CN117236144B - Method for determining heat conduction main axis of orthotropic heat-proof material based on mounting molded surface - Google Patents
Method for determining heat conduction main axis of orthotropic heat-proof material based on mounting molded surface Download PDFInfo
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- 239000000758 substrate Substances 0.000 claims description 2
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- HBMJWWWQQXIZIP-UHFFFAOYSA-N silicon carbide Chemical compound [Si+]#[C-] HBMJWWWQQXIZIP-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention discloses a method for determining a heat conduction main axis of an orthotropic heat-resistant material based on an installation profile, which relates to the field of heat conduction numerical calculation and comprises the following steps: obtaining a representation set of discrete units of the installation profile and an external normal vector set corresponding to the discrete units; establishing rays between the positions and external normal vectors of the discrete units, and obtaining a first expression of any point on the rays and a second expression of any point on the discrete units; establishing a simultaneous equation based on the first expression and the second expression, judging whether the simultaneous equation has object understanding, and if so, indicating that the ray has an intersection point with the discrete unit; the discrete units are replaced to obtain the first expression and the second expression in a returning mode until all the discrete units are traversed and accumulated to obtain a plurality of intersection points, and the first main shaft direction in the heat conduction main shaft of the heat protection structure is obtained based on the distance between the intersection points and the positions.
Description
Technical Field
The invention relates to the field of anisotropic material heat conduction numerical calculation, in particular to a method for determining a heat conduction main axis of an orthotropic heat-proof material based on a mounting profile.
Background
The hypersonic aircraft thermal protection system widely uses orthotropic materials, such as carbon/carbon woven materials, carbon/silicon carbide composite materials and the like, the thermal conductivity of the materials forms an ellipsoid in space, three main axis directions of the ellipsoid are called as thermal conduction main axes of the materials, the thermal conductivities of the three main axis directions are called as dominant thermal conductivity of the materials, large differences exist in the thermal conductivities of different main axis directions, and the differences are ignored to introduce excessive errors in the thermal conductivity analysis of the thermal protection structure, so that the design and evaluation of the thermal protection structure are directly influenced.
When the heat transfer calculation of the orthotropic heat-resistant material is carried out, the dominant heat rate of the material is measured through means such as experiments, the heat conductivity tensor under a calculation coordinate system is calculated according to the heat conduction main shaft and the dominant heat rate, the heat conductivity tensor is substituted into a heat conduction control equation, and finally the temperature field solution is carried out through numerical calculation methods such as a finite element method, a finite difference method and a finite volume method. Therefore, the determination of the heat conduction main axis directly influences the heat transfer calculation accuracy of the orthotropic heat-resistant material. In practical applications, the first principal axis direction of the orthotropic heat-shielding material is generally perpendicular to the mounting surface (adhesive surface or interface surface) to obtain the best heat-shielding effect, and the second and third principal axis directions are any vectors perpendicular to each other perpendicular to the first principal axis direction, but the principal axis directions are not explicitly expressed due to the complexity of the heat-shielding structure.
Disclosure of Invention
In order to solve the problem of determining the heat conduction main shaft of the orthotropic heat-proof material of the complex heat-proof structure, the invention provides a method for determining the heat conduction main shaft of the orthotropic heat-proof material based on the installation profile.
To achieve the above object, the present invention provides a method for determining a principal axis of heat conduction of an orthotropic heat shielding material based on a mounting profile, the method comprising:
step one: for a mounting profile of a heat protection structure, obtaining a representation set of discrete units of the mounting profile, and obtaining an external normal vector set corresponding to the discrete units based on the representation set of the discrete units, i=1, 2,3 1 ，N 1 Is the total number of discrete units in the installation profile;
step two: for any one first position in the heat-proof structure, the first position and the discrete units E are established i Is the external normal vector n of (2) i Rays in between, obtain arbitrary on the raysA first expression of a point, obtaining a discrete unit E i A second expression of any point above;
step three: establishing a simultaneous equation based on the first expression and the second expression, judging whether the simultaneous equation exists for understanding, and if so, representing the ray and the discrete unit E i Having an intersection point, if not, representing the ray with the discrete element E i No intersection point exists;
step four: and (3) replacing the value of i, returning to the execution step II until all the discrete units in the representation set of the discrete units are traversed, accumulating to obtain a plurality of intersection points, and obtaining the first main shaft direction in the heat conduction main shaft of the heat-proof structure based on the distance between the intersection points and the first position.
The method adopted by the invention is as follows: for any position in the material, firstly taking a vertical line from the material to the mounting profile, taking the vector direction of the connecting line from the vertical foot to the position as a first main axis direction, taking any two mutually perpendicular directions in a plane perpendicular to the first main axis as second and third main axis directions, and finally determining the heat conduction main axis of any position in the material.
In some embodiments, the representation set of discrete units is represented as set { E } i | i=1,2,3,...,N 1 }。
In some embodiments, the set of external normal vectors is represented as { n } i | i=1,2,3,...,N 1 }。
In some embodiments, the first expression is:；
wherein,pain order to be any point on the ray,p 0 as the coordinates of the first location,tto control parameters, n i As discrete unit E i Is defined as the outer normal vector of (2).
In some embodiments, the second expression is:；
wherein,pbas discrete unit E i At any point on the surface of the substrate,R 1 andR 2 as discrete unit E i The parameters of any one point of the above,p i1 、 p i2 and p i3 Discrete units E respectively i Is a node of the three nodes.
Wherein, based on the first expression and the second expression, establishing simultaneous equations, judging whether the simultaneous equations are understood by things or not, and makingpaEqual topbJudging whether the object understanding exists or not.
In some embodiments, the obtaining the first main axis direction in the heat conduction main axis of the heat protection structure based on the distance between the intersection point and the first position specifically includes:
and calculating the distance between all the intersection points and the first position to obtain the intersection point closest to the first position, wherein the intersection point is the vertical foot from the first position to the mounting profile in the heat-proof structure, and the direction from the first position to the vertical foot is the first main shaft direction.
For complex structures, the intersection points may be more than one, the intersection points with a longer distance are blocked by the complex structures, the requirement of an algorithm is not met, the determination of a main axis has local properties, for complex structures, the installation profile is also complex, the direction determined by the intersection points with a longer distance is difficult to ensure the perpendicularity with the local profile, and thus errors are caused, so that the latest intersection points are adopted, according to the installation profile and engineering application background, the in-plane thermal conductivity and the interlayer thermal conductivity are generally given, the main axis of the interlayer thermal conductivity is in the direction of the perpendicular installation profile (defined as the direction of the first main axis herein), and the main axis of the in-plane thermal conductivity is in the direction parallel to the installation profile.
In some embodiments, the method further comprises step five: and setting an arbitrary unit vector perpendicular to the first main axis direction as a second main axis direction in the heat conduction main axis of the heat-proof structure. The second main axis direction can be obtained in the above manner.
In some embodiments, the fifth step further comprises: and obtaining a third main shaft direction in the heat conduction main shaft of the heat protection structure based on the first main shaft direction and the second main shaft direction. The third main axis direction can be obtained in the above manner.
The one or more technical schemes provided by the invention have at least the following technical effects or advantages:
according to the method, according to the installation characteristics of the orthotropic heat-proof material in engineering, the installation molded surface of the heat-proof structure is taken as a reference, the problem of determining the heat conduction main shaft is converted into the problem of calculating the vertical line from any position inside the material to the installation molded surface, and finally, the heat conduction main shaft of the orthotropic heat-proof material is accurately determined, so that the accuracy of heat transfer calculation and analysis is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a flow chart of a method for determining a principal axis of thermal conductivity of an orthotropic thermal protection material based on a mounting profile;
FIG. 2 is a schematic diagram of a simplified cylindrical double-layer heat-resistant structural grid;
fig. 3 is a schematic diagram of the calculated first principal axis direction.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. In addition, the embodiments of the present invention and the features in the embodiments may be combined with each other without collision.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than within the scope of the description, and the scope of the invention is therefore not limited to the specific embodiments disclosed below.
Embodiment one;
referring to fig. 1, fig. 1 is a flow chart of a method for determining a principal axis of heat conduction of an orthotropic heat shielding material based on a mounting profile.
The method can accurately obtain the heat conduction main axis of the orthotropic heat-proof material when carrying out the heat transfer calculation and analysis of the orthotropic heat-proof material with the complex heat-proof structure. The basic idea is to calculate the vertical line from any position inside the material to the installation profile based on the installation profile of the heat-proof structure according to the installation characteristic that the main axis direction of the orthotropic heat-proof material in engineering is generally vertical to the material profile so as to obtain the best heat-proof effect, and finally accurately determine the heat conduction main axis of the orthotropic heat-proof material, thereby improving the accuracy of heat transfer calculation and analysis.
The specific steps of the implementation of the invention are as follows:
step one: mounting profile for a heat protection structureSIts discrete units are represented as a set { E } i | i=1,2,3,...,N 1 }，N 1 For this profile discrete unit total number, the external normal vector (directed from the mounting profile to the outside of the material) corresponding to the discrete unit is denoted as { n i | i=1,2,3,...,N 1 Taking triangle units as an example (quadrilateral units can be split into two triangle units), discrete unit E i Represented by nodes as {p ij |j=1,2,3}。
Step two: for any first location within the material, it is associated with discrete element E i Is the external normal vector n of (2) i A ray can be defined, and if the parameter t is greater than or equal to 0, the expression of any point on the ray is，paIn order to be any point on the ray,p 0 as the coordinates of the first location,tto control parameters, n i As discrete unit E i Is the external normal vector of (1), taking the parametersR 1 Is greater than or equal to 0 and is less than or equal to 0,R 2 is greater than or equal to 0 and is less than or equal to 0,R 1 addingR 2 Less than or equal to 1, then the expression at any point on discrete element i is。
Step three: coupled with the ray and discrete element E i The expression of (1), if any, indicates thatThe ray has an intersection point with the discrete unit, otherwise, the ray has no intersection point.
Step four: cycle traversing installation profileSThe closest point to the first position in the total intersection points is the first position in the material to the mounting profileSThe direction from the first position to the foot drop is the first main shaft direction.
Step five: setting an arbitrary unit vector perpendicular to the first principal axis direction as the second principal axis direction, and obtaining a third principal axis direction from the first principal axis direction and the second principal axis direction by a right-hand criterion.
Embodiment two;
based on the first embodiment, a simplified cylindrical double-layer heat-proof structure is selected in the second embodiment, the outer layer is made of anisotropic heat-proof materials, the inner layer is made of isotropic heat-proof materials, the mounting molded surface is an interface of the inner layer and the outer layer, and the dividing grid is shown in fig. 2.
And calculating the heat conduction main shaft of the outer anisotropic heat-proof material point by taking the mounting molded surface as a reference.
The first main axis directions of the outer anisotropic heat-proof materials are all directed to the central axis of the cylinder, and the calculation result of the method is shown in fig. 3, so that the method of the patent can accurately obtain the heat-conducting main axis direction by taking the installation profile as the reference.
Example III
On the basis of the first embodiment, the third embodiment of the invention also provides a heat transfer calculation method of an orthotropic heat-resistant material, which comprises the following steps: when the heat transfer calculation of the orthotropic heat-resistant material is carried out, the dominant heat rate of the material is usually measured through means such as experiments, then the heat conductivity tensor under a calculation coordinate system is obtained through the calculation of the heat conduction main shaft and the dominant heat rate according to the mode of the first embodiment, the heat conductivity tensor is substituted into a heat conduction control equation, and finally the temperature field solution is carried out through numerical calculation methods such as a finite element method, a finite difference method and a finite volume method. The heat conduction main shaft is accurately determined by adopting the mode of the embodiment, so that the heat transfer calculation precision of the orthotropic heat-resistant material can be improved.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (1)
1. An orthotropic heat protection material heat conduction main axis determining method based on a mounting profile, which is characterized by comprising the following steps:
step one: for a mounting profile of a heat protection structure, obtaining a representation set of discrete units of the mounting profile, and obtaining an external normal vector set corresponding to the discrete units based on the representation set of the discrete units, i=1, 2,3 1 ，N 1 Is the total number of discrete units in the installation profile;
step two: for any one first position in the heat-proof structure, the first position and the discrete units E are established i Is the external normal vector n of (2) i Rays between them, a first expression of any point on the rays is obtained, and a discrete unit E is obtained i A second expression of any point above;
step three: establishing a simultaneous equation based on the first expression and the second expression, judging whether the simultaneous equation exists for understanding, and if so, representing the ray and the discrete unit E i Having an intersection point, if not, representing the ray with the discrete element E i No intersection point exists;
step four: changing the value of i, returning to the execution step II until all the discrete units in the representation set of the discrete units are traversed, accumulating to obtain a plurality of intersection points, and obtaining a first main shaft direction in the heat conduction main shaft of the heat-proof structure based on the distance between the intersection points and the first position;
discrete sheetThe representation set of elements is denoted as set { E ] i | i=1,2,3,...,N 1 }；
The set of external normal vectors is denoted as { n } i | i=1,2,3,...,N 1 }；
The first expression is:
；
wherein,pain order to be any point on the ray,p 0 as the coordinates of the first location,tto control parameters, n i As discrete unit E i Is defined by the outer normal vector of (2);
the second expression is:
；
wherein,pbas discrete unit E i At any point on the surface of the substrate,R 1 andR 2 as discrete unit E i The parameters of any one point of the above,p i1 、p i2 andp i3 discrete units E respectively i Is a node of (a) and (b);
the method for obtaining the first main shaft direction in the heat conduction main shaft of the heat protection structure based on the distance between the intersection point and the first position specifically comprises the following steps:
calculating the distance between all the intersection points and the first position to obtain the intersection point closest to the first position, wherein the intersection point is the vertical foot from the first position to the mounting molded surface in the heat-proof structure, and the direction from the first position to the vertical foot is the direction of the first main shaft;
the method further comprises the step five of: setting an arbitrary unit vector perpendicular to the first main axis direction as a second main axis direction in the heat conduction main axis of the heat-proof structure; the fifth step further comprises: and obtaining a third main shaft direction in the heat conduction main shaft of the heat protection structure through a right-hand criterion based on the first main shaft direction and the second main shaft direction.
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