A Thermal Method for Measuring Cumulative Heterogeneous Thickness

Abstract

The present invention discloses a thermal method for measuring the cumulative heterogeneous thickness. A planar heat source is used to provide a constant heat flux, and the transient temperature rise value at the heat source and the heterogeneous interface and the heat flux passing through are measured by a temperature sensor and a heat flux sensor respectively. Based on the analytical solution of unsteady-state solid heat conduction, the quantitative relationship between the temperature rise at the interface, the heterogeneous cumulative thickness and time is deduced. Since an explicit solution for the heterogeneous cumulative thickness cannot be obtained, a data set of temperature rise dependent on thickness is established by enumerating all possible heterogeneous cumulative thicknesses, and the functional relationship between the temperature rise value and the heterogeneous continuous cumulative thickness is fitted by interpolation. When the measured temperature rise values at the interface for certain periods are provided, the actual thickness of the heterogeneous accumulation at this time can be quickly solved. The device adopted by this method has a simple structure, is cheap and convenient, and has universality for the measurement scenario of fully mixed fluid flowing over the heterogeneous surface.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement, and relates to a method for measuring the thickness of heterogeneous substances based on the principle of unsteady heat conduction of a sheet-shaped planar heat source. Background Art

[0002] Heterogeneous substances are likely to accumulate on the surfaces of media in small spaces such as freezers, pipe joints, and stirrers. When excessive heterogeneous substances accumulate on their surfaces, the operating performance will be severely affected, and even the machine may be damaged. Frost formation in the freezer seriously affects the refrigeration effect, reduces the refrigeration efficiency, increases the energy consumption, and causes waste of energy; impurity deposition in the pipe joint causes blockage of the pipeline and affects fluid transportation; the stirrer mixes multiple raw materials, and heterogeneous deposition and blockage are very likely to occur, resulting in machine malfunctions. Therefore, accurately detecting the presence of heterogeneous substances and precisely measuring their thickness are of great help for guiding the maintenance of machines and ensuring their optimal working performance.

[0003] According to different measurement principles, the commonly used methods for detecting the thickness of heterogeneous substances currently include ultrasonic method, magnetic method, eddy current method, isotope method, thermal method, etc. Among them, the thermal method has been widely studied due to its characteristics such as low cost and convenient measurement. The thermal method is to apply electric current to heat the measured medium, and calculate the accumulation of heterogeneous substances on the surface of the medium by monitoring the temperature response signal on the surface of the medium.

[0004] The current thermal method for measuring the thickness of heterogeneous substances mostly uses a steady-state method and has the following problems:

[0005] (1) The steady-state thermal method for measuring the thickness of heterogeneous substances needs to obtain a steady-state temperature field where the temperature distribution does not change with time. However, since it is relatively difficult to construct a stable temperature gradient by the steady-state method, the test period is relatively long;

[0006] (2) When the steady-state thermal method measures the thickness of heterogeneous substances, a stable measurement environment is required to ensure the measurement accuracy. When the measurement environment changes or the application scenario is switched, re-measurement arrangements are needed. Therefore, the steady-state thermal method measurement is not universal for multiple measurement scenarios. Summary of the Invention

[0007] In order to solve the problems existing in the prior art, the present invention provides a thermal method for measuring the thickness of heterogeneous substance accumulation. The measurement device is pre-arranged on the surface of the medium, and the transient temperature rise value is used to measure the thickness of heterogeneous substance accumulation, so as to solve the problems of long measurement time, low accuracy, and limited application scenarios of the steady-state thermal method for measuring the thickness of heterogeneous substances.

[0008] The technical solution of the present invention is as follows:

[0009] A thermal method for measuring the thickness of accumulated heterogeneous substances, characterized in that the measurement steps are as follows:

[0010] a. Arrange the temperature sensor, planar heat source, and heat flux sensor in sequence and make them fit tightly, and attach the combined device as a whole to the surface of the object where solid media are likely to deposit or accumulate in advance, for measuring the heterogeneous thickness accumulated on the surface of the object.

[0011] b. Keep the heating circuit in the off state and let the planar heat source stand still in the test environment. After the surface temperature field distribution is stable, use the temperature sensor to record the temperature T at the initial moment of the planar heat source and the heterogeneous interface. 0 ;

[0012] c. Turn on the heating circuit, and the planar heat source starts to generate heat. According to the input power Q and the effective heating area A of the planar heat source, the total heat flux q output by the heat source can be calculated as q = Q / A.

[0013] d. The heat flux sensor records the heat flux q transmitted by the heat source to the non-heterogeneous side. According to the principle of energy conservation, the accurate heat flux q transmitted along the heterogeneous to be measured can be obtained. 1 , and q = q - q e ; 1 ;

[0014] e. Use the temperature sensor to measure the temperature of the planar heat source and the heterogeneous interface. After the surface temperature is stable, record the temperature T 1 , and calculate the transient temperature rise ΔT E (t) = T 1 - T 0 ;

[0015] f. Combine the differential equation, boundary conditions, and initial conditions of the one-dimensional heat conduction process of the transient planar heat source to obtain the analytical solution ΔT(t) of the temperature rise at the position of the temperature sensor of the planar heat source within t time.

[0016] g. Establish the functional variation relationship between the temperature rise value and the thickness at the same moment through numerical solution. Substitute the temperature rise value of the planar heat source measured in step e to obtain the heterogeneous cumulative thickness l on the surface of the object at time i. i .

[0017] Compared with the existing thermal methods for measuring heterogeneous thickness, the beneficial effects of the present invention are as follows:

[0018] (1) The present invention measures the heterogeneous thickness by using the transient temperature rise value of the heat source, without the need to wait for a long time for the temperature of the measurement scenario to reach stability, shortening the test time and reducing the requirements for the test environment.

[0019] (2) The present invention has universality for the measurement scenarios where the fluid flowing over the heterogeneous surface is fully mixed, and can be applied to various measurement scenarios, such as the measurement of the cumulative thickness of media such as mixer blades, radiator fan blades, and the surfaces of refrigerators and freezers.

[0020] (3) With one measurement of the present invention, multiple sets of transient temperature rise data can be obtained. Based on the temperature rise data at different times, multiple sets of heterogeneous cumulative thicknesses on the surface of the object are solved and data processing is carried out. By taking the average method, the measurement accuracy of the heterogeneous thickness can be increased, and the measurement deviation that may occur in a single measurement of a single set of data can be avoided.

[0021] (4) The method of the present invention only needs to measure two key physical parameters, namely the transient temperature rise value on the surface of the heat source and the heat flux density transferred along the heterogeneity, to calculate the heterogeneous thickness. The method is simple, accurate, and highly operable. Description of the Drawings

[0022] Figure 1 is the heat transfer model for measuring the heterogeneous cumulative thickness provided by the present invention; in the figure: 1 is the heterogeneous to be measured; 2 is the heating body; q e is the heat flux density transferred along the heterogeneity, Wm -2 ;

[0023] Figure 2 is the schematic layout diagram of the heterogeneous thickness measuring device provided by the present invention; Figure 2 (a) is the overall layout diagram, Figure 2 (b) is the schematic diagram of the measurement probe structure; in the figure: 3 is the overall structure of the heterogeneous thickness measurement probe; 4 is the heating circuit; 5 is the planar heat source; 6 is the temperature sensor for measuring the temperature at the interface between the planar heat source and the heterogeneity; 7 is the heat flux sensor for measuring the surface heat flux on the side of the heat source not adjacent to the heterogeneity; U is the voltage supplied to the planar heat source, V; 8 is the surface of the object;

[0024] Figure 3 is the flow chart of a thermal method for measuring the heterogeneous cumulative thickness provided by the present invention; in the figure: T 0 is the temperature at the initial moment of the interface between the planar heat source and the heterogeneity, K; Q is the input power of the heating circuit, W; A is the effective heating area of the planar heat source, m 2 ; q is the total heat flux of the planar heat source, Wm -2 ; q 1 is the heat flux output by the planar heat source to the non-heterogeneous side, Wm -2 ; q e is the heat flux density transferred along the heterogeneity, Wm -2 ; T 1 is the transient temperature at the interface between the planar heat source and the heterogeneity after power-on, K; ΔT t is the transient temperature rise value at the interface between the planar heat source and the heterogeneity, K. Detailed Embodiments

[0025] The following will specifically describe the embodiments of the present invention with reference to the accompanying drawings.

[0026] A thermal method for measuring the thickness of heterogeneous accumulation is as follows:

[0027] 1) Place the temperature sensor 6 closely against the surface of the planar heat source 5 adjacent to the heterogeneous side in the manner shown in Figure 2 (b), attach the heat flux sensor 7 to the other surface not adjacent to the heterogeneous material, and attach the assembled device as a whole to the surface of the object where solid media are likely to deposit or accumulate in advance, for measuring the thickness of the heterogeneous material 1 accumulated on its upper side;

[0028] 2) Connect the planar heat source 5 to the heating circuit 4 in the manner shown in Figure 2 (a), and the on / off of the heating circuit can be controlled manually;

[0029] 3) Keep the heating circuit 4 in the off state, let the planar heat source 5 stand still in the test environment, and after the surface temperature field distribution is stable, use the temperature sensor 6 to record the temperature T at the initial moment of the interface between the planar heat source 5 and the heterogeneous material 0 ;

[0030] 4) Turn on the heating circuit 4, the planar heat source 2 starts to generate heat. According to the input power Q and the effective heating area A of the planar heat source 2, the total heat flux q output by the heat source can be calculated as q = Q / A; the heat flux sensor 7 records the heat flux q transmitted by the heat source to the non-heterogeneous side. According to the principle of energy conservation, the accurate heat flux q transmitted along the heterogeneous material 1 to be measured can be obtained 1 , and according to the principle of energy conservation, the accurate heat flux q transmitted along the heterogeneous material 1 to be measured can be obtained e = q - q 1 .

[0031] 5) Use the temperature sensor 6 to measure the temperature at the interface between the planar heat source 2 and the heterogeneous material. After the surface temperature is stable, record the temperature T 1 , and calculate the transient temperature rise ΔT at the interface between the planar heat source 2 and the heterogeneous material during the heating process t = T 1 - T 0 ;

[0032] 6) Establish the functional relationship between the temperature rise and the thickness at the same moment through numerical solution, and substitute the transient temperature rise of the planar heat source to obtain the thickness l of the heterogeneous accumulation on the surface of the object at the i-th moment i .

[0033] The calculation model used in the present invention is as follows:

[0034] The planar heat source is located at the boundary of the heterogeneous material to be measured with a thickness of l, and the other boundary of the heterogeneous material is in contact with a well-mixed fluid. The initial temperature field is uniform, and the planar heat source generates heat at a constant power. The heat transfer process in the heterogeneous material to be measured is simplified to a one-dimensional unsteady pure solid heat conduction process, and its heat conduction differential equation, boundary conditions, and initial conditions are:

[0035]

[0036] When

[0037] When

[0038] When \(t = 0\), \(T=T_0\) 0 (4)

[0039] Solve the above partial differential equations with reference to the method in H.S. Carlslaw, J.C. Jaeger. Conduction of Heat in Solids. 2nd Edition. Oxford Clarendon Press, 1986: 89 - 129, and the analytical solution of the temperature rise at the boundary \(x = 0\) of the measured heterogeneous material is obtained as:

[0040]

[0041] where \(l\) is the cumulative thickness of the heterogeneous material, \(m\); \(\Delta T(t)\) is the transient temperature rise at the interface between the plane heat source and the heterogeneous material, \(K\); \(a\) is the thermal diffusivity of the heterogeneous material, \(m^2 / s\); 2 s -1 ; \(t\) is the heating time of the plane heat source, \(s\); \(T\) is the temperature at any point inside the measured heterogeneous material, \(K\); \(T_0\) 0 is the initial temperature of the measured heterogeneous material, \(K\); \(q\) e is the heat flux density transmitted along the measured heterogeneous material, \(W / m^2\); -2 ; \(\lambda\) is the thermal conductivity of the measured heterogeneous material, \(W / (m\cdot K)\); -1 K -1 ; \(\rho\) is the density of the measured heterogeneous material, \(kg / m^3\); -3 ; \(c\) is the specific heat capacity of the measured heterogeneous material, \(J / (kg\cdot K)\); -1 K -1 ; \(c'\) is the specific heat capacity of the fluid flowing past, \(J / (kg\cdot K)\); -1 K -1 ; \(M'\) is the mass of the fully mixed fluid flowing past a unit area of the plane heat source, \(kg / m^2\); -2 ; \(\beta\) n is the root of \(\beta\cot\beta l=-h\), \(n = 1, 2, 3,\cdots\); \(h\) is \(\rho c / M'c'\).

[0042] The numerical solution method used in the present invention is as follows:

[0043] Assume that the temperature rise time is \(n\) moments. At the \(i\)-th moment, \(i = 0, 1, 2,\cdots, n\), the numerical solution method for the cumulative thickness \(l\) of the heterogeneous material on the surface of the object in step 6) i is as follows:

[0044] A. Determine the maximum finite thickness \(l_{max}\) of the heterogeneous material accumulation on the surface of the object according to the specific application scenariomax Enumerate all possible heterogeneous cumulative thicknesses l of the object surface to establish a dataset L(0, l max .

[0045] B. Substitute the enumerated cumulative thickness l into formula (5) as the assumed thickness for temperature rise calculation, and a set of analytical solution temperature rise datasets can be obtained.

[0046] C. Approximate the discrete data points in the temperature rise dataset as a continuous function through an interpolation function to obtain the functional relationship of l = f(ΔT), where the interpolation function can be an interpolation function method such as polynomial interpolation function, cubic spline interpolation function, piecewise interpolation, etc.

[0047] D. Substitute the measured temperature rise ΔT E,i (t) into l = f(ΔT), and the heterogeneous cumulative thickness l corresponding to the measured temperature rise at time i can be obtained i .

[0048] The recommended duration for temperature rise test is 100 s, the sampling interval of temperature rise is 1 s, and 100 sets of measured temperature rise values are obtained during the test. By repeating steps A - D, 100 heterogeneous cumulative thicknesses l can be obtained i , and the finally required heterogeneous cumulative thickness l is the average value of 100 sets of data. The average value can be average value processing methods such as arithmetic mean, harmonic mean, and geometric mean. Taking the arithmetic mean as an example, the heterogeneous cumulative thickness l can be obtained as follows

[0049]

[0050] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many variations without departing from the purpose of the present invention, and all of these fall within the protection scope of the present invention.

Claims

1. A thermal method for measuring the cumulative heterogeneous thickness, characterized in that, the measurement steps are as follows: a. Arrange a temperature sensor, a planar heat source, and a heat flux sensor in sequence and make them closely fit, and pre-attach the combined device as a whole to the surface of an object where solid media are likely to deposit or accumulate, for measuring the cumulative heterogeneous thickness on the surface of the object; b. Keep the heating circuit in the off state and let the planar heat source stand still in the test environment. After the surface temperature field distribution becomes stable, use a temperature sensor to record the temperature T at the initial moment of the planar heat source and the heterointerface at this moment. 0 ; c. Connect the heating circuit, the planar heat source starts to generate heat, and according to the input power Q and the effective heating area A of the planar heat source, calculate the total heat flux q output by the heat source as q = Q / A; d. The heat flux sensor records the heat flux q transmitted from the heat source to the non-heterogeneous side. 1 According to the principle of energy conservation, the accurate heat flux q transmitted along the heterogeneous material to be measured is obtained. e = q - q 1 ; e. Measure the temperature of the planar heat source and the heterogeneous interface using a temperature sensor. After the surface temperature stabilizes, record the temperature T at this moment. 1 And calculate the transient temperature rise ΔT of the planar heat source and the heterogeneous interface during the heating process. E (t) = T 1 - T 0 ; f. Combine the differential equation, boundary conditions, and initial conditions of the one-dimensional heat conduction process of the transient planar heat source to obtain the analytical solution ΔT(t) of the temperature rise at the position of the temperature sensor by the planar heat source within time t; g. Establish the functional variation relationship between the temperature rise value and the thickness at the same moment by means of numerical solution, and substitute the temperature rise value of the planar heat source measured in step e to obtain the heterogeneous cumulative thickness l of the object surface at time i. i .

2. The thermal method for measuring the cumulative heterogeneous thickness according to claim 1, characterized in that, the differential heat conduction equation, boundary conditions, and initial conditions of the analytical solution ΔT(t) of the temperature rise at the position of the planar heat source by the temperature sensor are: When When When t = 0, T = T 0 (4) Solve the above partial differential equation system to obtain the analytical solution of the temperature rise at the boundary of the measured heterogeneous x = 0 as: Wherein, l is the heterogeneous cumulative thickness, m; ΔT(t) is the transient temperature rise value at the interface between the planar heat source and the heterogeneous interface, K; a is the thermal diffusivity of the heterogeneous material, m 2 s -1 ; t is the heating time of the planar heat source, s; T is the temperature at any point inside the measured heterogeneous material, K; T 0 is the initial temperature of the measured heterogeneous material, K; q e is the heat flux density transmitted along the measured heterogeneous material, Wm -2 ; λ is the thermal conductivity of the measured heterogeneous material, Wm -1 K -1 ; ρ is the density of the measured heterogeneous material, kgm -3 ; c is the specific heat capacity of the measured heterogeneous material, Jkg -1 K -1 ; c' is the specific heat capacity of the fluid flowing over the surface, Jkg -1 K -1 ; M' is the mass of the fully mixed fluid flowing over a unit area of the planar heat source, kgm -2 ; β n is the root of βcotβl = -h, n = 1, 2, 3…; h is ρc / M'c'.

3. The thermal method for measuring the cumulative heterogeneous thickness according to claim 1, characterized in that: Assume that the temperature rise time is n time instants. At the i-th time instant, where i = 0, 1, 2, …, n, the specific numerical solution method for the heterogeneous cumulative thickness l of the object surface in step g i is as follows: A. Determine the maximum finite thickness l of the heterogeneous accumulation on the object surface according to the specific application scenario max , enumerate all possible heterogeneous accumulation thicknesses l on the object surface to establish a data set L(0, l max ; B. Substitute the enumerated cumulative thickness l into formula (5) as the assumed thickness for temperature rise calculation, and a set of analytical solution temperature rise data sets can be obtained; C. Approximate the discrete data points in the temperature rise data set as a continuous function through an interpolation function to obtain the functional variation relationship of l = f(ΔT), where the interpolation function can be an interpolation function method such as a polynomial interpolation function, a cubic spline interpolation function, or a piecewise interpolation; D. Substitute the measured temperature rise ΔT E,i (t) into l = f(ΔT), and the heterogeneous cumulative thickness l of the object surface corresponding to the measured temperature rise at time i can be obtained i .

4. The thermal method for measuring the cumulative heterogeneous thickness according to claim 3, characterized in that: The temperature rise test duration is 100 s, the sampling interval of the temperature rise is 1 s, and 100 sets of actual measured temperature rise values are obtained during the test. By repeating steps A - D, 100 heterogeneous cumulative thicknesses l can be obtained. i , and the finally required heterogeneous cumulative thickness l is the average value of 100 sets of data. The average value can be processed by average value methods such as arithmetic mean, harmonic mean, and geometric mean. Taking the arithmetic mean as an example, the heterogeneous cumulative thickness l can be obtained as follows:

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