CN110580402A - Construction method of composite solid propellant filler stacking structure characteristic unit - Google Patents
Construction method of composite solid propellant filler stacking structure characteristic unit Download PDFInfo
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Abstract
the invention discloses a construction method of a packing stacking structure characteristic unit of a composite solid propellant. On the premise that the density of the characteristic unit is equal to that of the propellant, the characteristic unit is characterized in that: the quantity ratio of the filling materials of each stage in the unit is the same as that of the filling materials of each stage in the actual propellant, and the quantity of the filling materials of at least one stage is 1. The construction method comprises the following steps: s1, determining the particle size and the number of each level of filler in a characteristic unit according to the filler composition in the propellant in unit volume; s2, determining the characteristic unit volume according to the condition that the characteristic unit density is equal to the propellant density; s3, taking a certain particle size as a demarcation point, and dividing filler particles into coarse particles and fine particles; s4, searching a coarse particle stacking structure which is not intersected with each other and is uniformly dispersed in the feature unit; s5, filling the fine particles into the gaps of the stacking structure formed by the coarse particles to construct a packing stacking structure characteristic unit. The invention can reflect the actual particle size distribution and density of the propellant, and has uniform particle distribution and wide applicable filler volume fraction range.
Description
Technical Field
the invention relates to the technical field of numerical simulation of performance of particle-reinforced composite materials, in particular to a construction method of a packing stacking structure characteristic unit of a composite solid propellant.
Background
the composite solid propellant is a particle-filled polymer matrix composite. In order to increase the packing density of propellant particles, optimize the performance of the propellant preparation process and achieve a certain burning rate index, the composite solid propellant filler usually adopts a multi-particle-size combination consisting of an oxidant (usually ammonium perchlorate, AP) with multi-particle-size grading and a metal fuel (usually aluminum powder, Al) with certain particle size. Through the process flows of fully mixing the filler and the matrix, curing and forming the propellant and the like, filler particles in the cured propellant matrix are in a stacking structure with macroscopic uniform distribution and microscopic random stacking. The grain size distribution and the grain accumulation structure of the filler particles directly influence the combustion surface structure and the stress distribution state of the propellant, and further influence the combustion performance and the mechanical performance of the propellant.
When the performance of the propellant is estimated by adopting a numerical simulation method, the establishment of a characteristic unit capable of reflecting the packing accumulation structure in the real propellant is the first premise. The packing structure characteristic unit is one of all possible packing random packing structures in the real propellant on the premise that the grain sizes and the number of each stage of the packing are consistent with those of the real propellant, but the volume average property (such as the average density of the characteristic unit) of the characteristic unit is consistent with that of the macroscopic propellant.
the average particle size of AP particles for propellant is about 250-425 μm (class I AP), 180-250 μm (class II AP), 106-150 μm (class III AP), while the average particle size of aluminum powder particles is only about 12 μm, and the particle size of ultra-fine AP particles is more below 10 μm. In the real propellant formula, the maximum difference of the number of particles at each stage can reach 4 orders of magnitude.
On the premise that the density of the characteristic unit is equal to the density of the real propellant, the total amount of particles in the unit is increased steeply along with the expansion of the calculation unit. Therefore, the constructed packing stacking structure characteristic unit also has the processing capacity of a computing platform, and the computing scale is controlled within a reasonable range. For a given propellant formulation, i.e. on the premise that the particle size and volume fraction of the particles in each stage of the filler size distribution are determined, the number ratio of the particles in each stage is roughly determined. The total amount of particles in the characteristic unit is minimized when the minimum number of particles in the characteristic unit (typically the largest particles in AP/Al/HTPB propellants) is 1, while maintaining the ratio of the number of particles in each stage of the filler.
At present, in the traditional composite solid propellant filler stacking structure unit construction method, the filler stacking microstructure is generally modeled only schematically. To reduce the calculated amount, fine and large amounts of fine AP or aluminum powder particles are considered homogeneous with the matrix, but fine particle size fillers (especially ultra-fine AP) have a significant impact on the propellant burning rate. Therefore, the traditional packing and stacking structure unit of the composite solid propellant does not reflect the real grain size distribution of the propellant, and can bring larger deviation to the combustion performance and mechanical property estimation of the propellant.
in addition, in the traditional construction method of the packing structure unit of the composite solid propellant, the final positions of all particles are indiscriminately determined by random initial states. For the characteristic unit provided by the invention, because the quantity of large particles in the characteristic unit is less, when a packing stacking structure is generated by adopting a traditional algorithm, the small-quantity large particles are likely to be aggregated or dispersed to a certain degree, and have deviation from the actual condition that the packing is uniformly dispersed in a matrix.
Disclosure of Invention
The invention provides a method for constructing a packing stacking structure characteristic unit of a composite solid propellant, which is used for overcoming the defect that the packing stacking structure has larger deviation with an actual propellant due to the fact that a large number of tiny AP or aluminum powder particles are taken as a matrix in the prior art, and constructing the packing stacking structure characteristic unit of the propellant, which has the same density with the actual propellant, the particle size of each level of packing is consistent with the particle size of each level of packing of the actual propellant, the volume fraction is close to the particle size, the calculation scale is smaller, and the packing is randomly and uniformly distributed in the unit.
In order to achieve the purpose, the invention provides a method for constructing a packing stacking structure characteristic unit of a composite solid propellant, which comprises the following steps:
s1: according to the formula of the composite solid propellant, the particle size and the volume fraction of each level of filler particles in the propellant filler particle size distribution are obtained, and the number of each level of filler particles in the unit volume of the propellant is calculated; defining the propellant filling stacking structure characteristic unit as: the solid propellant comprises a cube containing periodic boundaries, wherein the grain diameter of each level of filler particles in a characteristic unit is equal to that of each level of filler particles in the solid propellant, and the quantity of each level of filler particles is equal to the minimum integer quantity set of each level of filler particles in the solid propellant in unit volume;
S2: determining the volume and side length of the characteristic unit on the premise that the average density of the characteristic unit is equal to the density of the composite solid propellant;
s3: comprehensively considering the particle size and the number of filler particles at each level in the characteristic unit, selecting a certain particle size value as a demarcation point, and dividing the filler particles into coarse particles and fine particles;
S4: aiming at the coarse particle filler, searching a non-intersecting and uniformly dispersed coarse particle filler stacking structure in a characteristic unit by adopting a genetic algorithm, namely obtaining the coordinate positions of all coarse particles;
s5: and (4) aiming at the fine particle filler, filling the fine particles into the gaps of the coarse particle filler stacking structure determined in the step S4 by adopting an L-S algorithm, and constructing a composite solid propellant filler stacking structure characteristic unit.
Compared with the prior art, the invention has the beneficial effects that:
The method for constructing the packing stacking structure characteristic unit of the composite solid propellant is used for constructing the packing stacking structure based on all the packing particles with the particle size grades in the propellant formula, and the volume and the calculated amount of the characteristic unit are minimum on the premise of reflecting the particle size grading and the density of the real composite solid propellant; compared with the filler stacking structure which generates all particles in one step without difference in the traditional algorithm, the filler stacking structure which sequentially generates a small amount of coarse particles and a large amount of fine particles by adopting a two-step algorithm has the advantages that the particle distribution in the characteristic unit is more uniform, and the actual situation that multi-particle size grading particles in a real composite solid propellant are uniformly dispersed in a matrix is better met; the filler volume fraction range applicable to the method provided by the invention is wider, and the method is also applicable to modified biradical propellants with low solid content except for composite solid propellants with high solid content.
drawings
in order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. The drawings in the following description are only some embodiments of the invention and other drawings may be derived from the structure shown in these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for constructing a packing stacking structure characteristic unit of a composite solid propellant, provided by the invention;
FIG. 2a is the packing structure of coarse particles in the AP/Al/HTPB composite solid propellant feature cell of example 1 with 85% filler mass;
FIG. 2b is the packing structure of all particles in an AP/Al/HTPB composite solid propellant featured cell with 85% filler mass according to example 1;
FIG. 3 is a sectional view of the packing stacking structure of FIG. 2b in several 2-dimensional slices;
FIG. 4a is the packing structure of coarse particles in the AP/Al/HMX/PEG/NG-BTTN modified bipolymer propellant featured unit with 74% filler mass percent in example 2;
FIG. 4b is the packing structure of all particles in the AP/Al/HMX/PEG/NG-BTTN modified bipolymer of example 2 with a 74% filler mass percentage.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In addition, the technical solutions of the embodiments of the present invention may be combined with each other, but must be implemented by those skilled in the art. When combinations of technical solutions appear to be contradictory or impractical, it should be understood that such combinations do not exist and are not within the scope of the claimed invention.
The invention provides a method for constructing a packing stacking structure characteristic unit of a composite solid propellant, which comprises the following concrete implementation steps as shown in figure 1:
S1: according to the formula of the composite solid propellant, the particle size and the volume fraction of each level of filler particles in the propellant filler particle size distribution are obtained, and the number of each level of filler particles in the unit volume of the propellant is calculated; defining the propellant filling stacking structure characteristic unit as: the solid propellant comprises a cube containing periodic boundaries, wherein the grain diameter of each level of filler particles in a characteristic unit is equal to that of each level of filler particles in the solid propellant, and the quantity of each level of filler particles is equal to the minimum integer quantity set of each level of filler particles in the solid propellant in unit volume;
S2: determining the volume and side length of the characteristic unit on the premise that the average density of the characteristic unit is equal to the density of the composite solid propellant;
s3: comprehensively considering the particle size and the number of filler particles at each level in the characteristic unit, selecting a certain particle size value as a demarcation point, and dividing the filler particles into coarse particles and fine particles;
S4: aiming at the coarse particle filler, searching a non-intersecting and uniformly dispersed coarse particle filler stacking structure in a characteristic unit by adopting a genetic algorithm, namely obtaining the coordinate positions of all coarse particles;
S5: and (4) aiming at the fine particle filler, filling the fine particles into the gaps of the coarse particle filler stacking structure determined in the step S4 by adopting an L-S algorithm, and constructing a composite solid propellant filler stacking structure characteristic unit.
Preferably, the specific steps of S1 are:
s11: setting all levels of fillers to be spherical particles, and calculating the number of all levels of filler particles in the composite solid propellant per unit volume according to the particle size of all levels of filler particles in the formula of the composite solid propellant and the volume fraction of the filler particles in the composite solid propellant;
S12: dividing the quantity value of each level of filler particles in the composite solid propellant in unit volume by the quantity value of the first level of particles with the least quantity in the composite solid propellant in sequence, and rounding up by rounding up to obtain the minimum integer quantity set of each level of particles in the composite solid propellant in unit volume, wherein the quantity value of the particles with the least quantity in the minimum integer quantity set is 1;
s13: and taking the particle size of each level of filler particles in the characteristic unit as the particle size of particles in the formula of the composite solid propellant, and taking the number set of each level of filler particles as the minimum integer number set obtained by S12.
preferably, the specific steps of S2 are:
on the premise that the average density of the characteristic units is equal to the density of the real composite solid propellant, the total mass M of all levels of filler particles in the characteristic units is determined based on the particle sizes and the number of the fillers in the characteristic units obtained from S11-S13PIs calculated by the formula
In the formula, Kmax is the total number of particle size grading, and K represents the 1 st and 2 nd … … nd Kmax packing particles in the propellant when K is 1,2 and … … Kmax respectively; n is a radical ofKThe number of K-th grade particles; dKis the particle size of the K-th grade particles; rhoKis the density of the K-th order particles.
taking the non-filler part in the characteristic unit as a matrix, and taking the mass M of the matrix in the characteristic unitmIs calculated by the formula
wherein L is the side length of a cube of the feature unit; rhomis the average density of a propellant matrix consisting of a binder and a plasticizer; kmax is the total number of particle size grading, and K represents the 1 st and 2 nd … … nd Kmax packing particles in the propellant when K is 1,2 and … … Kmax respectively; n is a radical ofKthe number of K-th grade particles; dKIs the particle size of the K-th grade particles.
The calculation formula of the average density of the characteristic units and the relation between the calculation formula and the average density of the real composite solid propellant are
In the formula, ρunitIs a characteristic cell density equal to the average density of the filler and matrix in the characteristic cell; rhopropellantIs the average density of the real composite solid propellant; mPthe total mass of all levels of filler particles in the characteristic unit; mmthe mass of the matrix in the characteristic unit; and L is the side length of the cube of the characteristic unit.
In the formulas (1) to (3), except the characteristic unit side length L, other variables can be directly obtained or simply calculated by the formula of the composite solid propellant. Substituting the formula (1) and the formula (2) into the formula (3), a unique solution of the side length L of the characteristic unit can be calculated, and therefore the volume of the characteristic unit is obtained.
Preferably, the specific steps of S4 are:
s41: for coarse particles with the number of 1, fixing the spherical center position of the coarse particles to be the geometric center (0, 0, 0) of the characteristic unit; coordinates of the sphere center positions of the rest coarse particles in the x direction, the y direction and the z direction are respectively taken as random numbers between [ -L/2, L/2 ]; the combination of the grain diameter and the sphere center position of any group of coarse grains uniquely corresponds to a coarse grain stacking structure;
S42: detecting whether the coarse particles meet the condition that the coarse particles are not mutually intersected every two based on the coarse particle stacking structure randomly generated in the step S41;
Under the condition of periodic boundary, if any pair of coarse particles exist and the spherical center distance between the particles is smaller than or equal to the sum of the radii of the coarse particles, the particles are judged to be intersected with the particles, and the corresponding stacking structure is an invalid structure; if the coarse particles are not intersected with each other pairwise, the corresponding stacking structure is an effective structure;
S43: based on the coarse particle stacking structure randomly generated in step S41, and in combination with the result of determining the particle intersection obtained in step S42, the coarse particle diameter R, the coarse particle center position, and the feature cell side length L are used as arguments to construct a function F to evaluate the degree of uniform dispersion and the intersection of the particle distribution:
Wherein Nc is the total number of coarse particles; i and j refer to any two different coarse particles, respectively; r is the particle size of the coarse particles; delta xi,j,△yi,jAnd Δ zi,jThe absolute values of the spherical center coordinate difference values of the coarse particles i and the coarse particles j in the x direction, the y direction and the z direction respectively; l is the characteristic unit side length; PV is a penalty function.
Equation (4) equal sign first item on right
The expression of gravitational potential is used for describing the uniform dispersion degree of particle distribution. Wherein, the square-open term in the denominator is the sphere center distance of the particle i and the particle j under the periodic boundary condition. When particles i and j are aggregated or separated, i.e. Δ x, on the premise that characteristic unit side length L and particle radius R are determinedi,j、△yi,j、△ziThe value is smaller or larger, the square-opening terms in the denominator are smaller, and F is a larger value correspondingly. Therefore, it is considered that the smaller the F value is, the more uniform the particle distribution is in the packed structure. In the first term on the right of the equal sign of formula (4), (1/L) of the molecule6) And (1/L) in the denominator are introduced by non-dimensionalization, and after non-dimensionalization, the first term on the right of the equal sign of the formula (4) is summed to be a positive number smaller than 1.
The second term PV on the right of the equal sign of equation (4) is a penalty function term for the stacked structure where there is an intersection between particles. The PV value is: combining the judgment result of the step S42, if the stacking structure is an effective stacking structure in which every two particles are not intersected, taking PV as 0, and the F value corresponding to the stacking structure is less than 1; if the stacking structure is an invalid stacking structure with interparticle intersection, PV is taken as any normal number which is larger than 1, and the corresponding F value is larger than 1.
S44: and searching a coarse particle stacking structure corresponding to the minimum F value and the minimum F value less than 1 in all possible coarse particle stacking structures by using a genetic algorithm and a plurality of groups of randomly generated coarse particle stacking structures as initial solutions, wherein in the stacking structure, coarse particles are uniformly dispersed in a characteristic unit space and are mutually intersected in pairs.
The method adopts a genetic algorithm and comprises the following specific steps:
S441: and repeating the steps S41-S43M times to obtain M kinds of coarse particle stacking structures and F values corresponding to the M kinds of coarse particle stacking structures to form an initial population.
S442: and generating a progeny population through selection, crossing and mutation operations.
Selecting: repeating the M times, and randomly selecting a coarse grain stacking structure from the previous generation population to enter the next generation to generate a filial generation population containing M kinds of coarse grain structures. Wherein the smaller F the stacking structure is more likely to be selected into the next generation.
and (3) crossing: two different stacking structures in the offspring population exchange a plurality of coarse particle coordinates with random ranges according to a certain probability.
Mutation: and (4) generating a plurality of coarse grain coordinates again at random by a single stacking structure in the offspring population according to a certain probability.
s443: and calculating the F value of each stacking structure in the offspring population, and storing and recording the minimum value of F and the position coordinates of each coarse particle when the F is minimum. If the algebra of the current population does not reach the preset maximum iteration times, or the maximum iteration times is reached but the minimum F value is greater than 1, returning to the step S442 to generate a next generation population; and if the algebra of the current population is greater than or equal to the preset maximum iteration algebra and the minimum F value is less than 1, terminating the calculation.
Preferably, the specific steps of S5 are:
S51: and (5) initializing. For coarse particles, fixing the sphere center of the coarse particles at the corresponding coordinate position determined in the step S4, wherein the speed of the coarse particles is constant to zero, and the particle size of the coarse particles is equal to that of the coarse particles in the real composite solid propellant formula; for fine particles, the initial velocity is taken to be a random value between [ -L/2, L/2], the initial position is taken to be a random value in the feature cell cube not occupied by coarse particles, and the fine particle initial radius is zero.
S52: in the gap of the coarse particle accumulation structure, fine particles move, collide and grow up. The fine particles move linearly at a constant speed in the gap of the coarse particle stacking structure at the initial position and the initial speed described in S51. If the fine particles collide with another fine particle in the moving process, calculating and updating the moving speeds of the two collided fine particles according to the elastic collision process of momentum conservation and kinetic energy conservation; if the fine particles collide with the coarse particles with fixed positions in the moving process, the moving speed of the fine particles after collision is updated according to the fact that the fine particles are rebounded on the surfaces of the coarse particles and the coarse particles are still all the time.
S53: during particle movement and collision, the radii of all fine particles increase synchronously with time, and the ratio of the radius growth rates of the individual fine particles is equal to the ratio of their respective radii in the propellant formulation; and when the sum of the volume fractions of all the particles in the characteristic unit reaches the volume fraction of the particles in the propellant formula, the particle diameters of all the fine particles reach the corresponding values in the propellant formula, and the construction of the filler stacking structure characteristic unit is completed.
example 1
(1) particle size and number of particles in each stage in characteristic unit
For the AP/Al/HTPB composite solid propellant formulations shown in table 1 with 85% solid filler mass percent, the propellant contains a quaternary filler, and K is the number of filler particle stages. The particle diameter (D), density (. rho.), mass percent (MF) and volume percent (VF) of each component are known amounts.
TABLE 1 AP/Al/HTPB quaternary composite solid propellant formulation with 85% filler mass content
Remarking: here, the binder is a Hydroxyl Terminated Polybutadiene (HTPB) prepolymer and the plasticizer is dioctyl sebacate (DOS).
Based on the spherical particle hypothesis, 1mm was calculated3In the propellant, the number (Amount) of four-stage particles is respectively 18.29, 182.00, 1560832.64 and 105681.38, and the number (Amount) is sequentially divided by the corresponding number 18.29 of the class II AP with the least number to obtain the decimal number ratio of the particles of each stage of 1: 9.95: 85333.33: 5777.78. after rounding, the minimum integer number set of particles at each stage is 1: 10: 85333: 5778. the density rho of the propellant is calculated by the mass percent (MF) and the density (rho) of each component in the formula of the composite solid propellantpropellantIs 1.7211g/cm3。
the composition of each level of particles in the characteristic unit is shown in table 2, wherein K is the number of filler particle levels, D is the particle size of each component, N is the number of each level of particles in the minimum integer number set, VF-unit is the volume percentage of each component in the characteristic unit, and Error in VF is the relative Error between the volume percentage (VF-unit) of each component in the characteristic unit and the corresponding Value (VF) in the formula of the composite solid propellant.
TABLE 2 grading of particles in composite propellant characteristic units and their error from propellant formulation
(2) characteristic unit side length and volume
According to the method established by the invention, when the density of the characteristic unit is equal to that of the real composite solid propellant, the side length L of the characteristic unit is 379.79 mu m and the volume of the characteristic unit is 0.055mm through calculation3。
The volume percentages (VF-unit) of the quaternary particles in the characteristic unit were 13.21%, 30.99%, 17.62% and 9.54%, respectively. The relative Error in volume fraction of particles at each stage (Error in VF) in the characteristic units does not exceed 0.30% compared to the corresponding values in the composite solid propellant formulation (table 1 VF). The sum of the volume percentages of the particles in the characteristic units was 71.36%, with a relative error of only 0.03% compared to the volume percentage of the particles in the real composite solid propellant formulation (71.34%).
the built feature cells meet the desired objectives: the density of the solid propellant is equal to that of a real composite solid propellant, the grain diameters of the fillers of all levels and the fillers of all levels of the propellant are consistent, the volume fractions are close, and the calculation scale is small.
(3) Filling material stacking structure generated step by step
According to the particle size and the number of the various filler particles in the characteristic units shown in Table 2, class II AP and class III AP with larger particle size and no more than 10 in number are defined as coarse particles, and ultrafine AP and aluminum powder particles with smaller particle size and no less than 10 in number and more than 3-power are defined as fine particles.
For a coarse particle set consisting of 1 class II AP particle and 10 class III APs, the penalty function PV is taken as
Randomly generating 20 coarse particle stacking structures as search starting points, and taking the number of search iterations as 100000. Based on the genetic algorithm, the minimum value of the evaluation function F of the particle packing structure obtained by searching is 0.2831. At this time, the corresponding coarse particle stacking structure is shown in fig. 2a, and 11 coarse particles are uniformly distributed in the feature unit and do not intersect with each other.
Based on the coarse particle positions shown in fig. 2a, fine particles (ultrafine AP and aluminum powder particles) are randomly scattered in the gaps of the coarse particle packing structure by using an L-S algorithm. The calculation was terminated when the total volume fraction of particles in the signature unit reached the target value of 71.36%. The packed structure of all particles is shown in fig. 2 b. FIG. 3 is a plot of a number of representative 2-dimensional sections of FIG. 2 b.
For comparison, the side length of the feature unit, the number and the particle size of each level of particles in the feature unit, and the volume percentage of the target filler constructed in this embodiment are used as input conditions, and the L-S algorithm is directly adopted to generate the stacking structure of all filler particles.
in order to quantitatively describe the uniformity of particle distribution, the formula (6) is adopted to calculate the volume average centroid coordinates (Xc, Yc, Zc) of 11 coarse particles and all particles and the distance Lc from the centroid (Xc, Yc, Zc) to the geometric center (0, 0, 0) of the unit in the filler stack structure constructed by the invention and the filler stack structure constructed by the classic L-S algorithm respectively.
In the formula, xi、yi、ziRespectively are the coordinate values of the ith filler particle center in the finally generated filler stacking structure in 3 coordinate directions, RiRadius of the ith filler particle. The calculation results are shown in table 3.
TABLE 3 volume average centroid of particles in packing structure
Ideally, if the particles are uniformly distributed, the volume average centroid position should be located at the geometric center of the unit, i.e. Xc ═ Yc ═ Zc ═ Lc ═ 0. From the results in table 3, it can be seen that, compared with the method of directly constructing the packing structure of all the particle fillers by using the L-S algorithm, the method of the present invention divides the particles into coarse and fine particles, constructs the packing structure step by step, and the volume average centroid of the particle group is closer to the geometric center of the unit no matter only considering the coarse particles or considering all the particles, thereby proving that the particle fillers are distributed more uniformly in the packing structure constructed by the present invention.
Example 2
The filler volume fraction range applicable to the method provided by the invention is wider, and the method is also applicable to modified double-base propellants with low solid filler content besides the composite solid propellant with high solid filler content.
For the five-stage AP/Al/HMX/PEG/NG-BTTN modified dual-base propellant formulation shown in Table 4 with a 74% solids loading by weight. The composition of the granules at each level in the characteristic unit according to the method established by the invention is shown in table 5. Root of herbaceous plantAccording to the method established by the invention, the side length of the characteristic unit is 281.19 mu m and the volume of the characteristic unit is 0.028mm3。
TABLE 4 AP/Al/HMX/PEG/NG-BTTN five-level improved dual-base propellant formulation with 74% filler mass content
remarking: the binder here is polyethylene glycol (PEG) and the plasticizer is a nitrate plasticizer mixed in equal proportions from Nitroglycerine (NG) and 1,2, 4-Butanetriol (BTTN).
Defining class III AP and HMX-1 particles with the particle size not less than 86 microns and the number not more than 14 as coarse particles, wherein the number of the two types of coarse particles in a characteristic unit is 1 and 13 respectively, and the total number Nc of the coarse particles is equal to 14; the remaining fine AP, HMX-2 and aluminum powder particles are defined as fine particles. Firstly, a genetic algorithm is adopted to obtain a stacking structure with 14 coarse particles which are mutually intersected and uniformly dispersed, and the result is shown in figure 4 a; and (4) randomly filling fine particles in gaps of the coarse particle stacking structure by adopting an L-S algorithm. Fig. 4b shows the resulting complete packing structure.
Table 5 grading of particles in modified bis-based propellant feature units and their error from propellant formulation
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (5)
1. A construction method of a packing stacking structure characteristic unit of a composite solid propellant is characterized by comprising the following steps:
S1: according to the formula of the composite solid propellant, the particle size and the volume fraction of each level of filler particles in the propellant filler particle size distribution are obtained, and the number of each level of filler particles in the unit volume of the propellant is calculated; defining the propellant filling stacking structure characteristic unit as: the solid propellant comprises a cube containing periodic boundaries, wherein the grain diameter of each level of filler particles in a characteristic unit is equal to that of each level of filler particles in the solid propellant, and the quantity of each level of filler particles is equal to the minimum integer quantity set of each level of filler particles in the solid propellant in unit volume;
S2: determining the volume and side length of the characteristic unit on the premise that the average density of the characteristic unit is equal to the density of the composite solid propellant;
S3: comprehensively considering the particle size and the number of filler particles at each level in the characteristic unit, selecting a certain particle size value as a demarcation point, and dividing the filler particles into coarse particles and fine particles;
S4: aiming at the coarse particle filler, searching a non-intersecting and uniformly dispersed coarse particle filler stacking structure in a characteristic unit by adopting a genetic algorithm, namely obtaining the coordinate positions of all coarse particles;
S5: and (4) aiming at the fine particle filler, filling the fine particles into the gaps of the coarse particle filler stacking structure determined in the step S4 by adopting an L-S algorithm, and constructing a composite solid propellant filler stacking structure characteristic unit.
2. The method for constructing a packing structural feature unit of a composite solid propellant according to claim 1, wherein the step S1 specifically comprises the following steps:
S11: setting all levels of fillers as spherical particles, and calculating the number of all levels of filler particles in the composite solid propellant per unit volume according to the particle size of all levels of filler particles in the formula of the composite solid propellant and the volume fraction of the filler particles in the composite solid propellant;
S12: dividing the number value of each level of filler particles in the composite solid propellant in unit volume by the number value of the least level of particles in the composite solid propellant in unit volume in sequence, and rounding to obtain the minimum integer number set of each level of particles in the composite solid propellant in unit volume, wherein the number value of the least level of particles in the minimum integer number set is 1;
S13: and taking the particle size of each level of filler particles in the characteristic unit as the particle size of the filler particles in the compound solid propellant formula, and taking the number set of each level of filler particles as the minimum integer number set obtained by S12.
3. The method for constructing a packing structural feature unit of a composite solid propellant according to claim 1, wherein the step S2 is specifically as follows:
And (3) based on the grain diameter and the number of filler particles at each level in the characteristic units obtained from S11-S13, taking the non-filler part in the characteristic units as a matrix, and calculating to obtain the side length L and the volume of the cubic characteristic units under the condition that the average density of the characteristic units is equal to the average density of the composite solid propellant.
4. The method for constructing a packing structural feature unit of a composite solid propellant according to claim 1, wherein the step S4 specifically comprises the following steps:
s41: for coarse particles with the number of 1, fixing the spherical center position of the coarse particles to be the geometric center (0, 0, 0) of the characteristic unit; coordinates of the sphere center positions of the rest coarse particles in the x direction, the y direction and the z direction are respectively taken as random numbers between [ -L/2, L/2 ]; the combination of the grain diameter and the sphere center position of any group of coarse grains uniquely corresponds to a coarse grain stacking structure;
S42: detecting whether the coarse particles meet the condition that the coarse particles are not mutually intersected every two based on the coarse particle stacking structure randomly generated in the step S41;
S43: based on the coarse particle stacking structure randomly generated in step S41, and in combination with the result of determining the particle intersection obtained in step S42, the coarse particle diameter R, the coarse particle center position, and the feature cell side length L are used as arguments to construct a function F for evaluating the degree of dispersion and intersection of the particle distribution:
wherein Nc is the total number of coarse particles; i and j refer to any two different coarse particles, respectively; r is the particle size of the coarse particles; delta xi,j,△yi,jand Δ zi,jThe distances between the spherical centers of the coarse grains i and the coarse grains j in the directions of x, y and z respectively; l is the characteristic unit side length; PV is a penalty function for the presence of intersecting stacking structures between particles;
S44: and searching a coarse particle stacking structure with the most uniformly dispersed particles and mutually disjoint particles in all possible coarse particle stacking structures by using a genetic algorithm and a plurality of groups of randomly generated coarse particle stacking structures as an initial solution to obtain the sphere center coordinate position of each coarse particle in the characteristic unit.
5. The method for constructing a packing structural feature unit of a composite solid propellant according to claim 1, wherein the step S5 is specifically as follows:
s51: initializing the fine particles to geometric points having a radius of zero based on the coarse particle positions determined in step S4, the fine particle initial positions being random positions within the feature cells that are not occupied by the coarse particles, the fine particle initial velocities being random values between [ -L/2, L/2], the coarse particle velocities being constantly zero;
S52: in the gap of the coarse particle accumulation structure, fine particles move linearly at a given speed; in the motion process, if collision occurs between the fine particles, updating the speed of the two collided fine particles according to momentum conservation and energy conservation; if the collision between the coarse particles and the fine particles occurs, updating the movement speed of the fine particles according to the condition that the fine particles are rebounded on the surface of the coarse particles and the coarse particles are still all the time;
S53: during the particle movement and collision process, the radiuses of all fine particles synchronously increase along with time, and the ratio of the radius growth speed of each fine particle is equal to the ratio of the radius growth speed of each fine particle in the composite solid propellant formula; and when the sum of the volume fractions of all the particles in the characteristic unit reaches the volume fraction of the particles in the composite solid propellant formula, finishing the construction of the filler stacking structure characteristic unit.
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| CN105224727A (en) * | 2015-09-11 | 2016-01-06 | 郑州大学 | A kind of autodensing concrete almixture mixing proportion design method |
| CN106650018A (en) * | 2016-11-24 | 2017-05-10 | 中国人民解放军国防科学技术大学 | High volume fraction RVE (Representative Volume Element) model generation method used for VCFEM (Voronoi Cell Finite Element Method) analysis |
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| WO1998020323A1 (en) * | 1996-11-08 | 1998-05-14 | Purdue Research Foundation | Particle analysis system and method |
| CN105224727A (en) * | 2015-09-11 | 2016-01-06 | 郑州大学 | A kind of autodensing concrete almixture mixing proportion design method |
| CN106650018A (en) * | 2016-11-24 | 2017-05-10 | 中国人民解放军国防科学技术大学 | High volume fraction RVE (Representative Volume Element) model generation method used for VCFEM (Voronoi Cell Finite Element Method) analysis |
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