A transient method for measuring heat transfer coefficient of solid wall surface with wide applicability

Abstract

In order to address the shortcomings of the existing conventional transient heat transfer coefficient measurement method, the temperature measurement method is extended from narrow-band thermochromic liquid crystal to other non-contact temperature measurement methods, such as infrared thermal imagers, etc. The present invention proposes a transient solid wall surface heat transfer coefficient measurement method with wide applicability, further derives the non-steady-state thermal conductivity formula of a one-dimensional semi-infinite plate, and promotes the application of the fixed temperature measurement time method applicable to narrow-band thermochromic liquid crystal. The wall temperature measurement value is not limited, and the heat transfer coefficient can be calculated based on the temperature value measured at any time. Compared with narrow-band thermochromic liquid crystal, this method has better versatility and can be applied to non-contact temperature measurement equipment such as infrared thermal imagers whose temperature measurement accuracy is lower than that of narrow-band thermochromic liquid crystal. It also reduces the difficulty of experimental preparation and operation, and by increasing the initial temperature difference (T m ‑T i ) and comprehensive analysis of multiple groups of measurement data over a period of time to ensure the measurement accuracy of the heat transfer coefficient, which is more conducive to the promotion of non-contact temperature measurement technologies such as infrared thermal imagers.

Description

Technical Field

[0001] The present invention belongs to the technical field of heat transfer coefficient measurement, and relates to a heat transfer coefficient measurement method, and in particular to an experimental method for measuring the heat transfer coefficient of a solid wall surface based on a transient method and having wide applicability. The method is suitable for using various non-contact temperature measurement technologies to carry out transient heat transfer coefficient measurement on the surface of an object to be measured under wind tunnel conditions. Background Art

[0002] For example, turbine components, such as ground-based gas turbines and aircraft engines, operate in high-temperature fuel gas environments, where high heat loads can easily lead to failure. Therefore, accurate evaluation of the heat transfer coefficient distribution on the hot-end component walls is crucial. Heat transfer coefficient measurements are typically performed under laboratory conditions using simulated equivalent operating conditions. Heat transfer coefficient measurement methods include steady-state heat flux measurement, mass transfer analogy, and transient measurement. Transient heat transfer coefficient measurement is widely used due to its advantages, including short experimental cycles, minimal test component modifications, lack of influence of the measurement equipment on the measured surface, ability to obtain a two-dimensional distribution, and low error.

[0003] The transient heat transfer coefficient measurement method is based on the principle of non-steady-state heat conduction of one-dimensional semi-infinite objects and is described as follows: Figure 1 As shown, consider a semi-infinite object located in the half space x ≥ 0, with an initial temperature of T i Assume that the surface at position x = 0 is exposed to a temperature of T m In the fluid, T m ≠T i We further assume the following two conditions: (1) heat conduction occurs only in the direction perpendicular to the wall (i.e., the surface normal, which is approximately true when the lateral heat conduction heat flux is much smaller than the normal direction); (2) the convective heat transfer coefficient of the surface x = 0 does not change with time. Then, for this one-dimensional semi-infinite object, its heat conduction equation and boundary conditions are:

[0004]

[0005] t=0,T(c,t)=T i

[0006]

[0007] The relationship between the wall temperature and time is as follows (where is the complementary error function, η is an arbitrary real number):

[0008]

[0009] Based on the measurement principle, combined with the typical open plane wind tunnel technology in the existing technology (such as Figure 2 As shown), the initial condition of the transient heat transfer coefficient measurement method is that the object to be measured maintains a uniform temperature Ti , the incoming flow temperature instantly reaches T m By measuring the initial wind tunnel flow temperature T at t = 0 m , t=0 time the surface temperature of the object to be measured T i , at the initial temperature difference (T m -T i ) at a certain moment wall temperature T w And the corresponding time t, according to the one-dimensional semi-infinite object unsteady heat conduction calculation formula, the wall convection heat transfer coefficient h can be obtained. m -T i ) The method of instantaneously heating the object to be tested at room temperature in combination with the mainstream of the wind tunnel can be adopted, or the method of instantaneously placing the uniform high-temperature object to be tested into the wind tunnel at room temperature can be adopted. Narrow-band thermochromic liquid crystals have become the main temperature measurement method used in the transient heat transfer coefficient measurement method because of their narrow color temperature band and high temperature resolution. Taking the commonly used R35C1W narrow-band thermochromic liquid crystal from the American HALLCREST company as an example, the nominal starting color temperature is 35°C and the color range is 1°C. It has a higher temperature resolution than other non-contact temperature measurement methods, so that the wall temperature T w (nominal 35-36°C interval) and the corresponding time t are measured with high precision.

[0010] Due to the initial temperature difference (T m -T i ) and the color rendering temperature T measured by narrow-band thermochromic liquid crystal w For experimental settings, it is known that The heat transfer coefficient h can be obtained by solving the following implicit equation (2):

[0011]

[0012] However, the above methods have the following shortcomings: (1) The temperature measurement range is narrow and can only be based on the initial temperature difference (T m -T i ) and a set of T w , t, it is impossible to comprehensively evaluate the reliability of the heat transfer coefficient measurement method; (2) Narrow-band thermochromic liquid crystal is a protein, and high-temperature denaturation results in a narrow stable operating temperature range, which limits the initial temperature difference (T m -T i (3) Liquid crystal temperature measurement has high requirements for the spraying process. Uneven spraying thickness will affect the temperature measurement and may even cause cracks in the paint film. Summary of the Invention

[0013] (1) Purpose of the invention

[0014] In order to address the shortcomings of the existing conventional transient heat transfer coefficient measurement method, the temperature measurement method is extended from narrow-band thermochromic liquid crystal to other non-contact temperature measurement methods, such as infrared thermal imagers. The present invention proposes a transient solid wall surface heat transfer coefficient measurement method with wide applicability, further derives the non-steady-state thermal conductivity formula of a one-dimensional semi-infinite plate, and promotes the application of the fixed temperature measurement time method applicable to narrow-band thermochromic liquid crystal. The wall temperature measurement value is not limited, and the heat transfer coefficient can be calculated based on the temperature value measured at any time. This method is applied to non-contact temperature measurement equipment such as infrared thermal imagers, which reduces the difficulty of experimental preparation and operation. Compared with narrow-band thermochromic liquid crystals, although the temperature measurement accuracy is sacrificed, it is improved by increasing the initial temperature difference (T m -T i ), the measurement accuracy of the heat transfer coefficient can still be guaranteed, which is more conducive to the promotion of non-contact temperature measurement technologies such as infrared thermal imagers.

[0015] (2) Technical solution

[0016] In order to achieve the purpose of the present invention and solve the technical problems, the technical solutions adopted by the present invention are as follows:

[0017] A method for measuring the heat transfer coefficient of a solid wall surface using a transient method with wide applicability is characterized in that the method comprises at least the following steps when implemented:

[0018] SS1. Define dimensionless temperature And define a parameter proportional to time t A parameter proportional to the heat transfer coefficient h In the above definitions, T i is the temperature of the object to be measured at the initial time t=0, T m is the instantaneous incoming flow temperature at the initial time t=0, T w is the wall temperature of the object to be measured at time t, and the parameters t, k, ρ, and c are time, thermal conductivity of the object to be measured, incoming flow density, and heat capacity coefficient of the object to be measured, respectively;

[0019] SS2. According to the parameters defined in step SS1, the wall temperature of the object to be measured T i The relationship that changes with time t Rewrite it and according to α=β 2 t, we get the following relationship:

[0020]

[0021] SS3. Use at least one of the following two methods to analyze the relationship Solve and obtain the wall heat transfer coefficient h of the object to be measured:

[0022] Method 1: Direct solution get The dimensionless temperature θ at time t and the dimensionless temperature change rate with time Obtain β, and then according to the relationship The heat transfer coefficient h is calculated, that is, the wind tunnel inlet temperature T at time t = 0 measured in the wind tunnel experiment m , t=0 time the surface temperature of the object to be measured T i , at the initial temperature difference (T m -T i ) at a certain moment wall temperature T w , temperature change rate over time And the corresponding time t, the wall heat transfer coefficient h of the object to be measured can be solved;

[0023] Method 2: Substitute into the relation The temperature T of the wall of the object to be measured at two different moments, namely, at time t1 and t2, is obtained in the transient temperature measurement. w1 、T w2 ,get:

[0024]

[0025] According to this relationship, the wind tunnel inflow temperature T is measured at time t = 0 in the wind tunnel experiment. m , two moments t1, t2 and the wall temperature T of the object to be measured at the corresponding moments w,1 、T w,2 , temperature change rate over time The wall heat transfer coefficient h of the object to be measured can be calculated;

[0026] SS4. The operation steps for measuring the heat transfer coefficient using the transient method with wide applicability are as follows:

[0027] SS4.1 places a one-dimensional semi-infinite test piece in the wind tunnel test section. When the overall temperature of the test piece is kept uniform, that is, the internal temperature of the test piece is kept consistent with the wall temperature, the wall temperature T of the test piece is measured by non-contact temperature measurement at the initial time t=0. i , and start the wind tunnel fan to introduce air with a temperature of T into the wind tunnel test section. m The instantaneous flow, and T m ≠T i , that is, the instantaneous inflow temperature T at the initial time t = 0 m The surface temperature T of the test piece i Not equal;

[0028] SS4.2 at the initial temperature difference (T m -T i) conditions, the non-contact temperature measurement method is used to measure the wall temperature of the test piece of the object to be tested. The two-dimensional wall temperature distribution T of the test piece of the object to be tested at different times t is measured under wind tunnel conditions. w and / or calculate its rate of change over time t

[0029] SS4.3: Use method 1 or method 2 of step SS3 to process data at different positions on the wall of the test piece of the object to be tested, and calculate the wall heat transfer coefficient h at the corresponding position.

[0030] In a preferred embodiment of the present invention, the one-dimensional semi-infinite test object is a test piece with a certain thickness, and its surface to be tested is a plane or a curved surface.

[0031] In a preferred embodiment of the present invention, in the above step SS2, the wall temperature T i The relationship that changes with time t Rewriting it, we get the following relationship:

[0032]

[0033] Among them, among them, is the complementary error function, η is an arbitrary real number;

[0034] Solving for the derivative of θ with respect to α, we have

[0035] Further substitute α=β 2 t, then

[0036] In a preferred embodiment of the present invention, in the second method of step SS3, first Substitute into the relation get:

[0037]

[0038] In the transient temperature measurement, the wall temperature T of the object to be measured is obtained at two different moments, namely, at time t1 and time t2. w1 、T w2 , substitute And dividing, we get:

[0039]

[0040] According to this relationship, the wind tunnel inflow temperature T is measured at time t = 0 in the wind tunnel experiment. m , two moments t1, t2 and the wall temperature T of the object to be measured at the corresponding moments w,1 、T w,2, temperature change rate over time The wall heat transfer coefficient h of the object to be measured can be calculated.

[0041] In a preferred embodiment of the present invention, in the above step SS4, the non-contact temperature measurement method includes but is not limited to infrared thermal imager temperature measurement of narrow-band thermochromic liquid crystal.

[0042] In the transient method for measuring the heat transfer coefficient of a solid wall surface with wide applicability of the present invention, two methods for calculating the heat transfer coefficient h of the wall surface of the object to be measured are provided in step SS3. The advantage of using method 1 to solve the heat transfer coefficient h is that the temperature change rate over time is calculated by The introduction of the formula greatly simplifies the formula; it can be solved explicitly, reducing the amount of calculation; the temperature at different times in an experiment can be used to perform multiple data processing to facilitate statistical analysis. The advantages of using the second method to solve the heat transfer coefficient h are: eliminating the initial temperature T of the wall of the object to be measured i , for the test conditions of heating the object to be tested, the initial temperature does not need to be recorded; it can be solved linearly implicitly, with stable convergence and fast calculation speed; the temperature at different times in an experiment can be used for multiple data processing to facilitate statistical analysis.

[0043] (3) Technical effects

[0044] Compared with the existing technology, the transient method for measuring the heat transfer coefficient of a solid wall surface proposed in this invention has a wide applicability and is unprecedented in the currently known literature. The outstanding advantages of this measurement method are:

[0045] (1) The transient solid wall surface heat transfer coefficient measurement method of the present invention has wide applicability and can be combined with a variety of non-contact temperature measurement methods. It is not limited to using a fixed transient temperature value of the wall surface for data processing, nor is it limited to narrow-band thermochromic liquid crystals. It has a wider range of applications and is easier to operate experimentally.

[0046] (2) The transient method for measuring the heat transfer coefficient of a solid wall surface of the present invention has a wide applicability and is capable of further improving the temperature difference between the initial state airflow and the measured wall surface compared to narrow-band thermochromic liquid crystals. Under the condition that the temperature resolution is lower than that of narrow-band thermochromic liquid crystals, the heat transfer coefficient estimation accuracy is not significantly reduced.

[0047] (3) The transient method for measuring the heat transfer coefficient of a solid wall surface of the present invention has wide applicability and solves the heat transfer coefficient explicitly or linearly implicitly, with high calculation stability and low calculation amount;

[0048] (4) The transient method for measuring the heat transfer coefficient of a solid wall surface of the present invention has wide applicability and is highly flexible. It can avoid the measurement and evaluation of the initial temperature difference and can be solved by using any two sets of data in the measurement;

[0049] (5) The transient solid wall surface heat transfer coefficient measurement method of the present invention has wide applicability and can use multiple sets of wall temperature measurement values ​​in one experiment for statistical analysis, which is highly reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of unsteady heat conduction of a one-dimensional semi-infinite object;

[0051] Figure 2 This is a schematic diagram of the existing typical open plane wind tunnel structure.

[0052] Figure 3 The figure is a flow chart of the method for measuring the heat transfer coefficient of a solid wall surface using a transient method with wide applicability according to the present invention. DETAILED DESCRIPTION

[0053] In order to better understand the present invention, the content of the present invention will be further illustrated below in conjunction with the embodiments so that the advantages and features of the present invention can be more easily understood by those skilled in the art. It should be noted that the following are only preferred embodiments of the present invention, but the content of the present invention is not limited to the following embodiments. In fact, various modifications and variations can be made in the present invention without departing from the scope or spirit of the present invention, which will be apparent to those skilled in the art. For example, the features shown or described as part of one embodiment can be used together with another embodiment to produce another embodiment. Therefore, it is intended that the present invention include such modifications and variations within the scope of the appended claims and their equivalents.

[0054] like Figure 3 As shown, to address the shortcomings of existing conventional transient heat transfer coefficient measurement methods, the present invention extends the temperature measurement method from narrow-band thermochromic liquid crystal to other non-contact temperature measurement methods, such as infrared thermal imagers, and proposes a widely applicable transient solid wall surface heat transfer coefficient measurement method. As an optimal embodiment, the present invention's widely applicable transient solid wall surface heat transfer coefficient measurement method includes at least the following steps when implemented:

[0055] SS1. Define dimensionless temperature And define a parameter proportional to time t A parameter proportional to the heat transfer coefficient h In the above definitions, T i is the temperature of the object to be measured at the initial time t=0, T m is the instantaneous incoming flow temperature at the initial time t=0, T w is the wall temperature of the object to be measured at time t, and the parameters t, k, ρ, and c are time, thermal conductivity of the object to be measured, incoming flow density, and heat capacity coefficient of the object to be measured, respectively;

[0056] SS2. According to the parameters defined in step SS1, the wall temperature of the object to be measured T i The relationship that changes with time t Rewriting it, we get the following relationship:

[0057]

[0058] Among them, among them, is the complementary error function, η is an arbitrary real number;

[0059] Solving for the derivative of θ with respect to α, we have

[0060] Further substitute α=β 2 t, then

[0061] SS3. Use at least one of the following two methods to analyze the relationship Solve and obtain the wall heat transfer coefficient h of the object to be measured

[0062] Method 1: Direct solution get The dimensionless temperature θ at time t and the dimensionless temperature change rate with time Obtain β, and then according to the relationship The heat transfer coefficient h is calculated, that is, the wind tunnel inlet temperature T at time t = 0 measured in the wind tunnel experiment m , t=0 time the surface temperature of the object to be measured T i , at the initial temperature difference (T m -T i ) at a certain moment wall temperature T w , temperature change rate over time And the corresponding time t, the wall heat transfer coefficient h of the object to be measured can be solved;

[0063] The advantage of using this method to solve the heat transfer coefficient h is that the rate of change of temperature over time is The introduction of formulas greatly simplifies the formulas; the solutions can be obtained explicitly, reducing the amount of calculation; the temperatures at different times in an experiment can be used to perform multiple data processing to facilitate statistical analysis.

[0064] Method 2: Substitute into the relation get:

[0065]

[0066] In the transient temperature measurement, the wall temperature T of the object to be measured is obtained at two different moments, namely, at time t1 and time t2. w1 、T w2 , substitute And dividing, we get:

[0067]

[0068] According to this relationship, the wind tunnel inflow temperature T is measured at time t = 0 in the wind tunnel experiment. m , two moments t1, t2 and the wall temperature T of the object to be measured at the corresponding moments w,1 、T w,2 , temperature change rate over time The wall heat transfer coefficient h of the object to be measured can be calculated.

[0069] The advantages of using this method to solve the heat transfer coefficient h are: eliminating the initial temperature T of the wall of the object to be measured i , for the test conditions of heating the object to be tested, the initial temperature does not need to be recorded; it can be solved linearly implicitly, with stable convergence and fast calculation speed; the temperature at different times in an experiment can be used for multiple data processing to facilitate statistical analysis.

[0070] SS4. The operation steps of the transient heat transfer coefficient measurement method with wide applicability are as follows:

[0071] SS4.1 uses a test piece with a certain thickness (such as a flat test piece) as a substitute to simulate a one-dimensional semi-infinite object to be tested. The test surface is flat or curved. The test piece is placed in the wind tunnel test section. The overall temperature of the test piece is kept uniform, that is, the internal temperature of the test piece is kept consistent with the wall temperature. At the initial time t = 0, the wall temperature T of the test piece is measured by non-contact temperature measurement. i , and start the wind tunnel fan to introduce air with a temperature of T into the wind tunnel test section. m The instantaneous flow, and T m ≠T i , that is, the instantaneous inflow temperature T at the initial time t = 0 m and the test piece surface temperature T i Not equal;

[0072] SS4.2 uses non-contact temperature measurement methods such as infrared thermal imager or narrow-band thermochromic liquid crystal to measure the wall temperature of the test piece, and measures the two-dimensional temperature distribution T of the test piece wall changing with time t. w ;

[0073] SS4.3 uses the formula or Data processing is performed on different positions on the wall to calculate the heat transfer coefficient of the corresponding points.

[0074] Based on the above technical solution, the present invention has a widely applicable transient method for measuring the heat transfer coefficient of a solid wall surface. It further derives the non-steady-state heat conduction formula of a one-dimensional semi-infinite plate and promotes the application of the method of measuring the temperature at a fixed time for narrow-band thermochromic liquid crystals. It does not limit the wall temperature measurement value and can calculate the heat transfer coefficient based on the temperature value measured at any time. This method is applied to non-contact temperature measurement equipment such as infrared thermal imagers, which reduces the difficulty of experimental preparation and operation. Compared with narrow-band thermochromic liquid crystals, although the temperature measurement accuracy is sacrificed, it can improve the initial temperature difference (T m -T i ), the measurement accuracy of the heat transfer coefficient can still be guaranteed, which is more conducive to the promotion of non-contact temperature measurement technologies such as infrared thermal imagers.

[0075] It should be noted that the specific embodiments described in this specification may have different formula forms, names, etc. Any equivalent or simple changes made based on the structure, features and principles described in the inventive concept of the present invention are included in the scope of protection of the present invention. Those skilled in the art of the present invention may make various modifications or supplements to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should fall within the scope of protection of the present invention.

Claims

1. A transient method for measuring the heat transfer coefficient of a solid wall surface with wide applicability, characterized in that: The method comprises at least the following steps when implemented: SS1. Define dimensionless temperature And define a parameter proportional to time t A parameter proportional to the heat transfer coefficient h In the above definitions, T i is the temperature of the wall of the object to be measured at the initial time t=0, T m is the instantaneous wind tunnel inflow temperature at the initial time t=0, T w is the wall temperature of the object to be measured at time t, and the parameters t, k, ρ, and c are time, thermal conductivity of the object to be measured, incoming flow density, and heat capacity coefficient of the object to be measured, respectively; SS2. According to the parameters defined in step SS1, the wall temperature of the object to be measured T i The relationship that changes with time t Rewrite it and according to α=β 2 t, we get the following relationship: SS3. Use at least one of the following two methods to analyze the relationship Solve and obtain the wall heat transfer coefficient h of the object to be measured: Method 1: Direct solution get The dimensionless temperature θ at time t and the dimensionless temperature change rate with time Obtain β, and then according to the relationship The heat transfer coefficient h is calculated, that is, the instantaneous wind tunnel inflow temperature T at time t = 0 is measured in the wind tunnel experiment. m , t=0 time the temperature of the wall of the object to be measured T i 、The object to be measured has an initial temperature difference T m -T i The wall temperature T at a certain moment w , temperature change rate over time And the corresponding time t, the wall heat transfer coefficient h of the object to be measured can be solved; Method 2: Substitute into the relation The temperature T of the wall of the object to be measured at two different moments, namely, at time t1 and t2, is obtained in the transient temperature measurement. w1 、T w2 ,get: According to this relationship, the instantaneous wind tunnel inflow temperature T is measured at time t = 0 in the wind tunnel experiment. m , two moments t1, t2 and the wall temperature T of the object to be measured at the corresponding moments w1 、T w2 , temperature change rate over time The wall heat transfer coefficient h of the object to be measured can be calculated; SS4. The operation steps of the transient heat transfer coefficient measurement method with wide applicability are as follows: SS4.1 places a one-dimensional semi-infinite test piece in the wind tunnel test section. When the overall temperature of the test piece is kept uniform, that is, the internal temperature of the test piece is kept consistent with the wall temperature, the wall temperature T of the test piece is measured by non-contact temperature measurement at the initial time t=0. i , and start the wind tunnel fan to introduce air with a temperature of T into the wind tunnel test section. m The instantaneous flow, and T m ≠T i , that is, the instantaneous wind tunnel inflow temperature T at the initial time t = 0 m The wall temperature T of the test piece under test i Not equal; S S4.2 At the initial temperature difference T m -T i Under the wind tunnel conditions, the wall temperature of the test piece of the object to be tested is measured by non-contact temperature measurement. The two-dimensional wall temperature distribution T of the wall of the test piece of the object to be tested at different times t is measured. w and / or calculate its rate of change over time t SS4.3: Use method 1 or method 2 of step SS3 to process data at different positions on the wall of the test piece of the object to be tested, and calculate the wall heat transfer coefficient h at the corresponding position.

2. The method for measuring heat transfer coefficient of a solid wall surface using a transient method with wide applicability according to claim 1 is characterized in that: In the above step SS4, the one-dimensional semi-infinite object to be tested is a test piece with a certain thickness, and its surface to be tested is a plane or a curved surface.

3. The method for measuring heat transfer coefficient of a solid wall surface using a transient method with wide applicability according to claim 1, characterized in that: In the above step SS2, the wall temperature T i The relationship that changes with time t Rewriting it, we get the following relationship: in, is the complementary error function, η is an arbitrary real number; Solving for the derivative of θ with respect to α, we have Further substitute α=β 2 t, then 4. The method for measuring heat transfer coefficient of a solid wall surface using a transient method with wide applicability according to claim 1, characterized in that: In the second method of step SS3 above, first Substitute into the relation get: In the transient temperature measurement, the wall temperature T of the object to be measured is obtained at two different moments, namely, at time t1 and time t2. w1 、T w2 , substitute And dividing, we get: According to this relationship, the instantaneous wind tunnel inflow temperature T is measured at time t = 0 in the wind tunnel experiment. m , two moments t1, t2 and the wall temperature T of the object to be measured at the corresponding moments w1 、T w2 , temperature change rate over time The wall heat transfer coefficient h of the object to be measured can be calculated.

5. The method for measuring heat transfer coefficient of a solid wall surface using a transient method with wide applicability according to claim 1 is characterized in that: In the above step SS4, the non-contact temperature measurement method includes but is not limited to infrared thermal imager temperature measurement or narrow-band thermochromic liquid crystal.

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