CN112989618B - Multi-layer medium temperature distribution calculation method and device based on observation data - Google Patents
Multi-layer medium temperature distribution calculation method and device based on observation data Download PDFInfo
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Abstract
The embodiment of the invention provides a multilayer medium temperature distribution calculation method and device based on observation data, comprising the following steps: acquiring the excircle radius of a cylinder formed by multiple layers of media and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity; constructing a numerical calculation format according to a heat conduction equation, a thermophysical parameter and boundary conditions of a first class, a second class or a third class and by combining detectable temperature or heat flow observation data on the boundary; from the temperature or heat flow observation data detectable at the boundary, the temperature field and heat flow field at the investigation region are calculated in a calculation format. The method utilizes the multi-class part observation data on the boundary of the research area to design a stabilization algorithm, calculates the temperature field distribution of the multi-layer medium, and fills the blank of the numerical method and the simulation technology in the aspect.
Description
Technical Field
The invention relates to the technical field of multilayer medium temperature field distribution numerical simulation, in particular to a multilayer medium temperature distribution calculation method and device based on observation data.
Background
The multiple layers of material may cause different temperature profiles during heat transfer from different dielectric materials. The temperature varies with position inside the material and the temperature of the innermost side of the material varies with the time of heat transfer. Such problems have been widely studied since the 80 s of the 20 th century. In 1981, the temperature of the outer wall surface of the heat insulation layer and the calculation method thereof were studied by taking Yanan's study, and a method for calculating heat loss is given by theoretical deduction. In 2007, the heat conduction differential equation in the form of cylindrical coordinates under the boundary condition of the first class is used for calculating and analyzing the temperature distribution in the cylinder wall, and the heat flow density of the isothermal surface is the same. Zeng Jian and the like consider the inverse problem of the intermittent diffusion coefficient in a heat conduction equation, and prove the uniqueness and the stability of the minimum element when the time is relatively small. In 2018, chen Dawei calculated and plotted the numerical solution of one-dimensional heat conduction equation using the differential format of the heat conduction equation, thereby intuitively obtaining the temperature space-time distribution on the heat conduction medium. At present, researches on solutions of heat conduction equations and thus temperature distribution of heat conduction media during heat transfer are continued. There is no presently disclosed stabilization algorithm for how to calculate the temperature field distribution of a multi-layered medium given the multiple classes of observed data at part of the boundary.
Disclosure of Invention
Therefore, in order to fill the blank of a numerical method and a simulation technology under the condition that the temperature field distribution of the existing multilayer medium is known in a plurality of types of observation data on part boundaries, the embodiment of the invention provides a multilayer medium temperature distribution calculation method and a multilayer medium temperature distribution calculation system based on the observation data. The specific technical scheme is as follows:
in order to achieve the above object, an embodiment of the present invention provides a method for calculating a temperature distribution of a multi-layered medium based on observation data, including the steps of:
acquiring the excircle radius of a cylinder formed by multiple layers of media and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
and constructing a numerical calculation format according to the heat conduction equation, the thermophysical parameters and the boundary conditions of the first class, the second class or the third class and combining partial temperature or heat flow observation data on the boundary.
Calculating all temperature and heat flow data on the boundary according to a calculation format by using part of temperature or heat flow observation data on the boundary; and then calculating the temperature field and the heat flow field on the research area.
Further, the heat conduction equation is:
the expression of the heat flux density is:
wherein c is specific heat capacity, ρ is object density, ω is thermal conductivity, T i (r, t) is the temperature representation of the heat source at each layer, r is the radius of each layer, and f (r, t) is the initial temperature of each layer.
Further, the heat conduction equation is calculated to obtain the temperature field distribution of the heat source, which comprises the following steps:
respectively calculating to obtain a matrix D and a matrix H of the heat conduction equation;
and obtaining the relation between the temperature field distribution and the D matrix and the H matrix according to the D matrix and the H matrix.
Further, the relationship between the temperature field distribution and the D matrix and the H matrix is:
a second aspect of an embodiment of the present invention provides a multilayer medium temperature distribution calculating apparatus based on observation data, including:
the acquisition module is used for acquiring the outer circle radius of the cylinder formed by the multilayer medium and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
the calculation module is used for constructing a numerical calculation format according to a heat conduction equation, the thermal physical parameters and boundary conditions of the first class, the second class or the third class and combining partial temperature or heat flow observation data on the boundary to calculate all temperature and heat flow data on the boundary;
and the temperature field distribution calculation module is used for calculating the heat conduction equation according to all the temperature and heat flow data on the boundary, and calculating the temperature field and the heat flow field on the research area.
Further, the heat conduction equation is:
the expression of the heat flux density is:
where c is specific heat capacity, ρ is object density, ω is thermal conductivity, ti (r, t) is the temperature of the heat source at each layer, r is the radius of each layer, and f (r, t) is the initial temperature of each layer.
Further, the temperature field distribution calculation module comprises a matrix calculation module, which is used for calculating and obtaining a D matrix and an H matrix of the heat conduction equation;
and the relation mapping module is used for obtaining the relation between the temperature field distribution and the D matrix and the H matrix according to the D matrix and the H matrix.
A third aspect of the embodiments of the present invention further provides a computer readable storage medium, on which a computer program is stored, the computer program when executed by a processor causes the processor to process the steps of the above-described multi-layer medium temperature distribution calculating method based on partial boundary observation data.
A fourth aspect of the present invention provides an electronic device comprising:
a processor; the method comprises the steps of,
a memory arranged to store computer executable instructions that, when executed, cause the processor to perform the above-described method of multi-layer medium temperature profile calculation based on partial boundary observations.
The embodiment of the invention provides a multilayer medium temperature distribution calculation method based on observation data, which comprises the following steps: acquiring the outer circle radius of a cylinder composed of multiple layers of media, first temperature data or first heat flow data detected on the outermost layer of the medium of the cylinder, and thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity; according to a heat conduction equation, a thermal physical parameter and a first class, a second class or a third class boundary condition, and combining the detected first temperature data or the first heat flow data, calculating second temperature data and second heat flow data on each layer of medium; and calculating the temperature field of the cylinder according to the first temperature data and the second temperature data, and calculating the heat flow field of the cylinder according to the first heat flow data and the second heat flow data. The method utilizes a plurality of types of observation data which can be detected on the outer layer boundary of the research area, calculates the temperature and heat flow data of each layer of the research area layer by layer according to the observation data according to a heat conduction equation, has stable algorithm design, calculates the temperature field distribution of the multi-layer medium, and fills the numerical method and simulation technology blank of the aspect.
Drawings
FIG. 1 is a flow chart of a method for calculating temperature distribution of a multi-layered medium based on observation data according to embodiment 1 of the present invention;
FIG. 2 is a schematic block diagram of a temperature field of a cross-section of a three-layer cylinder according to embodiment 1 of the present invention;
fig. 3 is a schematic structural diagram of an electronic device according to embodiment 3 of the present invention;
FIG. 4 is a schematic diagram showing the structure of a computer-readable storage medium according to embodiment 4 of the present invention;
in the figure: 31-a processor; 32-a memory; 33-storage space; 34-program code; 41-program code.
Detailed Description
In order to make the technical solution of the present invention clearly and thoroughly revealed, the present invention is described below with reference to the accompanying drawings, but not limited to the scope of the present invention.
Referring to fig. 1, a flowchart of a method for calculating temperature distribution of a multi-layered medium based on observation data according to embodiment 1 of the present invention includes the steps of:
acquiring the outer circle radius of a cylinder composed of multiple layers of media, first temperature data or first heat flow data detected on the outermost layer of the medium of the cylinder, and thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
according to a heat conduction equation, a thermal physical parameter and a first class, a second class or a third class boundary condition, and combining the detected first temperature data or the first heat flow data, calculating second temperature data and second heat flow data on each layer of medium;
and calculating the temperature field of the cylinder according to the first temperature data and the second temperature data, and calculating the heat flow field of the cylinder according to the first heat flow data and the second heat flow data. According to the invention, temperature and heat flow data of the inner layer of the research area are calculated layer by combining a detectable temperature and heat flow of the outer layer of the research area with a heat conduction equation, a thermal physical parameter and a first class boundary condition, a second class boundary condition or a third class boundary condition, and a temperature field and a heat flow field are further calculated according to the temperature and heat flow data. The invention provides a method for calculating a temperature field and a heat flow field by partial observation data, provides a novel numerical value calculation method and fills the technical blank in the field. The specific calculation process is as follows:
consider a solid cylinder made up of N media, the cross-section of which is shown in figure 1 (which illustrates a one-dimensional three-layer medium). Setting: the outer circle radius of the N layers of media is R i The method comprises the steps of carrying out a first treatment on the surface of the The thermophysical parameter of the material is (c i ，ρ i ，λ i ) I=1, 2,3 …, N; c is specific heat capacity, ρ is object density, ω is thermal conductivity.
In the case of axisymmetry, the temperature field of the cylinder cross section is T (r, T);
T(r，t)| t＝0 =f (r) is the initial temperature of each layer;
q i (r，t)| i＝0，r＝0 =g (t) is the heat flux density inside the medium;
T i (r，t)| i＝0，r＝0 =h (t) is the temperature inside the medium;
Introducing heat flux density:
assuming that there is a heat source inside, T i The basic equation expression satisfied by (r, t) is as follows:
initial condition T i (r，t)| t＝0 ＝L i (r)，i＝1，2，3，…，N.
The relationship of continuity between layers is set as follows:
part temperature and heat flow observations at the boundary are known:
q N (R N ，t)＝g(t) (4)
T N (R N ，t)＝h(t). (5)
or alternatively, the process may be performed,
q i (r，t)| i＝0，r＝0 ＝G(t)， (6)
T i (r，t)| i＝0，r＝0 ＝H(t). (7)
from (1) - (3), the distribution of the entire temperature field is calculated in combination with any two of the observation conditions in (4) - (7).
Taking n=3 as an example, the distribution of the entire temperature field is calculated.
When n=3 (calculated by taking the temperature field of the cross section of the three-layer cylinder as an example), as shown in fig. 2, fig. 2 is a schematic diagram of the temperature field of the cross section of the three-layer cylinder, and the radius of the three-layer medium of the cross section is R 1 ，R 2 ，R 3 A1=0 at the center of the circle, known (c i ，ρ i ，ω i ) I=1, 2,3, initial temperature T i 0 (r，0)＝L i (r) the inner boundary temperature and heat flow are respectively:
the outer boundary temperature and the heat flow are respectively: />
The algorithm comprises the following steps:
the first step: d matrix is calculated. First, the eigenvalue lambda of the G matrix is calculated i1 、λ i2 And feature vector v i1 、v i2 Obtaining a conversion matrix p, wherein the conversion matrix p is formed by a characteristic vector v i1 And v i2 And then converting the G matrix by the conversion matrix p to obtain a D matrix. The mathematical expression of the G matrix is as follows:
the expression of the transformation matrix p is: p is p i ＝[v i1 v i2 ]The process of calculating the D matrix from the G matrix and the conversion matrix p is as follows:
analogize and calculate
And then calculating a D inverse matrix by the D matrix.
And a second step of: and calculating an H matrix. First, a time step Deltat is given k And an initial temperature T i 0 (r，0)＝L i (r) substituting the B matrix; then according to B matrix and eigenvalue lambda i1 、λ i2 And feature vector v i1 、v i2 ，
And (5) calculating an H matrix.
The expression of the above B matrix is as follows:
analogic calculation
Deriving
Finally record
Sequentially available temperature field distribution relation
Calculating the temperature field distribution relation expression when N is equal to 3 (when N is greater than 3, the same calculation is performed), and since the D matrix and the H matrix in the equation set are already calculated, only the calculation is known
And->
Two other quantities can be solved for.
The following is calculated in different cases.
(1)
One of them is known, and ∈ ->
Knowing one of them, a system of equations can be solved
Two other quantities were obtained.
(2) If it is
Is known and->
Unknown; or->
Known, but->
Unknown, the problem is an ill-posed problem, and is solved by the following regularization method.
From the following components
Get->
Order the
Y 1 k (0) By =x, then get->
First pair coefficient matrix
Singular value decomposition, i.e. into the form,/->
Regularized solution defining the above problem>
Satisfies (where alpha is a regularization parameter, delta is an observed data error),
obtaining the regularization solution (stable calculated value of X) of the equation set as
Wherein the method comprises the steps of
For the filtering factor, sigma i Is a coefficient matrix->
Singular values of u i ,v i The components of U and V, respectively.
From equation, initial conditions and resulting boundary conditions
And->
From the relationship type
The internal temperature field can be calculated layer by layer.
The embodiment of the invention provides a multilayer medium temperature distribution calculation method based on observation data, which comprises the following steps: acquiring the excircle radius of a cylinder formed by multiple layers of media and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity; constructing a numerical calculation format according to a heat conduction equation, a thermal physical parameter and boundary conditions of a first class, a second class or a third class and combining partial temperature or heat flow observation data on the boundary, and calculating all temperature and heat flow data on the boundary; and calculating the heat conduction equation according to all the temperature and heat flow data on the boundary, and calculating the temperature field and the heat flow field on the research area.
The method utilizes the multi-class part observation data on the boundary of the research area to design a stabilization algorithm, calculates the temperature field distribution of the multi-layer medium, and fills the blank of the numerical method and the simulation technology in the aspect.
A second aspect of an embodiment of the present invention provides a multilayer medium temperature distribution calculating apparatus based on observation data, including:
the acquisition module is used for acquiring the outer circle radius of the cylinder formed by the multi-layer medium, the first temperature data or the first heat flow data detected on the medium at the outermost layer of the cylinder and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
the calculation module is used for calculating second temperature data and second heat flow data on each layer of medium according to a heat conduction equation, a thermal physical parameter and a first class, a second class or a third class boundary condition by combining the detected first temperature data or the first heat flow data;
and the temperature field distribution calculation module is used for calculating the temperature field of the cylinder according to the first temperature data and the second temperature data, and calculating the heat flow field of the cylinder according to the first heat flow data and the second heat flow data.
Further, the heat conduction equation is:
the expression of the heat flux density is:
where c is specific heat capacity, ρ is object density, ω is thermal conductivity, ti (r, t) is the temperature of the heat source at each layer, r is the radius of each layer, and f (r, t) is the initial temperature of each layer.
Further, the temperature field distribution calculation module comprises a matrix calculation module, which is used for calculating and obtaining a D matrix and an H matrix of the heat conduction equation;
and the relation mapping module is used for obtaining the relation between the temperature field distribution and the D matrix and the H matrix according to the D matrix and the H matrix.
A third aspect of the embodiments of the present invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, causes the processor to process the above-described calculation steps.
A fourth aspect of the present invention provides an electronic device comprising:
a processor; the method comprises the steps of,
a memory arranged to store computer executable instructions which, when executed, cause the processor to perform the above-described computing method.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
It should be noted that:
the algorithms and displays presented herein are not inherently related to any particular computer, virtual machine, or other apparatus. Various general purpose devices may also be used with the teachings herein. The required structure for the construction of such devices is apparent from the description above. In addition, the present invention is not directed to any particular programming language. It will be appreciated that the teachings of the present invention described herein may be implemented in a variety of programming languages, and the above description of specific languages is provided for disclosure of enablement and best mode of the present invention.
In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
Similarly, it should be appreciated that in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. However, the disclosed method should not be construed as reflecting the intention that: i.e., the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
Those skilled in the art will appreciate that the modules in the apparatus of the embodiments may be adaptively changed and disposed in one or more apparatuses different from the embodiments. The modules or units or components of the embodiments may be combined into one module or unit or component and, furthermore, they may be divided into a plurality of sub-modules or sub-units or sub-components. Any combination of all features disclosed in this specification (including any accompanying claims, abstract and drawings), and all of the processes or units of any method or apparatus so disclosed, may be used in combination, except insofar as at least some of such features and/or processes or units are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise.
Furthermore, those skilled in the art will appreciate that while some embodiments described herein include some features but not others included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention and form different embodiments. For example, in the following claims, any of the claimed embodiments can be used in any combination.
Various component embodiments of the invention may be implemented in hardware, or in software modules running on one or more processors, or in a combination thereof. Those skilled in the art will appreciate that some or all of the functions of some or all of the components in an apparatus for detecting the wearing state of an electronic device according to an embodiment of the present invention may be implemented in practice using a microprocessor or Digital Signal Processor (DSP). The present invention can also be implemented as an apparatus or device program (e.g., a computer program and a computer program product) for performing a portion or all of the methods described herein. Such a program embodying the present invention may be stored on a computer readable medium, or may have the form of one or more signals. Such signals may be downloaded from an internet website, provided on a carrier signal, or provided in any other form.
For example, fig. 3 shows a schematic structural diagram of an electronic device according to an embodiment of the present invention. The electronic device conventionally comprises a processor 31 and a memory 32 arranged to store computer executable instructions (program code). The memory 32 may be an electronic memory such as a flash memory, an EEPROM (electrically erasable programmable read only memory), an EPROM, a hard disk, or a ROM. The memory 32 has a memory space 33 storing program code 34 for performing any of the method steps shown in fig. 1 and in various embodiments. For example, the memory space 33 for storing the program code may include individual program code 34 for implementing the various steps in the above method, respectively. The program code can be read from or written to one or more computer program products. These computer program products comprise a program code carrier such as a hard disk, a Compact Disc (CD), a memory card or a floppy disk. Such a computer program product is typically a computer readable storage medium as described for example in fig. 4. The computer readable storage medium may have memory segments, memory spaces, etc. arranged similarly to the memory 32 in the electronic device of fig. 3. The program code may be compressed, for example, in a suitable form. Typically, the memory space stores program code 41 for performing the method steps according to the invention, i.e. there may be program code such as read by the processor 31, which when run by an electronic device causes the electronic device to perform the steps in the method described above.
While the invention has been described in detail in the foregoing general description and specific examples, it will be apparent to those skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.
Claims (4)
1. The multilayer medium temperature distribution measuring and calculating method based on the observation data is characterized by comprising the following steps:
acquiring the outer circle radius of a cylinder composed of multiple layers of media, first temperature data or first heat flow data detected on the outermost layer of the medium of the cylinder, and thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
according to a heat conduction equation, a thermal physical parameter and a first class, a second class or a third class boundary condition, and combining the detected first temperature data or the first heat flow data, calculating second temperature data and second heat flow data on each layer of medium;
calculating the temperature field of the cylinder according to the first temperature data and the second temperature data, and calculating the heat flow field of the cylinder according to the first heat flow data and the second heat flow data;
the heat conduction equation is:
the expression of the heat flux density is:
in the method, in the process of the invention,c i is the specific heat capacity of the material,ρ i for the density of the object to be measured,ω i in order to be of a thermal conductivity coefficient,T i (r,t) For the temperature indication of the heat source at each layer,rfor each layer of the radius,f(r,t) Initial temperature for each layer;
according to the heat conduction equation, the thermal physical parameters and the boundary conditions of the first class, the second class or the third class, the second temperature data and the second heat flow data on each layer of medium are calculated by combining the detected first temperature data or the first heat flow data, and the method comprises the following steps:
respectively calculating to obtain a matrix D and a matrix H of the heat conduction equation;
obtaining the relation between the temperature field distribution and the D matrix and the H matrix according to the D matrix and the H matrix;
the relation between the temperature field distribution and the D matrix and the H matrix is as follows:
2. a multilayer medium temperature distribution measuring and calculating device based on observation data, characterized by comprising:
the acquisition module is used for acquiring the outer circle radius of the cylinder formed by the multi-layer medium, the first temperature data or the first heat flow data detected on the medium at the outermost layer of the cylinder and the thermophysical parameters of the material; wherein the thermophysical parameters include specific heat capacity, object density, and thermal conductivity;
the calculation module is used for calculating second temperature data and second heat flow data on each layer of medium according to a heat conduction equation, a thermal physical parameter and a first class, a second class or a third class boundary condition by combining the detected first temperature data or the first heat flow data;
the temperature field distribution calculation module is used for calculating the temperature field of the cylinder according to the first temperature data and the second temperature data, and calculating the heat flow field of the cylinder according to the first heat flow data and the second heat flow data;
the heat conduction equation is:
the expression of the heat flux density is:
in the method, in the process of the invention,c i is the specific heat capacity of the material,ρ i for the density of the object to be measured,ω i in order to be of a thermal conductivity coefficient,T i (r,t) For the temperature indication of the heat source at each layer,rfor each layer of the radius,f(r,t) Initial temperature for each layer;
according to the heat conduction equation, the thermal physical parameters and the boundary conditions of the first class, the second class or the third class, the second temperature data and the second heat flow data on each layer of medium are calculated by combining the detected first temperature data or the first heat flow data, and the method comprises the following steps:
respectively calculating to obtain a matrix D and a matrix H of the heat conduction equation;
obtaining the relation between the temperature field distribution and the D matrix and the H matrix according to the D matrix and the H matrix;
the relation between the temperature field distribution and the D matrix and the H matrix is as follows:
3. a computer readable storage medium having stored thereon a computer program which, when executed by a processor, causes the processor to process the observed data based multi-layered medium temperature distribution measuring method of claim 1.
4. An electronic device, the electronic device comprising:
a processor; and a memory arranged to store computer executable instructions that, when executed, cause the processor to perform the observed data based multi-layer medium temperature profile measurement method of claim 1.
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