CN117093817B - Radiation transfer factor correction method for non-closed radiation heat exchange system - Google Patents
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Abstract
The invention discloses a radiation transfer factor correction method for a non-closed radiation heat exchange system, which relates to the field of radiation heat exchange simulation methods.
Description
Technical Field
The invention relates to the field of radiation heat exchange simulation methods, in particular to a radiation transfer factor correction method for a non-closed radiation heat exchange system.
Background
The Monte Carlo method has the characteristics of simple and clear physical model, flexible application and the like, and is widely applied to the field of heat radiation and heat exchange. However, due to the presence of random errors, the monte carlo method calculates the obtained radiation transfer factor (radiation transfer factor RD i,j Defined as the fraction of the own radiant energy of unit i that is ultimately absorbed by unit j after one or more reflections and scattering by the units of the system) in a radiation transmission system is often not guaranteed to satisfy the reciprocal property, and thus the iterative convergence problem that arises when performing temperature field calculations. The iterative bidirectional statistical Monte Carlo method can effectively reduce the reciprocal error of the radiation transfer factor, thereby effectively improving the solving precision of the heat radiation transmission problem.
The iterative bidirectional statistical Monte Carlo method utilizes the principle of reversible light path during heat radiation transmission to carry out multiple bidirectional statistics on Monte Carlo simulation of heat radiation transmission, fully utilizes the path information of energy beam propagation, improves the reciprocal property of radiation transfer factors, and is applied to numerous engineering problems. However, the iterative bidirectional statistical Monte Carlo method is only suitable for closed radiation heat exchange systems, and for non-closed systems, the reciprocity of the radiation transfer factor cannot be improved, but the calculation result of the radiation transfer factor is deteriorated, and non-physical results are brought.
Disclosure of Invention
In order to solve the problem of radiation transfer factor reciprocal optimization in a non-closed radiation heat exchange system, the invention provides a radiation transfer factor correction method for the non-closed radiation heat exchange system, which comprises the following steps:
step one: calculating to obtain the radiation transfer factor matrix RD of the non-closed radiation transmission system i,j The non-closed radiation transmission system comprises N units, and in the non-closed radiation transmission system, the radiation power coefficients corresponding to the N units are expressed as a set E, E= { E i I=1, 2,3, N, for RD i,j And E, i=1, 2,3,..n, j=1, 2,3,..n, E i The ith radiant power coefficient in set E;
step two: adding a virtual blackbody unit into the non-closed radiation transmission system to enable the non-closed radiation transmission system to be changed into a closed radiation heat exchange system, wherein a radiation transfer factor matrix of the closed radiation heat exchange system is as followsThe closed radiation heat exchange system comprises n+1 units, and in the closed radiation heat exchange system, the radiation power coefficient corresponding to the n+1 units is expressed as a set E ', E' = { }>I=1, 2,3,..n+1 }, for +.>And E', i=1, 2,3,..n+1, j=1, 2,3,..n+1;
step three: RD-based i,j Computing to obtain the ith row and the (n+1) th column pairRadiation transfer factor matrix for response；
Step four: based onAnd E is i Calculating to obtain radiation power coefficient of virtual unit>；
Step five: based on、E i And->Calculation to get->，/>A radiation transfer factor matrix corresponding to the (n+1) th row and the (i) th column;
step six: based on the ith radiant power coefficient in set EThe j-th radiant power coefficient in set EThe kth radiation power coefficient in set E +.>Radiation transfer factor matrix corresponding to ith row and jth column obtained by n-1 th bidirectional statistics>Radiation transfer factor matrix corresponding to jth row and ith column obtained by n-1 th bidirectional statisticsAnd (d)Radiation transfer factor matrix corresponding to kth row and ith column obtained by n-1 times of bidirectional statistics>Calculated to obtainWherein->A radiation transfer factor matrix obtained for the nth bi-directional statistic, k=1, 2,3,..n+1;
step seven: removing the virtual blackbody unit from the non-closed radiation transmission system, and obtaining a corrected radiation transfer factor matrix of the non-closed radiation heat exchange system based on the radiation transfer factor matrix obtained by the nth bidirectional statistics。
The invention converts the non-closed system into the closed system by adding the virtual blackbody unit, so as to solve the inapplicability problem of the iterative bidirectional statistical Monte Carlo method under the non-closed system and improve the reciprocal property of the radiation transfer factor of the non-closed radiation heat exchange system.
In some embodiments, the third step calculates the radiation transfer factor matrix corresponding to the ith row and the (n+1) th column by using the following formula：
。
In some embodiments, the fourth step calculates the radiation power coefficient of the virtual cell using the following formula：
。
In some embodiments, the fifth step calculates the radiation transfer factor matrix corresponding to the (n+1) th row and the (i) th column using the following formula：
。
In some embodiments, the iterative formula in the step six is:；
wherein,radiation transfer factor matrix obtained for nth bi-directional statistics,>radiation transfer factor matrix corresponding to ith row and jth column obtained for nth-1 bi-directional statistics,/th row and jth column>Radiation transfer factor matrix corresponding to the j-th row and i-th column obtained for the n-1 th bi-directional statistics,/th row>The radiation transfer factor matrix corresponding to the kth row and the ith column obtained for the nth-1 bi-directional statistics, k=1, 2, 3.
In some embodiments, the radiation transfer factor of the non-closed radiation heat exchange system is calculated in the seventh step by using the following formula：
。
The one or more technical schemes provided by the invention have at least the following technical effects or advantages:
according to the characteristics of the radiation heat exchange system, the virtual blackbody unit is added to complement the non-closed radiation heat exchange system, so that the non-closed radiation heat exchange system is formed into a closed system without changing the original radiation heat exchange process, and then the iterative bidirectional statistical Monte Carlo method of the closed system is utilized for correction, so that the problem that the iterative bidirectional statistical Monte Carlo method is not applicable under the non-closed system is solved, and the reciprocal property of the radiation transfer factor of the non-closed radiation heat exchange system 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 radiation transfer factor correction method for a non-closed radiation heat exchange system;
FIG. 2 is a schematic diagram of a square cavity surface radiant heat exchange system.
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.
Example 1
According to the embodiment, a virtual unit is added on the basis of the non-closed radiation heat exchange system, the virtual unit is set to be a blackbody unit, the virtual unit can be regarded as a notch set of the non-closed system to form a new closed radiation heat exchange system, then an iterative bidirectional statistical Monte Carlo method is adopted to correct the radiation transfer factor of the closed radiation heat exchange system, and finally the added virtual unit is removed to obtain the radiation transfer factor of the corrected non-closed radiation heat exchange system.
Referring to fig. 1, fig. 1 is a schematic flow chart of a radiation transfer factor correction method for a non-closed radiation heat exchange system, and the specific steps implemented in the present invention are:
step one: for a non-closed radiation transmission system formed by N units, the radiation transfer factor matrix calculated by adopting the traditional Monte Carlo method is recorded as RD i,j Where i=1, 2,3,..n, j=1, 2,3,..n. The radiation power coefficients corresponding to the N units are represented as a set { E } i I=1, 2,3, N, for the face unit, the face unit is provided with a plurality of face units,wherein->For emissivity of face unit i, S i For the area of the face unit i, +.>Wherein->For emissivity of volume element i, V i For the volume of the body unit i, wherein the conventional monte carlo method can refer to "iterative bidirectional statistical monte carlo method of heat radiation problem", engineering thermophysics report 2017, 38 (3): 635-639, formulas 1 to 2.
Step two: a virtual blackbody unit is added on the basis of the original non-closed radiation heat exchange system to form a new closed radiation heat exchange system, and the radiation transfer factor matrix of the closed system is recorded asThe corresponding radiation power coefficients of n+1 units are denoted as set { +.>I=1, 2,3,..n+1 }, where i=1, 2,3,..n+1, j=1, 2,3,..n+1. For i=1, 2,3,..n, j=1, 2,3.., N, there is->=RD i,j ，/>=E i The method comprises the steps of carrying out a first treatment on the surface of the For i=n+1, j=1, 2,3,..n+1, there are。
Among them, a blackbody is an idealized object in the field of radiant heat exchange, capable of absorbing all external electromagnetic radiation (thermal radiation is one of electromagnetic radiation), and without any reflection and transmission. In other words, the absorption coefficient of the black body for electromagnetic waves of any wavelength is 1, and the transmission coefficient is 0.
Step three: calculating the radiation transfer factor of the (n+1) th column:
；
step four: calculating the radiation power coefficient of the virtual unit:
；
step five: calculating the radiation transfer factor of the (n+1) th column:
；
step six: and carrying out n times of bidirectional statistics by using an iterative bidirectional statistics Monte Carlo method, wherein the iterative formula is as follows:
；
the iterative bidirectional statistical Monte Carlo method can refer to the iterative bidirectional statistical Monte Carlo method of heat radiation problem, and engineering thermophysics report 2017, 38 (3): 635-639.
Step seven: removing the virtual unit to obtain the radiation transfer factor of the modified non-closed radiation heat exchange system：；
According to the method, the non-closed radiation heat exchange system can be converted into the closed radiation heat exchange system by adding the virtual blackbody unit, so that the problem that the iterative bidirectional statistics Monte Carlo method is not applicable under the non-closed system is solved, and the easiness of radiation transfer factors of the non-closed radiation heat exchange system is improved.
The method can be applied to solving the heat radiation transmission problem so as to improve the solving precision.
Example two
Based on the first embodiment, a square two-dimensional cavity surface radiation heat exchange system is selected in the second embodiment, the side length of the square two-dimensional cavity surface radiation heat exchange system is unit length, each side length is divided into 1 unit, and the surface emissivity of each unit is 1.0, as shown in fig. 2. 1-4 in FIG. 2 represent units 1-4, respectively, assuming that the unit 4 void forms a non-closed radiant heat exchange system comprised of 3 units.
Setting the number of analog energy beams of each unit to 100000, taking radiation transfer factor between the No. 1 unit and the No. 2 unit as an example, wherein the theoretical value of the radiation transfer factor is 0.29289322,1 unit and the radiation transfer factor matrix between the No. 2 unit is RD 1,2， The radiation transfer factor matrix between the No. 2 unit and the No. 1 unit is RD 2,1 RD is calculated by adopting the traditional Monte Carlo method 1,2 0.29362, RD 2,1 A reciprocal error between units 0.29160,1 and 2 ofThe reciprocal error between unit No. 2 and unit No. 1 is +.>The reciprocal error is +.>Wherein the reciprocal error between the i-th unit and the j-th unit is defined as +.>The reciprocal error between the j-th unit and the i-th unit is defined as +.>，/>Is->Is a symmetric matrix of:。
the radiation transfer factor matrix of the non-closed radiation transmission system is RD i,j ，RD j,i Is RD i,j Symmetric matrix of E j The j-th radiant power coefficient in set E; after a virtual unit is added to form a closed system, the radiation transfer factor matrix between the modified No. 1 unit and the modified No. 2 unit is as follows after 20 times of iteration bidirectional statisticsThe radiation transfer factor matrix between the modified cell number 2 and cell number 1 is +.>Obtain->0.293189->0.293189, error in easiness of inversion->。
The method of the patent can be seen to effectively improve the reciprocal property of the radiation transfer factor of the non-closed radiation heat exchange system, and ensure the calculation precision of the radiation transfer factor.
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. A method of modifying a radiation transfer factor for a non-closed radiation heat exchange system, the method comprising:
step one: calculating to obtain the radiation transfer factor matrix RD of the non-closed radiation transmission system i,j The non-closed radiation transmission system comprises N units, and in the non-closed radiation transmission system, the radiation power coefficients corresponding to the N units are expressed as a set E, E= { E i I=1, 2,3, N, for RD i,j And E, i=1, 2,3,..n, j=1, 2,3,..n, E i The ith radiant power coefficient in set E;
step two: adding a virtual blackbody unit into the non-closed radiation transmission system to enable the non-closed radiation transmission system to be changed into a closed radiation heat exchange system, wherein a radiation transfer factor matrix of the closed radiation heat exchange system is as followsThe closed radiation heat exchange system comprises n+1 units, and in the closed radiation heat exchange system, the radiation power coefficient corresponding to the n+1 units is expressed as a set E ', E' = { }>I=1, 2,3,..n+1 }, for +.>And E', i=1, 2,3,..n+1, j=1, 2,3,..n+1;
step three: RD-based i,j Calculating to obtain the radiation transfer factor matrix corresponding to the ith row and the (n+1) th column；
Step four: based onAnd E is i Calculating to obtain radiation power coefficient of virtual unit>；
Step five: based on、E i And->Calculation to get->，/>A radiation transfer factor matrix corresponding to the (n+1) th row and the (i) th column;
step six: based on the ith radiant power coefficient in set EThe j-th radiant power coefficient in set E->The kth radiation power coefficient in set E +.>Radiation transfer factor matrix corresponding to ith row and jth column obtained by n-1 th bidirectional statistics>Radiation transfer factor matrix corresponding to the jth row and ith column obtained by n-1 th bidirectional statistics>Radiation transfer factor matrix corresponding to kth row and ith column obtained by n-1 th bi-directional statistics +.>Calculation to get->Wherein->A radiation transfer factor matrix obtained for the nth bi-directional statistic, k=1, 2,3,..n+1;
step seven: removing the virtual blackbody unit from the non-closed radiation transmission system, and obtaining a corrected radiation transfer factor matrix of the non-closed radiation heat exchange system based on the radiation transfer factor matrix obtained by the nth bidirectional statisticsThe method comprises the steps of carrying out a first treatment on the surface of the The third step is to calculate and obtain the radiation transfer factor matrix corresponding to the ith row and the (n+1) th column by adopting the following formula>：The method comprises the steps of carrying out a first treatment on the surface of the The fourth step is to calculate and obtain the radiation power coefficient of the virtual unit by adopting the following formula>：
The method comprises the steps of carrying out a first treatment on the surface of the The fifth step is to calculate and obtain the radiation transfer factor matrix corresponding to the (n+1) th row and the (i) th column by adopting the following formula>：/>The method comprises the steps of carrying out a first treatment on the surface of the The iteration formula in the step six is as follows:
the method comprises the steps of carrying out a first treatment on the surface of the In the seventh step, the radiation transfer factor matrix of the non-closed radiation heat exchange system is calculated and obtained by adopting the following formula>：
。
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