Fast calculation method for heat transfer characteristics of compact tube heat exchange structure

Abstract

The present invention discloses a rapid calculation and analysis method for the heat transfer characteristics of a compact tube heat exchanger. The steps are as follows: Step 1, based on the basic theory of convective heat transfer and the geometric characteristics of the compact tube heat exchange structure, establish a mathematical model for the heat transfer coefficient on the shell side of the heat exchange structure; Step 2, based on the basic theory of convective heat transfer, establish a mathematical model for the heat transfer coefficient on the tube side of the heat exchange structure; Step 3, based on the porous medium theory and the volume average assumption, establish a quasi-three-dimensional mathematical model for the steady-state convective heat transfer of the compact tube heat exchange structure; Step 4, calculate and solve the temperature field based on the mathematical models established in the above steps. The present invention can rapidly calculate and analyze the heat transfer characteristics of the compact tube heat exchange structure under different spatial arrangements and geometric parameter conditions, especially can obtain the temperature field distribution of the cold and hot fluid media of the heat exchange structure, and at the same time can predict the influencing factors affecting the heat transfer characteristics and their influencing rules.

Description

Technical Field

[0001] The present invention relates to a rapid calculation and analysis method for the heat transfer characteristics of a compact tube heat exchanger. In particular, based on the structural characteristics of a large number of staggered micro-channels in the compact tube heat exchanger, a mathematical model, calculation method and process for efficiently and rapidly calculating its quasi-three-dimensional steady-state heat transfer characteristics are established to reasonably and efficiently obtain and analyze the detailed heat transfer characteristics of the heat exchanger. Background Art

[0002] In recent years, with the rapid development of science and technology and the rise of emerging disciplines, new and higher requirements have been put forward for heat exchangers. Since the 1930s, compact heat exchangers have developed rapidly in industrial fields such as petrochemical, thermal power, and aerospace. With the continuous improvement of the theory of enhanced heat transfer and the continuous improvement of the level of mechanical manufacturing technology, many new and efficient compact heat exchangers have emerged. They usually have a small hydraulic diameter and a high specific surface area (the ratio of heat transfer area to volume) on the heat transfer surface, exceeding 700 m2 / m3 on the gaseous fluid side. By reasonably designing the heat transfer surface and flow pattern, etc., the heat transfer process can be further enhanced, thereby continuously improving the heat transfer effect. The current technological development trends of compact heat exchangers include: continuously increasing the heat transfer area per unit volume, the application of new materials with high pressure, high temperature and corrosion resistance, the research on the heat transfer mechanism of micro-scale flow, and the research and application of new design methods based on CFD (Computational Fluid Dynamics) simulation technology, etc.

[0003] However, due to the inherent characteristic of the compact tube heat exchanger, namely a large number of staggered micro-channels, it is very difficult to conduct solid three-dimensional modeling, simulation analysis and evaluation on the three-dimensional flow and heat transfer process in this kind of compact tube heat exchanger, and the calculation cost is huge. Therefore, it is necessary to explore an efficient three-dimensional calculation and analysis method for the heat transfer characteristics of the compact tube heat exchanger. Establishing a set of quasi-three-dimensional mathematical models and evaluation methods that can be efficiently and rapidly calculated for the flow and heat transfer process in the compact tube heat exchanger to reasonably and efficiently obtain and analyze the heat transfer performance of the heat exchanger will provide a scientific basis and theoretical support for the development and improvement of the design theory and technology of compact tube heat exchangers in modern multi-fields. Summary of the Invention

[0004] The object of the present invention is to provide a theoretical prediction method for the heat transfer characteristics of a compact tube heat exchange structure to reasonably and efficiently obtain and analyze the heat transfer performance of the heat exchanger.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A rapid calculation method for the heat transfer characteristics of a compact tube heat exchanger, comprising the following steps:

[0007] Step 1: Based on the basic theory of convective heat transfer and the geometric characteristics of the compact tube heat exchanger structure, establish a mathematical model for the shell-side heat transfer coefficient of the heat exchanger structure;

[0008] Step 2: Based on the basic theory of convective heat transfer, establish a mathematical model for the tube-side heat transfer coefficient of the heat exchanger structure;

[0009] Step 3: Based on the porous medium theory and the volume-averaging hypothesis, establish a quasi-three-dimensional mathematical model for the steady-state convective heat transfer of the compact tube heat exchanger structure;

[0010] Step 4: Calculate and solve the temperature field based on the mathematical models established in the above Steps 1 to 3.

[0011] The specific steps of Step 1 are as follows:

[0012] Step 11: The shell-side qualitative temperature is taken as the average temperature of the shell-side fluid entering and leaving the tube bundle:

[0013]

[0014] where t′1 is the temperature of the hot fluid at the inlet, t″1 is the temperature of the hot fluid at the outlet, the subscript m represents average, and the subscript 1 represents the variable on the shell side;

[0015] Step 12: The shell-side fluid Reynolds number is described as:

[0016]

[0017] The flow velocity at the minimum cross-section of the tube bundle is described as:

[0018]

[0019] Here, the subscript o represents the shell side, d o is the outer diameter of the heat exchange tube, u o is the flow velocity of the hot fluid, S1 and S2 are the transverse pitch and longitudinal pitch of the staggered tube bundle respectively, ν o is the kinematic viscosity of the fluid at the shell-side qualitative temperature;

[0020] Step 13: For the heat transfer of the fluid flowing across the staggered tube bundle, select the calculation relation of the Nusselt number:

[0021]

[0022]

[0023]

[0024]

[0025] where Pr fois the Prandtl number of the shell-side fluid, Pr wo is the Prandtl number of the fluid in the near-wall region on the shell side;

[0026] Step 14. Based on the basic theory of convective heat transfer, the shell-side heat transfer coefficient is:

[0027]

[0028] where, λ o is the thermal conductivity of the shell-side fluid at the shell-side reference temperature, d o is the outer diameter of the heat exchange tube, Nu o is the Nusselt number on the shell side at the reference temperature;

[0029] Based on the shell-side heat transfer coefficient, the tube wall temperature t w = t m1 - q / h o , where q is the heat flux density.

[0030] The specific steps of the said Step 2 include the following steps:

[0031] Step 21. The tube-side reference temperature is taken as the average temperature of the inlet and outlet of the tube-side fluid:

[0032]

[0033] where, t′2 and t″2 are the inlet and outlet temperatures of the fluid inside the tube respectively;

[0034] Step 22. The Reynolds number of the tube-side fluid is described as:

[0035]

[0036] where, the subscript i represents the tube side, d i is the inner diameter of the heat exchange tube, ν i is the kinematic viscosity of the fluid inside the tube at the tube-side reference temperature, u i is the flow velocity of the fluid inside the tube;

[0037] Step 23. For the heat transfer of laminar flow on the tube side, select the experimental correlation formula proposed by Sieder and Tate:

[0038]

[0039] For the turbulent heat transfer inside the tube, refer to the Gnielinski formula to obtain the Nusselt number relationship:

[0040]

[0041] where, Pr i is the Prandtl number of the tube-side fluid, d i and l are the tube diameter and tube length respectively, f iis the Darcy friction factor for turbulent flow inside the tube:

[0042] f i =(1.81 lg Re i -1.5) -2 (9)

[0043] Step 24. Based on the basic theory of convective heat transfer, the heat transfer coefficient on the tube side of the heat exchange structure is described as

[0044]

[0045] λ i is the thermal conductivity of the fluid inside the tube at the qualitative temperature on the tube side, d i is the inner diameter of the heat exchange tube, Nu i is the Nusselt number at the qualitative temperature.

[0046] The specific steps of Step 3 are as follows:

[0047] Step 31. Establish an equivalent staggered microchannel structure. The flow direction of Gas 1 is parallel to x1, and the flow direction of Gas 2 is parallel to x2. Gas 1 and Gas 2 exchange heat with adjacent channels simultaneously through the microchannels. Since the actual wall thickness of the tube is relatively thin, the wall thermal resistance is ignored, and when forced convective heat transfer is the main heat transfer process, the thermal diffusion term is ignored. The temperature control equation in the microstructure is established by applying the volume averaging method as:

[0048]

[0049]

[0050] In the formula, ρ and C p are the density and specific heat capacity at constant pressure of the fluid respectively, u is the average velocity in the flow channel, h fs is the convective heat transfer coefficient, A fs and ε are the area ratio and porosity of the porous medium model respectively, T is the fluid temperature, and the subscripts 1 and 2 represent Fluid 1 and Fluid 2 respectively;

[0051] Step 32. Integrate Equations (11a) and (11b) in Step 31 to obtain the integral equations as

[0052] ε1ρ1C p1 u1T1 + h fs1 A fs (T1 - T2)x1 = C1 (12a)

[0053] (1 - ε1)ρ2C p2 u2T2 - h fs2 A fs (T1 - T2)x2 = C2 (12b)

[0054] Step 33: Substitute the boundary conditions x1 = 0, T1 = T 10 and x2 = 0, T2 = T 20 into equations (12a) and (12b) in Step 32 to obtain the coefficients C1 = ε1ρ1C p1 u1T 10 and C2 = (1 - ε1)ρ2C p2 u2T 20 , substitute the constants C1 and C2 back into equation (12) respectively, and conduct algebraic derivation to obtain the analytical solutions of the temperature distributions of fluid 1 and fluid 2:

[0055]

[0056]

[0057] Step 4 specifically includes the following steps:

[0058] Step 41: First, the initial design parameters of the heat exchange structure, including the flow rates m, flow velocities u, and initial temperatures t' of the two heat exchange fluids, are determined; secondly, based on the qualitative temperature t m , and further determine the material property parameters and heat transfer characteristic parameters of the fluid working medium, including the density ρ, specific heat capacity at constant pressure C p , thermal conductivity λ, kinematic viscosity ν, and heat transfer coefficient h of the fluid working medium; in combination with the arrangement and geometric parameters of the compact tube heat exchange structure, determine the porosity ε and area ratio A of the porous medium model fs ; then, substitute the relevant initial flow and heat transfer conditions, property parameters, and geometric parameters, etc. as coefficients into equation (13) to obtain a system of equations for T1 and T2;

[0059] Step 42: Calculate and solve the heat transfer system of equations constructed in Step 41 to obtain the temperature distribution of the heat exchange structure; based on the microchannel configuration of the heat exchange structure, divide the flow channels of fluid 1 and fluid 2 into k×j grid cells respectively, and calculate the fluid temperature in each grid cell in sequence. The steps are as follows:

[0060] I: For row j = 1, the value of T 2,k,j＝1 is the inlet boundary temperature condition of fluid 2, and use equation (13a) to calculate the variation law of T 1,k,j＝1 of fluid 1 with the position coordinate x1; for row k = 1, the value of T 1,k＝1,j is the inlet boundary temperature condition of fluid 1, and use equation (13b) to calculate the variation law of T 2,k＝1,j with the position coordinate x2; where the subscript 2 represents fluid 2, and k and j represent the grid cell numbers;

[0061] II: For j = 2, T 2,k,j＝2 is the temperature of the fluid 2 cell T2,k＝1,j＝2 Under the temperature condition, use Equation (13a) to calculate T 1,k,j＝2 The variation law of x1; for k = 2, T 1,k＝2,j Is the temperature of fluid 1 unit T 1,k＝2,j＝1 Under the inlet boundary temperature condition, use Equation (13b) to calculate T 2,k＝2,j The variation law of x2;

[0062] ……

[0063] Calculate the temperature values of fluid 1 and fluid 2 in the k-th and j-th rows and columns alternately until the temperature values in all k×j units are calculated;

[0064] Step 43: Compare the fluid outlet temperature and the tube wall temperature obtained in Step 42 with the initially set fluid outlet temperature and tube wall temperature in Step 41. If the deviation between the two is less than 5% and meets the design requirements, the calculation stops; otherwise, reset the outlet temperature and tube wall temperature and repeat Steps 1 to 4.

[0065] Beneficial effects: Based on the existing conventional theoretical analysis method for tube bundle heat exchangers, the average heat transfer coefficient of the heat exchanger and the outlet temperature of the fluid working medium after heat transfer can be calculated, but the temperature field distribution of the heat transfer structure cannot be obtained. Although the three-dimensional temperature field distribution can be obtained by means of CFD simulation technology, there are a large number of staggered micro-channels in the compact tube heat transfer structure. It is very difficult to perform solid three-dimensional modeling and simulation analysis on the three-dimensional flow and heat transfer process in this compact tube heat exchanger, and the cost of modeling and calculation is extremely high. The advantages of the present invention are reflected in: a fast calculation model and method for the quasi-three-dimensional steady-state heat transfer characteristics of the compact tube heat transfer structure are proposed. Based on this mathematical model and calculation method, the heat transfer characteristics of the compact tube heat transfer structure under different spatial arrangements and geometric parameter conditions can be calculated and analyzed. In particular, the temperature field distribution of the cold and hot fluid media in the heat transfer structure can be obtained, and at the same time, the influencing factors and their influencing laws affecting the heat transfer characteristics can be predicted, providing a basis and theoretical support for the development and improvement of the design theory and technology of the heat transfer structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Is a schematic diagram of a staggered tube bundle structure;

[0067] Where: S T , S L Are the transverse pitch and longitudinal pitch of the staggered tube bundle respectively, d is the diameter of the heat exchange tube, and u is the flow velocity of the fluid outside the tube;

[0068] Figure 2 Is a schematic diagram of the heat transfer structure, where (a) is a schematic diagram of the compact tube heat transfer structure, and (b) is an equivalent staggered micro-channel heat transfer structure;

[0069] Figure 3 Schematic diagram of computational grid division for fluid flow and heat transfer in an interleaved microchannel structure; where: i and j are grid number variables, and m1 and m2 are the flow rates of the heat exchange fluids;

[0070] Figure 4 Flow chart for calculating the temperature field of a compact tube heat exchange structure;

[0071] Figure 5 Contour maps of the temperature distributions of the cold and hot fluids in the embodiment. Detailed implementation manner

[0072] The present invention will be further explained below with reference to the accompanying drawings.

[0073] Starting from the requirements of engineering calculations and designs of the heat transfer characteristics of a compact tube heat exchanger, the present invention proposes a mathematical model and a calculation method that can efficiently and rapidly calculate its quasi-three-dimensional steady-state heat transfer characteristics. The specific implementation process of the present invention is shown in Figure 4 .

[0074] A calculation method for the heat transfer characteristics of a compact tube heat exchanger according to the present invention includes the following steps:

[0075] Step 1: Based on the basic theory of convective heat transfer and the geometric characteristics of the compact tube heat exchange structure, establish a mathematical model for the heat transfer coefficient on the shell side of the heat exchange structure, specifically:

[0076] Step 11: First, the initial design parameters of the heat exchange structure, including the inlet flow rate m o 、velocity u o and the initial temperature t′1 of the shell side fluid are generally known and determined.

[0077] Secondly, set the outlet temperature and the tube wall temperature of the shell side fluid after heat exchange as t″1 and t w , and calculate the qualitative temperature t m1

[0078]

[0079] where t′1 is the temperature of the hot fluid at the inlet, and t″1 is the temperature of the hot fluid at the outlet; here, the subscript m represents the average, and the subscript 1 represents the variable on the shell side.

[0080] Based on the preliminarily determined qualitative temperature t m1 and the tube wall temperature t w , the corresponding material property parameters of the shell side fluid working medium at this temperature can be further obtained, including density ρ o , specific heat capacity C po , thermal conductivity λ o and kinematic viscosity ν o . The Prandtl number Pr of the shell side fluidfo Determined according to the fluid physical property parameters under the qualitative temperature condition, Pr wo Determined according to the fluid physical property parameters under the average wall temperature condition of the tube bundle.

[0081] Step 12, calculate the Reynolds number of the shell-side fluid through Equation (2)

[0082]

[0083] The flow velocity at the minimum cross-section of the tube bundle is described as:

[0084]

[0085] u o Is the flow velocity of the hot fluid. S1 and S2 are the transverse pitch and longitudinal pitch of the staggered tube bundle respectively, as Figure 1 Shown. ν o Is the kinematic viscosity of the fluid at the qualitative temperature.

[0086] Step 13, for the heat transfer of the fluid flowing across the staggered tube bundle, refer to the experimental correlation given by Zhukauskas, select the calculation relationship of the Nusselt number. When the number of rows of the staggered tube bundle is less than 16 rows, the row number correction coefficient shown in Table 1 needs to be adopted.

[0087]

[0088]

[0089]

[0090]

[0091] Among them, Pr fo Is the Prandtl number of the shell-side fluid, Pr wo Is the Prandtl number of the fluid in the near-wall region of the shell side;

[0092] Table 1 Row number correction coefficient of Zhukauskas correlation

[0093]

[0094] Step 14, based on the basic theory of convective heat transfer, calculate the shell-side heat transfer coefficient through Equation (5)

[0095]

[0096] λ o Is the thermal conductivity of the shell-side fluid at the shell-side qualitative temperature, d o Is the outer diameter of the heat exchange tube. And the wall temperature t can be calculated based on the shell-side heat transfer coefficient w = t m1 - q / ho , where q is the heat flux density.

[0097] Step 2: Establish a mathematical model for the heat transfer coefficient on the tube side of the heat exchange structure, specifically as follows:

[0098] Step 21: The initial design parameters of the heat exchange structure, including the inlet flow rate m of the tube-side fluid i , velocity u i and the initial temperature t′2 are generally known and determined. Set the outlet temperature of the tube-side fluid after heat exchange and the wall temperature as t″2, and calculate the qualitative temperature t of the tube-side fluid through Equation (6) m2

[0099]

[0100] Based on the preliminarily determined qualitative temperature t m2 , the corresponding material property parameters of the tube-side fluid working medium at this temperature can be further obtained, including density ρ i , specific heat capacity C pi , thermal conductivity λ i , kinematic viscosity ν i and the Prandtl number Pr of the tube-side fluid fi .

[0101] Step 22: Calculate the Reynolds number of the tube-side fluid through Equation (7)

[0102]

[0103] where the subscript i represents the tube side, d i is the inner diameter of the heat exchange tube, ν i is the kinematic viscosity of the fluid inside the tube at the qualitative temperature of the tube side, and u i is the flow velocity of the fluid inside the tube;

[0104] Step 23: For the heat transfer of laminar flow inside the tube, select the experimental correlation formula proposed by Sieder and Tate to calculate the Nusselt number Nu i

[0105]

[0106] For the heat transfer of turbulent flow inside the tube, refer to the Gnielinski formula to calculate the Nusselt number Nu i

[0107]

[0108] where d i and l are the tube diameter and tube length respectively, and f i is the Darcy friction factor of the turbulent flow inside the tube:

[0109] f i= (1.81lgRe i - 1.5) -2 (9)

[0110] Step 24: Based on the basic theory of convective heat transfer, calculate the heat transfer coefficient on the tube side of the heat exchange structure through Equation (10).

[0111]

[0112] λ i is the thermal conductivity of the fluid inside the tube at the qualitative temperature on the tube side, and d i is the inner diameter of the heat exchange tube.

[0113] Step 3: Establish a quasi-three-dimensional steady-state mathematical model for convective heat transfer of the compact tube heat exchange structure, specifically as follows:

[0114] Combining the structural characteristics of the compact tube heat exchanger and the characteristics of fluid flow and heat transfer inside it, based on the volume averaging assumption and the porous medium theory, establish a quasi-three-dimensional mathematical model for convective heat transfer of the fluid on the shell side and tube side inside the compact tube heat exchange structure.

[0115] Step 31: Equivalent the actual dense tube bundle structure shown in (a) in Figure 2 to the staggered microchannel structure shown in (b) in Figure 2 . As shown in (b) in Figure 2 , the flow direction of gas flow 1 is parallel to x1, the flow direction of gas flow 2 is parallel to x2, and while gas flow 1 and gas flow 2 pass through the microchannels, heat transfer occurs with adjacent channels. Since the actual wall thickness of the tube is very thin, the wall thermal resistance is neglected. Apply the volume averaging method to establish the temperature control equation in the micro-structure as

[0116]

[0117]

[0118] In the formula, ρ and C p are the density and specific heat capacity at constant pressure of the fluid respectively, u is the average velocity in the flow channel, h fs is the convective heat transfer coefficient, A fs and ε are the area ratio and porosity of the porous medium model respectively. T is the fluid temperature. Subscript 1 and subscript 2 represent fluid working medium 1 and fluid working medium 2 respectively.

[0119] Step 32: Integrate Equation (11a) and Equation (11b) in Step 31 to obtain the integral equation as

[0120] ε1ρ1C p1 u1T1 + h fs1 A fs (T1 - T2)x1 = C1 (12a)

[0121] (1 - ε1)ρ2C p2 u2T2 - h fs2 A fs (T1 - T2)x2 = C2 (12b)

[0122] Step 33, based on Figure 2 the model shown, with x1 = 0, T1 = T 10 and x2 = 0, T2 = T 20 boundary conditions. Substitute these boundary conditions into equations (12a) and (12b) in Step 32 to obtain the coefficients C1 = ε1ρ1C p1 u1T 10 and C2 = (1 - ε1)ρ2C p2 u2T 20 . Substitute the constants C1 and C2 back into equation (12) respectively and perform algebraic derivation to obtain the analytical solutions for the temperature distributions of fluid 1 and fluid 2 as:

[0123]

[0124]

[0125] Step 4, calculate the quasi - three - dimensional temperature field of the heat transfer characteristics of the heat exchange structure, including the following steps:

[0126] Step 41, through the above Steps 1 - 3: The initial design parameters of the heat exchange structure generally include the flow rates and initial temperatures of the two heat exchange fluids, that is, u1, u2, T 10 and T 20 are determined; according to the qualitative temperature, the corresponding material property parameters and heat transfer coefficients of the fluid working medium at this temperature can be further determined, that is, ρ1, ρ2, C p1 , C p2 , h fs1 and h fs2 ; combined with the arrangement and geometric parameters of the compact tube - type heat exchange structure, determine the porosity and area ratio of the porous medium model, that is, ε1 and A fs are determined. Substitute these relevant initial flow and heat transfer conditions, property parameters, and geometric parameters, etc. as coefficients into equation (13) to obtain a system of equations about T1 and T2.

[0127] Step 42, calculate and solve the heat transfer system of equations constructed in Step 41 to obtain the temperature distribution of the heat exchange structure. Based on Figure 2 the micro - channel configuration of the heat exchange structure shown in (b), divide the flow channels of fluid 1 and fluid 2 into k×j grid cells respectively, as Figure 3 shown, and calculate the fluid temperature in each grid cell in sequence, the steps are as follows:

[0128] I: For column j = 1, T 2,k,j＝1 The value is the fluid 2 inlet boundary temperature condition. Apply Equation (13a) to calculate the variation of T of fluid 1 1,k,j＝1 with the position coordinate x1. For row k = 1, T 1,k＝1,j The value is the fluid 1 inlet boundary temperature condition. Apply Equation (13b) to calculate the variation of T 2,k＝1,j with the position coordinate x2. Here, the subscript 2 represents fluid 2, and k and j represent the grid cell numbers;

[0129] II: For column j = 2, T 2,k,j＝2 is the temperature condition of the fluid 2 cell T 2,k＝1,j＝2 Apply Equation (13a) to calculate the variation of T 1,k,j＝2 with x1. For row k = 2, T 1,k＝2,j is the fluid 1 cell T 1,k＝2,j＝1 inlet boundary temperature condition. Apply Equation (13b) to calculate the variation of T 2,k＝2,j with x2.

[0130] ……

[0131] Calculate the temperature values of fluid 1 and fluid 2 in the k and j rows and columns alternately until the temperature values in all k×j cells are calculated.

[0132] Step 43: Compare the fluid outlet temperature and the tube wall temperature obtained in Step 42 with the initially set fluid outlet temperature and tube wall temperature in Step 41. When the deviation between the two is small (less than 5%) and meets the requirements, the calculation stops; otherwise, reset the outlet temperature and tube wall temperature and repeat Steps 1 to 4. The calculation process is as Figure 4 shown.

[0133] The present invention will be further described below in conjunction with embodiments.

[0134] Embodiment

[0135] (1) Calculation of the shell-side heat transfer coefficient of the heat exchange structure

[0136] (1.1) Taking a certain compact tube heat exchange structure as an example, its geometric model schematic diagram is as Figure 2 (a) shown. The known initial design conditions and parameters are shown in Tables 2 and 3 respectively.

[0137] Table 2 Initial design flow rate and temperature conditions of the heat exchange structure

[0138]

[0139] Table 3 Geometric parameters of the heat exchange structure

[0140]

[0141] (1.2) Based on equations (1), (2), (4) and (5) in step 1, the qualitative temperature t m1 = 642.0 K, the shell-side Reynolds number Re o = 453.0, the shell-side Nusselt number Nu o = 7.5, and the shell-side convective heat transfer coefficient h o = 994.2 are obtained respectively.

[0142] (2) Calculation of the tube-side heat transfer coefficient of the heat exchange structure

[0143] Combining the basic design parameters in Table 2 and Table 3, and based on equations (6), (7), (8) and (10) in step 2, the qualitative temperature t m2 = 301.1 K, the shell-side Reynolds number Re i = 198.0, the shell-side Nusselt number Nu i = 2.8, and the shell-side convective heat transfer coefficient h i = 1192.4 are obtained respectively.

[0144] (3) Establish a quasi-three-dimensional mathematical model for the steady-state convective heat transfer of the compact tube heat exchange structure, as shown in the equations of (13):

[0145]

[0146]

[0147] (4) Calculate the quasi-three-dimensional steady-state temperature field of the heat transfer characteristics of the heat exchange structure

[0148] (4.1) Substitute the variable values obtained from the above analysis into the relevant coefficients of equation (13), and a system of equations about T1 and T2 is obtained. It should be noted that the fluid physical property parameters in equation (13) are functions of temperature, that is

[0149] The fitting relationship of the physical property parameters of nitrogen is as follows:

[0150] Density: ρ1 = 3.161942 - 0.009682608T + 1.202177e10 -5 T 2 -5.189068e10 -9 T 3

[0151] Specific heat capacity: C p1 = 1047.143 - 0.3461212T + 0.0008111318T 2 -3.71728e10 -7 T 3

[0152] The fitting relational expressions for the physical properties of supercritical helium are as follows:

[0153] Density: ρ1 = 100.7069 - 0.9549658T + 0.004865611T 2 -1.438563e10 -5 T 3 +2.536484e10 -8 T 4 -2.623537e10 -11 T 5 +1.466367e10 -14 T 6 -3.414229e10 -18 T 7

[0154] Specific heat capacity: C p1 = 5695.899 - 6.633854T + 0.03764684T 2 -0.0001169575T 3 +2.119099e10 -7 T 4 -2.22886e10 -10 T 5 +1.259755e10 -13 T 6 -2.956371e10 -17 T 7

[0155] (4.2) Based on the quasi-three-dimensional mathematical equations for the steady-state convective heat transfer of the heat exchange structure established above, and combined with Figure 4 the calculation process shown, the temperature field of the heat exchange structure is obtained through iterative calculation.

[0156] Figure 5The temperature distribution contour maps of the cold and hot fluids are given. As can be seen from the figures, the temperature of the hot fluid gradually decreases along the flow path (x direction). The temperature distribution near the inlet of the cold fluid (z→0) is significantly lower than that at the outlet of the cold fluid (z→40), and its temperature gradient is relatively large. Similarly, the temperature distribution of the cold fluid also shows a similar pattern: the temperature of the cold fluid gradually increases along the flow path (z direction). The temperature near the inlet of the hot fluid (x→0) is significantly higher than that at the outlet of the hot fluid (x→40), and the temperature gradient at this location is relatively large. At the location closest to the inlet of the cold fluid, the temperature difference between the inlet and outlet of the hot fluid is the largest (504K). The temperature difference between the inlet and outlet of the hot fluid is the smallest (327K) at the farthest point from the inlet of the cold fluid. At the inlet of the hot fluid, the temperature difference between the inlet and outlet of the cold fluid is the largest (496K). The temperature difference between the inlet and outlet of the cold fluid is the smallest (296K) at the farthest point from the inlet of the hot fluid. In addition, the calculated results of the temperature difference between the inlet and outlet of the cold fluid are compared with the experimental results in the literature [6] and the relative deviation between the two is less than 10%, reflecting the reliability of the calculation model and method of the present invention.

[0157] 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 also be regarded as the protection scope of the present invention.

Claims

1. A rapid calculation method for the heat transfer characteristics of a compact tube heat exchanger, characterized in that: It includes the following steps: Step 1: Based on the basic theory of convective heat transfer and the geometric characteristics of the compact tube heat exchanger structure, establish a mathematical model for the shell-side heat transfer coefficient of the heat exchanger structure; Specifically, it includes the following steps: Step 11: The shell-side qualitative temperature is the average temperature of the shell-side fluid entering and leaving the tube bundle: Among them, t1′ is the temperature of the hot fluid at the inlet, t1″ is the temperature of the hot fluid at the outlet, the subscript m represents the average, and the subscript 1 represents the variable on the shell side; Step 12: The shell-side fluid Reynolds number is described as: The flow velocity at the minimum cross-section of the tube bundle is described as: Here, the subscript o represents the shell side, and d o is the outer diameter of the heat exchange tube, u o is the flow velocity of the hot fluid. S1 and S2 are the transverse pitch and longitudinal pitch of the staggered tube bundle respectively, and ν o is the kinematic viscosity of the fluid at the qualitative temperature on the shell side; Step 13: For the heat transfer of the fluid flowing across the staggered tube bundle, select the calculation relation of the Nusselt number: where Pr fo is the Prandtl number of the shell-side fluid, and Pr wo is the Prandtl number of the fluid in the near-wall region of the shell side; Step 14: Based on the basic theory of convective heat transfer, the shell-side heat transfer coefficient is: Among them, λ o is the shell-side fluid thermal conductivity at the shell-side qualitative temperature, d o is the outer diameter of the heat exchange tube, Nu o is the shell-side Nusselt number at the qualitative temperature; Calculating the tube wall temperature t based on the shell-side heat transfer coefficient w = t m1 - q / h o , where q is the heat flux density; Step 2: Based on the basic theory of convective heat transfer, establish a mathematical model for the tube-side heat transfer coefficient of the heat exchanger structure; Specifically, it includes the following steps: Step 21: The tube-side qualitative temperature is the average temperature of the tube-side fluid at the inlet and outlet: Among them, t2′ and t2″ are the inlet and outlet temperatures of the fluid inside the tube respectively; Step 22: The Reynolds number of the tube-side fluid is described as: Among them, the subscript i represents the tube side, d i is the inner diameter of the heat exchange tube, ν i is the kinematic viscosity of the fluid inside the tube at the qualitative temperature on the tube side, u i is the flow velocity of the fluid inside the tube; Step 23: For the laminar flow heat transfer on the tube side, select the experimental correlation formula proposed by Sieder and Tate: For the turbulent heat transfer inside the tube, refer to the Gnielinski formula to obtain the Nusselt number relation: where Pr i is the Prandtl number of the fluid on the tube side, d i and l are the tube diameter and tube length respectively, and f i is the Darcy friction factor for turbulent flow inside the tube: f i = (1.81 lg Re i - 1.5) -2 (9) Step 24: Based on the basic theory of convective heat transfer, the tube-side heat transfer coefficient of the heat exchanger structure is described as λ i is the thermal conductivity of the fluid inside the tube at the qualitative temperature on the tube side, d i is the inner diameter of the heat exchange tube, Nu i is the Nusselt number at the qualitative temperature; Step 3: Based on the porous medium theory and the volume average hypothesis, establish a quasi-three-dimensional mathematical model for the steady-state convective heat transfer of the compact tube heat exchanger structure; Specifically, it includes the following steps: Step 31: Establish an equivalent staggered microchannel structure. The flow direction of gas flow 1 is parallel to x1, the flow direction of gas flow 2 is parallel to x2, and gas flow 1 and gas flow 2 exchange heat with adjacent channels through the microchannels at the same time; Since the actual wall thickness of the tube is relatively thin, the wall thermal resistance is ignored, and when the forced convection heat transfer is the main heat transfer process, the heat diffusion term is ignored. Apply the volume average method to establish the temperature control equation in the microstructure as: where ρ and C p are the density and specific heat capacity at constant pressure of the fluid, u is the average velocity in the flow channel, h fs is the convective heat transfer coefficient, A fs and ε are the area ratio and porosity of the porous medium model respectively, T is the fluid temperature, and the subscripts 1 and 2 represent fluid 1 and fluid 2 respectively; Step 32: Integrate equations (11a) and (11b) in Step 31 to obtain the integral equation as ε1ρ1C p1 u1T1+h fs1 A fs (T1 - T2)x1 = C1 (12a) (1 - ε1)ρ2C p2 u2T2 - h fs2 A fs (T1 - T2)x2 = C2 (12b) Step 33: Substitute the boundary conditions x1 = 0, T1 = T 10 and x2 = 0, T2 = T 20 into equations (12a) and (12b) in Step 32 to obtain the coefficients C1 = ε1ρ1C p1 u1T 10 and C2 = (1 - ε1)ρ2C p2 u2T 20 , and substitute the constants C1 and C2 back into equation (12) respectively, and perform algebraic derivation to obtain the analytical solutions of the temperature distributions of fluid 1 and fluid 2: Step 4: Calculate and solve the temperature field based on the mathematical models established in the above Steps 1 to 3.

2. The calculation method for the heat transfer characteristics of the compact tube heat exchanger according to claim 1, characterized in that: The specific content of Step 4 includes the following steps: Step 41: First, the initial design parameters of the heat exchange structure, including the flow rates m, flow velocities u, and initial temperatures t′ of the two heat exchange fluids, are determined; secondly, based on the qualitative temperature t m , and further determine the material property parameters and heat transfer characteristic parameters of the fluid working medium, including the density ρ, specific heat capacity at constant pressure C p , thermal conductivity λ, kinematic viscosity ν, and heat transfer coefficient h of the fluid working medium; combined with the arrangement and geometric parameters of the compact tube heat exchange structure, determine the porosity ε and area ratio A of the porous medium model fs ; then, substitute the relevant initial flow and heat transfer conditions, property parameters, geometric parameters, etc. as coefficients into Equation (13) to obtain a system of equations for T1 and T2; Step 42: Calculate and solve the heat transfer equation system constructed in Step 41 to obtain the temperature distribution of the heat exchanger structure; Based on the microchannel configuration of the heat exchanger structure, divide the flow channels of fluid 1 and fluid 2 into k×j grid cells respectively, and calculate the fluid temperature in each grid cell in sequence. The steps are as follows: I: For row j = 1, the value of T 2,k,j＝1 is the fluid 2 inlet boundary temperature condition, and Eq. (13a) is applied to calculate the variation law of T of fluid 1 1,k,j＝1 with the position coordinate x1; for row k = 1, the value of T 1,k＝1,j is the fluid 1 inlet boundary temperature condition, and Eq. (13b) is applied to calculate the variation law of T 2,k＝1,j with the position coordinate x2; where the subscript 2 represents fluid 2, and k and j represent the grid cell numbers; II: For j = 2, T 2,k,j＝2 is the temperature condition of fluid 2 unit T 2,k＝1,j＝2 Apply Equation (13a) to calculate the variation law of T 1,k,j＝2 with respect to x1; for k = 2, T 1,k＝2,j is the inlet boundary temperature condition of fluid 1 unit T 1,k＝2,j＝1 Apply Equation (13b) to calculate the variation law of T 2,k＝2,j with respect to x2; …… Calculate the temperature values of fluid 1 and fluid 2 in the k and j rows and columns alternately until the calculation of the temperature values in all k×j cells is completed; Step 43: Compare the fluid outlet temperature and the tube wall temperature calculated in Step 42 with the initially set fluid outlet temperature and tube wall temperature in Step 41. If the deviation between the two is less than 5% and meets the design requirements, the calculation stops. Otherwise, reset the outlet temperature and tube wall temperature and repeat Steps 1 to 4.

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