have excellent protective performance. The purpose of this paper is to study the ballistic limit of Ti/Al/Mg shields, which is an improved impedance-graded-material enhanced Whipple shield. Hypervelocity impact experiments on Ti/Al/Mg, Al/Mg and 2A12 shields were performed using a two-stage light-gas gun at impact velocities of 3.0–8.0 km/s. The hypervelocity impact characteristics, the ballistic limit curve and shielding performance of the Ti/Al/Mg shields were studied. The reason of its excellent performance is explained by comparative analysis. As the impact velocity increases, the failure mode of the rear wall showed a detached spall or tearing damage instead of tiny perforations similar to an aluminum shield. The results show that a high-acoustic-impedance titanium alloy layer can generate higher shock pressures and induce a greater temperature increase, which is more effective for fragmenting an impacting projectile. The shock pressure and specific internal energy in the projectile increased by 23.0% and 30.7% compared to the aluminum on aluminum impact event at 8.0 km/s, respectively. The shielding capability of a Ti/Al/Mg shield is significantly greater than that of 2A12 and Al/Mg shields when the bumper has the same areal density. The critical projectile diameter of Ti/Al/Mg shields is 6.58 mm at ~8.0 km/s, which is an improvement of approximately 34.8 % compared to the 4.88 mm of aluminum shields. Finally, to explore the transition velocities of the ballistic limit curve of the Ti/Al/Mg shields, a theoretical analysis was conducted, which suggests that for an aluminum projectile impacting a Ti/Al/Mg bumper, this value might be ＜7.0 km/s. However, a transition point is not apparent in the experimental ballistic limit curve, and the critical projectile diameter increases with increasing velocity in the range of 3.0–8.0 km/s. It is different from the typical Whipple shield. Further hypervelocity impact tests and additional research needs to be conducted to study in detail the ballistic limit of the Ti/Al/Mg shields.
2022, 42(2): 023302.
doi: 10.11883/bzycj-2021-0427
Abstract:
In order to study the penetration performance and failure modes of high-hardness steel plates against tungsten balls with different angles, a ballistic gun was used to carry out\begin{document}$ \varnothing $\end{document} ![]()
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In order to study the penetration performance and failure modes of high-hardness steel plates against tungsten balls with different angles, a ballistic gun was used to carry out
2022, 42(2): 023303.
doi: 10.11883/bzycj-2021-0181
Abstract:
The high hardness combined with its lower density makes silicon carbide (SiC) an attractive candidate for armor material. The main purpose of employing ceramics plate is to erode and fragment the impacting projectile, such as a 12.7 mm armor piercing incendiary (API) projectile with a very hard steel core. To explore the failure mechanism of the hard steel core, the ballistic impact experiments were carried out to study the dynamic responses of 12.7 mm API projectiles impacting ceramic/aluminium alloy composite armors. The SiC ceramics/6061T6 aluminium alloy composite targets with the composite cover on the front of the SiC were tested at speeds of 434.5, 503.1, 662.7, 704.6 and 844.6 m/s. The targets were entirely perforated by 12.7 mm API projectiles with the hard steel cores. The damages of projectiles, ceramic and back plates were analyzed phenomenologically. The damage modes of ceramic and steel backplates were identified. The resulting core fragments were collected and separated through a series of sized sieving screens, which allowing the core fragmentation to be quantified. The cumulative mass distribution curves of core after impact under various velocities were obtained. Microstructural and mechanical responses to the ballistic impacts were studied by using scanning electron microscope (SEM), showing that the core was broken into different particle sizes under the action of stress wave and impact. The cumulative mass of the steel core conforms to the Rosin–Rammler power function distribution. With the increase of impact velocity, both the power index k and the average characteristic size λ decreased. Average characteristic size λ can be used to characterize the fragmentation degree of the whole core to a certain extent. The failure mode of the larger equivalent diameter fragment (greater than 8 mm) in the process of impact was a tensile brittle fracture, while the local plastic shear fracture existed on the fragments with an equivalent diameter less than 2 mm.
The high hardness combined with its lower density makes silicon carbide (SiC) an attractive candidate for armor material. The main purpose of employing ceramics plate is to erode and fragment the impacting projectile, such as a 12.7 mm armor piercing incendiary (API) projectile with a very hard steel core. To explore the failure mechanism of the hard steel core, the ballistic impact experiments were carried out to study the dynamic responses of 12.7 mm API projectiles impacting ceramic/aluminium alloy composite armors. The SiC ceramics/6061T6 aluminium alloy composite targets with the composite cover on the front of the SiC were tested at speeds of 434.5, 503.1, 662.7, 704.6 and 844.6 m/s. The targets were entirely perforated by 12.7 mm API projectiles with the hard steel cores. The damages of projectiles, ceramic and back plates were analyzed phenomenologically. The damage modes of ceramic and steel backplates were identified. The resulting core fragments were collected and separated through a series of sized sieving screens, which allowing the core fragmentation to be quantified. The cumulative mass distribution curves of core after impact under various velocities were obtained. Microstructural and mechanical responses to the ballistic impacts were studied by using scanning electron microscope (SEM), showing that the core was broken into different particle sizes under the action of stress wave and impact. The cumulative mass of the steel core conforms to the Rosin–Rammler power function distribution. With the increase of impact velocity, both the power index k and the average characteristic size λ decreased. Average characteristic size λ can be used to characterize the fragmentation degree of the whole core to a certain extent. The failure mode of the larger equivalent diameter fragment (greater than 8 mm) in the process of impact was a tensile brittle fracture, while the local plastic shear fracture existed on the fragments with an equivalent diameter less than 2 mm.
2022, 42(2): 023304.
doi: 10.11883/bzycj-2021-0291
Abstract:
In order to study the penetrating trajectories of elliptical cross-section projectiles into semi-infinite metal targets, a penetration trajectory model was established based on the dynamic cavity expansion theory and local interaction model. The shape function of the elliptical cross-section projectile was developed based on the local interaction model, and the resistance model derived from the dynamic cavity expansion theory was used to calculate the forces and moments acting on the elliptical cross-section projectile under the local Cartesian coordinate system. Thus, the factors affecting the projectile penetration trajectory were considered, including the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity. Then, oblique penetrating experiments were carried out at a striking velocity ranging from 850 to950 m/s and an oblique angle ranging from 0° to 20°. Furthermore, the model was validated by experimental results. Finally, the influence of the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity on the penetration trajectory was analyzed. When the major axis to minor axis ratio is 1.0, the projectile is degenerated into an ogive-nosed one. With the increase of this ratio, the stability of the elliptical cross-section projectile reduces. The optimal value of the major axis to minor axis ratio is 1.0, and the penetration trajectory is the most stable at this time. The penetration trajectory will change from a two-dimensional plane curve to a three-dimensional space curve when the angle around the projectile axis varies. When the angle around the projectile axis is 0° or 90°, the penetration trajectory is in a two-dimensional plane. Otherwise, the penetration trajectory is a three-dimensional space curve. The increasement of the attitude angle of the elliptical cross-section projectile decreases from 18.6° to 17.8° when the striking velocity increases from 800 m/s to 1000 m/s.
In order to study the penetrating trajectories of elliptical cross-section projectiles into semi-infinite metal targets, a penetration trajectory model was established based on the dynamic cavity expansion theory and local interaction model. The shape function of the elliptical cross-section projectile was developed based on the local interaction model, and the resistance model derived from the dynamic cavity expansion theory was used to calculate the forces and moments acting on the elliptical cross-section projectile under the local Cartesian coordinate system. Thus, the factors affecting the projectile penetration trajectory were considered, including the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity. Then, oblique penetrating experiments were carried out at a striking velocity ranging from 850 to950 m/s and an oblique angle ranging from 0° to 20°. Furthermore, the model was validated by experimental results. Finally, the influence of the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity on the penetration trajectory was analyzed. When the major axis to minor axis ratio is 1.0, the projectile is degenerated into an ogive-nosed one. With the increase of this ratio, the stability of the elliptical cross-section projectile reduces. The optimal value of the major axis to minor axis ratio is 1.0, and the penetration trajectory is the most stable at this time. The penetration trajectory will change from a two-dimensional plane curve to a three-dimensional space curve when the angle around the projectile axis varies. When the angle around the projectile axis is 0° or 90°, the penetration trajectory is in a two-dimensional plane. Otherwise, the penetration trajectory is a three-dimensional space curve. The increasement of the attitude angle of the elliptical cross-section projectile decreases from 18.6° to 17.8° when the striking velocity increases from 800 m/s to 1000 m/s.
2022, 42(2): 024101.
doi: 10.11883/bzycj-2021-0184
Abstract:
Aiming to simulate the long-term continuous loading process of high confining pressure deep underground spaces under the explosion and impact disturbance, alignment and related tests on the simulation test apparatus were carried out. An air pressure driven piston was used to impact the shaping material and produce an impact disturbance. After passing through the conical cover, the wave front expanded, resulting in a uniform stress wave acting on the cabin body. Main parameters of the far-field disturbed stress wave under explosion were analyzed, and the instrument parameters satisfying the similarity law were obtained by dimensional analysis. The effects of gas pressure, solenoid valve opening time, piston speed, water pressure and shaping material on the shape, positive pressure time, rising pressure time and peak value of the stress wave were discussed by using the developed instrument. The results illustrate that the lower the stiffness of shaping materials, the longer the positive pressure time and rising pressure time of the stress wave, and the lower the peak value of stress. Although an increase in the piston impact velocity will bring an increase in the peak of the stress wave, it will not significantly affect the positive pressure time and waveform. The piston speed can be determined by controlling the opening time of the solenoid valve and the gas pressure in the air chamber. By changing the shaping material and impact speed of the piston, the positive pressure time can be adjusted between 3.5 ms and 5.0 ms, pressure rising time between 0.9 ms and 2.5 ms, and peak value between 4 MPa and 8 MPa. The adjusted pressure waveform output can effectively simulate the far-field explosion stress wave in the deep surrounding rock. The polymethyl methacrylate (PMMA) composite structure was used as the specimen to verify the feasibility and reliability of the apparatus in simulating the impact disturbance in the deep surrounding rock. The above tests prove that this apparatus can provide explosive ground shock disturbances with controllable parameters for laboratory tests. This apparatus enriches the research of simulating explosion disturbances in deep geomechanical test systems.
Aiming to simulate the long-term continuous loading process of high confining pressure deep underground spaces under the explosion and impact disturbance, alignment and related tests on the simulation test apparatus were carried out. An air pressure driven piston was used to impact the shaping material and produce an impact disturbance. After passing through the conical cover, the wave front expanded, resulting in a uniform stress wave acting on the cabin body. Main parameters of the far-field disturbed stress wave under explosion were analyzed, and the instrument parameters satisfying the similarity law were obtained by dimensional analysis. The effects of gas pressure, solenoid valve opening time, piston speed, water pressure and shaping material on the shape, positive pressure time, rising pressure time and peak value of the stress wave were discussed by using the developed instrument. The results illustrate that the lower the stiffness of shaping materials, the longer the positive pressure time and rising pressure time of the stress wave, and the lower the peak value of stress. Although an increase in the piston impact velocity will bring an increase in the peak of the stress wave, it will not significantly affect the positive pressure time and waveform. The piston speed can be determined by controlling the opening time of the solenoid valve and the gas pressure in the air chamber. By changing the shaping material and impact speed of the piston, the positive pressure time can be adjusted between 3.5 ms and 5.0 ms, pressure rising time between 0.9 ms and 2.5 ms, and peak value between 4 MPa and 8 MPa. The adjusted pressure waveform output can effectively simulate the far-field explosion stress wave in the deep surrounding rock. The polymethyl methacrylate (PMMA) composite structure was used as the specimen to verify the feasibility and reliability of the apparatus in simulating the impact disturbance in the deep surrounding rock. The above tests prove that this apparatus can provide explosive ground shock disturbances with controllable parameters for laboratory tests. This apparatus enriches the research of simulating explosion disturbances in deep geomechanical test systems.
2022, 42(2): 024102.
doi: 10.11883/bzycj-2021-0067
Abstract:
It is of great practical significance to expand the imaging field for the visualization research of shock wave propagation and dispersion caused by water-entry projectiles in water-filled tank. The shadowgraph technique is suitable for large field experiments, and the visualization of shock waves and disturbances in the flow field is simple and universal. Among them, the direct shadowgraph technique is the simplest, but the lack of reliable point light sources is the bottleneck hindering its development and application. Therefore, based on domestic short-arc xenon lamps a self-made short-arc xenon lamp point light source was designed. According to the principle of shadowgraph, a shadowgraph visualization system of shock waves caused by water-entry projectiles was designed, and its composition and operating principle were introduced in detail. The system had been used to conduct experimental research on high-speed water-entry projectiles. A shadowgraph technique was employed to visualize the shock wave generated by the water-entry projectile in a water-filled tank. Besides, by extracting pixel points from high-speed photos and calibrating the geometric dimensions in the photos, a spatial coordinate system was established to describe the motion of the projectile and shock wave. Simultaneously, the pressure time history curve of shock wave signal was obtained by means of the acquisition equipment of shock wave signal. With the combination of shadowgraphs and shock wave signals, the propagation characteristics of the shock wave produced by the water-entry projectile were analyzed, and they were verified by theoretical calculations. The results show that the reliability and rationality of the visual system of the shock wave generated by the water-entry projectile are demonstrated. After the projectile enters the water at a high speed, the initial shock wave has the highest intensity. As the shock wave propagates, the shock wave intensity gradually decreases, the propagation speed of the underwater shock wave continues to decrease, and the radius of the spherical shock wave gradually increases.
It is of great practical significance to expand the imaging field for the visualization research of shock wave propagation and dispersion caused by water-entry projectiles in water-filled tank. The shadowgraph technique is suitable for large field experiments, and the visualization of shock waves and disturbances in the flow field is simple and universal. Among them, the direct shadowgraph technique is the simplest, but the lack of reliable point light sources is the bottleneck hindering its development and application. Therefore, based on domestic short-arc xenon lamps a self-made short-arc xenon lamp point light source was designed. According to the principle of shadowgraph, a shadowgraph visualization system of shock waves caused by water-entry projectiles was designed, and its composition and operating principle were introduced in detail. The system had been used to conduct experimental research on high-speed water-entry projectiles. A shadowgraph technique was employed to visualize the shock wave generated by the water-entry projectile in a water-filled tank. Besides, by extracting pixel points from high-speed photos and calibrating the geometric dimensions in the photos, a spatial coordinate system was established to describe the motion of the projectile and shock wave. Simultaneously, the pressure time history curve of shock wave signal was obtained by means of the acquisition equipment of shock wave signal. With the combination of shadowgraphs and shock wave signals, the propagation characteristics of the shock wave produced by the water-entry projectile were analyzed, and they were verified by theoretical calculations. The results show that the reliability and rationality of the visual system of the shock wave generated by the water-entry projectile are demonstrated. After the projectile enters the water at a high speed, the initial shock wave has the highest intensity. As the shock wave propagates, the shock wave intensity gradually decreases, the propagation speed of the underwater shock wave continues to decrease, and the radius of the spherical shock wave gradually increases.
2022, 42(2): 024201.
doi: 10.11883/bzycj-2021-0214
Abstract:
Due to the complexity of the mechanism of the electro-hydraulic effect, few commercial numerical simulation software can describe the internal characteristics of the plasma channel. In order to apply shock waves generated by hydro-electric effects to the existing numerical simulation software to meet the needs of engineering applications, in this paper, two methods based on LS-DYNA were introduced to simulate indirectly the shock wave generated by the electro-hydraulic effect, i.e. Underwater explosion equivalence (including explosion energy equivalence and shock wave energy equivalence) and ideal gas equivalence. Explosion energy equivalence is mainly based on the principle that the deposited energy injected into the plasma channel is equal to the combustion energy of the explosive. Shock wave energy equivalence is mainly based on the principle that the shock wave energy generated by an explosion is equal to that generated by the hydro-electric effect. However, ideal gas equivalence method is different from underwater explosion equivalence. Adopting ideal gas equivalence method, the plasma channel is regarded as an adiabatic expansion ideal gas, and the pressure in the plasma channel is characterized by the relevant keywords in LS-DYNA. In addition, the peak pressure of the shock wave generated by various methods was compared, and underwater explosion equivalence was improved based on the empirical formula of an underwater explosion and the empirical formula of the hydro-electric effect. Moreover, the difference in peak pressure based on different equivalence methods under different deposition energies was analyzed. The results show that the peak pressure of shock wave calculated by three different equivalent methods is different. The peak pressure based on the explosion energy equivalence method is the highest, The peak pressure based on the explosion energy equivalence method is medium, and the peak pressure based on the explosion energy equivalence method is the lowest. The peak pressure based on the ideal gas equivalence method is one to two orders of magnitude less than that based on the former two methods. The shock wave velocity based on the explosion energy equivalence method is equal to that based on the shock wave energy equivalence method, and higher than that based on ideal gas equivalence method.With the decrease of the deposited energy, the peak pressures based on the three equivalence methods all decrease in varying degrees, however, the order of the peak pressure does not change. The improved method for underwater explosion equivalence can simulate the peak pressure of the shock wave more accurately at different deposited energies, and the peak pressure fits well with the Touya empirical formula. In order to simulate accurately the peak pressure of the shock wave based on LS-DYNA, in addition to selecting the appropriate equivalence method, we should also combine the specific discharge conditions and establish an appropriate numerical model to realize the rapid calculation of the peak pressure under the conditions satisfying the calculation requirements.
Due to the complexity of the mechanism of the electro-hydraulic effect, few commercial numerical simulation software can describe the internal characteristics of the plasma channel. In order to apply shock waves generated by hydro-electric effects to the existing numerical simulation software to meet the needs of engineering applications, in this paper, two methods based on LS-DYNA were introduced to simulate indirectly the shock wave generated by the electro-hydraulic effect, i.e. Underwater explosion equivalence (including explosion energy equivalence and shock wave energy equivalence) and ideal gas equivalence. Explosion energy equivalence is mainly based on the principle that the deposited energy injected into the plasma channel is equal to the combustion energy of the explosive. Shock wave energy equivalence is mainly based on the principle that the shock wave energy generated by an explosion is equal to that generated by the hydro-electric effect. However, ideal gas equivalence method is different from underwater explosion equivalence. Adopting ideal gas equivalence method, the plasma channel is regarded as an adiabatic expansion ideal gas, and the pressure in the plasma channel is characterized by the relevant keywords in LS-DYNA. In addition, the peak pressure of the shock wave generated by various methods was compared, and underwater explosion equivalence was improved based on the empirical formula of an underwater explosion and the empirical formula of the hydro-electric effect. Moreover, the difference in peak pressure based on different equivalence methods under different deposition energies was analyzed. The results show that the peak pressure of shock wave calculated by three different equivalent methods is different. The peak pressure based on the explosion energy equivalence method is the highest, The peak pressure based on the explosion energy equivalence method is medium, and the peak pressure based on the explosion energy equivalence method is the lowest. The peak pressure based on the ideal gas equivalence method is one to two orders of magnitude less than that based on the former two methods. The shock wave velocity based on the explosion energy equivalence method is equal to that based on the shock wave energy equivalence method, and higher than that based on ideal gas equivalence method.With the decrease of the deposited energy, the peak pressures based on the three equivalence methods all decrease in varying degrees, however, the order of the peak pressure does not change. The improved method for underwater explosion equivalence can simulate the peak pressure of the shock wave more accurately at different deposited energies, and the peak pressure fits well with the Touya empirical formula. In order to simulate accurately the peak pressure of the shock wave based on LS-DYNA, in addition to selecting the appropriate equivalence method, we should also combine the specific discharge conditions and establish an appropriate numerical model to realize the rapid calculation of the peak pressure under the conditions satisfying the calculation requirements.
2022, 42(2): 025101.
doi: 10.11883/bzycj-2021-0205
Abstract:
Curved steel-concrete-steel (CSCS) composite slabs can increase the compression range of concrete so as to give full play to the compressive strength of the concrete and the tensile strength of the steel plate. It has been used in high-rise buildings, nuclear reactor containment, Arctic caisson and oil storage tanks and other important building structures. According to the specifications, three CSCS composite slabs with different fittings were designed. Based on the nonlinear finite element program ANSYS/LS-DYNA, the damage modes, midpoint displacement, energy consumption, etc. of the composite slabs under the action of near field explosion were studied, and the energy consumption and damage mechanism of the three different slabswere compared. The midpoint displacement and pressure of the CSCS composite slab were extracted from the finite element simulations. The results of the midpoint displacement were compared with the existing field explosion test results, and the results of pressure were compared with the empirical formula, which verified the rationality and effectiveness of the finite element model. Taking the midpoint displacement of the backsteel plate as the index, the effects of the explosive quantity, concrete strength and steel plate thickness on the anti-explosion performance of the CSCScomposite slabswere analyzed. The results show that the curved slabs maintain good integrity under the action of near-field explosion, there is no concrete fragments dispersion phenomenon, and they still have a continuous bearing capacity. Meanwhile, they have a better anti-explosion performance than traditional planar steel-concrete-steel composite slabs. The connection performance of the overlapping studs is stronger than that of the discrete studs, but slightly weaker than that of the pair studs. Increasing the concrete strength can reduce the midpoint displacement but cannot improve the damage condition of the concrete. Increasing the thickness of the steel plate can significantly reduce the midpoint displacement of the steel plate and improve the anti-explosion ability of CSCS composite slabs.
Curved steel-concrete-steel (CSCS) composite slabs can increase the compression range of concrete so as to give full play to the compressive strength of the concrete and the tensile strength of the steel plate. It has been used in high-rise buildings, nuclear reactor containment, Arctic caisson and oil storage tanks and other important building structures. According to the specifications, three CSCS composite slabs with different fittings were designed. Based on the nonlinear finite element program ANSYS/LS-DYNA, the damage modes, midpoint displacement, energy consumption, etc. of the composite slabs under the action of near field explosion were studied, and the energy consumption and damage mechanism of the three different slabswere compared. The midpoint displacement and pressure of the CSCS composite slab were extracted from the finite element simulations. The results of the midpoint displacement were compared with the existing field explosion test results, and the results of pressure were compared with the empirical formula, which verified the rationality and effectiveness of the finite element model. Taking the midpoint displacement of the backsteel plate as the index, the effects of the explosive quantity, concrete strength and steel plate thickness on the anti-explosion performance of the CSCScomposite slabswere analyzed. The results show that the curved slabs maintain good integrity under the action of near-field explosion, there is no concrete fragments dispersion phenomenon, and they still have a continuous bearing capacity. Meanwhile, they have a better anti-explosion performance than traditional planar steel-concrete-steel composite slabs. The connection performance of the overlapping studs is stronger than that of the discrete studs, but slightly weaker than that of the pair studs. Increasing the concrete strength can reduce the midpoint displacement but cannot improve the damage condition of the concrete. Increasing the thickness of the steel plate can significantly reduce the midpoint displacement of the steel plate and improve the anti-explosion ability of CSCS composite slabs.
2022, 42(2): 025401.
doi: 10.11883/bzycj-2021-0231
Abstract:
Propane is a main component of liquefied petroleum gas, and the lower flammability limit is an important indicator for evaluating the safety of combustible gases. The addition of diluent gas can affect the lower flammability limit and reduce the flammable range of propane, so as to achieve the purpose of explosion suppression. CO2, N2 and Ar are commonly used as diluents in the industry. In order to explore their influence on the lower flammability limit of C3H8, the lower flammability limits of C3H8 under O2/CO2, O2/Ar and O2/N2 atmosphere were measured in a 5 L explosive container based on the American ASTM E681-09 standard. The gas mixture was configured according to the partial pressure of each gas, and a pair of high-voltage electrodes was used for ignition. The influences of dilution gas concentration, dilution gas type and O2 concentration on the lower flammability limit of C3H8 was analyzed. The results show that CO2 has the greatest impact on the lower flammability limit of C3H8, followed by N2 and Ar. With the increase of O2 concentration, the lower flammability limit under O2/CO2 atmosphere decreases significantly, and the lower flammability limit under O2/N2 and O2/Ar atmosphere shows a gentle increase. An energy balance equation was established to calculate the radiative heat loss (Qr) and endothermic loss (Qt) of the mixed gas at the lower flammability limit. The effects of specific heat and radiation on the lower flammable limit were compared. The results show that the change in the specific heat of the mixture is the main reason for the change of the lower flammability limit of C3H8, and the radiant heat loss is an important factor in the change of the lower flammability limit. As the concentration of diluent increases, CO2 has the largest impact on λ（Qt） and λ（Qr） followed by Ar and N2. The adiabatic flame temperature is an important factor that affects the change of the lower flammability limit.
Propane is a main component of liquefied petroleum gas, and the lower flammability limit is an important indicator for evaluating the safety of combustible gases. The addition of diluent gas can affect the lower flammability limit and reduce the flammable range of propane, so as to achieve the purpose of explosion suppression. CO2, N2 and Ar are commonly used as diluents in the industry. In order to explore their influence on the lower flammability limit of C3H8, the lower flammability limits of C3H8 under O2/CO2, O2/Ar and O2/N2 atmosphere were measured in a 5 L explosive container based on the American ASTM E681-09 standard. The gas mixture was configured according to the partial pressure of each gas, and a pair of high-voltage electrodes was used for ignition. The influences of dilution gas concentration, dilution gas type and O2 concentration on the lower flammability limit of C3H8 was analyzed. The results show that CO2 has the greatest impact on the lower flammability limit of C3H8, followed by N2 and Ar. With the increase of O2 concentration, the lower flammability limit under O2/CO2 atmosphere decreases significantly, and the lower flammability limit under O2/N2 and O2/Ar atmosphere shows a gentle increase. An energy balance equation was established to calculate the radiative heat loss (Qr) and endothermic loss (Qt) of the mixed gas at the lower flammability limit. The effects of specific heat and radiation on the lower flammable limit were compared. The results show that the change in the specific heat of the mixture is the main reason for the change of the lower flammability limit of C3H8, and the radiant heat loss is an important factor in the change of the lower flammability limit. As the concentration of diluent increases, CO2 has the largest impact on λ（Qt） and λ（Qr） followed by Ar and N2. The adiabatic flame temperature is an important factor that affects the change of the lower flammability limit.
