CN110008587B - Improved Monte Carlo method for solving exchange area of full heating furnace - Google Patents
Improved Monte Carlo method for solving exchange area of full heating furnace Download PDFInfo
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Abstract
The invention relates to a method for solving the exchange area of a full heating furnace by an improved Monte Carlo method, which comprises the following steps: 1) Inputting parameters of a two-dimensional closed system in a radiation field of a full heating furnace; 2) Calculating the share and proportion of each infinitesimal emission energy beam to other infinitesimal elements divided by the two-dimensional closed system according to the parameters; 3) Calculating and storing the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection; 4) Calculating whether the ratio of the residual energy to the emission energy of one beam of energy after multiple reflections meets the requirement or not; 5) If the requirements are met, calculating the total exchange area, and finishing the calculation process; 6) And if the precision requirement is not met, returning to the step of calculating and storing the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection. The method has higher efficiency than the traditional Monte Carlo method, especially when the grid division is finer and the precision requirement is higher, the method can save a large amount of calculation time and improve the accuracy of calculation.
Description
Technical Field
The invention relates to the field of solving of the radiation total exchange area of a heating furnace, in particular to an improved Monte Carlo method for solving the radiation total exchange area of the heating furnace.
Background
The heat exchange process in the heating furnace comprises radiation heat exchange and convection heat exchange between furnace gas and steel billets; the radiation heat exchange and the convection heat exchange between the furnace gas and the furnace enclosure; compared with the other two heat exchange modes, the radiation heat exchange between the furnace enclosure and the steel billet is the most difficult to solve. The radiation heat exchange has the following characteristics: the heat radiation propagation speed is high and the propagation is carried out at the light speed; the heat radiation always accompanies the interconversion of heat energy and electromagnetic energy in the heat exchange process; physical properties are difficult to determine; and a non-contact heat transfer process. Because the temperature in the hearth of the heating furnace is high (generally above 900 ℃), the proportion of the heat radiation is the highest and is above 90%, and therefore, it is very necessary to accurately solve the heat radiation exchange in the heating furnace.
The existing Monte Carlo method has low requirements on the uniformity of media and the geometric shape of a hearth space, so that a Monte Carlo method model still has good applicability to non-uniform media and complex geometric furnace types, and the Monte Carlo method is based on the probability principle to solve the total exchange area, so that the solution of the heavy integral is skilfully skipped, and the solution of the total exchange area is greatly simplified. The accuracy of the Monte Carlo method is greatly dependent on the number of tracing rays, the accuracy is higher when the number of tracing rays is larger, but the workload of a computer is greatly increased when the accuracy is improved. And the error of the calculation result is large, and the result of the radiation total exchange area cannot be truly reflected.
Disclosure of Invention
Aiming at the defects of large calculation amount, low accuracy and the like existing in the prior art when the traditional Monte Carlo method is adopted to solve the exchange area of the full heating furnace, the invention aims to solve the problem of providing the improved Monte Carlo method for solving the exchange area of the full heating furnace, which can save a large amount of computer time and improve the calculation accuracy.
In order to solve the technical problems, the invention adopts the technical scheme that:
the invention relates to an improved Monte Carlo method for solving the exchange area of a full heating furnace, which comprises the following steps:
1) Inputting parameters of a two-dimensional closed system in a radiation field of a full heating furnace;
2) Calculating the share and proportion of each infinitesimal emission energy beam to other infinitesimal elements divided by the two-dimensional closed system according to the parameters;
3) Calculating and storing the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection;
4) Calculating whether the ratio of the residual energy to the emission energy of one beam of energy after multiple reflections meets the requirement or not;
5) If the requirements are met, calculating the total exchange area, and finishing the calculation process;
6) And if the precision requirement is not met, returning to the step of calculating and storing the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection.
In the step 1), the parameters comprise a geometric value, gridding columns and rows of a two-dimensional closed system in a radiation field of the full heating furnace, the number of emission points of each two-dimensional rectangular surface section and the number of energy beams generated by each point, the number of emission points of each two-dimensional rectangular gas section and the number of energy beams generated by each point, the blackness of the surface section and the absorption coefficient of the gas section.
In the step 2), the fraction and the proportion of the energy beams emitted by the surface section and the gas section divided by the two-dimensional closed system to other infinitesimals are calculated, and the method specifically comprises the following steps:
201 The order of the elements is arranged as follows: sequentially naming the surface infinitesimal of a two-dimensional closed system as 1,2, \8230, arranging the gas infinitesimal behind the surface infinitesimal as Ns +1, ns +2, \8230, and arranging Ns + Ng, wherein Ng and Ns are the total number of the gas and the surface infinitesimal respectively, and then the total infinitesimal number is Ns + Ng;
calculating the fraction k U of all infinitesimal emission energy beams in the heat exchange field to other sections i J and ratio K i，j After the first round of sampling tracking, the method can obtain
Wherein, K i,j The proportion of energy emitted for the ith element to reach the jth element; n is a radical of i The total energy emitted for the ith bin; k =0,1,2,3 \8230, k =0 indicates that the energy emitted by the ith element directly reaches the energy of the jth element, and the other indicates that the energy emitted by the ith element reaches the energy of the jth element after k cycles.
In step 3), calculating the energy of each infinitesimal reaching the designated infinitesimal through reflection as follows:
301 Energy U) for transmitting the energy emitted by the ith element to the jth element i，j The energy directly reaching the absorption and the energy reaching the absorption after k times of reflection are accumulated;
302 8230when j =1,2, ns, i.e. the receiving surface is a surface infinitesimal
Wherein epsilon j -the surface blackness of the ith voxel, m being the number of the receiving surface voxel;
303 When the receiving element is a gas element
In the step 5), calculating the total exchange area, and when the ratio of the remaining energy to the transmitted energy after a beam of energy is reflected for multiple times is smaller than a set value a, finishing the calculation, wherein the energy reflection times are the total reflection times;
after the energy is reflected for k times, all sections in the heat exchange field emit total energy beams
Wherein k is the total number of reflections, N i The total energy emitted by the ith voxel.
The invention has the following beneficial effects and advantages:
1. the method adopts the improved Monte Carlo method to calculate the total heating furnace exchange area, has higher efficiency than the traditional Monte Carlo method, has more obvious advantages along with the increase of the number of the emitted energy beams, and can save a large amount of calculation time and improve the accuracy of the calculation when the improved Monte Carlo method is adopted to solve the total exchange area, particularly when the grid division is thinner and the precision requirement is higher.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention;
FIG. 2 is an exemplary partitioning of a two-dimensional model of the present invention;
FIG. 3A is a graph of the relative error at G1Gi (i = 1-9) for the total exchange area between the stages calculated by the method of the present invention and the Monte Carlo method;
FIG. 3B is a graph of the relative error at G1Si (i = 1-12) for the total exchange area between the stages calculated by the method of the present invention and the Monte Carlo method;
FIG. 3C is a graph of the relative error in S1Si (i = 1-12) for the total exchange area between the stages calculated by the method of the present invention and the Monte Carlo method;
FIG. 3D is a graph of the relative error for the total exchange area between the stages calculated by the method of the present invention and the Monte Carlo method at S1Gi (i = 1-9).
Detailed Description
The invention is further elucidated with reference to the accompanying drawings.
As shown in FIG. 1, the method for solving the exchange area of the full heating furnace by the improved Monte Carlo method comprises the following steps:
1) Inputting two-dimensional closed system parameters in a radiation field of a full heating furnace;
2) Calculating the fraction and proportion of each infinitesimal (including a surface section and a gas section) transmitted energy beam to other infinitesimal according to the parameters;
2) Calculating and storing the energy of each micro element (including a surface segment and a gas segment) divided by the two-dimensional closed system reaching the appointed micro element through reflection;
4) Calculating whether the ratio of the residual energy to the emission energy of one beam of energy after multiple reflections meets the requirement or not;
5) If the requirements are met, calculating the total exchange area, and finishing the calculation process;
6) And if the precision requirement is not met, returning to the step of calculating the energy of each micro element (comprising the surface segment and the gas segment) divided by the two-dimensional closed system to the specified micro element through reflection and storing.
In the method, during radiation heat exchange, the proportion of the energy of all the energy emitted by the element to other sections is assumed to be the same as the proportion of the energy reflected by the element to other sections, and the proportion is independent of the emitted energy share and the reflected energy share. Therefore, when the Monte Carlo method is adopted to solve the total exchange area, the energy beams emitted by all the micro-elements are sampled and tracked once, the energy and the proportion of the total energy emitted by each micro-element reaching other sections are recorded, the energy reaching the gas micro-elements is directly absorbed, the energy reaching the surface micro-elements is absorbed or reflected through the blackness judgment of the surface micro-elements, when the surface units reflect, the reflected energy beams are processed according to the emitted energy beams, and the proportion reaching other sections is determined before, and recalculation is not needed.
In the step 1), the parameters comprise a geometric value, gridding columns and rows of a two-dimensional closed system in a radiation field of the full heating furnace, the number of surface section emission points divided by each dimensional closed system and the number of energy beams generated by each point, the number of emission points of each two-dimensional closed system gas section and the number of energy beams generated by each point, the blackness of the surface section and the absorption coefficient of gas;
in this embodiment, the input parameters include a geometric value of 3m × 3m of a two-dimensional closed system in a radiation field of the total heating furnace, and the number of segments N divided in the gridding length direction x =3, number of segments N divided in height direction y =3, number of surface segment emission points M divided by each two-dimensional closed system s =100, and the number of energy beams N occurring per point number s =100 number of emission points M of gas segment divided by each two-dimensional closed system g =100 and number of energy beams N generated per point number g =100, blackness of surface segment ∈ =0.8, and absorption coefficient Ka of gas segment =0.5.
In step 2), the fraction and proportion of energy beams emitted by each micro element (including a surface segment and a gas segment) divided by the two-dimensional closed system to other micro elements are calculated, and the method specifically comprises the following steps:
201 The order of the elements is arranged as follows: sequentially naming the surface microelements divided by a two-dimensional closed system as 1,2, \8230, arranging the gas microelements behind the surface microelements to be Ns +1, ns +2, \8230, and Ns + Ng, wherein Ng and Ns are the total number of the gas and the surface microelements respectively, and then the total number of the microelements is Ns + Ng;
calculating the fraction k U of all infinitesimal emission energy beams in the heat exchange field to other sections i J and ratio K i，j After the first round of sampling tracking, the method can obtain
Wherein, K i,j The proportion of the energy emitted by the ith element to the energy reaching the jth element; n is a radical of i The total energy emitted for the ith bin; k =0,1,2,3 \8230, k =0 indicates that the energy emitted by the ith element directly reaches the energy of the jth element, and the other indicates that the energy emitted by the ith element reaches the energy of the jth element after k cycles.
In step 3), calculating the energy of each micro element (including the surface segment and the gas segment) divided by the two-dimensional closed system, which reaches the designated micro element by reflection, as follows:
301 Energy emitted by the ith element finally reaches the energy U of the jth element i，j The energy directly reaching the absorption and the energy reaching the absorption after k times of reflection are accumulated;
302 8230when j =1,2, ns, i.e. the receiving surface is a surface infinitesimal
Wherein epsilon j -the surface blackness of the ith voxel, m being the number of the receiving surface voxel.
303 When the receiving element is a gas element
In the step 5), calculating the total exchange area, and when the ratio of the remaining energy to the transmitted energy after a beam of energy is reflected for multiple times is smaller than a set value, finishing the calculation, wherein the energy reflection times are the total reflection times;
after the energy is reflected for k times, all the sections in the heat exchange field emit total energy beams
Wherein k is the total number of reflections, N i The total energy emitted by the ith bin, a, is a set precision value, here set to 0.001.
In this embodiment, the set parameters and the experimental results are shown in the following table, where M represents the number of emission points of each segment, N represents the number of energy rays emitted by each point, MCM represents the monte carlo method, and IMCM represents the improved monte carlo method.
As shown in FIG. 2, the present embodiment uses a two-dimensional closed system as an example, and divides the length direction of the gridding into the number of segments N x =3, number of segments N divided in height direction y =3, surface infinitesimal S named sequentially (bottom-top-left-right) 1 -S 12 The gas section being designated by the name G from bottom to top 1 -G 9 。
As shown in fig. 3A to 3D, wherein fig. 3A is based on the calculation result of the falling weight integral method, the gas segment G 1 Relative error with other gas segments; FIG. 3B shows a gas segment G based on the calculation result of the weight-reduction integration method 1 Relative error with other surface segments; FIG. 3C is a surface segment S based on the calculation result of the weight-reduction integration method 1 Relative error with other surface segments; FIG. 3D is a surface segment S based on the calculation result of the weight-reduction integration method 1 Relative error with other gas segments;
through the comparison, when the transmitted energy beams are the same, the result precision of the improved Monte Carlo method for calculating the total exchange area is higher than that of the traditional Monte Carlo method, namely the error is small and the stability is good.
The method adopts the improved Monte Carlo method to calculate the total heating furnace exchange area, has higher efficiency than the traditional Monte Carlo method, has more obvious advantages along with the increase of the number of the emitted energy beams, and can save a large amount of computer time and improve the accuracy of calculation when the improved Monte Carlo method is adopted to solve the total exchange area, particularly when the grid division is thinner and the precision requirement is higher.
Claims (4)
1. A Monte Carlo method for solving the exchange area of a full heating furnace is characterized by comprising the following steps:
1) Inputting parameters of a two-dimensional closed system in a radiation field of a full heating furnace;
2) Calculating the share and proportion of each infinitesimal emission energy beam to other infinitesimals divided by the two-dimensional closed system according to the parameters;
3) Calculating and storing the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection;
4) Calculating whether the ratio of the residual energy to the emission energy of one beam of energy after multiple reflections meets the requirement or not;
5) If the requirements are met, calculating the total exchange area, and finishing the calculation process;
6) If the precision requirement is not met, returning to the step of calculating the energy of each micro element divided by the two-dimensional closed system reaching the appointed micro element through reflection and storing;
in step 3), calculating the energy of each infinitesimal reaching the designated infinitesimal through reflection as follows:
301 Energy emitted by the ith element finally reaches the energy U of the jth element i，j The method is divided into two conditions of energy directly reaching the absorber and energy accumulated after k times of reflection;
302 When j =1,2, \ 8230;, ns, i.e., the receiving surface is a surface infinitesimal
Wherein epsilon j -the surface blackness of the jth infinitesimal, m being the number of the receiving surface infinitesimal;
303 When the receiving element is a gas element
2. The monte carlo method for solving the total heat exchanging area according to claim 1, wherein: in the step 1), the parameters comprise a geometric value, gridding columns and rows of a two-dimensional closed system in a radiation field of the full heating furnace, the number of emission points of each two-dimensional rectangular surface section and the number of energy beams generated by each point, the number of emission points of each two-dimensional rectangular gas section and the number of energy beams generated by each point, the blackness of the surface section and the absorption coefficient of the gas section.
3. The monte carlo method for solving the full heat exchanger area of claim 1, wherein: in the step 2), the fraction and the proportion of the energy beams emitted by the surface section and the gas section divided by the two-dimensional closed system to other infinitesimals are calculated, and the method specifically comprises the following steps:
201 The order of the elements is arranged as follows: sequentially naming the surface infinitesimal of a two-dimensional closed system as 1,2, \8230, arranging the gas infinitesimal behind the surface infinitesimal as Ns +1, ns +2, \8230, and arranging Ns + Ng, wherein Ng and Ns are the total number of the gas and the surface infinitesimal respectively, and then the total infinitesimal number is Ns + Ng;
calculating the fraction kU of all infinitesimal emission energy beams in the heat exchange field reaching other sections i,j And ratio K i，j After the first round of sampling tracking, the method can obtain
Wherein, K i,j Energy emitted for the ith element reaches the energy of the jth elementThe ratio of (A) to (B); n is a radical of i The total energy emitted for the ith infinitesimal; k =0,1,2,3 \8230, k =0 indicates that the energy emitted by the ith element directly reaches the energy of the jth element, and the other indicates that the energy emitted by the ith element reaches the energy of the jth element after k cycles.
4. The monte carlo method for solving the full heat exchanger area of claim 1, wherein: in the step 5), calculating the total exchange area, and when the ratio of the remaining energy to the transmitted energy after a beam of energy is reflected for multiple times is smaller than a set value a, finishing the calculation, wherein the energy reflection times are the total reflection times;
after the energy is reflected for k times, all the sections in the heat exchange field emit total energy beams
Wherein k is the total number of reflections, N i The total energy emitted for the ith bin.
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