CN107341339B - Particle dirt equivalent thermal conductivity coefficient calculation method based on porous medium characteristics - Google Patents
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
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- 229910000019 calcium carbonate Inorganic materials 0.000 description 10
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- 238000009776 industrial production Methods 0.000 description 1
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- QSHDDOUJBYECFT-UHFFFAOYSA-N mercury Chemical compound [Hg] QSHDDOUJBYECFT-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention relates to the field of heat conductivity coefficients of particle dirt on the surface of heat exchange equipment, in particular to a particle dirt equivalent heat conductivity coefficient calculation method based on the characteristics of a porous medium, which is characterized by comprising the following steps: based on an image processing method, the porosity of the particle dirt is obtained by considering the characteristics of the porous medium of the particle dirt, and the equivalent thermal conductivity coefficient of the particle dirt is calculated according to the equivalent derivative coefficient expression of the porous medium particle dirt obtained by theoretical analysis. The problems of high measurement cost and unreliable data of the existing thermal resistance of the dirt are solved, the surface research of the particle dirt is more accurate and standard, the transfer mechanism of heat in the particle dirt is more deeply disclosed, a new way is opened up for the calculation of the thermal resistance of the particle dirt, and a scientific basis is laid for reducing dirt damage.
Description
Technical Field
The invention relates to the field of heat conductivity coefficients of particle dirt on the surface of heat exchange equipment, in particular to a particle dirt equivalent heat conductivity coefficient calculation method based on the characteristics of a porous medium.
Background
Heat exchange equipment is one of the equipment of using often in industrial production and daily life, and heat exchange equipment is because the surface deposit dirt when moving for equipment heat transfer ability worsens, can accelerate heat exchange equipment's ageing when serious, shortens heat exchange equipment's life, can influence heat exchange equipment's safe operation even. The economical efficiency of the heat exchange equipment is greatly reduced, the operation cost is increased, and great energy waste is caused. Therefore, the calculation of the heat conductivity coefficient of the dirt can provide reference for selecting the heat conductivity coefficient of the dirt and determining the heat exchange area when the heat exchange equipment is designed, and also lays a theoretical basis for reducing the dirt damage.
The surface of the granular dirt is very obvious in irregularity and complexity, pores exist in the granular dirt, and the granular dirt is considered to be a porous medium consisting of a plurality of solid skeletons and pores among the skeletons, the internal structure of the granular dirt is complex and variable and is not easy to describe, and the heat conductivity coefficient of the dirt is difficult to obtain or has a large error. At present, the measurement of the thermal resistance of dirt can only depend on a thermal method and a non-thermal transmission method, but the method has the defects of complexity and high cost. The thermal process is described in patent application No.: 201210109422.3, which discloses a device and method for measuring thermal resistance and thermal conductivity of dirt. The method has the main defects that the complex structure of dirt is not considered, the actual heat conductivity coefficient of the dirt cannot be truly reflected, and the calculated data is unreliable. The experimental result of Roman Dyga suggests an expression of equivalent derivative coefficient of porous medium, which indicates that the equivalent thermal conductivity of porous medium is only related to porosity, while the current methods for measuring porosity include mercury intrusion method, density method, infiltration method and statistical method, but the methods are difficult to be applied to the measurement of the porosity of dirt.
Disclosure of Invention
Aiming at the problems of high measurement cost, complex method and unreliable data of the existing thermal resistance of dirt, the invention obtains the porosity of the particle dirt by considering the porous medium characteristic of the particle dirt based on the image processing technology, and provides a particle dirt equivalent thermal conductivity coefficient calculation method based on the porous medium characteristic according to theoretical analysis, thereby obtaining the equivalent thermal conductivity coefficient, enabling the particle dirt research to be more accurate and standard, further more deeply disclosing the heat transfer mechanism in the particle dirt, and laying a scientific basis for reducing dirt damage.
The technical scheme adopted for realizing the invention is as follows: a method for calculating equivalent thermal conductivity of particle dirt based on characteristics of a porous medium is characterized by comprising the following steps: based on a picture processing technology, the porosity of the particle dirt is obtained by considering the porous medium characteristic of the particle dirt, an equivalent thermal conductivity coefficient expression of the particle dirt with the porous medium characteristic is provided according to theoretical analysis, and the equivalent thermal conductivity coefficient of the particle dirt is calculated, and the method specifically comprises the following steps:
1) calculating the porosity of the particulate fouling:
the porosity was calculated as:
in the formula: ε is the porosity; s0Is the area of the pores of the dirt, m2(ii) a S is the area of the fouling, m2；
2) Theoretical analysis theories an equivalent thermal conductivity coefficient correlation formula of the particle dirt with the characteristics of the porous medium:
the granular dirt is considered to be a porous medium consisting of a solid framework and pores between the solid framework, the equivalent thermal conductivity of the granular dirt is related to the thermal conductivity of the solid framework, the thermal conductivity of fluid in the pores and the porosity, according to the microstructure of the dirt obtained by experiments, a unit model is taken as a cube, a spherical cavity of a gas medium is arranged in the middle, the spherical cavity is simplified into the cube cavity for simplifying calculation, the cavity is communicated with the periphery,
when heat flows pass through the unit bodies, the heat flows pass through the unit bodies in a shunting manner by three parallel paths when encountering different heat resistance media, and the heat resistance of each path is specifically expressed as follows by referring to a method of equivalent resistance in a circuit network: the thermal resistance of the first path is the thermal resistance of the middle air hole along the heat flow direction and is marked as Rf(ii) a The second path thermal resistance is the thermal resistance of 4 solid phase mediums along the heat flow direction and is marked as Rs(ii) a The third path thermal resistance is a series structure of three partial thermal resistances, wherein the first partial thermal resistance is a thermal resistance of a cross bar solid phase medium vertical to the heat flow direction and is marked as Rs1(ii) a The second part of thermal resistance is the thermal resistance of the vent holes at four sides along the heat flow direction and is marked as Rf1(ii) a The third part of the thermal resistance is also the thermal resistance of the solid phase medium of the cross bar perpendicular to the heat flow direction and is marked as Rs2，
Assuming that the heat transfer in the unit body is one-dimensional heat conduction, the effective thermal conductivity of the unit body, i.e. the equivalent thermal conductivity of the porous medium characteristic particle dirt, can be expressed as:
λε＝ελf+(1-ε)λe(2)
in the formula: lambda [ alpha ]εThe effective thermal conductivity of the unit body, namely the equivalent thermal conductivity of the porous medium characteristic particle dirt, W/(m.K); lambda [ alpha ]fThe thermal conductivity coefficient of fluid media in pores, W/(m.K); lambda [ alpha ]eThe effective thermal conductivity of the four sides of the unit body, namely the thermal conductivity W/(m.K) of the solid framework; ε is the porosity;
calculating formula (1) according to the porosity, substituting the cavity side length L and the solid framework side length h of the unit into formula (1) to obtain the porosity:
in the formula: l is the side length of the cavity of the unit body, m; h is the side length of the solid framework, m;
to calculate the effective thermal conductivity of the four sides of the unit cell, i.e. the thermal conductivity of the solid skeleton lambdaeIf the temperature difference between the upper and lower surfaces of the unit body is Δ T, the total heat flow is divided into 4 heat flows Q conducted through the solid-phase medium in the heat flow direction1And heat flow Q conducted by cross bar solid phase medium perpendicular to heat flow direction and vent holes on four sides2Two parts are obtained according to Fourier law:
in the formula: q1Is the heat flow conducted by 4 solid phase media along the heat flow direction, W; q2To pass perpendicular to the direction of heat flowHeat flow, W, conducted by the solid-phase medium of the cross rod and the vent holes on the four sides; lambda [ alpha ]sThe thermal conductivity coefficient of a solid phase medium, W/(m.K);
the effective thermal conductivity of the four sides of the unit body, i.e. the thermal conductivity of the solid skeleton lambdaeComprises the following steps:
substituting the formula (4) and the formula (5) into the formula (6) to obtain a solid framework heat conduction coefficient formula (7):
the transformation simplification of equation (3) yields:
the formula (8) is substituted into the formula (7) to further obtain the solid skeleton heat conductivity coefficient lambdaeComprises the following steps:
the heat conductivity coefficient lambda of the solid frameworkeThe formula (9) is substituted for the formula (2) to obtain the equivalent thermal conductivity expression of the granular dirt with the characteristics of the porous medium:
as can be seen from the formula (10), the equivalent thermal conductivity of the porous medium particle dirt can be obtained as long as the type, working medium type and dirt porosity of the particle dirt can be determined;
3) substituting the porosity epsilon calculated by the formula (1) into the porous medium particle fouling equivalent derivative coefficient expression (10) to calculate the particle fouling equivalent thermal conductivity coefficient.
The invention discloses a method for calculating equivalent thermal conductivity of particle dirt based on porous medium characteristics, which aims at solving the problems of high measurement cost, complex method and unreliable data of the existing thermal resistance of dirt, and aims to obtain the porosity of the particle dirt by considering the porous medium characteristics of the particle dirt based on an image processing technology, and provide a method for calculating equivalent thermal conductivity of particle dirt based on the porous medium characteristics according to theoretical analysis, so that the equivalent thermal conductivity is obtained, the particle dirt research is more accurate and standard, the heat transfer mechanism in the particle dirt is more deeply disclosed, a new way is opened for accurately calculating the thermal conductivity of the particle dirt, the method has important significance for the researches such as identification of the type of the particle dirt and the growth of the particle dirt, and the scientific basis is laid for reducing dirt. The method has the advantages of simplicity, low cost, reliable calculation result, strong practicability, good effect and the like.
Drawings
FIG. 1 is a simplified model of porous media particulate fouling;
FIG. 2 is a graph of a thermal fouling resistance network of porous media particles;
FIG. 3 is a scanning electron microscope image of calcium carbonate scale on the surface of a heat exchanger;
FIG. 4 is a binarized map of calcium carbonate fouling on the surface of a heat exchanger.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention discloses a method for calculating equivalent thermal conductivity of particle dirt based on porous medium characteristics, which is based on a picture processing technology, considers the porous medium characteristics of the particle dirt, obtains the porosity of the particle dirt, provides an equivalent thermal conductivity expression of the particle dirt with the porous medium characteristics according to theoretical analysis, and calculates the equivalent thermal conductivity of the particle dirt, and specifically comprises the following steps:
1) and (3) calculating the porosity of the particle dirt, wherein the porosity is calculated by the following formula:
in the formula: ε is the porosity; s0Is the area of the pores of the dirt, m2(ii) a S is the area of the fouling, m2；
2) Theoretical analysis deduces an equivalent thermal conductivity coefficient correlation formula of the particle dirt with the characteristics of the porous medium;
the particle dirt is considered to be a porous medium consisting of a solid framework and pores between the solid framework, the equivalent thermal conductivity of the particle dirt is related to the thermal conductivity of the solid framework, the thermal conductivity of fluid in the pores and the porosity, according to the microstructure of the dirt obtained by experiments, a unit model is taken as a cube, a spherical cavity of a gas medium is arranged in the middle, and the spherical cavity is simplified into the cube cavity for simplifying calculation, as shown in figure 1.
When heat flows pass through the unit bodies, the heat flows pass through the unit bodies in a shunting manner by different paths when meeting different heat resistance media, and the heat flows pass through the unit bodies in a shunting manner by three parallel paths according to a method of equivalent resistance in a circuit network, wherein a diagram of the heat resistance network of the unit bodies is shown in figure 2, and the heat resistance of each path is specifically expressed as follows: the thermal resistance of the first path is the thermal resistance of the middle air hole along the heat flow direction and is marked as Rf(ii) a The second path thermal resistance is the thermal resistance of 4 solid phase mediums along the heat flow direction and is marked as Rs(ii) a The third path thermal resistance is a series structure of three partial thermal resistances, wherein the first partial thermal resistance is a thermal resistance of a cross bar solid phase medium vertical to the heat flow direction and is marked as Rs1(ii) a The second part of thermal resistance is the thermal resistance of the vent holes at four sides along the heat flow direction and is marked as Rf1(ii) a The third part of the thermal resistance is also the thermal resistance of the solid phase medium of the cross bar perpendicular to the heat flow direction and is marked as Rs2。
Assuming that the heat transfer in the unit body is one-dimensional heat conduction, the effective thermal conductivity of the unit body, i.e. the equivalent thermal conductivity of the porous medium characteristic particle dirt, can be expressed as:
λε＝ελf+(1-ε)λe(2)
in the formula: lambda [ alpha ]εThe effective thermal conductivity of the unit body, namely the equivalent thermal conductivity of the porous medium characteristic particle dirt, W/(m.K); lambda [ alpha ]fThe thermal conductivity coefficient of fluid media in pores, W/(m.K); lambda [ alpha ]eEffective heat conduction system for four sides of unit bodyNumber, i.e., solid skeleton thermal conductivity W/(m.K); ε is the porosity;
calculating formula (1) according to the porosity, substituting the cavity side length L and the solid framework side length h of the unit into formula (1) to obtain the porosity:
in the formula: l is the side length of the cavity of the unit body, m; h is the side length of the solid framework, m; epsilon is the void fraction;
to calculate the effective thermal conductivity of the four sides of the unit cell, i.e. the thermal conductivity of the solid skeleton lambdaeIf the temperature difference between the upper and lower surfaces of the unit body is Δ T, the total heat flow is divided into 4 heat flows Q conducted through the solid-phase medium in the heat flow direction1And heat flow Q conducted by cross bar solid phase medium perpendicular to heat flow direction and vent holes on four sides2Two parts are obtained according to Fourier law:
in the formula: q1Is the heat flow conducted by 4 solid phase media along the heat flow direction, W; q2The heat flow is conducted through a cross bar solid phase medium perpendicular to the heat flow direction and vent holes on four sides; lambda [ alpha ]sThe thermal conductivity coefficient of a solid phase medium, W/(m.K);
the effective thermal conductivity of the four sides of the unit body, i.e. the thermal conductivity of the solid skeleton lambdaeComprises the following steps:
substituting the formula (4) and the formula (5) into the formula (6) to obtain a solid framework heat conduction coefficient formula (7):
the transformation simplification of equation (3) yields:
the formula (8) is substituted into the formula (7) to further obtain the solid skeleton heat conductivity coefficient lambdaeComprises the following steps:
the heat conductivity coefficient lambda of the solid frameworkeThe formula (9) is substituted for the formula (2) to obtain the equivalent thermal conductivity expression of the granular dirt with the characteristics of the porous medium:
as can be seen from equation (10), the equivalent thermal conductivity of the porous medium particle scale can be obtained as long as the type of the particle scale, the type of the working medium, and the porosity of the scale can be determined.
Therefore, the equivalent thermal conductivity coefficient of the particle fouling can be calculated by substituting the porosity epsilon calculated by the formula (1) into the expression (10) of the equivalent derivative coefficient of the particle fouling of the porous medium.
The specific embodiment is as follows:
a. determination of surface porosity of particulate soils
The method comprises the steps of taking calcium carbonate dirt on the surface of a heat exchanger as a sample, firstly scanning the calcium carbonate dirt by using a scanning electron microscope to obtain a scanning electron microscope Image (shown in figure 3) of the calcium carbonate dirt, then carrying out binarization treatment on the scanning electron microscope Image of the calcium carbonate dirt by using Image-pro plus 6.0 Image analysis processing software commonly used in the field to obtain a binarization Image (shown in figure 4) of the calcium carbonate dirt, finally measuring the pore area of the obtained binarization Image of the calcium carbonate dirt, and calculating by using a particle dirt surface porosity calculation formula (1) to obtain the porosity of the calcium carbonate dirt as epsilon.
By the formula of porosity ∈ ═ S0The porosity was calculated to be 37.14%.
b. Equivalent thermal conductivity of particulate fouling
The medium in the pores of the dirt is water, so the heat conductivity coefficient of the fluid is the heat conductivity coefficient of water, and lambda is takenf＝0.6W·(m·K)-1The fouling solid skeleton consists of calcium carbonate and takes lambdas＝2.9W·(m·K)-1. And (3) substituting each parameter into the porous medium particle dirt equivalent derivative coefficient correlation formula (10) to obtain:
the above embodiments are only intended to illustrate the present invention, but not to limit it, and it should be understood by those skilled in the art that any modifications and equivalent changes made with reference to the above embodiments are within the scope of the claims of the present invention.
Claims (1)
1. A method for calculating equivalent thermal conductivity of particle dirt based on characteristics of a porous medium is characterized by comprising the following steps: based on a picture processing technology, the porosity of the particle dirt is obtained by considering the porous medium characteristic of the particle dirt, an equivalent thermal conductivity coefficient expression of the particle dirt with the porous medium characteristic is provided according to theoretical analysis, and the equivalent thermal conductivity coefficient of the particle dirt is calculated, and the method specifically comprises the following steps:
1) calculating the porosity of the particulate fouling:
the porosity was calculated as:
in the formula: ε is the porosity; s0Is the area of the pores of the dirt, m2(ii) a S is the area of the fouling, m2；
2) Theoretical analysis theories an equivalent thermal conductivity coefficient correlation formula of the particle dirt with the characteristics of the porous medium:
the granular dirt is considered to be a porous medium consisting of a solid framework and pores between the solid framework, the equivalent thermal conductivity of the granular dirt is related to the thermal conductivity of the solid framework, the thermal conductivity of fluid in the pores and the porosity, according to the microstructure of the dirt obtained by experiments, a unit model is taken as a cube, a spherical cavity of a gas medium is arranged in the middle, the spherical cavity is simplified into the cube cavity for simplifying calculation, the cavity is communicated with the periphery,
when heat flows pass through the unit bodies, the heat flows pass through the unit bodies in a shunting manner by three parallel paths when encountering different heat resistance media, and the heat resistance of each path is specifically expressed as follows by referring to a method of equivalent resistance in a circuit network: the thermal resistance of the first path is the thermal resistance of the middle air hole along the heat flow direction and is marked as Rf(ii) a The second path thermal resistance is the thermal resistance of 4 solid phase mediums along the heat flow direction and is marked as Rs(ii) a The third path thermal resistance is a series structure of three partial thermal resistances, wherein the first partial thermal resistance is a thermal resistance of a cross bar solid phase medium vertical to the heat flow direction and is marked as Rs1(ii) a The second part of thermal resistance is the thermal resistance of the vent holes at four sides along the heat flow direction and is marked as Rf1(ii) a The third part of the thermal resistance is also the thermal resistance of the solid phase medium of the cross bar perpendicular to the heat flow direction and is marked as Rs2，
Assuming that the heat transfer in the unit body is one-dimensional heat conduction, the effective thermal conductivity of the unit body, i.e. the equivalent thermal conductivity of the porous medium characteristic particle dirt, can be expressed as:
λε＝ελf+(1-ε)λe(2)
in the formula: lambda [ alpha ]εThe effective thermal conductivity of the unit body, namely the equivalent thermal conductivity of the porous medium characteristic particle dirt, W/(m.K); lambda [ alpha ]fThe thermal conductivity coefficient of fluid media in pores, W/(m.K); lambda [ alpha ]eThe effective thermal conductivity of the four sides of the unit body, namely the thermal conductivity W/(m.K) of the solid framework; ε is the porosity;
calculating formula (1) according to the porosity, substituting the cavity side length L and the solid framework side length h of the unit into formula (1) to obtain the porosity:
in the formula: l is the side length of the cavity of the unit body, m; h is the side length of the solid framework, m;
to calculate the effective thermal conductivity of the four sides of the unit cell, i.e. the thermal conductivity of the solid skeleton lambdaeIf the temperature difference between the upper and lower surfaces of the unit body is Δ T, the total heat flow is divided into 4 heat flows Q conducted through the solid-phase medium in the heat flow direction1And heat flow Q conducted by cross bar solid phase medium perpendicular to heat flow direction and vent holes on four sides2Two parts are obtained according to Fourier law:
in the formula: q1Is the heat flow conducted by 4 solid phase media along the heat flow direction, W; q2The heat flow is conducted through a cross bar solid phase medium perpendicular to the heat flow direction and vent holes on four sides; lambda [ alpha ]sThe thermal conductivity coefficient of a solid phase medium, W/(m.K);
the effective thermal conductivity of the four sides of the unit body, i.e. the thermal conductivity of the solid skeleton lambdaeComprises the following steps:
substituting the formula (4) and the formula (5) into the formula (6) to obtain a solid framework heat conduction coefficient formula (7):
the transformation simplification of equation (3) yields:
the formula (8) is substituted into the formula (7) to further obtain the solid skeleton heat conductivity coefficient lambdaeComprises the following steps:
the heat conductivity coefficient lambda of the solid frameworkeThe formula (9) is substituted for the formula (2) to obtain the equivalent thermal conductivity expression of the granular dirt with the characteristics of the porous medium:
as can be seen from the formula (10), the equivalent thermal conductivity of the porous medium particle dirt can be obtained as long as the type, working medium type and dirt porosity of the particle dirt can be determined;
3) substituting the porosity epsilon calculated by the formula (1) into the porous medium particle fouling equivalent derivative coefficient expression (10) to calculate the particle fouling equivalent thermal conductivity coefficient.
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| US8165855B2 (en) * | 2009-05-27 | 2012-04-24 | King Fahd University Of Petroleum & Minerals | Method for modeling fluid flow over porous blocks |
| CN106248725A (en) * | 2016-09-16 | 2016-12-21 | 北京工业大学 | A kind of porous media Equivalent Thermal Conductivities measuring method |
| CN106596630A (en) * | 2016-12-20 | 2017-04-26 | 东北电力大学 | Calculation method of granular dirt equivalent heat conduction coefficient |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US8165855B2 (en) * | 2009-05-27 | 2012-04-24 | King Fahd University Of Petroleum & Minerals | Method for modeling fluid flow over porous blocks |
| CN106248725A (en) * | 2016-09-16 | 2016-12-21 | 北京工业大学 | A kind of porous media Equivalent Thermal Conductivities measuring method |
| CN106596630A (en) * | 2016-12-20 | 2017-04-26 | 东北电力大学 | Calculation method of granular dirt equivalent heat conduction coefficient |
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| Title |
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| heat transfer through metal foam-fluid system;Roman dyga 等;《Experimental thermal and fluid science》;20150227;全文 * |
| 基于有限元法的污垢等效导热系数计算;张仲彬 等;《中国电机工程学报》;20170520;第37卷(第10期);全文 * |
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