A method for obtaining the convection heat transfer coefficient of solid three-dimensional thermal conductivity
By constructing the temperature cost function and the Lagrangian function, combined with the Newton iteration method, the convection heat transfer coefficient of the solid surface is accurately calculated, and the problem of ignoring the three-dimensional thermal conductivity and shape limitations in the existing technology is solved, and the high accuracy exchange is achieved Thermal coefficient measurement.
Patent Information
- Application Number
- CN202111658456.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-12-31
- Publication Date
- 2025-02-18
- Estimated Expiration
- 2041-12-31
AI Technical Summary
When obtaining the heat transfer coefficient of the solid surface, the prior art ignores the three-dimensional thermal conductivity effect and has strict restrictions on the shape of the solid surface to be measured, resulting in large deviations in the measurement results.
By constructing the temperature cost function and the Lagrangian function, combined with the Newtonian iterative method, the convection heat transfer coefficient of the solid surface to be measured is accurately calculated, taking into account the influence of three-dimensional thermal conductivity, and there is no need to limit the shape of the solid surface to be measured.
Accurate consideration of the impact of three-dimensional thermal conductivity is achieved, breaking the shape limitation of solid surfaces, and improving the accuracy and efficiency of heat transfer coefficient measurement.
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Figure CN114460129B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of heat exchange testing, and in particular to a method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity. Background Art
[0002] The natural convection heat transfer coefficient is a basic parameter for evaluating the heat transfer capacity between a fluid and a solid surface, and has a wide range of applications in engineering fields involving heat transfer.
[0003] The existing technology uses a heat transfer analytical method based on a one-dimensional semi-infinite plate to calculate the heat transfer coefficient of the solid surface under different incoming flow conditions. This method can only consider the one-dimensional thermal conductivity effect on the normal vector of the solid surface, ignoring the three-dimensional thermal conductivity effect. It has strict requirements on the material properties and measurement environment of the solid surface to be tested, and requires the solid surface to be tested to be a plane. Therefore, this method may produce large deviations and is limited by the shape of the solid surface being tested. However, in most heat transfer tests, the thermal conductivity of the material is high, and it is difficult to meet the one-dimensional thermal conductivity assumption, and the solid surface studied is mostly not a plane. Therefore, it is necessary to study a method that can consider the influence of three-dimensional thermal conductivity and accurately obtain the heat transfer coefficient. Summary of the invention
[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity. This method can accurately obtain the heat transfer coefficient taking into account the influence of the three-dimensional thermal conductivity of the firmware to be tested, and has no restrictions on the shape of the solid surface to be tested.
[0005] The purpose of the present invention can be achieved by the following technical solutions:
[0006] The present invention provides a method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity, comprising the following steps:
[0007] S1: placing the solid to be measured in a uniformly flowing fluid at the initial moment, obtaining the fluid temperature, the initial surface temperature, thermal conductivity and thermal diffusion coefficient of the solid to be measured, measuring the specific temperature reached by the surface of the solid to be measured and the time consumed to reach the temperature by surface temperature measurement technology, and recording them as the measured temperature and the measured time respectively;
[0008] S2: Calculate the surface temperature of the solid to be measured at the initial moment within the measurement time according to the three-dimensional heat conduction control equation, construct a temperature cost function of the calculated surface temperature of the solid to be measured and the measured temperature, and construct a Lagrangian function for measuring the convective heat transfer coefficient according to the thermal diffusion coefficient of the solid to be measured and the temperature cost function;
[0009] S3: Estimate the initial convective heat transfer coefficient, obtain the temperature distribution and adjoint operator of the solid surface at all times within the measurement time according to the Lagrangian function, and obtain the convective heat transfer coefficient change gradient according to the adjoint operator and the cost function;
[0010] S4: According to the change gradient of the convective heat transfer coefficient, the optimal convective heat transfer coefficient is obtained by Newton iteration method.
[0011] Preferably, the formula of the temperature cost function in S2 is:
[0012]
[0013] Where τ is any moment in the measurement time, T(τ) is the calculated surface temperature of the solid to be measured, is the measured temperature and is the temperature cost function.
[0014] Preferably, the formula of the Lagrangian function in S2 is:
[0015]
[0016] Where x is the parallel flow direction of the fluid, y is the perpendicular flow direction of the fluid, z is the normal direction of the solid surface to be measured, λ is the adjoint operator, and a is the thermal diffusion coefficient of the solid to be measured.
[0017] Preferably, S3 comprises the following steps:
[0018] S3.1: Estimate the initial convective heat transfer coefficient;
[0019] S3.2: Set the first initial condition and the first boundary condition, and solve the three-dimensional heat conduction control equation in a discrete forward manner, that is, find the partial derivative of the Lagrangian function with respect to the adjoint operator to obtain the solid surface temperature distribution at all times during the measurement time;
[0020] S3.3: Set the second initial condition and the second boundary condition, solve the partial derivative of the Lagrangian function with respect to temperature in a discrete inverse manner, and obtain the adjoint operator of the solid surface at all times;
[0021] S3.4: According to the adjoint operator, solve the partial derivative of the cost function with respect to the convective heat transfer coefficient to obtain the change gradient of the convective heat transfer coefficient.
[0022] Preferably, the Crank-Nicolson difference format is used in S3.2 to perform discrete forward solution.
[0023] Preferably, the formula for the change gradient of the convective heat transfer coefficient is specifically:
[0024]
[0025] Where, T f is the fluid temperature.
[0026] Preferably, S4 comprises the following steps:
[0027] S4.1: Calculate the convective heat transfer coefficient for the next iteration step by Newton iteration method;
[0028] S4.2: Calculate the iteration residual according to the convective heat transfer coefficient of each iteration step, and set the residual threshold. When the iteration residual between a certain iteration step and the next iteration step is less than the residual threshold, the convective heat transfer coefficient calculated in the iteration step is used as the measured optimal convective heat transfer coefficient.
[0029] Preferably, the formula for the convective heat transfer coefficient of the next iteration step is:
[0030]
[0031] In the formula, h K+1 is the convective heat transfer coefficient of the K+1th iteration step, h K is the convective heat transfer coefficient of the Kth iteration step, J K Temperature cost function at the kth iteration step.
[0032] Preferably, the residual is calculated as follows:
[0033] ε=|h K+1 -h K |
[0034] Where ε is the iterative residual at the K+1th iteration step and the Kth iteration step.
[0035] Preferably, the residual threshold is 10 -5 .
[0036] Compared with the prior art, the present invention has the following advantages:
[0037] (1) The present invention constructs a temperature cost function of the calculated solid surface temperature to be measured and the measured temperature, and constructs a Lagrangian function for measuring the convective heat transfer coefficient. The Lagrangian function is sequentially discretely solved forward and discretely solved inversely to obtain the change gradient of the convective heat transfer coefficient. This can break the limitation of the prior art that the solid surface to be tested is a plane, and consider the influence of three-dimensional thermal conductivity to obtain the heat transfer coefficient considering the influence of three-dimensional thermal conductivity.
[0038] (2) The present invention uses the Newton iteration method to iterate the change gradient of the convective heat transfer coefficient, which greatly improves the iteration efficiency and can accurately calculate the convective heat transfer coefficient. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1A method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity provided in this embodiment;
[0040] Figure 2 Schematic diagram of the experimental device for obtaining the convective heat transfer coefficient of the transient liquid crystal surface to be tested by jet impact in Example 1;
[0041] Figure 3 This is an example diagram of a Newton iteration method residual variation curve of Example 1;
[0042] Figure 4 This is a schematic diagram of the convective heat transfer coefficient on the transient liquid crystal surface to be measured obtained in Example 1. DETAILED DESCRIPTION
[0043] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.
[0044] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0045] In the study of atmospheric science and ocean science, in order to explore the mechanism of natural phenomena, the combination of observational data and mathematical models is crucial. In recent years, scholars have widely used data assimilation methods to forecast weather and oceans. Among them, the adjoint method can effectively optimize model parameters, initial fields and boundary fields, and plays an increasingly important role in data assimilation. In the measurement of convective heat transfer coefficient, there are also solid heat transfer models and measurement values. Through the adjoint assimilation method, the physical model boundary quantity - convective heat transfer coefficient can be obtained according to the heat transfer test measurement value combined with the control equation. This method has no strict requirements on the model control equation. It can be applied not only to the solid three-dimensional heat conduction equation, but also to the complex coordinate system heat conduction equation under cylindrical coordinates. Therefore, it can be used in the precise calculation of the convective heat transfer coefficient in complex test environments and curved test surfaces.
[0046] refer to Figure 1 As shown, this embodiment provides a method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity, comprising the following steps:
[0047] S1: Place the solid to be tested in a uniformly flowing fluid at a certain moment, obtain the fluid temperature, the initial surface temperature of the solid to be tested, the thermal conductivity of the solid to be tested, and the thermal diffusion coefficient of the solid to be tested, and measure the temperature reached by the surface of the solid to be tested and the time consumed by the solid surface to reach the temperature through surface temperature measurement technology, and record them as the measured temperature and measurement time respectively.
[0048] As an optional implementation, the surface temperature measurement technology adopts infrared temperature measurement technology.
[0049] S2: Calculate the surface temperature of the solid to be measured at a certain moment within the measurement time according to the three-dimensional heat conduction control equation, and construct a temperature cost function of the calculated surface temperature of the solid to be measured and the measured temperature; and construct a Lagrangian function for measuring the convective heat transfer coefficient according to the thermal diffusion coefficient of the solid to be measured and the temperature cost function.
[0050] The three-dimensional heat conduction control equation is:
[0051]
[0052] Where: τ is any moment in the measurement time, T(τ) is the calculated solid surface temperature to be measured, x is the parallel flow direction of the fluid, y is the vertical flow direction of the fluid, z is the normal direction of the solid surface to be measured,
[0053]
[0054] In the formula, is the measured temperature, and J is the temperature cost function.
[0055] The Lagrangian function for measuring the convective heat transfer coefficient is:
[0056]
[0057] Where λ is the adjoint operator and a is the thermal diffusion coefficient of the solid to be measured.
[0058] S3: Estimate the initial convective heat transfer coefficient, obtain the temperature distribution and adjoint operator of the solid surface at all times within the measurement time according to the Lagrangian function, and obtain the convective heat transfer coefficient change gradient according to the adjoint operator and the cost function.
[0059] S3.1: Estimate the initial convective heat transfer coefficient;
[0060] S3.2: Set the first initial condition and the first boundary condition, and solve the three-dimensional heat conduction control equation in a discrete forward manner, that is, find the partial derivative of the Lagrangian function with respect to the adjoint operator λ Get the solid surface temperature distribution at all times during the measurement time.
[0061] The first initial condition and the first boundary condition are:
[0062] τ=0,T=T0
[0063]
[0064]
[0065] Where T0 is the initial temperature of the solid surface to be measured, T f is the fluid temperature, k is the thermal conductivity of the solid to be measured, and d is any integer except 0.
[0066] As an optional implementation, the Crank-Nicolson difference format is used for solving.
[0067] S3.3: Set the second initial condition and the second boundary condition, solve the partial derivative of the Lagrangian function with respect to temperature in a discrete inverse manner, and obtain the adjoint operator of the solid surface at all times;
[0068] S3.4: According to the adjoint operator, solve the partial derivative of the cost function with respect to the convective heat transfer coefficient and obtain the change gradient of the convective heat transfer coefficient:
[0069]
[0070] S4: According to the change gradient of the convective heat transfer coefficient, the optimal convective heat transfer coefficient is obtained by Newton iteration method.
[0071] S4.1: Calculate the convective heat transfer coefficient for the next iteration step using the Newton iteration method:
[0072]
[0073] S4.2: Calculate the iteration residual according to the convective heat transfer coefficient of each iteration step, and set the residual threshold. When the iteration residual between a certain iteration step and the next iteration step is less than the residual threshold, the convective heat transfer coefficient calculated in the iteration step is used as the measured optimal convective heat transfer coefficient.
[0074] ε=|h K+1 -h K |
[0075] Where K is the index of the iteration step, and ε is the iterative residual between the K+1th iteration step and the Kth iteration step.
[0076] As an optional implementation, the residual threshold is set to 10 -5 .
[0077] Example 1
[0078] This embodiment further describes in detail the method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity proposed by the present invention in combination with the technical test example of transient liquid crystal:
[0079] S1: Reference Figure 2 As shown, this embodiment uses a single-hole jet impact target surface convection heat transfer test device to obtain the thermal conductivity k of the transient liquid crystal to be tested = 0.449 W / (mK), the thermal diffusion coefficient a of the transient liquid crystal to be tested = 2.03×10 -7 m 2 / s, the initial temperature of the target surface of the transient liquid crystal to be tested is T0 = 24 °C and the fluid temperature is T f =40℃, set the hue extreme temperature of transient liquid crystal To measure the temperature, the device is used to measure the time taken for the target surface of the transient liquid crystal to reach the measurement temperature from the initial moment, which is the measurement time.
[0080] S2: Calculate the surface temperature of the transient liquid crystal to be measured at a certain time τ within the measurement time according to the three-dimensional heat conduction control equation, and construct the calculated surface temperature of the transient liquid crystal to be measured and the measured temperature and constructing a Lagrangian function L(T, λ) for measuring the convective heat transfer coefficient according to the thermal diffusion coefficient of the transient liquid crystal to be measured and the temperature cost function.
[0081]
[0082]
[0083] S3: Estimated surface convection heat transfer coefficient: h0 = 400 W / (m 2 ℃), discretely solve the three-dimensional heat conduction control equation forward to obtain the temperature distribution T on the solid surface at all times during the measurement time, discretely reversely solve the partial derivative of the Lagrangian function with respect to temperature to obtain the adjoint operator of the solid surface at all times; then solve and obtain the partial derivative of the cost function with respect to the convective heat transfer coefficient h, that is, obtain the change gradient of the convective heat transfer coefficient.
[0084] S4: According to the change gradient of the convective heat transfer coefficient, the convective heat transfer coefficient h of the next iteration step is calculated by Newton iteration method. K+1 , the iteration residual is calculated according to the convective heat transfer coefficient of each iteration step, and the residual threshold is set. When the iteration residual between a certain iteration step and the next iteration step is less than the residual threshold, the convective heat transfer coefficient calculated under the iteration step is taken as the optimal convective heat transfer coefficient.
[0085] Since the Newton iteration method converges squarely near the root, it converges very quickly. Since the derivative of the cost function at each step has been calculated through the above steps, the Newton iteration method can greatly improve the computational efficiency. Define the computational iterative residual ε = |h K+1 -h K |, reference Figure 2 The figure shows an example of the residual variation curve. It can be seen from the figure that the iterative convergence speed of the convective heat transfer coefficient is very fast. It is generally believed that when ε < 10 -5 After that, the iteration converges. And the heat transfer coefficient h under this iteration step can be obtained K , that is, the convection heat transfer coefficient on the entire transient liquid crystal surface to be tested, which can be referred to Figure 4 shown.
[0086] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.
Claims
1. A method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity, characterized in that: The following steps are involved: S1: placing the solid to be measured in a uniformly flowing fluid at the initial moment, obtaining the fluid temperature, the initial surface temperature, thermal conductivity and thermal diffusion coefficient of the solid to be measured, measuring the specific temperature reached by the surface of the solid to be measured and the time consumed to reach the temperature by surface temperature measurement technology, and recording them as the measured temperature and the measured time respectively; S2: Calculate the surface temperature of the solid to be measured at a certain moment within the measurement time according to the three-dimensional heat conduction control equation, construct a temperature cost function of the calculated surface temperature of the solid to be measured and the measured temperature, and construct a Lagrangian function for measuring the convective heat transfer coefficient according to the thermal diffusion coefficient of the solid to be measured and the temperature cost function; S3: Estimate the initial convective heat transfer coefficient, obtain the temperature distribution and adjoint operator of the solid surface at all times within the measurement time according to the Lagrangian function, solve the partial derivative of the temperature cost function with respect to the convective heat transfer coefficient according to the adjoint operator, and obtain the change gradient of the convective heat transfer coefficient; S4: obtaining an optimal convective heat transfer coefficient by Newton iteration method according to the change gradient of the convective heat transfer coefficient; The formula of the temperature cost function in S2 is: Where τ is any moment in the measurement time, T(τ) is the calculated surface temperature of the solid to be measured, is the measured temperature, J is the temperature cost function; The formula of the Lagrangian function in S2 is: Where x is the parallel flow direction of the fluid, y is the perpendicular flow direction of the fluid, z is the normal direction of the solid surface to be measured, λ is the adjoint operator, and a is the thermal diffusion coefficient of the solid to be measured.
2. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 1, characterized in that: The S3 comprises the following steps: S3.1: Estimate the initial convective heat transfer coefficient; S3.2: Set the first initial condition and the first boundary condition, and solve the three-dimensional heat conduction control equation in a discrete forward manner, that is, find the partial derivative of the Lagrangian function with respect to the adjoint operator to obtain the solid surface temperature distribution at all times during the measurement time; S3.3: Set the second initial condition and the second boundary condition, discretely reversely solve the partial derivative of the Lagrangian function with respect to temperature, and obtain the adjoint operator of the solid surface at all times within the measurement time; S3.4: According to the adjoint operator, solve the partial derivative of the temperature cost function with respect to the convective heat transfer coefficient to obtain the change gradient of the convective heat transfer coefficient.
3. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 2, characterized in that: In S3.2, the Crank-Nicolson difference format is used for discrete forward solution.
4. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 2, characterized in that: The formula for obtaining the change gradient of the convective heat transfer coefficient is specifically: Where, T f is the fluid temperature.
5. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 4, characterized in that: The S4 comprises the following steps: S4.1: Calculate the convective heat transfer coefficient for the next iteration step by Newton iteration method; S4.2: Calculate the iteration residual according to the convective heat transfer coefficient of each iteration step, and set the residual threshold. When the iteration residual between a certain iteration step and the next iteration step is less than the residual threshold, the convective heat transfer coefficient calculated in the iteration step is used as the measured optimal convective heat transfer coefficient.
6. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 5, characterized in that: The formula for calculating the convective heat transfer coefficient of the next iteration step is: In the formula, h K+1 is the convective heat transfer coefficient of the K+1th iteration step, h K is the convective heat transfer coefficient of the Kth iteration step, J K Temperature cost function at the kth iteration step.
7. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 6, characterized in that: The calculation formula of the iterative residual is: ε=|h K+1 -h K | Where ε is the iterative residual at the K+1th iteration step and the Kth iteration step.
8. The method for obtaining the convective heat transfer coefficient of solid three-dimensional thermal conductivity according to claim 5, characterized in that: The residual threshold is 10 -5 .