A pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis

Abstract

The present invention provides a pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis, which specifically includes the following steps: calculating the heat load and heat exchange area according to the actual application scenario and geometric size constraints, determining the number of heat exchange units, the number of spiral coils of the heat exchange unit, the microtube spacing and the microtube diameter; using the BBD module in the response surface analysis method to perform a sensitivity analysis of the geometric parameters, determine the significant factors affecting the flow and heat exchange performance of the pre-cooling heat exchanger, and obtain an optimized design scheme for the pre-cooling heat exchanger; judging whether the design scheme of the pre-cooling heat exchanger meets the geometric space size constraints and technical requirement parameters of the application scenario, if so, determining the geometric size of the pre-cooling heat exchanger, if not, continuing to adjust the parameters until the constraints are met. The technical solution of the present invention overcomes the problems in the prior art that the high heat exchange load leads to the overall structural size of the pre-cooling heat exchanger being too large, the heat exchange efficiency being low, and the flow resistance being too large.

Description

Technical Field

[0001] The present invention relates to the technical field of pre-cooling heat exchanger design, and in particular to a pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis. Background Art

[0002] The pre-cooling heat exchanger adopts an integrated spiral thin-wall micro-tube heat exchange unit to greatly increase the heat exchange area and heat exchange rate between hot air and refrigerant, and effectively reduce the internal flow resistance to achieve efficient cooling of hot air. The temperature drop is as high as 1000℃ and the heat exchange rate can be flexibly adjusted according to actual needs.

[0003] The pre-cooling heat exchanger adopts a spiral thin-walled micro-tube structure and an ultra-compact cross-micro-tube layout to achieve the dual effects of high heat transfer performance and low pressure loss. According to the specific actual heat transfer and the requirements of specific airflow conditions, thermal calculations are first used to determine the heat transfer area, overall structural parameters and corresponding heat transfer rate of the pre-cooling heat exchanger. Then, a sensitivity analysis method based on single factors and coupling factors is used to reveal the influence weights and optimal values ​​of the main geometric factors of the pre-cooling heat exchanger on its performance (number of micro-tube rows, micro-tube spacing, micro-tube diameter, etc.). Finally, the three-dimensional geometric structure of the pre-cooling heat exchanger and the corresponding heat transfer capacity and resistance conditions in the specific application scenario are determined. For pre-cooling heat exchangers, due to the high heat transfer load, the overall structural size is too large, the heat transfer efficiency is low, and the flow resistance is too large.

[0004] Therefore, there is a need for an optimization design method for a pre-cooling heat exchanger based on geometric parameter sensitivity analysis with a small overall structural size, high heat transfer efficiency and low flow resistance. Summary of the Invention

[0005] The main purpose of the present invention is to provide a pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis to solve the problems in the prior art that high heat exchange load leads to excessively large overall structural size of the pre-cooling heat exchanger, low heat exchange efficiency, and excessive flow resistance.

[0006] To achieve the above objectives, the present invention provides a pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis, which specifically includes the following steps:

[0007] S1. Calculate the heat load and heat exchange area based on the actual application scenario and geometric size constraints, determine the outer and inner diameters of the pre-cooling heat exchanger, and then determine the number of heat exchange units, the number of spiral coils in the heat exchange unit, the microtube spacing, and the microtube diameter.

[0008] S2, using the BBD module in the response surface analysis method to conduct a sensitivity analysis of the geometric parameters of the number of heat exchange units, microtube spacing, and microtube diameter, to determine the significant factors affecting the flow and heat transfer performance of the pre-cooling heat exchanger, and to obtain an optimized design scheme for the pre-cooling heat exchanger.

[0009] S3, determine whether the design scheme of the pre-cooling heat exchanger obtained in step S2 meets the geometric space size constraints and technical requirement parameters of the application scenario. If so, determine the geometric dimensions of the pre-cooling heat exchanger. If not, continue to execute step S1 to adjust the parameters until the geometric space size constraints and technical parameter requirements of the application scenario are met.

[0010] Furthermore, step S1 specifically includes the following steps:

[0011] S1.1, calculate the expected heat transfer Q based on the pre-cooling heat exchanger hot air temperature, air flow, pre-cooling heat exchanger constant pressure specific heat capacity and expected air outlet temperature air :

[0012] Q air =M air Cp air (Tt air,in -Tt air,out );

[0013] Among them, M air is the air flow rate, Cp air is the constant pressure specific heat capacity of air, Tt air,in is the hot air temperature of the precooling heat exchanger, Tt air,out is the expected air outlet temperature.

[0014] S1.2, calculating the outlet temperature of the cooling medium according to the cooling medium inlet temperature, cooling medium pressure, cooling medium flow rate, specific heat capacity of the cooling medium and the expected heat exchange obtained in step S1.

[0015] S1.3, calculate the surface heat transfer coefficient h on the air side air and the surface heat transfer coefficient h on the coolant side cool ;

[0016]

[0017] Among them, Nu air is the Nusselt number of air, λ air is the thermal conductivity of air, d is the outer diameter of the microtube;

[0018]

[0019] Among them, Nu cool is the Nusselt number of the cooling medium, λ coolis the thermal conductivity of the cooling medium, d i is the inner diameter of the microtubule.

[0020] Furthermore, step S1 further includes the following steps:

[0021] S1.4. Determine the heat transfer coefficient and calculate the logarithmic mean temperature difference based on the precooling heat exchanger hot air temperature, the cooling medium temperature, the expected air outlet temperature, and the cooling medium outlet temperature:

[0022] The heat transfer coefficient K is calculated as:

[0023]

[0024] Logarithmic mean temperature difference ΔT m The calculation formula is:

[0025]

[0026] ΔT1=Tt air,in -Tt cool,out ;

[0027] ΔT2=Tt air,out -Tt cool,in ;

[0028] Wherein, ΔT1 is the temperature difference between the air inlet and the coolant outlet, and ΔT2 is the temperature difference between the air outlet and the coolant inlet.

[0029] S1.5, calculate the heat transfer area A based on the heat transfer coefficient and logarithmic mean temperature difference:

[0030]

[0031] S1.6. Based on the heat exchange area, preliminarily determine the number of heat exchange units, microtube spacing, and microtube diameter.

[0032] Furthermore, step S1.2 specifically includes the following steps:

[0033] S1.2.1, the cooling medium is liquid nitrogen or liquid helium, and the cooling medium inlet temperature is Tt cool,in The critical temperature of the cooling medium is selected, and the cooling medium flow rate is set to 5-8 m / s based on experience.

[0034] S1.2.2, determine the specific heat capacity Cp of the cooling medium based on the cooling medium inlet temperature and cooling medium flow rate cool and cooling medium flow M cool .

[0035] S1.2.3, Expected heat transfer Q air Heat exchange rate Q with the cooling medium side cool Equal, that is, Qair =Q cool , Q cool =M cool Cp cool (Tt cool,in -Tt cool,out ), thereby determining the outlet temperature Tt of the cooling medium cool,out .

[0036] Furthermore, step S1.6 specifically includes the following steps:

[0037] S1.6.1, Determine the outside and inside diameter dimensions of the precooling heat exchanger based on the spatial geometry of the components upstream and downstream of the precooling heat exchanger and other constraints.

[0038] S1.6.2. The microtube diameter of the precooling heat exchanger microtube is selected in the range of 0.5-2.5 mm, and the wall thickness of the microtube is 1 / 20 of the microtube diameter.

[0039] S1.6.3. After selecting the micro-tube diameters of the pre-cooling heat exchanger, within the constraints of the outer and inner diameters of the pre-cooling heat exchanger, select the number of heat exchange units, the number of spiral coils z of the heat exchange unit, and the number of micro-tube rows arranged in a radially staggered pattern within each heat exchange unit. Use a plane equidistant Archimedean spiral to design the spiral geometry of the heat exchange unit within the pre-cooling heat exchanger. The selection range of z is between 0.2 and 1.0. The starting position of each spiral heat exchange unit within the pre-cooling heat exchanger is located at The end position is located on the inner diameter circular contour line of the pre-cooling heat exchanger, and the end position is located on the outer diameter circular contour line of the pre-cooling heat exchanger. Each heat exchange unit is evenly distributed along the circumferential direction inside the pre-cooling heat exchanger, and the arc lengths between the starting positions or end positions of adjacent heat exchange units are equal; each heat exchange unit contains 4 to 6 rows of microtube structures arranged in a staggered manner along the radial direction of the pre-cooling heat exchanger. The spacing between the microtubes arranged in a staggered manner in the heat exchange unit is 1 to 1.5 times the diameter of the microtubes, and the microtube spacing is the straight-line distance between the centers of adjacent microtubes arranged in a staggered manner.

[0040] Furthermore, step S1.6 further includes the following steps:

[0041] S1.6.4. Under the constraints of the outer and inner diameters of the pre-cooling heat exchanger, combined with the number of selected heat exchange units, the number of spiral coils of the heat exchange unit, and the number of microtube rows arranged radially in a cross-stack inside each heat exchange unit, all heat exchange units are integrated and arranged under the overall framework structure of the pre-cooling heat exchanger to obtain the geometric layout structure of the cross-section of the pre-cooling heat exchanger perpendicular to the axial direction, and then the microtube spacing size between adjacent microtubes of different heat exchange units on the cross-section is obtained.

[0042] S1.6.5, the radius of the inner circle O1 of the precooling heat exchanger is a i, the outer radius of the pre-cooling heat exchanger O2 is a o , the growth rate b is calculated as:

[0043]

[0044] Determine the specific Cartesian coordinates x and y of each point on the spiral using the following formula:

[0045] x=(a i +b·θ)cosθ

[0046] y=(a i +b·θ)sinθ;

[0047] Where θ is any value within the circumferential angle range of the helix [0, 2πz].

[0048] S1.6.6. The recommended microtube spacing between adjacent microtubes of different heat exchange units on the cross section is 4 to 8 times the microtube diameter. If the microtube spacing between adjacent microtubes of different heat exchange units exceeds the recommended value, the number of heat exchange units, the number of spiral coils of the heat exchange units, the number of microtube rows arranged in a staggered pattern within the heat exchange units, and the microtube spacing shall be readjusted until the microtube spacing between adjacent microtubes of different heat exchange units meets the recommended value.

[0049] S1.6.7. Based on the determined number of heat exchange units, the number of spiral coils in the heat exchange units, and the number of rows of microtubes arranged in a staggered pattern inside the heat exchange units, the total number of microtubes in the cross-section of the pre-cooling heat exchanger perpendicular to the axial direction and the corresponding surface heat exchange area are obtained. Combined with the calculated heat exchange area A of the pre-cooling heat exchanger, the number of microtube rows arranged along the axial direction of each heat exchange unit of the pre-cooling heat exchanger and the total number of microtubes required to be arranged inside the pre-cooling heat exchanger are calculated, thereby obtaining the axial length of the pre-cooling heat exchanger.

[0050] S1.6.8, reserve inlet and outlet transition areas at the outer and inner diameters of the precooling heat exchanger to determine the starting and ending positions of different heat exchange units in the precooling heat exchanger and the corresponding liquid collecting chamber positions.

[0051] Furthermore, step S2 includes the following steps:

[0052] S2.1. Select the optimal number of experimental levels and center points based on the number of experimental factors selected by the BBD module, namely, the number of microtube radial tube groups, the microtube spacing, and the microtube diameter.

[0053] S2.2, the number of experimental factor levels is 3, and the sample plan of the experimental factor levels is determined based on the increment of 5%-20% of the prototype value, and the number of center points is selected as 2.

[0054] S2.3. Determine the number of sensitivity test scenarios and the corresponding sample characteristics based on the number of experimental factor levels and the number of center points. The number of test scenarios n is defined as: n = 2s(s-1) + C; where s is the number of experimental factors and C is the number of center points.

[0055] Furthermore, step S2 further includes the following steps:

[0056] S2.4. Perform variance analysis on the test results to determine whether the test results meet the fitting accuracy. For test results that meet the fitting accuracy, analyze the degree and significance of the impact of the test factors on the flow and heat transfer characteristics of the pre-cooling heat exchanger.

[0057] S2.5, obtain the recommended optimal parameter values ​​through sensitivity analysis method to form the optimal design scheme of pre-cooling heat exchanger.

[0058] S2.6. Use numerical simulation methods to obtain the flow and heat transfer characteristics of the optimal geometric scheme of the pre-cooling heat exchanger, and compare them with various experimental schemes to verify the authenticity and rationality of the optimal geometric scheme. Summarize the exhaust temperature, flow rate and corresponding total pressure loss of the hot air after cooling by the pre-cooling heat exchanger, thereby completing the optimal design scheme of the pre-cooling heat exchanger based on the sensitivity analysis of geometric parameters.

[0059] Furthermore, the variance analysis in step S2.4 is based on the multivariate correlation coefficient R 2 To judge the fitting accuracy of the obtained response surface model, R 2 The range is between [0,1]. When R 2 The closer it is to 1, the more significant the response surface model is, which means that the fitting accuracy is met.

[0060] The significance of the experimental factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged by the P value in the variance analysis table. The P value is less than 0.05, indicating that the factor is a significant item.

[0061] The degree of influence of the test factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged according to the F value in the variance analysis table. The larger the F value, the greater the degree of influence, thereby determining the degree of influence of the test factors on the flow and heat transfer performance of the pre-cooling heat exchanger.

[0062] Furthermore, step S3 is specifically as follows:

[0063] If the calculated axial length of the pre-cooling heat exchanger does not meet the spatial geometric dimension constraints of the overall structure of the pre-cooling heat exchanger, it is necessary to return to steps S1.6.2 to S1.6.8 to iteratively adjust the number of heat exchange units, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, and the microtube spacing and microtube diameter between adjacent microtubes of different heat exchange units until the total axial length meets the geometric constraints, and determine the corresponding number of heat exchange units of the pre-cooling heat exchanger, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, the tube spacing between adjacent microtubes of different heat exchange units, the total axial length of the pre-cooling heat exchanger, and the total number of microtubes inside the heat exchange unit.

[0064] The present invention has the following beneficial effects:

[0065] The present invention proposes a pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis. While meeting the geometric size constraints and heat exchange requirements of actual application scenarios, it can also effectively take into account the optimization of heat exchange rate and flow resistance characteristics, thereby achieving relatively optimized comprehensive flow and heat exchange characteristics of the pre-cooling heat exchanger. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0067] Figure 1 The three-dimensional geometric structure diagram of the pre-cooling heat exchanger preliminarily determined in the second embodiment of the present invention is shown.

[0068] Figure 2 Shown Figure 1 A simplified diagram of .

[0069] Figure 3 A simplified diagram of the pre-cooling heat exchanger structure with the minimum calculation unit model is shown.

[0070] Figure 4 Shown Figure 3 Structural diagram of fan-shaped thin layer unit A.

[0071] Figure 5 Shown Figure 4 A magnified view of the detail at point B.

[0072] Figure 6 A diagram showing a pre-cooling heat exchanger model after optimization design based on a geometric parameter sensitivity analysis method according to the method provided by the present invention is shown.

[0073] Figure 7 Shown Figure 6 A simplified diagram of .

[0074] Figure 8 A schematic diagram of the geometric structure of a single heat exchange unit is shown.

[0075] Figure 9 The figure shows the structural diagram of the spiral heat exchange unit designed in the present invention.

[0076] The reference numerals in the above drawings are:

[0077] 10. Microtube; 20. Microtube group; 30. Heat exchange unit; 40. Helical line of heat exchange unit. DETAILED DESCRIPTION

[0078] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0079] Example 1

[0080] A pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis specifically includes the following steps:

[0081] S1, calculate the heat load and heat exchange area according to the actual application scenario and geometric size constraints, determine the outer diameter and inner diameter of the pre-cooling heat exchanger, and then determine the number of heat exchange units, the number of spiral coils of the heat exchange unit, the micro-tube spacing and the micro-tube diameter. Figure 1 As shown, the outer diameter of the pre-cooling heat exchanger is the diameter of the outer large circle, and the inner diameter of the pre-cooling heat exchanger is the diameter of the inner large circle.

[0082] S2, using the BBD module in the response surface analysis method to conduct a sensitivity analysis of the geometric parameters of the number of heat exchange units, microtube spacing, and microtube diameter, to determine the significant factors affecting the flow and heat transfer performance of the pre-cooling heat exchanger, and to obtain an optimized design scheme for the pre-cooling heat exchanger.

[0083] S3, determine whether the design scheme of the pre-cooling heat exchanger obtained in step S2 meets the geometric space size constraints and technical requirement parameters of the application scenario. If so, determine the geometric dimensions of the pre-cooling heat exchanger. If not, continue to execute step S1 to adjust the parameters until the geometric space size constraints and technical parameter requirements of the application scenario are met.

[0084] Specifically, step S1 includes the following steps:

[0085] S1.1, calculate the expected heat transfer Q based on the pre-cooling heat exchanger hot air temperature, air flow, pre-cooling heat exchanger constant pressure specific heat capacity and expected air outlet temperature air :

[0086] Q air =M air Cp air (Tt air,in -Tt air,out );

[0087] Among them, M air is the air flow rate, Cp air is the constant pressure specific heat capacity of air, Tt air,in is the hot air temperature of the precooling heat exchanger, Tt air,out is the expected air outlet temperature.

[0088] S1.2, calculating the outlet temperature of the cooling medium according to the cooling medium inlet temperature, cooling medium pressure, cooling medium flow rate, specific heat capacity of the cooling medium and the expected heat exchange obtained in step S1.

[0089] S1.3, calculate the surface heat transfer coefficient h on the air side air and the surface heat transfer coefficient h on the coolant side cool ;

[0090]

[0091] Among them, Nu air is the Nusselt number of air, λ air is the thermal conductivity of air, d is the outer diameter of the microtube;

[0092]

[0093] Among them, Nu cool is the Nusselt number of the cooling medium, λ cool is the thermal conductivity of the cooling medium, d i is the inner diameter of the microtubule.

[0094]

[0095] Among them, Re air is the Reynolds number of air, Pr air is the Prandtl number of air, Re cool is the Reynolds number of the cooling medium, Pr cool is the Prandtl number of the cooling medium, μ air is the dynamic viscosity of air, μ cool is the dynamic viscosity of the cooling medium; the dynamic viscosity of air is calculated using the Sutherland formula, where μ0 = 1.7894 × 10 -5, B = 110.4K; where μ0 is the initial air dynamic viscosity and B is an empirical constant;

[0096] The formula for calculating the Reynolds number is:

[0097]

[0098] Among them, ρ air and ρ cool are the densities of air and cooling medium, v air and v cool are the flow rates of air and cooling medium, μ air and μ cool are the viscosity coefficients of air and coolant, respectively.

[0099] Specifically, step S1 further includes the following steps:

[0100] S1.4. Determine the heat transfer coefficient and calculate the logarithmic mean temperature difference based on the precooling heat exchanger hot air temperature, the cooling medium temperature, the expected air outlet temperature, and the cooling medium outlet temperature:

[0101] The heat transfer coefficient K is calculated as:

[0102]

[0103] Logarithmic mean temperature difference ΔT m The calculation formula is:

[0104]

[0105] ΔT1=Tt air,in -Tt cool,out ;

[0106] ΔT2=Tt air,out -Tt cool,in ;

[0107] Wherein, ΔT1 is the temperature difference between the air inlet and the coolant outlet, and ΔT2 is the temperature difference between the air outlet and the coolant inlet.

[0108] S1.5, calculate the heat transfer area A based on the heat transfer coefficient and logarithmic mean temperature difference:

[0109]

[0110] S1.6. Based on the heat exchange area, preliminarily determine the number of heat exchange units, microtube spacing, and microtube diameter.

[0111] Specifically, step S1.2 includes the following steps:

[0112] S1.2.1, the cooling medium is liquid nitrogen or liquid helium, and the cooling medium inlet temperature is Tt cool,in The critical temperature of the cooling medium is selected, and the cooling medium flow rate is set to 5-8 m / s based on experience.

[0113] S1.2.2, determine the specific heat capacity Cp of the cooling medium based on the cooling medium inlet temperature and cooling medium flow rate cool and cooling medium flow M cool .

[0114] S1.2.3, Expected heat transfer Q air Heat exchange rate Q with the cooling medium side cool Equal, that is, Q air =Q cool , Q cool =M cool Cp cool (Tt cool,in -Tt cool,out ), thereby determining the outlet temperature Tt of the cooling medium cool,out .

[0115] Specifically, step S1.6 includes the following steps:

[0116] S1.6.1. Determine the outside and inside diameters of the precooling heat exchanger based on the spatial geometric constraints and other technical requirements of the upstream and downstream components of the precooling heat exchanger.

[0117] S1.6.2. The microtube diameter of the precooling heat exchanger microtube is selected in the range of 0.5-2.5 mm, and the wall thickness of the microtube is 1 / 20 of the microtube diameter.

[0118] S1.6.3, after selecting the micro-tube diameter of the pre-cooling heat exchanger, under the size constraints of the outer diameter and inner diameter of the pre-cooling heat exchanger, select the number of heat exchange units of the pre-cooling heat exchanger, the number of spiral coils of the heat exchange unit, and the number of micro-tube rows arranged in a radial cross-row along the pre-cooling heat exchanger in each heat exchange unit. The spiral geometric line of the heat exchange unit inside the pre-cooling heat exchanger can be designed using a plane equidistant Archimedean spiral after determining the outer diameter and inner diameter of the pre-cooling heat exchanger and selecting the number of spiral coils z. The selection range of z is between 0.2 and 1.0. The selected value of z determines the length of the spiral micro-tubes in the heat exchange unit and the corresponding surface area. In order to ensure that the processing difficulty and cost of the heat exchanger and micro-tubes are reduced, the z value should be selected as small as possible while ensuring that the heat load is met. For example Figure 9As shown, the starting position of each spiral heat exchange unit inside the pre-cooling heat exchanger is located on the inner diameter circle contour line of the pre-cooling heat exchanger, and the ending position is located on the outer diameter circle contour line of the pre-cooling heat exchanger. Each heat exchange unit is evenly distributed along the circumferential direction inside the pre-cooling heat exchanger, and the arc lengths between the starting positions or ending positions of adjacent heat exchange units are equal; each heat exchange unit contains 4 to 6 rows of microtube structures arranged in a staggered manner along the radial direction of the pre-cooling heat exchanger; the spacing between the microtubes arranged in a staggered manner in the heat exchange unit is 1 to 1.5 times the diameter of the microtubes, and the spacing between the microtubes is the straight-line distance between the centers of adjacent microtubes arranged in a staggered manner. Figure 8 Schematic diagram of the geometric structure of a single heat exchange unit. The heat exchange unit is spiral-shaped and consists of multiple microtubes 10.

[0119] Specifically, step S1.6 further includes the following steps:

[0120] S1.6.4. Under the constraints of the outer and inner diameters of the pre-cooling heat exchanger, combined with the number of selected heat exchange units, the number of spiral coils of the heat exchange unit, and the number of microtube rows arranged radially in a cross-stack inside each heat exchange unit, all heat exchange units are integrated and arranged under the overall framework structure of the pre-cooling heat exchanger to obtain the geometric layout structure of the cross-section of the pre-cooling heat exchanger perpendicular to the axial direction, and then the tube spacing size between adjacent microtubes of different heat exchange units on the cross-section is obtained.

[0121] S1.6.5, the distribution characteristics of the spiral geometric lines of the heat exchange unit on the cross section are obtained by designing the plane equidistant Archimedean spiral. The value range of the spiral coil number z is between 0.2 and 1.0. The selected value of z directly determines the length and corresponding surface area of ​​the spiral microtube in the heat exchange unit. In order to ensure that the processing difficulty and cost of the heat exchanger and microtube are reduced, the z value should be selected as small as possible while ensuring that the heat load is met. The starting position of the spiral line of the heat exchange unit is located on the inner diameter circle contour line of the pre-cooling heat exchanger, such as Figure 9 As shown, the distance from the inner diameter to the central axis (that is, the radius of the inner circle O1 of the precooling heat exchanger) is a i The end point is located on the outer diameter circle contour line of the pre-cooling heat exchanger, and the distance from the outer diameter to the central axis (that is, the radius of the outer circle O2 of the pre-cooling heat exchanger) is a o The growth rate b of the spiral can be calculated from the inner and outer circle radius values. The corresponding calculation formula is:

[0122]

[0123] like Figure 9 As shown, after determining the inner radius a of the spiral line of the heat exchange unit i, the number of spiral coils z and the growth rate b of the spiral line, the specific Cartesian coordinates x, y of each point on the spiral line can be determined according to the following formula, that is, the spiral line distribution characteristics of the heat exchange unit are determined, and θ is any value within the circumferential angle range of the spiral line [0,2πz].

[0124]

[0125] Figure 9 The midpoint S represents the starting position of the spiral line, and E represents the ending position of the spiral line. The spiral line between point S and point E is the heat exchange unit spiral line 40.

[0126] S1.6.6. The recommended spacing between adjacent microtubes in different heat exchange units on the cross section is 4 to 8 times the microtube diameter. If the spacing between adjacent microtubes in different heat exchange units exceeds the recommended value, the number of heat exchange units, the number of spiral coils in the heat exchange units, the number of microtube rows in the staggered arrangement within the heat exchange units, and the spacing between the tubes shall be readjusted until the spacing between adjacent microtubes in different heat exchange units meets the recommended value.

[0127] S1.6.7. Based on the determined number of heat exchange units, the number of spiral coils of the heat exchange units, and the number of rows of microtubes arranged in a staggered pattern inside the heat exchange units, the total number of microtubes in the cross section of the pre-cooling heat exchanger perpendicular to the axial direction and the corresponding surface heat exchange area are obtained. Combined with the calculated heat exchange area A of the pre-cooling heat exchanger, the number of microtube rows arranged along the axial direction of each heat exchange unit of the pre-cooling heat exchanger and the total number of microtubes required to be arranged inside the pre-cooling heat exchanger are calculated, thereby obtaining the axial length of the pre-cooling heat exchanger. The microtubes inside each heat exchange unit are also arranged in a staggered pattern along the axial direction, and the microtube spacing between the microtubes in the axial staggered pattern is equal to the microtube spacing between the microtubes in the radial staggered pattern.

[0128] S1.6.8, reserve inlet and outlet transition areas (the distance from the hot air inlet and outlet to the nearest micro-tube) at the outer diameter and inner diameter of the pre-cooling heat exchanger to determine the starting position, end position and corresponding liquid collection cavity position of different heat exchange units in the pre-cooling heat exchanger.

[0129] High temperature incoming hot air passes through Figure 1 After cooling to the expected outlet temperature, the pre-cooling heat exchanger is constructed using a lightweight, efficient, and compact pre-cooling heat exchanger. When using numerical methods to evaluate the flow and heat transfer characteristics of the pre-cooling heat exchanger, the computational domain of the pre-cooling heat exchanger involved in the performance simulation can be simplified to reduce resource consumption due to the relatively large geometric dimensions of the entire pre-cooling heat exchanger, the large number of microtubes it contains, and the symmetrical structural characteristics of its overall structure along both the circumferential and axial directions. Figure 1 、 Figure 4 and Figure 6 Where I1 represents the air inlet, I2 represents the coolant inlet, O1 represents the air outlet, and O2 represents the coolant outlet.

[0130] The specific simplification process is as follows:

[0131] Take a thin layer unit of the entire pre-cooling heat exchanger structure along the axial direction. The thin layer unit contains only two rows of micro-tube structures along the axial direction. Further divide the thin layer unit of the pre-cooling heat exchanger along the circumferential direction into a number equal to the total number of heat exchange units, such as Figure 3 As shown in the figure, only one of the fan-shaped thin layer units is taken as the calculation domain for the performance simulation of the pre-cooling heat exchanger, as shown in the figure. Figure 4 As shown. When the number of spiral coils z of the heat exchange unit is fixed (that is, the length of the corresponding spiral microtube remains unchanged), the number of radial microtube rows in the fan-shaped domain calculation unit corresponds to the number of heat exchange units in the pre-cooling heat exchanger, as shown in Figure 4 As shown, there are n micro-tube groups 20 in total, and the number of micro-tube groups corresponds to the number of heat exchange units.

[0132] After completing the modeling of the minimum calculation unit model of the pre-cooling heat exchanger, the numerical simulation method is usually used to perform numerical calculations on the minimum calculation unit model of the pre-cooling heat exchanger to obtain information such as the total pressure loss and heat transfer rate of the pre-cooling heat exchanger.

[0133] In actual application scenarios, the hot air inlet parameters have been given: air inlet temperature Tt air,in , inlet pressure Pt air,in 、Flow M air Under the premise of , three geometric parameters, namely the number of microtube radial tube groups (that is, the number of heat exchange units in the precooling heat exchanger), microtube spacing and microtube diameter in the fan-shaped calculation domain of the precooling heat exchanger, are selected as the geometric objects of sensitivity analysis. The heat transfer rate of the precooling heat exchanger (that is, the outlet temperature of the cooled air in the precooling heat exchanger) and the total pressure loss coefficient are selected as the objective functions. The response surface analysis method is used to perform sensitivity analysis on the above three geometric parameters. The variance analysis results give the geometric factors that have a more significant impact on the flow and heat transfer characteristics of the precooling heat exchanger and the corresponding optimal geometric scheme of the precooling heat exchanger, that is, the optimal number of radial microtube radial tube groups (that is, the number of heat exchange units), microtube spacing and microtube diameter under the constraints of heat load and spatial geometric dimensions in this application scenario.

[0134] The sensitivity analysis-based optimization process for the pre-cooling heat exchanger is as follows: The BBD (Box-Behnken Design) module within the response surface methodology is used to conduct a sensitivity analysis of the key geometric parameters of the pre-cooling heat exchanger to be optimized. This sensitivity analysis includes the significance and impact of each geometric factor on the pre-cooling heat exchanger's total pressure loss and heat transfer rate, as well as the determination of the optimal geometric solution for the pre-cooling heat exchanger that maximizes the heat transfer rate and minimizes the total pressure loss, meeting the flow and heat transfer requirements of the application scenario.

[0135] Specifically, step S2 includes the following steps:

[0136] S2.1. Select the optimal number of experimental levels and center points based on the number of experimental factors selected by the BBD module, namely, the number of microtube radial tube groups, the microtube spacing, and the microtube diameter.

[0137] S2.2, the number of experimental factor levels is 3, and the sample plan of the experimental factor levels is determined based on the increment of 5%-20% of the prototype value, and the number of center points is selected as 2.

[0138] S2.3. Determine the number of sensitivity test scenarios and the corresponding sample characteristics based on the number of experimental factor levels and the number of center points. The number of test scenarios n is defined as: n = 2s(s-1) + C; where s is the number of experimental factors and C is the number of center points.

[0139] Specifically, step S2 further includes the following steps:

[0140] S2.4. Perform variance analysis on the test results to determine whether the test results meet the fitting accuracy. For test results that meet the fitting accuracy, analyze the degree and significance of the impact of the test factors on the flow and heat transfer characteristics of the pre-cooling heat exchanger.

[0141] S2.5, obtain the recommended optimal parameter values ​​through sensitivity analysis method to form the optimal design scheme of pre-cooling heat exchanger.

[0142] S2.6. Use numerical simulation methods to obtain the flow and heat transfer characteristics of the optimal geometric scheme of the pre-cooling heat exchanger, and compare them with various experimental schemes to verify the authenticity and rationality of the optimal geometric scheme. Summarize the exhaust temperature, flow rate and corresponding total pressure loss of the hot air after cooling by the pre-cooling heat exchanger, thereby completing the optimal design scheme of the pre-cooling heat exchanger based on the sensitivity analysis of geometric parameters.

[0143] Specifically, in step S2.4, the variance analysis is based on the multivariate correlation coefficient R 2 To judge the fitting accuracy of the obtained response surface model, R 2 The range is between [0,1]. When R 2 The closer it is to 1, the more significant the response surface model is, meaning it meets the fitting accuracy. The response surface model is a model formed by the sensitivity analysis method and is used to determine whether the sensitivity analysis is feasible. If the model is significant, the next step is to determine the significance of the experimental factors.

[0144] The significance of the experimental factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged by the P value in the variance analysis table. The P value is less than 0.05, indicating that the factor is a significant item.

[0145] The degree of influence of the test factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged according to the F value in the variance analysis table. The larger the F value, the greater the degree of influence, thereby determining the degree of influence of the test factors on the flow and heat transfer performance of the pre-cooling heat exchanger.

[0146] Specifically, step S3 is as follows:

[0147] If the calculated axial length of the pre-cooling heat exchanger does not meet the spatial geometric dimension constraints of the overall structure of the pre-cooling heat exchanger, it is necessary to return to steps S1.6.2 to S1.6.8 to iteratively adjust the number of heat exchange units, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, and the microtube spacing and microtube diameter between adjacent microtubes of different heat exchange units until the total axial length meets the geometric constraints, and determine the corresponding number of heat exchange units of the pre-cooling heat exchanger, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, the tube spacing between adjacent microtubes of different heat exchange units, the total axial length of the pre-cooling heat exchanger, and the total number of microtubes inside the heat exchange unit.

[0148] Example 2

[0149] Step 1: Calculate the heat load and heat exchange area based on the actual application scenario and geometric size constraints, determine the outer and inner diameters of the pre-cooling heat exchanger, and then determine the number of heat exchange units, the number of spiral coils in the heat exchange unit, the microtube spacing, and the microtube diameter:

[0150] The application environment and technical requirements of the pre-cooling heat exchanger to be designed are as follows:

[0151] Application environment air intake conditions: pre-cooling heat exchanger hot air temperature Tt air,in =1181.72K, pre-cooling heat exchanger hot air pressure Pt air,in =39993.64Pa, air flow rate M air =15kg / s.

[0152] Technical requirements: Expected air outlet temperature Tt after cooling to be achieved air,out No more than 500K, and as compact as possible with minimal flow resistance.

[0153] The preliminary geometric design process of the pre-cooling heat exchanger is as follows:

[0154] (1) In this embodiment, Tt air,out Select 500K to determine the expected heat transfer Q air =M air Cp air (Tt air,in -Tt air,out ). Cp air is the constant pressure specific heat capacity of air, and Cp is determined according to the air temperature parameterair =1006.43J / (kg·K). Q is calculated air =10287.43kW.

[0155] (2) The cooling medium in this embodiment is liquid nitrogen (liquid helium can also be selected as the cooling medium according to actual conditions), and the cooling medium inlet temperature Tt cool,in Select its critical temperature as 77K, cooling medium flow rate as 6m / s, and determine the specific heat capacity Cp of the cooling medium according to the cooling medium inlet temperature and flow rate. cool =806.08J / (kg·K), cooling medium flow rate M cool =85.68kg / s. Expected heat transfer Q air Heat exchange rate Q with the cooling medium side cool Equal, that is, Q air =Q cool .Q cool =M cool Cp cool (Tt cool,in -Tt cool,out ). Thus determine the outlet temperature Tt of the cooling medium cool,out =135.8K.

[0156] (3) Determine the air side surface heat transfer coefficient h air and the surface heat transfer coefficient h on the coolant side cool , that is Where d is the outer diameter of the microtube, which is 1.05 mm, and d i The inner diameter of the microtube is 1 mm; the thermal conductivity of air is λ air and the thermal conductivity λ of the cooling medium cool It can be determined based on the physical parameters of air and coolant, air =0.0242W / (m·K),λ cool =0.149 W / (m·K); the Nusselt number Nu is calculated by the Dittus-Boelter formula (as follows).

[0157]

[0158] The dynamic viscosity μ is calculated using the Sutherland formula (as follows), where μ0 = 1.7894 × 10 -5 , B=110.4K.

[0159]

[0160] By using the above formula, we can calculate μ air =4.58×10 -5 kg / (m·s), μ cool=1.63×10 -4 kg / (m·s); Pr air =0.744,Pr cool =2.277;Re air =447.34,Re cool =32894.84; Nu air =12.25,Nu cool =131.34;h air =296.53W / (m 2 ·k), h cool =18238.73W / (m 2 ·k).

[0161]

[0162] (5) Use the following formula to calculate the logarithmic mean temperature difference ΔT m =688.09K.

[0163]

[0164] ΔT1=Tt air,in -Tt cool,out ;

[0165] ΔT2=Tt air,out -Tt cool,in ;

[0166] (6) Using the following formula, calculate the heat exchange area A = 50.34m 2 .

[0167]

[0168] (7) According to the geometric space constraint requirements of the pre-cooling heat exchanger, the outer diameter of the pre-cooling heat exchanger is determined to be 900 mm and the inner diameter is 430 mm. According to the heat exchange area A, after iterative adjustment, it is preliminarily determined that the number of heat exchange units of the pre-cooling heat exchanger is 20, the number of spiral coils of the heat exchange unit is 0.36, and the circumferential angle range corresponding to the starting position and the ending position of each heat exchange unit is 129.6°, as shown in Figure 2. Figure 2As shown. Each heat exchange unit contains 4 cross-row microtube structures along the radial direction. The spacing between the cross-row microtubes arranged radially and axially inside the heat exchange unit is 2mm. The microtube diameter is 1mm and the wall thickness is 0.05mm. According to the geometric constraints of the spatial structure of the pre-cooling heat exchanger on the axial length, the total axial length of the pre-cooling heat exchanger after iteration is 662.76mm. The microtube spacing between adjacent microtubes of different heat exchange units is 16.8mm. The entire pre-cooling heat exchanger contains a total of 30612 cross-row microtube structures. Therefore, a preliminary three-dimensional geometric entity structure of the pre-cooling heat exchanger is formed according to the above parameters, as shown in Figure 1 shown.

[0169] Step 2: Use the BBD module in the response surface analysis method to perform a sensitivity analysis of the geometric parameters of the number of heat exchange units, microtube spacing, and microtube diameter to determine the significant factors affecting the flow and heat transfer performance of the pre-cooling heat exchanger and obtain an optimized design scheme for the pre-cooling heat exchanger.

[0170] In actual application scenarios, the hot air inlet parameters have been given: pre-cooling heat exchanger hot air temperature Tt air,in , pre-cooling heat exchanger hot air pressure Pt air,in , air flow M air Under the premise of , the three geometric parameters of the pre-cooling heat exchanger, namely the number of spiral heat exchange units, micro-tube spacing and micro-tube diameter, are selected as the geometric objects of sensitivity analysis. The heat transfer rate of the pre-cooling heat exchanger (that is, the outlet temperature of the cooled air in the pre-cooling heat exchanger) and the total pressure loss coefficient are selected as the objective functions, where R1 is the total pressure loss coefficient and R2 is the heat transfer rate:

[0171]

[0172] R2=Cp air M air (Tt air,in -Tt air,out );

[0173] It should be noted that when using numerical methods to evaluate the flow and heat transfer characteristics of pre-cooling heat exchangers with different geometric structures, since the geometric size of the entire pre-cooling heat exchanger is relatively large, it contains a large number of microtubes, and its overall structure has symmetrical structural characteristics along the circumferential and axial directions, in order to reduce the resource consumption of simulation calculations, the calculation domain of the pre-cooling heat exchanger participating in the performance simulation can be simplified. The specific simplification process is as follows: a thin layer unit of the entire pre-cooling heat exchanger structure is taken along the axial direction, and the thin layer unit only contains 2 rows of microtube structures along the axial direction. The thin layer unit of the pre-cooling heat exchanger is further divided into 20 parts equal to the number of heat exchange units along the circumferential direction, and only one of the fan-shaped thin layer units is taken as the calculation domain for the performance simulation of the pre-cooling heat exchanger, such as Figure 3 and Figure 4As shown in the figure, when the number of spiral coils z in the precooling heat exchanger's spiral heat exchange unit is fixed, the number of radial microtube groups within the sector-shaped computational unit corresponds one-to-one with the number of heat exchange units in the precooling heat exchanger. Therefore, when performing sensitivity analysis on key geometric parameters within the precooling heat exchanger's sector-shaped computational domain, the number of radial microtube groups within the computational domain can be used to replace the number of heat exchange units in the precooling heat exchanger.

[0174] The response surface analysis method was used to conduct a sensitivity analysis of the three geometric parameters mentioned above. The variance analysis results revealed the geometric factors that significantly affected the flow and heat transfer characteristics of the pre-cooling heat exchanger and the corresponding optimal geometric scheme for the pre-cooling heat exchanger. In other words, the optimal number of micro-tube radial tube groups (that is, the number of heat exchange units in the pre-cooling heat exchanger), micro-tube spacing, and micro-tube diameter under the heat load and spatial geometric size constraints of this application scenario. The optimization process of the pre-cooling heat exchanger based on the sensitivity analysis method is as follows:

[0175] A sensitivity analysis of the key geometric parameters of the precooling heat exchanger to be optimized was conducted using the BBD (Box-Behnken Design) module within the response surface methodology. This sensitivity analysis examined the significance and impact of each geometric factor on the precooling heat exchanger's total pressure loss and heat transfer rate, as well as the optimal geometry for the precooling heat exchanger that maximized the heat transfer rate and minimized the total pressure loss, meeting the flow and heat transfer requirements of the application scenario.

[0176] According to the experimental factors selected by the BBD module (i.e. Figure 5 The number of microtube radial groups, microtube spacing S, and microtube diameter d in the experimental factor level table are shown in Table 1. The number of experimental factor levels is 3, based on a 20% change in the prototype value. The number of center points is 2.

[0177] Table 1 Experimental factor level table

[0178]

[0179] The number of sample scenarios and corresponding sample characteristics for the sensitivity test were determined based on the number of experimental factor levels and the number of center points. The number of experimental scenarios (n) was defined as: n = 2s(s-1) + C, where s is the number of experimental factors and C is the number of center points. This resulted in 14 experimental scenarios. In addition, six additional single-factor sample scenarios were set, for a total of 20 experimental scenarios.

[0180] According to the hot air temperature Tt air,in =1181.72K, pressure Pt air,in =39993.64Pa, flow rate M dir=15kg / s (based on the total hot air flow of 15kg / s, the air flow in the simplified pre-cooling heat exchanger sector calculation domain is 0.0014kg / s), determine the boundary conditions of the air: the air inlet is a pressure inlet, with a given total pressure and total temperature, and the air outlet is a mass flow outlet, with a given mass flow. According to the liquid nitrogen inlet temperature Tt coo1,in =77K, mass flow rate M cool = 85.68 kg / s (based on the total liquid nitrogen flow rate of 85.68 kg / s, the liquid nitrogen flow rate in the thin sector of the pre-cooling heat exchanger is 0.008 kg / s). The boundary conditions for the liquid nitrogen were determined as follows: the liquid nitrogen inlet is a mass flow inlet with a given mass flow rate and total temperature, and the liquid nitrogen outlet is a pressure outlet with a given static pressure. The turbulence model was selected as SST k-ω. Numerical simulations were performed on 20 experimental scenarios, and 20 experimental results were obtained. Flow performance evaluation (typically using numerical methods) was performed on each sample scenario, and the corresponding pre-cooling heat exchanger flow and heat transfer characteristics were obtained. The experimental scenarios and results are shown in Table 2.

[0181] Table 2 Experimental factor sample scheme and performance evaluation results

[0182]

[0183]

[0184] The variance analysis of the test results was performed to obtain the degree and significance of the influence of each factor on the flow and heat transfer characteristics of the pre-cooling heat exchanger. The variance analysis can be based on the multivariate correlation coefficient R 2 To judge the significance of the response surface model. 2 It is an evaluation index that reflects the degree of fit of the regression equation to the data. 2 The range is between [0,1], R 2 The closer the value is to 1, the more significant the response surface model. The P value in the variance analysis table determines the significance of each factor on the total pressure loss and heat transfer performance of the precooling heat exchanger. A P value less than 0.05 indicates that the factor is significant. The significant items identified based on the P value are then combined with the F value to further determine the impact of the significant items. For the significant items, the F value is used to determine the impact of each factor on the total pressure loss and heat transfer performance of the precooling heat exchanger. The larger the F value, the greater the impact. This determines the extent of the impact of key geometric factors on the flow and heat transfer performance of the precooling heat exchanger.

[0185] Table 3 is the variance analysis table of the total pressure loss coefficient of the pre-cooling heat exchanger. As can be seen from Table 3, the P value of the fitting model is <0.0001, indicating that the fitting model is highly significant. The R 2=0.9926, indicating a good fit between the predicted and measured values ​​within the experimental range. The P values ​​for the number of microtube radial groups, microtube spacing, and microtube diameter were all <0.05, indicating they were significant factors. Based on the F values, the microtube spacing had the most significant impact on the total pressure loss within the precooler, followed by the microtube diameter, and the number of tube rows had the least impact. AC had a P value greater than 0.05, indicating it was insignificant. AB and BC had P values ​​less than 0.05, indicating they were significant. However, their F values ​​were much smaller than those for a single factor, indicating that the coupling of these two factors reduced the impact on the total pressure loss coefficient of the precooler heat exchanger.

[0186] Table 3 Variance analysis of the influence of geometric factors of precooling heat exchanger on the total pressure loss coefficient

[0187]

[0188]

[0189] Table 4 is the variance analysis table of the heat transfer rate of the pre-cooling heat exchanger. As can be seen from Table 4, the P value of the fitting model is <0.0001, indicating that the fitting model is highly significant. 2 =0.9984, indicating a good fit between the predicted and measured values ​​within the experimental range. The P values ​​for the number of radial microtube groups, microtube spacing, and microtube diameter were all <0.05, indicating they were significant factors. Based on the F values, the number of radial microtube groups had the most significant impact on the heat transfer rate within the precooler, followed by microtube diameter, and the spacing had the least. The P values ​​for AB, AC, and BC were all >0.05, indicating they were non-significant, indicating that the coupling of these two factors significantly reduced the impact on the heat transfer rate of the precooler heat exchanger.

[0190] Table 4 Variance analysis of the influence of geometric factors of precooling heat exchanger on heat transfer rate

[0191]

[0192] This allows us to determine the specific sensitivity of each geometric factor in the experimental scheme to the flow and heat transfer characteristics of the precooling heat exchanger. Sensitivity analysis methods are then used to determine recommended optimal parameter values. Based on the sensitivity of each factor, the key geometric parameters of the precooling heat exchanger are structurally optimized to form the optimal design scheme for the precooling heat exchanger. Furthermore, numerical simulation methods are used to obtain the flow and heat transfer characteristics of this optimal geometric scheme for the precooling heat exchanger. This is then compared with various sample schemes to verify its rationality. The exhaust temperature, flow rate, and corresponding total pressure loss of the hot air after cooling through the precooling heat exchanger are summarized. This completes the optimal design scheme for the precooling heat exchanger based on geometric parameter sensitivity analysis.

[0193] The optimal design for the pre-cooling heat exchanger recommended by this example based on sensitivity analysis is: 12 microtube radial groups, a microtube spacing of 2.4 mm, and a microtube diameter of 1.2 mm. These geometric parameters correspond to a total pressure loss coefficient of 0.0173 and a heat transfer rate of 1285.159 kW (corresponding to an outlet temperature of 273.84 K). This was verified using numerical calculations, with the comparison results shown in Table 5, showing an error within 5%.

[0194] Table 5 Comparison of the predicted performance and numerical simulation evaluation performance of the optimized pre-cooling heat exchanger

[0195]

[0196] Optimize the design of pre-cooling heat exchanger based on geometric parameter sensitivity analysis:

[0197] Application environment air intake conditions: pre-cooling heat exchanger hot air temperature Tt air,in =1181.72K, pre-cooling heat exchanger hot air pressure Pt air,in =39993.64Pa, air flow rate M air =15kg / s.

[0198] The optimized pre-cooling heat exchanger has an outer diameter of 900 mm, an inner diameter of 430 mm, and an axial length of 795.15 mm. It contains a total of 36,734 spiral microtubes. The entire pre-cooling heat exchanger contains 24 heat exchange units (the number of microtube radial tube groups corresponding to the fan-shaped calculation domain is 12). The number of spiral coils in the spiral heat exchange unit is 0.36, and 4 microtubes are arranged in a radial staggered pattern inside the radial tube group of each heat exchange unit. The circumferential angle range corresponding to the starting and ending positions of each spiral heat exchange unit 30 is 129.6°, as shown in Figure 2. Figure 7 As shown in the figure, the micro-tube spacing between adjacent micro-tubes in different heat exchange units is 13.4mm. The micro-tube spacing of the staggered micro-tubes in each heat exchange unit along the radial and axial directions is 2.4mm, the micro-tube diameter is 1.2mm, and the micro-tube wall thickness is 0.05mm. The optimized three-dimensional geometric structure of the pre-cooling heat exchanger is shown in the figure. Figure 6 The outlet temperature of the hot air after cooling through the pre-cooling heat exchanger is 273.84K, and the corresponding total pressure loss coefficient is 0.0173. In other words, the pre-cooling heat exchanger achieves a lower expected air outlet temperature while minimizing the relative total pressure loss.

[0199] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis, characterized in that: The specific steps include: S1: Calculate the heat load and heat exchange area based on the actual application scenario and geometric size constraints, determine the outer and inner diameters of the pre-cooling heat exchanger, and then determine the number of heat exchange units, the number of spiral coils in the heat exchange unit, the microtube spacing, and the microtube diameter; S2: Using the BBD module in the response surface methodology, a sensitivity analysis of the geometric parameters of the number of heat exchange units, microtube spacing, and microtube diameter was performed to identify the significant factors affecting the flow and heat transfer performance of the pre-cooling heat exchanger, and an optimized design scheme for the pre-cooling heat exchanger was obtained. S3, determining whether the design of the pre-cooling heat exchanger obtained in step S2 meets the geometric space size constraints and technical parameter requirements of the application scenario. If so, determining the geometric dimensions of the pre-cooling heat exchanger; if not, continuing to step S1 to adjust the parameters until the geometric space size constraints and technical parameter requirements of the application scenario are met; Under the constraints of the outer and inner diameters of the pre-cooling heat exchanger, combined with the selected number of heat exchange units, the number of spiral coils in the heat exchange units, and the number of microtube rows arranged radially in a staggered pattern inside each heat exchange unit, all heat exchange units were integrated and arranged within the overall framework of the pre-cooling heat exchanger. The geometric layout structure of the pre-cooling heat exchanger on a cross-section perpendicular to the axial direction was obtained, and the microtube spacing between adjacent microtubes of different heat exchange units on the cross-section was then obtained. Determine the specific Cartesian coordinate values ​​of each point on the spiral line: the radius of the inner circle O1 of the pre-cooling heat exchanger is a i , the outer radius of the pre-cooling heat exchanger O2 is a o , the growth rate b is calculated as: Determine the specific Cartesian coordinates x and y of each point on the spiral using the following formula: x=(a i +b·θ)cosθ y=(a i +b·θ)sinθ; Where θ is any value within the circumferential angle range of the helix [0, 2πz]; Adjust the spacing between adjacent microtubes of different heat exchange units. If the spacing between adjacent microtubes of different heat exchange units exceeds the recommended value, readjust the number of heat exchange units, the number of spiral coils of the heat exchange units, the number of microtube rows arranged in a staggered pattern inside the heat exchange units, and the spacing between microtubes until the spacing between adjacent microtubes of different heat exchange units meets the recommended value. Based on the determined number of heat exchange units, the number of spiral coils in the heat exchange units, and the number of rows of microtubes arranged in a staggered pattern inside the heat exchange units, the total number of microtubes in the pre-cooling heat exchanger on a cross-section perpendicular to the axial direction and the corresponding surface heat exchange area are obtained. Combined with the calculated heat exchange area A of the pre-cooling heat exchanger, the number of microtube rows arranged along the axial direction for each heat exchange unit of the pre-cooling heat exchanger and the total number of microtubes required to be arranged inside the pre-cooling heat exchanger are calculated, thereby obtaining the axial length of the pre-cooling heat exchanger. Inlet and outlet transition areas are reserved at the outer diameter and inner diameter of the pre-cooling heat exchanger to determine the starting position, end position and corresponding liquid collecting cavity position of different heat exchange units in the pre-cooling heat exchanger.

2. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S1.1, calculate the expected heat transfer Q based on the pre-cooling heat exchanger hot air temperature, air flow, pre-cooling heat exchanger constant pressure specific heat capacity and expected air outlet temperature air : Q air =M air Cp air (Tt air,in -Tt air,out ); Among them, M air is the air flow rate, Cp air is the constant pressure specific heat capacity of air, Tt air,in is the hot air temperature of the precooling heat exchanger, Tt air,out is the expected air outlet temperature; S1.2, calculating the outlet temperature of the coolant based on the coolant inlet temperature, coolant pressure, coolant flow rate, specific heat capacity of the coolant, and the expected heat exchange capacity obtained in step S1; S1.3, calculate the surface heat transfer coefficient h on the air side air and the surface heat transfer coefficient h on the coolant side cool ; Among them, Nu air is the Nusselt number of air, λ air is the thermal conductivity of air, d is the outer diameter of the microtube; Among them, Nu cool is the Nusselt number of the cooling medium, λ cool is the thermal conductivity of the cooling medium, d i is the inner diameter of the microtubule.

3. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 2 is characterized in that: Step S1 also includes the following steps: S1.

4. Determine the heat transfer coefficient and calculate the logarithmic mean temperature difference based on the precooling heat exchanger hot air temperature, the cooling medium temperature, the expected air outlet temperature, and the cooling medium outlet temperature: The heat transfer coefficient K is calculated as: Logarithmic mean temperature difference ΔT m The calculation formula is: ΔT1=Tt air,in -Tt cool,out ; ΔT2=Tt air,out -Tt cool,in ; Wherein, ΔT1 is the temperature difference between the air inlet and the coolant outlet, and ΔT2 is the temperature difference between the air outlet and the coolant inlet; S1.5, calculate the heat transfer area A based on the heat transfer coefficient and logarithmic mean temperature difference: S1.

6. Based on the heat exchange area, preliminarily determine the number of heat exchange units, microtube spacing, and microtube diameter.

4. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 3 is characterized in that: Step S1.2 specifically includes the following steps: S1.2.1, the cooling medium is liquid nitrogen or liquid helium, and the cooling medium inlet temperature is Tt cool,in Select the critical temperature of the cooling medium and set the cooling medium flow rate to 5-8m / s based on experience; S1.2.2, determine the specific heat capacity Cp of the cooling medium based on the cooling medium inlet temperature and cooling medium flow rate cool and cooling medium flow M cool ; S1.2.3, Expected heat transfer Q air Heat exchange rate Q with the cooling medium side cool Equal, that is, Q air =Q cool , Q cool =M cool Cp cool (Tt cool,in -Tt cool,out ), thereby determining the outlet temperature Tt of the cooling medium cool,out .

5. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 4 is characterized in that: Step S1.6 specifically includes the following steps: S1.6.

1. Determine the outer and inner diameters of the precooling heat exchanger based on the spatial geometric constraints and other technical requirements of the upstream and downstream components of the precooling heat exchanger. S1.6.2, the microtube diameter of the precooling heat exchanger microtube is selected in the range of 0.5-2.5 mm, and the wall thickness of the microtube is 1 / 20 of the microtube diameter; S1.6.

3. After selecting the micro-tube diameters of the pre-cooling heat exchanger, within the constraints of the outer and inner diameters of the pre-cooling heat exchanger, select the number of heat exchange units, the number of spiral coils z of the heat exchange unit, and the number of micro-tube rows arranged in a radially staggered pattern within each heat exchange unit. Use a plane equidistant Archimedean spiral to design the spiral geometry of the heat exchange unit within the pre-cooling heat exchanger. The selection range of z is between 0.2 and 1.

0. The starting position of each spiral heat exchange unit within the pre-cooling heat exchanger is located at The end position is located on the inner diameter circular contour line of the pre-cooling heat exchanger, and the end position is located on the outer diameter circular contour line of the pre-cooling heat exchanger. Each heat exchange unit is evenly distributed along the circumferential direction inside the pre-cooling heat exchanger, and the arc lengths between the starting positions or end positions of adjacent heat exchange units are equal; each heat exchange unit contains 4 to 6 rows of microtube structures arranged in a staggered manner along the radial direction of the pre-cooling heat exchanger. The spacing between the microtubes arranged in a staggered manner in the heat exchange unit is 1 to 1.5 times the diameter of the microtubes, and the microtube spacing is the straight-line distance between the centers of adjacent microtubes arranged in a staggered manner.

6. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 5 is characterized in that: Step S2 includes the following steps: S2.1, select the optimal number of experimental levels and center points based on the number of experimental factors selected by the BBD module, namely the number of microtube radial tube groups, microtube tube spacing, and microtube diameter; S2.2, the number of experimental factor levels is 3, and the sample plan of the experimental factor levels is determined based on the increment of 5%-20% of the prototype value, and the number of center points is selected as 2; S2.

3. Determine the number of sensitivity test scenarios and the corresponding sample characteristics based on the number of experimental factor levels and the number of center points. The number of test scenarios n is defined as: n = 2s(s-1) + C; where s is the number of experimental factors and C is the number of center points.

7. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 6 is characterized in that: Step S2 also includes the following steps: S2.

4. Perform variance analysis on the test results to determine whether the test results meet the fitting accuracy. For test results that meet the fitting accuracy, analyze the degree and significance of the impact of the test factors on the flow and heat transfer characteristics of the pre-cooling heat exchanger. S2.5, obtain recommended optimal parameter values ​​through sensitivity analysis method to form the optimal design scheme of pre-cooling heat exchanger; S2.

6. Use numerical simulation methods to obtain the flow and heat transfer characteristics of the optimal geometric scheme of the pre-cooling heat exchanger, and compare them with various experimental schemes to verify the authenticity and rationality of the optimal geometric scheme. Summarize the exhaust temperature, flow rate and corresponding total pressure loss of the hot air after cooling by the pre-cooling heat exchanger, thereby completing the optimal design scheme of the pre-cooling heat exchanger based on the sensitivity analysis of geometric parameters.

8. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 7 is characterized in that: The variance analysis described in step S2.4 was performed based on the multivariate correlation coefficient R 2 To judge the fitting accuracy of the obtained response surface model, R 2 The range is between [0,1]. When R 2 The closer it is to 1, the more significant the response surface model is, which means that the fitting accuracy is met; The significance of the experimental factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged by the P value in the variance analysis table. If the P value is less than 0.05, it means that the factor is a significant item. The degree of influence of the test factors on the total pressure loss and heat transfer effect of the pre-cooling heat exchanger is judged according to the F value in the variance analysis table. The larger the F value, the greater the degree of influence, thereby determining the degree of influence of the test factors on the flow and heat transfer performance of the pre-cooling heat exchanger.

9. The pre-cooling heat exchanger optimization design method based on geometric parameter sensitivity analysis according to claim 8 is characterized in that: Step S3 is specifically as follows: If the calculated axial length of the pre-cooling heat exchanger does not meet the spatial geometric dimension constraints of the overall structure of the pre-cooling heat exchanger, it is necessary to return to steps S1.6.2 to S1.6.3 to iteratively adjust the number of heat exchange units, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, and the microtube spacing and microtube diameter between adjacent microtubes of different heat exchange units until the total axial length meets the geometric constraints, and determine the corresponding number of heat exchange units of the pre-cooling heat exchanger, the number of spiral coils of the heat exchange unit, the microtube diameter, the microtube spacing within the heat exchange unit, the tube spacing between adjacent microtubes of different heat exchange units, the total axial length of the pre-cooling heat exchanger, and the total number of microtubes inside the heat exchange unit.

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