CN116579259A - Ballistic three-dimensional transient flow field modeling and multi-physical field numerical calculation method and device - Google Patents
Ballistic three-dimensional transient flow field modeling and multi-physical field numerical calculation method and device Download PDFInfo
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Abstract
The embodiment of the specification provides a method and a device for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of a plurality of physical fields, wherein the method comprises the following steps: constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the bullet head; based on a step-by-step solving method of a propellant powder combustion process and a fuel gas in-bore flow process, constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model; and calculating the multi-physical field value of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode.
Description
Technical Field
The document relates to the technical field of internal trajectory of artillery, in particular to a method and a device for modeling three-dimensional transient flow field of internal trajectory of artillery and calculating numerical values of multiple physical fields.
Background
The development of the research of the ballistic parameters in the artillery can provide important theoretical support for the structural design of the artillery and the improved design of propellant charge, and further has important practical significance for improving the performance of the artillery and prolonging the service life of the artillery. Because the gun firing is a complex physical process related to high temperature, high pressure, high speed and transient characteristics, researchers at home and abroad explore for decades to form and perfect a gun inner trajectory parameter solving method, including classical inner ballistics theory and modern inner ballistics theory. The classical internal ballistics theory generally describes the gun launching process through a classical internal ballistics equation set, and an internal ballistics model is generally zero-dimensional or can be expanded to one dimension by Lagrange assumption, so that the change of internal ballistics parameters along the axial direction in a reaction chamber along with time can be only realized, and the flow and heat transfer characteristics near the wall surface of a body tube cannot be accurately described; modern inner ballistics is based on hydrodynamic theory, and can expand the inner ballistic flow field to two dimensions or even three dimensions, so that the change of the flow field at any position in the bore with time can be described. At present, researchers in related fields at home and abroad adopt Euler method, euler-Lagrange method and timely-empty conservation element solution method to construct two-dimensional and three-dimensional inner trajectory models, analyze the spatial distribution of pressure field and velocity field in the gun chamber and provide reference for the three-dimensional analysis of the inner trajectory process.
However, it must be pointed out that although the two-dimensional and three-dimensional inner trajectory models described above are capable of reflecting the flow field distribution of the post-bullet space, researchers generally ignore the combustion process of the propellant in the bore and do not consider the variation of the thermal physical parameters of the propellant gas with temperature, so that the accuracy of the three-dimensional flow field parameters is difficult to guarantee.
Disclosure of Invention
The invention aims to provide a method and a device for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of multiple physical fields, and aims to solve the problems in the prior art.
The invention provides a method for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of multiple physical fields, which comprises the following steps:
constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the bullet head;
based on a step-by-step solving method of a propellant powder combustion process and a fuel gas in-bore flow process, constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model;
and calculating the multi-physical field value of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode.
The invention provides a device for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of a plurality of physical fields, which comprises the following components:
the first construction module is used for constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the projectile head;
the second construction module is used for constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model based on a step-by-step solution method of a propellant combustion process and a fuel gas in-bore flow process;
and the calculation module is used for calculating the multi-physical field values of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode.
The embodiment of the invention also provides electronic equipment, which comprises: the method comprises the steps of a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the computer program realizes the method for modeling the three-dimensional transient flow field of the trajectory in the gun and calculating the numerical value of multiple physical fields when being executed by the processor.
The embodiment of the invention also provides a computer readable storage medium, wherein an implementation program for information transmission is stored on the computer readable storage medium, and the program is executed by a processor to realize the steps of the method for modeling the three-dimensional transient flow field of the trajectory in the gun and calculating the numerical value of multiple physical fields.
The internal trajectory three-dimensional transient flow field modeling and multi-physical field numerical solving method provided by the embodiment of the invention can effectively solve the evolution process of internal trajectory three-dimensional parameters along with time in the gun firing process, can intuitively reflect the flow state of gunpowder gas in a chamber, and has important guiding significance for solving the internal trajectory parameters, analyzing the ablation area in the chamber, and further optimizing the physical structure of a barrel and the design of propellant charge. Besides solving parameters of ballistic flow fields in the artillery, the theoretical method provided by the invention can be widely applied to the fields of electrothermal chemical artillery, rocket launching, hypersonic aircraft propulsion and the like, and has important reference value for optimizing and improving equipment performance.
Drawings
For a clearer description of one or more embodiments of the present description or of the solutions of the prior art, the drawings that are necessary for the description of the embodiments or of the prior art will be briefly described, it being apparent that the drawings in the description that follow are only some of the embodiments described in the description, from which, for a person skilled in the art, other drawings can be obtained without inventive faculty.
FIG. 1 is a flow chart of a method for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of a plurality of physical fields according to an embodiment of the present invention;
FIG. 2 is a flowchart of detailed processing of a method for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of multiple physical fields according to an embodiment of the present invention;
FIG. 3 is a schematic view of a three-dimensional axisymmetric physical model of an artillery according to an embodiment of the present invention;
FIG. 4 is a diagram showing a comparison of a QUICK format with a central differential format numerical solution in accordance with an embodiment of the present invention;
FIG. 5a is a schematic diagram of the mean rift-time curve of the internal ballistic parameter contrast obtained by solving the three-dimensional flow field model and the classical internal ballistics model of an embodiment of the present invention;
FIG. 5b is a schematic representation of a projectile velocity versus time curve of internal ballistic parameter contrast obtained by solving a three-dimensional flow field model and a classical internal ballistics model of an embodiment of the invention;
FIG. 5c is a schematic diagram of a projectile travel-time curve of internal ballistic parameter contrast obtained by solving a three-dimensional flow field model and a classical internal ballistics model according to an embodiment of the invention;
FIG. 5d is a schematic illustration of an intra-barrel average temperature-time curve of internal ballistic parameter contrast obtained by solving a three-dimensional flow field model and a classical internal ballistics model according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of pressure distribution across an xy section in a barrel at different times in accordance with an embodiment of the present invention;
FIG. 7 is a schematic representation of velocity profiles across an xy section in a barrel at different times in accordance with an embodiment of the present invention;
FIG. 8 is a schematic representation of turbulent kinetic energy distribution across an xy section within a barrel at various times in accordance with an embodiment of the present invention;
fig. 9 is a schematic diagram of the distribution of the thermal physical parameters of the gunpowder gas in the barrel at the time t=4ms in the embodiment of the invention;
FIG. 10 is a schematic diagram of temperature distribution in xy section within a barrel at different times in accordance with an embodiment of the present invention;
FIG. 11 is a schematic diagram of an artillery inner trajectory three-dimensional transient flow field modeling and multi-physical field numerical calculation device according to an embodiment of the present invention;
fig. 12 is a schematic diagram of an electronic device according to an embodiment of the invention.
Detailed Description
In order to solve the problems in the prior art, the embodiment of the invention provides a method for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and solving a multi-physical-field numerical value, which comprises the following steps: firstly, taking the slope bore structure and the gas resistance of the bullet head into consideration to construct a three-dimensional axisymmetric physical model of the gun barrel; then, based on the thought of 'step modeling', a step-by-step solving method for the propellant combustion process and the gas in-bore flow process is provided; then, designing a gun inner trajectory three-dimensional flow field numerical solution method based on a finite volume method, wherein the method comprises control equation dispersion, pressure-speed coupling solution and the like; furthermore, by taking a model gun as an example, the effectiveness of the numerical solving method provided by the invention is verified by comparing and analyzing the zero-dimensional inner trajectory parameters obtained by solving the classical inner ballistics model; finally, by carrying out numerical simulation of three-dimensional characteristics of a flow field of the inner trajectory of a certain gun, the spatial distribution of a physical property parameter field, a pressure field, a speed field and a temperature field in the gun is obtained, and the change rule of the parameters in the gun along with the inner trajectory time in the process of the inner trajectory of the gun is analyzed.
In order to enable a person skilled in the art to better understand the technical solutions in one or more embodiments of the present specification, the technical solutions in one or more embodiments of the present specification will be clearly and completely described below with reference to the drawings in one or more embodiments of the present specification, and it is obvious that the described embodiments are only some embodiments of the present specification, not all embodiments. All other embodiments, which can be made by one or more embodiments of the present disclosure without inventive faculty, are intended to be within the scope of the present disclosure.
Method embodiment
According to an embodiment of the invention, a method for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value is provided, and fig. 1 is a flowchart of the method for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value according to the embodiment of the invention, as shown in fig. 1, and the method for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value according to the embodiment of the invention specifically includes:
s101, constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the bullet head; the method specifically comprises the following steps: setting the inner diameter of the gun barrel as D in An outer diameter of D out The whole length of the barrel is L p Representing the distance from the rear side of the breech to the muzzle position; thrust of projectile in gunpowder fuel gas and projectile headThe gas in the barrel and the inner wall surface of the barrel perform forced convection heat exchange until the gas flows out of the muzzle under the action of air resistance, and the heat transfer coefficient is h w-in The method comprises the steps of carrying out a first treatment on the surface of the Heat is transferred in the pipe wall in a heat conduction mode, and the constant pressure specific heat C of the pipe body material pp And a thermal conductivity lambda p As a function of temperature; the outer wall surface of the barrel performs natural convection heat exchange and radiation heat exchange with the outside air, and the natural convection heat exchange coefficient is h w-out And constructing a three-dimensional axisymmetric physical model of the artillery.
Step S102, constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model based on a propellant combustion process and a gas in-bore flow process step-by-step solving method; the method specifically comprises the following steps: in a time step, the propellant burns to release a mass source and an energy source to generate gunpowder gas, thereby changing the pressure field and the temperature field in the barrel and pushing the projectile to move; after entering the next time step, solving the mass source and the energy source according to the formula 1 and the formula 2 continuously according to the pressure in the barrel, the current combustion surface area and the relative burnt thickness of the propellant powder, and solving and updating the three-dimensional flow field distribution in the barrel according to the formulas 4 to 8 until the projectile exits from the muzzle:
wherein ρ is p Is the density of the propellant; s is S p Is the combustion surface area; z is Z p Is the relative burnt thickness; f (f) p Is the powder strength; t is time; the relative burnt thickness is formula 3;
wherein u is p Is the combustion rate coefficient; e, e 1 Is the thickness of the combustion layer; p is the bodyAverage pressure of gunpowder gas in the pipe; η is the fuel rate index; z is Z k Is the relative fired thickness of the propellant at the end of combustion;
in the inner ballistic flow field, the mass conservation equation is expressed as formula 4;
wherein ρ is the density of the gunpowder gas;is Hamiltonian; u is the velocity vector of the gunpowder fuel gas;
the conservation of momentum equation is expressed as equation 5-equation 7
Wherein u, v and w respectively represent components of the speed of the gunpowder gas in the directions of x, y and z; p is the pressure; mu is the viscosity coefficient of the fuel gas; f (F) bx 、F by 、F bz The volume force of the gunpowder gas in the x, y and z directions is respectively applied;
the energy conservation equation is expressed as equation 8;
wherein T is the temperature of the fuel gas; λ is the thermal conductivity; c (C) p The constant pressure specific heat of the fuel gas.
And step S103, calculating the multi-physical field value of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode. The method specifically comprises the following steps: dispersing the diffusion terms in the formulas 4-8 by adopting a central differential format; dispersing the stream item by adopting a QUICK format with third-order precision, and processing the dispersion of nodes at the boundary by adopting a first-order windward format; the source item adopts an explicit scheme for dispersion; processing transient items by adopting a fully implicit discrete format; and solving the pressure-speed coupling problem in the flow field parameter solving by adopting a SIMPLE pressure correction algorithm. Specifically, the diffusion term discretized by the center differential format is expressed as:
wherein physical quantities at east, west, north, south, upper and lower nodes are respectively represented by subscripts E, W, N, S, T, B, subscripts e, w, n, s, t, b respectively represent east, west, north, south, upper and lower boundary surfaces of a control unit, phi is a generalized flow parameter, Γ is a generalized diffusion coefficient corresponding to phi,represents diffusion term, δx e 、δx w 、δy n 、δy s 、δz t 、δz b The distance between the node and the adjacent nodes on the east, west, north, south, upper and lower sides of the node, respectively,/->P represents node P; for the boundary of the control unit, there is A w ＝A e ＝ΔyΔz，A n ＝A s ＝ΔxΔz，A b ＝A t The values =Δx Δy, Δx, Δy, Δz are the distances between the east-west, north-south, upper and lower interfaces, respectively;
when the flow is in the positive direction, i.e. u e >0、u w >0、u n >0、u s >0、u t >0、ub>0, wherein the subscripts e, w, n, s, t, b are respectivelyRepresenting the east, west, north, south, upper and lower boundary surfaces of the control unit, the flow parameters at the interface are expressed as:
wherein, subscripts WW, SS and BB respectively represent upstream node values of left nodes in three directions, subscripts E, W, N, S, T, B respectively represent physical quantities at east, west, north, south, upper and lower nodes, phi is a generalized flow parameter, and P represents a node P;
combining the center differential format of the diffusion term and the QUICK format of the flow term to obtain a discrete control equation:
in the three-dimensional problem, the control equation at the node P contains the control quantity of E, W, N, S, T, B, EE, WW, NN, SS, TT, BB nodes after being discretized, and is in thirteen-point format, and the boundary problem is processed by adopting a first-order windward format, namely, at the first node, phie=phip, phiw=phiw, phin=phip, phis=phis, phit=phip and phib=phib.
Wherein, transient items are processed by adopting a fully implicit discrete format; for the pressure-speed coupling problem in the flow field parameter solving, the SIMPLE pressure correction algorithm is adopted for solving the problems specifically including:
and integrating the control equation over a time period delta t by adopting a full implicit time discrete format with second-order precision to obtain:
where ρu phi A represents the convective term, deltaV is the volume of the control volume, i.e., deltaV=Deltax Deltaz,flattening for generalized source items on control unitsThe average value;
the second order fully implicit time integration format is expressed as:
wherein n, n-1, n-2 represent the values of the current time step, the last time step and the last time step physical quantity, respectively;
after the dispersion of the conservation equation is completed, the algebraic equation set after the dispersion is solved by adopting a SIMPLE pressure correction algorithm, and the final solving of the numerical values of the multiple physical fields is completed.
After the operation is performed, the change rule of the parameters in the bore along with the inner trajectory time in the inner trajectory process of the gun can be determined according to the multiple physical field values.
The above technical solutions of the embodiments of the present invention are described in detail below with reference to the accompanying drawings.
As shown in fig. 2, the method for modeling the three-dimensional transient flow field of the inner trajectory of the gun and calculating the numerical value of the multiple physical fields according to the embodiment of the invention specifically comprises the following steps:
1. construction of three-dimensional physical model of artillery
A three-dimensional axisymmetric physical model of the artillery was constructed as shown in fig. 3. The inner diameter of the gun barrel is D in An outer diameter of D out The whole length of the barrel is L p Representing the distance from the rear side of the breech to the muzzle position; the projectile moves forward under the action of the thrust of the gunpowder and the gas resistance of the projectile head until the projectile exits the muzzle. The forced convection heat exchange is carried out between the gas in the tube and the inner wall surface of the tube, and the heat transfer coefficient is h w-in The method comprises the steps of carrying out a first treatment on the surface of the Heat is transferred in the pipe wall in a heat conduction mode, and the constant pressure specific heat C of the pipe body material pp And a thermal conductivity lambda p Setting according to related literature as a function of temperature; the outer wall surface of the barrel and the outside air perform natural convection heat exchange and radiation heat exchange, and the natural convection heat exchange coefficient is h w-out Can be set with reference to the related research results to be 13.4W/(m) 2 ·K)。
2. Construction of inner trajectory three-dimensional flow field mathematical model
The internal trajectory process comprises a propellant combustion process and a flow process of gunpowder gas in a barrel, and because the coupling calculation of combustion and a flow field in the barrel is very complex and has low precision, the embodiment of the invention is based on the concept of step modeling, the combustion process and the flow process of the gas are respectively solved, and meanwhile, the numerical simulation of the generation of a propellant mass source and an energy source, the flow of the gunpowder gas in the barrel and the movement of a projectile is completed by adopting Fluent software and UDF secondary development.
In the internal ballistic process, the propellant has a burnt mass(representing a mass source) and the released energy P p The time-dependent change (representing the energy source) can be expressed as
Wherein ρ is p Is the density of the propellant; s is S p Is the combustion surface area; z is Z p Is the relative burnt thickness; f (f) p Is the powder strength; t is time. According to the exponential combustion law of the propellant, the calculation formula of the relative burnt thickness is that
Wherein u is p Is the combustion rate coefficient; e, e 1 Is the thickness of the combustion layer; p is the average pressure of gunpowder gas in the barrel; η is the fuel rate index; z is Z k Is the relative fired thickness of the propellant at the end of combustion.
In an internal ballistic flow field, the mass conservation equation can be expressed as
Wherein ρ is the density of the gunpowder gas;is Hamiltonian; u is the velocity vector of the gunpowder gas.
Momentum conservation equations can be expressed as
Wherein u, v and w respectively represent components of the speed of the gunpowder gas in the directions of x, y and z; p is the pressure; mu is the viscosity coefficient of the fuel gas; f (F) bx 、F by 、F bz The volume forces of the gunpowder gas are respectively applied in the x, y and z directions.
The energy conservation equation can be expressed as
Wherein T is the temperature of the fuel gas; λ is the thermal conductivity; c (C) p The constant pressure specific heat of the fuel gas.
In summary, after the propellant powder fires, the advancing process of the three-dimensional flow field in the barrel along with time can be described as follows: in a time step, the propellant burns to release a mass source and an energy source to generate gunpowder gas, thereby changing the pressure field and the temperature field in the barrel and pushing the projectile to move; after entering the next time step, solving the mass source and the energy source according to the formula (1) and the formula (2) continuously according to the pressure in the barrel, the current combustion surface area and the relative burnt thickness of the propellant, and solving and updating the three-dimensional flow field distribution in the barrel according to the formulas (4) to (8); repeating the above steps until the projectile exits the muzzle.
3 design of numerical solution method
The solving method is a key for calculating the three-dimensional flow field parameters in the fire bore. The embodiment of the invention designs a solving algorithm under the theoretical framework of a finite volume method: the diffusion terms in the conservation equations (4) - (8) are scattered by adopting a central differential format; dispersing the stream item by adopting a QUICK format with third-order precision, and processing the dispersion of nodes at the boundary by adopting a first-order windward format; the source item adopts an explicit scheme for dispersion; processing transient items by adopting a fully implicit discrete format; in addition, for the pressure-speed coupling problem in the flow field parameter solving, a traditional SIMPLE pressure correction algorithm is adopted for solving. The following derives the solution algorithm of the diffusion term, the convection term and the transient term, and since SIMPLE is relatively mature, no further description is given.
3.1 discrete diffusion and convection terms
Converting the conservation equations (4) - (8) into a general transport equation expressed in terms of a scalar phi in a Cartesian coordinate system in the form of
Wherein phi is a generalized flow parameter, which in the present invention represents u, v, w, T, etc.; Γ is a generalized diffusion coefficient corresponding to phi, such as a viscosity coefficient, a thermal diffusion coefficient, etc.; s is S g Is a generalized source term.
Since the time derivative term in the conservation equation needs to take into account the discrete format alone, it will be explained later. After omitting the time derivative term in the control equation, the integral is obtained by taking the integral of the formula (9)
Where Δv is the volume of the control body, when the control body is sufficiently small, it may be expressed As the product of the distance between the boundary surfaces and the area of the control body cell surface, i.e., Δv=Δx Δy Δz, and for the boundary of the control cell, there is aw=ae=Δy Δz, an=as=Δx Δz, and ab=at=Δx Δy. The formula (10) can be further converted into
Wherein ρu φA andrespectively representing a convection item and a diffusion item, and obtaining according to a control quantity on a control unit node and a difference value algorithm; subscripts e, w, n, s, t, b represent the east, west, north, south, upper and lower boundary surfaces, respectively, of the control unit; Δx, Δy and Δz are distances among east-west, north-south and upper and lower interfaces respectively; />Is the average of the generalized source term over the control unit. To simplify (11), let
F e ＝(ρu) e A e ,F w ＝(ρu) w A w ,F n ＝(ρu) n A n ,F s ＝(ρu) s A s ,F t ＝(ρu) t A t ,F b ＝
(ρu) b A b
Wherein (δx) e, (δx) w, (δx) n, (δx) s, (δx) t, and (δx) b are distances between a node and its east, west, north, south, upper and lower neighboring nodes, respectively.
A large number of researches show that the requirement of calculation precision can be well met by adopting a central differential format for diffusion terms in a conservation equation. The central differential format calculates the physical quantity on the interface by using the linear interpolation of the physical quantity on the nodes at the two ends of the interface, and the solving process is relatively simple. When physical quantities at east, west, north, south, upper and lower nodes are respectively indicated by subscripts E, W, N, S, T, B, the diffusion term discretized using the center differential format can be expressed as
Because the radial velocity distribution in the circular tube is generally parabolic, when the low-order discrete format (such as a central differential format, a one-section windward format, a second-order windward format and the like) is adopted to process the convection item, the accuracy of the numerical simulation result is difficult to ensure. In view of this, the embodiment of the invention adopts a QUICK format discrete convective term with third-order calculation accuracy. The QUICK format adopts an upwind type quadratic polynomial interpolation function, curvature correction is introduced on the basis of center difference, and false diffusion errors in the convection diffusion problem can be effectively reduced by judging a parameter expression at a positive and negative correction interface of the convection mass flow. In dealing with parabolic problems, a comparison of the solution of the QUICK format to the center differential format is shown in FIG. 4. Analysis of fig. 4 shows that the flow parameters at the interface in the query format are determined by the node values on the left and right sides and the node values upstream of the left node, and therefore have higher accuracy than the center differential format. For three-dimensional problems, when the flow is in the positive direction, i.e., ue >0, uw >0, un >0, us >0, ut >0, ub >0, the flow parameters at the interface can be expressed as
Where the subscripts WW, SS, and BB represent the upstream node values of the left node in the three directions, respectively.
Based on the analysis, the center difference format of the diffusion term and the QUICK format of the flow term are combined to obtain a discrete control equation as follows
From the above analysis, it can be found that, in the three-dimensional problem, the control equation at the node P contains the control quantity of the E, W, N, S, T, B, EE, WW, NN, SS, TT, BB node after being discretized, which is in thirteen-point format, so that the discretized equation of the first internal node at the boundary cannot be established by the method, and based on the problem, the invention adopts the first-order windward format to process the boundary problem. I.e. at the first node let phie=phip, phiw=phiw, phin=phip, phis=phis, phit=phip, phib=phib.
3.2 discrete transient terms
In the conservation equation described above, there are transient terms related to time in addition to the convection term, diffusion term, and source term. Currently, commonly used transient term discrete methods include explicit time integration schemes, crank-Nicolson time integration schemes, implicit time integration schemes, and the like. The explicit integration scheme is simple and occupies little memory, but has only first-order precision, is stable in condition, and therefore has low precision. In order to improve the calculation accuracy, the embodiment of the invention adopts a full implicit time discrete format with second-order accuracy. Integrating the control equation over a period of time Δt
The second order fully implicit time integration format may be expressed as
/>
Where n, n-1, n-2 represent the values of the physical quantities of the current time step, the last time step, and the last time step, respectively.
After the dispersion of the conservation equation is completed, solving the algebraic equation set after the dispersion by adopting a Gaussian-Seeld correction algorithm, and completing the final solution of the three-dimensional flow field parameters.
Verification of 4 numerical solution method
And comparing and analyzing the inner trajectory parameters obtained by the numerical method of the embodiment of the invention with parameters obtained by the classical inner trajectory model, and verifying the validity of the constructed three-dimensional flow field model and the numerical method thereof. The classical internal ballistics model is an important theoretical model for guiding charge design and predicting ballistic performance, can reflect internal ballistics parameters in the process of gun firing more accurately, and can be expressed in the form of the following equation set:
in the psi- p Percent burned for propellant; x-shaped articles p 、λ p 、μ p Is the characteristic quantity of the shape before the division of the propellant powder; v p Is the speed of the projectile; l (L) p Is the stroke of the projectile; s is S b Is the maximum cross-sectional area of the projectile;is the secondary work coefficient; m is m b The quality of the pill is that of the pellet; l (L) ψ The diameter of the free volume of the medicine room is reduced; θ p Is the powder coefficient. The partial loading parameters of the propellant were as shown in table 1.
TABLE 1 partial filling parameters of propellant powder
From equation (17), it can be known that the combustion process of the propellant in the classical internal ballistics model is described by using the law of geometric combustion, which is consistent with the generation process of the mass source in the three-dimensional flow field modeling of the embodiment of the invention. The solution flow of the Dragon-Kutta method is described in detail in the existing research results and is easy to be programmed and realized in MATLAB, and the description is omitted here.
The average rifling-time (p-T) curve, pellet velocity-time (vb-T) curve, pellet travel-time (Lb-T) curve and average barrel temperature-time (T-T) curve obtained based on classical inner trajectory model and three-dimensional flow field model are shown in fig. 5 a-5 d.
As can be seen from FIG. 5a, the variation trend of the average rifling pressure obtained by the two methods with time keeps better consistency, the pressure peak value is about 1.5ms, and the maximum rifling pressure deviation is 6.49%; in addition, the inner ballistic time obtained by the three-dimensional flow field model and the classical inner ballistics model is 4.306ms and 3.926ms respectively, because the change of the air resistance of the front part of the bullet with the speed of the bullet is considered in the three-dimensional flow field model, the actual resistance of the bullet is larger, so that the movement time of the bullet in the bore is increased, and the calculation results of the bullet speed and the stroke in fig. 5b and fig. 5c are lower than those of the classical inner ballistics model; when the projectile reached the muzzle, the initial velocity of the projectile was 1166.81m/s and 985.37m/s, respectively, using the classical internal ballistics model and the three-dimensional flow field model, resulting in a 15.55% deviation, which was also related to the air resistance described above. As can be seen from fig. 5d, the average temperature of the fuel gas obtained by the two methods maintains good consistency in the variation trend, and the difference is that the temperature value obtained by the inner trajectory three-dimensional model has a longer stationary variation period (about 1.5 ms); in addition, the average temperature in the whole process of the inner trajectory is generally higher than 2000K, and the average temperature in the early stage of the inner trajectory reaches 3000K.
In summary, the inner trajectory three-dimensional flow field model and the numerical method provided by the embodiment of the invention can effectively solve the inner trajectory parameters and accurately reflect the basic rules of the inner trajectory process.
5 analysis of three-dimensional flow field characteristics of inner trajectory of gun
Based on the propellant charge parameters in table 1, the internal trajectory three-dimensional flow field parameters at the moment of gun firing are calculated by adopting the internal trajectory three-dimensional flow field modeling theory and the numerical method. The pressure and velocity profiles on the xy section in the barrel at different moments (2 ms, 3ms and 4 ms) are shown in figures 6 and 7. As can be seen from fig. 6, the pressure of the gunpowder gas in the barrel at different moments shows a gradually decreasing trend from the bottom of the barrel to the bottom of the bullet: taking t=3ms as an example, the pressure near the bottom of the chamber is highest when the gun is launched, and reaches about 140MP, and the pressure value is reduced to about 110MPa when the gun reaches the bottom of the bullet, which is consistent with the pressure distribution rule in the barrel, which is obtained based on Lagrange assumption in classical internal ballistics theory. The flow rate of the gunpowder gas in the barrel gradually increases from the bottom of the chamber to the bottom of the bullet, as shown in fig. 7. In addition, a high velocity flow region occurs at the rear sidewall surface of the bore due to the shrinkage of the inside diameter of the barrel at the bore position. The high flow velocity near the inner wall of the barrel will cause intense convective heat transfer between the gas and the wall.
The turbulent kinetic energy distribution over the xy section in the barrel at different times is shown in figure 8. As can be seen from fig. 8, the turbulence in the barrel is very intense and the turbulence kinetic energy is maximum near the inner wall surface of the barrel, and the turbulence kinetic energy at the rear side of the sloping bore gradually increases from the axis of the barrel to the wall surface; a vortex-like turbulence structure is formed near the rear side tube wall of the projectile, the maximum value of turbulence kinetic energy at the position can reach hundreds to thousands of m < 2 >/s < 2 >, and the vortex-like structure gradually dissipates along with the movement of the projectile.
At time t=4ms, the distribution of the gas thermophysical parameters of the gunpowder in the barrel is shown in fig. 9. As can be seen from fig. 9, except for the small-range conical area at the rear side of the projectile, the constant pressure specific heat of the gunpowder gas is gradually reduced along the axial direction of the barrel, and the specific heat is also gradually reduced from the central axis to the wall surface; in contrast, the coefficient of viscosity and the thermal conductivity gradually increase in the axial direction and the radial direction; furthermore, the maximum value of the thermal conductivity occurs at the combustion chamber, the ramp bore and the rear sidewall surface of the ramp bore, resulting in a greater thermal conductivity at this location.
The temperature distribution in the xy section of the barrel at different times is shown in figure 10. As can be seen from fig. 10, the temperature of the gunpowder gas in the barrel at different moments gradually increases from the bottom of the barrel to the bottom of the bullet; as the inner ballistic time increases, the temperature of the gas decreases; in addition, high temperature areas exist at the positions of the slope bore and the pipe wall at the rear side of the slope bore, and the temperature value can reach 3500K, which is the main reason for the most serious ablation of the slope bore and the rear side of the slope bore of the artillery. In combination with the above-mentioned distribution of turbulent kinetic energy in the barrel, it is known that the maximum value of the temperature in the barrel and the maximum value of the turbulent kinetic energy are simultaneously present in the bore and the rear sidewall surface of the bore.
Device embodiment
According to an embodiment of the present invention, a device for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value is provided, and fig. 11 is a schematic diagram of the device for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value according to the embodiment of the present invention, as shown in fig. 11, the device for modeling an internal trajectory three-dimensional transient flow field of an artillery and calculating a multi-physical field value according to the embodiment of the present invention specifically includes:
the first construction module 110 is used for constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the projectile head;
the second construction module 112 is configured to construct an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model based on a step-by-step solution method of a propellant combustion process and a gas in-bore flow process;
the calculation module 114 is configured to calculate the multi-physical field value of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solution method.
The embodiment of the present invention is an embodiment of a device corresponding to the embodiment of the method, and specific operations of each module may be understood by referring to descriptions of the embodiment of the method, which are not repeated herein.
Electronic device embodiment
An embodiment of the present invention provides an electronic device, as shown in fig. 12, including: a memory 120, a processor 122 and a computer program stored on the memory 120 and executable on the processor 122, which when executed by the processor 122 performs the steps as described in the method embodiments.
Computer-readable storage medium embodiments
Embodiments of the present invention provide a computer-readable storage medium having stored thereon a program for carrying out information transmission, which when executed by the processor 112, carries out the steps described in the method embodiments.
The computer readable storage medium of the present embodiment includes, but is not limited to: ROM, RAM, magnetic or optical disks, etc.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (10)
1. A method for modeling a three-dimensional transient flow field of an inner trajectory of an artillery and calculating a numerical value of a plurality of physical fields is characterized by comprising the following steps:
constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the bullet head;
based on a step-by-step solving method of a propellant powder combustion process and a fuel gas in-bore flow process, constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model;
and calculating the multi-physical field value of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode.
2. The method according to claim 1, wherein the method further comprises:
and determining the change rule of the parameters in the bore along with the inner trajectory time in the inner trajectory process of the gun according to the numerical values of the multiple physical fields.
3. The method according to claim 1, wherein constructing a three-dimensional axisymmetric physical model of the cannon based on the bore structure and the gas resistance of the projectile head comprises:
setting the inner diameter of the gun barrel as D in An outer diameter of D out The whole length of the barrel is L p Representing the distance from the rear side of the breech to the muzzle position; the projectile moves forward under the action of the thrust of the gunpowder and the gas resistance of the projectile head until the projectile exits the muzzle, the forced convection heat exchange is carried out between the gas in the barrel and the inner wall surface of the barrel, and the heat transfer coefficient is h w-in The method comprises the steps of carrying out a first treatment on the surface of the The heat is conducted in the pipe wall in a heat conduction mannerConstant pressure specific heat C of the pipe material pp And a thermal conductivity lambda p As a function of temperature; the outer wall surface of the barrel performs natural convection heat exchange and radiation heat exchange with the outside air, and the natural convection heat exchange coefficient is h w-out And constructing a three-dimensional axisymmetric physical model of the artillery.
4. The method of claim 1, wherein constructing an internal ballistic three-dimensional flow field mathematical model from the three-dimensional axisymmetric physical model based on a step-by-step solution of a propellant combustion process and a gas in-bore flow process specifically comprises:
in a time step, the propellant burns to release a mass source and an energy source to generate gunpowder gas, thereby changing the pressure field and the temperature field in the barrel and pushing the projectile to move; after entering the next time step, solving the mass source and the energy source according to the formula 1 and the formula 2 continuously according to the pressure in the barrel, the current combustion surface area and the relative burnt thickness of the propellant powder, and solving and updating the three-dimensional flow field distribution in the barrel according to the formulas 4 to 8 until the projectile exits from the muzzle:
wherein ρ is p Is the density of the propellant; s is S p Is the combustion surface area; z is Z p Is the relative burnt thickness; f (f) p Is the powder strength; t is time; the relative burnt thickness is formula 3;
wherein u is p Is the combustion rate coefficient; e, e 1 Is the thickness of the combustion layer; p is the average pressure of gunpowder gas in the barrel; η (eta)Is the burning rate index; z is Z k Is the relative fired thickness of the propellant at the end of combustion;
in the inner ballistic flow field, the mass conservation equation is expressed as formula 4;
wherein ρ is the density of the gunpowder gas;is Hamiltonian; u is the velocity vector of the gunpowder fuel gas;
the conservation of momentum equation is expressed as equation 5-equation 7
Wherein u, v and w respectively represent components of the speed of the gunpowder gas in the directions of x, y and z; p is the pressure; mu is the viscosity coefficient of the fuel gas; f (F) bx 、F by 、F bz The volume force of the gunpowder gas in the x, y and z directions is respectively applied;
the energy conservation equation is expressed as equation 8;
wherein T is the temperature of the fuel gas; λ is the thermal conductivity; c (C) p The constant pressure specific heat of the fuel gas.
5. The method of claim 4, wherein calculating the multi-physical field values of the internal ballistic three-dimensional flow field mathematical model using control equation discretization and pressure-velocity coupling solution specifically comprises:
dispersing the diffusion terms in the formulas 4-8 by adopting a central differential format; dispersing the stream item by adopting a QUICK format with third-order precision, and processing the dispersion of nodes at the boundary by adopting a first-order windward format; the source item adopts an explicit scheme for dispersion; processing transient items by adopting a fully implicit discrete format; and solving the pressure-speed coupling problem in the flow field parameter solving by adopting a SIMPLE pressure correction algorithm.
6. The method of claim 5, wherein the diffusion term in equations 4-8 is discretized in a center differential format; the discrete of the stream item by adopting the QUICK format with third-order precision specifically comprises the following steps:
the diffusion term discretized by the center differential format is expressed as:
wherein physical quantities at east, west, north, south, upper and lower nodes are respectively represented by subscripts E, W, N, S, T, B, subscripts e, w, n, s, t, b respectively represent east, west, north, south, upper and lower boundary surfaces of a control unit, phi is a generalized flow parameter, Γ is a generalized diffusion coefficient corresponding to phi,represents diffusion term, δx e 、δx w 、δy n 、δy s 、δz t 、δz b The distance between the node and the adjacent nodes on the east, west, north, south, upper and lower sides of the node, respectively,/->P represents node P; for the boundary of the control unit, there is A w ＝A e ＝ΔyΔz，A n ＝A s ＝ΔxΔz，A b ＝A t The values =Δx Δy, Δx, Δy, Δz are the distances between the east-west, north-south, upper and lower interfaces, respectively;
when the flow is in the positive direction, i.e. u e >0、u w >0、u n >0、u s >0、u t >0、ub>0, wherein the subscripts e, w, n, s, t, b represent the east, west, north, south, upper and lower boundary surfaces of the control unit, respectively, the flow parameters at the interface are expressed as:
wherein, subscripts WW, SS and BB respectively represent upstream node values of left nodes in three directions, subscripts E, W, N, S, T, B respectively represent physical quantities at east, west, north, south, upper and lower nodes, phi is a generalized flow parameter, and P represents a node P;
combining the center differential format of the diffusion term and the QUICK format of the flow term to obtain a discrete control equation:
in the three-dimensional problem, the control equation at the node P contains the control quantity of E, W, N, S, T, B, EE, WW, NN, SS, TT, BB nodes after being discretized, and is in thirteen-point format, and the boundary problem is processed by adopting a first-order windward format, namely, at the first node, phie=phip, phiw=phiw, phin=phip, phis=phis, phit=phip and phib=phib.
7. The method of claim 6, wherein transient items are processed in a fully implicit discrete format; for the pressure-speed coupling problem in the flow field parameter solving, the SIMPLE pressure correction algorithm is adopted for solving the problems specifically including:
and integrating the control equation over a time period delta t by adopting a full implicit time discrete format with second-order precision to obtain:
where ρu phi A represents the convective term, deltaV is the volume of the control volume, i.e., deltaV=Deltax Deltaz,an average value of generalized source items on the control unit;
the second order fully implicit time integration format is expressed as:
wherein n, n-1, n-2 represent the values of the current time step, the last time step and the last time step physical quantity, respectively;
after the dispersion of the conservation equation is completed, the algebraic equation set after the dispersion is solved by adopting a SIMPLE pressure correction algorithm, and the final solving of the numerical values of the multiple physical fields is completed.
8. The utility model provides a three-dimensional transient flow field modeling of trajectory and many physical field numerical calculation device in gun which characterized in that includes:
the first construction module is used for constructing a three-dimensional axisymmetric physical model of the gun according to the slope bore structure and the gas resistance of the projectile head;
the second construction module is used for constructing an inner trajectory three-dimensional flow field mathematical model according to the three-dimensional axisymmetric physical model based on a step-by-step solution method of a propellant combustion process and a fuel gas in-bore flow process;
and the calculation module is used for calculating the multi-physical field values of the inner trajectory three-dimensional flow field mathematical model by adopting a control equation discrete and pressure-speed coupling solving mode.
9. An electronic device, comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, which when executed by the processor, performs the steps of the method of modeling a ballistic three-dimensional transient flow field and computing a multi-physical field value in an artillery according to any one of claims 1 to 7.
10. A computer-readable storage medium, wherein a program for implementing information transfer is stored on the computer-readable storage medium, and the program, when executed by a processor, implements the steps of the method for modeling a ballistic three-dimensional transient flow field and calculating a multi-physical-field value in an artillery according to any one of claims 1 to 7.
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