CN113255072A - Method for rapidly calculating heat transfer process of solid rocket engine cladding sleeve structure - Google Patents

Abstract

The invention discloses a method for quickly calculating a heat transfer process of a solid rocket engine coating sleeve structure, which comprises the following steps: the method comprises an input stage, a calculation and calculation process prompting stage, a calculation result display stage and a calculation data storage stage. And the input stage is used for inputting geometric parameters, physical parameters, initial boundary value conditions, heat transfer time and unit geometric parameter reference values of all layers of the cladding sleeve structure. And the calculation and calculation process prompt stage is used for calculating the heat transfer process according to the numerical values and conditions of the input stage and displaying the prompt of the calculation completion condition according to the actual calculation completion degree. And the calculation result display stage is used for displaying the calculated data cloud picture and the calculated data curve after the heat transfer is finished. And the calculation data storage stage is used for storing calculation result data. The method has the advantages of convenient use, simple operation, short calculation time, intuitive calculation result, low cost and high benefit.

Description

A fast calculation method for heat transfer process of solid rocket motor cladding structure

technical field

The invention relates to a fast calculation method for the heat transfer process of a solid rocket motor cladding structure, and belongs to the technical field of solid rocket motors.

Background technique

The cladding structure is located between the solid rocket motor casing and the grain. It is an important structural component of the solid rocket motor and plays an important role in the structural integrity, working reliability and safety of the solid rocket motor. First of all, for the grain column in the form of wall-to-wall casting, the coating sleeve has the function of firmly bonding the shell and the grain column. Secondly, the cladding can play the role of stress buffer, and reduce the adverse effects of external impact and other loads on the grain performance during the process of engine loading and unloading, transportation and storage. Finally, the cladding sleeve plays the role of suppressing combustion, protecting the shell and grain. For the wall-mounted grain, the cladding sleeve can reduce the heat of the shell so that the shell has sufficient rigidity and is not burned through. Filling the grain, the covering sleeve can inhibit the heat transfer of the high-temperature gas in the gap between the shell and the grain to the grain after ignition, and prevent the side grain from being thermally decomposed or burned ahead of time, resulting in changes in internal ballistic performance, jumping fire, detonation, etc. ACCIDENT.

For the engine charge of the free-packed grain, there is a gap between the grain coating and the shell. After ignition, the high-temperature gas enters the gap, and a temperature is formed between the gas layer in the gap, the coating and the grain. If the thickness of the coating is insufficient and the temperature of the grain is too high, it will cause safety problems and the engine cannot work normally and reliably. Therefore, the thickness design of the cladding sleeve is very important for the safe and reliable operation of the engine. The heat transfer process calculation of the cladding structure is the basis for the thickness design of the cladding. Currently, for designers or simulators, the heat transfer calculation of the cladding generally requires the use of mature commercial software, such as Fluent software, whose calculation accuracy is relatively high. high. But at the same time, the use of this software has at least the following inconveniences: (1) The software requires users to have a certain foundation and experience, and non-fluid or heat transfer design or simulation personnel need to spend extra time and effort to learn and master the use of this software ; (2) The software needs to draw the geometric model, manually divide the unit, set the boundary conditions, post-processing and other complicated processes, which is not conducive to simplifying the process; (3) The software is versatile, and the calculation is often time-consuming. The problem is not conducive to saving computing time; (4) It is not easy to integrate into the solid rocket motor design and simulation integrated platform. Therefore, the software is difficult to meet the urgent needs of rapid design, optimization and simulation analysis of solid rocket motor cladding structures.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, and to provide a fast calculation method for the heat transfer process of a solid rocket motor cladding structure, the method of the present invention is convenient to use, simple to operate, short in calculation time, and intuitive in calculation results , low cost and high efficiency.

The technical scheme solved by the present invention is: a fast calculation method for the heat transfer process of a solid rocket motor cladding structure, which is characterized by comprising: an input stage, a calculation and calculation process prompt stage, a calculation result display stage and a calculation data storage stage;

The solid rocket motor cladding jacket structure is a four-layer structure, which is a grain layer, a cladding jacket layer, a fuel gas layer and a combustion chamber shell layer from the inside to the outside; each layer is a hollow cylinder; in the calculation process, Each layer of the cladding structure is divided into multiple units in the radial direction, and any unit only belongs to one layer of the four-layer structure;

The input stage is as follows:

(1) Input the geometric parameters, physical parameters and initial boundary value conditions of the combustion chamber shell layer, gas layer, cladding layer and grain layer in the cladding casing structure; set the heat transfer time and set the geometric parameters of the unit Reference;

The calculation and calculation process prompt stages are as follows:

(2) According to the geometric parameters of the combustion chamber shell layer, the fuel gas layer, the cladding layer and the grain layer determined in step (1) and the geometric parameter reference value of the set unit, determine the combustion chamber shell layer and the gas layer. , the number of units and the radial thickness of each layer in the coating layer and the grain layer;

(3) The geometric parameters, physical parameters, initial boundary value conditions of the combustion chamber shell layer, fuel gas layer, cladding layer, grain layer determined according to step (1) and the combustion chamber shell layer determined in step (2) , the number of units and the radial thickness of each layer in the gas layer, the coating layer and the grain layer, and the physical parameters of each unit in the combustion chamber shell layer, the gas layer, the coating layer and the grain layer are determined. Surface radial coordinates, initial temperature and heat flux density;

(4) Determine the heat transfer time step of the cladding structure according to the physical parameters and the radial coordinates of the inner and outer surfaces of each unit in the combustion chamber shell layer, the fuel gas layer, the cladding layer, and the grain layer determined in step (3) length and total number of heat transfer time steps M;

(5) According to the physical parameters, radial coordinates of inner and outer surfaces, initial temperature and heat flux density of each unit in the combustion chamber shell layer, gas layer, cladding layer and grain layer determined in step (3-4), determine the The temperature change of each unit in the first heat transfer time step of the cladding structure;

(6) Record the number of the current heat transfer time step as j (j=1, 2, . The temperature variation of each unit is added to the initial temperature of the corresponding unit determined in step (3), as the temperature of each unit corresponding to the jth heat transfer time step of the cladding structure;

(7) Determine whether j is equal to the total number of heat transfer time steps M; if not, according to the physical parameters, radial coordinates of the inner and outer surfaces, and the first The temperature and heat flux density corresponding to the j heat transfer time steps are calculated, and the temperature change of each unit in the j+1 heat transfer time step of the cladding structure is calculated, and added to the jth heat transfer of the cladding structure. From the temperature of each unit corresponding to the time step, the temperature of each unit corresponding to the j+1 heat transfer time step of the cladding structure is obtained; according to the heat transfer time step number j+1 and the total number of heat transfer time steps M, Determine the calculation completion degree W, and let j=j+1; if so, stop the calculation, and obtain the temperature of each unit of the cladding structure after the heat transfer time ends;

The calculation result display stage is as follows:

(8) Display the temperature map of each unit of the cladding structure after the end of the heat transfer time;

The calculation data storage phase is as follows:

(9) Save the temperature data of each unit of the cladding structure after the heat transfer time ends.

Further, the method for quickly calculating the heat transfer process of the solid rocket motor cladding structure is characterized in that: the geometric dimensions of the combustion chamber shell layer, the gas layer, the cladding layer, and the grain layer include: combustion The radial thickness of the chamber shell layer, the fuel gas layer, the cladding layer, the grain layer and the radial coordinates of the inner side of the grain.

Further, the method for quickly calculating the heat transfer process of the solid rocket motor cladding structure is characterized in that: the initial boundary value conditions of the combustion chamber shell layer, the gas layer, the cladding layer and the grain layer include: : Initial temperature and heat flux density of combustion chamber shell layer, gas layer, cladding layer and grain layer.

Further, the method for quickly calculating the heat transfer process of the solid rocket motor cladding structure is characterized in that: physical parameters include: the density of the combustion chamber shell layer, the fuel gas layer, the cladding layer, and the grain layer , thermal conductivity and constant pressure specific heat capacity.

Further, the method for quickly calculating the heat transfer process of the solid rocket motor cladding sleeve structure is characterized in that: the heat transfer time refers to the total time required for the heat transfer of the cladding sleeve structure.

Further, the method for rapidly calculating the heat transfer process of a solid rocket motor cladding structure is characterized in that: the reference value of the geometric parameter of the unit refers to the reference value of the radial thickness of the unit.

The advantages of the present invention compared with the prior art are:

(1) The present invention is convenient to use and simple to operate. Compared with the commercial software Fluent, there is no need to draw geometric models, manually divide units, and post-process the results. The calculation results are displayed intuitively, and the threshold for learning and use is low;

(2) The calculation time of the present invention is short, and the result is accurate and reliable. Compared with the commercial software Fluent, the calculation time is significantly reduced with the same structure and the same initial boundary value under the same element size and time step, and the calculation accuracy is comparable;

(3) The present invention has low cost and high benefit. There is no need to purchase expensive commercial software, which is easy to integrate into the solid rocket motor design and simulation integration platform. It has the intellectual property rights of self-developed software, which is fast and convenient to use, which is helpful for the rapid design, simulation and optimization of the cladding structure, shortening the R&D cycle and reducing R&D costs. cost, and help the rapid advancement of the mission of strengthening the aerospace force.

Description of drawings

Figure 1 is a schematic diagram of an axial cross-section of a solid rocket motor cladding sleeve structure.

Figure 2 is a schematic cross-sectional view of each radial unit of the solid rocket motor cladding sleeve structure.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

The invention discloses a fast calculation method for the heat transfer process of a solid rocket motor cladding structure, and establishes a rapid calculation method for the heat transfer process of the cladding structure suitable for the solid rocket motor in the form of free-packing grains according to the basic principle of heat transfer. The calculation method includes an input stage, a calculation and calculation process prompt stage, a calculation result display stage and a calculation data storage stage. The input stage is used for inputting geometric parameters, physical parameters, initial boundary value conditions, heat transfer duration and reference values of unit geometric parameters of each layer of the cladding structure. In the calculation and calculation process prompt stage, the heat transfer process calculation is performed according to the values and conditions of the input stage, and a calculation completion status prompt is displayed according to the actual calculation completion degree. The calculation result display stage is used to display the data cloud diagram and data curve after the calculation of heat transfer is completed. The calculation data storage stage is used for calculation result data storage. The method of the invention has the advantages of convenient use, simple operation, short calculation time, intuitive calculation result, low cost and high benefit.

In the design stage of the cladding structure scheme, when it is necessary to quickly compare or optimize the scheme, or when the solid rocket motor fails, and it is necessary to quickly carry out numerical simulation support failure reproduction test of the possible cladding structure, commercial software such as Fluent is used. It often takes a long time, which is not conducive to ensuring the timely completion of tasks such as scheme design or fault recurrence. Therefore, the rapid calculation method of the present invention can greatly save processing and calculation time, and quickly complete the above tasks.

A method for quickly calculating a heat transfer process of a solid rocket motor cladding structure, which is characterized by comprising: an input stage, a calculation and calculation process prompt stage, a calculation result display stage, and a calculation data storage stage;

The solid rocket motor cladding sleeve structure is a four-layer structure, as shown in FIG. 1 is an axial cross-sectional view of the cladding sleeve structure (cylindrical coordinate system, the radial direction is r, the circumferential direction is θ, and the axial direction is z), from The inside and outside are the grain layer, the coating layer, the gas layer and the combustion chamber shell layer; each layer is a hollow cylinder, and the material of each layer has the corresponding density, constant pressure specific heat capacity, thermal conductivity and other physical parameters and diameters. Dimensional parameters such as thickness; after the solid rocket motor is ignited, the initial temperature of the gas layer is high, while the initial temperature of the combustion chamber shell layer, the cladding layer and the grain layer is low, and the gas layer increases to the cladding layer, the grain layer and the combustion chamber. Shell layer heat transfer. There is no heat source in the heat transfer process, the heat convection process is not considered, only the heat conduction process is considered, and the above physical parameters and radial thickness parameters do not change during the heat transfer process; as shown in Figure 2, the radial direction of the solid rocket motor cladding sleeve structure Schematic diagram of the cross-section of the unit. In the calculation process, it is assumed that the temperature at any time is only a function of the radial position coordinates according to the characteristics of the large axial size of the cladding structure and the symmetry in the circumferential direction, which is simplified as a one-dimensional heat transfer problem. Divide the unit radially, take any representative unit, obtain the heat transfer control equation in discrete format according to the difference between the heat flowing into and out of the unit and the heat required for the temperature change of the unit, and then compile the heat transfer calculation program;

In the input stage, the preferred solutions are as follows:

(1) Input the geometric parameters, physical parameters and initial boundary value conditions of the combustion chamber shell layer, gas layer, cladding layer and grain layer in the cladding casing structure; set the heat transfer time and set the geometric parameters of the unit Reference value; the preferred solution is as follows:

Enter the radial thicknesses of the combustion chamber shell layer, the gas layer, the cladding layer, and the grain layer in the cladding jacket structure, denoted as h _kt , _hrq , h _bf , and _hyz respectively, and input the inner surface of the grain layer Radial coordinate r _nc ; set the heat transfer duration t, set the reference value of the geometrical parameters of the unit, that is, the reference value h ^* of the radial thickness of the unit;

in,

h _kt is the radial thickness of the combustion chamber shell layer, m;

h _rq is the radial thickness of the gas layer, m;

h _bf is the radial thickness of the cladding layer, m;

h _yz is the radial thickness of the grain layer, m;

r _nc is the radial coordinate of the inner surface of the grain layer, m;

t is the heat transfer time of the coating sleeve, s;

h ^* is the reference value of element radial thickness, m;

The calculation and calculation process prompt stages are as follows:

(2) According to the geometric parameters of the combustion chamber shell layer, the fuel gas layer, the cladding layer and the grain layer determined in step (1) and the geometric parameter reference value of the set unit, determine the combustion chamber shell layer and the gas layer. , the number of units and the radial thickness of each layer in the coating layer and the drug column layer; the preferred scheme is as follows:

The number of units in each layer is equal to the quotient obtained by dividing the radial thickness of each layer by the reference value of the unit radial thickness and then rounded up, that is,

n _kt = Ceiling(h _kt /h ^* ) (1)

n _rq = Ceiling(h _rq /h ^* ) (2)

n _bf = Ceiling(h _bf /h ^* ) (3)

n _yz = Ceiling(h _yz /h ^* ) (4)

in,

n _kt is the number of combustion chamber shell layer units;

n _rq is the number of gas layer units;

n _bf is the number of cladding layer units;

n _yz is the number of grain layer units;

Ceiling() means round up operation;

And the total number of units is n, then

n=n _kt +n _rq +n _bf +n _yz (5)

After the number of units in each layer and the total number of units are determined, the actual radial direction of the unit i (i=1, 2,...,n) is determined according to which layer any unit i (i=1, 2,...,n) belongs to. thickness _hi ,

If 1≤i≤n _yz , then h _i =h _yz /n _yz (6)

If n _yz +1≤i≤n _yz +n _bf , then h _i =h _bf /n _bf (7)

If n _yz +n _bf +1≤i≤n _yz +n _bf +n _rq , then h _i =h _rq /n _rq (8)

If n _yz +n _bf +n _rq +1≤i≤n, then h _i =h _kt /n _kt (9)

in,

h _i is the radial thickness of any unit i (i=1, 2,..., n), m;

It should be noted that the above method is to determine the actual total number of elements and the radial thickness through the reference value of the element radial thickness, and the actual total number of elements and the radial thickness can also be determined by setting the number of elements in each layer. former;

(3) The geometric parameters, physical parameters, initial boundary value conditions of the combustion chamber shell layer, fuel gas layer, cladding layer, grain layer determined according to step (1) and the combustion chamber shell layer determined in step (2) , the number of units and the radial thickness of each layer in the gas layer, the coating layer and the grain layer, and the physical parameters of each unit in the combustion chamber shell layer, the gas layer, the coating layer and the grain layer are determined. Surface radial coordinates, initial temperature and heat flux density; the preferred solutions are as follows:

Denote the densities of the combustion chamber shell layer, fuel gas layer, cladding layer, and grain layer as ρ _kt , ρ _rq , ρ _bf , and ρ _yz , respectively, and the thermal conductivity as k _kt , k _rq , k _bf , and _kyz , respectively, The constant pressure specific heat capacities are Cp _kt , Cp _rq , Cp _bf , and Cp _yz , respectively, and the initial temperatures are T _kt , _Trq , T _bf , and _Tyz , respectively, and the density, thermal conductivity, constant pressure specific heat capacity, and initial temperature of unit i are respectively ρ _i , k _i , Cp _i , T _i ⁽⁰⁾ , then determine which layer the unit i (i=1, 2, ..., n) belongs to, its density, thermal conductivity, specific heat capacity at constant pressure, initial temperature and the layer to which it belongs The density, thermal conductivity, constant pressure specific heat capacity, and initial temperature are equal respectively, namely

If 1≤i≤n _yz , then ρ _i =ρ _yz , _{ki =kyz , Cp i = Cp yz} , T _i ⁽⁰⁾ =T _yz (10)

If n _yz +1≤i≤n _yz +n _bf , then ρ _i =ρ _bf , _ki =k _bf , Cp _i =Cp _bf , T _i ⁽⁰⁾ =T _bf (11)

If n _yz +n _bf +1≤i≤n _yz +n _bf +n _rq , then ρ _i =ρ _rq , _ki =k _rq , Cpi =Cp _rq , T _{i (} ⁰⁾ =T _rq (12)

If n _yz +n _bf +n _rq +1≤i≤n, then ρ _i =ρ _kt , _ki =k _kt , Cpi =Cp _kt , T _{i (} ⁰⁾ =T _kt (13)

in,

ρ _kt is the density of the combustion chamber shell layer, kg/m ³ ;

ρ _rq is the density of the gas layer, kg/m ³ ;

ρ _bf is the density of the cladding layer, kg/m ³ ;

ρ _yz is the density of grain layer, kg/m ³ ;

k _kt is the thermal conductivity of the combustion chamber shell layer, W/(m·K);

k _rq is the thermal conductivity of the gas layer, W/(m·K);

k _bf is the thermal conductivity of the cladding layer, W/(m·K);

k _yz is the thermal conductivity of the grain layer, W/(m·K);

Cp _kt is the constant pressure specific heat capacity of the combustion chamber shell layer, J/(kg·K);

Cp _rq is the constant pressure specific heat capacity of the gas layer, J/(kg·K);

Cp _bf is the constant pressure specific heat capacity of the cladding, J/(kg·K);

Cp _yz is the specific heat capacity of the grain layer at constant pressure, J/(kg·K);

T _kt is the initial temperature of the combustion chamber shell layer, K;

_Trq is the initial temperature of the gas layer, K;

T _bf is the initial temperature of the cladding layer, K;

T _yz is the initial temperature of the grain layer, K;

ρ _i is the density of unit i (i=1, 2, . . . , n), kg/m ³ ;

ki is the thermal conductivity of unit _i (i=1, 2, . . . , n), W/(m·K);

Cp _i is the constant pressure specific heat capacity of unit i (i=1, 2,...,n), J/(kg·K);

T _i ⁽⁰⁾ is the initial temperature of unit i (i=1, 2, . . . , n), K;

It should be pointed out that the above-mentioned density, thermal conductivity, and constant pressure specific heat capacity can be functions of temperature. For the convenience of introduction, they are all treated as constants;

The radial coordinates of the inner and outer surfaces of the unit i ( _i =1, 2,...,n) are denoted as ri and ri ₊₁ respectively. Because the unit is continuous, the outer surface of the unit i (i=1, 2,...,n-1) The radial coordinates of the surface are the same as the radial coordinates of the inner surface of the unit i+1 (i=1, 2,...,n-1), both of which are r _i+1 . The calculation methods of the radial coordinates of the inner and outer surfaces are as follows:

in,

r _i is the radial coordinate of the inner surface of the unit i (i=1, 2, ..., n), m;

r _i+1 is the radial coordinate of the outer surface of the unit i (i=1, 2, ..., n), m;

为求和运算，表示对单元号从1到i-1的单元的径向厚度求和；

For the summation operation, it represents the summation of the radial thickness of the elements with element numbers from 1 to i-1;

为求和运算，表示对单元号从1到i的单元的径向厚度求和；

For the summation operation, it means summing the radial thickness of the elements with element numbers from 1 to i;

h _j is the radial thickness of element j (the range of element number j depends on the summation operation), m;

It should be pointed out that the deformation of the cladding sleeve structure caused by the temperature change is not considered in the calculation process, so the radial coordinates of the inner and outer surfaces of each element remain unchanged during the calculation process;

Denote the heat flux density on the inner and outer surfaces of unit i ( _i = ₁ , 2, . The heat flux density is the same as the heat flux density on the inner surface of the unit i+1 (i=1, 2, ..., n-1), both of which are q _i+1 , and the heat flux density on the inner and outer surfaces of the cladding structure is q _nc and q _wc , Then the innermost unit of the grain layer, that is, the inner surface heat flux density of unit 1, is

q ₁ =q _nc (16)

The heat flux density on the outer surface of the outermost unit of the combustion chamber shell layer, that is, unit n is:

q _n+1 = q _wc (17)

In formula (16-17),

q _nc is the heat flux density on the inner surface of the cladding structure, W/m ² ;

q _wc is the heat flux density on the outer surface of the cladding structure, W/m ² ;

q ₁ is the heat flux density on the inner surface of unit 1, W/m ² ;

q _n+1 is the heat flux density on the outer surface of unit n, W/m ² ;

It should be pointed out that the heat flux density inside and outside the cladding structure of the solid rocket motor is constant, so during the calculation process, the heat flux density on the inner surface of unit 1 and the heat flux density on the outer surface of unit n remain unchanged, and the total number of heat transfer time steps is recorded as M. , denote the heat flux density on the inner surface of unit 1 and the heat flux density on the outer surface of unit n at the jth (j=1, 2, ..., M) heat transfer time step as q ₁ ^(j) and q _n+1 ^(j) respectively, then

q ₁ ^(j) =q ₁ =q _nc (18)

q _n+1 ^(j) =q _n+1 =q _wc (19)

in,

q ₁ ^(j) is the heat flux density on the inner surface of the unit 1 at the jth (j=1, 2, . . . , M) heat transfer time step, W/m ² ;

q _n+1 ^(j) is the heat flux density on the outer surface of the jth (j=1, 2, ..., M) heat transfer time step unit n, W/m ² ;

(4) Determine the heat transfer time step of the cladding structure according to the physical parameters and the radial coordinates of the inner and outer surfaces of each unit in the combustion chamber shell layer, the fuel gas layer, the cladding layer, and the grain layer determined in step (3) length and the total number of heat transfer time steps M; the preferred scheme is as follows:

Record the heat transfer time step as Δt, because for any unit i (i=1, 2, ..., n), the stability condition should be satisfied

Δtk _i /(ρ _i Cpi (r _{i +1} -r _i ) ² )≤0.5 (20)

Therefore, take the minimum heat transfer time step that satisfies Equation (20) as the reference heat transfer time step Δt ^* , namely

Δt ^* =Min(0.5ρ ₁ Cp ₁ (r ₂ −r ₁ ) ² /k ₁ , 0.5ρ ₂ Cp ₂ (r ₃ −r ₂ ) ² /k ₂ , . . . , 0.5ρ _n Cp _n (r _{n+ 1} -r _n ) ² /k _n )

(twenty one)

Record the total number of heat transfer time steps as M, then

M=Ceiling(t/Δt ^* ) (22)

Thus, the actual heat transfer time step Δt is

Δt=t/M (23)

In formula (20-23),

Δt is the actual heat transfer time step, referred to as the heat transfer time step, s;

Δt ^* is the reference heat transfer time step, s;

Min() means to find the minimum value;

M is the total number of heat transfer time steps;

(5) According to the physical parameters, radial coordinates of inner and outer surfaces, initial temperature and heat flux density of each unit in the combustion chamber shell layer, gas layer, cladding layer and grain layer determined in step (3-4), determine the The temperature change of each unit in the first heat transfer time step of the cladding structure; the preferred solution is as follows:

Figure 2 is a schematic diagram of the cross-section of the radial element of the cladding structure (cylindrical coordinate system, the radial direction is r, the circumferential direction is θ, and the axial direction is z), without loss of generality, for any element i (i= 1, 2, ..., n), record the difference between the heat flux flowing into the outer surface and the heat flow out of the inner surface in the first heat transfer time step as ΔΦ _i ⁽¹⁾ , and record the area of the inner and outer surfaces as A _i respectively and A _i+1 , denoting that the axial length of each element is l, and the central angle subtended by the arcs on the inner and outer surfaces of each element is α, then

ΔΦ _i ⁽¹⁾ =A _i+1 q _i+1 ⁽¹⁾ -A _i q _i ⁽¹⁾ =αl(r _i+1 q _i+1 ⁽¹⁾ -r _i q _i ⁽¹⁾ ) (24 )

In the first heat transfer time step Δt, the difference between the heat flowing into the outer surface of unit i (i=1, 2,...,n) and the heat flowing out of the inner surface of unit i (i=1,2,...,n) is Q _i ⁽¹⁾ , then

Q _i ⁽¹⁾ = ΔΦ _i ⁽¹⁾ Δt = Δtαl(r _i+1 q _i+1 ⁽¹⁾ -r _i q _i ⁽¹⁾ ) (25)

According to the principle of continuous heat flux density on the interface of adjacent units, Fourier's law can obtain the heat flux density on the inner surface of unit i (i=2, 3, ..., n) as

q ₁ ⁽¹⁾ and q _n+1 ⁽¹⁾ see equations (16) and (17);

Denote the temperature change of unit i (i=1, 2,...,n) in the first heat transfer time step as ΔT _i ⁽¹⁾ , then the heat required for the temperature change ΔT _i ⁽¹⁾ is

Since the difference between the heat flux flowing into the outer surface of the unit and the heat flux flowing out of the inner surface of the unit per unit time is equal to the heat required for the temperature change of the unit, it can be obtained

Q _i ⁽¹⁾ = m _i Cp _i ΔT _i ⁽¹⁾ (28)

The simultaneous formula (25-28) can be obtained

In formula (24-29),

ΔΦ _i ⁽¹⁾ is the heat that flows into the outer surface of unit i (i=1, 2,…,n) and flows out of the inner surface of unit i (i=1,2,…,n) in the first heat transfer time step. Flow difference, W;

A _i is the inner surface area of unit i (i=1, 2, . . . , n), m ² ;

A _i+1 is the outer surface area of unit i (i=1, 2, . . . , n), m ² ;

q _i ⁽¹⁾ is the heat flux density on the inner surface of the unit i (i=1, 2, . . . , n) in the first heat transfer time step, W/m ² ;

q _i+1 ⁽¹⁾ is the heat flux density on the outer surface of the inner unit i (i=1, 2, . . . , n) in the first heat transfer time step, W/m ² ;

α is the central angle subtended by the inner and outer surface arcs of each unit, rad;

l is the axial length of each unit, m;

Q _i ⁽¹⁾ is the difference between the outer surface of the inflow unit i (i=1, 2,...,n) and the inner surface of the outflow unit i (i=1,2,...,n) in the first heat transfer time step Δt difference in heat, J;

T _i ⁽⁰⁾ is the initial temperature of unit i (i=1, 2, . . . , n), K;

T _i-1 ⁽⁰⁾ is the initial temperature of unit i-1 (i=2, 3, ..., n), K;

T _i+1 ⁽⁰⁾ is the initial temperature of unit i+1 (i=1, 2, ..., n-1), K;

ΔT _i ⁽¹⁾ is the temperature change of unit i (i=1, 2,...,n) in the first heat transfer time step, K;

m _i is the mass of unit i (i=1, 2, ..., n), kg;

V _i is the volume of unit i (i=1, 2, . . . , n), m ³ ;

(6) Record the number of the current heat transfer time step as j (j=1, 2, . The temperature variation of each unit is added to the initial temperature of the corresponding unit determined in step (3), as the temperature of each unit corresponding to the jth heat transfer time step of the cladding structure; the preferred scheme is as follows:

Denote the current heat transfer time step number as j (j=1, 2,...,M), let j=1, the unit i (i=1, 2,...,n) in the jth heat transfer time step The temperature is T _i ^(j) , and at the current heat transfer time step that is T _i ⁽¹⁾ , then

in,

T _i ⁽¹⁾ is the temperature of unit i (i=1, 2, . . . , n) in the first heat transfer time step, K;

(7) Determine whether j is equal to the total number of heat transfer time steps M; if not, according to the physical parameters, radial coordinates of the inner and outer surfaces, and the first The temperature and heat flux density corresponding to the j heat transfer time steps are calculated, and the temperature change of each unit in the j+1 heat transfer time step of the cladding structure is calculated, and added to the jth heat transfer of the cladding structure. From the temperature of each unit corresponding to the time step, the temperature of each unit corresponding to the j+1 heat transfer time step of the cladding structure is obtained; according to the heat transfer time step number j+1 and the total number of heat transfer time steps M, Determine the calculation completion degree W; and let j=j+1; if so, stop the calculation to obtain the temperature of each unit of the cladding structure after the heat transfer time ends; the preferred scheme is as follows:

If j=M, stop the calculation; if j<M, similar to step (5), according to the physical parameters of each unit in the combustion chamber shell layer, gas layer, cladding layer, and grain layer, the radial direction of the inner and outer surfaces Coordinates, temperature and heat flux density corresponding to the jth heat transfer time step, calculate the temperature change ΔT _i ^(j+1) within the j+1th heat transfer time step of each unit, and add it to each unit The temperature T _i ^(j) corresponding to the j-th heat transfer time step is obtained to obtain the temperature T _i ^(j+1) corresponding to the j+1-th heat transfer time step of each unit. According to the current heat transfer time step The long sequence number j+1 and the total number of heat transfer time steps M, determine the calculation completion degree W, and let j=j+1, that is

Among them, the heat flux density on the inner surface of the unit i (i=2, 3, ..., n) is

q ₁ ^(j+1) and q _n+1 ^(j+1) see equations (16) and (17);

Completion of the calculation is

W=(j+1)/M*100% (33)

Update heat transfer time step number

j=j+1 (34)

In formula (31-34),

T _i ^(j+1) is the temperature of unit i (i=1, 2, . . . , n) in the j+1th heat transfer time step, K;

T _i-1 ⁽¹⁾ is the temperature of unit i-1 (i=2, 3,..., n) in the j+1th heat transfer time step, K;

ΔT _i ^(j+1) is the temperature change of unit i (i=1, 2,...,n) in the j+1th heat transfer time step, K;

q _i ^(j+1) is the heat flux density on the inner surface of the unit i (i=1, 2, . . . , n) in the j+1th heat transfer time step, W/m ² ;

q _i+1 ^(j+1) is the heat flux density on the outer surface of the unit i (i=1, 2, . . . , n) in the j+1th heat transfer time step, W/m ² ;

The calculation result display stage is as follows:

(8) Display the temperature map of each unit of the cladding structure after the end of the heat transfer time; the preferred scheme is as follows:

After the calculation is completed, the temperature curve of the cladding structure along the radial coordinate corresponding to the last heat transfer time step and the temperature cloud map of the cladding structure are displayed;

In the calculation data storage stage, the preferred solution is as follows:

(9) Save the temperature data of each unit of the cladding structure after the heat transfer time period ends. The preferred options are as follows:

Save the temperature data along the radial coordinates of the cladding structure corresponding to the last heat transfer time step to a document such as Excel.

It is preferable to take the heat transfer condition of a solid rocket motor cladding structure as an example, the heat transfer time is 0.1s, and the densities of the combustion chamber shell layer, gas layer, cladding layer and grain layer are 1500kg/m ³ , 1.225kg/m ³ , 1390kg/m ³ , 1780kg/m ³ , the thermal conductivity is 0.42W/(m·K), 0.0242W/(m·K), 0.24W/(m·K), 0.2W/ (m·K), the specific heat capacities at constant pressure are 1100J/(kg·K), 1800J/(kg·K), 1713J/(kg·K), and 3660J/(kg·K), respectively, and the initial temperatures are 300K and 3000K, respectively. , 300K, 300K, the thicknesses are 5mm, 1.2mm, 0.8mm, 10mm respectively, the radial coordinate of the inner surface of the grain layer is 130mm, and the radial thickness of the set unit is 10 ^-4 m. Carry out the calculation of Fluent software and the calculation method of the present invention, and the result is:

(1) After the heat transfer is completed, the position of the maximum radial temperature difference of each unit is at the center of the gas layer. The calculation result of the Fluent software is 311.66K, and the calculation method of the present invention is 310.96K, and the difference between the two is 0.22%;

(2) The single calculation and pre- and post-processing time of Fluent software is about 4h, and the single calculation and pre- and post-processing time of the method of the present invention is about 2min, and the time is shortened to about 8/1,000.

The present invention is convenient to use and simple to operate. Compared with the commercial software Fluent, operations such as drawing geometric models, manually dividing units, and post-processing results are unnecessary, the calculation results are displayed intuitively, and the threshold for learning and use is low; the calculation time of the invention is short, and the results are accurate and reliable. Compared with the commercial software Fluent, the calculation time is significantly reduced with the same structure and the same initial boundary value under the same element size and time step, and the calculation accuracy is comparable;

The invention has low cost and high benefit. There is no need to purchase expensive commercial software, which is easy to integrate into the solid rocket motor design and simulation integration platform. It has the intellectual property rights of self-developed software, which is fast and convenient to use, which is helpful for the rapid design, simulation and optimization of the cladding structure, shortening the R&D cycle and reducing R&D costs. cost, and help the rapid advancement of the mission of strengthening the aerospace force.

Claims (6)

1. A method for rapidly calculating a heat transfer process of a solid rocket engine cladding sleeve structure is characterized by comprising the following steps: an input stage, a calculation and calculation process prompting stage, a calculation result display stage and a calculation data storage stage;

the coating sleeve structure of the solid rocket engine is a four-layer structure and comprises a drug column layer, a coating sleeve layer, a fuel gas layer and a combustion chamber shell layer from inside to outside; each layer is hollow cylindrical; in the calculation process, each layer of the cladding sleeve structure is radially divided into a plurality of units, and any unit only belongs to one layer of the four-layer structure;

the input stage is as follows:

(1) inputting the geometric parameters, physical parameters and initial boundary value conditions of a combustion chamber shell layer, a fuel gas layer, a coating sleeve layer and a drug column layer in a coating sleeve structure; setting heat transfer time and setting a geometric parameter reference value of a unit;

and a calculation and calculation process prompt stage, which is specifically as follows:

(2) determining the unit number and unit radial thickness of each layer in the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the drug column layer according to the geometric parameters of the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the drug column layer determined in the step (1) and the set geometric parameter reference values of the units;

(3) determining the physical parameters, inner and outer surface radial coordinates, initial temperature and heat flux density of each unit in the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer according to the geometric parameters, the physical parameters and the initial boundary value conditions of the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer determined in the step (1) and the unit number and the unit radial thickness of each layer in the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer determined in the step (2);

(4) determining the heat transfer time step length and the total number M of the heat transfer time step length of the cladding sleeve structure according to the physical parameters and the radial coordinates of the inner surface and the outer surface of each unit in the combustion chamber shell layer, the fuel gas layer, the cladding sleeve layer and the drug column layer determined in the step (3);

(5) determining the temperature variation of each unit in the 1 st heat transfer time step of the coating structure according to the physical parameters, the radial coordinates of the inner surface and the outer surface, the initial temperature and the heat flux density of each unit in the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer determined in the step (3-4);

(6) recording the serial number of the current heat transfer time step as j (j is 1, 2, …, M), making j be 1, adding the temperature variation of each unit in the 1 st heat transfer time step of the cladding sleeve structure determined in the step (5) to the initial temperature of each unit determined in the step (3) to be used as the temperature of each unit corresponding to the jth heat transfer time step of the cladding sleeve structure;

(7) judging whether j is equal to the total number M of the heat transfer time step; if not, calculating the temperature variation of each unit in the j +1 th heat transfer time step of the coating sleeve structure according to the physical parameters, the radial coordinates of the inner and outer surfaces, the temperature and the heat flow density corresponding to the j heat transfer time step of the combustion chamber shell layer, the gas layer, the coating sleeve layer and the drug column layer, and adding the temperature variation to each unit corresponding to the j +1 th heat transfer time step of the coating sleeve structure to obtain the temperature of each unit corresponding to the j +1 th heat transfer time step of the coating sleeve structure; determining the calculation completion degree W according to the heat transfer time step sequence number j +1 and the total number M of the heat transfer time steps, and making j equal to j + 1; if so, stopping calculating to obtain the temperature of each unit of the cladding sleeve structure after the heat transfer time is over;

and a calculation result display stage, which is specifically as follows:

(8) displaying a temperature chart of each unit of the cladding sleeve structure after the heat transfer time is over;

the calculation data storage stage specifically comprises the following steps:

(9) and storing the temperature data of each unit of the cladding sleeve structure after the heat transfer time is over.

2. The method for rapidly calculating the heat transfer process of the solid rocket engine jacket structure according to claim 1, wherein the method comprises the following steps: the geometric dimension on combustion chamber shell layer, gas layer, cladding jacket layer, explosive column layer includes: the radial thickness of the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer and the radial coordinate of the inner side of the explosive column.

3. The method for rapidly calculating the heat transfer process of the solid rocket engine jacket structure according to claim 1, wherein the method comprises the following steps: the initial boundary value condition of combustion chamber shell layer, gas layer, cladding jacket layer, explosive column layer includes: initial temperature and heat flux density of the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer.

4. The method for rapidly calculating the heat transfer process of the solid rocket engine jacket structure according to claim 1, wherein the method comprises the following steps: physical property parameters including: the density, the heat conductivity coefficient and the constant pressure specific heat capacity of the combustion chamber shell layer, the fuel gas layer, the coating sleeve layer and the explosive column layer.

5. The method for rapidly calculating the heat transfer process of the solid rocket engine jacket structure according to claim 1, wherein the method comprises the following steps: the length of heat transfer is: the total time required for heat transfer of the clad sleeve structure.

6. The method for rapidly calculating the heat transfer process of the solid rocket engine jacket structure according to claim 1, wherein the method comprises the following steps: the geometric parameter reference value of the unit refers to: a reference value for the radial thickness of the cell.

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