Arc-line-based design method and system for special-shaped microchannel heat exchange tubes

Abstract

The present invention discloses a method for designing a special-shaped microchannel heat exchange tube based on an arc line, comprising: taking point A (R A ,0) as the intersection of the center arc line of the heat exchange tube and the inner diameter of the heat exchanger, point B (R B ,θ B ) is the intersection of the center arc line of the heat exchange tube and the outer diameter of the heat exchanger, R A is the inner diameter of the heat exchanger, R B is the outer diameter of the heat exchanger, θ B is the polar angle of point B; determine the maximum arc length of the center arc of the heat exchange tube and the maximum number of heat exchange tubes that can be arranged; calculate the effective air flow area and total heat exchange area in the cross section of the heat exchanger; use R A ,θ B To control parameters, optimization is performed with the goal of ensuring that the effective air flow area meets preset conditions and the total heat exchange area is maximized, resulting in the optimal linear design for the central arc of the heat exchange tube. This invention, applied to heat exchanger design, uses an arc as the basic linear shape for a single heat exchange tube. Given the basic heat exchanger configuration and flow loss requirements, the design goal of maximizing the total heat exchange area within the heat exchanger is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of heat exchanger design, in particular to a method and system for designing a special-shaped microchannel heat exchange tube based on an arc line. Background Art

[0002] At present, there are few public reports on the design of the tube structure of air precoolers in the field of aerospace propulsion. In industry, the structural design of special-shaped spiral tube heat exchangers is mainly based on the heat exchange requirements, and the heat exchange tube length and shell-side heat exchange area are designed. The specific design is mainly based on the pitch, curvature, cross-sectional shape, heat exchange tube arrangement (such as staggered or straight), tube spacing, etc. of the spiral tube, and there is a lack of optimized design for the heat exchange tube line type. Although patent CN113505502A discloses a special-shaped microchannel heat exchange tube design method, it is mainly aimed at Archimedean spiral heat exchange tubes, and the heat exchanger based on the Archimedean spiral has a triple cycle in the design calculation, a large amount of calculation, and is prone to deviations in the actual processing process. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention provides a method and system for designing special-shaped microchannel heat exchange tubes based on arc lines. The method and system are mainly used for designing special-shaped heat exchange tubes for pre-cooling turbine engines or combined engine air pre-coolers. The arc is used as the basic line shape of a single heat exchange tube. Under the premise of knowing the basic configuration of the heat exchanger and the flow loss requirements, the design goal of maximizing the total heat exchange area in the heat exchanger is achieved.

[0004] To achieve the above object, the present invention provides a method for designing a special-shaped microchannel heat exchange tube based on an arc line, comprising the following steps:

[0005] Take the polar coordinate point A(R A , 0) as the intersection of the center arc line of the heat exchange tube and the inner diameter of the heat exchanger, and the polar coordinate point B (R B ,θ B ) is the intersection of the center arc line of the heat exchange tube and the outer diameter of the heat exchanger, where R A is the inner diameter of the heat exchanger, R B is the outer diameter of the heat exchanger, θ B is the polar angle of point B;

[0006] Based on the polar coordinate point A(R A ,0) and the polar coordinate point B(R B ,θ B ) Determine the maximum arc length of the center arc of the heat exchange tube Based on the inner diameter R of the heat exchanger A Determine the maximum number n of heat exchange tubes that can be arranged in the heat exchanger;

[0007] Calculate the effective air flow area A in the cross section of the heat exchanger when the number of heat exchange tubes is n air And the total heat exchange area S of n heat exchange tubes;

[0008] The inner diameter R of the heat exchanger A , polar angle θ B As the control parameter, the effective air flow area A air The optimization is performed with the goal of satisfying the preset conditions and maximizing the total heat exchange area S, and the optimal linear design of the central arc line of the heat exchange tube is obtained.

[0009] In one embodiment, the maximum arc length of the central arc line of the heat exchange tube is The determination process is:

[0010]

[0011]

[0012] Where AB is the length of the line segment between point A and point B, and 2α0 is the maximum arc length. The central angle of a circle.

[0013] In one embodiment, the maximum number of heat exchange tubes that can be arranged in the heat exchanger is determined by:

[0014]

[0015] Where, d i is the inner diameter of the heat exchange tube, δ is the wall thickness of the heat exchange tube, and the symbol Indicates rounding down.

[0016] In one embodiment, the effective air circulation area A air The determination process is:

[0017] A air =AA tube

[0018] in,

[0019]

[0020] Where A is the cross-sectional area of the heat exchanger, A tube is the area occupied by n heat exchange tubes in the cross section of the heat exchanger, d i is the inner diameter of the heat exchange tube, and δ is the wall thickness of the heat exchange tube.

[0021] In one embodiment, the total heat exchange area S is:

[0022]

[0023] In one embodiment, the effective air circulation area A air The preset conditions are met, specifically:

[0024]

[0025] Where A is the cross-sectional area of the heat exchanger, and σ% is the minimum effective air flow area ratio.

[0026] In one embodiment, during the optimization process, the inner diameter R A and polar angle θ B The search space is: R A ∈(0, R B ),θ B ∈[0,π].

[0027] To achieve the above objectives, the present invention further provides a circular arc-based special-shaped microchannel heat exchange tube design system, comprising:

[0028] Memory, used to store programs;

[0029] A processor is used to execute the program stored in the memory. When the program is executed, the processor is used to execute part or all of the steps of the above-mentioned method for designing a special-shaped microchannel heat exchange tube based on an arc line.

[0030] Compared with the prior art, the present invention has the following beneficial technical effects:

[0031] Choosing a circular arc as the basic line type reduces the parameter space dimension from three dimensions to two dimensions compared to the Archimedean spiral, resulting in fewer cycles and significantly reduced single calculation time. Furthermore, considering the inherent characteristics of the line type, the curvature of the Archimedean spiral varies at every point, while the curvature of the circular arc is constant. Using a circular arc can reduce the difficulty of the actual processing process, facilitate low-cost mass production, and reduce the relative deviation between the actual and theoretical curves, thereby achieving a better enhanced heat transfer effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0033] Figure 1 A flow chart of a design method according to an embodiment of the present invention;

[0034] Figure 2Schematic diagram of the basic working principle of the heat exchanger in an embodiment of the present invention;

[0035] Figure 3 Calculate the arc in the embodiment of the present invention Auxiliary diagram of arc length;

[0036] Figure 4 Schematic diagram of determining the value range of the semi-circular central angle α in an embodiment of the present invention;

[0037] Figure 5 is a graph showing the change of function f(α) with α in an embodiment of the present invention;

[0038] Figure 6 In the embodiment of the present invention, d is taken i =0.8mm, δ=0.3mm, R B Schematic diagram of the optimal heat exchange tube layout obtained when σ% = 80 mm and σ% = 0.7, where: (a) is a single tube diagram and (b) is an n-tube diagram.

[0039] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the 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.

[0041] It should be noted that all directional indications (such as up, down, left, right, front, and back) in the embodiments of the present invention are intended only to explain the relative positions and movements of various components in a specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indications will also change accordingly. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0042] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0043] This embodiment discloses a method for designing special-shaped microchannel heat exchange tubes based on circular arcs. This method is primarily used for designing special-shaped heat exchange tubes for precooling turbine engines or combined engine air precoolers. This design method uses a circular arc as the basic linear shape for a single heat exchange tube. Given the basic heat exchanger configuration and flow loss requirements, this method aims to maximize the total heat exchange area within the heat exchanger.

[0044] To facilitate subsequent calculations, this embodiment makes the following assumptions:

[0045] The axial length of the heat exchanger is set as unit length, and only the arrangement of the heat exchange tubes within the cross section of the heat exchanger is considered;

[0046] Taking the arc as the basic line shape of a single heat exchange tube, it is necessary to subsequently determine the radius r of the circle corresponding to the arc and the central angle 2α corresponding to the arc.

[0047] refer to Figure 1 The method for designing a special-shaped microchannel heat exchange tube in this embodiment specifically includes the following steps:

[0048] Step 1: Take the polar coordinate point A(R A , 0) as the intersection of the center arc line of the heat exchange tube and the inner diameter of the heat exchanger, and the polar coordinate point B (R B ,θ B ) is the intersection of the center arc line of the heat exchange tube and the outer diameter of the heat exchanger. A is the inner diameter of the heat exchanger, R B is the outer diameter of the heat exchanger, θ B is the polar angle of point B, specifically:

[0049] refer to Figure 2 This is a schematic diagram of the basic working principle of the heat exchanger. The coolant flows in from the outside of the heat exchanger, flows through the heat exchange tube, and finally flows into the liquid collecting cavity inside the heat exchanger. Therefore, in this embodiment, the intersection of the center arc line of the heat exchange tube and the inner and outer diameters of the heat exchanger are set as A(R A ,0)、B(R B ,θ B ), which is convenient for subsequent optimization calculations.

[0050] Step 2, based on the polar coordinate point A(R A ,0) and the polar coordinate point B(R B ,θ B ) Determine the maximum arc length of the center arc of the heat exchange tube Based on the inner diameter R of the heat exchanger A Determine the maximum number n of heat exchange tubes that can be arranged in the heat exchanger.

[0051] In this embodiment, the maximum arc length of the central arc line of the heat exchange tube is The determination process is:

[0052] refer to Figure 3 This is a schematic diagram of the auxiliary lines involved in the configuration of a single heat exchange tube in the heat exchanger. Assume that the polar coordinate point A(R A ,0) and the polar coordinate point B(R B ,θ B ) has been determined. Connect points A and B to form a line segment AB. Draw the perpendicular bisector l1 of line segment AB. Then the center of the arc passing through points A and B must be on the perpendicular bisector l1. Let the center of the arc be point C, and O be the coordinate origin.

[0053] Set arc The radius is r, the central angle is 2α, then the arc The arc length is:

[0054]

[0055] Since the coordinates of points A and B are known, the length of line segment AB can be calculated as follows:

[0056]

[0057] Depend on Figure 3 It can be seen that there is the following corresponding relationship between line segment AB, radius r, and central angle 2α:

[0058] AB=2r sinα:

[0059] Substituting into the arc length calculation formula, we have:

[0060]

[0061] To ensure There are only two intersection points, A and B, with the inner and outer diameters of the heat exchanger. The value range of α needs to be further limited. The process is as follows:

[0062] refer to Figure 4 , connect points O and B, and the line segment OB intersects the perpendicular bisector l1 at a point C0. Draw a tangent l2 to the outer circle through point B, then OB⊥l2, and similarly, C0B⊥l2;

[0063] Draw a circle with C0 as the center and C0B as the radius, and connect the two points AB on the circle to form an arc At this time, the arc There are only two intersection points with the outer circle of the heat exchanger, and the corresponding semi-circle central angle α0 is the upper limit of α, so:

[0064] 2r0sinα0=AB

[0065] In triangle AOC0, the cosine theorem gives

[0066]

[0067] The radius r0 and the semi-circle center angle α0 can be obtained by simultaneous solution as follows:

[0068]

[0069] Therefore, the arc The arc length calculation formula can be further standardized as:

[0070]

[0071] in,

[0072]

[0073] Figure 5 Given a function The curve of the change of α is given by Figure 5 It can be seen that in In the range of , the function f(α) is a monotonically increasing curve. The calculation formula of the function f(α) differs only by a coefficient AB, and the basic change trends of the two are the same, that is, the arc length The value of is proportional to α. Therefore, the arc length The maximum value will be achieved at α0 Right now:

[0074]

[0075] in,

[0076]

[0077] Where R A 、R B and θ B All are known quantities.

[0078] In order to maximize the heat exchange area, as many heat exchange tubes as possible should be arranged in the heat exchanger, and the number of heat exchange tubes is affected by the inner diameter R of the heat exchanger. A Under the premise of a given inner diameter of the heat exchanger, the maximum number of heat exchange tubes n can be:

[0079]

[0080] Where, d i is the inner diameter of a single heat exchange tube, δ is the wall thickness of a single heat exchange tube, and the symbol Indicates rounding down.

[0081] Step 3: Calculate the effective air flow area A in the cross section of the heat exchanger when the number of heat exchange tubes is n. air And the total heat exchange area S of n heat exchange tubes, the specific implementation process is:

[0082] In the cross section of the heat exchanger, the effective air flow area A air The cross-sectional area A of the heat exchanger minus the total area A of the n heat exchange tubes tube ,Right now:

[0083] A air =AA tube

[0084] in,

[0085]

[0086] Since heat exchange occurs between the coolant and the air on both sides of a single heat exchange tube, the equivalent total heat exchange area S after arranging n heat exchange tubes in a heat exchanger of unit axial length can be calculated by the following formula:

[0087]

[0088] Step 4: Take the inner diameter R of the heat exchanger A , polar angle θ B As the control parameter, the effective air flow area A air The optimal linear design of the central arc line of the heat exchange tube is obtained by optimizing the preset conditions and maximizing the total heat exchange area S, where the effective air flow area A is air The preset conditions are met, specifically:

[0089]

[0090] Where A is the cross-sectional area of the heat exchanger, and σ% is the minimum effective air flow area ratio.

[0091] During the optimization process, the inner diameter R A and polar angle θ B The search space is: R A ∈(0, R B ),θ B ∈[0,π]. A ∈(0, R B ) represents the inner diameter R of the heat exchanger A The upper limit of the value cannot be greater than the outer diameter R of the heat exchanger B Polar angle θ BThe actual value range of is [0, 2π], which can be divided into two intervals: [0, π] and [π, 2π]. Any arc L1 drawn in one interval can be used to obtain an arc L2 with the same radius and central angle as the arc L1 in another interval by using a method of symmetry about the y-axis, and the center coordinates of L1 and L2 are symmetric about the y-axis. Therefore, to simplify the calculation, one of the two intervals [0, π] and [π, 2π] is taken as the search area, that is, θ B ∈[0,π].

[0092] In the specific optimization calculation, the inner diameter R of the heat exchanger can be A and polar angle θ B Take m discrete points in the search space to form a two-dimensional parameter space with m×m points. Subsequently, the optimal parameter combination that meets the minimum air circulation area requirement will be searched in this two-dimensional parameter space. Of course, in the specific implementation process, the same principle of bisection can also be used to continuously reduce the inner diameter R of the heat exchanger during the optimization process. A and polar angle θ B The search space is narrowed down each time, and m discrete points are taken again to form a two-dimensional parameter space with m×m points for parameter search. This process is repeated until a parameter combination that meets the design accuracy requirements is obtained. You can also directly use the optimization algorithm to search in the search space (0, R B ), [0, π] search to get the optimal heat exchanger inner diameter R A and polar angle θ B parameter combination.

[0093] The arc-line-based special-shaped microchannel heat exchange tube design method in this embodiment will be further described below with reference to specific examples.

[0094] Given input parameter d i =0.8mm, δ=0.3mm, R B =80mm, σ%=0.7, calculate according to the process of steps 1-4, and obtain the optimal tube layout design results as shown in Table 1 and Figure 6 shown.

[0095] Table 1

[0096]

[0097] According to Table 1 and Figure 6 It can be seen that the optimal tube layout designed by this invention, when applied to a precooler, can maximize the heat exchange area. Since the amount of heat exchanged between the fluids on both sides is proportional to the heat exchange area, a larger heat exchange area means the coolant absorbs more heat from the air to be cooled, and the precooler's heat exchange efficiency improves.

[0098] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made by using the contents of the present invention description and drawings under the inventive concept of the present invention, or direct / indirect application in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A method for designing a special-shaped microchannel heat exchange tube based on an arc line, characterized in that: The steps include: Take the polar coordinate point A(R A ,0) as the intersection of the center arc line of the heat exchange tube and the inner diameter of the heat exchanger, and the polar coordinate point B(R B ,θ B ) is the intersection of the center arc line of the heat exchange tube and the outer diameter of the heat exchanger, where R A is the inner diameter of the heat exchanger, R B is the outer diameter of the heat exchanger, θ B is the polar angle of point B; Based on the polar coordinate point A(R A ,0) and the polar coordinate point B(R B ,θ B ) Determine the maximum arc length of the center arc of the heat exchange tube Based on the inner diameter R of the heat exchanger A Determine the maximum number n of heat exchange tubes that can be arranged in the heat exchanger; Calculate the effective air flow area A in the cross section of the heat exchanger when the number of heat exchange tubes is n air And the total heat exchange area S of n heat exchange tubes; The inner diameter R of the heat exchanger A , polar angle θ B As the control parameter, the effective air flow area A air The optimization is performed with the goal of satisfying the preset conditions and maximizing the total heat exchange area S, and the optimal linear design of the central arc line of the heat exchange tube is obtained.

2. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1, characterized in that: The maximum arc length of the central arc line of the heat exchange tube The determination process is: Where AB is the length of the line segment between point A and point B, and 2α0 is the maximum arc length. The central angle of a circle.

3. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1 or 2, characterized in that: The process for determining the maximum number of heat exchange tubes that can be arranged in a heat exchanger is as follows: Where, d i is the inner diameter of the heat exchange tube, δ is the wall thickness of the heat exchange tube, and the symbol Indicates rounding down.

4. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1 or 2, characterized in that: The effective air circulation area A air The determination process is: A air =A-A tube in, Where A is the cross-sectional area of the heat exchanger, A tube is the area occupied by n heat exchange tubes in the cross section of the heat exchanger, d i is the inner diameter of the heat exchange tube, and δ is the wall thickness of the heat exchange tube.

5. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1 or 2, characterized in that: The total heat exchange area S is:

6. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1 or 2, characterized in that: The effective air circulation area A air The preset conditions are met, specifically: Where A is the cross-sectional area of the heat exchanger, and σ% is the minimum effective air flow area ratio.

7. The arc-line-based special-shaped microchannel heat exchange tube design method according to claim 1 or 2, characterized in that: During the optimization process, the inner diameter R A and polar angle θ B The search space is: R A ∈(0,R B ),θ B ∈[0,π].

8. A special-shaped microchannel heat exchange tube design system based on arc lines, characterized in that: include: Memory, used to store programs; A processor is used to execute the program stored in the memory. When the program is executed, the processor is used to execute the arc-line-based special-shaped microchannel heat exchange tube design method as described in any one of claims 1 to 7.

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