The invention is with respect to the invaded material detection. A method was proposed for measuring the invaded foreign substance content into a porous material with a finite thickness based on virtual heat source principle.
The absorption or invasion of a foreign substance into a porous material may change the properties of the material itself. For example, once a porous insulation material absorbs water, the thermal insulation and acoustic attenuation performance would be greatly degraded. More critically, microbial growth and various types of corrosion will be resulted, leading to numerous adverse effects. Measurement of the invaded foreign substance content into the porous material would help minimize the negative impacts mentioned above. There are many methods for measuring the invaded foreign substance content, such as water, into porous materials. However, the existent methods still have flaws in terms of pricing, simplicity, and reliability, etc. The heat pulse method infers the absorbed water content based on the dynamic temperature response subject to a sudden heat pulse. The method has been widely studied because of its low cost, simplicity, and ease of implementation.
The article “Probe for measuring soil specific heat using a heat-pulse method” authored by Campbell G S, Calissendorff C, and Williams J H. and published in Soil Science Society of America Journal, 1991, 55 (1): 291-293, proposed a two-probe method for measuring the volumetric heat capacity of soil and the water content therein. The dual probe consisted of a heating needle probe and a temperature sensor probe. The heating needle was in parallel with the temperature sensor probe with a known fixed distance. The heating needle generated a heat pulse of 8 seconds, and the temperature sensor recorded the temperature responses. According to the analytical solution of the maximum temperature rise in an infinitely large medium, the volumetric heat capacity was calculated and then the moisture content was solved. Limited by the adopted assumption, this method can only be used to measure moisture in a material with a sufficiently large size and no heat transfer across the boundary. The paper “An adiabatic boundary condition solution for improving the heat-pulse measurement near the soil-atmosphere interface”, authored by Liu G, Zhao L, Wen M, et al., published in Soil Science Society of America Journal, 2013, 77(2): 422-426, proposed a method for measuring the moisture content in a material with an adiabatic boundary. The method was an improvement to the two-probe heat pulse method. The paper thought that the thermal diffusivity of soil is much larger than that of air, so the soil-air interface could be treated as an adiabatic boundary, as evaluated by their conducted COMSOL simulation. A virtual heat source with the same flux as the actual source, i.e., qvirtual=qreal, was added to the image of the actual heat source with respect to the assumed adiabatic boundary. Hence, the temperature response in a semi-infinite domain bounded by an adiabatic boundary can be approximated into the temperature response by two symmetric identical heat sources in an infinite domain. The temperature rises calculated by the above model were matched with the measured temperature rises to obtain the material's volumetric capacity and water content. However, the material-air interface may not be the exact adiabatic boundary especially when the heat probe was very close to the interface, which limits wide application of this method.
The Chinese invention patent application, No. CN107356627A, proposed a method for determining the invaded foreign substance content into a porous material based on principle of virtual heat source and using four-parameter matching. A virtual heat source in the image of the actual heat source with respect to the heat loss boundary was added into the domain. The ratio of the virtual heat source's intensity qvirtual to the actual heat source's intensity qreal was defined as n. Before proposing this method, n was assigned a fixed value of either −1 or 1. Consequently, the thermal boundary of either constant temperature (n=−1) or no heat flow (adiabatic, n=1) was reproduced. This invention extended n into an arbitrary value between −1 and 1. When n is assigned a value other than −1 and 1, it represents a certain thermal boundary with a finite heat transfer rate. In a solution, the virtual heat source's intensity (n), the material's thermal properties, and the mass content of the invaded substance were determined by matching the measured temperatures. Because the above method accounted for heat transfer across the boundary, the accuracy of measuring moisture content in a semi-infinite material with or without heat transfer can be much improved. The required test material's volume using this method is only half of that using the conventional heat pulse method. The heat transfer across the boundary can be arbitrary.
The above review reveals that there are many researches on development of the heat pulse method. The existing methods require that the measured material has a sufficiently large size or a semi-infinite size containing a single boundary for heat transfer. However, in practical use, most of the test materials have only a finite size in a thin plate shape, such as the thermal insulation materials to minimize the building's heat transfer. When adopting the heat pulse method for measurement, the heat transfer across boundaries is unknown and cannot be ignored. The existing methods cannot measure the foreign substance content into the plate-shape material with a finite thickness.
This invention proposed to employ an infinite number of virtual heat sources with two different heat intensities. The ratios of these two different heat intensities to the actual heat source's intensity qreal were defined as n1 and n2, respectively. n1 and n2 could be an arbitrary number between −1 and 1. Through superposition of temperatures by the actual and virtual heat sources in an infinite space, the temperature responses due to the heating of the probe inside the plate-shape material can be quickly solved. Then the volumetric heat capacity and the foreign substance content can be inferred provided with the measured temperatures.
The aim of this invention is to provide a method for measuring the foreign substance content into a thin plate porous material based on the principle of virtual heat sources.
The technical schemes of the invention are as follows:
The operating steps of a method for measuring the foreign substance content into a porous material with a finite thickness based on the principle of virtual heat sources:
(1) Place the plate-shape test material in a sunshade environment. Avoid strong radiation heat transfer between the surrounding environment and the surfaces of the test material. Deploy a needle like heating element inside the test material and assure the heating element is in parallel with the outer boundaries. Deploy the temperature sensors at two or more locations within the test material. The distances of each temperature sensor away from the heating element should be known and different.
(2) Before turning on the heating element, make sure the initial temperature of the test material is uniformly distributed and stable, and record the temperature as the initial temperature. Turn on the heating element according to the specified known constant intensity (heating power rate per unit length), and collect the temperature responses using the sensors. The differences of the recorded transient temperatures with the initial temperature are the temperature rises at the sensor positions.
(3) Establish an infinite number of virtual heat sources according to the principle of virtual heat sources, and obtain an approximate solution of the temperature rises at the sensor locations.
Following the Chinese Patent Application, No. CN107356627A, a virtual heat source was added to represent a specific heat transfer boundary in a semi-infinite domain. One of the heating elements in the domain is the actual one with a heating intensity of qreal. The other heating element is the virtual one located at the image of the actual heating element with respect to the heat transfer boundary. The virtual heating element has an intensity of qvirtual=n·qreal, where n is an arbitrary rational number between −1 and 1. If n=1, the boundary is adiabatic; if n=−1, the boundary has constant temperature; if −1<n<1, the boundary is between adiabatic and constant temperature.
In this invention, the test material has two parallel boundaries with a finite separating distance. As shown in
The actual source's heat intensity is qreal, which is known and controlled in the measurement process. The intensities of the virtual heat sources are divided into two categories, according to the above naming rule, the virtual heat sources with the subscript 1 have the same heating intensity of n1·qreal; the virtual heat sources with the subscript 2 share the same heating intensity of n2·qreal. n1 and n2 are arbitrary rational numbers ranging from −1 to 1. If n1 or n2 is equal to −1 or 1, it designates the outer boundary A or the outer boundary B as the constant temperature or adiabatic type, respectively.
In the actual measurement process, in most cases, the boundaries A and B are between the constant temperature and the adiabatic types, so n1 and n2 range from −1 to 1. Because the heat transfer conditions on boundaries A and B are unknown, the estimation of the heat transfer rates on boundaries A and B is converted into a solution for n1 and n2. It should be aware that the above description is based on the assumption that the impacts of the heating element itself to heat transfer are negligible. That is, the heating element can be simplified into an infinite long-line heat source.
As shown in
(4) Compare the recorded temperature rises at the sensor locations in step (2) with the approximate solution temperature rises at the corresponding positions in step (3). The root mean square error or other errors, such as DEV, can be adopted to evaluate the time-dependent temperature rise differences between the measurement and the solution. Then the following four parameters are searched: the thermal conductivity k of the test material, the volumetric heat capacity ρc, the parameter n1 representing the heat transfer on boundary A, and the parameter n2 representing the heat transfer on boundary B. The values or range of values of the four parameters should make the DEV minimum or within the set acceptable level.
(5) The content or content range of the foreign substance into the porous material is calculated based on the corresponding change of the volumetric heat capacity □c after the invasion of the foreign substance with a certain mass.
Beneficial effects of this invention: The present invention provides a method for measuring the invaded mass of the foreign substance into a finite-thickness flat plate material. An infinite number of virtual heat sources were proposed to approximate the certain heat transfer on boundaries of the plate material. Unlike the existent methods, there is no specific requirement on the domain size of the test materials and the heat transfer boundary conditions, which makes the measurement more readily.
The implementation of the invention will be further described by taking a finite-thickness flat plate porous material to measure the invaded foreign substance content, such as the water content therein, as an example.
The operating steps for measuring the foreign substance content into a porous material with a finite thickness based on the principle of virtual heat sources are as follows:
Temperature rise due to a linear heat source in an infinite space can be formulated as:
where ΔTM,th(q, r) is the temperature rise (° C.) at a distance r (m) from a heat source with the heating intensity q (Wm−1), k is the thermal conductivity of the test material (Wm−1 K−1), ρ is the test material's density (kgm−3), c is the specific heat capacity of the test material (Jkg−1 K−1), ρc is the volumetric heat capacity of the test material (Jm−3 K−1), τ is time (s).
According to the principle of virtual heat sources, as shown in
ΔTM=ΔTM,th(qreal,rreal)+ΔTM,th(q1,r1)+ΔTM,th(q2,r2)+ΔTM,th(q1′,r1′)+ΔTM,th(q2′,r2′) (2)
where ΔTM is the temperature rise (° C.) by the actual and a sufficient number of virtual heat sources; ΔTM,th(q, r) is the temperature rise (° C.) at a distance r from the heat source whose intensity is q; qreal is the heat source intensity of the actual heating element (Wm−1), which is known and controlled in the measurement process; rreal(m) is the distance between the temperature sensor and the actual heat source. rreal is RS1 or RS1. q1, q2, q1′ and q2′ are the heating intensities of the four virtual heat sources with a distance from the temperature sensor of r1, r2, r1′ and r2′ (m), respectively.
The relationship of q1, q2, q1′ and q2′ qreal is:
q
1
=q
1
′=n
1
·q
real (3)
q
2
=q
2
′=n
2
·q
real (4)
where n1 and n2 are the rational number representing the heat transfer rate on boundaries A and B, and n1 and n2 range from −1 to 1.
The distances of r1, r2, r1′ and r2′ are related to the position of the temperature sensor, and is a function of rreal, D1 and D2. According to
r
1=√{square root over (rreal2+(2D1)2)} (5)
r
2=√{square root over (rreal2+(2D2)2)} (6)
r
1′=√{square root over (rreal2+(2D1+2D2)2)} (7)
r
2′=√{square root over (rreal2+(2D1+2D2)2)} (8)
where ΔTM,i is the temperature rise (° C.) for the ith time interval index; ΔTE,i is the measured temperature rise (° C.) at the ith time interval index; and in is the total number of sampled temperature data points in the measurement. If using two temperature sensors, two sets of temperature rise data and DEV can be obtained, and the final DEV can be the average of the two DEVs.
The range of the four parameters for searching can be set into: the thermal conductivity k ranging from that of the pure test material without any invaded substance to that of the pure invaded substance, and so do for the volumetric heat capacity ρc; n1 and n2 ranging from −1 to 1. It is recommended to use the Matlab optimization toolbox to search for the above expected four parameters.
where xw is the volumetric mass of the invaded foreign substance (for water, the unit is kg H2Om−3); ρc is the volumetric heat capacity (Jm−3 K−1) of the test material with the invaded foreign substance; ρ0 is the density of the test material before invasion of the foreign substance (kgm−3); c0 is the specific heat capacity of the test material before invasion of the foreign substance (Jkg−1 K−1); and cw is the specific heat capacity of the pure invaded foreign substance (Jkg−1 K−1). The volumetric heat capacity of the test material before invasion of the foreign substance ρ0c0 can be obtained from the handbook, or measured by the proposed method in this invention.
Number | Date | Country | Kind |
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2018102856202 | Mar 2018 | CN | national |
Filing Document | Filing Date | Country | Kind |
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PCT/CN2018/088690 | 5/28/2018 | WO | 00 |