Simple thermal diffusion estimation method

Abstract

The invention discloses a simple thermal diffusion estimation method which comprises the following steps: step 1, basic data acquisition: acquiring basic data of a research water area, including hydro meteorological elements, hot water discharge temperature, water flow rate and flow velocity; 2, district division is conducted on the research water area, wherein the research water area is divided into a plurality of districts according to the position of the power plant; step 3, determining geometric elements of the cells: determining the geometric elements of each cell; step 4, calculating the average temperature rise value of the water body of each cell: carrying out flow distribution on each cell according to the flow formed by the flow of the research water area, and calculating the exchange flow between the adjacent cells; and listing a heat balance equation of each cell, and solving an average temperature rise value of the water body of each cell according to the obtained basic data and geometric elements of each cell. The method is simple and easy to implement and high in applicability, the average heating condition of the water body in the water area can be rapidly estimated, and a scientific reference basis is provided for preliminary design of warm water discharge of a power plant.

Description

Technical Field

[0001] The invention belongs to the technical field of environmental hydraulics, and in particular relates to a simple heat diffusion estimation method. Background Art

[0002] As the country pays more and more attention to ecological and environmental issues, the impact of power plant warm discharge on environmental water bodies has received more and more attention. At present, the simulation forecast of warm discharge adopts a method that combines large-scale warm discharge numerical simulation calculation with physical model test near the drainage outlet, which takes a long time and more manpower and material resources. Therefore, a simple heat diffusion estimation method is urgently needed, which can quickly give the average temperature rise of environmental water bodies in the initial stage of the design of power plant warm discharge scheme. Summary of the invention

[0003] The purpose of the present invention is to provide a simple thermal diffusion estimation method to solve the above technical problems.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] The present invention discloses a simple thermal diffusion estimation method, which comprises the following steps:

[0006] Step 1, basic data acquisition: obtain the basic data of the research waters, including hydrological and meteorological elements, hot water discharge temperature, water flow and flow rate; the meteorological elements include water temperature, air temperature, and heat dissipation coefficient;

[0007] Step 2: Divide the study water area into small areas: Divide the study water area into multiple small areas according to the location of the power plant. Divide the power plant into a separate small area and do not place the power plant in the most marginal area.

[0008] Step 3: Determine the geometric elements of each cell: Determine the geometric elements of each cell, including the length of each side of the cell, the water surface area of ​​the cell, the average water depth of each side, and the distance between the centroids of adjacent cells;

[0009] Step 4. Calculate the average temperature rise of the water body in each district: distribute the flow to each district according to the flow formed by the flow in the study water area, and calculate the exchange flow between adjacent districts; list the heat balance equation of each district to express the comprehensive heat balance state of each district under the influence of influencing factors; solve the average temperature rise of the water body in each district according to the basic data obtained and the geometric elements of each district.

[0010] Furthermore, the calculation of the exchange flow between adjacent cells in step 4 is specifically as follows: to calculate the exchange flow between two adjacent cells, the exchange flow between the two cells is obtained by multiplying the average flow velocity of the water body passing through by the flow area.

[0011] Furthermore, the influencing factors described in step 4 include convection, heat diffusion, water surface heat dissipation and source and sink items caused by water flow; convection is the heat exchange between the cells under the action of the average flow velocity of the water body; heat diffusion is the mutual heat exchange caused by the temperature difference between the cells; water surface heat dissipation is the exchange of heat in the cell with the atmosphere through the water surface; source and sink items include water intake and drainage.

[0012] Furthermore, the step 4 of solving the average temperature rise of water bodies in each community specifically includes the following steps:

[0013] Step 41: Calculate the heat of drainage and water intake in the community:

[0014] Assuming that the drainage outlet and water intake are both arranged in the community i, after the hot water flows into the community i, the water body in the community i will produce an average temperature rise ΔT due to the influence of convection, heat diffusion, water surface heat dissipation, and source and sink terms. i ;

[0015] The heat discharged from the drainage outlet into the cell i is Q1, which is the heat per unit time. If the drainage temperature rises ΔT 排i =0, the discharged heat is 0, and the calculation formula for the discharged heat is:

[0016] Q1=q 排i ΔT 排i (1)

[0017] Where Q1 is the drainage heat of cell i; q 排i is the drainage flow in cell i; ΔT 排i is the drainage temperature rise in cell i. If the drainage system in the cell is composed of other inflows that are not affected by the thermal drainage of the power station, then the drainage temperature rise ΔT 排i Take 0;

[0018] The heat taken away by the water from the cell i is Q2, and the calculation formula of the water heat is:

[0019] Q2=q 取i ΔT i (2)

[0020] Where, Q2 is the water intake heat of community i; q 取i is the water intake flow in community i; ΔT i is the average temperature rise of the water body in community i; if there is no water intake in community i, then q 取i =0;

[0021] Step 42: Calculate the convection heat of the cell:

[0022] Due to the convection of water bodies, heat exchange occurs between the water body in cell i and the adjacent cell j, namely, convection heat, and the calculation formula is:

[0023] Q3=q 流ij ΔT i (3)

[0024] or

[0025] Q'3=q 流ij ΔT j (4)

[0026] In the formula, q 流ij is the exchange flow between cell i and adjacent cell j due to water convection; if the water flow direction is from i to j, the convection heat of cell i is Q3, that is, the convection will raise the temperature by ΔT i If the water body is carried from i to j; on the contrary, if the water body flows from j to i, the convection heat of cell i is Q'3, and the convection will raise the temperature by ΔT j The water body is brought from j to i; ΔT j is the average temperature rise of water in cell j;

[0027] Step 43: Calculate the heat diffusion heat of the cell:

[0028] The heat transfer between adjacent cells i and j due to turbulent diffusion is the heat diffusion heat Q4. The heat diffusion heat is proportional to the vertical contact area and temperature gradient. The calculation formula is:

[0029]

[0030] Where, Q4 is the heat diffusion heat of cell i; A ij is the contact area between two cells i and j, with dimension m 2 , A ij =Lh, L is the horizontal contact length of the cell boundary, dimension is m, h is the average water depth on the corresponding boundary, dimension is m; ΔX ij is the distance between the centroids of adjacent cells i and j, with the dimension of m; D ij is the thermal diffusion coefficient, which indicates the magnitude of heat transfer due to thermal diffusion. Dx is along the water flow direction, Dy is perpendicular to the water flow direction, and the dimension is m 2 / s;

[0031] Rewrite the above formula as:

[0032]

[0033] In the formula, is the heat diffusion flux, dimension is m 3 / s,;

[0034] Step 44, calculate the heat dissipation of the community:

[0035] The heat dissipation is the heat removed by the water surface of cell i. The calculation formula is:

[0036]

[0037] Where Q5 is the heat dissipation of cell i; K is the water surface heat dissipation coefficient, unit is W / m 2 ℃; C is the specific heat of water; S i is the water surface area of ​​cell i;

[0038] Step 45, calculate the average temperature rise of the water body in the community:

[0039] In the state of thermal equilibrium, the heat brought into this cell i is equal to the heat taken out of cell i, that is, the heat balance equation of cell i is:

[0040] Q1-Q2-∑Q3(or+∑Q'3)-∑Q4-Q5=0(8)

[0041] Solving the above formula, we can get the average temperature rise ΔT of cell i: i ;

[0042] Similarly, the average temperature rise value of each cell under thermal equilibrium state can be obtained, starting from the boundary cell and then solving it one by one.

[0043] The beneficial effects of the present invention are as follows: the method of the present invention is simple and easy to implement, has strong applicability, can quickly estimate the average heating conditions of water bodies in water areas, and provide a scientific reference basis for the preliminary design of warm wastewater discharge from power plants.

[0044] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the principle of the method of the present invention;

[0046] Figure 2 This is a schematic diagram of the cell division in Example 1;

[0047] Figure 3 This is a schematic diagram of the exchange traffic of each cell in Example 1;

[0048] Figure 4 Schematic diagram of average temperature rise in each cell in Example 1. DETAILED DESCRIPTION

[0049] The present invention discloses a simple method for estimating heat diffusion, such as Figure 1 As shown, the method comprises the following steps:

[0050] Step 1. Obtain basic data: Obtain basic data such as hydrological and meteorological elements of the study waters (including water temperature, air temperature, heat dissipation coefficient, etc.), hot water discharge temperature, water flow rate and flow velocity.

[0051] Step 2: Divide the study water area into small areas: Divide the study water area into multiple small areas (area i, area j, etc.). There are generally no special requirements for the number and shape of the divided areas. The division is mainly based on the location of the power plant, which means that the power plant is divided into a separate area, and then combined with the possible impact range of the actual situation, multiple areas are divided upstream and downstream. Considering the impact of upstream and downstream, the power plant cannot be placed in the most marginal area.

[0052] Step 3: Determine the geometric elements of each cell: Determine the geometric elements of each cell, including the length of each side of the cell, the water surface area of ​​the cell, the average water depth of each side, the centroid distance of adjacent cells, etc.

[0053] Step 4: Calculate the average water temperature rise in each community:

[0054] According to the flow formed by the flow in the studied water area, the flow is distributed to each cell, and the exchange flow between adjacent cells is calculated (for example, to calculate the exchange flow from cell i and adjacent cell j, the average flow velocity of the passing water body is multiplied by the flow area, which is the exchange flow between cells i and j), and an intuitive plan view is drawn to facilitate understanding and error checking.

[0055] The heat balance equation of each community is listed to express the comprehensive heat balance state of each community under the influence of factors such as convection, diffusion and water surface heat dissipation (if the community has drainage or water intake, it is also included in the heat balance equation); based on the basic data obtained and the geometric elements of each community, the average temperature rise of each community is solved.

[0056] According to the concept of heat balance, the factors affecting heat balance mainly include convection caused by water flow, heat diffusion, water surface heat dissipation, and source and sink items. Convection is the heat exchange between the cells under the action of the average flow rate of the water body; heat diffusion is the heat exchange between the cells due to the temperature difference between the cells; and water surface heat dissipation is the exchange of heat in the cell with the atmosphere through the water surface; source and sink items include drainage and water intake.

[0057] Specifically, solving the average temperature rise value of each community includes the following steps:

[0058] Step 41: Calculate the heat of drainage and water intake in the community:

[0059] Assuming that the drainage outlet and water intake are both arranged in the community i, after the hot water flows into the community i, the water body in the community i will produce an average temperature rise ΔT due to factors such as convection, heat diffusion, water surface heat dissipation, and source and sink terms. i(The temperature rise in this article refers to the temperature rise relative to the ambient water temperature).

[0060] The heat discharged from the drainage outlet into the cell i is Q1, which is the heat per unit time. If the drainage temperature rises ΔT 排i =0, the heat discharged is 0, and the calculation formula for the heat discharged is (the water density ρ and the specific heat capacity C of water are omitted in the formula here because they are common factors in the formula and can be omitted at the same time):

[0061] Q1=q 排i ΔT 排i (1)

[0062] Where Q1 is the drainage heat of cell i; q 排i is the drainage flow in cell i; ΔT 排i is the drainage temperature rise in cell i (if the drainage system in the cell is composed of other inflows that are not affected by the thermal drainage of the power station, then the drainage temperature rise ΔT 排i Should be 0).

[0063] The heat taken away by the water from the cell i is Q2, and the calculation formula of the water heat is:

[0064] Q2=q 取i ΔT i (2)

[0065] Where, Q2 is the water intake heat of community i; q 取i is the water intake flow in community i; ΔT i is the average temperature rise of the water body in community i. If there is no water intake in community i, then q 取i =0.

[0066] Step 42: Calculate the convection heat of the cell:

[0067] Due to the convection of water bodies, heat exchange occurs between the water body in cell i and the adjacent cell j, namely, convection heat, and the calculation formula is:

[0068] Q3=q 流ij ΔT i (3)

[0069] or

[0070] Q'3=q 流ij ΔT j (4)

[0071] In the formula, q 流ij is the exchange flow between cell i and adjacent cell j due to water convection; if the water flow direction is from i to j, the convection heat of cell i is Q3, that is, the convection will raise the temperature by ΔT iIf the water body is carried from i to j; on the contrary, if the water body flows from j to i, the convection heat of cell i is Q'3, and the convection will raise the temperature by ΔT j (ΔT j The water body (where ) is the average temperature rise of the water body in community j is carried from j to i.

[0072] Step 43: Calculate the heat diffusion heat of the cell:

[0073] Regarding the heat diffusion heat, taking the adjacent cells i and j as an example, the heat transfer formed by turbulent diffusion between the adjacent cells i and j is Q4. The heat diffusion heat is proportional to the vertical contact area and the temperature gradient. The calculation formula is:

[0074]

[0075] Where, Q4 is the heat diffusion heat of cell i; A ij is the contact area between two cells i and j, with dimension m 2 , A ij =Lh, L is the horizontal contact length of the cell boundary, dimension is m, h is the average water depth on the corresponding boundary, dimension is m; ΔX ij is the distance between the centroids of adjacent cells i and j, with the dimension of m; D ij is the thermal diffusion coefficient, which is used to indicate the magnitude of heat transfer due to thermal diffusion. Dx is along the water flow direction, Dy is perpendicular to the water flow direction, and its dimension is m 2 / s.

[0076] The above formula can be rewritten as:

[0077]

[0078] In the formula, It is called the heat diffusion flux, and its dimension is m 3 / s, but it is not an actual flow rate, but a virtual flux used to transfer heat in calculation.

[0079] Step 44, calculate the heat dissipation of the community:

[0080] The heat dissipation is the heat removed by the water surface of cell i. The calculation formula is:

[0081]

[0082] Where Q5 is the heat dissipation of cell i; K is the water surface heat dissipation coefficient, unit is W / m 2 ℃; C is the specific heat of water; S i is the water surface area of ​​cell i.

[0083] Step 45, calculate the average temperature rise of the water body in the community:

[0084] In the state of thermal equilibrium, the heat brought into this cell i is equal to the heat taken out of cell i, that is, the heat balance equation of cell i is:

[0085] Q1-Q2-∑Q3(or+∑Q'3)-∑Q4-Q5=0(8)

[0086] Solving the above formula, we can get the average temperature rise ΔT of cell i: i .

[0087] In the same way, the average temperature rise value of each cell under the thermal equilibrium state can be obtained (starting from the boundary cell and solving in sequence).

[0088] Embodiment 1

[0089] This embodiment is an application example of the above method.

[0090] This embodiment discloses a simple thermal diffusion estimation method, comprising the following steps:

[0091] Step 1: Obtain basic data: There are two power plants A and B in a river section, both of which use river water as cooling water source. Now take the 76km river section as the calculation section and the research water area. The average river width is 500m, the average water depth is 10m, and the upstream flow is 200m 3 / s, the temperature rise of the power plant discharge water is 8℃, and the discharge flow rate of power plant A under the planned capacity is 62.3m 3 / s, the water flow rate of power plant B is 20m 3 / s, the thermal diffusion coefficient along the water flow direction is Dx = 100m 2 / s, vertical water flow direction is Dy=5m 2 / s. In order to compare the results of the two water surface heat dissipation coefficients, the water surface heat dissipation coefficient is selected as K = 30W / m 2 ℃、50W / m 2 ℃. According to the relative positions of the two power plants, the river section is divided into 18 areas, and the average temperature rise of each area under the planned capacity is calculated.

[0092] Step 2: Divide the study waters into 18 sub-areas: Figure 2 shown.

[0093] Step 3: Determine the geometric elements of each cell: Determine the geometric elements of each cell, including the length of each side of the cell, the water surface area of ​​the cell, the average water depth of each side, and the centroid distance of adjacent cells. The area of ​​each cell is shown in Table 1.

[0094] Table 1

[0095] Community 1 2 3 4 5 6 7 8 9 <![CDATA[S i (km 2 )]]> 1.6 3.0 0.6 2.0 1.6 1.6 1.6 1.6 1.6 Community 10 11 12 13 14 15 16 17 18 <![CDATA[S i (km 2 )]]> 2.4 4.5 0.9 3.0 2.4 2.4 2.4 2.4 2.4

[0096] Step 4: Calculate the average temperature rise of the water body in each community: According to the flow formed by the flow in the study water area, distribute the flow to each community and calculate the exchange flow between adjacent communities, such as Figure 3 The heat balance equation of each area is listed, and then the average temperature rise of the water body in each area is obtained. The calculation results are shown in Figure 4 , as shown in Table 2.

[0097] Table 2

[0098]

[0099] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred arrangement scheme, a person skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A simple method for estimating heat diffusion, characterized in that: The method comprises the following steps: Step 1, basic data acquisition: obtain the basic data of the research waters, including hydrological and meteorological elements, hot water discharge temperature, water flow and flow rate; the meteorological elements include water temperature, air temperature, and heat dissipation coefficient; Step 2: Divide the study water area into small areas: Divide the study water area into multiple small areas according to the location of the power plant. Divide the power plant into a separate small area and do not place the power plant in the most marginal area. Step 3: Determine the geometric elements of each cell: Determine the geometric elements of each cell, including the length of each side of the cell, the water surface area of ​​the cell, the average water depth of each side, and the distance between the centroids of adjacent cells; Step 4. Calculate the average temperature rise of the water body in each district: distribute the flow to each district according to the flow formed by the flow in the study water area, and calculate the exchange flow between adjacent districts; list the heat balance equation of each district to express the comprehensive heat balance state of each district under the influence of influencing factors; solve the average temperature rise of the water body in each district according to the basic data obtained and the geometric elements of each district.

2. A simple thermal diffusion estimation method according to claim 1, characterized in that: The calculation of the exchange flow between adjacent cells in step 4 is specifically as follows: to calculate the exchange flow between two adjacent cells, the exchange flow between the two cells is obtained by multiplying the average flow velocity of the water body passing through by the flow area.

3. A simple thermal diffusion estimation method according to claim 1, characterized in that: The influencing factors described in step 4 include convection, heat diffusion, water surface heat dissipation and source and sink items caused by water flow; convection is the heat exchange between the cells under the action of the average flow velocity of the water body; heat diffusion is the mutual heat exchange caused by the temperature difference between the cells; water surface heat dissipation is the exchange of heat in the cell with the atmosphere through the water surface; source and sink items include water intake and drainage.

4. A simple thermal diffusion estimation method according to claim 3, characterized in that: The method of solving the average water temperature rise value of each community in step 4 specifically includes the following steps: Step 41: Calculate the heat of drainage and water intake in the community: Assuming that the drainage outlet and water intake are arranged in the community i, after the hot water flows into the community i, the water body in the community i will produce an average temperature rise ΔT due to the influence of convection, heat diffusion, water surface heat dissipation, and source and sink terms. i ; The heat discharged from the drainage outlet into the cell i is Q1, which is the heat per unit time. If the drainage temperature rises ΔT 排i =0, the discharged heat is 0, and the calculation formula for the discharged heat is: Q1=q 排i ·ΔT 排i (1) Where Q1 is the drainage heat of cell i; q 排i is the drainage flow in cell i; ΔT 排i is the drainage temperature rise in cell i. If the drainage system in the cell is composed of other inflows that are not affected by the thermal drainage of the power station, then the drainage temperature rise ΔT 排i Take 0; The heat taken away by the water from the cell i is Q2, and the calculation formula of the water heat is: Q2=q 取i ·ΔT i (2) Where, Q2 is the water intake heat of community i; q 取i is the water intake flow in community i; ΔT i is the average temperature rise of the water body in community i; if there is no water intake in community i, then q 取i =0; Step 42: Calculate the convection heat of the cell: Due to the convection of water bodies, heat exchange occurs between the water body in cell i and the adjacent cell j, namely, convection heat, and the calculation formula is: Q3=q 流ij ·ΔT i (3) or Q'3=q 流ij ·ΔT j (4) In the formula, q 流ij is the exchange flow between cell i and adjacent cell j due to water convection; if the water flow direction is from i to j, the convection heat of cell i is Q3, that is, the convection will raise the temperature by ΔT i If the water body is carried from i to j; on the contrary, if the water body flows from j to i, the convection heat of cell i is Q'3, and the convection will raise the temperature by ΔT j The water body is brought from j to i; ΔT j is the average temperature rise of water in cell j; Step 43: Calculate the heat diffusion heat of the cell: The heat transfer between adjacent cells i and j due to turbulent diffusion is the heat diffusion heat Q4. The heat diffusion heat is proportional to the vertical contact area and temperature gradient. The calculation formula is: Where, Q4 is the heat diffusion heat of cell i; A ij is the contact area between two cells i and j, with dimension m 2 , A ij =Lh, L is the horizontal contact length of the cell boundary, dimension is m, h is the average water depth on the corresponding boundary, dimension is m; ΔX ij is the distance between the centroids of adjacent cells i and j, with the dimension of m; D ij is the thermal diffusion coefficient, which indicates the magnitude of heat transfer due to thermal diffusion. Dx is along the water flow direction, Dy is perpendicular to the water flow direction, and the dimension is m 2 / s; Rewrite the above formula as: In the formula, is the heat diffusion flux, dimension is m 3 / s,; Step 44, calculate the heat dissipation of the community: The heat dissipation is the heat removed by the water surface of cell i. The calculation formula is: Where Q5 is the heat dissipation of cell i; K is the water surface heat dissipation coefficient, unit is W / m 2 ℃; C is the specific heat of water; S i is the water surface area of ​​cell i; Step 45, calculate the average temperature rise of the water body in the community: In the state of thermal equilibrium, the heat brought into this cell i is equal to the heat taken out of cell i, that is, the heat balance equation of cell i is: Q1-Q2-∑Q3(or+∑Q'3)-∑Q4-Q5=0 (8) Solving the above formula, we can get the average temperature rise ΔT of cell i: i ; Similarly, the average temperature rise value of each cell under thermal equilibrium state can be obtained, starting from the boundary cell and then solving it one by one.

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