Optimal distance and thickness calculation method of heat conduction fin and phase change energy storage device

Abstract

The application relates to a method for calculating the optimal interval and thickness of heat-conducting fins and a phase change energy storage device, and relates to the technical field of space phase change energy storage, and can be applied to the size design of a phase change energy storage device containing heat-conducting fins. Optimal interval calculation: the height and length of the fins are known, an effective heat transfer boundary number X=2 is assumed, the optimal interval is calculated through a first calculation condition, whether the assumption is correct is deduced, if the assumption X=2 is correct, the calculation result is the optimal interval, if the assumption is not correct, an effective heat transfer boundary number X=4 is assumed, if the assumption X=4 is correct, the calculation result is the optimal interval, otherwise, X=6, the optimal interval is calculated through a third calculation condition. Optimal thickness calculation: the fin efficiency of a single fin is calculated f ; the entire ribbed surface is approximated as an array of single features, the total fin efficiency is calculated, alpha is defined as the phase change material filling ratio when there are no heat-conducting fins and when there are heat-conducting fins, and the fin thickness when alpha and the total efficiency alpha0 are the maximum value is the optimal fin thickness.

Description

Technical Field

[0001] This invention relates to the field of aerospace phase change energy storage technology, specifically to a method for calculating the optimal spacing and thickness of thermally conductive fins and a phase change energy storage device. Background Technology

[0002] With the development of aerospace technology, heat dissipation of periodic, high-heat-consumption single-unit applications has become a thorny problem frequently faced in thermal control design, and phase change energy storage devices are a better choice to solve this problem. Phase change materials are materials that can absorb or release heat when a phase change occurs, while the temperature of the material itself changes little, which is used to maintain the relative stability of the temperature of a single unit and avoid excessively high temperatures in the short term.

[0003] Because the thermal conductivity of existing phase change materials (PCMs) used in the aerospace industry is generally low, temperature uniformity is often improved by adding heat-conducting fins inside the energy storage device casing. However, the volume and mass of PCMs are usually limited during the structural design of PCMs, and increasing the volume occupied by heat-conducting fins inevitably leads to a decrease in the amount of PCM they contain. Therefore, it is necessary to rationally design the number, size, and distribution of heat-conducting fins to optimize the performance of the PCMs.

[0004] Existing phase change energy storage devices typically consist of a rectangular shell and internal heat-conducting fins, offering advantages such as large heat capacity, small size, and light weight compared to traditional energy storage devices. However, there is currently no universally applicable optimization design method for the heat-conducting fins, resulting in high design time and costs, and the simulation process lacks criteria for determining the optimal design. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for calculating the optimal thickness of thermally conductive fins for phase change energy storage devices, as well as a phase change energy storage device.

[0006] The technical solution of the present invention is as follows:

[0007] A method for calculating the optimal spacing of thermally conductive fins, wherein the thermally conductive fins are applied in a phase change energy storage device, the phase change energy storage device is a cuboid, the thermally conductive fins are rectangular cross-section straight ribs, and the thermally conductive fins and the device shell divide the phase change energy storage device into several phase change material filling units. The method is as follows:

[0008] Given the fin height and length, and assuming the effective heat transfer boundary number X = 2, calculate the optimal spacing H using the first calculation condition. r We then work backwards to determine if the assumption holds true. If the assumption that X = 2 holds true, then the calculated result is the optimal spacing H. r If the assumption is not valid, then similarly assume the effective heat transfer boundary number X = 4. If the assumption X = 4 is valid, then the calculated result is the optimal spacing H. rOtherwise, X=6, and the optimal spacing H is obtained through the third calculation condition. r .

[0009] Preferably, the method for determining the effective heat transfer boundary number X is as follows:

[0010] Let L be the distance between two opposite surfaces of a phase change material filling unit, both of which are shells or fins. When all six surface boundaries are shells or fins, the surface distances are arranged in descending order of length as L1, L2, and L3. When only four of the six surface boundaries are shells or fins, they are arranged in descending order of length as L1 and L2. When the distance is 0.7L1 > L3 and 0.7L2 > L3, X = 2; when 0.7L1 > L3 and 0.7L2 ≤ L3 or there is no L3 and 0.7L1 ≤ L2, X = 4; when 0.7L1 ≤ L3 and 0.7L2 ≤ L3, X = 6.

[0011] Preferably, in the first calculation case, the phase change material filling unit is considered to be flat, and the optimal spacing H under this case is... r It can be obtained by calculation using the following formula:

[0012]

[0013] Wherein, τ0 represents the temperature rise of the circumferential shell and fins of the phase change material filling unit to the intrinsic phase change temperature T of the phase change material. P At that moment, τ p The temperature representing the geometric center of the phase change material filling unit rises to T P At a time of -1 (°C), θ m (τ p ) indicates that the geometric center of the phase change material filling unit is at τ. p The excess temperature at time τ0, where θ0 represents the excess temperature at time τ0, and Fo is the Fourier number. a is the thermal diffusivity. λ is the thermal conductivity of the phase change material, ρ is the density of the phase change material, and C is the thermal conductivity of the phase change material. p For the specific heat capacity of phase change materials, l c For the characteristic length, l c Pick m is set to 0.4022, and n is set to 0.9188;

[0014] In the formula, μ is the first characteristic value of the geometry of the phase change material unit. Bi is the Biwo number. h is the surface heat transfer coefficient between the phase change material and the shell and fins.

[0015] Preferably, in the second calculation case, the phase change material filling unit is considered to be in the shape of a long cylinder, and the optimal spacing H is [missing information]. r It can be obtained by calculation using the following formula:

[0016]

[0017] Wherein, the feature length l c Pick Where one of L2 and L3 is the fin arrangement spacing, m is taken as 0.17, n is taken as 0.4349, and the expressions for J0(μ) and J1(μ) are as follows:

[0018] J0(μ)=0.9967+0.0354μ-0.3259μ 2 +0.0577μ 3 ,

[0019] J1(μ)=-J′0(μ).

[0020] Preferably, the third calculation case treats the phase change material filling unit as a sphere, and the optimal spacing H under this case is... r It can be obtained by calculation using the following formula:

[0021]

[0022] Wherein, the feature length l c Pick One of the values ​​L1, L2, and L3 is the fin arrangement spacing, where m is 0.0988 and n is 0.2779.

[0023] A method for calculating the optimal thickness of thermally conductive fins, wherein the optimal thickness is obtained by applying the method described above to the optimal spacing H. r The calculation yields the result, and the method specifically includes the following steps:

[0024] Calculate the rib efficiency η of a single fin. f :

[0025]

[0026] Where, λ s H is the thermal conductivity of the fin material, and h is the surface heat transfer coefficient between the phase change material and the shell and fins. L δ is the fin height. L This refers to the fin thickness;

[0027] Approximating the entire ribbed surface as an array of single features, the overall efficiency η0 of the ribbed surface is calculated:

[0028]

[0029] Define α as the phase change material filling ratio with and without thermally conductive fins:

[0030]

[0031] Calculate the fin thickness δ when αη0 is at its maximum value. L This is the optimal fin thickness.

[0032] A phase change energy storage device includes a housing and heat-conducting fins arranged inside the housing. The spacing of the heat-conducting fins is calculated according to the above-described method for calculating the optimal spacing of heat-conducting fins, and the thickness of the heat-conducting fins is calculated according to the above-described method for calculating the optimal thickness of heat-conducting fins.

[0033] Preferably, the height of the heat-conducting fins is 0.5 mm to 1 mm smaller than the internal height of the phase change energy storage device's casing.

[0034] Compared with existing technologies, this invention fills the gap in a universal optimization design method for heat-conducting fins, and its specific beneficial effects are as follows:

[0035] This invention calculates the arrangement parameters of rectangular cross-section straight-ribbed fins within an outer shell of arbitrary size, finding the optimal balance between the device's thermal conductivity and the amount of phase change material filling. This avoids blind spots in the design of phase change energy storage device dimensions and saves significant time compared to 3D simulation analysis. Under the premise that the overall thermal conductivity of the phase change energy storage device meets expectations, it maximizes the amount of phase change working fluid filling. In addition, this calculation method is based on the smallest repeatable unit within the shell, retaining the possibility of manual calculation and ensuring flexibility in the actual arrangement of the fins.

[0036] This invention is applied to the size design of phase change energy storage devices with thermally conductive fins, which can optimize the shell design of phase change energy storage devices, improve the heat storage performance of the devices, and provide the best solution for the arrangement of thermally conductive fins. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the process for calculating the optimal thickness of the thermally conductive fins according to the present invention;

[0038] Figure 2 This is a schematic diagram of one fin arrangement in the phase change energy storage device of the present invention;

[0039] Figure 3 This is a schematic diagram of the fin arrangement described in Example 10;

[0040] Figure 4 This is a schematic diagram of the cross-sectional structure of the fins described in Example 10. Detailed Implementation

[0041] To make the technical solutions of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that the following embodiments are only used to better understand the technical solutions of the present invention and should not be construed as limiting the present invention.

[0042] Example 1.

[0043] This embodiment provides a method for calculating the optimal spacing of heat-conducting fins, such as... Figure 1 As shown, the heat-conducting fins are used in a phase change energy storage device. The phase change energy storage device is a cuboid, and the heat-conducting fins are rectangular cross-section straight ribs. The heat-conducting fins and the device shell divide the phase change energy storage device into several phase change material filling units, such as... Figure 2 As shown.

[0044] The method is as follows:

[0045] Given the fin height and length, and assuming the effective heat transfer boundary number X = 2, calculate the optimal spacing H using the first calculation condition. r We then work backwards to determine if the assumption holds true. If the assumption that X = 2 holds true, then the calculated result is the optimal spacing H. r If the assumption is not valid, then similarly assume the effective heat transfer boundary number X = 4. If the assumption X = 4 is valid, then the calculated result is the optimal spacing H. r Otherwise, X=6, and the optimal spacing H is obtained through the third calculation condition. r .

[0046] A method for calculating the optimal thickness of thermally conductive fins for a phase change energy storage device, such as... Figure 1 As shown, the phase change energy storage device is a cuboid, and the heat-conducting fins are rectangular cross-section straight ribs. The heat-conducting fins and the device shell divide the phase change energy storage device into several phase change material filling units, such as... Figure 2 As shown.

[0047] This embodiment describes a method for calculating the spacing of heat-conducting fins in a phase change energy storage device. The calculation object is a phase change energy storage device with a rectangular outer shell and rectangular cross-section straight ribs for internal heat-conducting fins. Under the premise that the outer shell size envelope, the type of phase change material, and the fin arrangement are basically determined, the fin arrangement spacing and fin thickness are calculated.

[0048] Specifically, the shell size and phase change material type are jointly determined by factors such as single-unit heat consumption, size constraints, mass constraints, and target temperature control. The fin arrangement is determined by factors such as manufacturing process and cost. The fin spacing is determined by the temperature transfer rate of the smallest phase change material filling unit. The phase change material filling unit is an imaginary cube approximately divided by the shell and fins, with the length of each side corresponding to the fin height H. L fin length and the fin arrangement spacing H r The fin height is determined by the internal height of the shell, and is usually 0.5 to 1 mm smaller than the internal height of the shell. The fin length is determined by the internal length of the shell and the fin arrangement.

[0049] The temperature transfer rate is described as follows: Assuming the initial temperatures of the shell, fins, and phase change material are all T0, and the intrinsic phase change temperature of the phase change material is T... P After the high-power single unit generates heat, the temperature of the circumferential shell and fins of the smallest filling unit rises to T. P Let the time be τ0. Since the thermal conductivity of the phase change material is usually much lower than that of the shell and fins, assuming that the temperature of the phase change material is still T0 at τ0, the temperature at the geometric center of the phase change material rises to T. P The time when -1 (°C) is τ p The time required for this process is τ p The smaller τ0 is, the faster the temperature transfer rate. In engineering applications, τ p -τ0 must be less than a certain fixed value Φ p The fin arrangement spacing H r The selection principle is: in τ p -τ0 is less than Φ p Under the constraints, the maximum value of L3 is taken, which is the optimal fin arrangement spacing; the temperature value T0 should be the stable temperature before the instantaneous high heat consumption mode of the heating unit is turned on.

[0050] Example 2.

[0051] This embodiment is a further example of Embodiment 1. The method for determining the effective heat transfer boundary number X is as follows:

[0052] Let L be the distance between two opposite surfaces of a phase change material filling unit, both of which are shells or fins. When all six surface boundaries are shells or fins, the surface distances are arranged in descending order of length as L1, L2, and L3. When only four of the six surface boundaries are shells or fins, they are arranged in descending order of length as L1 and L2. When the distance is 0.7L1 > L3 and 0.7L2 > L3, X = 2; when 0.7L1 > L3 and 0.7L2 ≤ L3 or there is no L3 and 0.7L1 ≤ L2, X = 4; when 0.7L1 ≤ L3 and 0.7L2 ≤ L3, X = 6.

[0053] Example 3.

[0054] This embodiment is a further example of Embodiment 1. In the first calculation case, the phase change material filling unit is considered to be flat. Under this case, the optimal spacing H is... r It can be obtained by calculation using the following formula:

[0055]

[0056] Wherein, τ0 represents the temperature rise of the circumferential shell and fins of the phase change material filling unit to the intrinsic phase change temperature T of the phase change material. P At that moment, τ pThe temperature representing the geometric center of the phase change material filling unit rises to T P At a time of -1 (°C), θ m (τ p ) indicates that the geometric center of the phase change material filling unit is at τ. p The excess temperature at time τ0, where θ0 represents the excess temperature at time τ0, and Fo is the Fourier number. a is the thermal diffusivity. λ is the thermal conductivity of the phase change material, ρ is the density of the phase change material, and C is the thermal conductivity of the phase change material. p For the specific heat capacity of phase change materials, l c For the characteristic length, l c Pick m is set to 0.4022, and n is set to 0.9188;

[0057] In the formula, μ is the first characteristic value of the geometry of the phase change material unit. Bi is the Biwo number. h is the surface heat transfer coefficient between the phase change material and the shell and fins.

[0058] Example 4.

[0059] This embodiment is a further example of Embodiment 1. In the second calculation case, the phase change material filling unit is considered to be a long cylindrical shape. Under this case, the optimal spacing H is... r It can be obtained by calculation using the following formula:

[0060]

[0061] Wherein, the feature length l c Pick Where one of L2 and L3 is the fin arrangement spacing, m is taken as 0.17, n is taken as 0.4349, and the expressions for J0(μ) and J1(μ) are as follows:

[0062] J0(μ)=0.9967+0.0354μ-0.3259μ 2 +0.0577μ 3 ,

[0063] J1(μ)=-J′0(μ).

[0064] Example 5.

[0065] This embodiment is a further example of Embodiment 1. The third calculation case treats the phase change material filling unit as a sphere. Under this case, the optimal spacing H r It can be obtained by calculation using the following formula:

[0066]

[0067] Wherein, the feature length lc Pick One of the values ​​L1, L2, and L3 is the fin arrangement spacing, where m is 0.0988 and n is 0.2779.

[0068] Example 6.

[0069] This embodiment provides a method for calculating the optimal thickness of thermally conductive fins, wherein the optimal thickness is obtained by applying the optimal spacing H obtained by the method described in any one of embodiments 1-5. r The calculation yields the result, and the method specifically includes the following steps:

[0070] Calculate the rib efficiency η of a single fin. f :

[0071]

[0072] Where, λ s H is the thermal conductivity of the fin material, and h is the surface heat transfer coefficient between the phase change material and the shell and fins. L δ is the fin height. L This refers to the fin thickness;

[0073] Approximating the entire ribbed surface as an array of single features, the overall efficiency η0 of the ribbed surface is calculated:

[0074]

[0075] Define α as the phase change material filling ratio with and without thermally conductive fins:

[0076]

[0077] Calculate the fin thickness δ when αη0 is at its maximum value. L This is the optimal fin thickness.

[0078] Example 7.

[0079] This embodiment provides a phase change energy storage device, which includes a shell and heat-conducting fins arranged inside the shell. The arrangement spacing of the heat-conducting fins is calculated according to the optimal heat-conducting fin spacing calculation method as described in any one of Embodiments 1-5, and the thickness of the heat-conducting fins is calculated according to the optimal heat-conducting fin thickness calculation method as described in Embodiment 6.

[0080] Example 8.

[0081] This embodiment is a further example of embodiment 7, wherein the height of the heat-conducting fins is 0.5mm to 1mm smaller than the internal height of the phase change energy storage device's casing.

[0082] Example 9.

[0083] To verify the correctness of the general calculation method for the thermal fin structure dimensions of phase change energy storage devices, this embodiment uses a phase change energy storage device used for satellite heating units as a model for calculation.

[0084] The phase change material used in this device is n-octadecane, and both the shell and fins are made of aluminum alloy. The fin arrangement is as follows: Figure 3 As shown, the outer envelope dimensions of the device are 90mm*45mm*10mm, and the fin height H is... L The fins are 7mm thick and 82mm long. The stable temperature T0 before the single-unit instantaneous high power consumption mode is activated is 18℃, and the inherent phase transition temperature of the phase change material is T. P The temperature is 28℃.

[0085] Default fin spacing H r If it is L3, then the fin height H L The length of fin L2 is L1, and 0.7L1>L3 and 0.7L2>L3 are satisfied. The effective heat transfer boundary number is X=2.

[0086] τ p The temperature at the geometric center of the phase change material rises to T P At a time of -1 (°C), the excess temperature θ m (τ p The excess temperature θ0 is 10℃, and Φ is 1℃. p The time interval is 60 seconds; the thermal conductivity λ of the phase change material is 0.1507 W / m·K, and the density ρ of the phase change material is 814 kg / m³. 3 (Solid state), specific heat capacity C of phase change material p If the thermal diffusivity is 2160 J / kg·K, then the thermal diffusivity α is 8.57 × 10⁻⁶. 8 m 2 / s; The surface heat transfer coefficient h between the phase change material and the shell and fins is taken as 1000 W / m. 2 ·K.

[0087] The fin arrangement spacing H is derived based on the following formula (calculation condition 1). r The feature length is H. r Half of the time, with time τ taking its maximum value of 60s:

[0088]

[0089]

[0090]

[0091]

[0092] The optimal fin spacing H can be calculated. rThe thickness is 4.84 mm, which, after verification, meets the judgment condition of calculation condition 1, and the fin thickness δ can be further calculated. L The calculation.

[0093] Thermal conductivity λ of fin material s Given 121 W / m·K, calculate the fin thickness δ when αη0 reaches its maximum value. L :

[0094]

[0095]

[0096]

[0097] The optimal fin thickness δ can be calculated. L It is 7.8mm.

[0098] The amount of phase change material was checked and verified to meet the design requirements.

Claims

1. A method for calculating the optimal spacing of thermally conductive fins, wherein the thermally conductive fins are applied in a phase change energy storage device, the phase change energy storage device is a cuboid, the thermally conductive fins are rectangular cross-section straight ribs, and the thermally conductive fins and the device shell divide the phase change energy storage device into several phase change material filling units, characterized in that... The method is as follows: Given the fin height and length, and assuming the effective heat transfer boundary number X=2, calculate the optimal spacing using the first calculation condition. We then work backwards to determine if the assumption holds true. If the assumption that X=2 holds true, then the calculated result is the optimal spacing. If the assumption is not valid, then similarly assume the effective heat transfer boundary number X=4, and calculate the optimal spacing using the second calculation condition. We then work backwards to determine if the assumption holds true. If the assumption that X=4 holds true, then the calculated result is the optimal spacing. Otherwise, X=6, and the optimal spacing is obtained through the third calculation condition. ; The method for determining the effective heat transfer boundary number X is as follows: Let L be the distance between two opposite surfaces of a phase change material filling unit, both of which are shells or fins. When all six surface boundaries are shells or fins, the surface distances are arranged in descending order of length as follows: , and When only 4 out of the 6 surface boundaries are shells and fins, they are arranged in descending order of length as follows: and When the spacing is 0.7 > And 0.7 > When x=2, x=2; when x=0.7 > And 0.7 ≤ or none And 0.7 ≤ When x=4, x=4; when x=0.7 ≤ And 0.7 ≤ At that time, X=6; The first calculation case treats the phase change material filling unit as a flat plate shape, and the optimal spacing under this case is... It can be obtained by calculation using the following formula: ， in, This represents the temperature of the circumferential shell and fins of the phase change material filling unit rising to the intrinsic phase change temperature of the phase change material. At that moment, The temperature representing the geometric center of the phase change material filling unit rises to At the time of (°C), The geometric center of the phase change material filling unit is indicated at Excess temperature at any moment express Excess temperature at any moment For Fourier numbers, , For thermal diffusivity, λ is the thermal conductivity of the phase change material. For the density of phase change materials, This refers to the specific heat capacity of the phase change material. For characteristic length, Pick , Take 0.4022, Take 0.9188; In the formula The first eigenvalue of the geometry of the phase change material unit is . , For Biwo number, , It represents the surface heat transfer coefficient between the phase change material and the shell and fins.

2. The method for calculating the optimal spacing of heat-conducting fins according to claim 1, characterized in that, The second calculation case treats the phase change material filling unit as a long cylindrical shape, and the optimal spacing under this case is... It can be obtained by calculation using the following formula: ， Among them, the feature length Pick ,in , One of the values ​​is the fin arrangement spacing. Take 0.17, Take 0.4349, and The expression is as follows: ， 。 3. The method for calculating the optimal spacing of heat-conducting fins according to claim 1, characterized in that, The third calculation case treats the phase change material filling unit as a sphere, under which the optimal spacing is... It can be obtained by calculation using the following formula: ， Among them, the feature length Pick , , , One of the values ​​is the fin arrangement spacing. Take 0.0988, Take 0.2779.

4. A method for calculating the optimal thickness of thermally conductive fins, characterized in that, The optimal thickness is obtained by using the optimal spacing obtained by the method described in any one of claims 1-3. The calculation yields the result, and the method specifically includes the following steps: Calculate the rib efficiency of a single fin. : ， in, The thermal conductivity of the fin material, The heat transfer coefficient between the phase change material and the shell and fins. The height of the fin. This refers to the fin thickness; Approximate the entire ribbed surface as an array of single features and calculate the overall efficiency of the rib surface. : ； definition The phase change material filling ratio is shown for the case with and without thermally conductive fins: ； calculate Fin thickness at its maximum value This is the optimal thickness of the heat-conducting fins.

5. A phase change energy storage device, characterized in that, The phase change energy storage device includes a shell and heat-conducting fins arranged inside the shell. The spacing of the heat-conducting fins is calculated according to the optimal spacing calculation method for heat-conducting fins as described in any one of claims 1-3, and the thickness of the heat-conducting fins is calculated according to the optimal thickness calculation method for heat-conducting fins as described in claim 4.

6. The phase change energy storage device according to claim 5, characterized in that, The height of the heat-conducting fins is 0.5mm to 1mm smaller than the internal height of the phase change energy storage device's casing.

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