CN113656993A

CN113656993A - Thermoelectric stealth cloak based on temperature-dependent conversion thermoelectric design

Info

Publication number: CN113656993A
Application number: CN202110746346.6A
Authority: CN
Inventors: 黄吉平; 雷敏; 王骏
Original assignee: Fudan University
Current assignee: Fudan University
Priority date: 2021-07-01
Filing date: 2021-07-01
Publication date: 2021-11-16
Anticipated expiration: 2041-07-01
Also published as: CN113656993B

Abstract

The invention belongs to the field of new materials, energy technology and infrared technology, and particularly relates to a thermoelectric stealth cloak based on temperature-dependent transformation thermoelectric design. The thermoelectric effect of physical parameter temperature dependence is considered, the electric field and the thermal field are coupled through a Seebeck coefficient, and the thermal field and the electric field are simultaneously controlled by using a coordinate transformation theory containing temperature. Compressing a circular or spherical area from the circle center into an annular area through coordinate transformation, and further converting the change of the space into the change of material parameters to obtain the design parameters of the thermoelectric stealth cloak; the inside of the hot canopy is 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, considers the temperature effect at the same time, and is beneficial to practical application, such as: deception multi-field detection, thermoelectric protection.

Description

Thermoelectric stealth cloak based on temperature-dependent conversion thermoelectric design

Technical Field

The invention belongs to the field of new materials, energy technology and infrared technology, and particularly relates to a thermoelectric stealth cloak based on temperature-dependent transformation thermoelectric design.

Background

In the past decade, researchers have applied coordinate transformation theory to control a single physical field, achieving 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 crucial. When people face the technological challenges of integration, miniaturization and versatility, simultaneous and coordinated manipulation of different physical fields has been a long sought after and a key issue for mankind. The thermoelectric effect is an important coupled multi-physical scene, and temperature differences can generate voltages and vice versa. The thermoelectric effect 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 by a Seebeck coefficient, and a corresponding conversion theory is established in the dual-field metamaterial by converting the heat/electric conductivity and the Seebeck coefficient.

To date, almost all control of multiple physics has been limited to linear media, meaning that the properties of the material are not dependent on environmental conditions. However, this method may deviate from the actual situation to some extent. In previous studies, temperature-dependent transformation has provided 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 free regulation of the multi-physical field and promote practical application, the patent provides a thermoelectric stealth cloak realized by utilizing a temperature-dependent transformation theory in a thermoelectric effect. The thermoelectric cloak enables internal objects to not affect the temperature and potential distribution outside the cloak as if the intervening objects were not present. However, the conventional thermal stealth cloak is limited to a single field and a linear material, and is out of the actual situation.

Disclosure of Invention

In order to solve the technical problems in the prior art, the invention aims to expand the conversion theory from simple heat conduction to the thermoelectric effect, and simultaneously considers that the material parameters are temperature dependent, so as to design the thermoelectric stealth cloak with temperature dependence. The thermoelectric cloak can well protect devices, and a plurality of tiny sensitive devices are scrapped due to thermoelectric effect. The device is electrified to generate a temperature difference, and vice versa, people can find objects by detecting the temperature and the electric potential of the outside, and the thermoelectric cloak can protect one device from being found by the outside; the scheme provided by the invention can simultaneously solve the problems of thermal protection and electric protection aiming at heat conduction and electric conduction, thereby having an important effect on practical application.

The invention provides a temperature-dependent coordinate transformation theory which can simultaneously regulate and control a thermal field and an electric field in a thermoelectric effect. The thermoelectric cloak function is realized through specific coordinate transformation, namely: the designated area can be shielded from external heat flow and current flow and any objects placed therein will not be detected by external infrared detection and potentiometric 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. The temperature-dependent material parameters of the thermoelectric stealth cloak can be obtained by considering the temperature-dependent material parameters, compressing a circular area from the center of a circle into an annular area through coordinate transformation, and further converting the space change into the material change.

The method provided by the invention can be directly popularized from a two-dimensional situation to a three-dimensional situation.

The invention provides a method wherein the thermal and electric fields in the thermoelectric effect are coupled by a seebeck coefficient, taking into account that the thermal, electrical and seebeck coefficients are temperature dependent.

The main scientific principles of this device will be explained below:

for a thermoelectric system in a local equilibrium state (steady state), i.e. the thermodynamic parameters of the system parts do not change with time, the thermoelectric field control equation can be written as follows:

wherein J and J_QRespectively representing current density vector and heat flux densityA degree vector. The current density vector and the heat flux density vector satisfy the constitutive equation (2)

Where σ (T), κ (T) and s (T) are second order tensor expressions for temperature-dependent electrical conductivity, thermal conductivity and seebeck coefficient, respectively, μ and T represent electrochemical potential and temperature, respectively, and the superscript τ is the transposed symbol. The first term on the right side of the two equations (2) is the independent transport term of the current and the heat flow respectively, and the second term is the coupled transport term of the current and the heat flow, namely the temperature gradient in the system

And potential gradient

The presence of (a) results in new current and heat flow terms, respectively. The current and heat flow are coupled by the seebeck coefficient s (t).

The thermoelectric control equation is subjected to temperature-dependent transformation theory, the temperature-dependent material parameters are considered, 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^τIs the transpose of the Jacobian transformation matrix. If the seebeck coefficient before transformation is isotropic, it remains unchanged before and after transformation, and can be written as S' (T) ═ S (T) ═ yT (γ is a constant). The thermal conductivity before conversion can be written as k (T) ═ α + β Tⁿ(α, β and n are all constants), in materials where electronic thermal conduction is the dominant form, the relationship between thermal and electrical conductivity is κ/σ ═ LT (L is the lorentz number) according to the classical widemann-Franz law, so that the electrical conductivity before transformation can be written as σ (T) ═ α T (L) according to the lorentz law^-1/L+βT^n-1/L。

Considering the two-dimensional case, the formula for the coordinate change from the virtual space (r, theta) to the physical space (r ', theta') is

Wherein r is₁And r₂Respectively the inner diameter and the outer diameter of the thermoelectric cloak, and r is the same as 0 and r₂]，r′∈[r₁，r₂]. The physical meaning of equation (4) is to compress a circular region from the center of a circle into an annular region. The Jacobian transformation matrix A of the coordinate transformation is

By means of the Jacobian transformation matrix A, we can obtain the corresponding material change. Substituting the formula (5) into the formula (3) to obtain the annular region [ r ] of the thermoelectric cloak₁，r₂]The internal thermal and electrical conductivity is of the formula (6)

So far, 3 key parameters for designing thermoelectric cloaking have been determined.

The technique can be directly popularized to the three-dimensional situation, the only difference of the three-dimensional situation is the Jacobian transformation matrix A compared with the two-dimensional situation, the formula (5) can be directly transformed into the formula (7), and the rest algorithms are completely the same as those of the two-dimensional situation.

Substituting the formula (7) into the formula (3) to obtain the three-dimensional thermoelectric cloak spherical shell region [ r₁，r₂]The internal thermal and electrical conductivity is of the formula (8)

Compared with the prior art, the invention has the advantages that:

1) the thermoelectric stealth cloak designed based on the temperature-dependent transformation thermodynamics has universality, and a thermoelectric field can be flexibly regulated and controlled through coordinate change.

2) The thermoelectric cloak designed based on the temperature-dependent conversion thermodynamics has practical significance, and the material parameters are considered to be temperature-dependent.

3) The thermoelectric cloak designed based on the temperature-dependent conversion thermodynamics is suitable for a wide temperature range.

4) The thermoelectric cloaking cloak designed based on the temperature-dependent conversion thermodynamics is suitable for two-dimensional situations and three-dimensional situations.

Drawings

Fig. 1 is a two-dimensional schematic view of a thermoelectric cloak, wherein an annular region corresponding to the inner and outer diameters is the thermoelectric cloak, any object can be placed in a middle white region, a black line represents heat flow, and a white line represents current.

Fig. 2 is a two-dimensional simulation of a thermoelectric cloak. (a) The temperature is dependent 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 thermal canopy and the white lines represent equipotential lines. The temperature and potential of the left border of the square background were 600K and 10mV, the right border 300K and 0mV (ground), and the upper and lower borders were insulated both thermally and electrically. The simulation size is 8 multiplied by 8cm²，r₁＝1cm，r₂2 cm. The background parameter is n-3, L-1, alpha-100 Wm^-1K^-4，β＝10Wm^-1K^-4，γ＝3×10^-5VK^-2. The parameter settings of the thermoelectric cloak are designed according to equations (3) and (6), wherein 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. Column 1 and column 2 are plain background, thermoelectric cloak, respectively. All the right side of the simulation diagramThe low temperature of the boundary is fixed to 300K, the high temperature of the left boundary is set from line 1 to line 3 to be 700K, 1100K and 1500K respectively, 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 0 mV. In all simulations, the simulation size was 8X 8cm²，r₁＝1cm，r₂2 cm. The background parameter is n-3, L-1, alpha-100 Wm^-1K^-4，β＝10Wm^-1K^-4，γ＝3×10^-5VK^-2. The parameter settings of the thermoelectric cloak are designed according to equations (3) and (6), wherein the Jacobian matrix is determined by equation (5). The black lines and arrows indicate isotherms and heat flows, and the grey arrows indicate current flows.

Fig. 4 is a temperature/potential versus position curve for a thermoelectric cloak under different boundary conditions. Data were extracted from the horizontal centerline temperature and potential data in the finite element simulation plot of fig. 3, with the solid line representing the simulation in the presence of the thermal canopy and the dashed line representing the simulation in a pure background. (a) And (b) temperature and potential curves, respectively.

Fig. 5 is a three-dimensional simulation of a thermoelectric cloak. (a) The temperature is dependent 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 thermal canopy and the white lines represent equipotential lines. The temperature and potential of the left interface of the cube are 600K and 10mV, the right interface is 300K and 0mV, and the remaining four sides are insulated thermally and electrically. The simulation size is 8 multiplied by 8cm³，r₁＝1cm，r₂2 cm. The background parameter is n-3, L-1, alpha-100 Wm^-1K^-4，β＝10Wm^- ¹K^-4，γ＝3×10^-5VK^-2. The parameter settings of the thermoelectric cloak are designed according to equations (3) and (8), wherein the Jacobian matrix is determined by equation (7).

Detailed Description

The present invention will be described in detail below with reference to specific examples and drawings, but the present invention is not limited thereto.

A two-dimensional schematic of a thermoelectric cloaking cloak is shown in fig. 1, where 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 flow nor current flow through this region. The cloak can simultaneously solve the problems of heat conduction and electric conduction, thereby simultaneously realizing the functions of heat protection and electric protection of heat transportation and electric transportation.

To demonstrate the correctness of the theory, the invention was verified using commercially available finite element simulation software COMSOL Multiphysics. Therein, the two-dimensional simulation results of the thermoelectric cloak are shown in fig. 2. In the simulation process, the left side is set as a high-temperature heat source and a high potential, the right boundary is set as a low-temperature cold source and grounded, and the upper boundary and the lower boundary are insulated thermally and electrically at the same time. The simulation result is observed to find that: in the temperature evolution process, the isotherm of the background is always straight and not distorted, which indicates that external infrared detection cannot obtain any information of the middle white area, thereby achieving the effect of thermal stealth; the external equipotential lines are not distorted, and objects in the middle white area cannot be detected by 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, in order to show that the temperature-dependent thermoelectric conversion theory has universality and is also applicable in a wide temperature range, the patent further designs a thermoelectric cloak under different boundary conditions, which is shown in fig. 3. From the simulation results fig. 3 can find that: in a wide temperature range, the background isotherm and the equipotential line are not distorted, and heat flow and current do not enter the central white area, which shows that both heat and electricity achieve the stealth effect. To more intuitively demonstrate the effect of temperature dependence, the present patent extracts a plot of temperature and potential data for the horizontal centerline in the finite element simulation plot made in FIG. 3, shown in FIG. 4. It can be seen from fig. 4 that the larger the temperature difference between the high temperature heat source and the low temperature heat source in the environment of the material, the temperature and potential changes will no longer be linear, but the data outside the cloak still coincide with the data of the pure background image, and the excellent thermal and electrical stealth capabilities are exhibited.

Without loss of generality, the present patent also performs a three-dimensional steady state simulation, where the thermoelectric cloak is a three-dimensional shell, the results of which are shown in fig. 5. The left interface is a high-temperature heat source and a high-potential surface, the right interface is a low-temperature cold source and a low-potential surface, and the heat and electricity of the other four surfaces are insulated simultaneously. For convenience of illustration, the present invention is viewed with a section taken from the very middle. Similar to the two-dimensional results, the background isotherms and equipotential lines remain undistorted, exhibiting excellent thermal and electrical stealth capabilities.

Claims

1. A thermoelectric cloak based on temperature-dependent transformation thermoelectric design is characterized in that a thermoelectric effect of temperature dependence is considered, an electric field is coupled with a thermal field through a Seebeck coefficient, a circular or spherical area is compressed into an annular area from the center of a circle through coordinate transformation, the change of space is converted into the transformation of material parameters, the material parameters are adjusted, so that external heat flow and current are shielded in the inner circle or the inner sphere of the annular area, objects placed in the annular area cannot be found by external infrared detection and potential detection, the design parameters of the thermoelectric cloak based on temperature dependence are obtained, and the annular area is the thermoelectric cloak; wherein:

the coordinate transformation process is as follows:

for the two-dimensional case, the coordinates from the virtual space (r, θ) to the physical space (r ', θ') are transformed into:

wherein r is₁And r₂Respectively the inner diameter and the outer diameter of the thermoelectric cloak, and the inner radius and the outer radius are respectively r₁And r₂The annular area surrounded by the circle is the thermoelectric cloak;

the calculation method of the Jacobian transformation matrix under the two-dimensional condition comprises the following steps:

for three-dimensional cases, from virtualSpace(s)

To the physical space

Is transformed into:

the calculation method of the Jacobian transformation matrix under the three-dimensional condition comprises the following steps:

inner and outer diameters are r₁And r₂The annular area surrounded by the spherical surface is the thermoelectric cloak;

obtaining corresponding transformed material parameters according to the coordinate transformation, wherein the material parameters comprise thermal conductivity, electric conductivity and Seebeck coefficient, and the method comprises the following steps: the transformed seebeck coefficient is S' (T) ═ A^-τS(T)A^τAnd a transformed thermal conductivity of

Converted conductivity of

Where detA is the determinant of the Jacobian transformation matrix, A^τAs a transpose of the Jacobian transformation matrix, A^-τTranspose of inverse matrix of A; s (T), κ (T), and σ (T) are thermal conductivity, electrical conductivity, and seebeck coefficient before transformation.