CN118211517B - Jet flow pneumatic/infrared radiation coupling gradient calculation method based on accompanying method - Google Patents
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Abstract
The invention discloses a jet flow pneumatic/infrared radiation coupling gradient calculation method based on an accompanying method, which comprises the following steps: based on an integral form jet radiation transfer equation, a Lagrangian multiplier is introduced to obtain an accompanying equation of the infrared radiation problem; and solving the adjoint equation of the infrared radiation problem to obtain adjoint variables, and obtaining the gradient based on the adjoint method according to the adjoint variables. The invention can realize the rapid solving of the infrared radiation gradient.
Description
Technical Field
The invention relates to the technical field of jet infrared radiation optimization design of aircrafts, in particular to a jet pneumatic/infrared radiation coupling gradient calculation method based on an accompanying method.
Background
The tail jet is one of the important radiation sources of the infrared radiation of the exhaust system of the aircraft, the size of the tail jet can be several times of the size of the aircraft, and the infrared radiation can be detected in a wide angle range. The spray pipe appearance design can increase the mixing between the high-temperature jet flow and the environment atmosphere by increasing the contact area between the outlet jet flow and the external environment, and reduce the temperature of the tail jet flow, thereby achieving the purpose of inhibiting the infrared radiation illuminance. The data show that the infrared radiation illuminance of the tail jet can be reduced by 60% by adopting the blending technology. At present, the research on the spray tube appearance optimization design method aiming at the infrared radiation of the tail jet is less, the published research at present mainly adopts a trial-and-error method, the influence of the geometric parameters on the infrared radiation illuminance is discussed through manual change of the geometric parameters, and the automation of the design process is difficult to realize, so that the development of the design method suitable for the infrared radiation optimization of the tail jet is needed.
The accompanying method is an important method for precisely designing the high-dimensional design problem based on the gradient by deducing the accompanying equation of the control equation, solving the control equation once and solving the accompanying equation once to accurately and efficiently acquire the gradient of the objective function. How to apply the accompanying method to the spray pipe appearance design to realize the jet flow infrared radiation illuminance inhibition is the key for improving the pneumatic/infrared meter efficiency of the aircraft spray pipe.
Disclosure of Invention
In view of the above, the invention provides a jet flow pneumatic/infrared radiation coupling gradient calculation method based on an accompanying method, which solves the pneumatic/infrared radiation coupling accompanying equation to realize efficient and high-precision solving of the infrared radiation gradient.
The invention discloses a jet flow pneumatic/infrared radiation coupling gradient calculation method based on an accompanying method, which comprises the following steps:
Based on an integral form jet radiation transfer equation, a Lagrangian multiplier is introduced to obtain an accompanying equation of the infrared radiation problem; and solving the adjoint equation of the infrared radiation problem to obtain adjoint variables, and obtaining the gradient based on the adjoint method according to the adjoint variables.
Further, solving an integral form of the jet radiation transfer equation, ignoring wall contribution and atmospheric attenuation, the integral form of the jet radiation transfer equation being as follows:
Wherein, Is the target total irradiance; n is the number of boundary grids except the wall surface; Is the included angle between the normal vector of the infinitesimal plane m and the connecting line of the infinitesimal plane m and the detection point; The solid angle is formed by the infinitesimal plane m to the detection point;
when solving the jet radiation transfer equation in the integral form, rays are emitted from the detection points to boundary grids except the wall surface, the grids through which the light paths from the detection points to the boundary grids pass are calculated through the light path tracking algorithm of the structural grids, the light paths emitted from the detection points to the infinitesimal plane m are recorded as light paths m, and the target radiation illuminance of the light paths needs to be calculated Wherein n is the number of grids through which the optical path m passes,Is the blackbody spectrum radiation brightness; For the gas transmission of the ith cell through which the optical path passes, Is the gas transmissivity of the j-th unit along the light path.
Further, the objective function of the infrared radiation optimization is to minimize the radiation illuminance, and the optimization objective is to:
Wherein, As a function of the minimum value of the function,To be constrained, Q is a flow field variable, D is a design variable,Meaning that Q is a function of D and R is an N-S equation.
Further, lagrangian multipliers are introducedA new objective function L is constructed, since r=0, the value of L is equal toThe values of (2) are the same:
Then L derives the design variable D as:
Wherein, To derive a symbol;
Order the The previous coefficients are zero, deducing the concomitant equation for the infrared radiation problem:
Wherein, The partial derivative of the flow field residual error with respect to the flow field variable is calculated by an N-S equation accompanying solver.
Further, solving the accompanying equation can obtain the accompanying variableGradient calculations based on the accompanying method are:
the key to optimization based on concomitant jet infrared radiation is to derive The expression of (2) givesAnd then leading into a flow field adjoint solver, and solving adjoint equations of the infrared radiation problem to obtain adjoint variables.
Further, the method comprises the steps of,The development form of (2) is as follows:
regarding all grid points along the path m, for the path start grid i=1, there is:
when i=2, there are:
and so on to get Variation of the flow field variable in any grid point k along the path:
。
Further, calculate In (a) and (b)The process of (1) is as follows:
the calculation formula of the radiation brightness of the mth light path is as follows:
Construction calculation The first term i=1 has:
the second term i=2 is:
The third term i=3 is:
and so on:
I.e. Is given by the recurrence formula of (2)。
Further according toObtaining; According toObtaining：
Calculation of：
Calculation ofWhen the optical path is followed, each grid point i is calculated and storedObtainingAfter that, only need toThe first term of (1), sum1, constructs a recursive formula without processing sum2, for sum1 when i=1: When i=2 has; And so on i=k:
。
further, the algorithm for tracking the optical path through the structural grid calculates a grid through which the optical path from the detection point to the boundary grid passes, including:
according to the surface division strategy of the structural grid, the grid through which the light path from the detection point to the boundary grid passes is calculated by adopting the following steps:
Step 101: decomposing each blocking grid according to the surface division strategy of the structural grid, and judging whether the characteristic lines intersect all triangles obtained according to the surface division strategy of the structural grid and the positions of the intersection points by using an algorithm;
step 102: traversing grids of a plane where the intersection points are located in the partitioned grids with the intersection points, and finding grids through which the characteristic lines pass;
Step 103: decomposing the grid penetrated by the characteristic line according to the surface division strategy of the structural grid, and solving by using a ray triangle intersection algorithm to obtain the intersection point of the characteristic line and the grid; judging the next grid to which the characteristic line goes according to the logic coordinate relation between the intersection points and the structural grids;
step 104: repeating step 103 until the next grid exceeds the boundary of the partitioned grid; and after all the block grids are calculated, sequencing the obtained intersection points according to time.
Further, the surface division strategy of the structural grid is:
Dividing 6 faces of the structural grid into 12 triangles according to the logical coordinates of the structural grid, wherein three vertexes of each triangle are vertexes of the structural grid, and numbering the triangles according to the logical coordinates of the vertexes of the triangle; when the surface division strategy of the structural grid is adopted, the numbers of the sharing surfaces of the adjacent grids are fixed in the logic coordinate systems i, j and k.
Due to the adoption of the technical scheme, the invention has the following advantages: the method can realize rapid solution of jet infrared radiation, and can realize rapid solution of infrared radiation gradient by solving a pneumatic/infrared radiation coupling variation equation, thereby providing support for pneumatic/infrared coupling optimization based on the accompanying method.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments described in the embodiments of the present invention, and other drawings may be obtained according to these drawings for those skilled in the art.
FIG. 1 is a schematic view of an optical path through a structural grid in accordance with an embodiment of the present invention;
Fig. 2 is a schematic diagram of vertex numbering and triangle division of a structural mesh according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and examples, wherein the examples are shown only in a partial, but not in all embodiments of the invention. All other embodiments obtained by those skilled in the art are intended to fall within the scope of the embodiments of the present invention.
Referring to fig. 1, the present invention provides an embodiment of a jet pneumatic/infrared radiation coupling gradient calculation method based on an accompanying method, which includes:
Based on an integral form jet radiation transfer equation, a Lagrangian multiplier is introduced to obtain an accompanying equation of the infrared radiation problem; and solving the adjoint equation of the infrared radiation problem to obtain adjoint variables, and obtaining the gradient based on the adjoint method according to the adjoint variables.
The specific implementation steps of this embodiment are as follows:
solving an integral form of the jet radiation transfer equation, ignoring wall contribution and atmospheric attenuation, the integral form of the jet radiation transfer equation being as follows:
Wherein, Is the target total irradiance; n is the number of boundary grids except the wall surface; Is the included angle between the normal vector of the infinitesimal plane m and the connecting line of the infinitesimal plane m and the detection point; the solid angle of the infinitesimal plane m to the detection point. When solving the jet radiation transfer equation, a light path tracking method is adopted to send out rays from the detection points to the boundary grids except the wall surface, and the grids through which the light paths from the detection points to the boundary grids pass are calculated through a light path tracking algorithm. For the optical path (denoted as optical path m) emitted from the detection point to the infinitesimal m, it is necessary to calculate the optical path Where n is the number of grids traversed by the optical path m,Is the blackbody spectrum radiation brightness; is the gas transmittance of the ith cell through which the optical path passes.
The objective function of the infrared radiation optimization is to minimize the radiation illuminance, and the optimization objective is that:
Wherein, As a function of the minimum value of the function,To be constrained, Q is a flow field variable, D is a design variable,Representing Q as a function of D, R as an N-S equation, incorporating Lagrangian multipliersA new objective function L is constructed, since r=0, the value of L is equal toThe values of (2) are the same:
Then L derives the design variable D as:
Wherein, To derive a symbol;
Order the The previous coefficients are zero, deducing the concomitant equation for the infrared radiation problem:
Wherein, For the partial derivative of the flow field residual error with respect to the flow field variable, the partial derivative is calculated by an N-S equation accompanying solver, and an accompanying variable can be obtained by solving an accompanying equation. Gradient calculation based on the accompanying method is:
the key to optimization based on concomitant jet infrared radiation is to derive The expression of (2) givesAnd then leading into a flow field adjoint solver, and solving adjoint equations of the infrared radiation problem to obtain adjoint variables.
By the variation method of jet infrared radiation illuminance to along Cheng Liuchang variable, deducingThe process of the expression of (2) is:
The calculation formula of the target total radiation illuminance is to sum all light paths, and the target radiation illuminance of the light path m is as follows:
where n is the number of grids traversed by the optical path m (as in figure 1), Is the blackbody spectrum radiation brightness; For the gas transmission of the ith cell through which the optical path passes, Is the gas transmissivity of the j-th unit along the light path.
The development form of (2) is as follows:
regarding all grid points along the path m, for the path start grid i=1, there is:
when i=2, there are:
and so on to get Variation of the flow field variable in any grid point k along the path:
Referring to fig. 2, taking an example that the structural grid has 6 faces, dividing the 6 faces of the structural grid into 12 triangles according to logical coordinates, wherein the triangle 1 consists of points 4, 8 and 5; triangle number 2 consists of points 4, 5, 1; triangle No. 3 is composed of points 5, 6, 2; triangle No. 4 consists of points 5, 2, 1; triangle number 5 consists of points 4,1, 2; triangle 6 is composed of points 4, 2 and 3; triangle 7 is composed of points 3, 7, 6; triangle 8 is composed of points 3, 6 and 2; triangle 9 consists of points 3, 7 and 8; triangle number 10 is composed of points 3, 8, 4; the triangle 11 is composed of points 8, 7 and 6; triangle No. 12 consists of points 8, 6, 5. When the meshing strategy is adopted, the shared surface numbers of adjacent grids in the i, j and k directions are fixed.
Based on the surface division strategy, the optical path tracking method mainly comprises the following 6 steps:
(1) Decomposing each block grid (block) in the above manner and using The algorithm judges whether the characteristic line intersects 12 triangles or not and the position of the intersection point;
(2) Traversing grids of a plane where the intersection points are located in the partitioned grids with the intersection points, and finding grids (meshes) through which the characteristic lines pass;
(3) Decomposing the grid according to the grid decomposition strategy, and solving by using a ray triangle intersection algorithm to obtain a second intersection point of the characteristic line and the grid;
(4) Judging the next grid to which the characteristic line goes according to the logic coordinate relation between the intersection points and the structural grids;
(5) Repeating the steps 3 and 4; until the next grid exceeds the grid boundary of the block;
(6) And after all the block grids are calculated, sequencing the obtained intersection points according to time.
Recursive formula-based radiance variation solving method and calculationIn (a) and (b)The process of (1) is as follows:
the calculation formula of the radiation brightness of the mth light path is as follows:
Construction calculation The first term i=1 has:
the second term i=2 is:
The third term i=3 is:
and so on:
I.e. Is given by the recurrence formula of (2)。
The expression of (2) is:
Calculation of When the optical path is followed, each grid point i is calculated and stored. ObtainingAfter that, only need toThe first term (sum 1) of (2) constructs a recurrence formula without special handling of sum2. For sum1, there is when i=1: When i=2 has; And so on i=k:
。
finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (7)
1. A method for computing a jet aerodynamic/infrared radiation coupling gradient based on a concomitant method, comprising:
Based on an integral form jet radiation transfer equation, a Lagrangian multiplier is introduced to obtain an accompanying equation of the infrared radiation problem; solving an accompanying equation of the infrared radiation problem to obtain an accompanying variable, and obtaining gradient based on an accompanying method according to the accompanying variable;
solving an integral form of the jet radiation transfer equation, ignoring wall contribution and atmospheric attenuation, the integral form of the jet radiation transfer equation being as follows:
Wherein, Is the target total irradiance; n is the number of boundary grids except the wall surface; Is the included angle between the normal vector of the infinitesimal plane m and the connecting line of the infinitesimal plane m and the detection point; The solid angle is formed by the infinitesimal plane m to the detection point;
when solving the jet radiation transfer equation in the integral form, rays are emitted from the detection points to boundary grids except the wall surface, the grids through which the light paths from the detection points to the boundary grids pass are calculated through the light path tracking algorithm of the structural grids, the light paths emitted from the detection points to the infinitesimal plane m are recorded as light paths m, and the target radiation illuminance of the light paths needs to be calculated Wherein n is the number of grids through which the optical path m passes,Is the blackbody spectrum radiation brightness; For the gas transmission of the ith cell through which the optical path passes, The gas transmittance of the jth unit through which the light path passes;
The objective function of the infrared radiation optimization is to minimize the radiation illuminance, and the optimization objective is that:
Wherein, As a function of the minimum value of the function,To be constrained, Q is a flow field variable, D is a design variable,Representing Q as a function of D, R as an N-S equation;
Introducing Lagrangian multipliers A new objective function L is constructed, since r=0, the value of L is equal toThe values of (2) are the same:
Then L derives the design variable D as:
Wherein, To derive a symbol;
Order the The previous coefficients are zero, deducing the concomitant equation for the infrared radiation problem:
Wherein, The partial derivative of the flow field residual error with respect to the flow field variable is calculated by an N-S equation accompanying solver.
2. The method of claim 1, wherein solving the accompanying equation yields an accompanying variableGradient calculations based on the accompanying method are:
the key to optimization based on concomitant jet infrared radiation is to derive The expression of (2) givesAnd then leading into a flow field adjoint solver, and solving adjoint equations of the infrared radiation problem to obtain adjoint variables.
3. The method of claim 1, wherein the step of determining the position of the substrate comprises,The development form of (2) is as follows:
regarding all grid points along the path m, for the path start grid i=1, there is:
when i=2, there are:
and so on to get Variation of the flow field variable in any grid point k along the path:
。
4. a method according to claim 3, characterized in that the calculation is performed In (a) and (b)The process of (1) is as follows:
the calculation formula of the radiation brightness of the mth light path is as follows:
Construction calculation The first term i=1 has:
the second term i=2 is:
The third term i=3 is:
and so on:
I.e. Is given by the recurrence formula of (2)。
5. The method according to claim 4, characterized in thatObtaining; According toObtaining：
Calculation of：
Calculation ofWhen the optical path is followed, each grid point i is calculated and storedObtainingAfter that, only need toThe first term of (1), sum1, constructs a recursive formula without processing sum2, for sum1 when i=1: When i=2 has; And so on i=k:
。
6. the method of claim 1, wherein the computing a grid through which the optical path of the probe point to the boundary grid passes through the optical path tracking algorithm of the structural grid comprises:
according to the surface division strategy of the structural grid, the grid through which the light path from the detection point to the boundary grid passes is calculated by adopting the following steps:
Step 101: decomposing each blocking grid according to the surface division strategy of the structural grid, and judging whether the characteristic lines intersect all triangles obtained according to the surface division strategy of the structural grid and the positions of the intersection points by using an algorithm;
step 102: traversing grids of a plane where the intersection points are located in the partitioned grids with the intersection points, and finding grids through which the characteristic lines pass;
Step 103: decomposing the grid penetrated by the characteristic line according to the surface division strategy of the structural grid, and solving by using a ray triangle intersection algorithm to obtain the intersection point of the characteristic line and the grid; judging the next grid to which the characteristic line goes according to the logic coordinate relation between the intersection points and the structural grids;
step 104: repeating step 103 until the next grid exceeds the boundary of the partitioned grid; and after all the block grids are calculated, sequencing the obtained intersection points according to time.
7. The method of claim 6, wherein the surface partitioning strategy of the structural grid is:
Dividing 6 faces of the structural grid into 12 triangles according to the logical coordinates of the structural grid, wherein three vertexes of each triangle are vertexes of the structural grid, and numbering the triangles according to the logical coordinates of the vertexes of the triangle; when the surface division strategy of the structural grid is adopted, the numbers of the sharing surfaces of the adjacent grids are fixed in the logic coordinate systems i, j and k.
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| CN117669413A (en) * | 2023-11-28 | 2024-03-08 | 西安电子科技大学 | Offshore foam-containing and ocean wave infrared sea surface simulation method based on physics |
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