CN108804739A - A kind of coal store inside coal temperature field computation method - Google Patents
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Abstract
The invention discloses a kind of coal temperature field computation methods inside coal store, including：Establish Heat Conduction Differential Equations of the endogenous pyrogen inside coal store in rectangular coordinate system；Heat Conduction Differential Equations of the endogenous pyrogen in three-dimensional system of coordinate are obtained by coordinate transformation method；Step 3, it is radially divided into n-layer interface in storage bin inner wall, is divided into the bed boundarys m in an axial direction, interface forms grid lines in both direction, grid lines crosspoint is node, arranges temperature point at the coal store inner wall on i.e. outermost node layer, respectively on measuring temperature measuring point each node temperature value；In radial directions from outside to inside, and according to the external node layer of heat conduction differential difference equation the control volume represented establishes energy conservation equation, gradually in inquire into underlay nodes temperature.Beneficial effects of the present invention：Based on heat transfer theory, under conditions of obtaining coal store inner wall coal temperature and coal body surface temperature, using numerical computation method, accurate calculation produces coal the temperature of internal portion arbitrary point.
Description
Technical Field
The invention relates to the technical field of coal storage bins, in particular to a method for calculating a coal body temperature field in a coal storage bin.
Background
At present, among several common closed coal storage forms, the silo and the spherical silo have the characteristics of good sealing effect, small occupied area, attractive appearance, flexible coal distribution, good shock resistance, capability of resisting natural disasters such as hurricane and the like, and are widely applied to industries such as electric power, coal, cement, chemical raw materials, grain and the like. Currently, a coal temperature monitoring method for the coal storage bin inner part of a silo and a spherical bin is to install a temperature sensor on the inner wall of the coal storage bin to obtain the coal temperature of an inner wall measuring point, and install an infrared thermometer on the top to obtain the temperature of the upper surface of the coal in the coal storage bin. However, there is no accurate and effective method for monitoring the temperature of the coal in the coal bunker.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for calculating a coal temperature field inside a coal bunker, which is based on the theory of heat transfer, and accurately calculates the temperature of any point inside the coal body by using a numerical calculation method under the condition of obtaining the coal temperature on the inner wall of the coal bunker and the surface temperature of the coal body.
The invention provides a method for calculating a coal body temperature field in a coal storage bin, which comprises the following steps:
step 1, placing an internal heat source T inside a coal storage bin in a rectangular coordinate system, wherein the coordinate is (x, y, z), and establishing a heat conduction differential equation of the internal heat source T in the rectangular coordinate system according to an energy conservation law and a Fourier law:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the variation of temperature per unit time;
step 2, obtaining a heat conduction differential equation of the internal heat source T in a three-dimensional coordinate system by the internal heat source T (x, y, z) in the coal storage bin through a coordinate transformation method;
step 3, dividing the inner wall of the storage bin into n layers of interfaces along the radial direction, dividing the interfaces into m layers of interfaces along the axial direction, forming grid lines on the interfaces in two directions, taking the crossed points of the grid lines as nodes, respectively arranging temperature measuring points on the inner wall of the coal storage bin, namely the outermost nodes, and respectively measuring the temperature value of each node on the temperature measuring points through a temperature sensor;
step 4, establishing an energy conservation equation for the control volume represented by the outer-layer nodes from outside to inside in the radial direction according to the measured temperature and a heat conduction micro equation, gradually and inwards calculating the temperature of the inner-layer nodes, changing the positions of different outer-layer nodes to obtain the temperature of the inner-layer nodes in the whole grid line area, and further obtaining a coal body temperature field in the whole coal storage bin;
wherein, the control volume establishment energy conservation equation represented by any node (i, j) is as follows:
in the formula, QwEnergy exchange between the left end of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QeEnergy exchange between the right edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QnEnergy between the upper edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal bodyQuantity exchange, QsEnergy exchange between the lower edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, qvThe internal heat source intensity, DeltaV is the volume of the infinitesimal body, rho is the density of the heat conductor, lambda is the heat conductivity coefficient, and c is the heat capacity of the heat conductor.
As a further improvement of the invention, in step 2, when the coal storage bin is a silo, the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the cylindrical coordinate system, and the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the coordinates in the cylindrical coordinate system
Wherein,z, r is the vertical distance between the internal heat source T and the z axis,is the included angle between the projection line of OT on the xy surface and the positive x axis, and z is the distance between the T point and the xy surface;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
As a further improvement of the invention, in step 2, when the coal storage bin is a spherical bin, the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the sphereCoordinates in a coordinate system
Wherein,z is rcos theta, r is the distance between the internal heat source T and the origin O of the spherical coordinate, theta is the positive included angle between the directional line segment OT and the z axis,m is the projection of point P on the xOy plane, and is the angle rotated from the x-axis to OM in the counterclockwise direction as viewed from the positive z-axis;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
As a further improvement of the present invention, in step 4, when the coal bunker is a silo, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is obtained according to the fourier law and the newton cooling law:
in the formula, Ti-1,j、Ti,jRespectively representing nodes(ii) a temperature of (i-1, j), (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Denotes the temperature of the nodes (i +1, j), (i, j +1), (i, j-1), respectively, qwIs the node heat flux density.
As a further improvement of the present invention, in step 4, when the coal bunker is a spherical bunker, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is obtained according to the fourier law:
in the formula, Ti-1,j、Ti,jRespectively represent the temperatures of the nodes (i-1, j) and (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Respectively, the temperatures of the nodes (i +1, j), (i, j +1), and (i, j-1).
As a further improvement of the present invention, in step 4, when calculated from outside to inside in the radial direction:
firstly, establishing an energy conservation equation for a control volume represented by an outermost node according to a heat conduction micro equation, and solving a temperature value of a node at the second layer to the last number according to the measured temperature value of the outermost node and the energy conservation equations;
then, establishing an energy conservation equation for the control volume represented by the node of the second layer to the last but according to the heat conduction micro equation, and solving the temperature value of the node of the third layer to the last but according to the temperature value of the node of the second layer to the last but and the energy conservation equations;
pushing layer by layer;
and finally, solving the temperature value of the innermost node.
The invention has the beneficial effects that:
based on the theory of heat transfer science, under the condition of obtaining the temperature of the coal body on the inner wall of the coal storage bin and the surface temperature of the coal body, the temperature of any point in the coal body is accurately calculated by adopting a numerical calculation method, and the real-time monitoring of the temperature in the coal storage bin can be realized.
Drawings
Fig. 1 is a schematic flow chart of a method for calculating a coal temperature field inside a coal storage bunker according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a cylindrical coordinate system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a specific arrangement according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a spherical coordinate system according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to specific embodiments and with reference to the attached drawings.
As shown in fig. 1, a method for calculating a coal temperature field inside a coal storage bin according to an embodiment of the present invention includes:
step 1, placing an internal heat source T inside a coal storage bin in a rectangular coordinate system, wherein the coordinate is (x, y, z), and establishing a heat conduction differential equation of the internal heat source T in the rectangular coordinate system according to an energy conservation law and a Fourier law:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the variation of temperature per unit time;
step 2, obtaining a heat conduction differential equation of the internal heat source T in a three-dimensional coordinate system by the internal heat source T (x, y, z) in the coal storage bin through a coordinate transformation method;
step 3, dividing the inner wall of the storage bin into n layers of interfaces along the radial direction, dividing the interfaces into m layers of interfaces along the axial direction, forming grid lines on the interfaces in two directions, taking the crossed points of the grid lines as nodes, respectively arranging temperature measuring points on the inner wall of the coal storage bin, namely the outermost nodes, and respectively measuring the temperature value of each node on the temperature measuring points through a temperature sensor;
step 4, establishing an energy conservation equation for the control volume represented by the outer-layer nodes according to the measured temperature from outside to inside in the radial direction and a heat conduction micro equation, gradually calculating the temperature of the inner-layer nodes, changing the positions of different outer-layer nodes to obtain the temperature of the inner-layer nodes in the whole grid line area, and further obtaining a coal body temperature field in the whole coal storage bin;
wherein, the control volume establishment energy conservation equation represented by any node (i, j) is as follows:
in the formula, QwEnergy exchange between the left end of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QeEnergy exchange between the right edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QnEnergy exchange between the upper edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QsEnergy exchange between the lower edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, qvIs internal heatThe source intensity, Δ V, is the volume of the infinitesimal body, ρ is the thermal conductor density, λ is the thermal conductivity, and c is the thermal conductor heat capacity.
When calculated from outside to inside in the radial direction:
firstly, establishing an energy conservation equation for a control volume represented by an outermost node according to a heat conduction micro equation, and solving a temperature value of a node at the second layer to the last number according to the measured temperature value of the outermost node and the energy conservation equations;
then, establishing an energy conservation equation for the control volume represented by the node of the second layer to the last but according to the heat conduction micro equation, and solving the temperature value of the node of the third layer to the last but according to the temperature value of the node of the second layer to the last but and the energy conservation equations;
pushing layer by layer;
and finally, solving the temperature value of the innermost node.
Example 1 the coal storage silo is a silo
At this time, in step 2, the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the cylindrical coordinate system, and the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the coordinates in the cylindrical coordinate system
As shown in fig. 2, in which,z, r is the vertical distance between the internal heat source T and the z axis,is the included angle between the projection line of OT on the xy surface and the positive x axis, and z is the distance between the T point and the xy surface;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
In this case, in step 4, when the coal bunker is a silo, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is obtained according to the fourier law and the newton cooling law:
in the formula, Ti-1,j、Ti,jRespectively represent the temperatures of the nodes (i-1, j) and (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Denotes the temperature of the nodes (i +1, j), (i, j +1), (i, j-1), respectively, qwIs the node heat flux density.
Taking a specific implementation scheme as an example, as shown in fig. 3, temperature measuring points are arranged on the inner wall of the storage bin, namely the outermost nodes 11, 12, 13, 14, 15, 16 and 17, so that the temperatures T of the nodes 11, 12, 13, 14, 15, 16 and 17 are measured11、T12、T13、T14、T15、T16、T17Are all known.
Respectively establishing energy conservation equations for the node 13, the node 14 and the node 15 according to the heat conduction micro equation as follows:
in the above formula, the first and second carbon atoms are,controlling the volume angle variation for the node, Δ r being the radial variation of the node control volume, qiIs the flow density at node i, r1Is the first layer radius, i.e. the inner diameter ri，r2、r3、r4Respectively the radius of the second, third and fourth layers, r5Is the fifth layer radius outer diameter ro；
Solving the three energy conservation equations to obtain the temperatures of the third layer of the node 7, the node 8 and the node 9 respectively:
then, an energy conservation equation is established for the node 8 according to the heat conduction micro equation as follows:
the temperature at node 3 can be found to be:
a first type boundary condition is formed after a temperature measuring point is arranged on the inner wall of the storage bin, and a third type boundary condition is formed at a coal drop. The thermal conductivity lambda is a variable value due to different thermal conductivity at each position, and can be obtained by thermal conductivity prediction calculation.
When the temperature of other nodes is obtained, according to the method, the temperature of the inner-layer node in the whole inverse problem solving area is correspondingly obtained only by changing the positions of different outer-layer nodes, and then the transient temperature field of the section inverse problem solving area is obtained.
Example 2 the coal storage bunker was a spherical bunker
At this time, in step 2, when the coal storage bunker is a spherical bunker, the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed to the coordinates in the spherical coordinate system
As shown in fig. 4, in which,z is rcos theta, r is the distance between the internal heat source T and the origin O of the spherical coordinate, theta is the positive included angle between the directional line segment OT and the z axis,m is the projection of point P on the xOy plane, and is the angle rotated from the x-axis to OM in the counterclockwise direction as viewed from the positive z-axis;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
In this case, in step 4, when the coal bunker is a spherical bunker, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is obtained according to the fourier law:
in the formula, Ti-1,j、Ti,jRespectively represent the temperatures of the nodes (i-1, j) and (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Respectively, the temperatures of the nodes (i +1, j), (i, j +1), and (i, j-1).
According to the invention, temperature measuring points are arranged on the inner wall of the storage bin along different interfaces in the height direction, and the temperature inside the section can be calculated by establishing an energy conservation equation from outside to inside according to the measured temperature, so that the temperature field in the internal area of the storage bin can be obtained.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A coal temperature field calculation method in a coal storage bin is characterized by comprising the following steps:
step 1, placing an internal heat source T inside a coal storage bin in a rectangular coordinate system, wherein the coordinate is (x, y, z), and establishing a heat conduction differential equation of the internal heat source T in the rectangular coordinate system according to an energy conservation law and a Fourier law:
in which λ is leadThermal coefficient, c is heat capacity of the heat conductor, ρ is density of the heat conductor, qvThe intensity of the internal heat source is the intensity of the internal heat source,is the variation of temperature per unit time;
step 2, obtaining a heat conduction differential equation of the internal heat source T in a three-dimensional coordinate system by the internal heat source T (x, y, z) in the coal storage bin through a coordinate transformation method;
step 3, dividing the inner wall of the storage bin into n layers of interfaces along the radial direction, dividing the interfaces into m layers of interfaces along the axial direction, forming grid lines on the interfaces in two directions, taking the crossed points of the grid lines as nodes, respectively arranging temperature measuring points on the inner wall of the coal storage bin, namely the outermost nodes, and respectively measuring the temperature value of each node on the temperature measuring points through a temperature sensor;
step 4, establishing an energy conservation equation for the control volume represented by the outer-layer nodes from outside to inside in the radial direction according to the measured temperature and a heat conduction micro equation, gradually and inwards calculating the temperature of the inner-layer nodes, changing the positions of different outer-layer nodes to obtain the temperature of the inner-layer nodes in the whole grid line area, and further obtaining a coal body temperature field in the whole coal storage bin;
wherein, the control volume establishment energy conservation equation represented by any node (i, j) is as follows:
in the formula, QwEnergy exchange between the left end of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QeEnergy exchange between the right edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QnEnergy exchange between the upper edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, QsEnergy exchange between the lower edge of the infinitesimal body represented by node (i, j) and the adjacent infinitesimal body, qvThe internal heat source intensity, DeltaV is the volume of the infinitesimal body, rho is the density of the heat conductor, lambda is the heat conductivity coefficient, and c is the heat capacity of the heat conductor.
2. The method for calculating the coal body temperature field inside the coal storage bin according to claim 1, wherein in the step 2, when the coal storage bin is a silo, the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the cylindrical coordinate system, and the coordinates (x, y, z) of the internal heat source T (x, y, z) in the rectangular coordinate system are transformed into the coordinates (x, y, z) in the cylindrical coordinate system
Wherein,z, r is the vertical distance between the internal heat source T and the z axis,is the included angle between the projection line of OT on the xy surface and the positive x axis, and z is the distance between the T point and the xy surface;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
3. The method for calculating the coal body temperature field inside the coal storage bin according to claim 1, wherein in the step 2, when the coal storage bin is a spherical bin, the coordinates (x, y, z) of the internal heat source T (x, y, z) in a rectangular coordinate system are transformed into the coordinates in a spherical coordinate system
Wherein,z is rcos theta, r is the distance between the internal heat source T and the origin O of the spherical coordinate, theta is the positive included angle between the directional line segment OT and the z axis,m is the projection of point P on the xOy plane, and is the angle rotated from the x-axis to OM in the counterclockwise direction as viewed from the positive z-axis;
and (3) after the converted coordinates are taken into a heat conduction differential equation in a rectangular coordinate system, obtaining a heat conduction differential equation of the internal heat source T in a spherical coordinate system:
wherein λ is the thermal conductivity, c is the thermal capacity of the heat conductor, ρ is the density of the heat conductor, q isvThe intensity of the internal heat source is the intensity of the internal heat source,is the amount of change in temperature per unit time.
4. The method for calculating the coal body temperature field inside the coal storage bin according to claim 1, wherein in the step 4, when the coal storage bin is a silo, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is obtained according to the Fourier law and the Newton's cooling law:
in the formula, Ti-1,j、Ti,jRespectively represent the temperatures of the nodes (i-1, j) and (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Denotes the temperature of the nodes (i +1, j), (i, j +1), (i, j-1), respectively, qwIs the node heat flux density.
5. The method for calculating the coal body temperature field inside the coal storage bin according to claim 1, wherein in step 4, when the coal storage bin is a spherical bin, the boundary between the node (i, j) and the node (i-1, j) is used as a heat conduction area, the distance between the nodes is used as a heat conduction thickness, and the energy exchange from the node (i-1, j) to the node (i, j) is calculated according to the Fourier law as:
in the formula, Ti-1,j、Ti,jRespectively represent the temperatures of the nodes (i-1, j) and (i, j);
similarly, the energy exchange between node (i, j) and nodes (i +1, j), node (i, j +1) and (i, j-1) is obtained as:
in the formula, Ti+1,j、Ti,j+1、Ti,j-1Respectively, the temperatures of the nodes (i +1, j), (i, j +1), and (i, j-1).
6. The method for calculating the coal body temperature field in the coal storage bin according to the claim 1, wherein in the step 4, when the calculation is carried out from outside to inside in the radial direction:
firstly, establishing an energy conservation equation for a control volume represented by an outermost node according to a heat conduction micro equation, and solving a temperature value of a node at the second layer to the last number according to the measured temperature value of the outermost node and the energy conservation equations;
then, establishing an energy conservation equation for the control volume represented by the node of the second layer to the last but according to the heat conduction micro equation, and solving the temperature value of the node of the third layer to the last but according to the temperature value of the node of the second layer to the last but and the energy conservation equations;
pushing layer by layer;
and finally, solving the temperature value of the innermost node.
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| CN201810274358.1A CN108804739A (en) | 2018-03-29 | 2018-03-29 | A kind of coal store inside coal temperature field computation method |
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| CN110260988A (en) * | 2019-07-04 | 2019-09-20 | 西安交通大学 | Temperature sensor casing processing method, temperature sensor casing and temperature sensor |
| WO2022147978A1 (en) * | 2021-01-08 | 2022-07-14 | 深圳中广核工程设计有限公司 | Straight pipeline inner wall surface temperature measurement and transient identification method and computer terminal |
| CN116562184A (en) * | 2023-04-18 | 2023-08-08 | 中南大学 | Rapid prediction calculation method for mold temperature field in autoclave molding process |
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