CN110598258B

CN110598258B - Thermal phantom device based on equivalent thermal dipole

Info

Publication number: CN110598258B
Application number: CN201910751411.7A
Authority: CN
Inventors: 黄吉平; 须留钧; 杨帅
Original assignee: Fudan University
Current assignee: Fudan University
Priority date: 2019-08-15
Filing date: 2019-08-15
Publication date: 2022-12-20
Anticipated expiration: 2039-08-15
Also published as: CN110598258A

Abstract

The invention belongs to the technical field of thermodynamics, and particularly relates to a thermal phantom device based on equivalent thermal dipoles. The thermal phantom device comprises two different particle systems, wherein the two different particle systems have the same thermal effect, namely temperature distribution, so that the two different systems cannot be distinguished in the detection of the thermal infrared imager, thereby realizing the thermal phantom. In the invention, each particle is regarded as an equivalent thermocouple, and the macroscopic equivalent thermocouple moment of all particles is obtained by summing; then, two different systems are designed to have the same macroscopic equivalent thermal dipole moment, whereby the effect of the thermal phantom can be obtained. Compared with the traditional core-shell device, the device only needs to perform calculation once, and is beneficial to improving the efficiency and expanding the application. The feasibility of the device is verified through theoretical analysis, finite element simulation and experiments. The invention provides an effective scheme for realizing multi-particle thermal illusion, has wide application prospect, and can be used for deception infrared detection, heat flow manipulation and the like.

Description

Thermal phantom device based on equivalent thermal dipole

Technical Field

The invention belongs to the technical field of thermodynamics, and particularly relates to a thermal phantom device based on equivalent thermal dipoles.

Background

The last decade has witnessed the rapid development of thermal metamaterials. Recently, thermal phantom devices have attracted extensive research interest due to their wide military industrial use. The relevant solutions are mostly based on core-shell structures, namely: a special shell is designed to disguise the core of the center. Although the core-shell structure works well to deal with the single particle problem, it does not work well to deal with the multi-particle problem. In other words, if there are N particles to be camouflaged, N calculations are required to design N specific shells. This approach is extremely inefficient.

To solve this problem we cannot be limited to core-shell solutions, only focusing on the local effect of a single particle. Instead, we focus more on the macroscopic effects of the N particles. However, since the thermal conductivities cannot be directly added or subtracted, the next problem is how to deal with the macroscopic effect of N particles. Inspired by electrostatics, we treated each particle as an equivalent thermal dipole. The present invention fully discusses the relationship between particles and dipoles, especially taking into account material anisotropy and geometric anisotropy. In this way, thermal conductivity can be vectorized to an equivalent dipole moment and be additive. Thus, the thermal phantom can be implemented with the concept of an equivalent thermal dipole, namely: consider the macroscopic equivalent thermal dipole moment of N particles. The scheme only needs one-time calculation, and is beneficial to improving the efficiency.

Disclosure of Invention

The invention aims to provide a thermal phantom device which has a simple structure and excellent performance.

The thermal phantom device provided by the invention is based on an equivalent thermal dipole technology, and comprises two different particle systems, wherein the two different particle systems have the same thermal effect (temperature distribution) and cannot be distinguished in the detection of a thermal infrared imager, so that the thermal phantom is realized, and the aim of deceiving the infrared detection is fulfilled.

In the invention, two different particle systems are designed to have the same macroscopic thermal dipole moment, so that the aim of thermal illusion can be fulfilled. Specifically, each particle in the particle system is regarded as an equivalent thermal dipole, and then the macroscopic thermal dipole moment of all the particles in the particle system is obtained through summation calculation.

The invention can be directly popularized from two dimensions to three dimensions.

The invention relates to the calculation of the equivalent thermal dipole moment of each particle, the basic rule of which is described by Fourier law, and the specific introduction is as follows:

for two different systems, the thermal phantom is to design the macroscopic equivalent thermal dipole moment of the two systems to be equal, and can be specifically expressed as:

where N represents the total number of types of particles, system 1 has j types of particles, system 2 has N-j types of particles, N _i Indicates the number of particles of the i-th particle,

the equivalent thermal dipole moment of the i-th particle is shown.

The equivalent thermocouple polar moments of the different particles are calculated in detail below

For convenience, it is abbreviated as

I.e. the subscript i is omitted.

For the two-dimensional case, let a radius be r and the anisotropic thermal conductivity be κ _p ＝diag(κ _rr ,κ _θθ ) Embedded in a round particle having a thermal conductivity of κ _m The equivalent thermal dipole moment of the particles is:

wherein the content of the first and second substances,

is the equivalent thermal conductivity, K, of the anisotropic particles ₀ Is an external horizontal thermal field. Kappa type _rr ,κ _θθ Respectively the radial and tangential thermal conductivity of the round particles.

For a minor semi-axis of s, a major semi-axis of t, an isotropic thermal conductivity of κ _p The equivalent thermal dipole moment of the particle is:

wherein L is the shape factor of the particle and can be calculated by the following formula:

where d is the sign of the differential and a is the integration parameter (from 0 to ∞ integration).

The above discussion is a two-dimensional calculation result, and the scheme can be popularized from a two-dimensional situation to a three-dimensional situation. Correspondingly, in the three-dimensional case, for the case of spherical particles, the anisotropic thermal conductivity is

Wherein κ _θθ ,

For tangential and azimuthal thermal conductivity, assumptions are made for ease of discussion

The equivalent thermocouple polar moment (change of equation (2)) of the particles is:

wherein, the first and the second end of the pipe are connected with each other,

is the equivalent thermal conductivity of the three-dimensional anisotropic particles.

In the case of an ellipsoid as the particle, let the semiaxial length of the third direction of the ellipsoid be w, the equivalent thermal dipole moment (variation of equation (3)) of the particle be:

wherein L is the three-dimensional shape factor of the particle and can be calculated by the following formula:

The relationship between particle thermal conductivity and the dipole moment is explained in detail above, so that a thermal phantom result between any two different systems can be obtained.

The invention has the advantages that:

(1) The invention is simple and efficient;

(2) The invention is applicable to the treatment of multi-particle systems;

(3) The invention is applicable to both material anisotropic and geometrically anisotropic particles.

The feasibility of the device is verified through theoretical analysis, finite element simulation and experiments. The invention provides an effective scheme for realizing multi-particle thermal illusion, and has wide application prospect, such as being used for deception infrared detection, heat flow manipulation and the like.

Drawings

Fig. 1 is a schematic of a particle and a dipole. Wherein (a) and (b) are electrically corresponding; (c) and (d) are thermal correspondences.

Fig. 2 is a schematic view of a thermal phantom apparatus. Wherein the circular particles in (a) and (b) are regarded as the thermal dipoles in (c) and (d). The thermal phantom results can be obtained by designing the dipole moment of the thermal couples in the two different systems to be equal.

Fig. 3 is a simulation result of the thermal phantom. The simulated size is 10 x 10cm ² . The high temperature on the left side is 313K, the low temperature on the right side is 273K, and the upper and lower sides are adiabatic boundary conditions. A pair of thermal phantom devices (a) and (b), and another pair of thermal phantom devices (c) and (d). The specific parameters are as follows. (a) and (b): background thermal conductivity of 200Wm ^-1 K ^-1 The distance between the particles is 10mm; (a) The thermal conductivity of 50 light-colored particles is 400Wm ^-1 K ^-1 The radius is 2.52mm; the thermal conductivity of 50 dark color particles is 400Wm ^-1 K ^-1 The radius is 4.37mm; (b) The thermal conductivity of 100 particles is 41Wm ^-1 K ^-1 The radius is 3.57mm. (c) and (d): background thermal conductivity of 400Wm ^-1 K ^-1 The thermal conductivity of the particles is 0.025, and the distance between the particles is 10mm; (c) 25 particles (represented by the first one in the first row), with a major and minor semiaxis of 2.93, 1.95mm;25 particles (represented by the second in the first row), the major and minor semiaxis3.66, 2.44mm;25 particles (represented by the second in the second row), with a major and minor semiaxis of 3.24, 2.16mm;25 particles (represented by the first one of the second row), with a major and minor semiaxis of 3.91, 2.61mm; (d) 100 particles with a radius of 2.82mm.

FIG. 4 is a schematic representation of two samples and measurements made according to FIGS. 3 (c) and (d).

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. In the embodiment, the temperature difference of the system is 40K, and the system is in a steady state.

In fig. 1, (a) and (b) are that particles in electricity correspond to dipoles. Inspired by this, it was established that (c) and (d) the particles in thermal correspond to dipoles. The corresponding method can effectively deal with the thermal problem of the multi-particle system, thereby obtaining the effect of thermal illusion.

The design idea for realizing the thermal illusion is shown in fig. 2. (a) and (b) are two different particle systems. Each particle is considered to be an equivalent thermal dipole. Then, the macroscopic equivalent thermal dipole moments in (c) and (d) are calculated, both having the same value, according to the formula (1), so that the thermal illusion of two different particle systems is achieved. The system is reasonably designed by using the result obtained by theoretical calculation and finite element simulation is carried out by using commercial software COMSOL. The simulation results are shown in FIG. 3.

FIGS. 3 (a) and (b) show a pair of thermal illusions; (c) and (d) show a pair of thermal illusions. We observed that: (a) And (b) the isotherm distribution outside the dashed box is substantially the same; similarly, the isotherm distributions outside the dashed boxes of (c) and (d) are substantially the same. This is illustrated as follows: when an infrared thermal imager detects temperature distribution outside the dotted line, the difference between the two systems cannot be distinguished. In practice, however, the corresponding particles of the two systems are distinct, thereby achieving the thermal illusion. Wherein the shape parameter and the thermal conductivity of the particles are calculated according to the formula (1).

Based on the simulation results of fig. 3 (c) and (d), we prepared two samples of fig. 4 (a) and (b) as well, and the measurement schematic is also shown therein. Thus, when the two different samples are in a temperature gradient, the same effect can be shown through the detection of the thermal infrared imager.

Claims

1. A thermal phantom device based on equivalent thermal dipole is characterized by comprising two different particle systems, wherein the two different particle systems have the same thermal effect, namely temperature distribution, so that the two different systems cannot be distinguished in infrared thermal imager detection, and thermal phantom is realized;

regarding each particle in the particle system as an equivalent thermocouple, and then obtaining the macroscopic thermocouple moment of all particles in the two particle systems through summation calculation; by designing two different particle systems such that they possess the same macroscopic thermal dipole moment, a thermal illusion is achieved; here, the two particle systems have the same macroscopic thermal dipole moment, i.e.

represents the equivalent thermal dipole moment of the i-th particle;

equivalent thermal dipole moment of different particles

The specific calculation method is as follows, and is abbreviated as

I.e. omitting subscript i;

for the two-dimensional case, one radius is r and the anisotropic thermal conductivity is κ _p ＝diag(κ _rr ,κ _θθ ) Embedded in a round particle having a thermal conductivity of κ _m The equivalent thermal dipole moment of the particles is:

is the equivalent thermal conductivity, K, of the anisotropic particles ₀ Is an external horizontal thermal field; kappa type _rr ,κ _θθ The radial and tangential thermal conductivities of the round particles, respectively;

for a minor semi-axis of s, a major semi-axis of t, an isotropic thermal conductivity of κ _p Of ellipsoidal particles embedded in a matrix of thermal conductivity kappa _m The equivalent thermal dipole moment of the particles is:

wherein L is the shape factor of the particle and is calculated by the following formula:

in the three-dimensional case, when the particles are spherical, the anisotropic thermal conductivity is

Wherein κ _θθ ,

For tangential and azimuthal thermal conductivity, assume

The equivalent thermocouple polar moment of the particles is:

wherein the content of the first and second substances,

is the equivalent thermal conductivity of the three-dimensional anisotropic particles;

when the particles are ellipsoids, the semiaxial length of the third direction of the ellipsoid is w, and the equivalent thermocouple polar moment of the particles is:

wherein L is the three-dimensional shape factor of the particle and is calculated by the following formula: