Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2024; 8(2): 138-150
Published online April 25, 2024 https://doi.org/10.3807/COPP.2024.8.2.138
Copyright © Optical Society of Korea.
Kisung Park^{1}, Soonhwi Hwang^{2}, Hwanseok Yang^{2}, Chul Hyun^{2}, Jai-ick Yoh^{1}
Corresponding author: ^{*}jjyoh@snu.ac.kr, ORCID 0000-0002-5622-8368
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study is essential for advancing our knowledge about the interaction between long-range high-power lasers and energetic materials, with a particular emphasis on understanding the response of a 155-mm shell under various surface irradiations, taking into account external factors such as atmospheric disturbances. The analysis addresses known limitations in understanding the use of non-realistic targets and the negligence of ambient conditions. The model employs the three-dimensional level-set method, computer-aided design (CAD)-based target design, and a message-passing interface (MPI) parallelization scheme that enables rapid calculations of the complex chemical reactions of the irradiated high explosives. Important outcomes from interaction modeling include the accurate prediction of the initiation time of ignition, transient pressure, and temperature responses with the location of the initial hot spot within the shell, and the relative magnitude of noise with and without the presence of physical ambient disturbances. The initiation time of combustion was increased by approximately a factor of two with atmospheric disturbance considered, while slower heating of the target resulted in an average temperature rise of approximately 650 K and average pressure increase of approximately 1 GPa compared to the no ambient disturbance condition. The results provide an understanding of the interaction between the high-power laser and energetic target at a long distance in an atmospheric condition.
Keywords: Atmospheric disturbances, Energetic material, Heat transfer, High-power laser, Modeling
OCIS codes: (010.1330) Atmospheric turbulence; (010.3310) Laser beam transmission; (140.3390) Laser materials processing; (140.3450) Laser-induced chemistry; (140.6810) Thermal effects
There has been increasing interest recently in understanding the complex interactions between high-power lasers and energetic materials [1–6]. These interactions open up possibilities for new technology development in the fields of defense, energy, and material science [7, 8]. Accurate modeling of these interactions poses a challenge for researchers, especially due to experimental limitations in real-world settings. The aim of the present study is to enhance our capability in interaction modeling between high-power lasers and energetic materials in the presence of atmospheric disturbances, specifically for a laser beam irradiating a 155-mm shell carrying explosive loads from a long distance.
Existing modeling studies related to the interaction between energetic materials and lasers are divided into two categories. First, the interaction between a laser and materials is based on a series of processes where an explosion occurs when the temperature of an energetic material exceeds the activation energy of the combustible substance, leading to a full explosion from strong surface irradiation [9]. In this case, one considers the rise in temperature of the target due to the beam intensity and the impact of temperature increase on the mechanical properties of the target [10–14]. Secondly, the influence of external factors that can cause changes in the intensity and phase of the laser beam are studied. For example, changes in beam characteristics due to atmospheric properties such as molecular and aerosol absorption and scattering, and wind in turbulent atmospheric conditions are studied numerically [15–17] and experimentally [18–20].
Nevertheless, reported studies are rather limited in considering real-world situations and actual settings. For instance, studies have often focused on small model samples rather than full-sized explosive samples in the field [1–3, 9]. Also, while the impact of atmospheric disturbances on laser beam characteristics has been emphasized [15–20], how this affects the initiation of a high-energy system that eventually results in either fast or slow cook-offs has not been analyzed. Such a significant gap in the past research provides a motivation for considering realistic conditions in this area of research to understand the complex interactions between laser beams and explosive targets.
The present study elucidates a novel approach by simulating the presence of atmospheric disturbances while using a large quantity of RDX (Hexogen) inside a 155 mm shell in an actual scenario. This method not only bridges the mentioned gap identified previously but also aims to provide a more comprehensive and realistic analysis of the response of energetic materials to laser ignition.
A three-dimensional numerical solver was developed using the level-set method that enables the analysis of the combustion characteristics of high-energy material explosions with and without atmospheric disturbances [21]. This solver leverages precise numerical techniques such as the third-order Runge-Kutta method and weighted essentially non-oscillatory (WENO) method to analyze the transient thermos-fluidic and chemical reactive characteristics of high-energy materials at high accuracy. It also uses MPI parallelization to reduce the simulation time for three-dimensional target shapes [22]. The developed solver conducts an in-depth analysis of the combustion characteristics of high-energy materials under various conditions, including the initiation time of combustion, distribution of pressure and temperature during an explosion. The difference in combustion characteristics of high-energy materials caused by fast heating and slow heating in the target, depending on the presence and absence of atmospheric disturbances, was also analyzed to precisely locate the initial hot-spot generation [23]. Additionally, the relative magnitude of acoustic noise produced during an explosion at different distances with changes in laser parameters such as power and irradiation time was estimated.
Therefore, the results of this study greatly assist in understanding and predicting the interaction between high-power lasers and high-energy materials in the presence or absence of atmospheric disturbances, and it is expected to expand the possibilities of using laser technology in various fields. The objective is to improve the understanding of the modeling of laser-material interactions under realistic atmospheric conditions. The investigation focuses on the effects of atmospheric disturbances on the interactions and their consequences on material responses, which can enhance predictive capability for the interaction between high-power lasers and energetic targets, leading to advancements in defense, energy, and materials science applications.
A high-power laser with a wavelength of 1.064 μm and diameter of 25 mm is continuously irradiated at intensities of 2.5 kW, 5 kW, and 7.5 kW and is focused on the top surface of a 155 mm shell made of stainless steel (SUS304). The artillery shell has a total mass of 43.2 kg, length of 605.3 mm, and body diameter of 154.71 mm with an inner energetic material mass of 6.86 kg. Since RDX is used as an energetic material in the defense sector, RDX inside a 155 mm shell is used for the present simulation. The simulations considered heat transfer on the surface metal and the opto-thermally ignited energetic material inside. The numerical domain for the shell used in the simulation is shown in Fig. 1. The irradiation distance of the laser was set to 5 km.
As for the degree of atmospheric disturbance, the average atmospheric condition of the absorption coefficient is taken as 5 × 10^{−6}/m, scattering coefficient as 5 × 10^{−5}/m, air transmittance as 0.82, refractive index structure coefficient as 0.391 × 10^{−14} /m^{−2/3}, and wind speed as 5 m/s [24].
Such atmospheric disturbance conditions can reduce the efficiency of the high-power laser system by dispersing the focus of the laser beam at the target. In addition, the distortion of the laser beam is significantly influenced by variations in temperature and refractive index, as well as the existence of water vapor and wind in the atmosphere.
In order to predict such distortion of the laser beam, the atmospheric disturbance condition was modeled and applied to the initial laser beam condition at the target. Then, the results of the distortion of the laser beam and the explosive tendency were derived. Next, a domain was set up to measure the relative noise in an open field after the shell exploded.
A scenario was conceived to measure the intensity of the noise propagated as a 155 mm shell located at the bottom left of an open field, measuring 100 m by 20 m began to explode due to the high-power laser. The domain used in this study is shown in Fig. 2. With this, it was possible to calculate the relative size of the noise generated at various distances when the shell exploded in the open field.
The full process of surface irradiation that leads to the explosion of energetic material is calculated by solving the following equations:
Here, ρ is the density (kg/m^{3}), u_{x}, u_{y}, and u_{z} are the velocities (m/s) in x, y and z, and E is the total energy (J). λ is the reaction progress variable, p is pressure (Pa), Q is the heat of reaction (J/kg), and ẇ is the rate of reaction. The Jones-Wilkins-Lee (JWL) equation of state for calculating the pressure and sound speed of RDX is listed in Eq. (2) [25].
Here, the terms A, B, R_{1} and R_{2} refer to the relationship between the volume and pressure of RDX. These coefficients are crucial in describing how the high-pressure area works. C and ω represent the energy released by explosives as they explode. C is a coefficient representing the contribution to energy release, and ω is an index representing energy release according to a proportional volume change.
The Mie-Gruneisen equation of state in Eq. (3) is for calculating the pressure and sound speed in inert substance such as SUS304 [26].
Here, e_{0} is the internal energy, μ is defined ρ/ρ_{0} − 1, c is the sound speed, and s is the coefficient of the Hugoniot slope.
To calculate the heat transfer in SUS304, the three-dimensional heat diffusion equation shown in Eq. (4) is used.
Here, C is the specific heat (J/kgK), and κ is the thermal conductivity (W/mK). T is the temperature (K) and r_{α} is the reaction rate (kg/m^{2} s).
Then, sound propagation per calculated pressure is obtained by using Eq. (5) [27].
Here, P_{rms} is the root mean square of the change in pressure, and P_{ref} is the threshold of human hearing, which is 2 × 10^{−5} Pa. Propagation equations such as Eq. (6) and Eq. (7) are used to model atmospheric disturbances [25].
Here, I_{target} is the laser intensity at the target (W/m^{3}), W is the initial beam width (m), and W(z) is the change in beam width according to the increase in the z value. Δn is the change in the refractive index, ϕ_{bloom} is the phase of the laser beam by thermal blooming, z is the propagation distance, υ is the transverse wind speed, α_{a} is the absorption coefficient, and α_{s} is the scattering coefficient.
As can be seen in Eq. (6) and Eq. (7), knowing the beam width and diffraction-limited beam radius, the intensity of the laser beam at the target can be calculated, and knowing the wave number and change in the reactive index, the phase change of the beam can be calculated. Figure 3 represents the changes in intensity and phase of a laser reaching the target under different atmospheric disturbance conditions. The simulation was conducted by irradiating a high-power laser of 62 kW at a distance of 5 km, using Eq. (6) and Eq. (7). The average atmospheric disturbance conditions mentioned in Section 2.1 were taken into account.
When no atmospheric disturbance was applied, it was observed that the laser intensity decreased due to the irradiation distance, while the phase showed minimal change [see Fig. 3(b)]. However, when the average atmospheric conditions were applied, a significant reduction in laser intensity and a substantial change in phase were observed, as inferred from Fig. 3(c). This shows that the shape of the laser beam reaching the target was altered.
Figure 4 shows the intensity values along the centerline as shown in Figs. 3(b) and 3(c). The results were derived by substituting the variable when the atmospheric disturbance was not applied, and the variable when the average atmospheric disturbance was applied to Eq. (6). As a consequence, it was observed that the peak intensity was about 10 times higher.
The level set technique was applied to track the interface between the surface material, SUS304, with the core RDX [28] as shown in Eq. (8).
The point where the distance function ϕ becomes 0 is expressed as the interface, when ϕ < 0 is expressed as the inner region of the material, and when ϕ > 0 is expressed as the outer region. Equation 8 is integrated into the WENO technique in space and the third Runge-Kutta technique in time. In the process of calculating the distance function, if there is a point where the physical properties of a material change rapidly, distortion may occur at the interface. To account for this, distance function initialization is periodically performed. If the boundary plane is found accurately through the distance function, appropriate boundary conditions for material and material or material and empty space should be applied.
Parallelization of numerical analysis codes for shock waves was performed using a region division technique. The area division technique is a method in which the entire area is divided into several detailed areas and each area is calculated by each processor. Message-passing is used for data exchange at the interface of the detailed areas. The message-passing method has the advantage of high parallelization performance, although it is difficult to write code and designate a corresponding processor in parallelization.
In this study, parallelization was performed using MPI, the most commonly used message-passing library in parallelization tasks. In the divided detailed area, there is a physical interface and a virtual interface between the detailed areas. At the physical interface, appropriate boundary values are given based on physical fitness, and at the virtual interface due to area division, boundary values are given based on data exchange through communication between different detailed areas. In addition, when higher-order spatial accuracy is required at the virtual interface, an overlapping lattice system is formed to overlap one inner area and one virtual lattice interface.
Parallelization of codes for analyzing flow is based on basic sequential codes. Subroutines that require parallelization in sequential code are made with parallelization techniques. This research performed parallelization based on a parallelization algorithm of 2D and 3D Euler codes based on sequential codes. The algorithm can be divided into the part where the main processor operates and the part where all processors operate. In the case of subroutines that require parallelization, data is exchanged with MPI_Send and MPI_Recv statements, which are the basic communication statements of MPI.
In the existing sequential code, the code was created using the cell-vertex lattice technique, a method of performing calculations by considering the existing lattice point as the center of the cell. The parallelization of codes using the cell-vertex lattice technique has the disadvantage that it is difficult to maintain high-order spatial accuracy as the generation of detailed regions by region division becomes ambiguous, and it becomes difficult to apply physical boundary conditions. To solve this problem, high-order accuracy was maintained by adding virtual cells while overlapping grids between neighboring detailed regions in creating detailed regions.
In the case of the detailed area boundary generated by area division, it is a part corresponding to the internal calculation area in the sequential code and is an area that maintains a high-order spatial accuracy. However, due to area division, high-order spatial accuracy cannot be maintained at the detailed area boundary.
In the case of two dimensions, to compensate for these shortcomings, raw variables corresponding to two one-dimensional arrays are exchanged as boundary conditions of the detailed regions for parallelization, by placing detailed region boundaries and one virtual region. The raw variables used in the exchange of boundary conditions are density, speed, energy, and reaction rate. The amount of change in flow in the entire area is also exchanged every iteration.
As mentioned above, the level-set method defines the distance function. However, it is almost impossible to fit the complex boundaries based on an analytical equation in three dimensions. For this reason, we used the level-set algorithm that distinguishes the inside and outside of the 3D shape by parameterizing the stereolithography (STL) format [29].
The level-set function applied by default is shown in Eq. (8). The difference is that the existing level-set function ϕ was defined as an equation, whereas in this simulation, ϕ was replaced with a parameterized level-set algorithm. As can be seen in Fig. 5, the STL format divides the modeled shape into n-triangles to provide positional coordinates for the three vertices of each triangle and unit normal vectors for the outer direction.
From the STL-shaped triangle, the v_{1,n}, v_{2,n}, v_{3,n} vectors perpendicular to each side are generated. Subsequently, three q_{1,n}, q_{2,n}, q_{3,n} planes perpendicular to the triangle are generated using the v_{1,n}, v_{2,n}, v_{3,n} vectors, and lattice point G_{k} as shown in Eq. (9).
The generated plane becomes a triangular pillar that limits the triangle. Using Eq. (10), it is possible to obtain the first distance function that gives a level value to the lattice point in the triangle, limited to the triangular pillar as shown in Fig. 6.
Since n-triangular planes may exist around the grid point, Eq. (11) is used to assign the minimum distance value with a sign to one grid point as the level value.
If only the first signed distance function is applied, an exceptional situation may occur in which the level value cannot be specified at the grid point. For example, in the case of a shape where each face is bent and tangent, the lattice point is located outside of the restricted triangular pillar boundary, resulting in inappropriate boundary surfaces. In this case, if the relationship between the linear equation and the grid point is defined, a level value can be assigned to the exceptional grid point. The corners formed by meeting different surfaces are organized in a three-dimensional space as shown in Eq. (12).
V^{→}_{1,n} in Eq. (12) is a parameterized straight line equation for t formed by the two vertices of the triangle, and V_{1,n} is the intersection where the corner meets the straight line of minimum distance from any grid point to the corner within the range of 0 < t < 1. In the part where t < 0, the distance between the vertex P_{1,n} and the lattice point G_{1} forms the shortest distance. Likewise, in the portion where t > 1, the distance between the vertex P_{2,n} and the lattice point G_{3} becomes the shortest distance. In the case of grid point G_{2}, the point perpendicular to the corner becomes the shortest distance as shown in Fig. 7. In other words, the distance between two specific points becomes the shortest depending on the range of parameter t, and the distance between the point and the straight line also becomes the shortest. This can be expressed as Eq. (13).
However, since Eq. (13) can only find the distance, the sign that distinguishes the inside and outside of the distance is defined by Eq. (14).
By combining Eq. (13), Eq. (14), and Eq. (15), a level value with a sign that determines the inside and outside can be given to the lattice point.
With this, it is possible to obtain a second signed distance function capable of giving a level value to the lattice point even in an exceptional situation. Since there may be several surfaces around the lattice point, the shortest distance with a sign is obtained using Eq. (16).
Figure 1(b) is an example of the result of setting a boundary surface separating the inside and the outside on the 3D alignment grid using STL shape information extracted by the CAD program with the above modeling. A domain consisting of 2,756 STL triangles is set as the boundary of the area using the parameterized level-set algorithm as illustrated in Fig. 5. When the area to be analyzed is modeled with a CAD program, extracted in STL format, and applied with a new algorithm, a level value is assigned to the 3D alignment grid, and a set of grid points with the same level value is set as the interface of the analysis area as shown in Fig. 8.
Before applying the code to model the interaction between reactive materials and a beam, the validation of the code was carried out. For this, the Chapman-Jouguet (C-J) pressure and detonation velocity of RDX, as reported in studies that experimentally measured these parameters for explosives, were compared with the C-J pressure and detonation velocity of RDX obtained from the simulations in this study [30]. The domain used for the validation process is shown in Fig. 9.
Prior to validation, to check the grid independence of the simulation results, a comparison of the simulation results (RDX detonation velocity) at different mesh sizes was conducted. Mesh sizes of 150 × 50, 300 × 100, 600 × 200, and 900 × 300 were used. As can be seen in Fig. 10, the detonation velocity was calculated to be 6,681 m/s for the 150 × 50 mesh size, while it was 8,597 m/s for 300 × 100, 8,613 m/s for 600 × 200, and 8,619 m/s for 900 × 300, showing that the results were almost identical.
These results indicate that the accuracy of the simulation results improved as the mesh size increased, and the variation observed in the 150 × 50 mesh results was interpreted as being due to the inability to sufficiently resolve fine details of the mesh. Taking into account both accuracy and computational efficiency, it was concluded that a mesh size of 300 × 100 is most suitable for code validation. This enhances the credibility of the study and reaffirms the accuracy of the code used for modeling the key dynamic characteristics of high-performance explosives like RDX.
As shown in Fig. 11, the C-J plane in the domain used for this study is located at x = 0.1; therefore, the measurement location for each property was set to (0.1, 0.05). Figure 12 shows graphs of pressure and velocity distribution over time at this measurement location. The simulation results indicate a C-J pressure of 33.11 GPa and a detonation velocity of 8,597 m/s, showing considerable agreement with the C-J pressure of 33.79 GPa and detonation velocity of 8,639 m/s for RDX reported in the literature.
Collectively, these results demonstrate that the code used in this study can simulate the interaction between energetic materials and a beam in an accurate and reliable manner. Table 1 presents a comparison between the literature values and the simulation results of this study, emphasizing the accuracy of the code used.
The interaction between the beam and energetic material heavily depends on the presence or absence of atmospheric disturbances. Laser outputs of 2.5 kW, 5 kW, and 7.5 kW were irradiated on the upper location of the domain as described in Fig. 3(a). The irradiation distance of the laser was set to 5 km in an open atmosphere. When a material is rapidly heated to a high temperature, the surface temperature of the material increases sharply, which can accelerate the combustion reaction. This leads to a phenomenon where the interior region of the material is not sufficiently heated, resulting in non-uniform heating. Consequently, the material starts burning from the surface, leading to a relatively moderate level of explosion. This phenomenon is known as fast cook-off (FCO).
Conversely, when the material is slowly heated, ensuring uniform heating from the surface to the inner region, the entire area of the material is evenly heated. This uniform heating can result in an intense explosion originating from within the material, often accompanied by a strong shock wave and high explosion temperature. This is known as slow cook-off (SCO).
In this study, it was confirmed that, regardless of the laser irradiation intensity at 2.5 kW, 5 kW, and 7.5 kW, the heating of RDX was determined to proceed either as a FCO or a SCO process, depending on the presence or absence of atmospheric disturbances.
The time to ignition was tracked by the change in the progress of reaction. It uses the term species, and if it has a value of 0, it refers to non-reaction and if it has a value of 1, it refers to complete reaction. When the atmospheric disturbance was not considered as shown in Fig. 13 at 2.5 kW, it was shown that it took 29.33 seconds until the reaction occurred. At 5 kw, it took 19.24 seconds for the reaction to start. Likewise, it took 15 seconds in the case of 7.5 kw of laser irradiation. When the average atmospheric disturbance was applied, as shown in Fig. 14, the ignition of RDX occurred at 62.26 seconds with 2.5 kW. For 5 kW, it was 39.02 seconds, and it took 30.75 seconds for 7.5 kw. Thus, the time to ignition is approximately two times slower when atmospheric disturbance is applied. Table 2 shows the laser intensity and the time to ignition according to the presence or absence of atmospheric disturbance.
TABLE 2 Time to ignition
Laser Intensity (Kw) | Without Disturbance (s) | With Disturbance (s) |
---|---|---|
2.5 | 29.33 | 62.26 |
5 | 19.24 | 39.02 |
7.5 | 15.00 | 30.75 |
The temperature and pressure distribution inside the domain were analyzed according to the intensity of the laser and the application of atmospheric disturbance. Regardless of the presence or absence of atmospheric disturbance, the temperature and pressure distribution following the explosion did not show significant differences at the laser intensities of 2.5 kW, 5 kW, and 7.5 kW.
In all three cases, when no atmospheric disturbance was applied, a rapid rise in temperature occurred at the point where the laser reached the domain, and high thermal energy above the ignition point was transferred to the surface of RDX, initiating the reaction from the surface, a phenomenon known as FCO.
Conversely, when average atmospheric disturbance was applied, the slow rise in temperature resulted in relatively lower thermal energy being transferred to the inner parts of RDX, leading to an explosion starting from the interior of the energetic material, a phenomenon known as SCO. Figures 15 and 16 show the results of simulating the temperature and pressure distribution inside the domain after the explosion when the atmospheric disturbance is not applied during laser irradiation of 7.5 kW. It was found that the maximum temperature was about 1,200 K, the average temperature was about 650 K, the maximum pressure was about 12 × 10^{9} Pa, and the average pressure was about 11 × 10^{9} Pa. Similar results were obtained when irradiating at intensities of 2.5 kW and 5 kW.
Next, Figs. 17 and 18 show the results of simulating the temperature and pressure distribution inside the domain after the explosion when the average atmospheric disturbance is applied during laser irradiation of 7.5 kW. This result corresponds to the time when the values of species were the same as those without atmospheric disturbance. The maximum temperature was determined to be around 2,100 K, the average temperature to be around 1,300 K, the maximum pressure to be around 13 × 10^{9} Pa, and the average pressure to be around 12 × 10^{9} Pa. Table 3 shows the maximum temperature, average temperature, maximum pressure, and average pressure depending on the presence or absence of atmospheric disturbance.
TABLE 3 Temperature and pressure distribution depending on the presence or absence of atmospheric disturbance
Parameter | Without Disturbance | With Disturbance |
---|---|---|
Highest Temperature (K) | 1,200 | 2,100 |
Average Temperature (K) | 650 | 1,300 |
Highest Pressure (GPa) | 12 | 13 |
Average Pressure (GPa) | 11 | 12 |
When an energetic material exploded in an open area, the relative size of the explosion sound according to the distance was analyzed. The magnitude of the explosion sound was calculated with the SPL equation. Since the magnitude of the explosion sound is calculated based on the propagation of the explosion pressure, the difference between applying and not applying atmospheric disturbance is only the difference in initial pressure at the start of the explosion.
In this study, the magnitude of the explosion sound was calculated based on the initial pressure when atmospheric disturbance was not applied. The measurement distance was set from the point where the explosion began to 100 m at intervals of 25 m. Figure 19 is a graph showing the magnitude of the explosion sound calculated from the pressure of the shock wave according to time and distance. Figure 20 is the result of simulating the propagation of the explosion sound over time. Since the sound should be measured based on the sound pressure, which is the pressure at the time of stabilization, not when the shock wave pressure reaches, the sound was measured at about 0.056 seconds as shown in Fig. 19.
As a result, values of about 131.545 dB at a distance of 25 m, about 128.586 dB at a distance of 50 m, about 125.265 dB at a distance of 75 m, and about 121.507 dB at a distance of 100 m were measured. The relative noise magnitude measured at the same distance will differ depending on the type or quantity of explosive used inside the domain. Table 4 shows the arrival time and relative size of the explosion sound at each distance.
TABLE 4 Relative size of explosion sound at increasing distance
Distance (m) | Noise (dB) |
---|---|
25 | 131.545 |
50 | 128.586 |
75 | 125.265 |
100 | 121.507 |
This study plays a crucial role in advancing our understanding of the interaction between high-power lasers and energetic materials. The characteristics of opto-thermal transport and chemical reactions were analyzed depending on the laser intensity and the presence or absence of atmospheric disturbance. The reported results derived the ignition time of the high-energy target, the temperature and pressure distribution during the explosion, and the relative magnitude of noise generated by distance when an explosion occurred in the open area.
Without atmospheric disturbance, the explosion initiated approximately 29 seconds after irradiation at an intensity of 2.5 kW, 19 seconds with 5 kW intensity, and 15 seconds with 7.5 kW intensity. Conversely, with atmospheric disturbance, the explosion occurred about 62 seconds after 2.5 kW intensity, 39 seconds with 5 kW, and 31 seconds with 7.5 kW. This clearly demonstrates that applying average atmospheric disturbance significantly delays the explosion start time by about two times compared to when no disturbance is applied.
Interestingly, considering atmospheric disturbance, thermal energy transport at the target surface was delayed, resulting in longer and deeper heat penetration, which led to a center-ignited scenario known as the slow cook-off process within the shell. Without atmospheric disturbance, the fast-cook-off results were comparatively benign, and the resulting temperature and pressure were noted to be lower than in the case of slow-cook-off.
Therefore, these findings are expected to enhance the current prediction capability regarding the interaction between high-power lasers and energetic materials in real-world situations. However, the model developed in this study comes with several significant limitations and assumptions. The model does not consider the mechanical deformation and fragmentation of the shell. In real-world conditions, irradiation by high-power lasers could affect the structural integrity of the shell, which could be a critical variable in the reaction of energetic materials. Neglecting these factors could have an impact on the accuracy of the model predictions. Also, to manage the complexity of chemical reactions, the chemical reaction mechanisms have been significantly simplified. While this approach enhances modeling efficiency, it might not capture all chemical details. Specifically, reaction pathways under high temperature and pressure conditions may not be fully explained by the simplified mechanisms. The uncertainty of atmospheric conditions could also affect the model predictions. Factors such as molecular and aerosol absorption and scattering, along with wind speed in the atmosphere, can affect the propagation of the laser beam, leading to discrepancies between experimental outcomes and model predictions. Although efforts have been made to minimize these uncertainties, the elimination of all mentioned assumptions remains a challenge.
It is important to recognize these limitations and assumptions when interpreting and generalizing the results. Additional effort is undertaken to incorporate the effects of mechanical deformation and fragmentation into the model, to refine the modeling of chemical reaction mechanisms, and to accurately handle the variability of atmospheric conditions. Moreover, improvement of the experimental design to precisely measure the effects of atmospheric conditions may also be necessary.
The authors are grateful to LIG Nex1 for providing the research grant contracted through IAAT and IOER at Seoul National University.
Financial support by LIG Nex1 through IAAT and IOER at Seoul National University.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
All data generated or analyzed during this study are included in this published article.
Curr. Opt. Photon. 2024; 8(2): 138-150
Published online April 25, 2024 https://doi.org/10.3807/COPP.2024.8.2.138
Copyright © Optical Society of Korea.
Kisung Park^{1}, Soonhwi Hwang^{2}, Hwanseok Yang^{2}, Chul Hyun^{2}, Jai-ick Yoh^{1}
^{1}Department of Aerospace Engineering, Seoul National University, Seoul 08826, Korea
^{2}Laser R&D Laboratory, LIG Nex1, Yongin 16911, Korea
Correspondence to:^{*}jjyoh@snu.ac.kr, ORCID 0000-0002-5622-8368
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study is essential for advancing our knowledge about the interaction between long-range high-power lasers and energetic materials, with a particular emphasis on understanding the response of a 155-mm shell under various surface irradiations, taking into account external factors such as atmospheric disturbances. The analysis addresses known limitations in understanding the use of non-realistic targets and the negligence of ambient conditions. The model employs the three-dimensional level-set method, computer-aided design (CAD)-based target design, and a message-passing interface (MPI) parallelization scheme that enables rapid calculations of the complex chemical reactions of the irradiated high explosives. Important outcomes from interaction modeling include the accurate prediction of the initiation time of ignition, transient pressure, and temperature responses with the location of the initial hot spot within the shell, and the relative magnitude of noise with and without the presence of physical ambient disturbances. The initiation time of combustion was increased by approximately a factor of two with atmospheric disturbance considered, while slower heating of the target resulted in an average temperature rise of approximately 650 K and average pressure increase of approximately 1 GPa compared to the no ambient disturbance condition. The results provide an understanding of the interaction between the high-power laser and energetic target at a long distance in an atmospheric condition.
Keywords: Atmospheric disturbances, Energetic material, Heat transfer, High-power laser, Modeling
There has been increasing interest recently in understanding the complex interactions between high-power lasers and energetic materials [1–6]. These interactions open up possibilities for new technology development in the fields of defense, energy, and material science [7, 8]. Accurate modeling of these interactions poses a challenge for researchers, especially due to experimental limitations in real-world settings. The aim of the present study is to enhance our capability in interaction modeling between high-power lasers and energetic materials in the presence of atmospheric disturbances, specifically for a laser beam irradiating a 155-mm shell carrying explosive loads from a long distance.
Existing modeling studies related to the interaction between energetic materials and lasers are divided into two categories. First, the interaction between a laser and materials is based on a series of processes where an explosion occurs when the temperature of an energetic material exceeds the activation energy of the combustible substance, leading to a full explosion from strong surface irradiation [9]. In this case, one considers the rise in temperature of the target due to the beam intensity and the impact of temperature increase on the mechanical properties of the target [10–14]. Secondly, the influence of external factors that can cause changes in the intensity and phase of the laser beam are studied. For example, changes in beam characteristics due to atmospheric properties such as molecular and aerosol absorption and scattering, and wind in turbulent atmospheric conditions are studied numerically [15–17] and experimentally [18–20].
Nevertheless, reported studies are rather limited in considering real-world situations and actual settings. For instance, studies have often focused on small model samples rather than full-sized explosive samples in the field [1–3, 9]. Also, while the impact of atmospheric disturbances on laser beam characteristics has been emphasized [15–20], how this affects the initiation of a high-energy system that eventually results in either fast or slow cook-offs has not been analyzed. Such a significant gap in the past research provides a motivation for considering realistic conditions in this area of research to understand the complex interactions between laser beams and explosive targets.
The present study elucidates a novel approach by simulating the presence of atmospheric disturbances while using a large quantity of RDX (Hexogen) inside a 155 mm shell in an actual scenario. This method not only bridges the mentioned gap identified previously but also aims to provide a more comprehensive and realistic analysis of the response of energetic materials to laser ignition.
A three-dimensional numerical solver was developed using the level-set method that enables the analysis of the combustion characteristics of high-energy material explosions with and without atmospheric disturbances [21]. This solver leverages precise numerical techniques such as the third-order Runge-Kutta method and weighted essentially non-oscillatory (WENO) method to analyze the transient thermos-fluidic and chemical reactive characteristics of high-energy materials at high accuracy. It also uses MPI parallelization to reduce the simulation time for three-dimensional target shapes [22]. The developed solver conducts an in-depth analysis of the combustion characteristics of high-energy materials under various conditions, including the initiation time of combustion, distribution of pressure and temperature during an explosion. The difference in combustion characteristics of high-energy materials caused by fast heating and slow heating in the target, depending on the presence and absence of atmospheric disturbances, was also analyzed to precisely locate the initial hot-spot generation [23]. Additionally, the relative magnitude of acoustic noise produced during an explosion at different distances with changes in laser parameters such as power and irradiation time was estimated.
Therefore, the results of this study greatly assist in understanding and predicting the interaction between high-power lasers and high-energy materials in the presence or absence of atmospheric disturbances, and it is expected to expand the possibilities of using laser technology in various fields. The objective is to improve the understanding of the modeling of laser-material interactions under realistic atmospheric conditions. The investigation focuses on the effects of atmospheric disturbances on the interactions and their consequences on material responses, which can enhance predictive capability for the interaction between high-power lasers and energetic targets, leading to advancements in defense, energy, and materials science applications.
A high-power laser with a wavelength of 1.064 μm and diameter of 25 mm is continuously irradiated at intensities of 2.5 kW, 5 kW, and 7.5 kW and is focused on the top surface of a 155 mm shell made of stainless steel (SUS304). The artillery shell has a total mass of 43.2 kg, length of 605.3 mm, and body diameter of 154.71 mm with an inner energetic material mass of 6.86 kg. Since RDX is used as an energetic material in the defense sector, RDX inside a 155 mm shell is used for the present simulation. The simulations considered heat transfer on the surface metal and the opto-thermally ignited energetic material inside. The numerical domain for the shell used in the simulation is shown in Fig. 1. The irradiation distance of the laser was set to 5 km.
As for the degree of atmospheric disturbance, the average atmospheric condition of the absorption coefficient is taken as 5 × 10^{−6}/m, scattering coefficient as 5 × 10^{−5}/m, air transmittance as 0.82, refractive index structure coefficient as 0.391 × 10^{−14} /m^{−2/3}, and wind speed as 5 m/s [24].
Such atmospheric disturbance conditions can reduce the efficiency of the high-power laser system by dispersing the focus of the laser beam at the target. In addition, the distortion of the laser beam is significantly influenced by variations in temperature and refractive index, as well as the existence of water vapor and wind in the atmosphere.
In order to predict such distortion of the laser beam, the atmospheric disturbance condition was modeled and applied to the initial laser beam condition at the target. Then, the results of the distortion of the laser beam and the explosive tendency were derived. Next, a domain was set up to measure the relative noise in an open field after the shell exploded.
A scenario was conceived to measure the intensity of the noise propagated as a 155 mm shell located at the bottom left of an open field, measuring 100 m by 20 m began to explode due to the high-power laser. The domain used in this study is shown in Fig. 2. With this, it was possible to calculate the relative size of the noise generated at various distances when the shell exploded in the open field.
The full process of surface irradiation that leads to the explosion of energetic material is calculated by solving the following equations:
Here, ρ is the density (kg/m^{3}), u_{x}, u_{y}, and u_{z} are the velocities (m/s) in x, y and z, and E is the total energy (J). λ is the reaction progress variable, p is pressure (Pa), Q is the heat of reaction (J/kg), and ẇ is the rate of reaction. The Jones-Wilkins-Lee (JWL) equation of state for calculating the pressure and sound speed of RDX is listed in Eq. (2) [25].
Here, the terms A, B, R_{1} and R_{2} refer to the relationship between the volume and pressure of RDX. These coefficients are crucial in describing how the high-pressure area works. C and ω represent the energy released by explosives as they explode. C is a coefficient representing the contribution to energy release, and ω is an index representing energy release according to a proportional volume change.
The Mie-Gruneisen equation of state in Eq. (3) is for calculating the pressure and sound speed in inert substance such as SUS304 [26].
Here, e_{0} is the internal energy, μ is defined ρ/ρ_{0} − 1, c is the sound speed, and s is the coefficient of the Hugoniot slope.
To calculate the heat transfer in SUS304, the three-dimensional heat diffusion equation shown in Eq. (4) is used.
Here, C is the specific heat (J/kgK), and κ is the thermal conductivity (W/mK). T is the temperature (K) and r_{α} is the reaction rate (kg/m^{2} s).
Then, sound propagation per calculated pressure is obtained by using Eq. (5) [27].
Here, P_{rms} is the root mean square of the change in pressure, and P_{ref} is the threshold of human hearing, which is 2 × 10^{−5} Pa. Propagation equations such as Eq. (6) and Eq. (7) are used to model atmospheric disturbances [25].
Here, I_{target} is the laser intensity at the target (W/m^{3}), W is the initial beam width (m), and W(z) is the change in beam width according to the increase in the z value. Δn is the change in the refractive index, ϕ_{bloom} is the phase of the laser beam by thermal blooming, z is the propagation distance, υ is the transverse wind speed, α_{a} is the absorption coefficient, and α_{s} is the scattering coefficient.
As can be seen in Eq. (6) and Eq. (7), knowing the beam width and diffraction-limited beam radius, the intensity of the laser beam at the target can be calculated, and knowing the wave number and change in the reactive index, the phase change of the beam can be calculated. Figure 3 represents the changes in intensity and phase of a laser reaching the target under different atmospheric disturbance conditions. The simulation was conducted by irradiating a high-power laser of 62 kW at a distance of 5 km, using Eq. (6) and Eq. (7). The average atmospheric disturbance conditions mentioned in Section 2.1 were taken into account.
When no atmospheric disturbance was applied, it was observed that the laser intensity decreased due to the irradiation distance, while the phase showed minimal change [see Fig. 3(b)]. However, when the average atmospheric conditions were applied, a significant reduction in laser intensity and a substantial change in phase were observed, as inferred from Fig. 3(c). This shows that the shape of the laser beam reaching the target was altered.
Figure 4 shows the intensity values along the centerline as shown in Figs. 3(b) and 3(c). The results were derived by substituting the variable when the atmospheric disturbance was not applied, and the variable when the average atmospheric disturbance was applied to Eq. (6). As a consequence, it was observed that the peak intensity was about 10 times higher.
The level set technique was applied to track the interface between the surface material, SUS304, with the core RDX [28] as shown in Eq. (8).
The point where the distance function ϕ becomes 0 is expressed as the interface, when ϕ < 0 is expressed as the inner region of the material, and when ϕ > 0 is expressed as the outer region. Equation 8 is integrated into the WENO technique in space and the third Runge-Kutta technique in time. In the process of calculating the distance function, if there is a point where the physical properties of a material change rapidly, distortion may occur at the interface. To account for this, distance function initialization is periodically performed. If the boundary plane is found accurately through the distance function, appropriate boundary conditions for material and material or material and empty space should be applied.
Parallelization of numerical analysis codes for shock waves was performed using a region division technique. The area division technique is a method in which the entire area is divided into several detailed areas and each area is calculated by each processor. Message-passing is used for data exchange at the interface of the detailed areas. The message-passing method has the advantage of high parallelization performance, although it is difficult to write code and designate a corresponding processor in parallelization.
In this study, parallelization was performed using MPI, the most commonly used message-passing library in parallelization tasks. In the divided detailed area, there is a physical interface and a virtual interface between the detailed areas. At the physical interface, appropriate boundary values are given based on physical fitness, and at the virtual interface due to area division, boundary values are given based on data exchange through communication between different detailed areas. In addition, when higher-order spatial accuracy is required at the virtual interface, an overlapping lattice system is formed to overlap one inner area and one virtual lattice interface.
Parallelization of codes for analyzing flow is based on basic sequential codes. Subroutines that require parallelization in sequential code are made with parallelization techniques. This research performed parallelization based on a parallelization algorithm of 2D and 3D Euler codes based on sequential codes. The algorithm can be divided into the part where the main processor operates and the part where all processors operate. In the case of subroutines that require parallelization, data is exchanged with MPI_Send and MPI_Recv statements, which are the basic communication statements of MPI.
In the existing sequential code, the code was created using the cell-vertex lattice technique, a method of performing calculations by considering the existing lattice point as the center of the cell. The parallelization of codes using the cell-vertex lattice technique has the disadvantage that it is difficult to maintain high-order spatial accuracy as the generation of detailed regions by region division becomes ambiguous, and it becomes difficult to apply physical boundary conditions. To solve this problem, high-order accuracy was maintained by adding virtual cells while overlapping grids between neighboring detailed regions in creating detailed regions.
In the case of the detailed area boundary generated by area division, it is a part corresponding to the internal calculation area in the sequential code and is an area that maintains a high-order spatial accuracy. However, due to area division, high-order spatial accuracy cannot be maintained at the detailed area boundary.
In the case of two dimensions, to compensate for these shortcomings, raw variables corresponding to two one-dimensional arrays are exchanged as boundary conditions of the detailed regions for parallelization, by placing detailed region boundaries and one virtual region. The raw variables used in the exchange of boundary conditions are density, speed, energy, and reaction rate. The amount of change in flow in the entire area is also exchanged every iteration.
As mentioned above, the level-set method defines the distance function. However, it is almost impossible to fit the complex boundaries based on an analytical equation in three dimensions. For this reason, we used the level-set algorithm that distinguishes the inside and outside of the 3D shape by parameterizing the stereolithography (STL) format [29].
The level-set function applied by default is shown in Eq. (8). The difference is that the existing level-set function ϕ was defined as an equation, whereas in this simulation, ϕ was replaced with a parameterized level-set algorithm. As can be seen in Fig. 5, the STL format divides the modeled shape into n-triangles to provide positional coordinates for the three vertices of each triangle and unit normal vectors for the outer direction.
From the STL-shaped triangle, the v_{1,n}, v_{2,n}, v_{3,n} vectors perpendicular to each side are generated. Subsequently, three q_{1,n}, q_{2,n}, q_{3,n} planes perpendicular to the triangle are generated using the v_{1,n}, v_{2,n}, v_{3,n} vectors, and lattice point G_{k} as shown in Eq. (9).
The generated plane becomes a triangular pillar that limits the triangle. Using Eq. (10), it is possible to obtain the first distance function that gives a level value to the lattice point in the triangle, limited to the triangular pillar as shown in Fig. 6.
Since n-triangular planes may exist around the grid point, Eq. (11) is used to assign the minimum distance value with a sign to one grid point as the level value.
If only the first signed distance function is applied, an exceptional situation may occur in which the level value cannot be specified at the grid point. For example, in the case of a shape where each face is bent and tangent, the lattice point is located outside of the restricted triangular pillar boundary, resulting in inappropriate boundary surfaces. In this case, if the relationship between the linear equation and the grid point is defined, a level value can be assigned to the exceptional grid point. The corners formed by meeting different surfaces are organized in a three-dimensional space as shown in Eq. (12).
V^{→}_{1,n} in Eq. (12) is a parameterized straight line equation for t formed by the two vertices of the triangle, and V_{1,n} is the intersection where the corner meets the straight line of minimum distance from any grid point to the corner within the range of 0 < t < 1. In the part where t < 0, the distance between the vertex P_{1,n} and the lattice point G_{1} forms the shortest distance. Likewise, in the portion where t > 1, the distance between the vertex P_{2,n} and the lattice point G_{3} becomes the shortest distance. In the case of grid point G_{2}, the point perpendicular to the corner becomes the shortest distance as shown in Fig. 7. In other words, the distance between two specific points becomes the shortest depending on the range of parameter t, and the distance between the point and the straight line also becomes the shortest. This can be expressed as Eq. (13).
However, since Eq. (13) can only find the distance, the sign that distinguishes the inside and outside of the distance is defined by Eq. (14).
By combining Eq. (13), Eq. (14), and Eq. (15), a level value with a sign that determines the inside and outside can be given to the lattice point.
With this, it is possible to obtain a second signed distance function capable of giving a level value to the lattice point even in an exceptional situation. Since there may be several surfaces around the lattice point, the shortest distance with a sign is obtained using Eq. (16).
Figure 1(b) is an example of the result of setting a boundary surface separating the inside and the outside on the 3D alignment grid using STL shape information extracted by the CAD program with the above modeling. A domain consisting of 2,756 STL triangles is set as the boundary of the area using the parameterized level-set algorithm as illustrated in Fig. 5. When the area to be analyzed is modeled with a CAD program, extracted in STL format, and applied with a new algorithm, a level value is assigned to the 3D alignment grid, and a set of grid points with the same level value is set as the interface of the analysis area as shown in Fig. 8.
Before applying the code to model the interaction between reactive materials and a beam, the validation of the code was carried out. For this, the Chapman-Jouguet (C-J) pressure and detonation velocity of RDX, as reported in studies that experimentally measured these parameters for explosives, were compared with the C-J pressure and detonation velocity of RDX obtained from the simulations in this study [30]. The domain used for the validation process is shown in Fig. 9.
Prior to validation, to check the grid independence of the simulation results, a comparison of the simulation results (RDX detonation velocity) at different mesh sizes was conducted. Mesh sizes of 150 × 50, 300 × 100, 600 × 200, and 900 × 300 were used. As can be seen in Fig. 10, the detonation velocity was calculated to be 6,681 m/s for the 150 × 50 mesh size, while it was 8,597 m/s for 300 × 100, 8,613 m/s for 600 × 200, and 8,619 m/s for 900 × 300, showing that the results were almost identical.
These results indicate that the accuracy of the simulation results improved as the mesh size increased, and the variation observed in the 150 × 50 mesh results was interpreted as being due to the inability to sufficiently resolve fine details of the mesh. Taking into account both accuracy and computational efficiency, it was concluded that a mesh size of 300 × 100 is most suitable for code validation. This enhances the credibility of the study and reaffirms the accuracy of the code used for modeling the key dynamic characteristics of high-performance explosives like RDX.
As shown in Fig. 11, the C-J plane in the domain used for this study is located at x = 0.1; therefore, the measurement location for each property was set to (0.1, 0.05). Figure 12 shows graphs of pressure and velocity distribution over time at this measurement location. The simulation results indicate a C-J pressure of 33.11 GPa and a detonation velocity of 8,597 m/s, showing considerable agreement with the C-J pressure of 33.79 GPa and detonation velocity of 8,639 m/s for RDX reported in the literature.
Collectively, these results demonstrate that the code used in this study can simulate the interaction between energetic materials and a beam in an accurate and reliable manner. Table 1 presents a comparison between the literature values and the simulation results of this study, emphasizing the accuracy of the code used.
The interaction between the beam and energetic material heavily depends on the presence or absence of atmospheric disturbances. Laser outputs of 2.5 kW, 5 kW, and 7.5 kW were irradiated on the upper location of the domain as described in Fig. 3(a). The irradiation distance of the laser was set to 5 km in an open atmosphere. When a material is rapidly heated to a high temperature, the surface temperature of the material increases sharply, which can accelerate the combustion reaction. This leads to a phenomenon where the interior region of the material is not sufficiently heated, resulting in non-uniform heating. Consequently, the material starts burning from the surface, leading to a relatively moderate level of explosion. This phenomenon is known as fast cook-off (FCO).
Conversely, when the material is slowly heated, ensuring uniform heating from the surface to the inner region, the entire area of the material is evenly heated. This uniform heating can result in an intense explosion originating from within the material, often accompanied by a strong shock wave and high explosion temperature. This is known as slow cook-off (SCO).
In this study, it was confirmed that, regardless of the laser irradiation intensity at 2.5 kW, 5 kW, and 7.5 kW, the heating of RDX was determined to proceed either as a FCO or a SCO process, depending on the presence or absence of atmospheric disturbances.
The time to ignition was tracked by the change in the progress of reaction. It uses the term species, and if it has a value of 0, it refers to non-reaction and if it has a value of 1, it refers to complete reaction. When the atmospheric disturbance was not considered as shown in Fig. 13 at 2.5 kW, it was shown that it took 29.33 seconds until the reaction occurred. At 5 kw, it took 19.24 seconds for the reaction to start. Likewise, it took 15 seconds in the case of 7.5 kw of laser irradiation. When the average atmospheric disturbance was applied, as shown in Fig. 14, the ignition of RDX occurred at 62.26 seconds with 2.5 kW. For 5 kW, it was 39.02 seconds, and it took 30.75 seconds for 7.5 kw. Thus, the time to ignition is approximately two times slower when atmospheric disturbance is applied. Table 2 shows the laser intensity and the time to ignition according to the presence or absence of atmospheric disturbance.
TABLE 2. Time to ignition.
Laser Intensity (Kw) | Without Disturbance (s) | With Disturbance (s) |
---|---|---|
2.5 | 29.33 | 62.26 |
5 | 19.24 | 39.02 |
7.5 | 15.00 | 30.75 |
The temperature and pressure distribution inside the domain were analyzed according to the intensity of the laser and the application of atmospheric disturbance. Regardless of the presence or absence of atmospheric disturbance, the temperature and pressure distribution following the explosion did not show significant differences at the laser intensities of 2.5 kW, 5 kW, and 7.5 kW.
In all three cases, when no atmospheric disturbance was applied, a rapid rise in temperature occurred at the point where the laser reached the domain, and high thermal energy above the ignition point was transferred to the surface of RDX, initiating the reaction from the surface, a phenomenon known as FCO.
Conversely, when average atmospheric disturbance was applied, the slow rise in temperature resulted in relatively lower thermal energy being transferred to the inner parts of RDX, leading to an explosion starting from the interior of the energetic material, a phenomenon known as SCO. Figures 15 and 16 show the results of simulating the temperature and pressure distribution inside the domain after the explosion when the atmospheric disturbance is not applied during laser irradiation of 7.5 kW. It was found that the maximum temperature was about 1,200 K, the average temperature was about 650 K, the maximum pressure was about 12 × 10^{9} Pa, and the average pressure was about 11 × 10^{9} Pa. Similar results were obtained when irradiating at intensities of 2.5 kW and 5 kW.
Next, Figs. 17 and 18 show the results of simulating the temperature and pressure distribution inside the domain after the explosion when the average atmospheric disturbance is applied during laser irradiation of 7.5 kW. This result corresponds to the time when the values of species were the same as those without atmospheric disturbance. The maximum temperature was determined to be around 2,100 K, the average temperature to be around 1,300 K, the maximum pressure to be around 13 × 10^{9} Pa, and the average pressure to be around 12 × 10^{9} Pa. Table 3 shows the maximum temperature, average temperature, maximum pressure, and average pressure depending on the presence or absence of atmospheric disturbance.
TABLE 3. Temperature and pressure distribution depending on the presence or absence of atmospheric disturbance.
Parameter | Without Disturbance | With Disturbance |
---|---|---|
Highest Temperature (K) | 1,200 | 2,100 |
Average Temperature (K) | 650 | 1,300 |
Highest Pressure (GPa) | 12 | 13 |
Average Pressure (GPa) | 11 | 12 |
When an energetic material exploded in an open area, the relative size of the explosion sound according to the distance was analyzed. The magnitude of the explosion sound was calculated with the SPL equation. Since the magnitude of the explosion sound is calculated based on the propagation of the explosion pressure, the difference between applying and not applying atmospheric disturbance is only the difference in initial pressure at the start of the explosion.
In this study, the magnitude of the explosion sound was calculated based on the initial pressure when atmospheric disturbance was not applied. The measurement distance was set from the point where the explosion began to 100 m at intervals of 25 m. Figure 19 is a graph showing the magnitude of the explosion sound calculated from the pressure of the shock wave according to time and distance. Figure 20 is the result of simulating the propagation of the explosion sound over time. Since the sound should be measured based on the sound pressure, which is the pressure at the time of stabilization, not when the shock wave pressure reaches, the sound was measured at about 0.056 seconds as shown in Fig. 19.
As a result, values of about 131.545 dB at a distance of 25 m, about 128.586 dB at a distance of 50 m, about 125.265 dB at a distance of 75 m, and about 121.507 dB at a distance of 100 m were measured. The relative noise magnitude measured at the same distance will differ depending on the type or quantity of explosive used inside the domain. Table 4 shows the arrival time and relative size of the explosion sound at each distance.
TABLE 4. Relative size of explosion sound at increasing distance.
Distance (m) | Noise (dB) |
---|---|
25 | 131.545 |
50 | 128.586 |
75 | 125.265 |
100 | 121.507 |
This study plays a crucial role in advancing our understanding of the interaction between high-power lasers and energetic materials. The characteristics of opto-thermal transport and chemical reactions were analyzed depending on the laser intensity and the presence or absence of atmospheric disturbance. The reported results derived the ignition time of the high-energy target, the temperature and pressure distribution during the explosion, and the relative magnitude of noise generated by distance when an explosion occurred in the open area.
Without atmospheric disturbance, the explosion initiated approximately 29 seconds after irradiation at an intensity of 2.5 kW, 19 seconds with 5 kW intensity, and 15 seconds with 7.5 kW intensity. Conversely, with atmospheric disturbance, the explosion occurred about 62 seconds after 2.5 kW intensity, 39 seconds with 5 kW, and 31 seconds with 7.5 kW. This clearly demonstrates that applying average atmospheric disturbance significantly delays the explosion start time by about two times compared to when no disturbance is applied.
Interestingly, considering atmospheric disturbance, thermal energy transport at the target surface was delayed, resulting in longer and deeper heat penetration, which led to a center-ignited scenario known as the slow cook-off process within the shell. Without atmospheric disturbance, the fast-cook-off results were comparatively benign, and the resulting temperature and pressure were noted to be lower than in the case of slow-cook-off.
Therefore, these findings are expected to enhance the current prediction capability regarding the interaction between high-power lasers and energetic materials in real-world situations. However, the model developed in this study comes with several significant limitations and assumptions. The model does not consider the mechanical deformation and fragmentation of the shell. In real-world conditions, irradiation by high-power lasers could affect the structural integrity of the shell, which could be a critical variable in the reaction of energetic materials. Neglecting these factors could have an impact on the accuracy of the model predictions. Also, to manage the complexity of chemical reactions, the chemical reaction mechanisms have been significantly simplified. While this approach enhances modeling efficiency, it might not capture all chemical details. Specifically, reaction pathways under high temperature and pressure conditions may not be fully explained by the simplified mechanisms. The uncertainty of atmospheric conditions could also affect the model predictions. Factors such as molecular and aerosol absorption and scattering, along with wind speed in the atmosphere, can affect the propagation of the laser beam, leading to discrepancies between experimental outcomes and model predictions. Although efforts have been made to minimize these uncertainties, the elimination of all mentioned assumptions remains a challenge.
It is important to recognize these limitations and assumptions when interpreting and generalizing the results. Additional effort is undertaken to incorporate the effects of mechanical deformation and fragmentation into the model, to refine the modeling of chemical reaction mechanisms, and to accurately handle the variability of atmospheric conditions. Moreover, improvement of the experimental design to precisely measure the effects of atmospheric conditions may also be necessary.
The authors are grateful to LIG Nex1 for providing the research grant contracted through IAAT and IOER at Seoul National University.
Financial support by LIG Nex1 through IAAT and IOER at Seoul National University.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
All data generated or analyzed during this study are included in this published article.
TABLE 2 Time to ignition
Laser Intensity (Kw) | Without Disturbance (s) | With Disturbance (s) |
---|---|---|
2.5 | 29.33 | 62.26 |
5 | 19.24 | 39.02 |
7.5 | 15.00 | 30.75 |
TABLE 3 Temperature and pressure distribution depending on the presence or absence of atmospheric disturbance
Parameter | Without Disturbance | With Disturbance |
---|---|---|
Highest Temperature (K) | 1,200 | 2,100 |
Average Temperature (K) | 650 | 1,300 |
Highest Pressure (GPa) | 12 | 13 |
Average Pressure (GPa) | 11 | 12 |
TABLE 4 Relative size of explosion sound at increasing distance
Distance (m) | Noise (dB) |
---|---|
25 | 131.545 |
50 | 128.586 |
75 | 125.265 |
100 | 121.507 |