Model selection and construction method of periodic cell body structure of porous medium burner

Abstract

The invention belongs to the technical field of porous medium combustors, and particularly relates to a model selection construction method of a periodic cell body structure of a porous medium combustor, which comprises the steps of constructing a heat transfer device, constructing a cell body unit to be selected, installing the cell body unit to be selected, measuring data parameters, analyzing results and the like. From a plurality of perspectives of convective heat transfer coefficient, area excellent factor, effective heat conductivity coefficient, longitudinal diffusion coefficient and the like, the performance of the porous medium burner can be influenced by using different periodic cell body structures under the condition of the same porosity; the invention further provides a model selection construction method for the periodic cell body structure when the porosity is the same, a theoretical basis is provided for model selection of the periodic cell body structure of the porous medium burner, and several periodic cell body structures recommended to be constructed and used under common porosity conditions are given.

Description

Technical Field

[0001] The present invention belongs to the technical field of porous medium burners, and in particular relates to a method for selecting and constructing a periodic cell structure of a porous medium burner. Background Art

[0002] Porous media combustion technology enhances gas-solid heat transfer through a porous matrix, achieving superenthalpic combustion. This technology boasts high efficiency and clean performance, and holds significant application prospects in industrial combustion equipment. Traditional porous media materials primarily include stacked spheres and disordered foam ceramics. Stacked spheres, composed of randomly stacked spherical particles, have a low porosity (0.36-0.45). While simple to prepare, they suffer from high flow resistance and limited isotropic heat transfer performance. Disordered foam ceramics, formed through a foaming process into a three-dimensional network structure, have a high porosity (0.75-0.95). However, their wide pore size distribution leads to uneven flow velocity distribution, which can easily create localized high-temperature zones, increasing nitrogen oxide (NOx) and hydrocarbon emissions. Furthermore, thermal stress concentration caused by high-temperature gradients can shorten the structural lifespan. Furthermore, the effective thermal conductivity of traditional structures decreases significantly with increasing porosity. This limits heat recovery efficiency at high porosity, making it difficult to achieve both low pressure drop and high heat transfer performance. Consequently, researchers in this field have recently proposed replacing random pore structures with periodic cellular structures.

[0003] Current research experience shows that when the porosity is the same, the thermal conductivity, heat transfer and flow capabilities of different cell structures are the same, so the specific periodic cell structure used has no effect on the performance of the porous media burner. Summary of the Invention

[0004] After experimental research and analysis, the present invention found that under the condition of the same porosity, there are differences in performance between different periodic cell structures, which will also affect the performance of the porous medium burner. In view of this, the present invention aims to provide a method for selecting and constructing a periodic cell structure of a porous medium burner, provide a theoretical basis for the selection of a periodic cell structure of a porous medium burner, and give several periodic cell structures recommended for construction and use under common porosity conditions.

[0005] The specific technical solution adopted is: a method for selecting and constructing a periodic cell structure of a porous medium burner, wherein the porous medium burner body contains a periodic cell structure, and the periodic cell structure is composed of a plurality of identical cell units arranged periodically, including the following steps:

[0006] Step 1. Construct a heat transfer device: In a device with symmetrical boundary conditions, closed on all sides, and air inlet and outlet at both ends, a bottom plate is set at the bottom of the heat transfer device, and a constant temperature boundary condition is set on the surface of the bottom plate;

[0007] Step 2. Constructing the cell units to be selected: Prepare n types of cell units to be selected, and the dimensions of each cell unit match the cross-sectional dimensions of the heat transfer device described in Step 1; divide each type of cell unit to be selected into multiple experimental groups according to the size of the porosity, and the cell units to be selected in the same experimental group have the same porosity;

[0008] Step 3. Install the selected cell units: First, determine the porosity required for the porous medium burner. Then, select one of the n types of cell units to be selected and find an experimental group of cells with the same porosity. Arrange several cells of the selected experimental group periodically on the bottom plate of the heat transfer device. Heat is transferred to the periodic cell structure through contact between the bottom plate surface and the cells.

[0009] Step 4. Airflow velocity at the air inlet: Pass constant temperature air into the air inlet, measure the data parameters required for the following formula, calculate the corresponding results, and record them as Result 1-1:

[0010]

[0011] In formula 1, h is the convection heat transfer coefficient, Q is the heat flow, and T s is the average surface temperature of the cell structure, T f is the average temperature of the fluid, A is the fluid-solid contact surface area;

[0012]

[0013] In formula 2, j / f is the area quality factor, f is the friction coefficient and , where ΔP is the pressure drop, ΔL is the distance from the inlet to the outlet of the entire periodic cell structure, and d h is the hydraulic diameter, ρ is the density, v is the air velocity at the air inlet, Nu is the Nusselt number and Where h is the convective heat transfer coefficient, d h is the hydraulic diameter, λ is the thermal conductivity, Pr is the Planck number and Pr = 0.744, Re is the Reynolds number;

[0014]

[0015] k in formula 3 eff is the effective thermal conductivity, Qw is the heat transfer rate, L is the unit cell length, A is the fluid-solid contact surface area, and △T is the average temperature difference between the solid surface at the inlet and outlet of the entire periodic cell structure;

[0016] D L (t) / D M Formula 4

[0017] Formula 4 calculates the longitudinal diffusion coefficient, where where σ sim 2 is the second-order moment of the gradient, t is the time, D M =1.3*10 -5 m 2 / s;

[0018] Step 5. Without changing the porosity used in Step 3, change the airflow velocity at the airflow inlet in Step 4. Repeat Step 4 m times at different airflow velocities. Measure and calculate the data parameters required for the public disclosure at different airflow velocities, and record them in order as Results 1-2 to Results 1-m.

[0019] Step 6. Without changing the porosity used in Step 3, select another type of cell unit from the selected type, find a corresponding experimental group with the same porosity, and replace several cell units in the heat transfer device. Repeat Steps 3, 4, and 5 until the data parameters of n types of cell units to be selected are measured and calculated, and recorded in sequence as Result 2-1 to Result 2-m...Result n-1 to Result nm;

[0020] Step 7. Count results 1-1 to 1-m, results 2-1 to 2-m, ... results n-1 to nm, and compare the results of n types of cell units to be selected at the same porosity;

[0021] Step 8. Determine the type of cell unit and construct it: First, select the cell unit with the best convective heat transfer coefficient measurement result; when the difference in the convective heat transfer coefficient measurement results is within 1%, then select the cell unit with the best area quality factor measurement result; when the difference in the convective heat transfer coefficient and area quality factor measurement results are both within 1%, then select the cell unit with better performance in the effective thermal conductivity and longitudinal diffusion coefficient measurement results;

[0022] Step 9. When the porosity size of the porous media burner to be used is changed, repeat steps 3 to 8.

[0023] Moreover, the bottom plate thickness of the heat transfer device in step 1 is 1 mm, and the constant temperature boundary condition is set at 350K on the bottom plate surface.

[0024] Moreover, in step 3, the number of cell structures periodically arranged in sequence on the bottom plate in the heat transfer device is ≥10.

[0025] Moreover, the temperature of the constant temperature air in step 4 is 350K, and the air flow velocity at the air flow inlet is 0.5-10 m / s.

[0026] Moreover, the cell units to be selected in step 2 include at least a Kelvin structure, a face-centered cube structure, and a face-centered cube structure. The face-centered cube has a structure in which each face has two connecting diagonals, and the face-centered cube has a structure in which each face has only one connecting diagonal. Figure 2 shown.

[0027] Moreover, when the porosity required for the porous medium burner is 0.80-0.90, the cell unit selected and constructed is a Kelvin structure; when the porosity required for the porous medium burner is 0.95, the cell unit selected and constructed is a face-centered cubic structure.

[0028] Compared with the existing technology, the beneficial effects of this technical solution are:

[0029] 1. Discarding the existing belief that different cell structures have no effect on the performance of porous media burners when the porosity is the same, this paper examines the area quality factor, convective heat transfer coefficient, effective thermal conductivity, and longitudinal diffusion coefficient. It is found that using different periodic cell structures at the same porosity does affect the performance of porous media burners. Furthermore, a method for selecting and constructing periodic cell structures at the same porosity is proposed.

[0030] 2. This method quantifies the convective heat transfer capacity of different periodic cell structures through pressure drop, convective heat transfer coefficient and area quality factor; quantifies the thermal conductivity of different periodic cell structures through effective thermal conductivity; quantifies the flow mixing ability of different periodic cell structures through longitudinal diffusion coefficient; and then determines the performance differences of different cell structures under the same selected porosity conditions.

[0031] 3. Based on the priority of convective heat transfer coefficient, area quality factor, effective thermal conductivity and longitudinal diffusion coefficient, the selection recommendation of cell structure under normal porosity conditions is given: when the porosity is in the range of 0.80-0.90, the periodic cell structure composed of Kelvin structure cell units is selected, which has the highest area quality factor and the best overall convective heat transfer performance; when the porosity increases to 0.95, the periodic cell structure composed of face-centered cubic structure cell units is selected, which exhibits the best overall convective heat transfer performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram of the heat transfer device structure constructed for the embodiment;

[0033] Figure 2 Schematic diagrams of three different cell structures: (a) is the Kelvin structure, (b) is the face-centered cubic structure, and (c) is the face-centered cubic structure;

[0034] Figure 3 The results of calculating the area quality factor of three different cell structures under four conditions of the same porosity are shown in the examples. The horizontal axis represents the airflow velocity at the airflow inlet, and the vertical axis represents the area quality factor, where (a) porosity = 0.80; (b) porosity = 0.85; (c) porosity = 0.90; (d) porosity = 0.95;

[0035] Figure 4 The results of calculating the effective thermal conductivity of three different cell structures are shown in the example, with the abscissa representing the porosity and the ordinate representing the effective thermal conductivity;

[0036] Figure 5 The results of calculating the longitudinal diffusion coefficients of three different cell structures are shown in the embodiment. The horizontal axis is the air flow velocity at the air flow inlet and the vertical axis is the effective thermal conductivity. DETAILED DESCRIPTION

[0037] The present invention will be described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0038] like Figure 1 The heat transfer device is constructed as shown in FIG. 1 , and the porous medium burner body is composed of a periodic cell structure. The periodic cell structure is composed of a number of identical cell units arranged periodically. The cell unit structure selected for the experiment in the embodiment is as follows: Figure 2 Shown are three types of structures: Kelvin structure, face-corner cube structure and face-centered cubic structure. Figure 1 The heat transfer device shown here features 10 Kelvin-structured cells arranged in the direction of airflow. Connected to the cell structure below is a 1mm-thick baseplate with a constant temperature boundary condition of 350K applied to its surface. Through contact with the cells, the baseplate transfers heat to the periodic cell structure. At the inlet plane, constant-temperature air at 300K is used as the inlet gas, with a flow rate ranging from 0.5 to 10 m / s. Symmetrical boundary conditions are applied on both sides of the cell structure.

[0039] The side length of the cross section of the cell unit is 8 mm. In order to complete the parameter data under the four conditions of the same porosity of 0.80, 0.85, 0.90, and 0.95 required for the measurement of this method, each cell unit should be divided into 4 experimental groups, and the three cell units total 12 experimental groups, that is, at least 10 Kelvin structure cell units with a porosity of 0.80 are made as the first group, 10 Kelvin structure cell units with a porosity of 0.85 are made as the second group, 10 Kelvin structure cell units with a porosity of 0.90 are made as the third group, 10 Kelvin structure cell units with a porosity of 0.95 are made as the fourth group, 10 face-centered cubic structure cell units with a porosity of 0.80 are made as the fifth group... and so on until 10 face-centered cubic structure cell units with a porosity of 0.95 are made as the twelfth group. The experiment in this embodiment can also be completed by numerical simulation method.

[0040] The following is a detailed embodiment of steps 4 to 8 of this method:

[0041] In the experiment, the air flow velocity at the air inlet was set to 10 types: 1 m / s, 2 m / s, 3 m / s..., 10 m / s.

[0042] When the actual working conditions require a periodic cell structure with a porosity of 0.80 for a porous media burner:

[0043] When 10 Kelvin structure cell units with a porosity of 0.80 are used to form a periodic cell structure, 300K constant temperature air is introduced into the air flow inlet at a flow rate of 1 m / s. The data parameters required for the following formula are measured and the corresponding results are calculated and recorded as result 1-1:

[0044]

[0045] In formula 1, h is the convection heat transfer coefficient, Q is the heat flow, and T s is the average surface temperature of the cell structure, T f is the average temperature of the fluid, A is the fluid-solid contact surface area;

[0046]

[0047] In formula 2, j / f is the area quality factor, f is the friction coefficient and , where ΔP is the pressure drop, ΔL is the distance from the inlet to the outlet of the entire periodic cell structure (i.e., the total length of the entire periodic cell structure. In order to ensure that the entire periodic cell structure is placed in the heat transfer device, the total length of the entire periodic cell structure is usually less than the total length of the heat transfer device), and d h is the hydraulic diameter, ρ is the density, v is the air velocity at the air inlet, Nu is the Nusselt number and Where h is the convective heat transfer coefficient, dh is the hydraulic diameter, λ is the thermal conductivity, Pr is the Planck number and Pr = 0.744, Re is the Reynolds number;

[0048]

[0049] k in formula 3 eff is the effective thermal conductivity, Qw is the heat transfer rate, L is the unit cell length, A is the fluid-solid contact surface area, and △T is the average temperature difference between the solid surface at the inlet and outlet of the entire periodic cell structure;

[0050] D L (t) / D M Formula 4

[0051] Formula 4 calculates the longitudinal diffusion coefficient, where where σ sim 2 is the second-order moment of the gradient, t is the time, D M =1.3*10 -5 m 2 / s;

[0052] When 10 Kelvin structure cell units with a porosity of 0.80 are used to form a periodic cell structure, constant temperature air is introduced into the air flow inlet at a flow rate of 2 m / s, and the data parameters required for the above four formulas are measured and the corresponding results are calculated and recorded as results 1-2;

[0053] The same logic is repeated until a periodic cell structure is formed using 10 Kelvin structure cell units with a porosity of 0.80. Constant temperature air is introduced into the air flow inlet at a flow rate of 10 m / s. The data parameters required for the above four formulas are measured and the corresponding results are calculated and recorded as results 1-10.

[0054] At this point, the measurement calculation of the periodic cell structure composed of Kelvin structure cell units with a porosity of 0.80 is completed.

[0055] Then, the periodic cell structure is replaced, and 10 face-to-face corner cube structure cell units with a porosity of 0.80 are used to form a periodic cell structure. When constant temperature air is introduced into the air flow inlet at a flow rate of 1 m / s, the data parameters required for the above four formulas are measured, and the corresponding results are calculated and recorded as result 2-1; ...and so on until 10 face-to-face corner cube structure cell units with a porosity of 0.80 are used to form a periodic cell structure, constant temperature air is introduced into the air flow inlet at a flow rate of 10 m / s, and the data parameters required for the above four formulas are measured, and the corresponding results are calculated and recorded as result 2-10; thus, the measurement and calculation of the periodic cell structure composed of face-to-face corner cube structure cell units with a porosity of 0.80 are completed.

[0056] The periodic cell structure is replaced again, and 10 face-centered cubic structure cell units with a porosity of 0.80 are used to form a periodic cell structure. When constant temperature air is passed into the air flow inlet at a flow rate of 1 m / s, the data parameters required for the above four formulas are measured, and the corresponding results are calculated and recorded as result 3-1; ...and so on until 10 face-centered cubic structure cell units with a porosity of 0.80 are used to form a periodic cell structure, constant temperature air is passed into the air flow inlet at a flow rate of 10 m / s, and the data parameters required for the above four formulas are measured, and the corresponding results are calculated and recorded as result 3-10; thus, the measurement and calculation of the periodic cell structure composed of face-centered cubic structure cell units with a porosity of 0.80 are completed.

[0057] The above experiment was repeated according to the conditions that the porosity of the porous medium burner used was 0.85, 0.90, and 0.95 as required by actual working conditions.

[0058] The final experimental results are as follows Figure 3 、 Figure 4 and Figure 5 The results of the experiment show that the area quality factor calculation results are very similar to the convective heat transfer coefficient calculation results. The cell structure with the best area quality factor also has the best convective heat transfer coefficient. Therefore, the convective heat transfer coefficient is omitted. The reason is that the area quality factor is a dimensionless quantity that balances the convective heat transfer coefficient and pressure drop. Therefore, the structure with both low pressure drop and high convective heat transfer coefficient has a higher area quality factor.

[0059] like Figure 3As shown in the figure, when the porosity is in the range of 0.80-0.90, the area quality factor of the Kelvin structure is the highest, which is 21%-37% higher than that of the face-centered cube and face-corner cube structures, respectively, showing the best overall convective heat transfer performance and the lowest pressure drop characteristics; when the porosity is 0.9, the face-corner cube structure has the highest pressure drop, but its heat transfer is the largest among the three structures; when the porosity increases to 0.95, the face-centered cube structure exhibits the best overall convective heat transfer capacity.

[0060] like Figure 4 As shown in the figure, the effective thermal conductivity decreases with increasing porosity. At lower porosity, the influence of structure on the effective thermal conductivity is more significant. At a porosity of ε = 0.80, the effective thermal conductivity of the Kelvin structure is 1.75 W / (m·K), 7.8% higher than that of the face-angled cube structure. When the porosity increases to 0.95, the difference between the two decreases to 3%, exhibiting the strongest thermal conductivity.

[0061] like Figure 5 As shown in the figure, compared with the other two structures, the streamlines of the Kelvin structure present continuous spiral trajectories between the pillars, and its circuitous route is longer (while the fluid trajectories of the face-centered cube and face-centered cube structures are almost straight lines), resulting in a larger longitudinal diffusion coefficient and a better diffusion effect. Therefore, by utilizing the characteristics of the Kelvin structure, the longitudinal diffusion coefficient can be improved (50% higher than that of the face-centered cube structure) and the mixing efficiency can be optimized.

[0062] According to the priority of convective heat transfer coefficient - area quality factor - effective thermal conductivity and longitudinal diffusion coefficient, based on the above experimental results, the selection and construction of the periodic cell structure of the porous medium burner are recommended as follows: when the porosity required for the porous medium burner is 0.80-0.90, the cell unit selected and constructed is the Kelvin structure; when the porosity required for the porous medium burner is 0.95, the cell unit selected and constructed is the face-centered cubic structure.

[0063] In summary, the beneficial effects of this technical solution are:

[0064] 1. Discarding the existing belief that different cell structures have no effect on the performance of porous media burners when the porosity is the same, this paper examines the area quality factor, convective heat transfer coefficient, effective thermal conductivity, and longitudinal diffusion coefficient. It is found that using different periodic cell structures at the same porosity does affect the performance of porous media burners. Furthermore, a method for selecting and constructing periodic cell structures at the same porosity is proposed.

[0065] 2. This method quantifies the convective heat transfer capacity of different periodic cell structures through pressure drop, convective heat transfer coefficient and area quality factor; quantifies the thermal conductivity of different periodic cell structures through effective thermal conductivity; quantifies the flow mixing ability of different periodic cell structures through longitudinal diffusion coefficient; and then determines the performance differences of different cell structures under the same selected porosity conditions.

[0066] 3. Based on the order of priority of convective heat transfer coefficient, area quality factor, effective thermal conductivity, and longitudinal diffusion coefficient, a cell structure selection recommendation is given under conventional porosity conditions: when the porosity is in the range of 0.80-0.90, a periodic cell structure composed of Kelvin structured cell units is selected, which has the highest area quality factor and the best overall convective heat transfer performance; when the porosity increases to 0.95, a periodic cell structure composed of face-centered cubic structured cell units is selected, which exhibits the best overall convective heat transfer performance. If the actual operating conditions have other requirements for the porosity size of the porous media burner, the theoretical basis provided by this method can still be used for data parameter calculation and selection analysis.

Claims

1. A method for selecting and constructing a periodic cell structure of a porous medium burner, wherein the porous medium burner body comprises a periodic cell structure, which is composed of a plurality of identical cell units arranged periodically, and is characterized in that The following steps are involved: Step 1. Construct a heat transfer device: In a device with symmetrical boundary conditions, closed on all sides, and air inlet and outlet at both ends, a bottom plate is set at the bottom of the heat transfer device, and a constant temperature boundary condition is set on the surface of the bottom plate; Step 2. Constructing the cell units to be selected: Prepare n types of cell units to be selected, and the dimensions of each cell unit match the cross-sectional dimensions of the heat transfer device described in Step 1; divide each type of cell unit to be selected into multiple experimental groups according to the size of the porosity, and the cell units to be selected in the same experimental group have the same porosity; Step 3. Install the selected cell units: First, determine the porosity required for the porous medium burner. Then, select one of the n types of cell units to be selected and find an experimental group of cells with the same porosity. Arrange several cells of the selected experimental group periodically on the bottom plate of the heat transfer device. Heat is transferred to the periodic cell structure through contact between the bottom plate surface and the cells. Step 4. Determine the airflow velocity at the air inlet. Pass constant temperature air into the air inlet. Measure the data parameters required for the following formula and calculate the corresponding results, recording them as Result 1-1: In formula 1, h is the convection heat transfer coefficient, Q is the heat flow, and T s is the average surface temperature of the cell structure, T f is the average temperature of the fluid, A is the fluid-solid contact surface area; In formula 2, j / f is the area quality factor, f is the friction coefficient and , where ΔP is the pressure drop, ΔL is the distance from the inlet to the outlet of the entire periodic cell structure, and d h is the hydraulic diameter, ρ is the density, v is the air velocity at the air inlet, Nu is the Nusselt number and Where h is the convective heat transfer coefficient, d h is the hydraulic diameter, λ is the thermal conductivity, Pr is the Planck number and Pr = 0.744, Re is the Reynolds number; k in formula 3 eff is the effective thermal conductivity, Qw is the heat transfer rate, L is the unit cell length, A is the fluid-solid contact surface area, and △T is the average temperature difference between the solid surface at the inlet and outlet of the entire periodic cell structure; D L (t) / D M Formula 4 Formula 4 calculates the longitudinal diffusion coefficient, where where σ sim 2 is the second-order moment of the gradient, t is the time, D M =1.3*10 -5 m 2 / s; Step 5. Without changing the porosity used in Step 3, change the airflow velocity at the airflow inlet in Step 4. Repeat Step 4 m times according to the airflow velocity. Measure and calculate the data parameters required for the public disclosure at different airflow velocities, and record them in sequence as Results 1-2 to Results 1-m. Step 6. Without changing the porosity used in Step 3, select another type of cell unit from the selected type, find a corresponding experimental group with the same porosity, and replace several cell units in the heat transfer device. Repeat Steps 3, 4, and 5 until the data parameters of n types of cell units to be selected are measured and calculated, and recorded in sequence as Result 2-1 to Result 2-m...Result n-1 to Result nm; Step 7. Count results 1-1 to 1-m, results 2-1 to 2-m, ... results n-1 to nm, and compare the results of n types of cell units to be selected at the same porosity; Step 8. Determine the type of cell unit and construct it: First, select the cell unit with the best convective heat transfer coefficient measurement result; when the difference in the convective heat transfer coefficient measurement results is within 1%, then select the cell unit with the best area quality factor measurement result; when the difference in the convective heat transfer coefficient and area quality factor measurement results are both within 1%, then select the cell unit with better performance in the effective thermal conductivity and longitudinal diffusion coefficient measurement results; Step 9. When the porosity size of the porous media burner to be used is changed, repeat steps 3 to 8.

2. The method for selecting and constructing a periodic cell structure of a porous medium burner according to claim 1, characterized in that: In step 1, the bottom plate thickness of the heat transfer device is 1 mm, and the constant temperature boundary condition is set at 350K on the bottom plate surface.

3. The method for selecting and constructing a periodic cell structure of a porous medium burner according to claim 1, characterized in that: In step 3, the number of cell structures periodically arranged in sequence on the bottom plate in the heat transfer device is ≥10.

4. The method for selecting and constructing a periodic cell structure of a porous medium burner according to claim 1, characterized in that: In step 4, the temperature of the constant temperature air is 350K, and the air flow velocity at the air flow inlet is 0.5-10 m / s.

5. The method for selecting and constructing a periodic cell structure of a porous medium burner according to claim 1, characterized in that: The cell units to be selected in step 2 include at least a Kelvin structure, a face-corner cube structure and a face-centered cube structure.

6. The method for selecting and constructing a periodic cell structure of a porous medium burner according to claim 5, characterized in that: When the porosity of the porous medium burner is required to be 0.80-0.90, the cell unit selected and constructed is a Kelvin structure; when the porosity of the porous medium burner is required to be 0.95, the cell unit selected and constructed is a face-centered cubic structure.

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