Measurement method and results of divergence angle of laser-controlled solid propellants used in space propulsion

Yang OU, Jianjun WU, Yuqiang CHENG, Yu ZHANG, Yuqi LI

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

KEYWORDS

Abstract The plume divergence angle is an important reference index for evaluating the thrust efficiency and propellant utilization of space propulsion systems.However, the characteristics of the dynamic variation of plume divergence angle over time cannot be measured using current methods.This paper utilizes high-speed photography and image processing methods to develop a strategy that can give a quick,non-destructive and real-time detection of the divergence angle.Effectiveness of the strategy is verified, and the characteristics of plume divergence angles of different lasercontrolled solid propellants were further analyzed and fitted.The experimental results indicate that graphene could effectively reduce the divergence angle,while oxide-doped samples had larger divergence angles than alloy-doped and carbon-doped samples.

1.Introduction

Currently, countries in the world are boosting different kinds of ambitious space programs.There is no doubt that aerospace technology is showing strong growth with the advancement of micro-machines, smart nanomaterials, accurate sensors, and plasma physics.1–3In parallel, intense use of space technology will continue to benefit the entire society—From using small space assets for asteroid tracking,global internet access,global positioning systems, precise weather prediction, advanced communication to near-Earth space exploration for the evaluation of influences of radiation and corpuscular fluxes on communication systems and weather.4–7Recently, there has been an increased interest in deep space missions such as mining of space resources, space travel, asteroid capture, and even voyages to Mars and the Moon.These ambitious aims require that the spacecraft is capable of traversing enormous distance over long periods of time.These missions are feasible only with highly efficient means of advanced space propulsion that allow for reduction of overall spacecraft mass while increasing spacecraft maneuverability.8,39

The cost of launching a spacecraft is comparable with the value of its weight in gold.Typically,it takes thousands of dollars to send one kilogram into low Earth orbit, and often ten times more than that.When it comes to going farther or returning materials, the cost would further surge.The smaller such spacecraft become, the less energy they need to run, and the lighter and cheaper they are to launch.10,11Although significant progress has already been made in reducing the size and improving the performance of these spacecrafts,12–14scientists and engineers are continuing their search for novel technologies and new physical principles to boost the efficiency and prolong the service life of miniaturized space thrusters.15,16

The most widely used thrusters in aerospace engineering are Hall thrusters and ion thrusters, being fed with noble gases including argon and xenon.However, further uptake of these thrusters is hindered by some challenges.First of all, the price of gaseous propellants would greatly increase the cost burden.According to the data presented in Ref.17, if the spacecraft moves from Earth to Mars, at least 40 t of xenon are needed as the propellant, and the expected cost is as high as 800 million yuan.On the other hand, the mass of the supercritical storage tank for gaseous propellants would be bulky, leading to limits on miniaturization of spacecraft.

Laser ablation propulsion seems to be a feasible solution to the above issues.As presented in Fig.1, the pulse laser with high energy is focused on the propellant, and then gas ionization quickly occurs to generate high-temperature, highpressure and gaseous plasma flow.The thrust is expected to be generated as the plasma flow expands.Generally,laser ablation propulsion can achieve impulses of over 1000 s.Thanks to its special design, the most outstanding advantage of laser ablation propulsion is that it is not needed to carry a lot of fuel, and the laser that provides power can be deployed on the ground.Therefore, it is expected that the payload of the carrier will significantly increase, while the launch cost may be significantly reduced.On the other hand, solid propellants with light-weight, rather than those gaseous propellants that require bulky storage tanks, are commonly utilized in laser ablation propulsion.As a result, the volume and weight of satellites could be greatly reduced.Because of its high payload,low cost,and safety,the laser propulsion system is far superior to other space propulsion systems.Nowadays,laser propulsion is more and more favored in aerospace engineering, and is widely used in low earth orbit launch, earth orbit debris removal, microsatellite attitude control, and other fields.

According to unique operations of laser propulsion, the solid–gas conversion process is an indispensable process for the laser ablation thruster supplied with solid propellants,and the expansion of plasma flow is a prerequisite for ensuring the subsequent thrust generation.The properties of gaseous products, including ionization degree, temperature, velocity,and divergence angle,would be closely related to the expansion process, and ultimately affect the propulsion performance of the thruster.Several papers have analyzed the influence of different properties of gas products on thruster’s performance,and other studies have compared the characteristics of vaporized products of different propellants.5,18–22However, rather limited articles focus on the divergence angle of gaseous products.The divergence angle represents the ratio of the momentum perpendicular to the axis to the momentum parallel to the axis.23If the divergence angle of gas products is large, the utilization and efficiency of the thruster propellant would be low.Therefore, whether the thruster operates in chemical propulsion, electric propulsion or laser propulsion, the plume divergence angle is an important parameter to evaluate the performance of thrusters.

The Ferrari probe and spectrum are the main methods to measure the divergence angle of micro-thrusters.24–30Both methods can measure the radial distribution of ion current,and then can be integrated to calculate the divergence angle of the plume.They can accurately measure the divergence angle of steady-state plumes, and do not work with dynamically changing plumes.Besides, the two methods are suitable for measuring the plume far from the outlet; otherwise, the probe and fiber will be overheated due to ion bombardment.In addition, they are intrusive measuring methods, in which the motion of the Ferrari probe and spectral probe in the plume region can unavoidably affect the plume’s characteristics.23,31,32To address these disadvantages, some researchers adopted image processing to extract relevant features through plume images, which is called the image method.This nonintrusive method can avoid interference with gas products,and is simple in operation, large in acquisition range, and fast in acquisition.However, the image method is mainly used in the steady-state plume measurement of the Hall thruster.23,31,33The plasma flow expansion in the laser ablation thruster is a transient process, which needs special image acquisition and processing strategies.

In this paper, we developed a strategy for measuring the divergence angle of gaseous products on the basis of the image method.After verification,this improved strategy is utilized to compare and analyze the divergence degree of different solid propellants after being ignited by laser.The rest of the paper is organized as follows.The basic principle and processing flow for the divergence angle detection is presented in Section 2.Experimental results and analysis are presented in Section 3,and the conclusion is given in Section 4.

2.Fundamentals of measurement method

The reaction mechanism will be different if different types of lasers are used for propulsion.In the field of laser propulsion,nanosecond-millisecond pulse lasers are commonly adopted.When the solid propellant is ablated by these lasers,the formation of gaseous products can be described by classical lasermatter interaction,as shown in Fig.2.Typically,the evolution process of gaseous products can be divided into three stages.Firstly, the surface of the solid propellant is irradiated by the pulse laser, and its surface temperature increases until melting and vaporization.Secondly, the interaction between the pulse laser and vapor causes the temperature to rise, and the vapor ionizes until the plasma is formed.Finally, the plasma continues to absorb the pulse laser energy to support its own movement.34,35

Fig.2 Evolution process of gaseous products.

With the above analysis,it is known that gasification products would be generated from the laser spot on the surface,and then expand and diffuse around.Therefore, the gasification products of solid propellants ignited by laser have cylindrical symmetry,but their plume boundary fluctuates due to external interference.When the ICCD camera is adopted to record the movement of gasification products, we can obtain series of images as presented in Fig.3.The main topic of this paper is to extract the plume divergence angle from these images.

Fig.4 illustrates the experimental setup for detection of the plume divergence angle.All experiments were conducted in a vacuum chamber under the pressure of 5×10-4Pa, and solid propellants were mounted on a fixed platform.The solid propellants were ignited by the fiber laser with a wavelength of 1080 nm.The laser spot radius reaching the surface was 4×10-3cm after the laser was focused by a lens with a focal length of 400 mm.A high-speed ICCD camera (HS VISION PCO dimax S4) was placed horizontally at a height as high as the laser spot.The computer-controlled laser and the camera were triggered synchronously, and the camera records the expansion movement of the gasification products of solid propellant after ignition.

2.1.Divergence angle measurement

Based on the experimental set-up, an overview of the solution strategy for the plume divergence angle measurement method proposed in this paper is presented in Fig.5.In the measurement process, the camera exposure and placement position were firstly determined according to laser parameters, then the background light and image scale were calibrated.Secondly, a series of images of the gaseous products were taken with the ICCD camera,and the image illuminance values were calculated using image processing methods.Furthermore, the radial distribution of spatial illuminance of some circular sections was calculated.subsequently, the maximum illuminance of different sections was calculated and the positions of 98%maximum illuminance in different sections was found.Finally,linear regression on these positions was conducted, and the slope of the regression line was the tangent function of the divergence angle.

2.1.1.Image capture

The exposure time of the ICCD camera should be far less than the laser pulse width time.Meanwhile, the exposure time should be small to obtain as many images as possible within one laser pulse width time.According to the data analysis, it is recommended that the exposure time of the ICCD camera(tb) be less than one-thousandth of the laser pulse width time(tl).In our experiments, tbwas set as 4.6 μs.

The ICCD camera was put on the outside of the germanium glass,which was on the side of the solid propellant and kept at a distance of 80 cm.Meanwhile, the axis of the camera lens was vertical to the axis of the propellant, and the camera was placed horizontally at a height as high as the laser spot.

The ambient light cannot be completely isolated in the measurement process, so it is necessary to determine the value of the background light to eliminate its impact on the measurement process.Before photographing the expansion movement of the gasification products,the camera was used to record the images when there was no laser ignition, and the maximum illumination value of these photos was calculated.This illuminance value was considered as the background illuminance I0.In addition, the actual size of the un-ignited solid propellant could be known,and the pixel number it occupies in the image can be calculated.If the diameter of the propellant is assumed to be D0, and the corresponding number of occupied pixels is assumed to be X0, then the image scale is 1: D0/X0.

Fig.3 Some images of gasification products.

Fig.5 Flowchart of proposed measurement method for plume divergence angle.

After completing the above steps,the ICCD camera can be used to record the expansion movements of the gasification products of solid propellants.

2.1.2.Image processing

RGB(Red,Green,and Blue)is the three colors of light,which can be mixed to produce any other color.Colored images are often stored as a sequence of RGB triplets or as separate red,green and blue overlays, though this is not the only possible representation.Each image can be regarded as composed of innumerable pixels, and each pixel can obtain the light intensity values in the red, green, and blue channels.

Suppose that the intensity of a pixel in the RGB three channels is Nr,Ng,Nbrespectively.Then,the gray values Gr,Ggand Gbcorresponding to the red, green and blue channels can be calculated by the following equations:

where μ is the photoelectric conversion coefficient of the camera; η is the conversion coefficient between the gray value and the camera current; a is the entrance pupil aperture; f′is the image focal length; k is the transmittance; Y is the spectral response characteristic function of different channels; l is the corresponding actual length of a single pixel, l = D0/X0; Kr,Kgand Kbrespectively represent the conversion coefficients of red,green and blue channels.The values of the three conversion coefficients can be obtained through experimental calibration.

The illuminance of every pixel in the images can be calculated via the empirical equation as follows23:

where I is the illuminance of the pixel, and Hr, Hgand Hbrespectively represent illuminance of the red, green and blue channels.

Therefore,the above equations can be used to calculate the illuminance value of each image.For these images record the movements of gaseous products, they need to subtract the ambient illuminance I0from the image illuminances to obtain their actual illuminance values.

2.1.3.Transformation calculation

(1) Radial distribution of spatial illuminance As mentioned above, the gasification product can be assumed as a prismatic light source.The illuminance of the image is the projection of the prismatic light source on the Oxz plane as presented in Fig.6.Each pixel of the image is the superposition of multiple pixels lying on the chord of the circular cross profile of the gaseous product cylinder, whose axial position is of the same value.Therefore, the illuminance of every pixel is the weighted sum of all points’ illuminance whose height is as the same as their corresponding pixel in the gaseous product.Based on the above analysis, it can be known that the illuminance of the pixel points in the image and the illuminance of the point of the gasification product in the actual space can be expressed by Eq.(5):23,31

where I (x,y ) is the illuminance of pixel(x,z)in the image,P(yi)is the illuminance of point i(x,yi,z),and diis the distance between point i(x,yi,z) and the ICCD camera.

The radius R of gasification products is generally less than 3 cm, and the distance L between the camera and the gaseous products is larger than 80 cm.As L ?R,the distances between the ICCD camera and all points in the gaseous products can be assumed to be L.Therefore, Eq.(5) can be simplified as follows:23,31

where I (x0,z0) is the illuminance of the pixel m(x0,z0), and IA1Bis the sum of the illuminance of the points on Chord A1B.

The illuminance of pixel point m′(x0-1, z0), which is adjacent to the pixel point m(x0,z0),can be calculated according to Eq.(8):23

Fig.6 Projection diagram of gasification products.

Therefore, if the illuminance of each pixel in the image can be obtained,the illuminance of every point in gaseous products can be calculated via Eq.(9).The illuminance of each point on ChordO and the radial illuminance distribution of gaseous products in this circular section can be obtained.

Theoretically, the illuminance distribution of the upper image pixels in the image (z > 0) should be equal to that of the lower image pixels(z<0),so the radial illuminance distributions calculated by using the upper/lower image pixels of the image respectively should also be the same.However,external interference is inevitable, so the image contour of gasification products will fluctuate slightly.As a result, the radial illuminance distribution solved by using the upper and lower parts might not be completely consistent.Therefore, we calculate the upper and lower radial distribution of each section in the measurement.

(2) Total illuminance value Itand position of 98%It

Since the minimum unit of the image is a pixel, the minimum resolution of the radial distribution is also the actual length of a pixel in space, that is l = D0/X0.The sum of the illuminances of all points in the radial distribution, i.e., Point O to, is called the total illuminance value It.

To calculate the position corresponding to 98%of the maximum illuminance value, the illuminance value of each point should be accumulated in turn along the radius direction starting from Point O to.It is assumed that the accumulated illuminance value from the first point O to the ith point is Isumi.When the jth point meets the condition of Eq.(10), the linear interpolation method can be used to calculate the position of 98%Itas shown in Eq.(11).

where r98%is the distance between the position of 98%Itand Point O.

Similarly, the position of 98%Itcalculated by using the upper radial distribution,and the lower radial distribution will also be different.Here, we define r98%uas the result of using the upper distribution, while r98%las the result of using the lower distribution.

(3) Linear regression and divergence angle

The projection point of the gasification products section on the Oxz plane has the same z coordinate value, which is defined as zn(n = 1, 2, ???).For a given section zn, its corresponding position (r98%unand r98%ln) of 98%Itcan be obtained.Then, we can get two groups of arrays, as shown in Eqs.(12) and (13):

Although this paper focuses on the gaseous products of solid propellants, the measurement method developed in this paper can be also used in the calculation of the plume divergence angle of electric thrusters.For example, in Hall thrusters, the divergence angle α of each section can be calculated by the following Eq.(14):

where rlis the radius of the laser spot.In the thruster, the divergence angle of every section needs to be calculated according to its parameters, and each section’s angle may be different.

In the analysis of laser-matter interactions, we found that the expansion of the plume morphology at the front end of the gasification product is approximately linear, that is, the plume divergence angles at the front end should be approximately the same.With the increase of expansion distance,the plume divergence angle at different sections becomes different.However, the gasification products of electric thrusters using solid propellants usually do not undergo expansion and diffusion for a long time,but quickly enter the discharge channel.Therefore, we focus on the front end of the gasification product.As a result, this method does not directly calculate the plume divergence angle of each section by using Eq.(14),but the linear regression is expected to be the performance on the two arrays in Eqs.(12)and(13).It should be noted that this method is also applicable for calculation of the divergence angle of each section.

Before linear regression, it is necessary to distinguish the front area of gasification products, and then select the array range for regression.In this paper, we mainly adopt the Douglas–Peucker algorithm to perform polygon fitting on the boundary of the gasification products in the image from the laser spot.In the fitted polygons, if the slope of three consecutive edges is all less than zero in the z>0 plane or larger than zero in the z<0 plane,then we assume that the area from the laser spot to the three edges is the front of gaseous products.As a result,the array corresponding to all sections in this area is the data set of subsequent linear regression.

By linear regression of the above two arrays, two lines can be obtained.Assuming that the slopes of the two lines are kland, the divergence angle (α) of gaseous products is calculated by the following equation:

2.1.4.Validation

To demonstrate the accuracy of the measurement method developed in this paper, the predicted divergence angles were compared with those obtained by experiments in the Hall thruster23and laser ablation thruster.37

Fig.723presents two plume images of Hall thrusters, and their plume divergence angles obtained from the probe measurement were 11.5° and 26.6°.The method developed in this paper was adopted to process these two plume images, and the corresponding plume divergence angle can be calculated as 12.6° and 24.3°.

Fig.7 Plume images of Hall thrusters: (a) 11.5°; (b) 26.6°.23

Fig.8 shows the jet patterns of the ablation plume with different pulse widths, and the theoretical divergence angles (αt)of these jet patterns were 17.7°, 24.5°, 33.3°, 41.1°, and 47.4°.Similarly, using the image measurement mentioned above,we can obtain the divergence angles in Fig.8, which are 16.3°, 26.7°, 36.0°, 38.4°, and 43.6°.By analyzing these data,we can see that in the above two cases, the deviation between the calculated angle and the reference data is less than 10%.Therefore,the excellent fit between the predicted and reference results validated the reasonableness of this measurement method.

The indicators of ICCD, such as the exposure time and minimum pixel size,can determine the accuracy and resolution of the measurement method.The shorter the exposure time,the better its continuous sampling performance.The smaller the minimum pixel size, the better its spatial sampling performance.For the ICCD camera adopted in this paper, the minimum spatial resolution is about 0.10 mm/pixel, the minimum time resolution is about 1 μs, and the uncertainty is about 12%.There might be three main sources of errors.Firstly,the background light inevitably affects the measurement process.Although the background light has been particularly processed in the section of image capture, it may dynamically change,which in turn affects the accuracy of the measurement process.Secondly, the plasma flow contains some nonluminescent particles that cannot be captured by the camera,resulting in smaller detected results than the actual results.23In addition, the placement of the ICCD camera should be at the same height as the center of the laser spot on the material,and perpendicular to each other.Any deviation in the height or angle can lead to a considerable deviation in divergence angle measurement.

2.2.Plume length and area

To better analyze the characteristics of gasification products,we introduce three parameters,namely,plume length,velocity and average area, which were obtained from the moving images of gasification products.As shown in Fig.9,the plume length Lpwas assumed to be the lateral displacement of the plume leading edge from the ablation surface, and the plume area Apwas converted from the area occupied by the plume in the image to the proportional real two-dimensional area.

3.Results and discussion

3.1.Solid propellants preparation

A single solid material is difficult to meet the multi-mission propulsion requirements of thrusters, and nowadays composite propellants have become a better alternative.In previous works, it has been proved that the composite propellants prepared by the modification of the Polytetrafluoroethylene(PTFE) matrix with different fillers are expected to achieve better performances.Here, we mainly analyze and compare the plume divergence angle of this type of propellants.In the experiments,all propellant samples were prepared by the same steps under the shielding gas as given in Fig.10.The properties of the polytetrafluoroethylene matrix and fillers are presented in Table 1.Although the particle radiuses of the dopants were not exactly the same, they were far smaller than the particle radius of the matrix, so we can ignore the influence of particle radius on the results in the experiment.

3.2.Measurement results

Fig.8 Plume images of laser ablation thrusters.37

Fig.10 Preparation route of propellant samples.

To compare and analyze the characteristics of different gasification products, all doped samples were examined under the same operations.In these experiments, the laser width was set as 5 ms, and the laser energy was set as 5 mJ.The laser beam irradiated the propellant surface vertically via a lens, and the diameter of the laser spot on the surface was around 5 mm.In addition, the adopted fiber laser was a Gaussian beam,and the spatial distribution of the laser spot meets the Gaussian distribution law.The characteristics of gasification products change dynamically with laser time, and the width of laser ignition is far shorter than the acceleration time of the subsequent discharge process in electric thrusters.Therefore,the parameters of the gasification products at the end of the laser can be regarded as the entrance parameters of the subsequent discharge process.For the above reasons, we mainly compare the divergence angle, plume length, plume velocity and average illuminance of different gasification products at the half width (2.5 ms) and the end time (5.0 ms) of the laser,as given in Table 2.

As presented in Table 2, the samples doped with oxides have larger plume divergence angles than the other samples,and the sample doped with Fe2O3ranked the top value of divergence angle, which was 63.588° at 2.5 ms and 57.816° at 5 ms.With a number of dispersed particles, the gasification products of the samples doped with oxides were relatively dispersed,resulting in a large divergence angle.The sample doped with NiO did not even form a stable plume.Although the plume length and velocity can be calculated, these values fluctuated with the intermittent plumes.Therefore, oxides can worsen the stability of thruster operation, and these results were consistent with the previous experimental analysis in Ref.19,38.The divergence angles, plume lengths, and expansion velocities of carbon-doped samples got lower values than other samples,with graphene-doped samples having the smallest divergence angle of 3.055° at 2.5 ms and 1.827° at 5.0 ms.Due to its small plume divergence angle,the thrusters fed with carbon-doped samples achieved better propulsion performance, as presented in Ref.4.The samples doped with alloy particles exhibited different characteristics.The samples doped with Co-Cr and Ni-Ti particles had smaller divergence angles,while the sample doped with Cu-Zn had a larger divergence angle,but the Al-Si doped sample got the largest plume length and expansion velocity.In addition, the divergence angle and plume velocity of most samples decreased over time because the adopted pulsed laser was a Gaussian laser, with the most concentrated energy distribution in the middle and less energy at the end.

In addition, the plume areas of oxide-doped samples were the smallest, but their divergence angles were the largest, indicating that the mass of gasification products is low but dispersed.The plume areas of carbon-doped and alloy-doped samples were relatively large, resulting from the large mass of their gasification products.Besides, the plume area of almost all samples increased over time, indicating that themass of gasification products continued to increase in the ablation process.

Table 1 Properties of polytetrafluoroethylene matrix and filler s.

Table 2 Plume characteristics of different gasification products.

To further analyze the variation of plume characteristics,the variation of divergence angle and plume length over time for different samples were analyzed.

3.3.Alloy particles

The plume divergence angles of samples doped with alloy particles are presented in Fig.11.All points in the figures are directly measured using the method proposed in this article,and the solid lines are fitted based on the data for analysis.

As shown in Fig.11, the divergence angle of the plume in most samples underwent a significant change at the initial moment, which was due to the ablation caused by laser spot irradiation.However, the initial reaction process was not stable,and the morphology of the ablation products fluctuated greatly,resulting in a sudden change in the divergence angle of the plume.For the sample doped with Al-Si alloy, its divergence angle rapidly increased to around 30°, then approximately linearly decreased, and finally stabilized at around 10°.The divergence angle of the sample doped with Co-Cr particles was large at the beginning, approximately 70°, and then gradually decreased to 60°in about 1 ms.Afterward,the curve showed a discontinuity, because two plumes were generated here.After the first one disappeared, a new stable plume appeared on the surface, with an initial divergence angle of about 28°, and then remained stable at around 12° after 3 ms.The variation of the sample doped with Ni-Ti particles was similar to that of the sample doped with Al-Si particles,with a rapid decrease from 28° to 7°, and then remained dynamically stable at around 7°after 2 ms.However,the sample doped with Cu-Zn particles exhibited characteristics different from other samples, with its divergence angle gradually increasing from 0° to 30° and then decreasing, but fluctuating around 25° in the end.

Overall, the sample doped with Ni-Ti alloy got the lowest divergence angle and best stability, while the sample doped with Cu-Zn alloy had the largest divergence angle.Therefore,for the category of metal doping modification, the sample doped with Ni-Ti alloy exhibited smaller plume divergence angles and stabilized at a fixed value faster.The reason for this is that Ni-Ti alloy is a memory metal that resists changes in the thermal ablation process to a certain extent, thereby weakening the particle sputtering effect and stabilizing the ablation products at a small divergence angle.

Fig.11 Plume divergence angle of samples doped with alloy particles.

3.4.Oxide particles

The divergence angles of samples doped with oxides are large,and do not maintain a dynamically stable value like alloys.Besides,there was no stable plume but plenty of dispersed particles formed in the ablation products of the sample doped with NiO, and its divergence angle was not calculated here.The fitting equations of the samples doped with CuO, VO2,and Fe2O3are given as follows.

As given in Fig.12, the divergence angle of the sample doped with CuO varied periodically, but the amplitude can be observed to gradually decrease.At the beginning of ablation, its angle increased from 25° to 50° and then decreased around 10°, followed by dynamic periodic variations.The divergence angle of the sample doped with VO2approximately linearly decreased from 30°to 20°and continued to increase to around 70°.The divergence angle of the sample doped with Fe2O3was much larger than that of other samples,which first increased to 90°,then decreases to 70°,and finally experienced considerable growth.

Fig.12 Plume divergence angle of samples doped with oxide particles.

In general, the average divergence angle of the sample doped with CuO was the smallest among the three samples doped with oxide particles, but all divergence angles of the samples doped with oxides were larger than those of alloys.Under the same conditions, the larger the divergence angle of the plume, the worse the performance of the thruster fed by this propellant.In the previous experimental studies,38it was also found that the thruster supplied with oxide-doped propellant obtained a low discharge success rate and poor working stability, which may be because the supplied plasma flow is too dispersed to form a stable and reliable discharge circuit.Therefore, from the perspective of stability and plume divergence, oxides are not suitable as dopants for solid propellants.

3.5.Carbon particles

The divergence angles of the samples doped with carbon particles exhibited a similar variation trend, with initial angles being around 75° and immediately plummeting below 20°.The fitting relationships of the samples doped with toner,graphite and graphene are expressed as the following equations.

As presented in Fig.13,the initial angles of these three samples are all large,but they are all very small in the later stage of ablation.For the sample doped with toner,its initial angle was approximately 75°, and after continuously decreasing to around 10°(after 2 ms),the divergence angle remained dynamically stable at 10°.The initial angle of the graphene-doped sample was approximately 70°,and after continuously decreasing to 3°,it maintained an average divergence angle of 5°with dynamic periodic fluctuation.The initial angle of the graphitedoped sample was approximately 80°, and its angle continued to decrease over time without maintaining a stable value.

Although the initial angle of these carbon-doped samples was relatively large,the plume divergence angle after stabilization was smaller than that of other metal-doped and oxidedoped samples.In addition,the divergence angle of the sample doped with graphene was the smallest among all samples,and the average angle was only 5° in the dynamically stable process.Therefore,the doping particle of graphene could improve the divergence of gasification products, and the solid thruster supplied with the graphene-doped sample is expected to achieve better propulsion performance, which is consistent with the experimental results presented in Ref.4.

3.6.Discussion

Fig.13 Plume divergence angle of samples doped with carbon particles.

Based on all the above images,it can be seen that these propellant samples doped with Al-Si alloy, Co-Cr alloy, Ni-Ti alloy,toner, graphene, and graphite all exhibited similar variation trends, with the divergence angles rapidly changing to large values at the beginning of ablation and then decreasing to a stable value.These doped particles all have high laser absorption efficiency, thermal conductivity and high melting point,which would facilitate energy absorption to promote the decomposition of the surrounding polymeric matrix into plasma flow.Since the doped particles in the early stage absorbed the main energy, less energy was transferred to the surrounding polymer matrix at the beginning of ablation,and stable and continuous erosion is not formed.At this time,the shape of the plume is irregular, resulting in a larger divergence angle of the plume.As the ablation goes on,these doped particles absorb sufficient energy, but their own melting point is extremely high and difficult to be ablated.At this time,they stably promote the ablation of the polymer matrix, and thus the divergence angle of the plume remains roughly dynamically stable.Besides, although impurities are difficult to be ablated,when the polymer matrix around them is ablated,these doped particles will also be exploited and shed into the plume,which is one of the reasons for the fluctuation of the divergence angle.In addition, it can be noted that the sample doped with Ni-Ti alloy first reached a stable value because this alloy is a shape memory alloy.When its temperature rose, the alloy would appear to have the shape memory effect, which weakened the particle exploitation effect and thus made the variation of the divergence angle more stable.Moreover, the divergence angles of the samples doped with carbon particles got the lowest value after stability.This was contributed to the fact that nano toner, graphene and graphite could adsorb and desorb various atoms and molecules, so the particles generated by exploitation would be integrated with the plasma flow to reduce the degree of dispersion.On the other hand, because graphite exhibited thermal insulation at high temperatures, it could hinder the reaction between laser and propellant.As a result, the generated plasma flow was small and intermittent in the latter ablation process, leading to low and fluctuating divergence angle.

The absorption efficiency of the particles including Cu-Zn alloy, CuO, Fe2O3, and VO2is lower than that of those particles mentioned above, so the plasma flow was not formed immediately at the beginning of ablation but after a certain period of time.The divergence angles of these samples doped with Cu-Zn alloy,CuO,Fe2O3,and VO2did not achieve stable values during the ablation process, for the diffusion varied with different properties of these particles.The Cu-Zn alloy would undergo intergranular fracture at high temperatures,which worsens the continuity of the interaction between laser and propellant and thus results in a large and constantly changing angle.The nanoparticle of CuO could promote ionization and generate more plasma flow.However, excessive plasma would result in the shielding effect, which could cause fluctuations in the energy reaching the ablation surface and lead to unstable ablation processes and unstable variation of the divergence angle.As a magnetic particle, the exploitation of Fe2O3caused the generated ionized plasma particles to disperse, without forming a stable and continuous flow and resulting in the maximum divergence angle.VO2could strongly reflect the laser at high temperatures,which worsened the dynamic interaction between the laser and propellant and led to poor performance in terms of the divergence angle.

4.Conclusions

In this article,a method based on image processing is proposed to calculate the divergence angle of gaseous products, and its effectiveness is verified by comparison with other reference values.By using this method,the divergence angles of gasification products generated from different propellant samples were analyzed and compared.The main conclusions are as follows:

(1) The variations of divergence angles in most samples doped with alloy and carbon particles exhibited similar characteristics, with large initial divergence, then decreasing with time, and finally maintaining a dynamically stable value.

(2) The oxide-doped samples had the highest divergence angle, and their variations did not show a dynamic stable process.

(3) The samples doped with carbon particles had smaller divergence angles than other samples.

(4) Graphene has significant positive effects on improving the divergence of solid propellants.

Declaration of Competing Interest

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.

Acknowledgements

This study was co-supported by the Innovative Research Groups of the National Natural Science Foundation of China(No.T2221002).