CN113656993B - Thermoelectric stealth cloak based on temperature-dependent transformation thermophysics design - Google Patents
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Abstract
The invention belongs to the fields of new materials, energy technology and infrared technology, and particularly relates to a thermoelectric stealth cloak designed based on temperature-dependent transformation thermoelectrics. The invention considers the thermoelectric effect of temperature dependence of physical parameters, couples the electric field and the thermal field through the Seebeck coefficient, and uses the coordinate transformation theory containing temperature to control the thermal field and the electric field simultaneously. Compressing a circular or spherical area from the center of a circle into an annular area through coordinate transformation, and further converting the space change into material parameter change, so that the design parameters of the thermoelectric stealth cloak can be obtained; the thermoelectric cloak is internally shielded from external heat and current while not being detected by external infrared or potential detection. The invention verifies the feasibility of design through finite element simulation, provides a brand new method for regulating and controlling multiple physical fields, and simultaneously considers the temperature effect, thereby being beneficial to practical application, such as: spoofing multi-field detection, thermoelectric protection.
Description
Technical Field
The invention belongs to the fields of new materials, energy technology and infrared technology, and particularly relates to a thermoelectric stealth cloak designed based on temperature-dependent transformation thermoelectrics.
Background
Over the past decade, researchers have applied coordinate transformation theory to control a single physical field, enabling manipulation of various physical fields. However, multiple physical fields are ubiquitous in nature, industrial production, and daily life, and thus manipulation of multiple physical fields is critical. Simultaneous and coordinated manipulation of different physical fields has been a long-felt and critical problem for humans when facing technological challenges of integration, miniaturization and versatility. The thermoelectric effect is an important coupled multiphysics scenario where temperature differences can create voltages and vice versa. Thermoelectric effects can be used to generate electrical energy and to measure or control the temperature of an object. By means of the thermoelectric effect, the heat flux and the electric flux can be coupled with the seebeck coefficient, and a corresponding conversion theory is established in the double-field metamaterial by converting the heat/electric conductivity and the seebeck coefficient.
To date, almost all control over multiphysics has been limited to linear media, meaning that the properties of the material are independent of environmental conditions. However, this approach may deviate to some extent from the actual situation. In previous studies, temperature dependent transformation thermal provides a powerful tool for designing multifunctional, switchable or intelligent metamaterials in diffusion systems. In order to solve the problem of multi-physical field regulation, realize the free regulation of the multi-physical field and promote the practical application, the patent proposes to utilize the transformation theory of temperature dependence to realize the thermoelectric stealth cloak in the thermoelectric effect. The thermoelectric stealth cloak can be such that internal objects do not affect the temperature and potential distribution outside the cloak as if the intermediate objects were not present. However, the conventional thermal cloak is limited to single-field and linear materials, which deviates from the actual situation.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention aims to expand the transformation theory from pure heat conduction to the thermoelectric effect, and design the thermoelectric stealth cloak with temperature dependence by considering that material parameters are temperature dependent. The thermoelectric cloak can well protect devices, and many tiny sensitive devices are scrapped due to the thermoelectric effect. The device is electrified to generate temperature difference, and vice versa, people can find objects by detecting the temperature and the potential of the outside, and the thermoelectric stealth cloak can protect one device from being found by the outside; the scheme provided by the invention can simultaneously treat the heat protection and electric protection problems aiming at heat conduction and electric conduction, thereby having important effect on practical application.
The invention provides a temperature-dependent coordinate transformation theory, which can regulate and control a thermal field and an electric field in a thermoelectric effect at the same time. The thermoelectric stealth cloak function is realized through specific coordinate transformation, namely: the designated area can be shielded from external heat flow and current, and any object placed therein is not found by external infrared detection and potential detection.
The method provided by the invention is a temperature-dependent coordinate transformation theory, and can establish a bridge with space change and material change. And (3) compressing a circular area from the center of a circle to an annular area through coordinate transformation by considering the temperature-dependent material parameters, and further converting the space change into the material change, so that the temperature-dependent material parameters of the thermoelectric stealth cloak can be obtained.
The method provided by the invention can be directly popularized from two-dimensional conditions to three-dimensional conditions.
The present invention provides a method wherein the thermal field and the electric field in the thermoelectric effect are coupled by a seebeck coefficient, which is temperature dependent taking into account thermal conductivity, electrical conductivity, seebeck coefficient.
The main scientific principles of this device will be explained below:
for a thermoelectric system in a localized equilibrium state (steady state), i.e., where the thermodynamic parameters of the various parts of the system do not change over time, the thermoelectric field control equation can be written as follows:
wherein J and J Q Representing a current density vector and a heat flux density vector, respectively. The current density vector and the heat flow density vector satisfy constitutive equation (2)
Wherein σ (T), κ (T) and S (T) are second-order tensor expressions of electrical conductivity, thermal conductivity and seebeck coefficient, respectively, in relation to temperature, μ and T represent electrochemical potential and temperature, respectively, and the superscript τ is a transposed symbol. The first term on the right side of the equation (2) is the independent transport term of the current and the heat flow, and the second term is the coupled transport term of the current and the heat flow, namely the temperature gradient in the systemAnd potential gradient->The presence of (c) results in new current and heat flow term generation, respectively. The current and heat flow are coupled through the seebeck coefficient S (T).
The thermoelectric control equation uses the temperature-dependent transformation theory, and the transformed thermal conductivity, electrical conductivity and Seebeck coefficient can be respectively written as
Where detA is the determinant of the Jacobian transformation matrix, A τ Is the transpose of the jacobian transform matrix. If the seebeck coefficient before transformation is isotropic, it remains unchanged before and after transformation, it can be written as S' (T) =s (T) =yt (γ is a constant). The thermal conductivity before transformation can be written as κ (T) =α+βt n (α, β and n are constants), in a material with electron conduction as the main form, the relationship between thermal conductivity and electrical conductivity is κ/σ=lt (L is lorentz number) according to classical Wei Deman-friemann-Franz law (Wiedemann-Franz law), so the electrical conductivity before transformation can be written as σ (T) =αt -1 /L+βT n-1 /L。
Considering the two-dimensional case, the coordinate change formula from the virtual space (r, θ) to the physical space (r ', θ') is as follows
Wherein r is 1 And r 2 The inner diameter and the outer diameter of the thermoelectric stealth cloak, r epsilon [0, r respectively 2 ]，r′∈[r 1 ，r 2 ]. The physical meaning of equation (4) is to compress a circular region from the center of a circle to an annular region. The Jacobian transformation matrix A of the coordinate transformation is
By means of the jacobian transformation matrix a, we can get the corresponding material variation. Substituting the formula (5) into the formula (3) to obtain the thermoelectric stealth cloak annular area [ r ] 1 ，r 2 ]The internal thermal conductivity and electrical conductivity are given in formula (6)
So far, 3 key parameters about designing thermoelectric stealth have been determined.
The technology can be directly popularized to the three-dimensional situation, and compared with the two-dimensional situation, the three-dimensional situation is only different from the two-dimensional situation in that the Jacobian transformation matrix A is adopted, the formula (5) can be directly transformed into the formula (7), and the algorithms of the rest and the two-dimensional situation are identical.
Substituting the formula (7) into the formula (3) to obtain the three-dimensional thermoelectric stealth cloak spherical shell area [ r ] 1 ，r 2 ]The internal thermal conductivity and the electrical conductivity are shown as formula (8)
Compared with the prior art, the invention has the advantages that:
1) The thermoelectric stealth cloak based on temperature-dependent transformation thermodynamic design has universality, and a thermal electric field can be flexibly regulated and controlled through coordinate change.
2) The thermoelectric stealth cloak based on temperature-dependent transformation thermodynamic design has practical significance, and material parameters are considered to be temperature-dependent.
3) The thermoelectric cloak designed based on temperature-dependent transformation thermodynamics is applicable to a wide temperature range.
4) The thermoelectric stealth cloak based on temperature-dependent transformation thermodynamic design is suitable for two-dimensional situations and three-dimensional situations.
Drawings
FIG. 1 is a two-dimensional schematic view of a thermoelectric cloak, wherein the annular region corresponding to the inner and outer diameters is the thermoelectric cloak, any object can be placed in the middle white region, black lines represent heat flow, and white lines represent current.
FIG. 2 is a two-dimensional simulated view of a thermoelectric cloak. (a) The temperature depends on the temperature profile of the thermoelectric cloak and the black line represents the isotherm. (b) The temperature depends on the potential profile of the thermoelectric cloak and the white line represents the equipotential lines. The temperature and potential of the left boundary of the square background is 600K and 10mV, the right boundary is 300K and 0mV (ground), and the upper and lower boundaries are thermally and electrically insulated at the same time. The simulated size is 8X 8cm 2 ，r 1 ＝1cm，r 2 =2cm. The background parameter is n=3, l=1, α=100 Wm -1 K -4 ，β＝10Wm -1 K -4 ，γ＝3×10 -5 VK -2 . The parameter settings of the thermoelectric cloak are designed according to equations (3) and (6), where the jacobian matrix is determined by equation (5).
FIG. 3 is a finite element simulation of a two-dimensional thermoelectric cloak under different boundary conditions. Columns 1 and 2 are respectively a pure background, thermoelectric stealth cloak. The low temperature of the right boundary of all simulated diagrams is fixed to 300K, the high temperature of the left boundary is set to 700K, 1100K and 1500K from the 1 st row to the 3 rd row, the upper boundary and the lower boundary are insulated thermally and electrically at the same time, the potential of the left boundary is 10mV, and the potential of the right boundary is 0mV. In all simulations, the simulated dimensions were 8X 8cm 2 ，r 1 ＝1cm，r 2 =2cm. The background parameter is n=3, l=1, α=100 Wm -1 K -4 ，β＝10Wm -1 K -4 ，γ＝3×10 -5 VK -2 . The parameter settings of the thermoelectric cloak are designed according to equations (3) and (6), where the jacobian matrix is determined by equation (5). Black lines and arrows indicate isotherms and heat flow, and gray arrows indicate current.
FIG. 4 is a temperature/potential versus position plot of a thermoelectric cloak under different boundary conditions. The data is extracted from the temperature and potential data for the horizontal center line in the finite element simulation graph made in fig. 3, with the solid line representing the simulation results in the presence of a thermoelectric cloak and the dashed line representing the simulation results in a pure background. (a) and (b) are temperature and potential profiles, respectively.
FIG. 5 is a three-dimensional simulated view of a thermoelectric stealth cloak. (a) The temperature depends on the temperature profile of the thermoelectric cloak and the black line represents the isotherm. (b) The temperature depends on the potential profile of the thermoelectric cloak and the white line represents the equipotential lines. The temperature and potential of the left boundary surface of the cube are 600K and 10mV, the right boundary surface is 300K and 0mV, and the other four surfaces are insulated thermally and electrically at the same time. The simulation size is 8 multiplied by 8cm 3 ，r 1 ＝1cm，r 2 =2cm. The background parameter is n=3, l=1, α=100 Wm -1 K -4 ，β＝10Wm - 1 K -4 ，γ＝3×10 -5 VK -2 . The parameter settings of the thermoelectric cloak are designed according to formulas (3) and (8), wherein the jacobian matrix is determined by formula (7).
Detailed Description
The present invention will be described in detail with reference to specific examples and drawings, but the present invention is not limited thereto.
A two-dimensional schematic of a thermoelectric cloak is shown in fig. 1, wherein the annular region between the inner and outer diameters is the thermoelectric cloak, and any object can be placed in the middle white region, and neither heat nor current will flow through this region. The stealth cloak can simultaneously solve the problem of heat conduction and electric conduction, so that the heat protection and electric protection functions of heat transportation and electric transportation can be simultaneously realized.
To demonstrate the correctness of theory, the present invention utilizes commercial finite element modeling software COMSOL Multiphysics for verification. The two-dimensional simulation results of the thermoelectric cloak are shown in fig. 2. In the simulation process, the left side is set to be a high-temperature heat source and a high potential, the right boundary is set to be a low-temperature cold source and a ground, and the upper boundary and the lower boundary are insulated thermally and electrically at the same time. From the observation of the simulation results, it can be found that: in the temperature evolution process, the isotherm of the background is straight and not distorted all the time, which indicates that the external infrared detection can not know any information of the middle white area, thereby achieving the effect of thermal stealth; the external equipotential lines are not distorted, and the object in the middle white area cannot be detected by the external potential detection, so that the effect of electric stealth is achieved.
Since the material parameters considered by the temperature-dependent thermoelectric conversion theory are temperature-dependent, the thermoelectric stealth cloak is applicable in a wide temperature range in order to show that the temperature-dependent thermoelectric conversion theory is universal, and the thermoelectric stealth cloak under different boundary conditions is further designed by the patent and is shown in fig. 3. From the simulation results fig. 3, it can be found that: in a very wide temperature range, neither the background isotherm nor the equipotential line is distorted, neither the heat flow nor the current enters the central white region, indicating that both the heat and the electricity achieve stealth effects. To more intuitively embody the effect of temperature dependence, the patent extracts a plot of temperature and potential data of the horizontal center line in the finite element simulation diagram made in fig. 3, which is shown in fig. 4. It can be seen from fig. 4 that the greater the temperature difference between the high temperature heat source and the low temperature cold source in the environment where the material is located, the change in temperature and potential will no longer be linear, but the data outside the cloak will still coincide with the data of the pure background map, exhibiting excellent thermal and electrical stealth capabilities.
The three-dimensional steady-state simulation was also performed without loss of generality in this patent, where the thermoelectric cloak was a three-dimensional shell, the results of which are shown in fig. 5. The left boundary surface is a high-temperature heat source and a high-potential surface, the right boundary surface is a low-temperature cold source and a low-potential surface, and the other four surfaces are insulated thermally and electrically. For convenience of presentation, the invention is viewed with a section taken in the middle. Similar to the two-dimensional results, the background isotherms and equipotential lines remain untwisted, exhibiting excellent thermal and electrical stealth capabilities.
Claims (1)
1. The thermoelectric cloak is characterized in that a thermoelectric cloak designed based on temperature-dependent transformation thermophysics is considered, a thermal electric effect is considered, an electric field and a thermal field are coupled through Seebeck coefficients, a circular or spherical area is compressed from a circle center into an annular area through coordinate transformation, the change of space is converted into the transformation of material parameters, the material parameters are adjusted, so that an inner circle of the annular area or an inner sphere shields external heat flow and current, objects placed in the annular area cannot be found by external infrared detection and potential detection, the design parameters of the thermoelectric cloak are obtained, and the annular area is the thermoelectric cloak; wherein:
the coordinate transformation process is as follows:
for the two-dimensional case, the coordinate transformation from the virtual space (r, θ) to the physical space (r ', θ') is:
wherein r is 1 And r 2 The inner diameter and the outer diameter of the thermoelectric stealth cloak are respectively, and the inner radius and the outer radius are respectively r 1 And r 2 The annular area formed by the circles of the two layers is the thermoelectric stealth cloak;
the method for calculating the Jacobian transformation matrix under the two-dimensional condition comprises the following steps:
for the three-dimensional case, from virtual spaceTo physical space->The coordinate transformation of (2) is:
the Jacobian transformation matrix calculation method under the three-dimensional condition comprises the following steps:
the inner diameter and the outer diameter are respectively r 1 And r 2 An annular area surrounded by the spherical surface of the cover is the thermoelectric stealth cloak;
obtaining corresponding transformed material parameters according to coordinate transformation, wherein the material parameters comprise thermal conductivity, electric conductivity and Seebeck coefficient, and the material parameters comprise: the transformed seebeck coefficient is S' (T) =a -τ S(T)A τ The heat conductivity after transformation isThe conductivity after transformation is +.>Wherein detA is determinant of Jacobian transformation matrix, A τ Transpose of Jacobian transform matrix, A -τ Is the transpose of the inverse matrix of A; s (T), κ (T), and σ (T) are the thermal conductivity, electrical conductivity, and seebeck coefficient before no transformation.
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| CN110826265A (en) * | 2019-10-01 | 2020-02-21 | 复旦大学 | Heat stealth cloak designed based on heat radiation conversion and heat conduction theory |
| CN110826271A (en) * | 2019-10-26 | 2020-02-21 | 复旦大学 | Thermal stealth cloak device simultaneously suitable for conduction, convection and radiation |
| CN110826266A (en) * | 2019-10-01 | 2020-02-21 | 复旦大学 | Thermal rotator device designed based on conversion thermal radiation and heat conduction theory |
| CN113008355A (en) * | 2021-03-10 | 2021-06-22 | 北京大学 | Stealth evaluation method for acoustic cloak |
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| CN110826265A (en) * | 2019-10-01 | 2020-02-21 | 复旦大学 | Heat stealth cloak designed based on heat radiation conversion and heat conduction theory |
| CN110826266A (en) * | 2019-10-01 | 2020-02-21 | 复旦大学 | Thermal rotator device designed based on conversion thermal radiation and heat conduction theory |
| CN110826271A (en) * | 2019-10-26 | 2020-02-21 | 复旦大学 | Thermal stealth cloak device simultaneously suitable for conduction, convection and radiation |
| CN113008355A (en) * | 2021-03-10 | 2021-06-22 | 北京大学 | Stealth evaluation method for acoustic cloak |
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