Flat heat shield wall temperature calculation method based on air system network automatic numbering and hole row blocking

Abstract

The invention discloses a flat heat shield wall temperature calculation method based on air system network automatic numbering and hole row partitioning, and the method comprises the steps: carrying out the geometric discrete grid division of a wall surface for a flat heat shield in a binary convergent-divergent nozzle in order to accurately calculate the wall surface temperature of the flat heat shield, i.e., dividing a continuous calculation region into a plurality of calculation control bodies, calculating points in all the calculating areas are determined, and heat exchange parameters are calculated through the flow parameters; then, the wall surface temperature is updated through the heat exchange parameters, and the flow heat exchange parameters of the next step are calculated through the new wall surface temperature till the calculation result converges. According to the method, the calculation precision and speed are greatly improved, the wall temperature of the heat insulation screen can be calculated more efficiently and accurately, and then more reliable data support is provided for optimization of a cooling system.

Description

Technical Field

[0001] The invention belongs to the field of aviation technology, and in particular relates to a method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of an air system network and hole row blocking. Background Art

[0002] Existing air system network numbering and blocking technologies have significant limitations. Air system network numbering methods typically rely on manual input or inefficient algorithms to identify and number complex system components, resulting in lengthy calculation times and prone to errors. Furthermore, traditional hole row blocking techniques are often inefficient when dealing with complex geometries and cannot flexibly adapt to changes in different geometric shapes, thus limiting calculation accuracy and speed. These issues are particularly prominent when dealing with large-scale, complex air systems, especially when faced with complex flat-plate thermal shield structures, where traditional methods are unable to quickly provide accurate wall temperature predictions. Summary of the Invention

[0003] To overcome the shortcomings of the existing technology, the present invention provides a method for calculating the wall temperature of a flat-plate heat shield based on automatic air system network numbering and hole row segmentation. For the flat-plate heat shield in a binary convergent-divergent nozzle, to accurately calculate its wall temperature, the wall surface is geometrically discretized into a grid. This involves dividing the continuous calculation region into multiple calculation control volumes, determining the calculation points within each calculation region, and calculating the heat transfer parameters using the flow parameters. The heat transfer parameters are then used to update the wall temperature, and the next flow and heat transfer parameters are calculated using the new wall temperature until the calculation results converge. This invention significantly improves calculation accuracy and speed, enabling more efficient and accurate calculation of the heat shield wall temperature, thereby providing more reliable data support for cooling system optimization.

[0004] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0005] Step 1: Automatic numbering and hole row division;

[0006] Step 2: Calculate air conditioning parameters;

[0007] Step 3: Heat conduction calculation and wall temperature calculation;

[0008] Step 4: Determine whether the wall temperature is stable, that is, determine whether the wall temperature difference obtained in two adjacent cycles is less than the set advance. If it is stable, end the calculation; if it is unstable, restart the convection and radiation heat transfer calculation.

[0009] Preferably, the step 1 is specifically as follows:

[0010] Step 1-1: Determine parameters;

[0011] The cooling system includes the following geometric parameters:

[0012] L1: length of heat shield in convergent section;

[0013] L2: Length of heat shield in expansion section;

[0014] H1: Height of the cold air duct entrance in the convergent section;

[0015] H2: outlet height of the cold air duct in the convergent section;

[0016] H3: Height of the cold air duct entrance in the expansion section;

[0017] H4: end height of the expansion section cold air channel;

[0018] H5: double wall impact height;

[0019] H6: Main stream inlet height;

[0020] H7: throat height;

[0021] H8, mainstream outlet height;

[0022] The geometry of the heat shield is determined by the following parameters:

[0023] The heat shield's flow direction length and span direction width, the distance from the front edge of the heat shield to the first row of holes in the flow direction, the total number of hole rows in the flow direction and span direction, the hole row range and hole row spacing corresponding to each sub-area in the flow direction and span direction, and the diameters of the film holes and impact holes;

[0024] Step 1-2: Mesh division;

[0025] After determining the geometric parameters, the internal node method is used to mesh the two-dimensional heat shield wall.

[0026] The grid division of the two-dimensional heat insulation screen wall is a regular area grid division, which is divided by two clusters of mutually perpendicular straight lines in the flow direction and the span direction; the smallest area enclosed by the grid lines is the calculation unit for the numerical discretization of the two-dimensional heat conduction equation; the center of each calculation unit is the calculation point, and there is also a circle of calculation points at the edge of the wall, which are located in the middle of two adjacent grid lines and on the edge of the wall.

[0027] Preferably, the step 2 is specifically as follows:

[0028] The cooling air flow path of the heat shield is considered a tree-like flow network consisting of an inlet, multiple outlets, and several flow branches. The flow network is divided according to the cooling air flow path. The flow network consists of an inlet, outlet, chamber, and flow branches between chambers. The number of the chamber at the end of the flow branch in the flow network is equal to the branch number, the chamber at the inlet of the cooling air channel is numbered last, and the cooling air channel at the end of the expansion section is closed. The cooling air flows in a one-dimensional steady state on the flow branch, and several flow resistance elements are connected in series on the branch, with calculation points between the elements. During the calculation, the initial values ​​of the cooling air parameters and the aerodynamic parameters of the flow network inlet and outlet are known quantities, while the cooling air flow parameters along the flow network are unknown quantities.

[0029] The steps for solving the cooling air flow parameters in the flow network are as follows:

[0030] (1) Given the network inlet total pressure, total temperature, and outlet static pressure;

[0031] (2) Given the initial Mach number of the cold air inlet, the static pressure of each chamber in the network and the initial value of the flow rate of each branch;

[0032] (3) Calculate the aerodynamic parameters at the inlet of the cooling air duct;

[0033] (4) Calculate the aerodynamic parameters at each calculation point from the beginning to the end of each branch in ascending order of branch number and calculation point number to obtain the static pressure drop of each branch; if the static pressure drop is not equal to the static pressure difference between the first and last chambers of the branch, adjust the branch mass flow rate and recalculate the static pressure drop until they are equal;

[0034] (5) fine-tune the mass flow of each branch and calculate the change in the branch static pressure drop after the branch mass flow is fine-tuned; the ratio of the two is the approximate value of the partial derivative function of the branch mass flow to the branch static pressure drop;

[0035] (6) Calculate whether the net mass flow rate of each chamber is zero; if it is non-zero, list the chamber static pressure correction equations based on the chamber mass flow residual and the approximate value of the partial derivative function of the branch mass flow rate with respect to the static pressure drop, solve them, and return to (4) after correcting the chamber static pressure;

[0036] (7) Calculate the Mach number and total pressure based on the inlet mass flow rate, static pressure, and total temperature;

[0037] (8) If the total pressure at the cold air inlet is inconsistent with the specified total pressure at the cold air inlet, the total pressure at the cold air inlet is assigned to the specified total pressure, the Mach number at the cold air inlet is the current value, and the process returns to (3); otherwise, the cold air flow calculation ends;

[0038] (9) During the chamber static pressure correction process, the flow parameters in each branch are continuous; when the static pressure correction is completed and the mass conservation flow network is obtained, the flow parameters of the cooling air are continuous and accurate between the branches, and the cooling air parameter solution is completed at this time.

[0039] Preferably, the step 3 is specifically as follows:

[0040] Step 3-1: Control equations;

[0041] In the rectangular coordinate system, the two-dimensional constant steady-state heat conduction equation with internal heat source is:

[0042]

[0043] Where T = T(x,y) represents the temperature field; x and y are rectangular coordinates; λ is the thermal conductivity of the material; S is the internal heat source intensity per unit volume, in W / m 3 ;

[0044] The air film plate, impact plate, and outer wall are regarded as two-dimensional planes without thickness, and heat conduction along the wall thickness direction is not considered. Equation (1) is the governing equation for solving the heat conduction inside the wall.

[0045] Step 3-2: numerical discretization;

[0046] Assuming uniform temperature inside the microelement and uniform heat flux density on the boundary, the energy of the microelement represented by the microelement P is conserved, and the heat transfer process occurs between the microelement P and a heat source with a driving temperature difference from P. Heat conduction occurs between the microelement P and the four microelement bodies surrounding it. There are solid or gas heat sources above and below P, and heat exchange occurs through radiation with the solid heat source and convection and radiation with the gas heat source.

[0047] Use formula (1) to integrate the infinitesimal body P;

[0048] Thermal conduction integral:

[0049]

[0050] in,

[0051]

[0052] Where, T E is the temperature of block E, Q is the heat flow, the subscript cond represents heat conduction, conv represents convection heat transfer, rad represents radiation heat transfer, down represents the direction below the wall, and up represents the direction above the wall;

[0053] In formula (1), the source term S includes the heat flux density of convective heat transfer between the microelement P and the fluids on both sides, and the heat flux density of radiative heat transfer between the microelement P and the radiative heat sources on both sides. The source term S is integrated over the volume of the microelement and the heat flux density to become the heat flux of the heat transfer surface.

[0054]

[0055] The heat flow is expressed in terms of temperature, pressure and total area thermal resistance:

[0056]

[0057] The control equation after discretization is:

[0058]

[0059] After moving:

[0060] A P T P =A W T W +A E T E +A N T N +A S T S

[0061] +A conv,down T conv,down +A conv,up T conv,up +A rad,down T rad,down +A rad,up T rad,up (6)

[0062] in:

[0063] A P =A W +A E +A N +A S +A conv,down +A conv,up +A rad,down +A rad,up (7)

[0064]

[0065] Where R is the total area thermal resistance;

[0066] Step 3-3: Step 3-2 is to numerically discretize the governing equation in the middle region of the wall. At the edge of the wall, the wall temperature is calculated based on the boundary condition type of the heat conduction problem. There are three types of boundary conditions for heat conduction problems:

[0067] (1) Given boundary temperature;

[0068] (2) heat flux density on a given boundary;

[0069] (3) Heat source temperature and heat transfer resistance on a given boundary;

[0070] For steady-state problems, the boundary temperature, boundary heat flux, heat transfer resistance, and heat transfer temperature are constant. The leading edges of the expansion section air film plate, expansion section impact plate, and expansion section outer wall are first-class boundary conditions. During calculations, the temperature of the leading edge calculation point of the expansion section air film plate and impact plate is equal to the temperature of the corresponding calculation point on the trailing edge of the convergence section air film plate. The temperature of the leading edge calculation point of the expansion section outer wall is equal to the temperature of the corresponding calculation point on the trailing edge of the convergence section outer wall.

[0071] The remaining edges of the wall are second-type boundary conditions with zero heat flux. When calculating, the temperature of the outermost calculation point on the edge is equal to the temperature of the adjacent calculation point in the second outermost layer. When calculating the wall temperature, the temperature of the non-edge calculation point is calculated first, and then the temperature of the second outermost calculation point is assigned to the outermost layer.

[0072] Preferably, the step 4 is specifically as follows:

[0073] Step 4-1: Convective heat transfer;

[0074] Step 4-1-1: Convection heat transfer on the gas side of the heat shield;

[0075] The heat flux density calculation formula of the convection heat transfer between the film plate and the mainstream during film cooling is:

[0076] q=h aw (T aw -T w ) (9)

[0077] Where, T aw is the adiabatic wall temperature; h aw is the convective heat transfer coefficient defined by the adiabatic wall temperature; T w is the wall temperature;

[0078] Step 4-1-2: The convective heat transfer coefficient is calculated using the following empirical correlation formula:

[0079]

[0080] Where λ is the thermal conductivity of the gas; D h is the hydraulic diameter of the mainstream channel; Re is the Reynolds number of the gas flow; Pr is the Prandtl number of the gas;

[0081] Step 4-1-3: Calculation formula for adiabatic wall temperature:

[0082] T aw (x) = T g (x)-η(x)[T g (x)-T c ] (11)

[0083] Where, T g (x) is the static temperature of the gas flowing to a certain location; T cis the static temperature of the cold air at a certain outflow position; η(x) is the adiabatic film cooling effect at a certain position; when calculating, the adiabatic film cooling effect downstream of a single hole is calculated first, and then the cooling effect superposition between multiple rows of holes is considered;

[0084] Step 4-2: Radiative heat transfer;

[0085] Step 4-2-1: Radiation heat exchange between gas and air film plate;

[0086] Select the empirical correlation formula for calculating the heat flux density of the radiation heat transfer between the combustion chamber gas and the heat insulation screen:

[0087]

[0088] Where: σ is the Stefan-Boltzmann constant, σ = 5.67 × 10 -8 W / (m 2 ·K), ε g The gas at temperature T g The emissivity under w The wall is at temperature T w emissivity under ;

[0089] Thermal resistance per unit area of ​​radiation heat transfer:

[0090]

[0091] Step 4-2-2: Radiation heat transfer between walls;

[0092] The radiation heat transfer between the convergent film plate and the outer wall of the convergent section, the divergent film plate and the impact plate, and the divergent impact plate and the outer wall are all considered as radiation heat transfer systems between two infinite parallel plates with an angle coefficient of 1. The radiation heat flux density is calculated using the following formula:

[0093]

[0094] Where: σ is the Stefan-Boltzmann constant, ε1 and ε2 are the wall emissivities, T1 and T2 are the wall temperatures, A1 and A2 are the heat transfer areas, and A1 / A2 = 1;

[0095] Thermal resistance per unit area of ​​radiation heat transfer:

[0096]

[0097] Step 4-2-3: Radiation heat exchange between the outer wall and the environment;

[0098] The radiation heat transfer between the nozzle outer wall and the environment is considered as a radiation heat transfer system between a non-concave surface and an infinite space, with a angular coefficient of 1. The radiation heat flux density is calculated using the following formula:

[0099]

[0100] Among them, T w is the outer wall temperature, T ∞ is the ambient temperature, ε w is the outer wall emissivity;

[0101] Thermal resistance per unit area of ​​radiation heat transfer:

[0102]

[0103] A computer program enables a computer to execute the above-mentioned method for calculating the wall temperature of a flat-plate heat insulation screen.

[0104] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above-mentioned flat-plate thermal insulation screen wall temperature calculation method.

[0105] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for calculating the wall temperature of a flat-plate heat insulation screen.

[0106] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned method for calculating the wall temperature of a flat-plate heat insulation screen.

[0107] A computer program product, comprising a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and wherein when the instructions are executed by the at least one processor, the above-mentioned method for calculating the wall temperature of a flat thermal insulation screen is implemented.

[0108] The beneficial effects of the present invention are as follows:

[0109] The present invention is an improvement on the traditional air system network numbering method. It can realize the rapid, efficient and modular identification and numbering of complex air system components, improve the automation level and calculation efficiency of the calculation program, and realize the rapid and efficient calculation of wall temperature. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 Flow chart of the method of the present invention;

[0111] Figure 2 Schematic diagram of the geometric parameters of the heat shield;

[0112] Figure 3 Schematic diagram of setting hole row spacing and hole spacing for different areas of the heat shield;

[0113] Figure 4This is a schematic diagram of the division of calculation points along the flow direction of gas and cold air;

[0114] Figure 5 Provide a schematic diagram for flow network division;

[0115] Figure 6 Schematic diagram of flow branches in the cold air channel;

[0116] Figure 7 The process of solving the cooling parameters; DETAILED DESCRIPTION

[0117] The present invention will be further described below with reference to the accompanying drawings and examples.

[0118] This paper establishes a thermal analysis and calculation method for the wall temperature of a flat heat shield in a binary convergent-divergent nozzle. To accurately calculate the wall temperature of a flat heat shield operating between the gas, cold air, and ambient medium, the wall surface must first be geometrically discretized. This involves dividing the continuous calculation region into multiple computational control volumes and determining the computational points within each region. Specifically, this process includes the following key steps:

[0119] 1. Input geometric parameters into the calculation program to determine the wall shape;

[0120] 2. Use the internal node method to mesh the wall surface to form a computational grid;

[0121] 3. Run the calculation program to predict the insulation wall temperature and optimize the cooling system design accordingly.

[0122] This paper proposes an improved automatic numbering and hole row segmentation technology for air system networks. Leveraging advanced algorithms and modular design, it enables rapid, automated identification and numbering of complex air system components. By optimizing the geometric parameter input method, this invention not only improves air system processing efficiency but also significantly reduces the error rate caused by human error. Furthermore, the improved hole row segmentation method can flexibly adapt to changes in complex geometric shapes, significantly improving calculation accuracy and speed. These innovations enable the present invention to more efficiently and accurately calculate the insulation shield wall temperature, thereby providing more reliable data support for cooling system optimization.

[0123] The calculation method of this invention is based on an iterative solution approach: first, the heat transfer parameters are calculated using the flow parameters; then, the wall temperature is updated using the heat transfer parameters, and the next flow and heat transfer parameters are calculated using the new wall temperature until the calculation results converge. In this calculation process, the geometric parameter setting of the heat shield is a key initial step, while the automatic numbering and hole row block division of the air system network play an important role in data reading and meshing. Figure 1 The process shown is shown.

[0124] The air system network automatic numbering and hole row blocking technology proposed in this invention is an improvement on the traditional air system network numbering method. It aims to achieve fast, efficient, modular identification and numbering of complex air system components, improve the automation level and calculation efficiency of the calculation program, and realize fast and efficient calculation of wall temperature.

[0125] Hole row block-mesh division:

[0126] Before calculating the flow parameters of gas and cold air, and the temperature of the heat insulation screen and outer wall, the calculation domain must be gridded, the spatially continuous calculation area must be divided into many calculation control volumes, and the calculation points of each calculation control volume must be determined.

[0127] Before meshing, the geometric parameters of the flat heat shield cooling system must be determined, such as Figure 4 The cooling system has the following geometric parameters: L1, the length of the heat shield in the convergent section; L2, the length of the heat shield in the divergent section; H1, the height of the inlet of the convergent section cooling channel; H2, the height of the outlet of the convergent section cooling channel; H3, the height of the inlet of the divergent section cooling channel; H4, the end height of the divergent section cooling channel; H5, the height of the double wall impact; H6, the height of the mainstream inlet; H7, the height of the throat; H8, the height of the mainstream outlet. Figure 2 The geometric shape of a heat shield is determined by the following parameters: the flow direction length and span direction width of the heat shield, the distance from the leading edge of the heat shield to the first row of holes in the flow direction, the total number of hole rows in the flow direction and span direction, the hole row range and hole row spacing corresponding to each sub-area in the flow direction and span direction, and the diameters of the film holes and impact holes. Figure 3 Representing a rectangular opening wall, the hole row spacing is set in different areas within the range of different hole rows in the flow direction and span direction, which can meet the requirements of zoned opening in the flow direction and span direction.

[0128] After determining the geometric parameters, the internal node method is used to divide the two-dimensional wall into grids, see Figure 3 Lower left area. The grid division of the two-dimensional heat insulation screen wall is the grid division of regular areas, which can be divided by two clusters of mutually perpendicular straight lines (grid lines) in the flow direction and the span direction. The smallest area enclosed by the grid lines is the calculation unit for the numerical discretization of the two-dimensional heat conduction equation. The center of each calculation unit is the calculation point, and there is also a circle of calculation points on the edge of the wall. They are located in the middle of two adjacent grid lines and on the edge of the wall. To solve the wall temperature, it is necessary to know the heat transfer parameters (heat transfer temperature, heat transfer, heat transfer resistance) on both sides of each calculation point on the wall. The mainstream, cold air channel, and environment must all be gridded. The parameters of the mainstream gas vary along the flow direction and the span direction, and the calculation points correspond one-to-one to the calculation points on the wall; the solution of the cold air flow parameters is one-dimensional along the flow direction, and there is only one calculation node in the span direction; the flow and heat transfer parameters on the environment side are constant, and no calculation points are divided. Figure 4 Indicates the calculation points along the flow direction in the cold air channel and near the wall of the mainstream.

[0129] Flow Network Method:

[0130] The cooling air flow path of the heat shield can be regarded as a tree-like flow network consisting of one inlet, multiple outlets and several flow branches. Figure 5 The flow network is shown in Figure 1. The flow network consists of an inlet, an outlet, a chamber, and flow branches between chambers. The chamber at the end of a flow branch in the flow network is numbered equal to the branch number. The chamber at the inlet of the cooling channel is numbered last. The cooling channel at the end of the expansion section is closed. The cooling air flows in a one-dimensional steady state on the flow branch. Several flow resistance elements are connected in series on the branch, and the calculation points are between the elements, such as Figure 6 During the calculation, the initial values ​​of the cooling air parameters and the aerodynamic parameters at the inlet and outlet of the flow network are known, while the cooling air flow parameters along the process are unknown.

[0131] The steps for solving the cooling air flow parameters in the flow network are as follows:

[0132] (1) Given the network inlet total pressure, total temperature, and outlet static pressure;

[0133] (2) Given the initial Mach number of the cold air inlet, the static pressure of each chamber in the network and the initial value of the flow rate of each branch;

[0134] (3) Calculate the aerodynamic parameters at the inlet of the cooling air duct;

[0135] (4) Calculate the aerodynamic parameters at each calculation point from the beginning of each branch to the end of each branch in ascending order of branch number and calculation point number to obtain the static pressure drop of each branch. If the static pressure drop is not equal to the static pressure difference between the first and last chambers of the branch, adjust the branch mass flow rate and recalculate the static pressure drop until they are equal.

[0136] (5) Fine-tune the mass flow of each branch and calculate the change in the branch static pressure drop after the fine-tuning of the branch mass flow. The ratio of the two is the approximate value of the partial derivative function of the branch mass flow with respect to the branch static pressure drop;

[0137] (6) Calculate whether the net mass flow rate of each chamber is zero. If it is non-zero, list and solve the chamber static pressure correction equations based on the chamber mass flow residual and the partial derivative function value of the branch mass flow with respect to the static pressure drop. After correcting the chamber static pressure, return to (4).

[0138] (7) Calculate the Mach number and total pressure based on the inlet mass flow rate, static pressure, and total temperature.

[0139] (8) If the total pressure at the cold air inlet is inconsistent with the specified total pressure at the cold air inlet, the total pressure at the cold air inlet is assigned to the specified total pressure, the Mach number at the cold air inlet is the current value, and the process returns to (3). Otherwise, the cold air flow calculation ends.

[0140] (Explanation: The inlet static pressure of the flow network at (3)-(7) remains unchanged. If the total pressure at the cold air inlet at (8) is greater than the specified total pressure, it means that the current cold air inlet Mach number and mass flow rate are too large. The cold air inlet total pressure is assigned a specified value. After correcting the chamber static pressure again, the flow rate in the flow network is reduced, and more accurate cold air flow parameters are obtained.)

[0141] (9) During the chamber static pressure correction process, the flow parameters within each branch are continuous. When the static pressure correction is completed and the mass conservation flow network is obtained, the cooling air flow parameters are continuous and accurate between the branches, and the cooling air parameter solution is completed.

[0142] Step 3: Calculation of heat conduction and wall temperature;

[0143] The purpose of solving the heat conduction equation is to obtain the wall temperature corresponding to the current flow and heat transfer parameters. The temperatures of the convergent film plate, the divergent film plate and the impingement plate, and the nozzle outer wall are all obtained by solving the two-dimensional heat conduction equation.

[0144] 1. Control equation:

[0145] In the rectangular coordinate system, the two-dimensional constant steady-state heat conduction equation with internal heat source is:

[0146]

[0147] If the film plate, impact plate, and outer wall are considered as two-dimensional planes without thickness and heat conduction along the wall thickness is not considered, then the above equation is the governing equation for heat conduction within the wall. This equation includes the net heat flux from conduction in the x and y directions and the heat source term within the wall.

[0148] The energy of the microelement represented by the calculation point P is conserved, and the heat transfer process occurs between the microelement P and a heat source with a driving temperature difference from P. Heat conduction occurs between the microelement P and the four microelement bodies around it; there are solid or gas heat sources above and below P, and heat transfer occurs through radiation with the solid heat source and convection and radiation with the gas heat source. Numerical Discretization

[0149] Assuming that the temperature inside the microelement is uniform and the heat flux density on the boundary is uniform, formula (1) Figure 2 The infinitesimal body P is shown as an integral.

[0150] Thermal conduction integral:

[0151]

[0152] in:

[0153]

[0154] In Equation (1), the source term S includes the convective heat flux between the microelement P and the fluids on both sides, and the radiative heat flux between the microelement P and the radiative heat sources on both sides. The source term S is integrated over the volume of the microelement, and the integrated heat flux becomes the heat flux of the heat transfer surface.

[0155]

[0156] The heat flow is expressed in terms of temperature, pressure and total area thermal resistance:

[0157]

[0158] The control equation after discretization is:

[0159]

[0160] After moving:

[0161] A P T P =A W T W +A E T E +A N T N +A S T S

[0162] +A conv,down T conv,down +A conv,up T conv,up +A rad,down T rad,down +A rad,up T rad,up (6)

[0163] in:

[0164] A P =A W +A E +A N +A S +A conv,down +A conv,up +A rad,down +A rad,up (7)

[0165]

[0166] The above is the numerical discretization of the control equation in the middle area of ​​the wall. At the edge of the wall, the wall temperature must be calculated according to the boundary condition type of the heat conduction problem. There are three types of boundary conditions for heat conduction problems: (1) given boundary temperature; (2) given heat flux density on the boundary; (3) given heat source temperature and heat transfer resistance on the boundary. For steady-state problems, the above boundary temperature, boundary heat flux density, heat transfer resistance and heat transfer temperature are constant. The leading edge of the expansion section air film plate, expansion section impact plate and expansion section outer wall are the first type of boundary conditions. When calculating, let the temperature of the calculation point at the leading edge of the expansion section air film plate and impact plate be equal to the temperature of the corresponding calculation point on the trailing edge of the convergence section air film plate; let the temperature of the calculation point at the leading edge of the expansion section outer wall be equal to the temperature of the corresponding calculation point at the trailing edge of the convergence section outer wall. The remaining edges of the wall are the second type of boundary conditions, with zero heat flux density. When calculating, let the temperature of the outermost calculation point of the edge be equal to the temperature of the adjacent calculation point in the next outermost layer. When calculating the wall temperature, the temperature of the non-edge calculation point is calculated first, and then the temperature of the second outermost calculation point is assigned to the outermost layer.

[0167] Step 5: Determine whether the wall temperature is stable, that is, determine whether the wall temperature difference obtained in two adjacent cycles is less than the set advance. If it is stable, end the calculation; if it is unstable, restart the convection and radiation heat transfer calculation.

[0168] Convection and radiation heat transfer calculations:

[0169] Convective heat transfer:

[0170] (1) Convective heat transfer on the gas side of the heat shield

[0171] The heat flux density calculation formula of the convection heat transfer between the film plate and the mainstream during film cooling is:

[0172] q=h aw (T aw -T w ) (9)

[0173] Where, T aw is the adiabatic wall temperature; h aw is the convective heat transfer coefficient defined by the adiabatic wall temperature; T w is the wall temperature.

[0174] The convective heat transfer coefficient is calculated using the following empirical correlation:

[0175]

[0176] Where λ is the thermal conductivity of the gas; D h is the hydraulic diameter of the mainstream channel; Re is the Reynolds number of the gas flow; Pr is the Prandtl number of the gas.

[0177] The calculation formula of adiabatic wall temperature is:

[0178] Taw (x) = T g (x)-η(x)[T g (x)-T c ] (11)

[0179] Where, T g (x) is the static temperature of the gas flowing to a certain location; T c is the static temperature of the cold air at a specific outflow location; η(x) is the adiabatic film cooling effect at a specific location. The film holes on the film plate are arranged in a staggered pattern. The calculation of the adiabatic film cooling effect requires considering the combined cooling effects of multiple rows of holes. The calculation begins with the adiabatic film cooling effect downstream of a single hole, then considers the combined cooling effects of multiple rows of holes.

[0180] Radiative heat transfer:

[0181] (1) Radiative heat exchange between gas and air film plate

[0182] Select the empirical correlation formula for calculating the heat flux density of the radiation heat transfer between the combustion chamber gas and the heat insulation screen:

[0183]

[0184] Where: σ is the Stefan-Boltzmann constant, σ = 5.67 × 10 -8 W / (m 2 ·K), ε g The gas at temperature T g The emissivity under w The wall is at temperature T w The emissivity under .

[0185] Thermal resistance per unit area of ​​radiation heat transfer:

[0186]

[0187] (2) Radiation heat transfer between walls

[0188] The radiation heat transfer between the convergent film plate and the outer wall of the convergent section, the divergent film plate and the impact plate, and the divergent impact plate and the outer wall can all be regarded as a radiation heat transfer system between two infinite parallel plates with an angle coefficient of 1. The radiation heat flux density is calculated using the following formula:

[0189]

[0190] Where: σ is the Stefan-Boltzmann constant, ε1 and ε2 are the wall emissivities, T1 and T2 are the wall temperatures, A1 and A2 are the heat transfer areas, and A1 / A2=1.

[0191] Thermal resistance per unit area of ​​radiation heat transfer:

[0192]

[0193] (3) Radiation heat exchange between the outer wall and the environment

[0194] The radiation heat transfer between the nozzle outer wall and the environment can be regarded as a radiation heat transfer system between a non-concave surface and an infinite space, with an angle coefficient of 1. The radiation heat flux density is calculated using the following formula:

[0195]

[0196] Among them, T w is the outer wall temperature, T ∞ is the ambient temperature, ε w is the outer wall emissivity, and σ is the radiation constant.

[0197] Thermal resistance per unit area of ​​radiation heat transfer:

[0198]

[0199] A thermal analysis program was developed for a flat-plate heat shield cooling system with a two-dimensional converging-diverging nozzle, taking into account the coupling relationships between various flow and heat exchange links. This program is suitable for mainstream flows with variable cross-sections in two-dimensional converging-diverging nozzles. It features the ability to set the hole spacing in different regions along the flow and span directions, and can calculate the complete two-dimensional temperature field of the heat shield.

[0200] Input data:

[0201] Input parameters: nozzle mainstream channel geometry, heat shield wall geometry and outlet hole arrangement, cooling air channel geometry, and outer wall geometry. Mainstream inlet aerodynamic parameters, nozzle exit back pressure, cooling air inlet aerodynamic parameters, atmospheric static parameters, and flight Mach number.

[0202] Output parameters: flow parameters of gas and cold air, heat flux density and thermal resistance of convection and radiation heat exchange links, and temperature of each wall surface.

[0203] Global variables are uniformly declared in the parameter declaration module, temporary variables are declared in each subroutine, and each subroutine references the parameter declaration module for data transfer.

[0204] Calculation process:

[0205] Determine the relationship between input data, mesh division, flow solution, convection and radiation heat transfer solution, and wall temperature solution. Figure 1 The solution process is shown in Figure 1. The program iterates through the flow-heat-wall temperature cycle to obtain converged results. The calculation is terminated when the wall temperatures obtained in two consecutive iterations are sufficiently close.

Claims

1. A method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of air system networks and hole row division, characterized in that: The steps include: Step 1: Automatic numbering and hole row division; Step 2: Calculate air conditioning parameters; Step 3: Heat conduction calculation and wall temperature calculation; Step 4: Determine whether the wall temperature is stable, that is, determine whether the wall temperature difference obtained in two adjacent cycles is less than the set advance. If it is stable, end the calculation; if it is unstable, restart the convection and radiation heat transfer calculation.

2. A method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of air system networks and hole row division according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Determine parameters; The cooling system includes the following geometric parameters: L1: length of heat shield in convergent section; L2: Length of heat shield in expansion section; H1: Height of the cold air duct entrance in the convergent section; H2: outlet height of the cold air duct in the convergent section; H3: Height of the cold air duct entrance in the expansion section; H4: end height of the expansion section cold air channel; H5: double wall impact height; H6: Main stream inlet height; H7: throat height; H8, mainstream outlet height; The geometry of the heat shield is determined by the following parameters: The heat shield's flow direction length and span direction width, the distance from the front edge of the heat shield to the first row of holes in the flow direction, the total number of hole rows in the flow direction and span direction, the hole row range and hole row spacing corresponding to each sub-area in the flow direction and span direction, and the diameters of the film holes and impact holes; Step 1-2: Mesh division; After determining the geometric parameters, the internal node method is used to mesh the two-dimensional heat shield wall. The grid division of the two-dimensional heat insulation screen wall is a regular area grid division, which is divided by two clusters of mutually perpendicular straight lines in the flow direction and the span direction; the smallest area enclosed by the grid lines is the calculation unit for the numerical discretization of the two-dimensional heat conduction equation; the center of each calculation unit is the calculation point, and there is also a circle of calculation points at the edge of the wall, which are located in the middle of two adjacent grid lines and on the edge of the wall.

3. A method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of air system networks and hole row division according to claim 2, characterized in that: The step 2 is specifically as follows: The cooling air flow path of the heat shield is considered a tree-like flow network consisting of an inlet, multiple outlets, and several flow branches. The flow network is divided according to the cooling air flow path. The flow network consists of an inlet, outlet, chamber, and flow branches between chambers. The number of the chamber at the end of the flow branch in the flow network is equal to the branch number, the chamber at the inlet of the cooling air channel is numbered last, and the cooling air channel at the end of the expansion section is closed. The cooling air flows in a one-dimensional steady state on the flow branch, and several flow resistance elements are connected in series on the branch, with calculation points between the elements. During the calculation, the initial values ​​of the cooling air parameters and the aerodynamic parameters of the flow network inlet and outlet are known quantities, while the cooling air flow parameters along the flow network are unknown quantities. The steps for solving the cooling air flow parameters in the flow network are as follows: (1) Given the network inlet total pressure, total temperature, and outlet static pressure; (2) Given the initial Mach number of the cold air inlet, the static pressure of each chamber in the network and the initial value of the flow rate of each branch; (3) Calculate the aerodynamic parameters at the inlet of the cooling air duct; (4) Calculate the aerodynamic parameters at each calculation point from the beginning to the end of each branch in ascending order of branch number and calculation point number to obtain the static pressure drop of each branch; if the static pressure drop is not equal to the static pressure difference between the first and last chambers of the branch, adjust the branch mass flow rate and recalculate the static pressure drop until they are equal; (5) fine-tune the mass flow of each branch and calculate the change in the branch static pressure drop after the branch mass flow is fine-tuned; the ratio of the two is the approximate value of the partial derivative function of the branch mass flow to the branch static pressure drop; (6) Calculate whether the net mass flow rate of each chamber is zero; If it is non-zero, the chamber static pressure correction equations are listed and solved based on the approximate values ​​of the partial derivative functions of the chamber mass flow residual and the branch mass flow to the static pressure drop, and the chamber static pressure is corrected and returned to (4); (7) Calculate the Mach number and total pressure based on the inlet mass flow rate, static pressure, and total temperature; (8) If the total pressure at the cold air inlet is inconsistent with the specified total pressure at the cold air inlet, the total pressure at the cold air inlet is assigned to the specified total pressure, the Mach number at the cold air inlet is the current value, and the process returns to (3); otherwise, the cold air flow calculation is terminated; (9) During the chamber static pressure correction process, the flow parameters in each branch are continuous; when the static pressure correction is completed and the mass conservation flow network is obtained, the flow parameters of the cooling air are continuous and accurate between the branches, and the cooling air parameter solution is completed at this time.

4. A method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of air system networks and hole row division according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: Control equations; In the rectangular coordinate system, the two-dimensional constant steady-state heat conduction equation with internal heat source is: Where T = T(x,y) represents the temperature field; x and y are rectangular coordinates; λ is the thermal conductivity of the material; S is the internal heat source intensity per unit volume, in W / m 3 ; The air film plate, impact plate, and outer wall are regarded as two-dimensional planes without thickness, and heat conduction along the wall thickness direction is not considered. Equation (1) is the governing equation for solving the heat conduction inside the wall. Step 3-2: numerical discretization; Assuming that the temperature inside the microelement is uniform, the heat flux density on the boundary is uniform, the energy of the microelement represented by the microelement P is conserved, and the heat transfer process occurs between the microelement P and the heat source with a driving temperature difference from P; Heat conduction occurs between the microelement P and the four microelements around it; there are solid or gas heat sources above and below P, which exchange heat with the solid heat source through radiation and with the gas heat source through convection and radiation; Use formula (1) to integrate the infinitesimal body P; Thermal conduction integral: in, Where, T E is the temperature of block E, Q is the heat flow, the subscript cond represents heat conduction, conv represents convection heat transfer, rad represents radiation heat transfer, down represents the direction below the wall, and up represents the direction above the wall; In formula (1), the source term S includes the heat flux density of convective heat transfer between the microelement P and the fluids on both sides, and the heat flux density of radiative heat transfer between the microelement P and the radiative heat sources on both sides. The source term S is integrated over the volume of the microelement and the heat flux density to become the heat flux of the heat transfer surface. The heat flow is expressed in terms of temperature, pressure and total area thermal resistance: The control equation after discretization is: After moving: A P T P =A W T W +A E T E +A N T N +A S T S +A conv,down T conv,down +A conv,up T conv,up +A rad,down T rad,down +A rad,up T rad,up (6) in: A P =A W +A E +A N +A S +A conv,down +A conv,up +A rad,down +A rad,up (7) Where R is the total area thermal resistance; Step 3-3: Step 3-2 is to numerically discretize the governing equation in the middle region of the wall. At the edge of the wall, the wall temperature is calculated based on the boundary condition type of the heat conduction problem. There are three types of boundary conditions for heat conduction problems: (1) Given boundary temperature; (2) heat flux density on a given boundary; (3) Heat source temperature and heat transfer resistance on a given boundary; For steady-state problems, the boundary temperature, boundary heat flux, heat transfer resistance, and heat transfer temperature are constant. The leading edges of the expansion section air film plate, expansion section impact plate, and expansion section outer wall are first-class boundary conditions. During calculations, the temperature of the leading edge calculation point of the expansion section air film plate and impact plate is equal to the temperature of the corresponding calculation point on the trailing edge of the convergence section air film plate. The temperature of the leading edge calculation point of the expansion section outer wall is equal to the temperature of the corresponding calculation point on the trailing edge of the convergence section outer wall. The remaining edges of the wall are second-type boundary conditions with zero heat flux. When calculating, the temperature of the outermost calculation point on the edge is equal to the temperature of the adjacent calculation point in the second outermost layer. When calculating the wall temperature, the temperature of the non-edge calculation point is calculated first, and then the temperature of the second outermost calculation point is assigned to the outermost layer.

5. A method for calculating the wall temperature of a flat thermal insulation screen based on automatic numbering of air system networks and hole row division according to claim 4, characterized in that: The step 4 is specifically as follows: Step 4-1: Convective heat transfer; Step 4-1-1: Convection heat transfer on the gas side of the heat shield; The heat flux density calculation formula of the convection heat transfer between the film plate and the mainstream during film cooling is: q=h aw (T aw -T w ) (9) Where, T aw is the adiabatic wall temperature; h aw is the convective heat transfer coefficient defined by the adiabatic wall temperature; T w is the wall temperature; Step 4-1-2: The convective heat transfer coefficient is calculated using the following empirical correlation formula: Where λ is the thermal conductivity of the gas; D h is the hydraulic diameter of the mainstream channel; Re is the Reynolds number of the gas flow; Pr is the Prandtl number of the gas; Step 4-1-3: Calculation formula for adiabatic wall temperature: T aw (x)=T g (x)-η(x)[T g (x)-T c ] (11) Where, T g (x) is the static temperature of the gas flowing to a certain location; T c is the static temperature of the cold air at a certain outflow location; η(x) is the adiabatic film cooling effect at a certain position; When calculating, the cooling effect of the adiabatic film downstream of a single hole is calculated first, and then the cooling effect superposition between multiple rows of holes is considered; Step 4-2: Radiative heat transfer; Step 4-2-1: Radiation heat exchange between gas and air film plate; Select the empirical correlation formula for calculating the heat flux density of the radiation heat transfer between the combustion chamber gas and the heat insulation screen: Where: σ is the Stefan-Boltzmann constant, σ = 5.67 × 10 -8 W / (m 2 ·K), ε g The gas at temperature T g The emissivity under w The wall is at temperature T w emissivity under ; Thermal resistance per unit area of ​​radiation heat transfer: Step 4-2-2: Radiation heat transfer between walls; The radiation heat transfer between the convergent film plate and the outer wall of the convergent section, the divergent film plate and the impact plate, and the divergent impact plate and the outer wall are all considered as radiation heat transfer systems between two infinite parallel plates with an angle coefficient of 1. The radiation heat flux density is calculated using the following formula: Where: σ is the Stefan-Boltzmann constant, ε1 and ε2 are the wall emissivities, T1 and T2 are the wall temperatures, A1 and A2 are the heat transfer areas, and A1 / A2 = 1; Thermal resistance per unit area of ​​radiation heat transfer: Step 4-2-3: Radiation heat exchange between the outer wall and the environment; The radiation heat transfer between the nozzle outer wall and the environment is considered as a radiation heat transfer system between a non-concave surface and an infinite space, with a angular coefficient of 1. The radiation heat flux density is calculated using the following formula: Among them, T w is the outer wall temperature, T ∞ is the ambient temperature, ε w is the outer wall emissivity; Thermal resistance per unit area of ​​radiation heat transfer:

6. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 5.

7. An electronic device, characterized in that: include: processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

9. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes the method according to any one of claims 1 to 5.

10. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 5 is implemented.

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