Calibration method for plate-fin heat exchanger considering axial heat transfer effect of baffles and fins

Abstract

A calibration method for a plate-fin heat exchanger that considers the axial heat conduction effect of baffles and fins comprises the following steps: firstly, parameters are given, then model simplification and initialization are performed, then physical property fitting is performed, then pressure field distribution is calculated, then temperature fields of the fins and baffles are calculated, then the fluid temperature field is calculated, then temperature residuals are judged, and the calculated results are used for the design of the plate-fin heat exchanger; the present invention considers the axial heat conduction effect in the baffles and fins of a counterflow plate-fin heat exchanger, is suitable for the precise calculation of low-temperature counterflow plate-fin heat exchangers with straight fins or small-porosity perforated fins in the channels, and reduces the cost and cycle of heat exchanger design.

Description

Technical Field

[0001] The present invention relates to the technical field of plate-fin heat exchangers, and in particular to a calibration method for plate-fin heat exchangers taking into account the axial heat conduction effects of partitions and fins. Background Art

[0002] Plate-fin heat exchanger is a highly efficient, compact and lightweight heat exchange equipment, which is widely used in air separation, petrochemical industry, synthetic ammonia, natural gas liquefaction and separation, air conditioning industry, aerospace, metallurgy and other fields.

[0003] In low-temperature systems (Kang Rui, Li Yanzhong, Yang Yujie, Wang Zhe, Si Biao, Zheng Jieyu. Influence of axial heat conduction on the heat transfer performance of plate-fin heat exchangers [J]. Journal of Xi'an Jiaotong University, 2017, 51(02): 140-148.), plate-fin heat exchangers have a large inlet and outlet temperature difference. In addition to heat transfer from the cold fluid to the cold fluid through the partition, heat is also transferred from the high-temperature end to the low-temperature end along the partition axis. This axial heat conduction phenomenon seriously restricts the heat transfer performance of the plate-fin heat exchanger. For straight fins or small-porosity perforated fins (which can also be approximately regarded as straight fins), the axial heat conduction effect along the fin axis cannot be ignored. Currently, the calculation programs for multi-stream plate-fin heat exchangers on the market often rarely consider this axial heat conduction effect, resulting in low calculation accuracy. However, the cooling capacity under low-temperature conditions is very valuable, so it is necessary to perform more accurate calculations. Summary of the Invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a calibration method for plate-fin heat exchangers that takes into account the axial heat conduction effect of baffles and fins. The method can calculate the overall temperature and pressure field distribution of a multi-stream plate-fin heat exchanger and take into account the axial heat conduction effect in the fins and baffles.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A calibration method for a plate-fin heat exchanger taking into account the axial heat transfer effect of baffles and fins comprises the following steps:

[0007] 1) Given parameters: Select a multi-stream plate-fin heat exchanger. If perforated fin channels are used, the parameters include fin height h i , wing span s i , wing thickness t i , porosity φ i If a straight fin channel is used, the parameters include fin height h i , wing span s i , wing thickness t i , where i is the number of each layer of fin channels, the inlet temperature, flow rate, inlet pressure of multiple fluids, and the arrangement code of multiple fluid channels;

[0008] 2) Model simplification and initialization: Assuming that the fluid in each layer is uniformly distributed along the z direction, the surface heat transfer area of ​​the fins and partitions is concentrated in the two-dimensional plane, n layers of fin channels and n+1 layers of partitions are set, and the fluid temperature node is set in the flow channel. The fluid temperature node T fl，i，k and T fl，i，k+1 The fluid unit defined, and the partition unit adjacent to the fluid unit are respectively represented by the temperature node T in the partition w，i，k and T w，i+1.k Characterized by concentrating all the fin heat transfer areas into a two-dimensional plane, the two-dimensional heat conduction equation of the fin is obtained:

[0009]

[0010] Where λ is the thermal conductivity of the partition, which is a fixed value or can be written as λ i，k This way of writing indicates that the thermal conductivity changes with the change of the qualitative temperature, and different fluid units take different fluid qualitative temperatures; A x is the heat conduction cross-sectional area of ​​the fin along the x-direction, which is equivalent to concentrating all the fins in the plane and then calculating the cross-sectional area along the x-direction; A y is the heat conduction cross-sectional area of ​​the fin along the y direction; S is the source term in the heat conduction equation, which represents the heat obtained by a certain fin unit from the fluid;

[0011] Assumptions introduced: a. Only the fluid, fins, and baffle solid domains are considered, and other incidental structures are ignored; b. Heat leakage losses in the heat exchanger are ignored; c. The heat exchanger is in steady state; d. Heat conduction in the fluid is ignored, and only convection is considered; e. The fluid is uniformly distributed in the fin channel;

[0012] The fluid temperature node in the fluid channel is initialized to the inlet temperature of the fluid channel in this layer, and the initial temperature of each partition unit is given as the average temperature of the adjacent fluid units. In the fins contained in each fluid unit, multiple temperature nodes are arranged along the fin height and initialized to the average value of the temperature nodes of the two adjacent partitions of the fluid unit.

[0013] 3) Physical property fitting: First, estimate the temperature and pressure range of each fluid, call the NIST database to fit the physical properties of each fluid, fit the relationship between density, temperature and pressure on the spline surface, and fit the relationship between other physical parameters such as specific heat, dynamic viscosity and thermal conductivity and temperature on the spline curve. The fitted spline surface and spline curve parameters are loaded into memory for future use;

[0014] 4) Calculation of pressure field distribution: The calculation formula for the pressure drop in each fluid unit is:

[0015]

[0016] The first term on the right side of this equation is the friction pressure drop, and the second term is the pressure drop caused by density change; where: G i is the mass flow rate of the fluid in each layer of fin channels, L is the length of the heat exchanger core along the flow direction, N is the number of fluid units arranged along the flow direction of the heat exchanger, D i is the equivalent diameter of the plate-fin heat exchanger, the subscript i is the layer number, f is the friction factor, and ρ is the density. The friction factor and density are calculated based on the qualitative pressure and qualitative temperature in the fluid unit. The fluid temperature node T fl，i，k and T fl，i，k+1 The temperature of the defined fluid unit, that is, the qualitative temperature of the fluid unit:

[0017]

[0018] Calculate the physical properties of the fluid unit and then calculate its Reynolds number Re:

[0019]

[0020] Where μ i，k is the dynamic viscosity;

[0021] Then the correlation formula is used to calculate the f factor;

[0022] The qualitative temperature is calculated based on the temperature field determined by the previous outer iteration round. The pressure drop in each fluid unit is calculated by formula (2), and then the distribution of the pressure field in all fluid channels is determined point by point starting from the inlet, which is equivalent to updating the pressure field once. At this time, the residual of the pressure field is judged, that is, the newly calculated pressure field is compared with the pressure field distribution calculated by the previous inner iteration step. If the convergence condition is not met, the pressure field is updated using formula (2). Otherwise, step 5) is entered. In the subsequent steps involving the calculation of physical properties, the latest pressure field distribution determined in step 4) is used as the qualitative pressure of each fluid unit.

[0023] 5) Calculation of fin and baffle temperature field:

[0024] Discretizing equation (1) yields the following equations for solving the fin temperature field distribution:

[0025]

[0026] Where: T P is a node in the selected fin, then the four points adjacent to this point are T S , T N , T W , T E; S is south, N is north, W is west, E is east; λ SP Represents the temperature node T S and T P For a uniform grid, the thermal conductivity on the interface is:

[0027]

[0028] λ in the formula P and λ S It is based on the node temperature value T P and T S It is determined that the thermal conductivity of the solid is only a function of temperature; W in Eq. (7) fin，i is the effective width of the fin in the i-th channel. The simplified model is to compress the fin to the plane along the z direction. W fin，i satisfy s i and t i is the fin pitch and fin thickness in the fin channel of the i-th layer; Δl in formula (7) x is the length of the divided fluid unit along the x direction, and Δh y is the length of the grid divided along the fin height direction; the last term on the left side of Equation (7) represents the heat transfer source term of the fin unit represented by point P in the fin solid domain, that is, the heat transfer between the fin unit surface and the fluid, A s，i is the secondary heat transfer area per unit length along the x direction, which is calculated as n fin，i is the number of nodes arranged along the wing height direction. If the number of nodes arranged along the wing height direction in each layer of fin channels is the same, the subscript i is removed and it is expressed as n fin , h c is the convective heat transfer coefficient;

[0029] A temperature node in the fin is measured by T i，ii，k To index, where the first subscript i is the layer number, the subscript (ii, k) is the number of the fin node in the i-th layer, and in the i-th layer, the value range of ii is (i-1)×n fin +1≤ii≤i×n fin ; Further refine formula (7) to obtain the calculated fin node temperature value T i，ii，k , the system of equations expressed in the form of influence coefficients:

[0030]

[0031] The calculation method of the influence coefficient is:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] A i，ii，k =A i，ii，k-1 +A i，ii，k+1 +A i，ii-1，k +A i，ii+1，k +A fl，i，k (10) λ in the formula i，ii，(k-)-k Represents the temperature node T in the fin i，ii，k-1 and T i，ii，k Thermal conductivity at the interface, λ i，(ii-1)-ii，k Represents the temperature node T in the fin i，ii-1，k and T i，ii，k The thermal conductivity coefficient on the interface, if a fixed thermal conductivity coefficient is taken, can be directly written as λ;

[0038] The calculation method shown in formula (10) can be used only when the influence coefficient in formula (9) is within the given range. If ii = (i-1) × n fin +1, the form of formula (9) is:

[0039]

[0040] Tw in formula (11) ，i，j is the node temperature in the partition, and its influence coefficient is expressed as:

[0041]

[0042] In the formula is the partition temperature node T w，i，k and fin temperature nodes Thermal conductivity at the interface;

[0043] If ii=i×n fin , then the form of formula (9) is:

[0044]

[0045] Where A w，i+1，k The expressions of the influence coefficients other than A are similar to those in (10), and A w，i+1，k The form is:

[0046]

[0047] is the partition temperature node T w，i+1，k and fin temperature nodes Thermal conductivity at the interface;

[0048] Only one layer of nodes is arranged in the partition, and the temperature node T in the partition w，i，k The partition unit represented by , exchanges heat with the adjacent partition units in front and behind, with the fin unit where the adjacent fin temperature node is located, and with the adjacent fluid unit. Based on this, the equation group for calculating the partition temperature node value is derived:

[0049]

[0050] The calculation method of the influence coefficient in formula (15) is:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] A sp，i，k =A sp，i，k-1 +A w，i，k+1 +A fin，i-1，k +A fin，i，k +A fl，i-1，k +A fl，i，k (16)

[0058] Where W is the width of the plate-fin heat exchanger, t sp is the thickness of the partition, A b，i is the primary heat transfer area per unit length of the plate-fin heat exchanger along the x direction, which is calculated by is the temperature node T of the partition in the fin channel of the i-1th layer of the plate-fin heat exchanger. w，i，k Node with fin temperature Thermal conductivity at the interface;

[0059] The expressions of the influence coefficients in equations (10) and (16) include the convective heat transfer coefficient h c，i，k and h c，i-1，k ,To calculate the convective heat transfer coefficient, it is necessary to first determine the j factor of the plate-fin heat exchanger according to the correlation formula;

[0060] When the j factor in the fluid unit is calculated, the convective heat transfer coefficient in the fluid unit is calculated:

[0061]

[0062] Where λ fl is the thermal conductivity of the fluid, Pr is the Prandtl number, μ is the dynamic viscosity, and the subscripts (i, k) represent the fluid temperature node T fl，i，k and T fl，i，k+1 The qualitative temperature of the fluid units characterized is derived from the temperature field determined in the previous outer iteration, and the qualitative pressure is derived from the pressure field updated in step 4).

[0063] Equations (9), (11), and (13) need to be solved simultaneously and iteratively to obtain the partition temperature field and the fin temperature field. The process of solving this simultaneous equation system is an inner iterative calculation process in the entire outer iterative round:

[0064]

[0065] Equations (9), (11), and (13) are reduced to the form of equation (20), where It is classified into item b, n0 is the identifier of the inner iteration round. In an inner iteration round, it scans from one side to the other. Each time it scans a line, all the temperature nodes on the line are solved simultaneously, as shown in equation group (20). The temperature node T E and T W The temperature value determined by the previous inner iteration step is used; after advancing column by column and scanning all fin temperature nodes and partition temperature nodes, an inner iteration step is completed, the fin and partition temperature fields are updated once, and the residual of the temperature field is calculated once:

[0066]

[0067] Formula (21) traverses each temperature node in the fin and partition temperature field, and ε is the allowed temperature residual. If this convergence condition is not met, the fin and partition temperature field is updated according to formula (20). Otherwise, go to step 6).

[0068] 6) Calculation of fluid temperature field: If the fluid in the fin channel flows along the +x direction, the heat transfer in the fluid unit satisfies the energy conservation condition:

[0069] c p，i，k+1 m i T fl，i，k+1 -c p，i，k m i T fl，i，k =Q sp，i，k +Q fin，i，k(twenty two)

[0070] c in the formula p，i，k+1 It is based on the nodal temperature T of the fluid fl，i，k+1 Determined specific heat capacity, m i is the flow rate of the fluid in the fin channel of the i-th layer, Q sp，i，k is the temperature node T of the fluid in the fin channel of the i-th layer fl，i，k and T fl，i，k+1 The heat that the defined fluid element receives from the adjacent partition, Q fin，i，k is the heat that the fluid unit obtains from the fins it surrounds; Q sp，i，k The calculation method is:

[0071]

[0072] Q fin，i，j The calculation method is:

[0073]

[0074] According to equations (22), (23), and (24), the equations for calculating the fluid temperature field distribution in each layer of fin channels are derived as follows:

[0075]

[0076] The calculation method of each influence coefficient in the formula is:

[0077] B w，i-1，k =A b，i h c，i，k Δl x

[0078] B w，i，k =A b，i h c，i，k Δl x

[0079]

[0080]

[0081]

[0082] If the fluid flows along the -x direction, the energy conservation equations of the fluid unit are in the form of:

[0083]

[0084] The equation group (27) is derived into a form similar to the equation group (25):

[0085]

[0086] The calculation method of each influence coefficient in the formula is:

[0087] B w，i-1，k =A b，i h c，i，k Δl x

[0088] B w，i，k =A b，i h c，i，k Δl x

[0089]

[0090]

[0091]

[0092] Equations (25) and (28) are solved point by point along the flow direction;

[0093] 7) Determination of temperature residuals: Compare the fluid temperature field calculated in step 6) with the fluid temperature field obtained in the previous outer iteration round to calculate the fluid temperature field residual. Compare the fin and baffle temperature fields calculated in step 5) with the fin and baffle temperature fields obtained in the previous outer iteration round to calculate the temperature residual of the fin and baffle solid domain. The larger of the two calculated temperature residuals is taken as the temperature residual of the outer iteration round. If the temperature residual of the outer iteration round meets the convergence condition, the calculation results are output, including the temperature field distribution of the fin, baffle and fluid, and the pressure field distribution of the fluid. If the temperature field residual does not meet the convergence condition, a new round of outer iteration is started from step 4).

[0094] 8) Use the calculated results in the design of plate-fin heat exchangers.

[0095] In step 4), the f factor is calculated for straight fins using the following correlation:

[0096]

[0097] For perforated fins, the f factor is calculated using the following correlation:

[0098] ln f i，k =28.78906-12.31399ln Re i，k +1.565191(ln Re i，t ) 2 -0.06736098(lnRe i，k ) 3 (6)

[0099] In step 5), for the perforated fin, the following correlation is used to calculate the j factor:

[0100] ln j i，k =34.57583-15.92678ln Re i，k +2.137607(ln Re i，k ) 2 -0.09544151×(lnRe i，k ) 3 (17)

[0101] For straight fins, the correlation is:

[0102]

[0103] Compared with the prior art, the present invention has the following beneficial effects:

[0104] 1. This invention is a calibration method for low-temperature multi-stream plate-fin heat exchangers. In addition to incorporating the axial heat conduction factor in the baffle, it also considers the axial heat conduction effect in straight fins or perforated fins, achieving high calculation accuracy and speed.

[0105] 2. The present invention is a general method that can be written into a general program. This method can be used to calculate any arrangement of multi-stream plate-fin heat exchangers. It can calculate the overall pressure distribution and temperature field distribution of the plate-fin heat exchanger, providing theoretical guidance for the design and verification of low-temperature multi-stream plate-fin heat exchangers, thereby reducing the cost and cycle of heat exchanger design. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 Schematic diagram of the three-dimensional structure and fin structure parameters of the plate-fin heat exchanger.

[0107] Figure 2 A simplified two-dimensional model of a plate-fin heat exchanger and a schematic diagram of the node arrangement in temperature (fluid, baffles, and fins).

[0108] Figure 3 Schematic diagram of a flow chart of an embodiment of the present invention.

[0109] Figure 4 This is a schematic diagram of the fluid temperature distribution along the flow direction (+x direction) in the three-layer fin channel calculated according to an embodiment of the present invention.

[0110] Figure 5 This is a schematic diagram of the distribution of outlet temperatures of each layer calculated according to an embodiment of the present invention.

[0111] Figure 6 The middle section (parallel to Figure 2Temperature distribution along the y direction on the yz plane. DETAILED DESCRIPTION

[0112] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0113] A calibration method for a plate-fin heat exchanger taking into account the axial heat transfer effect of baffles and fins comprises the following steps:

[0114] 1) Given parameters:

[0115] A three-stream plate-fin heat exchanger is selected, with high, medium and low pressure helium streams. Each stream uses the same perforated fin channel, with a fin height of h. i =4.0mm, wing pitch s i =1.4mm, pitch l i =3.0mm, wing thickness t i =0.2mm, porosity φ i = 0.05, where i is the channel number of each layer of fins. The inlet temperatures of the three fluids are 43.05K, 11K and 43.05K, the flow rates are 17g / s, 62g / s and 45g / s, and the inlet pressures are 1.219MPa, 0.144MPa and 0.650MPa, respectively. The three fluids are arranged in 6, 20 and 13 layers, respectively, for a total of 39 layers. The channel arrangement code is

[0116] BCBCBABCBCBABCBCBABCBCBABCBCBABCBCBABCBCB, where A, B, and C are the numbers of the fluids. Given that the channel arrangement of these three fluids is in the opposite direction ( Figure 1 -x direction), positive direction ( Figure 1 +x direction) and reverse direction ( Figure 1 -x direction), this type of plate-fin heat exchanger is often used in low-temperature helium liquefaction systems (Claude cycle);

[0117] 2) Model simplification and initialization:

[0118] Figure 1 This is a three-dimensional model of a plate-fin heat exchanger. Since the porosity is very small (0.05) and the pores are usually arranged irregularly in practice, it is not included in the model. Figure 1 Draw the holes in the middle. Assuming that the fluid in each layer is evenly distributed along the z direction, the surface heat transfer area of ​​the fins and partitions can be concentrated to the following: Figure 2 In the two-dimensional plane shown in the left figure, Figure 2 In the left figure, there are n layers of fin channels and n+1 layers of partitions. Only the fluid temperature nodes are drawn in the flow channel, for example Figure 2 The shaded area in the left figure is the fluid temperature node Tfl，i，k and T fl，i，k+1 The fluid unit defined, and the partition unit adjacent to the fluid unit are respectively represented by the temperature node T in the partition w，i，k and T w，i+1，k Represented by Figure 2 The figure on the right shows the arrangement of the temperature nodes for the solid domain of the fin contained in the fluid element. Figure 2 The dashed box in the right figure represents the fin unit represented by the fin temperature node. By concentrating all the fin heat transfer areas on a two-dimensional plane, the two-dimensional heat conduction equation of the fin is obtained:

[0119]

[0120] The λ in the formula is the thermal conductivity of the partition, which can be a fixed value or written as λ i，k This way of writing indicates that the thermal conductivity changes with the change of the qualitative temperature, and different fluid units take different fluid qualitative temperatures; A x is the heat conduction cross-sectional area of ​​the fin along the x-direction, which is equivalent to concentrating all the fins in the plane and then calculating the cross-sectional area along the x-direction; A y is the heat conduction cross-sectional area of ​​the fin along the y direction; S is the source term in the heat conduction equation, which represents the heat obtained by a certain fin unit from the fluid;

[0121] In addition, the following assumptions are introduced in the calculation: a. Only the solid domains of the fluid, fins, and baffles are considered, and other incidental structures are ignored; b. Heat leakage losses in the heat exchanger are ignored; c. The heat exchanger is in steady state; d. The heat conduction term in the fluid is ignored, and only the convection term is considered; e. The fluid is evenly distributed in the fin channel;

[0122] Figure 2 The fluid temperature node in the fluid channel shown in the left figure can be initialized to the inlet temperature of the fluid channel layer, and the initial temperature of each partition unit is given as the average temperature of the adjacent fluid units. In the fins contained in each fluid unit, multiple temperature nodes are arranged along the fin height, which can be initialized to the average value of the two adjacent partition temperature nodes of the fluid unit;

[0123] 3) Physical property fitting:

[0124] If the NIST database is continuously called to solve the physical properties in subsequent iterative calculations, the running time of the program will be greatly increased. Therefore, before officially entering the iterative calculation round, the temperature and pressure range of each fluid should be estimated first, and the physical properties of each fluid should be fitted by calling the NIST database. Generally speaking, the relationship between density, temperature and pressure is fitted on a spline surface, and the relationship between other physical parameters such as specific heat, dynamic viscosity and thermal conductivity and temperature is fitted on a spline curve. Before the iterative calculation, the fitted spline surface and spline curve parameters should be loaded into the memory for subsequent calculations to be called at any time.

[0125] 4) Calculation of pressure field distribution:

[0126] This step officially begins the first inner iteration calculation step of the outer iteration round. The calculation formula for the pressure drop in each fluid unit is:

[0127]

[0128] The first term on the right side of this equation is the friction pressure drop, and the second term is the pressure drop caused by density change; where: G i is the mass flow rate of the fluid in each layer of fin channels, L is the length of the heat exchanger core along the flow direction, N is the number of fluid units arranged along the flow direction of the heat exchanger, D i is the equivalent diameter of the plate-fin heat exchanger, the subscript i is the layer number, f is the friction factor, and ρ is the density. The friction factor and density are calculated based on the qualitative pressure and qualitative temperature in the fluid unit. The fluid temperature node T fl，i，k and T fl，i，k+1 The temperature of the defined fluid unit, that is, the qualitative temperature of the fluid unit:

[0129]

[0130] Once the qualitative temperature is determined, the physical properties of the fluid unit can be calculated, and then its Reynolds number Re can be calculated:

[0131]

[0132] Where μ is the dynamic viscosity;

[0133] Then, the f factor is calculated using the correlation formula. For straight fins, the f factor is calculated using the following correlation formula:

[0134]

[0135] For perforated fins, the f factor is calculated using the following correlation:

[0136] ln f i，k=28.78906-12.31399ln Re i，k +1.565191(ln Re i，k ) 2 -0.06736098(lnRe i，k ) 3 (6)

[0137] The qualitative temperature here is calculated based on the temperature field determined by the previous outer iteration round. The pressure drop in each fluid unit can be calculated by formula (2), and then the distribution of the pressure field in all fluid channels is determined point by point starting from the inlet, which is equivalent to updating the pressure field once. At this time, the residual of the pressure field is judged (the newly calculated pressure field is compared with the pressure field distribution calculated by the previous inner iteration step). If the convergence condition is not met, the pressure field is updated using formula (2). Otherwise, step 5) is entered. In the subsequent steps involving the calculation of physical properties, the latest pressure field distribution determined in step 4) is used as the qualitative pressure of each fluid unit.

[0138] 5) Calculation of fin and baffle temperature field:

[0139] Discretizing equation (1) yields the following equations for solving the fin temperature field distribution:

[0140]

[0141] Where: T P is a node in the selected fin, then the four points adjacent to this point are T S , T N , T W , T E (S is south, N is north, W is west, E is east); SP Represents the temperature node T S and T P For a uniform grid, the thermal conductivity on the interface is:

[0142]

[0143] λ in the formula P and λ S It is based on the node temperature value T P and T S Determined (assuming that the solid thermal conductivity is only a function of temperature); W in formula (7) fin，i is the effective width of the fin in the i-th channel. Since the simplified model here compresses the fin to a plane along the z direction, W fin，i satisfy si and t i is the fin pitch and fin thickness in the fin channel of the i-th layer; Δl in formula (7) x is the length of the divided fluid unit along the x direction ( Figure 2 As shown in the left figure), and Δh y is the length of the grid divided along the wing height direction ( Figure 2 As shown in the left figure), if the grid is evenly divided, then the distance between points P and E, or between points P and W is Δl x , the distance between P and S or P and N is Δh y The last term on the left side of formula (7) represents the heat transfer source term of the fin unit represented by point P in the fin solid domain, that is, the heat transfer between the surface of the fin unit and the fluid, A s，i is the secondary heat transfer area per unit length along the x direction, which is calculated as n fin，i is the number of nodes arranged along the wing height direction. If the number of nodes arranged along the wing height direction in each layer of fin channels is the same, the subscript i can be removed and expressed as n fin , h c is the convective heat transfer coefficient;

[0144] In order to facilitate the preparation of calculation programs, a temperature node in the fin is measured by T i，ii，k To index, where the first subscript i is the layer number, the subscript (ii, k) is the number of the fin node in the i-th layer, and in the i-th layer, the value range of ii is (i-1)×n fin +1≤ii≤i×n fin Further refinement of formula (7) can be used to calculate the fin node temperature value T i，ii，k , the system of equations expressed in the form of influence coefficients:

[0145]

[0146] A in the formula i，ii，k-1 , A i，ii，k+1 The calculation method of the equal influence coefficient is:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] A i，ii，k =A i，ii，k-1+A i，ii，k+1 +A i，ii-1，k +A i，ii+1，k +A fl，i，k (10)

[0153] λ in the formula i，ii，(k-1)-k Represents the temperature node T in the fin i，ii，k-1 and T i，ii，k Thermal conductivity at the interface, λ i，(ii-1)-ii，k Represents the temperature node T in the fin i，ii-1，k and T i，ii，k The thermal conductivity on the interface can be directly written as λ if a fixed thermal conductivity is taken;

[0154] The calculation method shown in formula (10) can be used only when the influence coefficient in formula (9) is within the given range. If ii = (i-1) × n fin +1, the form of formula (9) is:

[0155]

[0156] T in formula (11) w，i，j is the node temperature in the partition, and its influence coefficient is expressed as:

[0157]

[0158] In the formula is the partition temperature node T w，i，k and fin temperature nodes Thermal conductivity at the interface;

[0159] If ii=i×n fin , then the form of formula (9) is:

[0160]

[0161] Where A w，i+1，k The expressions of the influence coefficients other than A are similar to those in (10), and A w，i+1，k The form is:

[0162]

[0163] is the partition temperature node T w，i+1，k and fin temperature nodes Thermal conductivity at the interface;

[0164] Only one layer of nodes is arranged in the partition, and the temperature node T in the partition w，i，jThe partition unit represented by , exchanges heat with the adjacent partition units in front and behind, with the fin unit where the adjacent fin temperature node is located, and with the adjacent fluid unit. Based on this, the equation group for calculating the partition temperature node value can be derived:

[0165]

[0166] The calculation method of the influence coefficient in formula (15) is:

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] A sp，i，k =A sp，i，k-1 +A w，i，k+1 +A fin，i-1，k +A fin，i，k +A fl，i-1，k +A fl，i，k (16)

[0174] Where W is the width of the plate-fin heat exchanger, t sp is the thickness of the partition, A b，i is the primary heat transfer area per unit length of the plate-fin heat exchanger along the x direction, which is calculated by is the temperature node T of the partition in the fin channel of the i-1th layer of the plate-fin heat exchanger. w，i，k Node with fin temperature Thermal conductivity at the interface;

[0175] The expressions of the influence coefficients in equations (10) and (16) include the convective heat transfer coefficient h c，i，k and h c，i-1，k To calculate the convective heat transfer coefficient, it is necessary to first determine the j factor of the plate-fin heat exchanger according to the correlation formula. For perforated fins, the following correlation formula is used to calculate the j factor:

[0176] ln j i，k =34.57583-15.92678ln Re i，k +2.137607(ln Re i，k ) 2 -0.09544151×(lnRei，k ) 3 (17)

[0177] For straight fins, the correlation is:

[0178]

[0179] Once the j factor in the fluid unit is calculated, the convective heat transfer coefficient in the fluid unit can be calculated:

[0180]

[0181] Where λ fl is the thermal conductivity of the fluid, Pr is the Prandtl number, μ is the dynamic viscosity, and the subscripts (i, k) here represent the fluid temperature node T fl，i，k and T fl，i，k+1 The qualitative temperature of the fluid units characterized is derived from the temperature field determined in the previous outer iteration, and the qualitative pressure is derived from the pressure field updated in step 4).

[0182] Equations (9), (11), and (13) need to be solved simultaneously and iteratively to obtain the partition temperature field and the fin temperature field. The process of solving this simultaneous equation system is an inner iterative calculation process in the entire outer iterative round:

[0183]

[0184] Equations (9), (11), and (13) can all be summarized as equations (20), where It is classified into item b, n0 is the identifier of the inner iteration round. In an inner iteration round, it scans from east (E) to west (W). Each time it scans a line, all the temperature nodes on the line are solved simultaneously, as shown in equation group (20). The temperature node T E and T W The temperature value determined by the previous inner iteration step is used; in this way, the process advances from east to west, and after scanning all the fin temperature nodes and the partition temperature nodes, an inner iteration step is completed, the fin and partition temperature fields are updated once, and the residual of the temperature field can be calculated once:

[0185]

[0186] Formula (21) traverses each temperature node in the fin and partition temperature field, and ε is the allowed temperature residual. If this convergence condition is not met, the fin and partition temperature field is updated according to formula (20). Otherwise, go to step 6).

[0187] 6) Calculation of fluid temperature field:

[0188] If the fluid in the fin channel flows along the +x direction, the heat transfer in the fluid unit satisfies the energy conservation condition:

[0189] c p，i，k+1 m i T fl，i，k+1 -c p，i，k m i T tl，i，k =Q sp，i，k +Q fin，i，k (twenty two)

[0190] c in the formula p，i，k+1 It is based on the nodal temperature T of the fluid fl，i，k+1 Determined specific heat capacity, m i is the flow rate of the fluid in the fin channel of the i-th layer, Q sp，i，k is the temperature node T of the fluid in the fin channel of the i-th layer fl，i，k and T fl，i，k+1 The heat (positive or negative) obtained by the defined fluid unit from the adjacent partition, Q fin，i，k is the heat that the fluid unit obtains from the fins it surrounds; Q sp，i，k The calculation method is:

[0191]

[0192] Q fin，i，j The calculation method is:

[0193]

[0194] According to equations (22), (23), and (24), the equations for calculating the fluid temperature field distribution in each layer of fin channels are derived as follows:

[0195]

[0196] The calculation method of each influence coefficient in the formula is:

[0197] B w，i-1，k =A b，i h c，i，k Δl x

[0198] B w，i，k =A b，i h c，i，k Δl x

[0199]

[0200]

[0201]

[0202] If the fluid flows along the -x direction, the energy conservation equations of the fluid unit are in the form of:

[0203] c p，i，k m i T fl，i，k -c p，i，k+1 m i T fl，i，k+1 =Q sp，i，k +Q fin，i，k (27)

[0204] The equation group (27) is derived into a form similar to the equation group (25):

[0205]

[0206] The calculation method of each influence coefficient in the formula is:

[0207] B w，i-1，k =A b，i h c，i，k Δl x

[0208] B w，i，k =A b，i h c，i，k Δl x

[0209]

[0210]

[0211]

[0212] Equation groups (25) and (28) can be solved point by point along the flow direction. It is necessary to distinguish the difference in the influence coefficients of the two equation groups;

[0213] 7) Determination of temperature residual:

[0214] Compare the fluid temperature field calculated in step 6) with the fluid temperature field obtained in the previous outer iteration round to calculate the fluid temperature field residual. Compare the fin and baffle temperature fields calculated in step 5) with the fin and baffle temperature fields obtained in the previous outer iteration round to calculate the temperature residual of the fin and baffle solid domain. The larger of the two calculated temperature residuals is taken as the temperature residual of the outer iteration round. If the temperature residual of the outer iteration round meets the convergence condition, the calculation results are output, including the temperature field distribution of the fin, baffle and fluid, and the pressure field distribution of the fluid. If the temperature field residual does not meet the convergence condition, a new round of outer iteration is started from step 4).

[0215] 8) Use the calculated results in the design of plate-fin heat exchangers.

[0216] The above steps 4) to 7) are a complete outer iteration round. Step 4) is the inner iteration calculation process used to calculate the fluid pressure field distribution in the outer iteration round. Step 5) is the inner iteration calculation process used to calculate the partition and fin temperature field distribution. Step 6) uses the step calculation method to update the fluid temperature node point by point along the flow direction. The entire method flow is as follows: Figure 3 shown. Figures 4 to 6 is the calculation result of this embodiment, Figure 4 The temperature distribution of the fluid in the 6th, 7th and 8th fluid channels of the plate-fin heat exchanger along the flow direction (+x direction) is extracted. Figure 5 is the outlet temperature distribution of each layer of the fin channel of the plate-fin heat exchanger, and the horizontal axis is the layer number. Figure 6 It is the middle section of the plate-fin heat exchanger (parallel to Figure 2 The temperature distribution along the y direction on the middle yz plane) is analyzed. Since the three-dimensional model of the entire heat exchanger is shrunk to the xy plane for research, the middle section of the heat exchanger parallel to the yz plane is shrunk to a straight line parallel to the y axis. The fluid temperature, partition temperature and fin temperature distribution of each layer can be read on the middle section.

Claims

1. A calibration method for a plate-fin heat exchanger taking into account the axial heat conduction effect of baffles and fins, characterized in that: The following steps are involved: 1) Given parameters: Select a multi-stream plate-fin heat exchanger. If perforated fin channels are used, the parameters include fin height h i , wing span s i , wing thickness t i , porosity φ i If a straight fin channel is used, the parameters include fin height h i , wing span s i , wing thickness t i , where i is the number of each layer of fin channels, the inlet temperature, flow rate, inlet pressure of multiple fluids, and the arrangement code of multiple fluid channels; 2) Model simplification and initialization: Assuming that the fluid in each layer is uniformly distributed along the z direction, the surface heat transfer area of ​​the fins and partitions is concentrated in the two-dimensional plane, and n layers of fin channels and n+1 layers of partitions are set. Only the fluid temperature nodes are drawn in the flow channel. The fluid temperature nodes T fl,i,k and T fl,i,k+1 The fluid unit defined, and the partition unit adjacent to the fluid unit are respectively represented by the temperature node T in the partition w,i,k and T w,i+1,k Characterized by concentrating all the fin heat transfer areas into a two-dimensional plane, the two-dimensional heat conduction equation of the fin is obtained: Where λ is the thermal conductivity of the partition, which is a fixed value or can be written as λ i,k This way of writing indicates that the thermal conductivity changes with the change of the qualitative temperature, and different fluid units take different fluid qualitative temperatures; A x is the heat conduction cross-sectional area of ​​the fin along the x-direction, which is equivalent to concentrating all the fins in the plane and then calculating the cross-sectional area along the x-direction; A y is the heat conduction cross-sectional area of ​​the fin along the y direction; S is the source term in the heat conduction equation, which represents the heat obtained by a certain fin unit from the fluid; Assumptions introduced: a. Only the fluid, fins, and baffle solid domains are considered, and other incidental structures are ignored; b. Heat leakage losses in the heat exchanger are ignored; c. The heat exchanger is in steady state; d. Heat conduction in the fluid is ignored, and only convection is considered; e. The fluid is uniformly distributed in the fin channel; The fluid temperature node in the fluid channel is initialized to the inlet temperature of the fluid channel in this layer, and the initial temperature of each partition unit is given as the average temperature of the adjacent fluid units. In the fins contained in each fluid unit, multiple temperature nodes are arranged along the fin height and initialized to the average value of the temperature nodes of the two adjacent partitions of the fluid unit. 3) Physical property fitting: First, estimate the temperature and pressure range of each fluid, call the NIST database to fit the physical properties of each fluid, fit the relationship between density, temperature and pressure on the spline surface, and fit the relationship between other physical parameters such as specific heat, dynamic viscosity and thermal conductivity and temperature on the spline curve. The fitted spline surface and spline curve parameters are loaded into memory for future use; 4) Calculation of pressure field distribution: The calculation formula for the pressure drop in each fluid unit is: The first term on the right side of this equation is the friction pressure drop, and the second term is the pressure drop caused by density change; where: G i is the mass flow rate of the fluid in each layer of fin channels, L is the length of the heat exchanger core along the flow direction, N is the number of fluid units arranged along the flow direction of the heat exchanger, D i is the equivalent diameter of the plate-fin heat exchanger, the subscript i is the layer number, f is the friction factor, and ρ is the density. The friction factor and density are calculated based on the qualitative pressure and qualitative temperature in the fluid unit. The fluid temperature node T fl,i,k and T fl,i,k+1 The temperature of the defined fluid unit, that is, the qualitative temperature of the fluid unit: Calculate the physical properties of the fluid unit and then calculate its Reynolds number Re: Where μ i,k is the dynamic viscosity; Then the correlation formula is used to calculate the f factor; The qualitative temperature is calculated based on the temperature field determined by the previous outer iteration round. The pressure drop in each fluid unit is calculated by formula (2), and then the distribution of the pressure field in all fluid channels is determined point by point starting from the inlet, which is equivalent to updating the pressure field once. At this time, the residual of the pressure field is judged, that is, the newly calculated pressure field is compared with the pressure field distribution calculated by the previous inner iteration step. If the convergence condition is not met, the pressure field is updated using formula (2). Otherwise, step 5 is entered. In the subsequent steps involving the calculation of physical properties, the latest pressure field distribution determined in step 4) is used as the qualitative pressure of each fluid unit. 5) Calculation of fin and baffle temperature field: Discretizing equation (1) yields the following equations for solving the fin temperature field distribution: Where: T P is a node in the selected fin, then the four points adjacent to this point are T S ,T N ,T W ,T E ; S is south, N is north, W is west, E is east; λ SP Represents the temperature node T S and T P For a uniform grid, the thermal conductivity on the interface is: λ in the formula P and λ S It is based on the node temperature value T P and T S It is determined that the thermal conductivity of the solid is only a function of temperature; W in Eq. (7) fin,i is the effective width of the fin in the i-th channel. The simplified model is to compress the fin to the plane along the z direction. W fin,i satisfy s i and t i is the fin pitch and fin thickness in the fin channel of the i-th layer; Δl in formula (7) x is the length of the divided fluid unit along the x direction, and Δh y is the length of the grid divided along the fin height direction; the last term on the left side of Equation (7) represents the heat transfer source term of the fin unit represented by point P in the fin solid domain, that is, the heat transfer between the fin unit surface and the fluid, A s,i is the secondary heat transfer area per unit length along the x direction, which is calculated as n fin,i is the number of nodes arranged along the wing height direction. If the number of nodes arranged along the wing height direction in each layer of fin channels is the same, the subscript i can be removed and expressed as n fin , h c is the convective heat transfer coefficient; A temperature node in the fin is measured by T i,ii,k To index, where the first subscript i is the layer number, the subscript (ii, k) is the number of the fin node in the i-th layer, and in the i-th layer, the value range of ii is (i-1)×n fin +1≤ii≤i×n fin ; Further refine formula (7) to obtain the calculated fin node temperature value T i,ii,k , the system of equations expressed in the form of influence coefficients: (i-1)×n fin +1<ii <i×n fin ,1≤k≤N The calculation method of the influence coefficient is: A i,ii,k =A i,ii,k-1 +A i,ii,k+1 +A i,ii-1,k +A i,ii+1,k +A fl,i,k λ in formula (10) i,ii,(k-1)-k Represents the temperature node T in the fin i,ii,k-1 and T i,ii,k Thermal conductivity at the interface, λ i,(ii-1)-ii,k Represents the temperature node T in the fin i,ii-1,k and T i,ii,k The thermal conductivity coefficient on the interface, if a fixed thermal conductivity coefficient is taken, can be directly written as λ; The calculation method shown in formula (10) can be used only when the influence coefficient in formula (9) is within the given range. If ii = (i-1) × n fin +1, the form of formula (9) is: ii=(i-1)×n fin +1.1≤k≤N T in formula (11) w,i,k is the node temperature in the partition, and its influence coefficient is expressed as: In the formula is the partition temperature node T w,i,k and fin temperature nodes Thermal conductivity at the interface; If ii=i×n fin , then the form of formula (9) is: ii=i×n fin ,1≤k≤N Where A w,i+1,k The expressions of the influence coefficients other than A are similar to those in (10), and A w,i+1,k The form is: is the partition temperature node T w,i+1,k and fin temperature nodes Thermal conductivity at the interface; Only one layer of nodes is arranged in the partition, and the temperature node T in the partition w,i,k The partition unit represented by , exchanges heat with the adjacent partition units in front and behind, with the fin unit where the adjacent fin temperature node is located, and with the adjacent fluid unit. Based on this, the equation group for calculating the partition temperature node value is derived: The calculation method of the influence coefficient in formula (15) is: A sp,i,k =A sp,i,k-1 +A w,i,k+1 +A fin,i-1,k +A fin,i,k +A fl,i-1,k +A fl,i,k Where W is the width of the plate-fin heat exchanger, t sp is the thickness of the partition, A b,i is the primary heat transfer area per unit length of the plate-fin heat exchanger along the x direction, which is calculated by is the temperature node T of the partition in the fin channel of the i-1th layer of the plate-fin heat exchanger. w,i,k Node with fin temperature Thermal conductivity at the interface; The expressions of the influence coefficients in equations (10) and (16) include the convective heat transfer coefficient h c,i,k and h c,i-1,k ,To calculate the convective heat transfer coefficient, it is necessary to first determine the j factor of the plate-fin heat exchanger according to the correlation formula; When the j factor in the fluid unit is calculated, the convective heat transfer coefficient in the fluid unit is calculated: Where λ fl is the thermal conductivity of the fluid, Pr is the Prandtl number, μ is the dynamic viscosity, and the subscripts (i, k) represent the fluid temperature node T fl,i,k and T fl,i,k+1 The qualitative temperature of the fluid units characterized is derived from the temperature field determined in the previous outer iteration, and the qualitative pressure is derived from the pressure field updated in step 4). Equations (9), (11), and (13) need to be solved simultaneously and iteratively to obtain the partition temperature field and the fin temperature field. The process of solving this set of simultaneous equations is an inner iterative calculation process in the entire outer iterative round: Equations (9), (11), and (13) are reduced to the form of equation (20), where It is classified into item b, n0 is the identifier of the inner iteration round. In an inner iteration round, it scans from one side to the other. Each time it scans a line, all the temperature nodes on the line are solved simultaneously, as shown in equation group (20). The temperature node T E and T W The temperature value determined by the previous inner iteration step is used; after advancing column by column and scanning all fin temperature nodes and partition temperature nodes, an inner iteration step is completed, the fin and partition temperature fields are updated once, and the residual of the temperature field is calculated once: Formula (21) traverses each temperature node in the fin and partition temperature field, and ε is the allowed temperature residual. If this convergence condition is not met, the fin and partition temperature field is updated according to formula (20). Otherwise, go to step 6). 6) Calculation of fluid temperature field: If the fluid in the fin channel flows along the +x direction, the heat transfer in the fluid unit satisfies the energy conservation condition: c p,i,k+1 m i T fl,i,k+1 -c p,i,k m i T fl,i,k =Q sp,i,k +Q fin,i,k (22) c in the formula p,i,k+1 It is based on the nodal temperature T of the fluid fl,i,k+1 Determined specific heat capacity, m i is the flow rate of the fluid in the fin channel of the i-th layer, Q sp,i,k is the temperature node T of the fluid in the fin channel of the i-th layer fl,i,k and T fl,i,k+1 The heat that the defined fluid element receives from the adjacent partition, Q fin,i,k is the heat that the fluid unit obtains from the fins it surrounds; Q sp,i,k The calculation method is: Q fin,i,k The calculation method is: According to equations (22), (23), and (24), the equations for calculating the fluid temperature field distribution in each layer of fin channels are derived as follows: B fl,i,k+1 T fl,i.k+1 =B w,i-1,k T w,i-1,k +B w,i,k T w,i,k +B fl,i,k T fl,i,k +S fin,i,k (25) 1≤i≤n,1≤k≤N The calculation method of each influence coefficient in the formula is: B w,i-1,k =A b,i h c,i,k Δl x B w,i,k =A b,i h c,i,k Δl x If the fluid flows along the -x direction, the energy conservation equations of the fluid unit are in the form of: c p,i,k m i T fl,i,k -c p,i,k+1 m i T fl,i,k+1 =Q sp,i,k +Q fin,i,k (27) The equation group (27) is derived into a form similar to the equation group (25): B fl,i,k T fl,i,k =B w,i-1,k T w,i-1,k +B w,i,k T w,i,k +B fl,i,k+1 T fl,i,k+1 +S fin,i,k (28) 1≤i≤n,1≤k≤N The calculation method of each influence coefficient in the formula is: B w,i-1,k =A b,i h c,i,k Δl x B w,i,k =A b,i h c,i,k Δl x The equations (25) and (28) are solved point by point along the flow direction; 7) Determination of temperature residuals: Compare the fluid temperature field calculated in step 6) with the fluid temperature field obtained in the previous outer iteration round to calculate the fluid temperature field residual. Compare the fin and baffle temperature fields calculated in step 5) with the fin and baffle temperature fields obtained in the previous outer iteration round to calculate the temperature residual of the fin and baffle solid domain. The larger of the two calculated temperature residuals is taken as the temperature residual of the outer iteration round. If the temperature residual of the outer iteration round meets the convergence condition, the calculation results are output, including the temperature field distribution of the fin, baffle and fluid, and the pressure field distribution of the fluid. If the temperature field residual does not meet the convergence condition, a new round of outer iteration is started from step 4). 8) Use the calculated results in the design of plate-fin heat exchangers.

2. The method according to claim 1, wherein: In step 4), the f factor is calculated for straight fins using the following correlation: For perforated fins, the f factor is calculated using the following correlation: lnf i,k =28.78906-12.31399lnRe i,k +1.565191(lnRe i,k ) 2 -0.06736098(lnRe i,k ) 3 (6)。 3. The method according to claim 1, wherein: In step 5), for the perforated fin, the following correlation is used to calculate the j factor: lnj i,k =34.57583-15.92678lnRe i,k +2.137607(lnRe i,k ) 2 -0.09544151×(lnRe i,k ) 3 (17) For straight fins, the correlation is:

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