Iterative calculation method for concrete temperature field under surface water flow state of thermal insulation material

Abstract

The application provides a concrete temperature field iterative calculation method under a water flowing state on the surface of a thermal insulation material. The inner side temperature of the thermal insulation material is derived according to the concrete heat flow and the outer side temperature of the thermal insulation material, and the inner side temperature of the thermal insulation material is taken as a first type boundary condition to calculate the concrete temperature field. The application can more accurately calculate the concrete temperature field under the water flowing state on the surface of the thermal insulation material, and provides a scientific basis for formulating and adjusting mass concrete temperature control and crack prevention measures.

Description

Technical Field

[0001] This invention relates to a method for calculating the temperature field of concrete, specifically, to an iterative calculation method for the temperature field of concrete under conditions where the surface of the thermal insulation material on the concrete surface is in a flowing water state. This invention belongs to the field of water conservancy and hydropower engineering technology. Background Technology

[0002] Concrete is a poor conductor of heat, easily leading to significant temperature differences between its internal and external surfaces, which in turn causes cracking. In high-altitude and cold regions, temperature load is the primary cause of dam cracking. Effective insulation measures can effectively control temperature load and reduce cracking. For example, a power station neglected insulation measures during construction and operation, resulting in numerous cracks in the dam. During operation, these cracks caused leakage, and despite substantial repair efforts, leakage persisted, significantly threatening the dam's safety and durability.

[0003] Surface insulation and internal water permeation are the main measures for temperature control and crack prevention in large-volume concrete. When formulating and implementing temperature control and crack prevention measures, it is necessary to accurately grasp the temperature distribution at the interface of the insulation materials and the surface of the unit containing the insulation material, so as to formulate and adjust the temperature control and crack prevention measures in a timely manner. Laying insulation materials on the concrete surface can reduce the surface heat transfer coefficient and reduce the temperature difference between the inside and outside, thus achieving the purpose of temperature control and crack prevention. For both dry and humid environments, there are already relevant studies on the relationship between the thermal conductivity of insulation materials and the heat transfer coefficient of the concrete surface. For example, Academician Zhu Bofang has derived a model relating the thermal conductivity of insulation materials and the heat transfer coefficient of the concrete surface when laying dry insulation materials. Some scholars have also conducted relevant research on the insulation performance of insulation materials under humid conditions.

[0004] However, in actual engineering projects, the surface of thermal insulation materials is often in a state of running water and surface icing. Moreover, the thermal insulation material is relatively thin and lightweight, and its heat absorption is limited, acting similarly to an air retention layer. In this case, it is inaccurate to use the existing model of the relationship between the thermal conductivity of thermal insulation materials and the heat release coefficient of concrete surface to analyze and calculate the temperature distribution of the unit's air-filled node where the thermal insulation material is located at the interface of the thermal insulation material. This affects the formulation and implementation of temperature control and crack prevention measures, resulting in unsatisfactory temperature control and crack prevention effects. Summary of the Invention

[0005] In view of the above reasons, the purpose of this invention is to provide an iterative calculation method for the concrete temperature field when the surface of the thermal insulation material is in a flowing state. The concrete temperature field calculated by this iterative calculation method can accurately reflect the actual temperature distribution at the nodes of the unit where the thermal insulation material is located in the flowing state at the interface of the thermal insulation material, providing a scientific basis for formulating and adjusting concrete temperature control and crack prevention measures.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an iterative calculation method for the temperature field of concrete under flowing water conditions on the surface of thermal insulation materials, characterized in that it includes the following steps:

[0007] S1. Determine the heat release coefficient β of the concrete surface under flowing water conditions on the surface of the insulation material. S :

[0008] (2)

[0009] in: Let be the thickness of the i-th layer of insulation material. Let be the thermal conductivity of the i-th layer of insulation material;

[0010] S2. Calculate the initial temperature field of the large-volume concrete based on the three-dimensional temperature field finite element calculation method and the heat release coefficient of the concrete surface in step S1.

[0011] S3. Determine the heat flow rate Q0 across the air-filled surface of the unit containing the surface water insulation material:

[0012] (3)

[0013] in: The thermal conductivity of concrete. This represents the normal temperature gradient at the node on the air surface of the unit containing the surface water-cooled insulation material. This represents a small element representing the area at a node. Indicates the step size in the calculation;

[0014] S4. Determine the temperature of the node on the air surface of the unit where the surface water-flow insulation material is located. :

[0015] The nodal temperature of the surface of the unit containing the surface water-flowing insulation material can be obtained by using the heat flow Q0 through the open surface of the unit and the temperature of the external environment. :

[0016] (4)

[0017] in: The temperature of water or ice on the surface of the insulation material. Temperature of the node on the air surface of the unit containing the surface water-flow insulation material;

[0018] S5. The initial temperature of the node on the free surface of the unit containing the surface water insulation material in the initial temperature field of the large-volume concrete calculated in step S2. Temperature of the air-filled node of the unit containing the surface water-flow insulation material The temperature T at the nodal on the surface of the element containing the surface water-flow insulation material was calculated after the first iteration. s1 :

[0019] (5)

[0020] in: α represents the initial temperature of the node on the free surface of the unit containing the surface water-cooled insulation material; α is the iterative convergence control coefficient.

[0021] Will As the initial value for the second iteration, and referring to equations (4) and (5), the following is calculated: and Therefore, it can be deduced that and Relational expression:

[0022] (6)

[0023] in: This represents the temperature of the node on the free surface of the element containing the surface water-flow insulation material after the (n-1)th iteration calculation. This represents the temperature of the node on the free surface of the unit containing the surface water insulation material after the nth iteration calculation;

[0024] Therefore, the residual of the nth iteration can be calculated:

[0025] (7)

[0026] S6. Set the minimum value of the residual. When the residual is less than the set value, stop the iterative calculation.

[0027] In a preferred embodiment of the present invention, the minimum residual value in step S6 is 0.01℃.

[0028] In a preferred embodiment of the present invention, for a single thermal insulation material, the concrete temperature field iterative convergence control coefficient... The selection should satisfy the following formula:

[0029] (15)

[0030] in: λ is the thermal conductivity of the insulation material; h is the thickness of the insulation material, in meters; λ c The thermal conductivity of concrete; This is a coefficient, with units of 0.05m;

[0031] For composite insulation materials, first calculate the average thermal conductivity of the insulation material:

[0032] (16)

[0033] in, Substituting equation (16) into equation (15) will yield the solution. .

[0034] In a preferred embodiment of the present invention, the product of the normal temperature gradient and the surface area at the node of the unit containing the surface water-cooled thermal insulation material in step S3 should satisfy the following relationship:

[0035] (17)

[0036] in: This represents the temperature gradient vector at the node of the airborne surface. Represents the surface area vector at the nodes of the airborne surface;

[0037] For the finite element method of calculating three-dimensional temperature fields, the temperature gradient vector at the nodes of the elevated surface is calculated using the following method:

[0038] (18)

[0039] in: Describe the shape function of the i-th node. This represents the temperature of the i-th node;

[0040] Let the concrete surface of the unit be... Then the surface area vector at the nodes of the airborne surface can be calculated using the following method:

[0041] (19)

[0042] in: , and Local coordinates;

[0043] Therefore, the temperature of the node on the air-supported surface of the unit containing the surface water-insulating material is:

[0044] (20).

[0045] In a preferred embodiment of the present invention, when the node where the surface water insulation material is located belongs to only one surface of the unit where the surface water insulation material is located, the temperature of the node where the surface water insulation material is located is calculated based on the surface; when the node where the surface water insulation material is located belongs to multiple surface of the unit where the surface water insulation material is located, multiple node temperatures are calculated based on different surface and the average value is taken as the final node temperature.

[0046] This invention calculates the temperature inside the insulation material based on the heat flow of the concrete and the temperature of the outer side of the insulation material, and recalculates the concrete temperature field using the temperature of the inner side of the insulation material as a first-type boundary condition. This invention can more accurately calculate the concrete temperature field under flowing water conditions on the surface of the insulation material, providing a scientific basis for formulating and adjusting temperature control and crack prevention measures for large-volume concrete. Attached Figure Description

[0047] Figure 1 This is a flowchart of the concrete temperature field iterative calculation method of the present invention;

[0048] Figure 2 This describes the surface temperature of the unit's air-level node where water flows at the interface of the insulation material when the thickness of the insulation material changes. Detailed Implementation

[0049] The structure and features of the present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that various modifications can be made to the embodiments disclosed herein; therefore, the embodiments disclosed in this specification should not be considered as limitations on the present invention, but merely as examples to make the features of the present invention readily apparent.

[0050] When the surface of the thermal insulation material on the concrete surface is in a flowing state, this invention calculates the temperature inside the thermal insulation material based on the principle of heat flow balance, according to the heat flow and the temperature outside the thermal insulation material, and uses the temperature inside the thermal insulation material as the first type of boundary condition to calculate the concrete temperature field.

[0051] Depending on the mode of heat exchange between concrete and the external environment and the influencing factors, the boundary conditions of the concrete temperature field also vary. When the concrete surface is covered with insulation material or multiple layers of insulation material, the insulation material has limited heat absorption due to its thinness and light volume. Its function is similar to that of an air retention layer, and the equivalent heat release coefficient β of the concrete surface is... S for:

[0052] (1)

[0053] in: and These represent the thickness and thermal conductivity of each layer of insulation material, This represents the heat exchange coefficient of the air on the surface of the insulation material. Combining the three-dimensional temperature field finite element calculation method and equation (1), the temperature field of the concrete can be obtained by using the finite element variational method.

[0054] The selection of initial values ​​for iterative calculation of concrete is crucial, and these initial values ​​should be as close as possible to the actual values. For cases where water flows or ice forms on the surface of the insulation material, the surface of the insulation material is considered a first-type boundary condition, and equation (1) is used as a reference. The heat release coefficient β of the concrete surface under this condition can then be obtained. S for:

[0055] (2)

[0056] The initial value of the temperature field of a large-volume concrete can be obtained by using the three-dimensional temperature field finite element method and equation (2). Let the initial value be... Based on the initial values, the heat flow rate across the air-filled surface of the unit containing the surface-flowing thermal insulation material can be obtained, i.e.:

[0057] (3)

[0058] in: The thermal conductivity of concrete. This represents the normal temperature gradient at the node on the air surface of the unit containing the surface water-cooled insulation material. This represents a small element representing the area at a node. This indicates the step size in the calculation.

[0059] The node temperature of the unit with the surface water-flow insulation material can be obtained by considering the heat flow through the air-filled surface of the unit and the ambient temperature. :

[0060] (4)

[0061] in: This indicates the temperature of water or ice on the surface of the insulation material. This indicates the temperature of the node on the air surface of the unit where the surface water-flow insulation material is located.

[0062] Based on the initial temperature of the node on the air surface of the unit where the surface water insulation material is located. and the calculated surface water insulation material unit's free-floating node temperature The temperature T of the node on the free surface of the unit containing the surface water-flow insulation material can be obtained after the first iteration. s1 :

[0063] (5)

[0064] in: The initial temperature of the node on the air surface of the unit where the surface water-cooled insulation material is located. α represents the temperature of the node on the air surface of the unit containing the surface water-cooled insulation material, and α is the iterative convergence control coefficient.

[0065] Will As the initial value for the second iteration, and referring to equations (4) and (5), it is possible to calculate... and Therefore, it can be deduced that and Relational expression:

[0066] (6)

[0067] Therefore, the residual of the nth iteration can be calculated:

[0068] (7)

[0069] Set a minimum residual value (e.g., 0.01℃). When the residual is less than the set value, the iteration can be stopped.

[0070] Iterative convergence conditions and constants for concrete temperature field Method for determining:

[0071] Assuming the actual temperature of the node on the air surface of the unit containing the surface water insulation material is... ,and:

[0072] (8)

[0073] but:

[0074] (9)

[0075] if If it is small enough, then the following conditions must be met:

[0076] (10)

[0077] at this time:

[0078] (11)

[0079] Therefore:

[0080] (12)

[0081] Therefore if If the value is small enough, the algorithm will converge to the true value. In this case, The larger the value of , the faster the convergence rate.

[0082] if If the value exceeds a certain threshold, the following situation will inevitably occur:

[0083] (13)

[0084] at this time:

[0085] (14)

[0086] During the iteration process, the temperature value of the node on the air surface of the unit containing the surface water insulation material jumps between the two ends of the true value. The larger the value, the slower the convergence speed, and it is very likely to lead to non-convergence.

[0087] Because of the iterative convergence control coefficient The magnitude of this value depends only on the thermal conductivity of the concrete, the thermal conductivity of the insulation material, and the thickness of the insulation material. It is directly proportional to the thermal conductivity of the concrete and inversely proportional to the thickness and thermal conductivity of the insulation material. Therefore:

[0088] For a single insulation material, The selection should satisfy the following formula:

[0089] (15)

[0090] in: λ is the thermal conductivity of the insulation material; h is the thickness of the insulation material, in meters; λ c The thermal conductivity of concrete; This is a coefficient, with units of 0.05m.

[0091] For composite insulation materials, the average thermal conductivity of the insulation material is:

[0092] (16)

[0093] in, ;

[0094] Substituting equation (16) into equation (15) will yield the solution. .

[0095] When the interface between concrete and insulation material is considered as a first-type boundary condition, the implementation method is to directly assign a temperature to the node and assign a large value to the surface heat transfer coefficient. If the unit containing the surface-flowing insulation material is covered with multiple insulation materials, the numerical calculation in this paper can only be achieved by directly assigning a temperature to the node. When the thickness of the insulation material changes, the temperature difference between the concrete at the two ends of the insulation material interface is significant. As shown in the figure, T C The temperature is significantly higher than T B The temperature. If a very large value is assigned to the surface heat transfer coefficient to achieve the first type of boundary condition, then T cannot be reflected. C With T B The temperature difference between them can cause the iteration to fail to converge.

[0096] Therefore, when using an iterative algorithm for calculation, such as Figure 2 As shown, the temperature difference between the outside air temperature and point B must be calculated. And the temperature difference between the outside temperature and point C. T is calculated in this way C and T B This is how the iteration converges to the true value, and the method can be applied to various insulation materials.

[0097] The product of the normal temperature gradient and the surface area at the free-face node of the unit containing the surface water-flow insulation material should satisfy the following relationship:

[0098] (17)

[0099] in: This represents the temperature gradient vector at the node of the airborne surface. This represents the surface area vector at the nodes of the air surface.

[0100] For the finite element method of a three-dimensional temperature field, the temperature gradient vector at the nodes of the air surface can be calculated using the following method:

[0101] (18)

[0102] in: and Let these represent the shape function of the node and the temperature of the node, respectively.

[0103] Let the surface of the unit containing the surface water-flow insulation material be the free surface. Then the surface area vector at the nodes of the airborne surface can be calculated using the following method:

[0104] (19)

[0105] in , and These are local coordinates.

[0106] Therefore, the temperature of the node on the air surface of the unit where the surface water-flow insulation material is located is:

[0107] (20).

[0108] When the node containing the surface water-flow insulation material belongs to only one surface of the surface water-flow insulation material unit, the node temperature is calculated based on that surface. When the node containing the surface water-flow insulation material belongs to multiple surface of the surface water-flow insulation material unit, multiple node temperatures are calculated based on different surface and the average value is taken as the final node temperature.

[0109] Advantages of this invention: This invention can more accurately calculate the temperature field of concrete under flowing water conditions on the surface of various thermal insulation materials, providing a scientific basis for formulating and adjusting temperature control and crack prevention measures for large-volume concrete.

[0110] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An iterative calculation method for the temperature field of concrete on the surface of thermal insulation material under flowing water conditions, characterized in that: It includes the following steps: S1. Determine the heat release coefficient β of the concrete surface under flowing water conditions on the surface of the insulation material. S : Where: h i Let λ be the thickness of the i-th layer of insulation material. i Let be the thermal conductivity of the i-th layer of insulation material; S2. Calculate the initial temperature field of the large-volume concrete based on the three-dimensional temperature field finite element calculation method and the heat release coefficient of the concrete surface in step S1. S3. Determine the heat flow rate Q0 on the air-filled surface of the unit containing the surface water insulation material: Where: λ c The thermal conductivity of concrete. Let ds represent the normal temperature gradient at the node on the free surface of the unit containing the surface water insulation material, ds represent the infinitesimal area of ​​the node, and Δτ represent the step size of the calculation. S4. Determine the temperature T of the node on the air surface of the unit where the surface water insulation material is located. B0 : The nodal temperature T of the unit's surface surface can be obtained by using the heat flow Q0 through the surface water insulation material and the ambient temperature. B0 : Wherein: T A T represents the temperature of water or ice on the surface of the insulation material. B0 Temperature of the node on the air surface of the unit containing the surface water-insulating material; S5. The initial temperature T of the node on the free surface of the unit containing the surface water insulation material in the initial temperature field of the large-volume concrete calculated in step S2. s0 Temperature T of the air-mounted node of the unit containing the surface water-flow insulation material B0 The temperature T at the nodal on the surface of the element containing the surface water-flow insulation material was calculated after the first iteration. s1 : T s1 =(1-α)T s0 +αT B0 (5) Wherein: T s0 α represents the initial temperature of the node on the free surface of the unit containing the surface water-cooled insulation material; α is the iterative convergence control coefficient. T s1 As the initial value for the second iteration, and referring to equations (4) and (5), T is calculated. B1 and T s2 Therefore, T is derived. sn and T sn-1 Relational expression: T sn =(1-α)T sn-1 +αT Bn (6) Wherein: T sn-1 T represents the temperature of the node on the free surface of the element containing the surface water-flow insulation material after the (n-1)th iteration calculation. sn This represents the temperature of the node on the free surface of the unit containing the surface water insulation material after the nth iteration calculation; Therefore, the residual of the nth iteration can be calculated: ω=|T sn -T sn-1 | (7) S6. Set the minimum value of the residual. When the residual is less than the set value, stop the iterative calculation.

2. The method for iterative calculation of concrete temperature field under flowing water conditions on the surface of thermal insulation material according to claim 1, characterized in that: The minimum residual value in step S6 is 0.01℃.

3. The method for iterative calculation of concrete temperature field under flowing water conditions on the surface of thermal insulation material according to claim 2, characterized in that: For a single thermal insulation material, the selection of the iterative convergence control coefficient α of the concrete temperature field should satisfy the following equation: Where: λ s λ is the thermal conductivity of the insulation material; h is the thickness of the insulation material, in meters; λ c is the thermal conductivity of concrete; k is a coefficient, with units of 0.05m; For composite insulation materials, first calculate the average thermal conductivity of the insulation material: Where h = ∑h i Substituting equation (16) into equation (15) will give us the solution for α.

4. The method for iterative calculation of concrete temperature field under flowing water conditions on the surface of thermal insulation material according to claim 3, characterized in that: In step S3, the product of the normal temperature gradient and the surface area at the node of the free surface of the unit containing the surface water-flow insulation material should satisfy the following relationship: Where: N represents the temperature gradient vector at the node of the air surface, and S represents the surface area vector at the node of the air surface. For the finite element method of calculating three-dimensional temperature fields, the temperature gradient vector at the nodes of the elevated surface is calculated using the following method: Where: N i Let RF(i) represent the shape function of the i-th node, and let RF(i) represent the temperature of the i-th node. Let the free surface of the concrete element be ζ ​​= -1. Then the surface area vector at the nodes of the free surface is calculated using the following method: Where: ξ, η, and ζ are local coordinates; Therefore, the temperature of the node on the air-supported surface of the unit containing the surface water-insulating material is:

5. The method for iterative calculation of concrete temperature field under flowing water conditions on the surface of thermal insulation material according to any one of claims 1-4, characterized in that: When the node containing the surface water-flow insulation material belongs to only one surface of the surface water-flow insulation material unit, the node temperature is calculated based on that surface. When the node containing the surface water-flow insulation material belongs to multiple surface of the surface water-flow insulation material unit, multiple node temperatures are calculated based on different surface and the average value is taken as the final node temperature.

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