An optimized quick calculation method for plate heat exchangers under finite volume constraints

Abstract

The present invention discloses an optimized quick calculation method for a plate heat exchanger under finite volume constraints. The method includes: keeping the compactness of the plate heat exchanger and the convective heat transfer coefficients on both the hot and cold sides unchanged, and substituting the known ratio of the convective heat transfer coefficients on the hot and cold sides into the optimization algorithm proposed by the present invention under the premise of neglecting other heat conduction resistances. Taking the partial derivative of the total thermal resistance with respect to the heat transfer area on the hot side to find the extreme value, and determining whether the obtained value is a minimum value based on monotonicity. If so, it corresponds to the minimum total thermal resistance of the heat transfer area on the hot side, and finally determining the structural parameters of the heat exchanger such as the number of hot and cold side plate fins, the shape and size of the plate fins. The present invention can accurately and efficiently calculate the optimal ratio of the heat transfer areas and thermal resistances of the hot and cold side fluids under the given constraints of the heat exchanger, quickly optimize the configuration of the heat transfer areas on the hot and cold sides, thereby reducing the total thermal resistance of the heat exchanger and enabling the heat exchanger to obtain better heat transfer performance under a limited volume.

Description

Technical Field

[0001] The present invention relates to an optimization method for a plate heat exchanger, and particularly to an optimized quick calculation method for a plate heat exchanger under finite volume constraints. Background Art

[0002] Currently, plate heat exchangers mainly include plate-fin heat exchangers, plate heat exchangers, printed circuit board heat exchangers, etc. formed by stacking standard plates. Plate heat exchangers use processing and manufacturing techniques such as diffusion welding, brazing, and additive manufacturing to connect microchannel heat exchange plates into a compact heat exchange module, which has the properties of being structurally compact, small in volume, and resistant to high temperature and high pressure. Due to the presence of fins, finned heat exchangers are not only very light and firm as a whole and have strong pressure-bearing capacity, but also can generate a very high heat exchange area in a very compact space, thus achieving a very high heat exchange capacity. Plate heat exchangers are also heat exchange elements with high heat exchange efficiency and a compact self-structure, and have high economy.

[0003] While the existing heat exchangers have increasing requirements for volume and compactness, they also hope to obtain better heat exchange effects. The traditional design theory based on unequal areas on both sides of the fluid utilizes the principle that the heat exchange area on both sides of the fluid is inversely proportional to the heat transfer coefficient, and strengthens the heat exchange effect by increasing the heat exchange area on the side with a small heat transfer coefficient. However, this method of increasing the heat exchange area will, on the one hand, make the volume of the heat exchanger larger and the compactness decrease, and on the other hand, will lead to an increase in flow resistance, resulting in an increase in investment costs and operating costs, and poor economy and rationality. And some heat exchanger optimization design methods proposed based on intelligent algorithms, such as CN201510066295.7, an optimized method for the core structure of a plate-fin heat exchanger based on dynamic pixel granularity, CN201210065122.X, an optimized design method for the fluid channel arrangement of a multi-stream plate-fin heat exchanger, etc., are difficult to be utilized especially in the initial design stage and under limited calculation conditions due to reasons such as cumbersome mathematical modeling procedures, large calculation tasks, and long time consumption.

[0004] Therefore, there is an urgent need to provide an optimization method under finite volume constraints for the design stage of plate heat exchangers to reduce the total thermal resistance in the heat exchanger, improve the heat exchange area configuration on the cold and hot sides of the plate heat exchanger and the heat exchange effect under volume constraint conditions, and improve the comprehensive performance of the heat exchanger. Summary of the Invention

[0005] Object of the Invention: The present invention provides an optimized quick calculation method for a plate heat exchanger under finite volume constraints, which optimizes the heat exchange area configuration on the cold and hot sides of the heat exchanger and reduces the total thermal resistance in the heat exchanger, so as to achieve the purpose of increasing the heat exchange capacity of the heat exchanger.

[0006] Technical Solution: The optimized quick calculation method for a plate heat exchanger under finite volume constraints described in the present invention includes the following steps:

[0007] (1) Input the volume constraint value of the plate heat exchanger and the heat transfer parameters of the hot and cold fluids, select the heat exchanger plate type, determine the compactness β, and define Calculate the total heat transfer area A of the plate heat exchanger. Assume the heat transfer area of the hot-side fluid is A1, then the heat transfer area of the cold-side fluid surface is A - A1; calculate the heat transfer coefficient of the cold-side fluid surface as α, and the heat transfer coefficient of the hot-side fluid surface is k times that of the cold-side fluid surface. Ignoring the heat conduction resistance of the metal partition wall surface, the total thermal resistance R of the heat exchanger is obtained through Equation (1):

[0008]

[0009] (2) Find the partial derivative of the total thermal resistance R of the heat exchanger with respect to the heat transfer area of the hot side, set the partial derivative equal to zero, obtain the extreme value of the total thermal resistance with respect to the heat transfer area of the hot side, and determine whether the obtained extreme value is a minimum value according to monotonicity: If the obtained extreme value is a minimum value, obtain the minimum total thermal resistance of the heat exchanger corresponding to the heat transfer area of the hot side; if the obtained extreme value is not a minimum value, reselect the heat exchanger plate type, determine the compactness, assume the heat transfer area A1 of the hot side, and recalculate the minimum total thermal resistance of the heat exchanger corresponding to the heat transfer area of the hot side according to Equation (1);

[0010] (3) According to the minimum total thermal resistance of the heat exchanger obtained in step (2), convert the proportion of the hot-side volume in the total volume, determine the number of hot and cold side plates, plate shape and size of the plate heat exchanger, and obtain the structure of the plate heat exchanger with the highest heat transfer efficiency.

[0011] In the present invention, the values of the heat transfer coefficient α of the cold-side fluid surface and the heat transfer coefficient kα of the hot-side fluid surface are obtained by calculating in combination with the performance correlation formula. As a specific embodiment of the present invention, the Dittus - Boelter performance correlation formula Nu = 0.023Re 0.8 Pr 0.4 is used, and combined with the heat transfer coefficient calculation formula to obtain the heat transfer coefficient α of the cold-side fluid surface. Similarly, the heat transfer coefficient kα of the hot-side fluid surface can be calculated. Among them, Re is the Reynolds number of the fluid, which can characterize the fluid flow state; Pr is the Prandtl number of the fluid; λ is the thermal conductivity of the fluid; d h is the hydraulic diameter of the flow channel.

[0012] The optimized quick calculation method of the plate heat exchanger under the finite volume constraint of the present invention assumes that the total heat transfer area per unit volume of the heat exchanger and the heat transfer coefficients on both the hot and cold sides remain unchanged, and other heat conduction resistances are ignored. First, substitute the given heat transfer area and heat transfer coefficient parameters of the heat exchanger into the formula to obtain the total thermal resistance, then differentiate the total thermal resistance with respect to the heat transfer area per unit of the hot side, and set the differential equal to zero to find the minimum value. It is determined by monotonicity that the obtained extreme value is a minimum value, that is, the minimum thermal resistance per unit area of the hot side, and finally the relationship between the heat transfer area and the heat transfer coefficient is obtained.

[0013] As a preferred embodiment of the present invention, in step (2), the partial derivative is calculated as follows: substituting the total heat resistance R of the heat exchanger obtained from Equation (1) into Equation (2) to calculate the partial derivative of the total heat resistance R of the heat exchanger with respect to the heat-side heat transfer area A1

[0014]

[0015] Let the obtained partial derivative obtain the extreme value of the total heat resistance R of the heat exchanger varying with the heat-side heat transfer area A1, as shown in Equation (3):

[0016]

[0017] According to the monotonicity determination, when is the minimum value, then the minimum total heat resistance R of the heat exchanger obtained from Equation (3) corresponding to A1

[0018] According to the obtained minimum total heat resistance R of the heat exchanger, in accordance with the layout method of stacking standard plates of the plate heat exchanger, the proportion of the heat-side volume V1 of the heat exchanger in the total volume V is equal to the calculated value of Equation (3) In this way, the number of cold and heat side plates, the shape and size of the plates of the plate heat exchanger can be determined to obtain the minimum total heat resistance of the heat exchanger

[0019] In the said step (1), the total heat transfer area per unit volume of the heat exchanger remains unchanged, and the heat-side fluid surface heat transfer area A1 is the only independent variable

[0020] In the partial derivative of the total heat resistance R with respect to the heat-side heat transfer area A1 obtain the relational expression between the heat transfer area and the heat transfer coefficient parameter When

[0021] When When The function the curve of is monotonically decreasing

[0022] When When The function the curve of is monotonically increasing, and it can be obtained that when is the minimum value, that is, corresponding to the heat-side fluid heat transfer area A1, the heat exchanger can obtain the minimum total heat resistance R, and the heat transfer capacity of the heat exchanger is greater under the same volume constraint

[0023] The design optimization method of the plate heat exchanger provided by the present invention, under the condition of changing parameters such as the given heat exchanger compactness, heat exchanger volume, and heat transfer coefficient, only needs to substitute the new heat transfer area A1 of the hot-side fluid into formula (1), and according to the method in step (2), to complete the configuration of the heat transfer areas of the hot and cold sides of the heat exchanger and obtain the minimum total thermal resistance R.

[0024] The optimization quick calculation method of the plate heat exchanger under the finite volume constraint provided by the present invention is applicable to plate-fin heat exchangers, plate heat exchangers, printed circuit board heat exchangers, etc. of the type of plate heat exchangers stacked with standard plates.

[0025] As a preferred embodiment of the present invention, the optimization method of the plate heat exchanger under the finite volume constraint of the present invention includes the following steps:

[0026] (1) For a plate heat exchanger stacked with conventional standard plates, according to the definition of the finite volume value V and the heat exchanger compactness β Calculate the total heat transfer area A of the plate heat exchanger. Assuming that the heat transfer area of the hot-side fluid is A1, then the heat transfer area of the cold-side fluid surface is A - A1; assuming that the heat transfer coefficients of the hot and cold-side fluid surfaces remain unchanged, combined with the performance correlation formula, estimate the heat transfer coefficients α of the hot and cold-side fluid surfaces, and the heat transfer coefficient of the hot-side fluid surface is k times that of the cold-side fluid surface;

[0027] (2) Ignoring the heat conduction thermal resistance of the metal partition wall surface, use formula (1) to calculate the total thermal resistance R of the heat exchanger;

[0028]

[0029] (3) Substitute the total thermal resistance R of the heat exchanger obtained in step (2) into formula (2), and calculate the partial derivative of the total thermal resistance R of the heat exchanger with respect to the heat transfer area A1 of the hot side

[0030]

[0031] (4) Let the partial derivative obtained in step (3) Obtain the extreme value of the total thermal resistance R of the heat exchanger changing with the heat transfer area A1 of the hot side, as shown in formula (3),

[0032]

[0033] According to the monotonicity determination, such as when is the minimum value, then the relational expression (3) is the minimum total thermal resistance R of the heat exchanger obtained corresponding to the independent variable heat transfer area A1 of the hot side.

[0034] (5) According to the conventional layout method of stacking standard plates of the plate heat exchanger, the proportion of the hot-side volume V1 of the heat exchanger in the total volume V is equal to the calculated value of the relational expression (3) In this way, the number, shape, and size of the hot and cold side plates of the plate heat exchanger can be determined.

[0035] Beneficial effects: (1) The optimization method proposed in the present invention overcomes the problems of traditional intelligent optimization algorithms, such as cumbersome mathematical modeling procedures, large computational tasks, and long calculation times. Given the compactness and heat transfer coefficients on the hot and cold sides of the plate heat exchanger, this optimization method only uses the heat transfer area on the hot side as the only design variable, with fewer variables and convenient calculations, significantly shortening the initial design process of the plate heat exchanger and enabling rapid calculation of the optimal design of the plate heat exchanger under finite volume constraints; (2) The optimization method proposed in the present invention does not follow the traditional design theory based on unequal areas on both sides of the fluid, simply increasing the heat transfer area of the side with a smaller heat transfer coefficient in equal proportion to improve the heat transfer effect. Instead, by optimizing the configuration of the heat transfer areas on the hot and cold sides and reducing the total thermal resistance, under the premise of maintaining the compactness requirements of the plate heat exchanger, a larger heat transfer capacity can be obtained within a limited volume, and the optimization rapid calculation method has good economy and rationality; (3) The present invention is applicable to many types of plate heat exchangers, such as plate-fin heat exchangers, plate heat exchangers, and printed circuit board heat exchangers formed by stacking standard plates, and is applicable to design conditions such as different ranges of heat exchanger compactness, volume, and heat transfer coefficients. Description of the Drawings

[0036] Figure 1 It is a flow schematic diagram of the optimization rapid calculation method of the plate heat exchanger under finite volume constraints of the present invention. Detailed Embodiments

[0037] The following provides a detailed description of an optimization rapid calculation method of a plate heat exchanger under finite volume constraints proposed by the present invention in combination with embodiments and drawings.

[0038] Embodiment 1: Figure 1 It is a flow schematic diagram of the optimization rapid calculation method of the plate heat exchanger under finite volume and constraints of the present invention. As Figure 1 shown, an optimization rapid calculation method of a plate heat exchanger under finite volume constraints proposed by the present invention includes the following steps:

[0039] (S1) For a plate heat exchanger formed by stacking conventional standard plates, according to the definition of the finite volume value V and the heat exchanger compactness β calculate the total heat transfer area A of the plate heat exchanger. Assume the heat transfer area of the hot side fluid is A1, then the surface heat transfer area of the cold side fluid is A - A1; assume that the surface heat transfer coefficients of the hot and cold side fluids remain unchanged, and by combining the Dittus - Boelter performance correlation formula, calculate the surface heat transfer coefficient α of the cold side fluid and the surface heat transfer coefficient kα of the hot side fluid; among them, the total heat transfer area A per unit volume of the heat exchanger remains unchanged, and the heat transfer area A1 of the hot side fluid is the only independent variable;

[0040] (S2) Neglect the heat conduction thermal resistance of the metal partition wall surface, and calculate the total heat resistance R of the heat exchanger using formula (1);

[0041]

[0042] (S3) Substitute the total heat resistance R of the heat exchanger obtained in step (S2) into formula (2) to calculate the partial derivative of the total heat resistance R of the heat exchanger with respect to the heat side heat transfer area A1

[0043]

[0044] (S4) Let the partial derivative obtained in step (S3) Obtain the extreme value of the total heat resistance R of the heat exchanger varying with the heat side heat transfer area A1, as shown in formula (3),

[0045]

[0046] According to the monotonicity determination, for example, when is the minimum value, then the relational expression (3) is the minimum total heat resistance R of the heat exchanger obtained corresponding to the independent variable heat side heat transfer area A1; when calculating the partial derivative of the total heat resistance R with respect to the heat side heat transfer area A1 to obtain the relational expression between the heat transfer area and the heat transfer coefficient parameter the monotonicity determination method is that when at this time, the function the curve of is monotonically decreasing; when at this time, the function the curve of is monotonically increasing, and it can be obtained that when is the minimum value, that is, corresponding to the heat side fluid heat transfer area A1, the heat exchanger can obtain the minimum total heat resistance, and the heat transfer capacity of the heat exchanger is larger under the same volume constraint;

[0047] (S5) According to the conventional layout method of stacking standard plates of the plate heat exchanger, the proportion of the heat side volume V1 of the heat exchanger in the total volume V is equal to the calculated value of formula (3) In this way, the number of hot and cold side plates, the shape and size of the plates of the plate heat exchanger can be determined.

[0048] Among them, A is the total heat transfer area per unit of the heat exchanger, A1 is the heat transfer area per unit volume of the heat side, k is the ratio between the heat transfer coefficient of the heat side fluid surface and the heat transfer coefficient of the cold side fluid surface, and α is the heat transfer coefficient of the cold side fluid surface.

[0049] When calculating the total heat resistance of the heat exchanger in step (S3), other heat conduction thermal resistances are not considered. Table 1 shows some calculation examples using the optimized quick calculation method proposed by the present invention.

[0050] Table 1 Partial calculation examples using the optimized fast calculation method proposed by the present invention

[0051]

[0052] When optimizing the heat transfer performance of a plate heat exchanger, due to the high requirements for compactness and volume, when using the traditional design theory based on unequal areas on both sides of the fluid, if the heat transfer coefficient on the hot side fluid surface is twice that of the cold side fluid surface, then the heat transfer area on the cold side is designed to be twice that of the hot side. At this time, the total thermal resistance is 3 / Aα; while when designing according to an optimization method for plate heat exchangers under finite volume constraints proposed by the present invention, with the heat transfer coefficient remaining unchanged, the heat transfer area on the hot side is designed to be 0.414 times that of the cold side. At this time, the total thermal resistance is 2.91 / Aα, and the total thermal resistance is smaller. By comparing the results obtained by the two methods, it can be seen that using the optimized fast calculation method proposed by the present invention can obtain a larger heat transfer amount under the same volume.

[0053] Application Example 1: For a plate-fin heat exchanger, both the hot and cold sides use a 95JC1402 type standard serrated finned tube bundle (fin height 9.5 mm, fin thickness 0.2 mm, fin pitch 1.4 mm), and its compactness is 1500 m 2 / m 3 , combined with the Dittus - Boelter performance correlation, the calculation results of the heat transfer parameters of the fluids on both the hot and cold sides are shown in Table 2.

[0054] Table 2 Heat transfer parameters of the fluids on the hot and cold sides of the plate - fin heat exchanger

[0055]

[0056] When using the traditional design theory based on unequal areas on both sides of the fluid, if the heat transfer coefficient on the hot side fluid surface is 0.1 times that of the cold side fluid surface, then the heat transfer area on the hot side is designed to be 10 times that of the cold side. At this time, the total thermal resistance is 22 / Aα; while when designing according to an optimization method for plate heat exchangers under finite volume constraints proposed by the present invention, when determining the extreme value as a minimum value according to monotonicity, the heat transfer area on the hot side is designed to be 3.17 times that of the cold side. At this time, the total thermal resistance is 17.32 / Aα, and the total thermal resistance is smaller. By comparing the results obtained by the two methods, it can be seen that using the optimized fast calculation method proposed by the present invention can obtain a larger heat transfer amount under the same volume.

[0057] Furthermore, when the volume of the designed heat exchanger is constrained within 0.2 m 3When, from the compactness, its total heat transfer area is 315.8 ㎡, it can be known from the above analysis that to minimize the total thermal resistance, the heat-side heat transfer area is 240 ㎡ and the cold-side heat transfer area is 75.8 ㎡. Then, combined with the heat exchanger volume constraint, the specific structural parameters of the heat exchanger as shown in Table 3 below can be obtained.

[0058] Table 3 Structural Parameters of the Plate-Fin Heat Exchanger

[0059]

[0060] Application Example 2: For a printed circuit board heat exchanger with a compactness of 2500 m 2 / m 3 , the heat transfer parameters of the fluids on both the hot and cold sides are calculated as shown in Table 4.

[0061] Table 4 Heat Transfer Parameters of Fluids on the Hot and Cold Sides of the Printed Circuit Board Heat Exchanger

[0062]

[0063] When using the traditional design theory based on unequal areas on both sides of the fluid, if the surface heat transfer coefficient of the hot-side fluid is 0.38 times that of the cold-side fluid, the hot-side heat transfer area is designed to be 2.63 times that of the cold-side heat transfer area. At this time, the total thermal resistance is 3.63 / Aα; while when designing according to an optimized quick calculation method for plate heat exchangers under finite volume constraints proposed by the present invention, when the extreme value is determined to be a minimum value according to monotonicity, the hot-side heat transfer area is designed to be 0.612 times that of the cold-side heat transfer area. At this time, the total thermal resistance is 2.63 / Aα, and the total thermal resistance is smaller. Comparing the results obtained by the two methods, it can be seen that using the optimized quick calculation method proposed by the present invention can obtain a larger heat transfer capacity under the same volume.

[0064] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should be regarded as the scope protected by the claims of the present invention.

Claims

1. An optimized quick calculation method for plate heat exchangers under finite volume constraints, characterized in that, The method includes the following steps: (1) Input the volume constraint value of the plate heat exchanger and the heat exchange condition parameters of the hot and cold fluids, select the type of heat exchanger plates, and determine the compactness of the plate heat exchanger Calculate the total heat transfer area A of the plate heat exchanger. Assume that the heat transfer area of the hot-side fluid is A1, then the heat transfer area of the cold-side fluid surface is A - A1; calculate the heat transfer coefficient of the cold-side fluid surface as α, and the heat transfer coefficient of the hot-side fluid surface is k times that of the cold-side fluid surface. Ignoring the heat conduction resistance of the metal partition wall surface, the total thermal resistance R of the heat exchanger is obtained through Equation (1): (2) Obtain the partial derivative of the total heat resistance R of the heat exchanger with respect to the heat-side heat transfer area, set the partial derivative equal to zero to obtain the extreme value of the total heat resistance with respect to the heat-side heat transfer area, and determine whether the obtained extreme value is a minimum value according to monotonicity: If the obtained extreme value is a minimum value, obtain the minimum total heat resistance of the heat exchanger corresponding to the heat-side heat transfer area; if the obtained extreme value is not a minimum value, reselect the heat exchanger plates, determine the compactness, assume the heat-side heat transfer area A1, and recalculate the minimum total heat resistance of the heat exchanger corresponding to the heat-side heat transfer area according to Equation (1); (3) According to the minimum total heat resistance of the heat exchanger obtained in step (2), convert the proportion of the heat-side volume in the total volume, determine the number, shape and size of the cold and heat-side plates of the plate heat exchanger, and obtain the structure of the plate heat exchanger with the highest heat transfer efficiency.

2. The optimized quick calculation method for a plate heat exchanger under finite volume constraints according to claim 1, wherein, In step (2), the partial derivative is calculated as follows: Substitute the total heat resistance R of the heat exchanger obtained from Equation (1) into Equation (2) to calculate the partial derivative of the total heat resistance R of the heat exchanger with respect to the heat-side heat transfer area A1 3. The optimized quick calculation method for plate heat exchangers under finite volume constraints according to claim 2, characterized in that, Let the obtained partial differential Obtain the extreme value of the total thermal resistance R of the heat exchanger varying with the heat-side heat transfer area A1, as shown in Equation (3): According to the monotonicity determination, when is the minimum value, the minimum total heat resistance R of the heat exchanger obtained by Equation (3) corresponding to A1.

4. The optimized quick calculation method for plate heat exchangers under finite volume constraints according to claim 3, characterized in that According to the obtained minimum total heat resistance R of the heat exchanger, in accordance with the layout method of stacking standard plates of the plate heat exchanger, the proportion of the hot-side volume V1 of the heat exchanger in the total volume V is equal to the calculated value of Equation (3). In this way, the number of hot and cold side plates, the shape and size of the plates of the plate heat exchanger can be determined, and the minimum total heat resistance of the heat exchanger can be obtained.

5. The optimized quick calculation method of the plate heat exchanger under the finite volume constraint according to claim 1, characterized in that, In step (1), the total heat transfer area per unit volume of the heat exchanger remains unchanged, and the heat-side fluid surface heat transfer area A1 is the only independent variable.

6. The optimized quick calculation method for plate heat exchangers under finite volume constraints according to claim 4, characterized in that The partial derivative of the total thermal resistance R with respect to the heat transfer area A1 on the hot side Obtain the relationship between the heat transfer area and the heat transfer coefficient parameter When, the monotonicity determination method is as follows: When , the curve of the function is monotonically decreasing; When , The curve of the function is monotonically increasing. It can be obtained that when is the minimum value, that is, corresponding to the heat-side fluid heat transfer area A1, the minimum total thermal resistance R that the heat exchanger can achieve, and the heat transfer capacity of the heat exchanger is greater under the same volume constraint.

Images