Method for calculating convective heat transfer coefficient of pipe flow based on discrete data
By using a discrete data-based approach, the law of conservation of energy and mean filtering method, the problems of large data volume and slow convergence in the calculation of convective heat transfer coefficient in pipeline flow are solved, achieving efficient and accurate calculation results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGZHOU UNIV
- Filing Date
- 2022-10-26
- Publication Date
- 2026-06-26
AI Technical Summary
Existing technologies for calculating the convective heat transfer coefficient of pipe flow involve large amounts of data and slow convergence, resulting in high computational costs and difficulty in meeting the accuracy requirements of thermal analysis.
A computational method based on discrete data is adopted. By obtaining a particular solution of the fully developed flow energy equation, the region is uniformly discretized, and a smooth curve is obtained by using the mean filtering method, which reduces the number of data points and improves the computational accuracy and speed.
It reduces computational costs, improves computational accuracy, reduces the number of data points, achieves rapid convergence, and is suitable for calculating convective heat transfer coefficients under different pipe shapes and temperature conditions.
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Figure CN115659864B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of heat pipe technology, and more specifically, relates to a method for calculating the convection heat transfer coefficient of pipe flow based on discrete data. Background Technology
[0002] The research objectives in the field of heat pipe technology are twofold: firstly, to fully utilize low-grade energy sources and conserve energy; and secondly, to improve the accuracy and reliability of calculations, enabling the development of economical and safe operating schemes for heat exchange equipment such as geothermal heat pumps and hot oil pipelines, thereby reducing their manufacturing, maintenance, and operating costs. Currently, thermal analysis processes typically apply the fluid temperature and the corresponding convective heat transfer coefficient as boundary conditions to the finite element model based on Newton's law of cooling. Accurate calculation of the convective heat transfer coefficient is crucial for equipment thermal analysis, and developing methods for calculating this coefficient has significant practical and theoretical value in the field of heat pipe technology.
[0003] For calculating the convective heat transfer coefficient in pipe flow, if the boundary conditions are isothermal or constant heat flux, it can be obtained through empirical formulas. However, for arbitrary temperature conditions, traditional methods can be used, which first require obtaining the pipe wall temperature gradient and the average temperature of the corresponding pipe cross-section, and then substituting them into theoretical formulas for calculation. Typically, the convective heat transfer coefficient is influenced by many factors, and the pipe wall temperature gradient is large, resulting in a large number of meshes required for calculation, slow convergence of the computational model, and difficulty in solving the problem. Therefore, it is still necessary to develop new mathematical calculation methods to improve the speed and accuracy of the calculation. Summary of the Invention
[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the convective heat transfer coefficient of pipeline flow, which can reduce the number of data points required and save calculation costs, and solve the problems of large data volume and slow calculation convergence in traditional technology.
[0005] To address at least one of the aforementioned technical problems, according to one aspect of the present invention, a method for calculating the convective heat transfer coefficient of pipe flow based on discrete data is provided, comprising the following steps:
[0006] To obtain a particular solution to the fully developed flow energy equation;
[0007] Using this particular solution as a reference solution, the velocity and temperature data are assigned to discrete points in the region;
[0008] Based on the discrete data obtained above, from the perspective of energy conservation, the convective heat transfer coefficient of the pipe flow is inferred from the average temperature of the pipe cross section, and a smooth curve is obtained by means filtering method.
[0009] Approximate solutions for the convective heat transfer coefficient are obtained using both the proposed method and the traditional method.
[0010] Based on the error between the approximate solution and the particular solution, the accuracy of the proposed calculation method is compared with that of the traditional method;
[0011] By changing the number of data points, and under the same accuracy conditions, the number of data points required by the proposed method and the traditional method are compared, and the method with fewer data points is selected as the better method.
[0012] Using water as the fluid medium, the proposed method is used to calculate the convective heat transfer coefficient of ordinary circular pipes and annular pipes (non-)fully developed flow under different pipe wall temperatures.
[0013] Furthermore, obtaining a particular solution to the fully developed flow energy equation includes:
[0014] The polar coordinate expression of the fully developed flow energy equation is as follows:
[0015]
[0016] Where [r,z] represents the coordinates of a point along the radial direction and along the pipe direction, T represents the water flow temperature field, α represents the thermal conductivity, and Ω represents the computational domain of the circular pipe. Here, v(r) is the partial derivative, and v(r) is the fully developed flow velocity related to r. The expression for v(r) is as follows:
[0017] v(r) = 2v0(1-r) 2 / R 2 ), (S.2)
[0018] Where R is the radius of the circular pipe and v0 is the average flow velocity in the pipe.
[0019] The expression for the particular solution up obtained from equation (S.1) is as follows:
[0020]
[0021] Where a and b satisfy the following relationship:
[0022]
[0023] a and b can be obtained by solving equation (S.4).
[0024] Furthermore, using a particular solution as a reference solution, the velocity and temperature data are assigned to discrete points in the region, where:
[0025] The region is uniformly discretized, and the number of discretization points in the radial direction and along the pipe direction satisfy the following relationship:
[0026]
[0027] Where Nr and Nz are the number of discrete points in the radial direction and along the pipe direction, respectively, L is the pipe length, and ceil represents the rounding function. Equation (S.5) demonstrates that uniform discretization of the region can be achieved by setting the number of discrete points in the radial direction.
[0028] The temperature field and velocity field at the discrete point are assigned values using a particular solution, where the velocity field v(r) and the temperature field T(r,z) are given by equations (S.2) and (S.3) in claim 2, respectively, where [r,z] are the coordinates of the discrete point, represented by the matrix determinant.
[0029] Further, based on the aforementioned discrete data v(r) and T(r,z), from the perspective of energy conservation, the convective heat transfer coefficient of the pipe flow is inferred from the average temperature of the pipe cross-section, and a smooth curve is obtained using the mean filtering method, including:
[0030] From Fourier's law of heat transfer and Newton's law of cooling, we can obtain:
[0031]
[0032] Where q represents the heat flux through the pipe wall, and λ is the thermal conductivity. It is the pipe wall temperature gradient, h represents the convective heat transfer coefficient, T p It is the pipe wall temperature. This is the average temperature of the pipe cross section. From equation (S.6), the expression for the conventional convective heat transfer coefficient can be obtained:
[0033]
[0034] As can be seen from equation (S.7), traditional calculation methods require discrete point data to approximate the simulation. and
[0035] Furthermore, based on the law of conservation of energy, the following relationship can be derived between the convective heat transfer coefficient of the pipe flow and the average temperature of the pipe cross section:
[0036]
[0037] in, The average temperature of the pipe cross section is represented by discrete data v(r) and T(r,z):
[0038]
[0039] `sum` represents the sum of the columns of a matrix. From horizontal quantity Represented as:
[0040]
[0041] Similarly, Tp1 ,T p2 Temperature T at discrete points on the pipe wall p Represented as:
[0042] T p1 =T p (1,...,N z -1),T p2 =T p (2,...,N z ), (S.11)
[0043] dz represents the temperature difference and displacement distance of the pipe wall temperature at discrete points, respectively, denoted as:
[0044] dz = z2 - z1, (S.12)
[0045] z1 and z2 can be written as:
[0046] z1=z(1,...,N z -1), z2=z(2,...,N z (S.13)
[0047] As can be seen from equation (S.8), the proposed method for calculating the convective heat transfer coefficient only requires approximate solution of the average value based on the data points. However, to avoid the need for approximate solutions using traditional methods... The proposed method is simpler than the previous one. However, the approximate convective heat transfer coefficient h obtained by the proposed method exhibits numerical fluctuations, therefore, a mean filtering method is required to obtain a smooth curve.
[0048] The core statements of the Matlab program for the mean filtering method used are as follows:
[0049]
[0050] This includes three key parameters: nq is the number of iterations, and f(1) and f(end) are the function values at the start and end points, respectively.
[0051] The key parameters are obtained as follows:
[0052] (1) The number of iterations nq is selected. Each time the loop is repeated, the results of the previous two loops are compared until their relative deviation is within a small value, such as within 10-6. The loop number at this time is denoted as nq.
[0053] (2) Obtaining f(1) and f(end) is crucial. Since the values at the start and end points fluctuate significantly, to avoid their influence, the first p points at the start point and the last p points at the end point are deleted. Then, the average of the first and last p points is taken as the start and end points, respectively. The minimum values of the number of points p to be deleted and the number of points q used for averaging are given by the following formula:
[0054]
[0055] Where ceil is the floor function, N rc N r N can be used to represent the number of difference points and data points in the radial direction. rc N r Substituting into equation (S.5) and discretizing through the grid yields the overall interpolation points and data points. The values of p and q can be adjusted as needed depending on the specific circumstances.
[0056] Then, the approximate solutions of the convective heat transfer coefficient are obtained by using the proposed calculation method and the traditional method respectively. The proposed calculation method uses equation (S.8), and the traditional method uses equation (S.7).
[0057] Equation (S.5) is used to obtain interpolation points. The total number of interpolation points is greater than the number of data points. When analyzing the results, the calculation accuracy is judged based on the approximate values at the interpolation points.
[0058] Use as many interpolation points as possible, which can be 10 to 30 times the number of data points in one direction, until the result converges.
[0059] To obtain approximate values at interpolation points, a griddata method based on Qhull data triangulation is introduced.
[0060] To ensure the accuracy of the analysis results, the results obtained by the above methods are all processed using mean filtering to obtain smooth curves.
[0061] Furthermore, based on the error between the approximate solution and the particular solution, the accuracy of the proposed calculation method is compared with that of traditional methods, including:
[0062] The particular solution expressed by Equation (S.3) is used as the reference solution to obtain the error between the proposed method and the traditional method at the interpolation point, which is used to reflect the specific accuracy of each method.
[0063] The error is given by the standard deviation between the approximate solution and the reference solution, expressed as follows:
[0064]
[0065] Where N is the total number of interpolation points, u p (i),u b(i) represent the numerical results of the approximate solution and the reference solution, respectively.
[0066] Furthermore, by varying the number of data points, and under the same accuracy conditions, comparing the number of data points required by the proposed method with that of traditional methods, the method requiring fewer data points is selected as the superior method, including:
[0067] According to equation (S.5), the total number of data points is adjusted accordingly by changing the number of points Nr in the radial direction. Based on the data points, the Qhull method is used to calculate the approximate solution at the interpolation points.
[0068] The method to quickly obtain the number of data points required under the same accuracy conditions is as follows: By increasing or decreasing the number of data points, observe the error trends of the proposed method and the traditional method respectively, obtain the number of data points required under the same accuracy conditions, and obtain the method with fewer data points required by comparison, and then determine the better method.
[0069] The accuracy is calculated using equation (S.14).
[0070] Using water as the fluid medium, the proposed method is employed to calculate the convective heat transfer coefficients of ordinary circular pipes and annular pipes (non-)fully developed flow under different pipe wall temperatures, including:
[0071] The fluid medium is not limited to water, but can be oil, gas, etc.; the pipe is not limited to ordinary circular pipe and annular pipe, but can be porous medium pipe, micro pipe, shrink sleeve, etc.; the calculation method used is the method given in equation (S.8); different pipe wall temperature conditions may also involve heat flux conditions; the approximate solution at the data point is an analytical solution or an approximate solution obtained by other calculation methods.
[0072] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data according to the present invention.
[0073] According to another aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data according to the present invention.
[0074] Compared with the prior art, the present invention has at least the following beneficial effects:
[0075] This invention can reduce the number of required data points and lower computational costs, solving the problems of large number of grids or points, large computational load, and slow convergence in the calculation of the convective heat transfer coefficient of pipeline flow in existing technologies. It has the characteristics of simple mathematical and physical model, small number of required grids, small computational load, fast computational convergence, and high computational accuracy. It is an effective method for fully developing the solution of convective heat transfer coefficient and meets the heat transfer characteristics requirements of pipeline structures in fields such as hot oil transportation, concrete cooling, and buried pipe heat exchange. The convective heat transfer coefficient calculation method derived from the law of conservation of energy achieves an accuracy one order of magnitude higher than traditional methods, reaching 10⁻² to 10⁻⁴, given a fixed number of data points. Through improved mean filtering techniques, data jitter is eliminated, reducing the number of data points required for the same calculation accuracy; the number of data points in a single direction is only 1 / 10 of the original. This energy conservation-based method only requires obtaining the average temperature from the temperature and velocity at the data points, eliminating the need for pipe wall temperature gradients, thus reducing computational difficulty and improving convergence speed and accuracy. The proposed method is adaptable to the calculation of convective heat transfer coefficients in ordinary circular and annular pipes at engineering scale, covering applications such as hot oil pipeline transportation and concrete water pipe cooling. Attached Figure Description
[0076] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below. Obviously, the drawings described below only relate to some embodiments of the present invention and are not intended to limit the present invention.
[0077] Figure 1 This is a flowchart of the method of the present invention;
[0078] Figure 2 This is a flowchart of obtaining a smooth curve using the mean filtering method provided in Embodiment 1 of the present invention;
[0079] Figure 3 This is a schematic diagram illustrating the calculation results of different data points and interpolation points using the conventional method provided in Embodiment 1 of the present invention;
[0080] Figure 4 This is a schematic diagram illustrating the calculation results of different data points and interpolation points in the method provided in Embodiment 1 of the present invention;
[0081] Figure 5 This is a schematic diagram illustrating the calculation results of different data points and the number of interpolation points after average filtering, provided in Embodiment 1 of the present invention.
[0082] Figure 6 This is a comparative schematic diagram of the calculation results of the convective heat transfer coefficient of a common circular tube provided in Embodiment 1 of the present invention;
[0083] Figure 7This is a comparative schematic diagram of the calculation results of the convection heat transfer coefficient of the annular pipe provided in Embodiment 1 of the present invention. Detailed Implementation
[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention.
[0085] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.
[0086] like Figure 1-7 As shown,
[0087] Example 1:
[0088] This embodiment presents a method for calculating the convective heat transfer coefficient of pipe flow based on discrete data, such as... Figure 1 As shown, it includes the following steps:
[0089] Step 1: Obtain a particular solution to the fully developed flow energy equation. The polar coordinate form of the fully developed flow energy equation is:
[0090]
[0091] Where [r,z] represents the coordinates of a point along the radial direction and along the pipe direction, T represents the water flow temperature field, α represents the thermal conductivity, and Ω represents the computational domain of the circular pipe. Here, v(r) is the partial derivative, and v(r) is the fully developed flow velocity related to r. The expression for v(r) is as follows:
[0092] v(r) = 2v0(1-r) 2 / R 2 ), (S.2)
[0093] Where R is the radius of the circular pipe and v0 is the average flow velocity in the pipe.
[0094] The particular solution u obtained from equation (S.1) p The expression is:
[0095]
[0096] Where a and b satisfy the following relationship:
[0097]
[0098] a and b can be obtained by solving equation (S.4).
[0099] Step 2: Using the particular solution as the reference solution, assign the velocity and temperature data to discrete points in the region, where:
[0100] The region is uniformly discretized, and the number of discretization points in the radial direction and along the pipe direction satisfy the following relationship:
[0101]
[0102] Where, N r N z Let L be the number of discrete points in the radial direction and along the pipe direction, L be the pipe length, and ceil be the rounding function. Equation (S.5) shows that uniform discretization of the region can be achieved by setting the number of discrete points in the radial direction.
[0103] The temperature field and velocity field at the discrete point are assigned values using the particular solution of step one, wherein the velocity field v(r) and the temperature field T(r,z) are given by equations (S.2) and (S.3) in claim 2, respectively, where [r,z] are the coordinates of the discrete point, represented by the matrix determinant.
[0104] Step 3: Based on the discrete data v(r) and T(r,z) obtained in Step 2, from the perspective of energy conservation, the convective heat transfer coefficient of the pipe flow is inferred from the average temperature of the pipe cross-section, and a smooth curve is obtained using the mean filtering method, where:
[0105] From Fourier's law of heat transfer and Newton's law of cooling, we can obtain:
[0106]
[0107] Where q represents the heat flux through the pipe wall, and λ is the thermal conductivity. It is the pipe wall temperature gradient, h represents the convective heat transfer coefficient, T p It is the pipe wall temperature. This is the average temperature of the pipe cross section. From equation (S.6), the expression for the conventional convective heat transfer coefficient can be obtained.
[0108]
[0109] As can be seen from equation (S.7), traditional calculation methods require discrete point data to approximate the simulation. and
[0110] Furthermore, based on the law of conservation of energy, the following relationship can be derived between the convective heat transfer coefficient of the pipe flow and the average temperature of the pipe cross section:
[0111]
[0112] in, The average temperature of the pipe cross section is represented by discrete data v(r) and T(r,z):
[0113]
[0114] `sum` represents the sum of the columns of a matrix. From horizontal quantity Represented as:
[0115]
[0116] Similarly, T p1 ,T p2 Temperature T at discrete points on the pipe wall p Represented as:
[0117] T p1 =T p (1,...,N z -1),T p2 =T p (2,...,N z ), (S.11)
[0118] dz represents the temperature difference and displacement distance of the pipe wall temperature at discrete points, respectively, denoted as:
[0119] dz = z2 - z1. (S.12)
[0120] z1 and z2 can be written as:
[0121] z1=z(1,...,N z -1), z2=z(2,...,N z (S.13)
[0122] As can be seen from equation (S.8), the proposed method for calculating the convective heat transfer coefficient only requires approximate solution of the average value based on the data points. However, to avoid the need for approximate solutions using traditional methods... The proposed method is simpler than the previous one. However, the approximate convective heat transfer coefficient h obtained by the proposed method exhibits numerical fluctuations, therefore, a mean filtering method is required to obtain a smooth curve.
[0123] The core statements of the Matlab program for the mean filtering method used are as follows:
[0124]
[0125]
[0126] This includes three key parameters: nq is the number of iterations, and f(1) and f(end) are the function values at the start and end points, respectively.
[0127] The key parameters are obtained as follows:
[0128] (1) The number of iterations nq is selected. After each iteration, the results of the previous and next iterations are compared until their relative deviation is within a small value, such as 10. -6 The loop stops when the time reaches nq.
[0129] (2) Obtaining f(1) and f(end) is crucial. Since the values at the start and end points fluctuate significantly, to avoid their influence, the first p points at the start point and the last p points at the end point are deleted. Then, the average of the first and last p points is taken as the start and end points, respectively. The minimum values of the number of points p to be deleted and the number of points q used for averaging are given by the following formula:
[0130]
[0131] Where ceil is the floor function, N rc N r N can be used to represent the number of difference points and data points in the radial direction. rc N r Substituting into equation (S.5) and discretizing through the grid yields the overall interpolation points and data points. The values of p and q can be adjusted as needed depending on the specific circumstances.
[0132] Step 4: Obtain approximate solutions for the convective heat transfer coefficient using both the proposed method and the traditional method, where:
[0133] The proposed calculation method uses equation (S.8), while the traditional method uses equation (S.7).
[0134] Equation (S.5) is used to obtain interpolation points. The total number of interpolation points is greater than the number of data points. When analyzing the results, the calculation accuracy is judged based on the approximate values at the interpolation points.
[0135] Use as many interpolation points as possible, which can be 10 to 20 times the number of data points in a single direction, until the results converge.
[0136] To obtain approximate values at interpolation points, a griddata method based on Qhull data triangulation is introduced.
[0137] To ensure the accuracy of the analysis results, the results obtained by the above methods are all processed using mean filtering to obtain smooth curves.
[0138] Step 5: Based on the error between the approximate solution and the particular solution, compare the accuracy of the proposed calculation method with that of the traditional method, where:
[0139] The particular solution expressed by Equation (S.3) is used as the reference solution to obtain the error between the proposed method and the traditional method at the interpolation point, which is used to reflect the specific accuracy of each method.
[0140] The error is given by the standard deviation between the approximate solution and the reference solution, expressed as follows:
[0141]
[0142] Where N is the total number of interpolation points, u p (i),u b (i) represent the numerical results of the approximate solution and the reference solution, respectively.
[0143] The length of a standard circular pipe is L = 0.3m, the direction of pipe length is denoted as x, the pipe radius R is 0.01m, and the average velocity of the fluid in the pipe cross-section is v0 = 0.01m / s; the inlet fluid (initial) temperature is T0 = 20℃; the isothermal pipe wall boundary condition is T1 = 30℃, and the variable-temperature pipe wall boundary condition is T... p =-(T1-T0)(xL) 2 / L 2 +T1+1℃.
[0144] The annular pipe has a length L = 0.3 m, an inner diameter R1 of 0.01 m, an outer diameter R2 of 0.02 m, and an average fluid velocity v0 = 0.01 m / s across the pipe cross-section. The inlet fluid (initial) temperature is T0 = 20℃. The isothermal pipe wall boundary condition is T1 = 30℃, and the variable-temperature pipe wall boundary condition is T... p =-(T1-T0)(xL) 2 / L 2 +T1+1℃.
[0145] The heat transfer parameters of water are as follows: density is 998.2 kg / m³. 3 Its specific heat capacity is 4183 J / (kg℃), and its thermal conductivity is 0.599 W / (m℃).
[0146] From equation (S.4), we get a = 10000, b = 0.28691; substituting these into the particular solution expression (S.3), we get:
[0147]
[0148] Figure 3 (a) and (b) present the calculation results of different data points and interpolation points using the traditional method, comparing them with the particular solution as the analytical solution. Figure 3The calculation results in (a) show that as the number of interpolation points increases, the simulation results approach the analytical solution. When the number of data points in one direction is 10 and the number of interpolation points is greater than 50, the simulation results converge to around 122, still with an error of about 2% compared to the analytical solution 119.81. Figure 3 (b) shows that as the number of data points increases, the simulation results approach the analytical solution. When the number of interpolation points in one direction is 100 and the number of data points is greater than 100, the simulation results converge to about 120.4, with an error of 0.5% compared to the analytical solution of 119.81. The results are relatively accurate, but the number of data points in one direction reaches 100, and the amount of data required per unit pipe length reaches 1 million, which is a huge amount of data.
[0149] Figure 4 Images (a) and (b) present the calculation results for different data points and the number of interpolation points using the proposed method, with the particular solution used as the analytical solution for comparison. Figure 4 Analysis of the calculation results in (a) and (b) shows that when the number of interpolation points is the same as the number of data points, the result is a smooth line segment; when the number of interpolation points is greater than the number of data points, the result exhibits significant regular fluctuations. After introducing the mean filtering method for improvement... Figure 4 After processing, (a) and (b) can be obtained Figure 5 (a), (b). From Figure 5 The calculation results in (a) show that as the number of interpolation points increases, the simulation results approach the analytical solution. When the number of data points in one direction is 10 and the number of interpolation points is greater than 50, the simulation results converge to approximately 119.89, with an error of only 0.067% compared to the analytical solution of 119.81. The accuracy of the results reaches 10. -4 ;from Figure 5 The calculation results in (b) show that as the number of data points increases, the simulation results continue to approach the analytical solution. When the number of interpolation points in a single direction is 100 and the number of data points is 20, the simulation results are almost identical to the analytical solution, with an error of 0.017%. Analysis of the above results shows that when the number of data points in a single direction is 10, the accuracy of the proposed method (0.067%) is nearly two orders of magnitude higher than the 2% accuracy of the traditional method. Furthermore, as the number of data points increases, the results of the proposed method become even more accurate, at least one order of magnitude higher than the accuracy of the traditional method. Only 10,000 data points are needed per unit pipe length, which is 1 / 100th of the traditional method.
[0150] Figure 6 and Figure 7 The calculation results of the convective heat transfer coefficients of ordinary circular pipes and annular pipes under different boundary conditions are presented and compared with those of traditional methods. The relative deviation between the two methods is within 5%, and the deviation will continue to decrease as the number of data points increases. The calculation results of the proposed method are closer to those of the proposed method, which is similar to the case where an analytical solution exists, thus verifying the accuracy of the proposed method.
[0151] The above results show that the proposed method requires only fewer data points to achieve a computational accuracy at least an order of magnitude higher than that of traditional methods.
[0152] In summary, this invention provides a method for accurately calculating the convective heat transfer coefficient of pipeline flow based on discrete data. This method, derived from the law of conservation of energy, reduces the difficulty of solving for the convective heat transfer coefficient, decreasing the required data points while improving accuracy by an order of magnitude. This invention follows the heat transfer laws and characteristics of pipelines, featuring high accuracy, fast calculation, simple program, and low data requirements. It is applicable to the accurate calculation of the convective heat transfer coefficient of pipeline flow, such as heat transfer calculations for long pipeline systems like concrete water pipe cooling, hot oil pipe transportation, and buried pipe heat exchange, meeting the requirements of low data volume, high efficiency, accuracy, and stability in predicting the convective heat transfer coefficient of pipeline flow.
[0153] Experimental comparisons show that the novel method proposed in this invention can accurately analyze the changes in convective heat transfer coefficient under different pipe wall temperatures and pipe shapes, accurately describe the variation law of the convective heat transfer coefficient of the pipe wall, and require fewer samples to achieve similar accuracy. The accuracy is maintained at an order of magnitude higher than that of traditional methods, and the advantages of the proposed method become more obvious as the accuracy improves. The proposed method obeys the energy conservation law, the process is clear and concise, and it can calculate the convective heat transfer coefficient with an accuracy maintained at 10. -3 It can be used for various situations such as ordinary circular pipes and annular pipes, and the amount of data required is greatly reduced while providing accurate solutions; it can be further extended to the accurate calculation of convective heat transfer coefficients for incompletely developed flows, contraction pipes, and sleeves.
[0154] This invention provides a simple and efficient method for accurately calculating the convective heat transfer coefficient of pipe flow. It is an effective tool for accurate simulation of heat transfer in pipe structures and can also be extended to calculate heat transfer in similar incompletely developed flows, contraction pipes, and sleeves.
[0155] Example 2:
[0156] The computer-readable storage medium of this embodiment stores a computer program that, when executed by a processor, implements the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data in Embodiment 1.
[0157] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.
[0158] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.
[0159] Example 3:
[0160] The computer device of this embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data in Embodiment 1.
[0161] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.
[0162] Those skilled in the art will understand that the content disclosed in the embodiments can be provided as a method, system, or computer program product. Therefore, this solution can take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this solution can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage) containing computer-usable program code.
[0163] This solution is described with reference to flowchart illustrations and / or block diagrams of methods and computer program products according to embodiments of this solution. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0164] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0165] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0166] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.
[0167] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.
Claims
1. A method for calculating the convective heat transfer coefficient of pipe flow based on discrete data, characterized in that, Includes the following steps: S1. Obtain a particular solution to the fully developed flow energy equation; S2. Using the particular solution as a reference solution, assign the velocity and temperature data to the discrete points in the region; S3. Based on the obtained discrete data, from the perspective of energy conservation, the convective heat transfer coefficient of the pipe flow is inferred from the average temperature of the pipe cross section, and a smooth curve is obtained by means filtering method. S4. The approximate solutions for the convection heat transfer coefficient are obtained by using the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data and the traditional method, respectively. S5. Based on the error between the approximate solution and the particular solution, compare the accuracy of the pipe flow convection heat transfer coefficient calculation method based on discrete data with that of the traditional method; S6. Change the number of data points, and under the same accuracy conditions, compare the number of data points required by the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data with the traditional method, and select the method with fewer data points as the better method. S7. Using water as the fluid medium, the convective heat transfer coefficient of pipe flow based on discrete data is calculated to calculate the convective heat transfer coefficient of fully developed flow in ordinary circular pipes and annular pipes under different pipe wall temperatures. The polar coordinate expression of the fully developed flow energy equation in step S1 is as follows: (S.1) in, This represents the coordinates of a point along the radial direction and along the pipe direction. Represents the temperature field of the water flow. Indicates thermal conductivity. Represents the computational domain of the circular tube. It is a partial derivative. It is the fully developed flow velocity related to r; The expression is as follows: (S.2) Where R is the radius of the circular pipe, and v0 is the average flow velocity in the pipe; The particular solution u obtained from equation (S.1) p The expression is: (S.3) Where a and b satisfy the following relationship: (S.4) By solving equation (S.4), we can obtain a and b; In step S2, the region is uniformly discretized, and the number of discretization points in the radial direction and along the pipe direction satisfy the following relationship: (S.5) Where, N r , N z Let L be the number of discrete points in the radial direction and along the pipe direction, L be the pipe length, and ceil be the rounding function. Equation (S.5) shows that the uniform discretization of the region can be achieved by setting the number of discrete points in the radial direction. The temperature and velocity fields at discrete points are assigned values using particular solutions, where the velocity field... and temperature field Given by equations (S.2) and (S.3) respectively, where [r, z] are the coordinates of discrete points, represented by the matrix determinant; In step S3, the obtained discrete data and From the perspective of energy conservation, the convective heat transfer coefficient of the pipe flow is inferred from the average temperature of the pipe cross-section, and a smooth curve is obtained using the mean filtering method. From Fourier's law of heat transfer and Newton's law of cooling, we can obtain: (S.6) in, This represents the heat flux through the pipe wall. It is the thermal conductivity. It is the temperature gradient of the pipe wall. Indicates the convective heat transfer coefficient. It is the pipe wall temperature. It is the average temperature of the pipe cross section; from equation (S.6), the expression for the traditional convective heat transfer coefficient is obtained: (S.7) As can be seen from equation (S.7), traditional calculation methods require discrete point data to approximate the simulation. and ; Based on the law of conservation of energy, the following relationship is derived between the convective heat transfer coefficient of the pipe flow and the average temperature of the pipe cross section: (S.8) in, The average temperature of the pipe cross section is given by discrete data. and Represented as: (S.9) `sum` represents the sum of the columns of a matrix. From horizontal quantity Represented as: (S.10) Similarly, Temperature at discrete points on the pipe wall Represented as: (S.11) Tp() means: N on the pipe wall z An array of temperature values at discrete points; These are the temperature difference and displacement distance of the pipe wall temperature at discrete points, denoted as: (S.12) Written as: (S.13) As can be seen from equation (S.8), the proposed method for calculating the convective heat transfer coefficient only requires approximate solution of the average value based on the data points. ; In step S4, the proposed calculation method uses equation (S.8), while the traditional method uses equation (S.7); The interpolation points are obtained using Equation (S.5). The total number of interpolation points is greater than the number of data points. When analyzing the results, the calculation accuracy is judged based on the approximate values at the interpolation points. Use as many interpolation points as possible, which can be 10 to 20 times the number of data points in a single direction, until the results converge. To obtain approximate values at interpolation points, a griddata method based on Qhull data triangulation is introduced. To ensure the accuracy of the analysis results, the mean filtering method was used to obtain smooth curves.
2. The method for calculating the convective heat transfer coefficient of pipe flow based on discrete data according to claim 1, characterized in that, In step S5, the particular solution represented by equation (S.3) is used as the reference solution to obtain the error between the proposed method and the traditional method at the interpolation point, which is used to reflect the specific accuracy of each method. The error is given by the standard deviation between the approximate solution and the reference solution, expressed as follows: (S.14) in, The total number of interpolation points. These represent the numerical results of the approximate solution and the reference solution, respectively.
3. The method for calculating the convective heat transfer coefficient of pipe flow based on discrete data according to claim 2, characterized in that, In step S6, according to equation (S.5), the number of points N in the radial direction is changed. r Adjust the total number of data points accordingly; use the Qhull method to calculate the approximate solution at the interpolation points based on the data points; The method to quickly obtain the number of data points required under the same accuracy is as follows: By increasing or decreasing the number of data points, observe the error trend of the proposed method and the traditional method respectively, obtain the number of data points required under the same accuracy, and obtain the method with fewer data points by comparison, and then determine the better method. The accuracy is calculated using equation (S.14).
4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data as described in any one of claims 1 to 3.
5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the method for calculating the convection heat transfer coefficient of pipe flow based on discrete data as described in any one of claims 1 to 3.