Method for calculating surface temperature uniformity of prefabricated radiant panel

Abstract

The invention belongs to the technical field of heating, ventilation and air conditioning, and discloses a method for calculating the surface temperature uniformity of a prefabricated radiant panel. Through measurement or understanding of related characteristic parameters of the structural material of the radiant panel, the surface temperature uniformity of the prefabricated radiant panel can be rapidly obtained according to the water supply and return temperature and the indoor target set temperature. According to the method, a designer is effectively assisted in model selection of a radiant panel structure material, a radiation system is assisted in completing water temperature adjustment and room temperature control, and local supercooling and condensation and local thermal discomfort possibly caused by uneven surface temperature distribution are avoided. The surface temperature uniformity of the radiant panel is only influenced by the structural characteristics, the water supply flow and the water specific heat value of the radiant panel, and a designer can be guided to optimize the structure of the radiant panel so as to improve the performance of the radiant panel.

Description

Technical Field

[0001] The present invention relates to the technical field of heating, ventilation and air conditioning, and in particular to a method for calculating the surface temperature uniformity of a prefabricated radiation panel. Background Art

[0002] Surface temperature uniformity is a key factor in evaluating the performance of prefabricated radiant panels and significantly impacts the effectiveness of radiant cooling and heating systems. Under heating conditions, uneven surface temperature distribution can lead to localized thermal discomfort, while under cooling conditions, excessively low surface temperatures can cause condensation. These phenomena not only affect indoor comfort but also the panels' cooling and heating capabilities. Therefore, accurately measuring and predicting the surface temperature and uniformity of radiant panels is crucial for radiant panel engineering design, control, and optimization. Existing patents CN209961268U and CN103411685B measure radiant surface temperature uniformity using specific radiation measurement equipment. However, the variation in surface temperature uniformity of radiant panels is a function of the combined effects of the system's waterside parameters, the panel's structural characteristics, and the indoor environment. Surface temperature uniformity of radiant panels should be physically correlated with relevant parameters to provide designers with a design basis and assist in establishing control strategies during system operation. Summary of the Invention

[0003] This invention provides a method for measuring the surface temperature uniformity of prefabricated radiant panels. By measuring or understanding the characteristic parameters of the panel's structural materials, the panel's surface temperature uniformity can be quickly determined based on the supply and return water temperatures and the target indoor temperature. This method effectively assists designers in selecting radiant panel materials and facilitates water temperature regulation and room temperature control in radiant systems, preventing uneven surface temperature distribution that can lead to localized overcooling, condensation, and thermal discomfort.

[0004] The present invention achieves the above-mentioned technical solutions as follows:

[0005] A method for calculating the surface temperature uniformity of a prefabricated radiation panel is provided, wherein the prefabricated radiation panel is used as the object. The basic structure of the prefabricated radiation panel is as follows: Figure 1 As shown, it includes a surface layer A1, a heat-saturating layer A2, hot and cold water pipes A3, and an insulation layer A4. When installed on a ceiling, due to the ceiling installation process, there will be a certain air gap layer A5 between the ceiling structure layer A6. When installed on the ground, the structure layer A6 can be closely attached to the original floor of the room.

[0006] The surface temperature uniformity γ of the prefabricated radiation panel is defined as the average surface temperature t s With air reference temperature t a The difference between the two is the same as the maximum surface temperature of the prefabricated radiation panel when heated or the minimum surface temperature when cooled.s,max / min With air reference temperature t a The ratio of the difference between them is as follows:

[0007] (1)

[0008] The combined heat transfer between the surface of the prefabricated radiant panel and the indoor environment is equal to the effective heat transfer from the hot and cold water in the prefabricated radiant panel to the surface of the prefabricated radiant panel q under the condition of steady-state equilibrium. eff ; h t It represents the comprehensive convection-radiation heat transfer coefficient between the surface of the prefabricated radiation panel and the indoor environment, and the Newton cooling formula is used to express the average surface temperature t of the prefabricated radiation panel. s and indoor air reference temperature t a The relationship is shown in the following formula:

[0009] (2)

[0010] Based on the effective heat transfer resistance R of the prefabricated radiation panel eff The concept simplifies the heat transfer of prefabricated radiant panels into a two-dimensional heat transfer problem. The effective heat transfer from hot and cold water in the prefabricated radiant panels to the indoor environment is q eff The average temperature of hot and cold water in the prefabricated radiant panels t w and indoor air reference temperature t a It is obtained by the following formula:

[0011] (3)

[0012] The point where the surface temperature of the prefabricated radiation panel is the highest when heated or the point where the surface temperature is the lowest when cooled is the surface position corresponding to the inlet of hot and cold water in the prefabricated radiation panel; ws represents the inlet temperature of hot and cold water, η represents the heat transfer efficiency coefficient, and the maximum or minimum surface temperature of the prefabricated radiation panel is t s,max / min Use the following formula to calculate:

[0013] (4)

[0014] Take the water supply temperature t ws and return water temperature t wr The average water temperature t w According to the heat balance relationship, the actual heat transfer of hot and cold water in the prefabricated radiant panel is equal to the enthalpy difference between the hot and cold water inlets and outlets in the prefabricated radiant panel. The temperature difference between the supply and return water of the prefabricated radiant panel is usually within 5°C. The change in the physical parameters of the water caused by the temperature difference is negligible. The enthalpy difference between the supply and return water can be calculated using the specific enthalpy and the temperature difference. Therefore, the heat transfer balance is described by the following formula:

[0015] (5)

[0016] (6)

[0017] Where R tot is the total heat transfer resistance of the prefabricated radiant panel, G is the flow rate of hot and cold water, c is the specific heat value of water, and A is the surface area of ​​the prefabricated radiant panel.

[0018] Substituting equations (2), (3), (4), (5), and (6) into equation (1), we can obtain the physical calculation formula for the surface temperature uniformity γ of the radiation panel:

[0019] (7)

[0020] The transverse heat transfer of the prefabricated radiation panel is mainly achieved by the heat-sinking layer that wraps the hot and cold water pipes. The heat-sinking layer is regarded as a fin extending from the hot and cold water pipes, and a fin heat transfer model is established. The heat transfer efficiency coefficient η based on the fin heat transfer model is calculated by the following formula:

[0021] (8)

[0022] (9)

[0023] (10)

[0024] (11)

[0025] Where: M is the distance between the cold water pipes in the prefabricated radiant panel, δ cl is the thickness of the thermal blanket, λ cl is the thermal conductivity of the heat-sinking layer, R f is the thermal resistance from the heat-saturating layer to the surface layer of the prefabricated radiation panel to the indoor environment, R b It is the thermal resistance from the heat-saturating layer to the environment corresponding to the back side of the prefabricated radiation panel.

[0026] Total heat transfer resistance R of prefabricated radiation panel tot and the effective heat transfer resistance R of the prefabricated radiation panel eff The calculation expression is as follows:

[0027] (12)

[0028] (13)

[0029] Where R f is the thermal resistance from the heat-saturating layer to the indoor environment of the prefabricated radiation panel, R b is the thermal resistance from the heat-saturating layer to the indoor environment of the adjacent room of the prefabricated radiation panel, R l It is the thermal resistance from the hot and cold water in the pipe to the uniform heat layer.

[0030] Beneficial effects of the present invention:

[0031] The surface temperature uniformity of the radiation panel proposed in the present invention is only affected by the structural characteristics of the radiation panel itself, the water supply flow rate and the specific heat value of water, which can guide designers to optimize the radiation panel structure to improve its performance.

[0032] The surface temperature uniformity value of the radiation panel proposed in this invention ranges from 0 to 1. The closer it is to 1, the more uniform it is, and the closer it is to 0, the more uneven it is. It is relatively stable under a specific radiation panel structure and can be used to measure the performance of the radiation panel.

[0033] The method proposed in the present invention can calculate the required surface temperature of the radiation panel after giving the room cooling and heating loads and the indoor target air temperature. It can also calculate the maximum or minimum surface temperature of the radiation panel through the uniformity γ to avoid surface condensation and local thermal discomfort, providing guidance for the control of the radiation air-conditioning system.

[0034] The method proposed in the present invention can calculate the surface temperature uniformity γ of the radiation plate by using formula (7) when the structural parameters of the radiation plate are known, or it can calculate the surface temperature uniformity γ by using formula (1) by measuring the temperature of different points on the surface of the radiation plate. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present invention will be further described below with reference to the accompanying drawings and specific implementations.

[0036] Figure 1 Schematic diagram of the basic structure of the prefabricated radiation panel calculated by the method of the present invention. (a) is ground installation, and (b) is ceiling installation.

[0037] Figure 2 This is the equivalent structural thermal resistance network diagram of the prefabricated radiant panel calculated by the method of the present invention. (a) is ground installation, and (b) is ceiling installation.

[0038] Figure 3 It is a schematic diagram of the surface temperature measurement points of the prefabricated radiation panel which is the calculation object of the method of the present invention.

[0039] Figure 4 The following is a schematic diagram of some results of the method for calculating the surface temperature uniformity of the radiation panel of the present invention. (a) is the heating condition, and (b) is the cooling condition. DETAILED DESCRIPTION

[0040] The prefabricated radiation panels commonly found in the current market are taken as the research object. The main structure of the prefabricated radiation panels includes a surface layer, a heat-saturating layer, hot and cold water pipes, an insulation layer, etc.

[0041] The surface temperature uniformity γ of the prefabricated radiation panel is defined as the average surface temperature t s With air reference temperature t aThe difference between the maximum surface temperature (when heating) or the minimum surface temperature (when cooling) of the prefabricated radiation panel is t s,max / min With air reference temperature t a The ratio of the difference between them. As shown in the following formula:

[0042] (1)

[0043] The combined heat transfer of convection and radiation between the surface of the prefabricated radiant panel and the indoor environment is equal to the effective heat transfer q from the hot and cold water in the prefabricated radiant panel to the surface of the prefabricated radiant panel under the condition of steady-state equilibrium. eff . t As the comprehensive convection-radiation heat transfer coefficient between the surface of the prefabricated radiation panel and the indoor environment, the average surface temperature t of the prefabricated radiation panel can be expressed by the Newton cooling formula. s and indoor air reference temperature t a The relationship is shown in the following formula:

[0044] (2)

[0045] Effective heat transfer resistance R using prefabricated radiation panels eff The concept (heat transfer resistance from hot and cold water in the prefabricated radiant panel to the surface of the radiant panel) simplifies the heat transfer of the prefabricated radiant panel into a two-dimensional problem. Therefore, the effective heat transfer from hot and cold water in the prefabricated radiant panel to the indoor environment is q eff The average temperature of hot and cold water in the prefabricated radiant panels can be w and indoor air reference temperature t a It is obtained by the following formula:

[0046] (3)

[0047] The point with the highest surface temperature (when heating) or the lowest surface temperature (when cooling) of the prefabricated radiation panel appears at the surface position corresponding to the inlet of hot and cold water in the prefabricated radiation panel. ws As the inlet temperature of hot and cold water (system water supply temperature), η as the heat transfer efficiency coefficient, the maximum surface temperature or the minimum surface temperature of the prefabricated radiation panel t s,max / min It can be expressed as follows:

[0048] (4)

[0049] The lateral heat transfer of prefabricated radiant panels is primarily achieved through the heat-sinking layer surrounding the hot and cold water pipes. Therefore, the heat-sinking layer can be considered as fins extending from the hot and cold water pipes. The fin heat transfer model can be used to predict the surface temperature distribution and the maximum or minimum surface temperature of the prefabricated radiant panel. Therefore, based on the fin heat transfer model, the heat transfer efficiency coefficient η can be calculated using the following formula:

[0050] (5)

[0051] (6)

[0052] (7)

[0053] (8)

[0054] Where: M is the distance between the cold water pipes in the prefabricated radiant panel, δ cl is the thickness of the thermal blanket, λ cl is the thermal conductivity of the heat-sinking layer, R f is the thermal resistance from the heat-saturating layer to the indoor environment of the prefabricated radiation panel, R b is the thermal resistance from the soaking layer to the indoor environment of the adjacent room of the prefabricated radiant panel.

[0055] In the calculation, the water supply temperature t is usually taken ws and return water temperature t wr The average water temperature t w According to the heat transfer equilibrium, the actual heat transfer of hot and cold water in a prefabricated radiant panel should be equal to the enthalpy difference between the hot and cold water inlets and outlets. Since the temperature difference between the supply and return water in a prefabricated radiant panel is typically within 5°C, the change in water properties caused by the temperature difference is negligible. Therefore, the enthalpy difference between the supply and return water can be calculated using the specific enthalpy and the temperature difference. Therefore, the heat transfer equilibrium can be described by the following equation:

[0056] (9)

[0057] (10)

[0058] Where R tot is the total heat transfer resistance of the radiant panel, G is the flow rate of hot and cold water, and c is the specific heat value of water.

[0059] Substituting equations (2), (3), (4), (9), and (10) into equation (1), the relevant physical expression of the surface temperature uniformity γ of the prefabricated radiation panel can be obtained as follows:

[0060] (11)

[0061] The total heat transfer resistance R of the prefabricated radiation panel mentioned in the present invention is tot and the effective heat transfer resistance R of the prefabricated radiation panel eff The calculation expression is as follows:

[0062] (12)

[0063] (13)

[0064] Where R f is the thermal resistance from the heat-saturating layer to the indoor environment of the prefabricated radiation panel, R b is the thermal resistance from the heat-saturating layer to the indoor environment of the adjacent room of the prefabricated radiation panel, R l is the thermal resistance from the hot and cold water in the pipe to the uniform heat distribution layer. These thermal resistances are easy to understand and obtain for relevant designers.

[0065] like Figure 1 As shown, the basic structure of the prefabricated radiant panel includes a surface layer A1, a heat-diffusion layer A2, hot and cold water pipes A3, and an insulation layer A4. However, different installation methods vary. When installed on a ceiling, the suspended ceiling installation process creates an air gap A5 between the panel and the structural layer A6. When installed on the ground, the structural layer A6 can be placed flush against the existing floor of the room.

[0066] like Figure 2 The figure shows the equivalent thermal resistance network diagram of the prefabricated radiation panel proposed by the method of the present invention. This thermal resistance network diagram is the core calculation basis of the method of the present invention. The heat-absorbing layer is regarded as an important heat transfer node, and the thermal resistance of the radiation panel is divided into three parts for calculation: the thermal resistance R from the heat-absorbing layer to the surface layer of the radiation panel corresponding to the indoor environment. f , thermal resistance R from the heat spreader to the environment on the back of the radiation panel b And the thermal resistance R from the hot and cold water in the pipe to the uniform heat layer l Thermal resistance R f Including the equivalent thermal resistance from the soaking layer to the surface layer and the comprehensive heat transfer (convective heat transfer and radiation heat transfer) thermal resistance of the radiation surface; thermal resistance R b Calculation with R f The calculation is basically the same, where ΔR ins The size is related to the groove design of the insulation board (the groove changes the structure of the insulation layer, resulting in a decrease in the actual thermal resistance of the insulation layer. This reduced thermal resistance is recorded as ΔR ins ); Thermal resistance R l It consists of four parts: the thermal resistance R of the hot and cold water that transfers heat to the inner wall of the pipe through convection heat transfer. co The thermal resistance R of the inner wall of the tube transferring heat to the outer wall of the tube through heat conduction p The thermal resistance R of the outer wall of the hot and cold water pipe transferring heat to the grooved heat-dissipating layer that wraps the pipe wall p-cl And the thermal resistance R of the heat spreader cl The composition and calculation method of the three parts of thermal resistance are shown in the following formula:

[0067] (14)

[0068] (15)

[0069] (16)

[0070] Where δ i is the thickness of each layer from the soaking layer to the surface layer, λ i is the thermal conductivity of each layer from the heat-saturating layer to the surface layer, h t is the comprehensive heat transfer coefficient between the radiation panel surface and the indoor environment. Among them, the comprehensive convection and radiation heat transfer coefficient h between the radiation panel surface and the indoor environment and the adjacent indoor environment when the floor is heated and the ceiling is cooled t Take 11W / (m 2 ·K) and 7W / (m 2 K), the comprehensive convection-radiation heat transfer coefficient h between the radiant panel surface and the indoor environment and the adjacent indoor environment when the floor is cooled and the ceiling is heated t Take 7W / (m 2 ·K) and 11W / (m 2 ·K). δ j is the thickness of each layer from the soaking layer to the structural layer, λ j is the thermal conductivity of each layer from the heat-saturating layer to the structural layer.

[0071] Designers can obtain detailed calculation methods for the aforementioned sub-items of thermal resistance for radiant panels from relevant reference design manuals or standards and will not be detailed here. The thickness and thermal conductivity of the structural materials required for thermal resistance calculations can be determined by the designer or provided by the material supplier.

[0072] The definition of the temperature uniformity of the radiation plate surface given by the method of the present invention is the average temperature of the radiation plate surface t s The maximum surface temperature (when heating) or the minimum surface temperature (when cooling) of the radiation panel is t s,max / min The experimental measurement system is implemented in accordance with the provisions of the industry standard "Test Method for Thermal Performance of Radiant Cooling and Heating Devices (JG / T 403-2013)". The arrangement of the surface temperature measurement points of the radiation panel is as follows: Figure 3 As shown, the corresponding measurement calculation method is as follows:

[0073] (17)

[0074] (18)

[0075] Where, t i Indicates the corresponding numbered measurement point ( Figure 3 ) at the temperature.

[0076] The basic definition of measuring the surface temperature uniformity of the prefabricated radiation panel proposed in the present invention is shown in formula (1), and the physical calculation formula (11) of the uniformity definition is given through theoretical analysis. It is clear that the proposed surface temperature uniformity of the prefabricated radiation panel is only affected by the structural characteristics of the prefabricated radiation panel itself, the water supply flow rate and the specific heat value of water, which can guide designers to optimize the structure of the prefabricated radiation panel to improve its performance. The structural characteristics of the prefabricated radiation panel itself include the spacing between the hot and cold water pipes in the prefabricated radiation panel, the diameter of the hot and cold water pipes, and the thickness and thermal conductivity of each structural layer. Figure 4 As shown in the figure, the surface temperature uniformity of the prefabricated radiation panel calculated by the method of the present invention according to the physical relationship (11) changes with the water supply temperature. It can be seen that the surface temperature uniformity of the prefabricated radiation panel hardly changes with the water supply temperature. Therefore, according to the industry standard "Test Method for Thermal Performance of Radiant Cooling and Heating Devices (JG / T 403-2013)", when determining the indoor temperature t a Measure the t of a given prefabricated radiation panel under s With t s,max / min After that, the surface temperature uniformity γ of the prefabricated radiation panel can be calculated. As long as the structure of the radiation panel does not change and the water supply flow rate is maintained within a certain range, the measured surface temperature uniformity γ can be applied to different operating conditions. Based on the surface temperature uniformity γ and the relevant structural parameters of the prefabricated radiation panel, the designer can use the method provided by the present invention to calculate the average surface temperature t of the prefabricated radiation panel. s and the maximum or minimum surface temperature of the prefabricated radiation panel t s,max / min , thus guiding the water supply temperature t when the prefabricated radiation panel is controlled by variable water temperature ws settings.

[0077] With the above-described preferred embodiments of the present invention as inspiration, and with reference to the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical scope of this invention. The technical scope of this invention is not limited to the contents of the specification and must be determined according to the scope of the claims.

Claims

1. A method for calculating the surface temperature uniformity of a prefabricated radiation panel, characterized in that: The measurement object is a prefabricated radiation panel, which includes a surface layer, a heat-saturating layer, hot and cold water pipes, and an insulation layer. When installed on the ceiling, there is a certain air gap between the panel and the structural layer of the ceiling. When installed on the ground, the panel is close to the structural layer of the original room floor. The surface temperature uniformity γ of the prefabricated radiation panel is defined as the average surface temperature t s With air reference temperature t a The difference between the two is the same as the maximum surface temperature of the prefabricated radiation panel when heated or the minimum surface temperature when cooled. s,max / min With air reference temperature t a The ratio of the difference between As shown in the following formula: (1) The combined heat transfer between the surface of the prefabricated radiation panel and the indoor environment is equal to the effective heat transfer from the hot and cold water in the prefabricated radiation panel to the surface of the prefabricated radiation panel q under the condition of steady-state equilibrium. eff ; h t It represents the comprehensive convection-radiation heat transfer coefficient between the surface of the prefabricated radiation panel and the indoor environment, and the Newton cooling formula is used to express the average surface temperature t of the prefabricated radiation panel. s and indoor air reference temperature t a The relationship is shown in the following formula: (2) Based on the effective heat transfer resistance R of the prefabricated radiation panel eff The concept simplifies the heat transfer of prefabricated radiation panels into a two-dimensional heat transfer problem; the effective heat transfer from hot and cold water in the prefabricated radiation panels to the indoor environment q eff The average temperature of hot and cold water in the prefabricated radiant panels t w and indoor air reference temperature t a It is obtained by the following formula: (3) The point where the surface temperature of the prefabricated radiation panel is the highest when heated or the point where the surface temperature is the lowest when cooled is the surface position corresponding to the inlet of hot and cold water in the prefabricated radiation panel; t ws represents the inlet temperature of hot and cold water, η represents the heat transfer efficiency coefficient, and the maximum or minimum surface temperature of the prefabricated radiation panel is t s,max / min It is expressed as follows: (4) , take the water supply temperature t ws and return water temperature t wr The average water temperature t w According to the heat transfer balance, the actual heat transfer amount of hot and cold water in the prefabricated radiation panel is equal to the enthalpy difference between the inlet and outlet of the prefabricated radiation panel. The change in the physical parameters of water caused by the temperature difference is negligible. The enthalpy difference of the supply and return water can be calculated by the specific enthalpy and temperature difference. Therefore, the heat transfer balance is described by the following formula: (5) , (6) , where R tot is the total heat transfer resistance of the prefabricated radiant panel, G is the flow rate of hot and cold water, c is the specific heat value of water, and A is the surface area of ​​the prefabricated radiant panel; Substituting equations (2), (3), (4), (5), and (6) into equation (1), we can obtain the surface temperature uniformity γ of the radiation plate: (7) 。 2. The method for calculating the surface temperature uniformity of a prefabricated radiation panel according to claim 1, characterized in that: The transverse heat transfer of the prefabricated radiation panel is mainly achieved by the heat-sinking layer that wraps the hot and cold water pipes. The heat-sinking layer is regarded as a fin extending from the hot and cold water pipes, and a fin heat transfer model is established. The heat transfer efficiency coefficient η based on the fin heat transfer model is calculated by the following formula: (8) ， (9) ， (10) ， (11), where: M is the distance between the cold water pipes in the prefabricated radiant panel, δ cl is the thickness of the thermal blanket, λ cl is the thermal conductivity of the heat-sinking layer, R f is the thermal resistance from the heat-saturating layer to the indoor environment of the prefabricated radiation panel, R b is the thermal resistance from the soaking layer to the indoor environment of the adjacent room of the prefabricated radiant panel.

3. The method for calculating the surface temperature uniformity of a prefabricated radiation panel according to claim 1, characterized in that: Total heat transfer resistance R of prefabricated radiation panel tot and the effective heat transfer resistance R of the prefabricated radiation panel eff The calculation expression is as follows: (12) ， (13) , where R f is the thermal resistance from the heat-saturating layer to the surface layer of the prefabricated radiation panel to the indoor environment, R b is the thermal resistance from the heat-saturating layer to the environment on the back of the prefabricated radiation panel, R l It is the thermal resistance from the hot and cold water in the pipe to the uniform heat layer.

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