CN116127794A - Solid propellant combustion surface pushing method based on material particle method - Google Patents
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Abstract
The invention provides a solid propellant combustion surface pushing method based on a mass point method, which comprises the following steps of: constructing an implicit function characterizing the burnt area, the combustion interface and the unburned area; generating a k text file containing grid node information and boundary division information through a grid division tool; importing a k file and creating a grid data instance; creating a grid node scalar data instance, and dividing grids to discretize the solid propellant; setting iteration time steps, initial conditions, boundary conditions and combustion surface pushing speed; calculating scalar gradients of grid nodes of the current time step; updating the grid node scalar data; calculating the dosage of the solid propellant consumed by combustion in dt time; updating the inner trajectory parameters; time advance updating is performed according to the grid scalar gradient, the time step and the burning speed. The invention has no numerical value interruption problem under the condition of simulating the large deformation of the propellant after the burning of Cheng Zheyi, and the simulation of the burning surface-meat thickness relationship of the propellant is accurate and reliable.
Description
Technical Field
The invention relates to the technical field of solid propellants, in particular to a solid propellant combustion surface pushing method based on a mass point method.
Background
Rocket engines play an important role in propulsion systems, wherein solid rocket engines are widely applied to various fields such as various rockets and missiles, aerospace, meteorological observation, artificial disaster reduction and the like because of the advantages of the solid rocket engines. The solid rocket engine is fixed in advance with the charge, and the internal trajectory of the solid rocket engine is difficult to adjust in the working process, so that the method has important significance for the solid rocket engine if the internal trajectory of the engine can be accurately estimated. The internal trajectory of the engine depends on the shape design of the propellant to a great extent, so that the solid rocket engine charge is one of the core contents of the solid rocket engine design, and the finding of the general combustion face pushing calculation method for three-dimensional charge has important engineering application value.
Because of the high manufacturing cost of the propellant and the strong experimental risk, the numerical simulation method of the propellant combustion process has become one of the important methods for calculating the charge combustion surface pushing because of the advantages of rapidness, safety and low cost. The traditional method for calculating propellant combustion based on finite element grids has grid distortion defect, and under the condition that the topological structure of the propellant is greatly changed, accurate and reliable propellant combustion surface-meat thickness relation simulation cannot be obtained.
Disclosure of Invention
In view of the above, the invention provides a solid propellant fuel surface pushing algorithm based on a mass point method. The method overcomes the grid distortion defect of the traditional finite element method, has no numerical value interruption problem under the condition that the simulated propellant burns Cheng Zheyi with large deformation, and simulates the combustion surface-meat thickness relationship of the propellant accurately and reliably.
In order to achieve the above purpose, the technical scheme of the invention comprises the following steps:
s1 constructing an implicit function for characterizing a burnt area, a burning interface and an unburnt area
S2, carrying out grid division on the solid propellant through a grid division tool to generate a k text file containing grid node information and boundary division information; importing a.k file and creating a grid data instance.
S3, creating a grid node scalar data instance to obtain a discretization result of the grid.
S4, setting the following parameters: iteration time step size, initial conditions, boundary conditions, and combustion face pushing speed.
S5, calculating the scalar gradient of the grid node of the current time step, and updating the scalar data of the grid node.
S6, calculating the dosage of the solid propellant consumed by combustion in dt time, and updating the inner trajectory parameters.
S7, performing time advance updating according to the grid scalar gradient, the time step and the burning speed.
Further, implicit functions
Scalar->
And carrying out assignment according to the physical process described by the transport equation.
Scalar quantity
Without actual physical meaning, it is only used to characterize the state of the current spatial node, i.e. three states in the burnt region, on the combustion interface, in the unburned region, so that an implicit function +.>
The following formula is shown: />
In the formula omega - Indicating the inside of the closed space,
representing the boundary of a closed space, Ω + Represents the outside of the enclosed space>
Representing the coordinates of the object point in the spatial calculation domain.
Further, in S2, the solid propellant is gridded by a gridding tool, specifically:
according to the geometric model of the solid propellant charge, a modeling tool is used for dividing grids in the geometric space of the charge to generate discrete grid nodes.
Further, in S4, setting an initial condition and a boundary condition includes:
according to the space distribution of the initial combustion surface, initializing scalar quantities on grid nodes according to the following formula, and setting corresponding boundary conditions:
in the formula omega - Indicating the inside of the closed space,
representing the boundary of a closed space, Ω + Represents the outside of the enclosed space>
Representing the coordinates of the object point in the spatial calculation domain.
Further, in S5, when calculating the scalar gradient of the current time step grid node, the following criteria should be followed, depending on the actual combustion characteristics of the solid propellant:
the solid propellant combustion surface can only move from the burnt area to the unburned area;
the burnt areas cannot be converted again into unburned areas;
the burnt zone, i.e. the mesh node gradient with scalar value-1, is constantly zero, expressed as
Wherein, v represents a gradient value, < ->
At t for the ith mesh node n Scalar of time step>
The gradient of the implicit function of the grid node p at the nth iteration step;
at a value of (0, 1)]When calculating scalar gradients on grid nodes of (a), in order to ensure that the combustion surface of the propellant can affect an unburned region without false convergence of constant scalar of the nodes, a central differential or windward format is used for gradient calculation, and when a one-dimensional grid node is taken as an example, a central differential format is adopted
Time-to-time type adopting first-order windward format
In the method, in the process of the invention,
at t for the ith mesh node n Scalar of time step>
At t for the (i+1) th mesh node n+1 Scalar of time step>
Is the gradient of the implicit function of the grid node p at the nth iteration step, Δx is the (i+1) th grid node at t n+1 The coordinates of the time step and the ith grid node are at t n The time step is the difference in coordinates, u being the burning rate value of the solid propellant.
Further, in S7, the following criteria should be followed when performing a time-advance update according to the grid scalar gradient, the time step and the burn rate:
it is impossible for the burned area grid nodes to reversely change back to the unburned state, so the scalar value of the grid node having a scalar value of-1 remains unchanged.
Grid nodes on the combustion surface inevitably enter a burnt state after the combustion surface is pushed, the scalar update value of the grid nodes is changed from 0 to-1, and the gradient value is-1;
the grid nodes in the solid propellant space can only be in three states of burnt, burning and unburned, namely-1, 0 and 1 specified above, but scalar values on the grid nodes of the unburned region near-burning surface, which are affected by the pushing of the burning surface in the numerical calculation process, can be in an intermediate state of (0 and 1);
a is considered to be a, without regard to erosive combustion and assuming a uniform pressure distribution within the combustion chamber n Are equal everywhere on the combustion interface.
The setting of the time iteration time step length is carried out to meet the CFL condition, so that iteration divergence is avoided.
For the case where the scalar of the adjacent mesh node is (0, 1), it is shown that the combustion face has not yet shifted to the adjacent node, where the gradient of the node is 0, avoiding false shifting of the combustion face.
For the grid nodes on the boundary, if the grid nodes are positioned on the burnt area or the combustion surface, the state can be directly updated, and if the grid nodes are positioned on the unburned area, virtual nodes can be extended outwards along the normal, and the value is still 1.
The beneficial effects are that:
1. the shape function of the method is established based on a background grid, a finite element shape function is introduced, and the calculated amount of the method is much smaller than that of other grid-free methods; the method overcomes the grid distortion defect of the traditional finite element method, has no numerical value interruption problem under the condition that the simulated propellant burns Cheng Zheyi with large deformation, and simulates the combustion surface-meat thickness relationship of the propellant accurately and reliably.
2. The solid propellant combustion surface pushing method based on the object point method has interpolation characteristics, so that the boundary condition of the propellant is easier to apply; the particles in the object particle method are fixedly connected with the background grid nodes, so that a large amount of time is not required to be consumed for searching, and the calculation efficiency is greatly improved.
3. Compared with the common grid-free rule which is determined by the minimum distance between particles, the solid propellant combustion surface pushing method based on the material particle method provided by the invention has the advantage that the critical time step of the material particle method is determined by the size of a background grid unit, and the time step can be kept stable due to the fact that the grid size of the material particle method is unchanged.
4. According to the solid propellant combustion surface pushing method based on the material dot method, no penetration phenomenon can be generated among the material dots due to single-value mapping between the material dots and the background grid nodes even if no contact algorithm is adopted. Therefore, the method has great advantages compared with the existing algorithm in the solid propellant combustion surface pushing algorithm.
Drawings
FIG. 1 is a flow chart of a solid propellant fuel surface displacement algorithm based on the mass point method in an embodiment of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The invention relates to a solid propellant combustion face pushing algorithm based on a material particle method, which specifically comprises the following steps as shown in figure 1:
step 1: constructing implicit functions characterizing burned regions, combustion interfaces, and unburned regions
/>
For solid propellant with more complex combustion surface shape, and the abrupt change of topology shape can cause discontinuous combustion surface, more complex topology structure change can occur in the process of pushing combustion surface, so the substance point method based on Euler description is used in the embodiment. The expression of the particle equation of the thrust matter on the combustion surface of the propellant is
The implicit function is
In the method, in the process of the invention,
is an implicit function of characterizing the closed entity of the propellant grains in three-dimensional space, Ω - Indicating the inside of the enclosed space,/->
Representing the boundary of a closed space, Ω + Represents the outside of the enclosed space>
Representing the coordinates of the object point in the spatial calculation domain.
In the process of the propellant combustion, the law of parallel layer combustion is followed, so that the propellant combustion boundary layer can be approximately regarded as that the boundary point moves at uniform speed along the normal direction, and then the combustion boundary layer has the following characteristics
Further can obtain
In the formula (I)>
Indicating the burning rate of the solid propellant, u indicating the burning rate value of the solid propellant, +.>
Represents a unit vector, v represents a gradient value, < ->
Scalar gradient for mesh nodes, +.>
Representing the scalar of the grid node over time t.
Step 2: generating a k text file containing grid node information and boundary division information through a grid division tool; importing a.k file and creating a grid data instance.
And drawing grids for the propellant grain model by adopting grid drawing software, setting boundary condition information, and setting the grids to be unstructured grids generally in order to ensure accurate calculation results and no interruption, wherein the grid distortion rate is preferably controlled within 10% in order to ensure accurate calculation results. In this example, the mesh maximum dimension was 1mm, the total number of generated bulk meshes was 2000 ten thousand, and the total number of mesh nodes was 330 ten thousand, in order to spatially preserve and restore the shape characteristics of the geometric model as much as possible due to the size limitations of the tooth-shaped propellant projections.
Importing a k file and creating a grid data instance through a MeshData handle class;
opposite type
Performing time dispersion of first order accuracy to obtain +.>
Wherein the method comprises the steps of
At t for the ith mesh node n Scalar of time step>
At t for the ith mesh node n+1 Scalar of time step>
At t for the ith mesh node n Scalar gradient corresponding to time step, u n At t as a solid propellant n The burning rate of the time step.
The MeshData handle class of the k file is processed, and the main function is to read corresponding fields from the k file containing grain grid information and boundary division information and generate a node coordinate matrix, a unit node number matrix and a grid node adjacent information matrix which meet the calculation requirement. The fun_node_nb_id () function of the grid node adjacent information matrix is calculated and is a preprocessing program for calculating the scalar gradient of the grid node in a subsequent reconstruction mode.
Step 3: and creating a grid node scalar data instance through the NodeData handle class, dividing grids, and discretizing the solid propellant to obtain a discretization result of the grids.
The handle of the method is used for storing scalar data and scalar gradient data of grid nodes and calculating the scalar gradient data, and a variable NodeResults is set for storing a matrix of the scalar data of the grid nodes; temp_ GXN is used for storing a matrix of scalar gradient temporary data X directions among grid nodes; temp_GYN is used for storing a matrix in the Y direction of scalar gradient temporary data among grid nodes; temp_GZN is used for storing a matrix in the Z direction of scalar gradient temporary data among grid nodes; nodeGX is used for storing a matrix of scalar data X direction of grid nodes; nodeGY is used for storing a matrix in the Y direction of scalar data of grid nodes; the NodeGZ is used for storing a matrix in the Z direction of scalar data of the grid nodes; a handle of h_mesh_data grid data; time points of calculation iteration are carried out by the tlist; n_step total iteration time steps; i_step current time step; time current time; dtime current time step; u_pp is the current propellant burn rate.
The method is characterized by comprising the steps of processing handle class MeshData of grid node data, wherein the handle class MeshData is mainly used for processing scalar values on grid nodes in a preservation time iteration process, reconstructing scalar gradients of unstructured grid nodes according to the node scalar values, calculating and analyzing scalar gradients between the current grid nodes and adjacent nodes of the same unit, and reconstructing the scalar gradients on the current grid nodes through a least square method.
Step 4: the following parameters were set: iteration time step size, initial conditions, boundary conditions, and combustion face pushing speed.
Setting an iteration time step length: the function called fun_set_timer (obj, tlist) is set to solve the time steps according to the initially set total duration of combustion and the time steps. Preferably, the combustion duration in this embodiment is set to 0.03s and the time step is set to 0.001s, and the time step is put into the matrix of time steps.
Setting initial conditions: and performing node data initialization setting by using a fun_nodata_init (obj, phi) function. According to the time step, the scalar gradient temporary data among the corresponding storage grid nodes and the zero matrix in the direction of the scalar data X, Y, Z of the storage grid nodes are set so as to update and use the subsequent data.
Setting boundary conditions: and setting a fun_set_boundary (obj, phi) function for acquiring data information of the boundary conditions, acquiring a boundary node data value by adopting a nested loop algorithm, and giving the phi a scalar value.
Setting the pushing speed of the combustion surface: and setting the initial combustion speed of the combustion surface pushing according to the internal trajectory predicted value so as to carry out subsequent iteration. Preferably, the initial combustion speed value in this embodiment is set to be 10mm/s, and the selection of the initial combustion speed value does not affect the final result, but affects the middle calculation process, and the unreasonable initial combustion speed increases the number of iterations in the calculation process, so that the calculation time increases.
Step 5: calculating the scalar gradient of the grid node at the current time step, and updating the scalar data of the grid node;
an fun_nodata_gradient (obj) function is set, which is a method of the nodata handle class, for calculating the scalar gradient of the node.
(1) Writing a nested loop, traversing all nodes on the grid, and calculating scalar gradients between the nodes and adjacent nodes: if the number of the adjacent node is smaller than the number of the current node, the scalar gradient between the two points is indicated to be calculated in the front, and the scalar gradient does not need to be calculated repeatedly;
(2) Setting a matrix to store scalar values of current nodes in a current time step: if the scalar values of the two nodes are smaller than or equal to 0 or larger than 0, the two nodes are in the burnt area or in the unburned area, no combustion surface is pushed between the two nodes, and the scalar gradient is zero; if the scalar signs of the two nodes are opposite, the scalar gradient indicates that one node is in a burnt area and the other node is in an unburnt area, the combustion surface is pushed between the two nodes, and the scalar gradient is not zero;
(3) Calculating a distance vector between the current node and the adjacent node and a scalar gradient between the current node and the adjacent node;
(4) The non-zero elements in each row of Temp_GXN, temp_GYN, temp_GZN are counted and summed and then averaged.
Updating the grid node scalar data: the fun_nodata_update (obj) function is written for updating grid node scalar data:
starting to update the scalar value on the grid node in time, if the scalar value < = -1 on the grid node shows that the node is already in a burnt area, the updating state is not needed, and the next time step is directly set to-1; and (5) for the dead zone node, assigning a grid node scalar value minimum value of-1, and updating to the next time step.
Step 6: calculating the dosage of the solid propellant consumed by combustion in dt time; updating the inner trajectory parameters;
and acquiring the node gradient obtained by storage, and carrying the node gradient into the internal trajectory of the solid rocket engine to calculate and obtain the updated internal trajectory parameters of each time step.
Step 7: performing time propulsion updating according to the grid scalar gradient, the time step and the burning speed;
updating the grid scalar gradient, the time step and the fuel curved meat thickness (namely the fuel speed) in unit time which are obtained through iteration into an inner trajectory, obtaining the parameter value under each time step, and analyzing and summarizing the trend after obtaining the data.
Based on a combustion surface pushing algorithm of object points (MPM), the simulation simulates the combustion process of the explosive column in an end pack mode, the inner surface and the outer surface of a circular hole of the explosive column are combusted simultaneously with the tooth-shaped side surface, the inner surface of the circular hole is pushed outwards continuously, the outer surface of the circular hole is pushed inwards continuously, the tooth-shaped side surface is pushed inwards continuously, the thickness of the explosive column meat is reduced continuously, the inner surface is intersected with the outer surface finally, and the whole explosive column is combusted.
Compared with the traditional method for calculating the propellant combustion based on the finite element grid, the method has the advantages that: based on Euler description substance points, under the condition that the propellant powder topology structure is greatly changed, the invention can obtain more accurate combustion face state judgment and accurate normal vector. The discrete grid is fixed, the combustion face pushing process is hidden in the propagation process of an implicit function scalar transport equation, complex conditions such as intersection of combustion faces, topological structure change and the like can be naturally processed, and the problem that the combustion result is strong in step nature and discontinuous in the previous combustion face pushing calculation process is solved.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The solid propellant combustion surface pushing method based on the material point method is characterized by comprising the following steps of:
s1 constructing an implicit function for characterizing a burnt area, a burning interface and an unburnt area
S2, carrying out grid division on the solid propellant through a grid division tool to generate a k text file containing grid node information and boundary division information; importing a k file and creating a grid data instance;
s3, creating a grid node scalar data instance to obtain a discretization result of the grid;
s4, setting the following parameters: iteration time step length, initial condition, boundary condition and combustion face pushing speed;
s5, calculating the scalar gradient of the grid node at the current time step, and updating the scalar data of the grid node;
s6, calculating the dosage of the solid propellant consumed by combustion in dt time, and updating an inner trajectory parameter;
s7, performing time advance updating according to the grid scalar gradient, the time step and the burning speed.
2. A solid propellant combustion surface pushing method based on the mass point method as claimed in claim 1, wherein the implicit function
Scalar->
And carrying out assignment according to the physical process described by the transport equation.
Scalar quantity
Without actual physical meaning, it is only used to characterize the state of the current spatial node, i.e. three states in the burnt region, on the combustion interface, in the unburned region, so that an implicit function +.>
The following formula is shown:
in the formula omega - Indicating sealInside the closed space,
representing the boundary of a closed space, Ω + Represents the outside of the enclosed space>
Representing the coordinates of the object point in the spatial calculation domain.
3. The solid propellant combustion surface pushing method based on the object point method according to claim 1 or 2, wherein in S2, the solid propellant is gridded by a gridding tool, specifically:
according to the geometric model of the solid propellant charge, a modeling tool is used for dividing grids in the geometric space of the charge to generate discrete grid nodes.
4. The solid propellant combustion surface pushing method based on the mass point method as claimed in claim 1, wherein in S4, initial conditions and boundary conditions are set, comprising:
according to the space distribution of the initial combustion surface, initializing scalar quantities on grid nodes according to the following formula, and setting corresponding boundary conditions:
in the formula omega - Indicating the inside of the closed space,
representing the boundary of a closed space, Ω + Represents the outside of the enclosed space>
Representing the coordinates of the object point in the spatial calculation domain.
5. A solid propellant combustion surface pushing method based on the object point method as claimed in claim 1, 2 or 4, wherein in S5, when calculating the scalar gradient of the grid node of the current time step, the following criteria should be followed according to the actual combustion characteristics of the solid propellant:
the solid propellant combustion surface can only move from the burnt area to the unburned area;
the burnt areas cannot be converted again into unburned areas;
the burnt zone, i.e. the mesh node gradient with scalar value-1, is constantly zero, expressed as
In the formula (I), the total number of the components,
representing gradient values +.>
At t for the ith mesh node n Scalar of time step>
The gradient of the implicit function of the grid node p at the nth iteration step;
at a value of (0, 1)]When calculating scalar gradients on grid nodes of (a), in order to ensure that the combustion surface of the propellant can affect an unburned region without false convergence of constant scalar of the nodes, a central differential or windward format is used for gradient calculation, and when a one-dimensional grid node is taken as an example, a central differential format is adopted
Time-to-time type adopting first-order windward format
In the method, in the process of the invention,
at t for the ith mesh node n Scalar of time step>
At t for the (i+1) th mesh node n+1 Scalar of time step>
Is the gradient of the implicit function of the grid node p at the nth iteration step, Δx is the (i+1) th grid node at t n+1 The coordinates of the time step and the ith grid node are at t n The time step is the difference in coordinates, u being the burning rate value of the solid propellant.
6. The solid propellant fuel surface pushing method based on the object point method as claimed in claim 5, wherein in S7, the following criteria should be followed when the time pushing update is performed according to the grid scalar gradient, the time step and the fuel speed:
the burnt area grid nodes cannot be reversely changed into an unburned state again, so that the scalar value of the grid nodes with the scalar value of-1 is kept unchanged;
grid nodes on the combustion surface inevitably enter a burnt state after the combustion surface is pushed, the scalar update value of the grid nodes is changed from 0 to-1, and the gradient value is-1;
the grid nodes in the solid propellant space can only be in three states of burnt, burning and unburned, namely-1, 0 and 1 specified above, but scalar values on the grid nodes of the unburned region near-burning surface, which are affected by the pushing of the burning surface in the numerical calculation process, can be in an intermediate state of (0 and 1);
a is considered to be a, without regard to erosive combustion and assuming a uniform pressure distribution within the combustion chamber n Everywhere equal at the combustion interface;
setting the time iteration time step length to meet the CFL condition, and avoiding iteration divergence;
for the case that the scalar of the adjacent grid node is (0, 1), the condition shows that the combustion face is not yet shifted to the adjacent node, the gradient of the node is 0, and the false shift of the combustion face is avoided;
for the grid nodes on the boundary, if the grid nodes are positioned on the burnt area or the combustion surface, the state can be directly updated, and if the grid nodes are positioned on the unburned area, virtual nodes can be extended outwards along the normal, and the value is still 1.
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| CN117932792A (en) * | 2024-03-18 | 2024-04-26 | 东方空间(江苏)航天动力有限公司 | Method for reducing thrust imbalance of binding boosting solid rocket engine |
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| CN117932792A (en) * | 2024-03-18 | 2024-04-26 | 东方空间(江苏)航天动力有限公司 | Method for reducing thrust imbalance of binding boosting solid rocket engine |
| CN117932792B (en) * | 2024-03-18 | 2024-05-28 | 东方空间(江苏)航天动力有限公司 | Method for reducing thrust imbalance of binding boosting solid rocket engine |
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