Embedded measurement of process monitoring in melt-cast explosive based on distributed optical fiber sensing and numerical verification

The solidification sequence during the solidification of fusion-cast explosives is an important parameter for the optimization of the manufacturing process, which can be analyzed by using numerical simulation experiments. However, the numerical simulations are not totally reliable due to the inherent errors in the algorithms and parameters. To address this issue, a measurement method is proposed to monitor the solidification process based on the embedded method of distributed fiber optic sensing. And a method is developed to identify the solid–liquid phase change interface region, which can be effectively demodulated and analyzed for sensing data. The experimental results were verified by using numerical simulations based on casting simulation software and compared. It can be found that the total solidification time and pattern of both are relatively consistent. However, some of the solidification characteristics in the numerical simulation are lack of precision due to the inaccuracy of the heat transfer parameters.


Introduction
Melt-cast explosive is a traditional but still widely used charging technology.To be specific, it refers to the process that high-temperature explosive melt first starts to cool down, and then solidifies at room temperature [1].The internal temperature distribution during the solidification of molten cast explosives is significantly uneven with sharp temperature gradients.This may lead to severe thermal stresses, and cracking or damage to the casting in the case that the mechanical strength of the explosive is not sufficient enough to withstand the forces generated [2,3].Therefore, accurate monitoring of the solidification process of molten explosives becomes essential to the improvement of product quality and environmental adaptability.Most of the research institutions engaged in the study of explosives melt-cast molding still basically follow the static observation [4].While previous simulation experiments [5,6] have focused on exploring the characteristics of experimental research methods, there is currently a lack of literature and experimental studies that specifically address the monitoring and characterization of the solidification process of explosives, including phase change at the interface and related aspects.
To effectively study the melting and casting process, researchers usually rely on numerical simulations to investigate the process [7][8][9].In this paper, some discrepancies with the actual situation were presented.For example, there are many problems in the mathematical model of temperature variation in the low-pressure casting solidification process for aluminum alloy wheels, making a large gap between the simulation and the actual temperature variation [10].On the other hand, inaccurate intrinsic relationships of high-temperature alloys at low strain rates and paste depletion temperatures have led to inaccurate predicted and actual dimensions [11].To improve the process monitoring of molten explosives and the movement of phase change interfaces, the technology selected has to be good in spatial resolution and the resistance to high temperatures and chemicals [12].Due to the specific nature of explosives requiring no electrical sparks, distributed fiber optic sensing (DOFS) was used as an embedded device to monitor the solidus process.DOFS can modify its properties depending on the coating, for instance, polyimide coating can be used to resist chemical corrosion [13], and it is also a passive device that does not require any power supply, and therefore does not incur any danger [14].
Fiber optic sensors have been widely used in various fields for decades due to their excellent performance, showing extraordinary prospects.In recent years, DOFS has been applied in aircraft structures [15], civil engineering [16], medical devices [17], structural health monitoring [18] and other fields [19][20][21].As a sensor, optical fiber has many key advantages over other traditional sensors, such as large range, adaptability to harsh environments, high embeddability, sensitivity to a wide range of parameters, resistance to electromagnetic and voltage, etc [22].
In particular, the high density of DOFS sensing points facilitates the continuous monitoring of various parameters in space, thereby making the changes of state in the range more visible and perceptible.Owing to its excellent accuracy and adaptability to the environment, DOFS is often used as an embedded device to measure data [23].Pre-embedding the optical fiber in concrete can be used in various important applications, such as monitoring performance indicators [24] and structural health monitoring [25] by detecting strain.Furthermore, as a result of its good corrosion resistance, DOFS can even be used as an embedded instrument to evaluate cell performance throughout its lifetime by simultaneously measuring the formation of the solid electrolyte interface and the structural deformation within the anode [26].The embedment of fiber optic sensors into offshore wind turbine blades made of composite carbon fiber panels allows for structural health monitoring and multi-directional strain sensing of the equipment [27].Although it is an artificially created 'defect' from a mechanical and material point of view, no adverse effect has been proved to exist on the mechanical properties of smart composites provided that DOFS is arranged using a suitable method [28].Therefore, fiber optics, as an embedded device, can serve the function of complete data acquisition without deteriorating the original performance of the device.This paper aims to experimentally investigate the internal behavior of the solidification process of molten explosives, and analyze the behavior related to thermal stress and its scientific aspects based on local measurements inside the castings.In addition, we included a simulation experiment to compare and evaluate the validity of existing numerical simulations.For this purpose, DOFS was embedded in the mold in a pre-arranged form, which allows us to obtain the coupled stress and temperature changes during the phase transition from liquid to solid after pouring the liquid to the explosive.

Experimental setup
The experimental setup adopted is mainly divided into two parts, namely the metal type casting module and the high definition distributed fiber optic sensing (HD-DOFS) demodulation module.Figure 1 shows the schematic diagram of the entire model.The main shape of the metal casting mold in this paper is a cylinder, which is 300 mm in diameter and 360 mm in height, accompanied by a metal cone at the bottom of 240 mm in diameter and 180 mm in height.The cone was used only for shaping a special shape to prove that our measurement method also performs well in complex situations.
An ordinary single-mode fiber of 5.3 m is arranged in the mold, which is fixed in our pre-set position from the bottom up after entering from the top, and leaving from the seam between the riser and the mold.A common single-mode fiber for sensing has an overall diameter of 155 µm, which includes the fiber core and the fiber coating (polyimide).The tensile strength of the fiber is 1379 MPa and it has an operating temperature range of −55 • C to 300 • C .The end of the fiber is not specially treated, and the other end is connected to the demodulation module which has two main parts, as shown in figure 1, i.e. the remote module, and the HD-DOFS demodulator.A fiber optic cable containing two fiber cores connects the two modules which transmit incident light and scattered light, respectively.The main function performed by the remote module is similar to that of an external circulator, at which point we can leave the control computer unpositioned in the experimental site.
We fixed the optical fiber to the metal wall of the mold using transferred high-temperature-resistant tape, as shown in figure 2. We fixed the optical fibers of each sensing region in the corresponding space position in steps from bottom to top, the reason for bottom-up is that there is a big positional obstruction if the upper optical fiber is arranged first and then the lower optical fiber is arranged.
We use a self-developed OFDR test system that allows us to simultaneously sense strain in up to two fibers, each of which can be up to 20 M long.The experiment was conducted at a data sampling frequency of 1 Hz for 18 h, with one point sampled every 0.65 mm.In this experiment, the mixture of molten explosive, octogen and trinitrotoluene was heated to   90 • C and poured through the spout before being cooled at room temperature.And we waited for 18 h to ensure that it was completely cooled down.

DFOS with Rayleigh scattering
Distributed fiber optic sensing uses certain properties of the optical fiber to sense some of the information (e.g.strain and temperature) by demodulating different types of scattered light along the transmission path of the fiber in both spatial and temporal dimensions [29].Fiber optic is both a sensor and a transmission medium for optical signals in the technology.In addition, it has the advantages of large spatial sensing range, simple structure and ease of use, and high cost performance.The common distributed fiber optic sensors can be simply classified into Rayleigh scattering, Brillouin scattering and Raman scattering according to the measurement principle.Due to the differences in their mechanisms, there are functional variations and diverse application scenarios.
High measurement accuracy and excellent spatial resolution are the major factors that drive us to choose distributed fiber optic sensing based on Rayleigh scattering.Though the Rayleigh scattering distributed fiber optic sensing with optical frequency domain reflectometer (OFDR) has the disadvantage of short sensing distance, it has nothing to do with our test which does not need long distance sensing.Its temperature and strain sensitive characteristics can meet our experimental demand.
Inherent defects in the interior of the fiber (e.g.inhomogeneities, impurities, etc) may cause variations in the refractive index of the fiber, and these variations are uniformly distributed throughout the fiber.These defects are mainly due to the fiber optic machine matrix material quartz glass itself defects and the inclusion of metal transition impurities, which causes light scattering in the transmission process.When photons collides with these defects, scattering occurs.As shown in figure 3, assuming some defects exist in the fiber, when temperature or force is applied to the fiber, the position of these defects will change accordingly.The part of the fiber under strain will be compressed or stretched, changing the length and refractive index distribution of that part.The change in the location of the defects may result in a change in the phase of the backscattered light.
As shown in figure 3, it is assumed that two identifiable defects exist in the fiber, and the distance between them before the fiber strain occurs is x, which becomes x + dx 2 at the occurrence of this fiber strain.The relative position of the two defects in the fiber is shifted by dx 1 and dx 1 + dx 2 .The reason is that the phase of light changes when it moves here, and similarly, the phase of scattered light varies, therefore, the strain can be obtained by demodulating the phase of scattered light.
The changes in temperature or strain under the initial conditions may cause a shift in the spectrum of Rayleigh Scattering in the fiber.The spectral shift of the scattering in the fiber in response to the strain or temperature is similar to the resonant wavelength ∆λ or spectral shift ∆v of a Bragg grating: The default values of these constants are set to common values for most silica-based fiber, that is, K T = 6.45 × 10 −6 • C −1 and K ε = 0.780 [30].The K T and K ε values are somewhat related to.K T and K ε are somewhat related to the type of dopant and the concentration in the fiber core, but less related to the cladding composition.

Segmenting data
The total length of the common single-mode fiber used in this test was 5.15 m, although only part of the sensing area of it was actually used.Without the unused fibers at the end and the necessary fibers at the beginning, the effective length of the data point area was approximately 1.16 m.We marked the data before the beginning of the experiment to make it more convenient to distinguish valid data from invalid ones at the data processing phase.The specific range is shown in figure 4, and the data in the legend comes from the experimental data 793 s after the start of the experiment.The horizontal coordinate in figure 4 is the one-dimensional distance of the sensing point in an ordinary single-mode fiber used for sensing from the initial point of the fiber.The horizontal axis 'x-axis' is independent of the actual spatial position of the fiber, it is the one-dimensional distance along the fiber interface to the sensing point.In the same way, we divide the effective data area into four sections, namely A, B, C, and D according to the height of the experimental setup as we have marked the data in advance.As shown in figure 5, the specific segmentation basis can be referred to figure 1, which follows the descending sequence of the segments of the fiber.
The initial endpoint is the location where the fiber is connected to the remote module, and the unconstrained endpoint refers to the end of the fiber.The topmost segment is section A, which starts at 3.66 m and ends at 3.96 m in the fiber.Section B is below section A, whose position in the fiber starts at 3.30 m and ends at 3.60 m.Section C is arranged in the interval of 2.90 m to 3.20 m of the entire fiber.Section D is at the bottom part of the mold.Due to the asymmetry of the entire mold, we only arranged the segment from the center point to the boundary.The segment arrangement is from 2.72 m to 2.88 m of the entire fiber.

Strain changes in each segment throughout the solidification process
After the pouring of the liquid explosive, the strain of the fiber during solidification is monitored by using a HD-DOFS demodulator, and the value is determined by equation (1).The calculated strains cannot be directly used to determine the degree of solidification of the explosive because the strains are not directly related to the solid phase rate, and the calculated strains are not yet decoupled from the temperature.Individual strain values are not directly correlated with solidification rates.Our main approach is to use the strain gradient between spatially neighbouring points to identify and define the relevant states, the derivation of which is described in section 3.3.Figure 6 shows the the coupled strain values over time during the solidification.The presence of continuous and regular changes in the strain values forced us to find the pattern.
It can be observed from figure 6 that there is a brief and concentrated increase in the strain value of the fiber at the beginning, which is due to a thermal strain based on the temperature of the molten explosive into the mold, causing the temperature to reach 90 • C from room temperature.This phenomenon coincidently proves that the uncoupled temperature in this experiment has little impact on the actual strain, and can be neglected.It can be seen from the figure that the magnitude of the uncoupled strain change in the primary fiber from room temperature directly to the temperature of the molten explosive is low compared to the magnitude of the strain change over the course of the experiment.In addition, as can be seen from 1, there is also an order of magnitude difference between the term for the temperature change and the term for the strain change.Obviously, there exists a strain area in each fiber section where the strain value does not change with time.This area becomes progressively smaller over time, and eventually concentrates on the middle section of the fiber.The stress on this section of the fiber increases dramatically, and the signal is lost after a period of time.The loss of signal is considered to be attributed to excessive strain values, which results in light leakage or low signal-tonoise ratio in the fiber.It can be seen from figure 6 that the compression strain of the fiber gradually increases due to the embodiment of the cold shrinkage of the explosive.This shows that the strain transfer is excellent, and there is no slippage, otherwise, such high values of compressive strain would not exist.This provides strong evidence for the subsequently proposed method of identification of solid-liquid phase change interfaces.
Even though the strain data we obtained from the embedded measurements are those that are not decoupled from the temperature, the trend of the strain prior to its multiple neighboring data points is sufficient to identify the solid-liquid phase change interface.This is the advantage of distributed fiber optics, where a dense number of data points can form a monitoring area with a wide range, increasing the level of detection of the object being monitored.

Identification of solid-liquid phase change interfaces
As the fiber is immersed in the molten explosive, its surface is subjected to a positive liquid pressure of which the magnitude is related to the height of the fiber in the mold.When the liquid flows or shrinks, the strain is transferred to the fiber briefly, which then disappears due to the fluidity of the liquid.Therefore, there is no continuous large strain transfer between the liquid explosive and the fiber, even if there is a large coefficient of friction.As shown in figure 7, three temporal stages of strain schematically correspond to the early, middle and late stages shown in figure 6.
The difference is that when the explosive changes from liquid to solid, it is firmly attached to the fiber.The strain transfer after solidification can no longer be explained by using a simple model of friction, but a model of shear strain.The explosive in the solid phase ceases to flow, and the volume decrease due to the temperature drop will also drives the compression strain in the fiber.As time progresses and the temperature decreases, the volume of the explosive continues to decrease.This is reflected in the progressive increase in compression strain in the fiber, and it does not occur in the liquid phase.This is the main principle available to distinguish the solid phase zone from the liquid one.
There is a temperature gradient from the outside to the inside of the process, indicating that the outermost layer of the explosive has the lowest temperature, and the volume shrinkage is the largest.Taking figure 7(b) as an example, the volume shrinkage is the highest at the lowest temperature, and the strain value appears to be larger in the fiber even when the strain transfer is not efficient.Since the strain transfer efficiency is basically in accordance with equation ( 2), the overall trend of positive correlation is presented, which means that the trend of volume contraction can be reflected.x where x refers to the original length, and σ stands for the strain transfer efficiency.Although a temperature gradient was also observed in the intermediate region of the explosive, there was no strain gradient, which was attributed to the lack of solidification.A transition region exists between the region of strain gradient and that of non-strain gradient, which is considered to be the solidliquid coexistence region.The monitoring of the solidification process of molten explosives can be used to accurately identify the cured and uncured areas, which is of great significance in guiding the process improvement of molten explosives.

Process monitoring of liquid-solid phase change interface
The main purpose of this section is to apply the theory of section 3.3 to the data obtained from this experiment, and analyze the solidification process.

Section A.
The uppermost part of the mold close to the riser, as shown in figure 1, is the location for fiber optic monitoring in section A. The particularity of this location makes the solidification process of the explosive in this paper more complicated.According to the method of identification of solid-liquid phase change interfaces, we divided the spatial-temporal data collected in section A into three parts, namely, solid-phase region, solid-liquid mixing region and liquid-phase region, as shown in figure 8.In figure 8, region A is the liquid phase region, region B the intermediate region state, and region C the solid domain state.
From the time point of view, the explosives in this area solidify more quickly due to large heat transfer surface and the fact that this location is already close to the boundary.For process monitoring, it was found that the plane was almost completely solidified in about five hours, indicating that the replenishment channel was closed at this time.Premature closure of the filler channel may lead to a large number of shrinkage holes, which has a significant impact on product quality and performance.To improve the process of this experiment, we can start from slowing down the solidification of the upper layer of explosives.

Section B.
The solid-liquid phase change interface is most evident in the middle region of the mold, as shown in figure 9.The rate of solidification in the region with the fiber of section B is relatively slow, which is mainly due to the small contact area of the rest of the mold, and the slow heat transfer.When the upper area of section A of the fiber optic monitoring was completely solidified, only half of section B was solidified, indicating that the process design of this test casting was highly defective.
As shown in figure 9, when the solidification is almost completed, there is an abnormal and sudden increase in the strain value, accompanied by a wide range of data loss.This is because that both sides of the fiber are completely cured, and the volume continues to shrink due to the temperature drop.This indicates a high strain in the most central explosive at the completion of solidification, which may directly cause cracks and subsequent strain release according to fracture theory [31].Based on the knowledge of the mechanical properties of the explosive, it is possible to know whether the product has been damaged during the melting and casting process according to the process monitoring strain.However, the experimental fiber will lose signal when there is a large tensile strain, which should be solved in subsequent experiments.

Section C.
Since the situation is similar to that in section B, the data obtained from the process monitoring in section C is also similar.As shown differently in figure 10, the area where section C is located takes longer time to solidify.For the same reason, in the area of section A, section B solidified earlier, which caused the complementary shrinkage in the area of section C not to proceed properly.

Section D.
Different from the other sections, only the area equivalent to half of the other sections was monitored in section D. This is because that the overall structure is symmetrical, as shown in 11, and we only need to collect strains from half of the area to achieve process monitoring.Due to the presence of the conical mold at the bottom, the explosives near the middle part solidify faster.This is reflected in 11 by the asymmetry of the strain diagram, and the size of the solidliquid coexistence zone.Similar to the case of section A, the time required for solidification in section D is approximately 6 h.The peculiarity that exists in section D compared with other regions is that there is no sharp increase in the pulling strain surge where the final solidification takes place.We speculate that the solidification process is conduct too fast with a large heat transfer area, resulting in a smaller temperature gradient and less volume shrinkage.With the decrease of temperature, the explosive, as a solid, exhibits certain tensile properties, which results in the fact that the tensile stress is not transferred to the fiber.

Numerical simulation and comparison
This section involves the use of a casting simulation software to numerically simulate the curing process of molten explosives, and compare the numerical results with the experimental ones.The casting simulation software is a finite element analysis software specially designed for the casting process, which can be used to calculate the temperature field, stress field and flow field of the solidification process.In this paper, the solid phase ratio of the temperature field was solved and analyzed to compare with the results and conclusions obtained from our embedded measurements, which will be further discussed in section 4.2.

Numerical model
To better compare the results of numerical simulation and embedded measurement, the dimensions of the mold in the simulation are the same as those in the experiment, as shown in figure 12.The model was established by using UG, and then assembled and meshed by meshcast for pre-processing.There are 118 476 2D elements and 1084 798 3D elements.
The physical parameters of the explosives used are shown in table 1 where λ represents the thermal conductivity, ρ refers to the density, C, LH stand for the specific heat capacity and latent heat, respectively, µ denotes the Newtonian viscosity coefficient, and T L and T S are the liquid and solidus temperature, respectively.These parameters were input into the material database of the software as a new material which was used in subsequent simulation experiments.Although the molten explosive utilized is not a complete liquid with 100% liquid phase, it is treated as a Newtonian fluid by convention [32].To make the process more similar to the one used in our experiments, the air temperature was set at 24 • C. The initial temperature of the explosive was set at 90 • C by the numerical model, which is consistent with the experiment, and the mold was also preheated to 60 • C. heat transfer conditions were built, one is with a heat transfer coefficient of 8 W (m• K) −1 used in the mold based on normal convection heat exchange with air, and the other is with a heat transfer coefficient of 4 W (m• K) −1 used in the riser covered with a layer of insulation cotton.

Simulation results
The calculated termination condition is set at 100% of solid phase ratio, and the cooling time is 8 h before this condition is reached.The time required for the explosive to reach the solid state is shown in figure 13 which is a cross-section of a casting, but it is enough to show the solidification time of the whole casting.The solidification time of the numerical simulation differs from the actual experiment by 1 h.

Comparison with experiments
To compare the experimental and numerical simulations, the data obtained by using both methods were compared and analyzed.The results were compared at the same height and the same time for the diameter of the unconsolidated part in both ways.As can be seen from figure 14, the diameters obtained in both ways are similar after starting the experiment, and there are some small gaps, which appear with different trends and changes of the gaps over time.
In section A, the difference in diameter reached 1.31 cm in two hours at the beginning cooling.The gap grew larger before reaching its maximum in fourth hour.In reality, there is still a part of the material that is not cured after five hours, but it is cured in the numerical simulation, which is probably because that the heat transfer coefficient of the upper layer is not set accurately.In general, we do not know exactly the heat transfer coefficient and some other parameters for each experiment, because the possible cases are not exactly the same.In section B, a different situation emerges, that is, the experimental results show the same drop rate, although slightly lower than the simulation results.At the completion of solidification in the area of section B, also the last whole casting solidification, the simulation results and the experimental ones appear to be inconsistent, and the experimental rate of decline is significantly slower.Section C is the region where the numerical  simulation result is the closest to the experimental ones, and the solidification time and the diameter of the unconsolidated region are similar.The situation in section D is similar to that in section A, where the explosive solidifies faster in the numerical simulation.
Numerical simulations can only be calculated accurately if the parameters are accurately known, while embedded distributed fiber optic sensing technology, as a measurement technology, can be used to accurately monitor in each experiment.Although the data collected experimentally is not as much as the numerical simulation, we sometimes need the data to be more accurate than this advantage.In the case that we can combine the two approaches, we can get more accurate and diverse data.

Conclusion
Melt-cast explosives in the solidification of the appearance of shrinkage and cracking can greatly affect the charge quality.Until this paper, there is no appropriate method to measure the stress from inside, though it is the most important parameter for shrinkage and cracking.Therefore, a measurement instrument is needed for process monitoring of the stresses inside the explosives.In this paper, a distributed fiber optic sensingbased approach is investigated for monitoring the entire curing process of the internal strain of explosives, which refers to the strain that is not decoupled from the temperature.This uncoupled strain is not yet the actual strain value, but it is possible to identify the solid-liquid phase change interface according to our method, which is attributed to the distributed fiber optic sensing with a dense number of sensing points.Again, this gives us an idea for subsequent work to consider decoupling temperature and strain to obtain actual accurate quantitative strain values.
This paper presents, for the first time, the identification of solid-liquid phase change interfaces which can be used to improve the process by monitoring the solidification sequence of molten explosives at different locations.For the first time, the method proposed in this paper is based on embedded measurements of optical fibers, which can be used to distinguish between solid-phase, liquid-phase and solid-liquid mixture zones using strain transfer theory.In addition, numerical simulations were performed by using casting simulation software.The results deviated from the experimental results, indicating that the embedded measurements based on distributed fiber optic sensing can avoid the deviation of the numerical simulation results due to the inaccuracy of some parameters.
The strains monitored in the paper were not the temperature decoupled, therefore could not be characterized to quantify the internal stresses and strains.The follow-up plan is to quantitatively investigate the law of strain transfer from explosives at different solid phase rates to optical fibers, which needs to be further mastered by experimental design and theoretical analysis.

Figure 2 .
Figure 2. Fiber optic layout and fixing method.

Figure 3 .
Figure 3.The position of the defect in the fiber before and after the strain occurs.

Figure 4 .
Figure 4. Valid and invalid data in the overall.

Figure 5 .
Figure 5. section A, B, C and D area in the valid data.

Figure 6 .
Figure 6.Strain changes in each segment throughout the solidification process.

Figure 7 .
Figure 7. Principle diagram of the method to identify the solid-liquid phase change interface.

Figure 14 .
Figure 14.Comparison of the diameter of the unconsolidated area between experimental and simulated results.

Table 1 .
Material parameters of the explosives used.