CN110826265B - Heat stealth cloak based on heat radiation and heat conduction conversion theory design - Google Patents

Abstract

The invention belongs to the field of energy technology and infrared technology, and particularly relates to a thermal stealth cloak designed based on a theory of changing heat radiation and heat conduction. The thermal stealth cloak designed by the invention adopts a coordinate transformation method to establish the connection between the space change and the material change, namely, a circular area is compressed from the circle center to an annular area through the coordinate change, and then the space change is converted into the material change, and the material parameters of the thermal stealth cloak are determined to obtain the stealth cloak; wherein, the heat conduction and the heat radiation can be regulated and controlled simultaneously, and the heat stealth function is realized; the heat radiation is approximated by Rosseland diffusion, and the heat conduction is approximated by Fourier's law. The feasibility of the design of the invention was verified by finite element simulation. The invention provides a brand new scheme for regulating and controlling heat radiation, and can be used in the fields of infrared detection and heat protection.

Description

Thermal cloak designed based on the theory of thermal radiation and heat conduction

Technical Field

The invention belongs to the field of energy and infrared technology, and in particular relates to a thermal stealth cloak designed based on the theory of conversion of thermal radiation and heat conduction.

Background Art

There are three main ways of heat energy transport: heat conduction, heat convection and heat radiation. For heat conduction and heat convection, corresponding transformation theories have been developed in the past decade to control heat conduction and heat convection, but the transformation theory for thermal radiation has not been proposed. This greatly limits practical applications, because any object with a non-zero temperature will emit thermal radiation. It can be said that thermal radiation exists everywhere in human life: the working principle of night vision devices is to detect thermal radiation; thermal radiation is also used in military confrontations. Therefore, if thermal radiation can be freely controlled, it will greatly promote practical applications in these fields.

In order to solve this problem, realize the free regulation of thermal radiation and promote practical applications, this patent proposes to realize thermal stealth cloak by using coordinate transformation method. Thermal stealth cloak can make the internal objects not affect the temperature distribution outside the cloak, as if the object in the middle does not exist. However, previous thermal stealth cloaks were designed based on heat conduction and lacked the ability to regulate thermal radiation. The purpose of this patent is to solve this problem, expand the transformation theory from simple heat conduction to thermal radiation, and then design a thermal stealth cloak that can deal with thermal radiation problems. This plays an important role in the field of high-temperature thermal protection. This is because at high temperatures, thermal radiation is the main mode of heat energy transport, so if the device only considers the thermal conduction effect without considering the thermal radiation effect, it will fail at high temperatures, thereby losing the ability to protect against heat. The solution proposed by this technology can simultaneously deal with thermal protection problems for heat conduction and thermal radiation, so it plays an important role in practical applications.

Summary of the invention

The purpose of the present invention is to provide a thermal stealth cloak designed based on the theory of transformed thermal radiation and heat conduction, so that any object placed in it will not be discovered by external infrared detection.

The thermal stealth cloak proposed in the present invention, which is designed based on the theory of transformed thermal radiation and heat conduction, adopts a coordinate transformation method to establish a connection between spatial changes and material changes, that is, a circular area is compressed from the center of the circle into an annular area through coordinate changes, and then the spatial changes are converted into material changes, the material parameters of the thermal stealth cloak are determined, and the stealth cloak is obtained to realize the thermal stealth function - any object placed in it will not be discovered by external infrared detection.

In the present invention, based on the coordinate transformation theory, heat conduction and heat radiation can be regulated simultaneously to achieve a thermal stealth function.

In the present invention, the heat radiation is processed by Rosseland diffusion approximation, and the heat conduction is processed by Fourier's law.

The thermal cloak provided by the present invention can be applicable to two-dimensional situations as well as three-dimensional situations; it can be applicable to steady-state heat conduction situations as well as transient heat conduction situations.

The following is a further deduction of the conditions for the thermal stealth cloak to achieve thermal stealth:

Considering the transient heat transport process of thermal radiation and heat conduction, its thermodynamic evolution process is determined by the following formula (1):

为拉普拉斯算子。J_rad为辐射热流，由Rosseland扩散近似给出公式(2)：Where ρ and C represent the density and heat capacity of the material, T represents temperature, and t represents time.

is the Laplace operator. _{J rad} is the radiation heat flux, and the Rosseland diffusion approximation gives formula (2):

Where β is the Rosseland average extinction coefficient, n is the relative refractive index, and σ is the Stefan-Boltzmann constant (its value is equal to 5.67×10 ^-8 Wm ^-2 K ^-4 ). _{J con} is the conduction heat flow, which is given by Fourier's law as formula (3):

Where κ is the thermal conductivity of the material.

Considering the two-dimensional case, the coordinate change from the virtual space (r, θ) to the physical space (r′, θ′) is as shown in formula (4):

Among them, r ₁ and r ₂ are the inner diameter and outer diameter of the thermal cloak, that is, the thermal cloak is an annular area surrounded by two concentric circles with radii r ₁ and r ₂ ; the physical meaning of formula (4) is to compress a circular area from the center of the circle into an annular area. The Jacobian transformation matrix A of this coordinate transformation is shown in formula (5):

The corresponding material changes can be obtained through the Jacobian change matrix A. Since the relative refractive index range of natural materials is not wide, the present invention assumes that the relative refractive index n after transformation does not change, as shown in formula (6):

n′＝n， (6)

Where n' is the relative refractive index after transformation. Correspondingly, the Rosseland average extinction coefficient β, thermal conductivity κ, density and heat capacity (ρC) are transformed as follows:

The transformed Rosseland average extinction coefficient β′ is determined by formula (7):

Where detA is the determinant of the Jacobian transformation matrix, and A ^τ is the transpose of the Jacobian transformation matrix.

The transformed thermal conductivity κ′ is determined by formula (8):

The transformed density and heat capacity (ρC)′ are determined by formula (9):

So far, the four key parameters for designing thermal radiation stealth have been determined, namely: Formula (6)-Formula (9). These parameters are expressed in the cylindrical coordinate system.

到物理空间

的坐标变化由公式(4)变为公式(4-1)所示：The present invention can be extended to three-dimensional situations.

To physical space

The coordinate change of is changed from formula (4) to formula (4-1):

Among them, r ₁ and r ₂ are the inner and outer diameters of the thermal cloak, that is, the thermal cloak is an annular area surrounded by two concentric spherical surfaces with radii r ₁ and r ₂ ;

The Jacobian transformation matrix A of formula (4-1) is directly transformed from formula (5) to formula (10)

The only difference between the three-dimensional case and the two-dimensional case is the Jacobian transformation matrix A. The rest of the algorithms are exactly the same as those for the two-dimensional case, that is, the transformations of the relative refractive index n, Rosseland average extinction coefficient β, thermal conductivity κ, density and heat capacity (ρC) are also as shown in formulas (6)-(9).

Since the material of the thermal cloak designed by the transformation theory is non-uniform, anisotropic, and even singular, it brings difficulties to the actual design. Therefore, the present invention further designs a multi-layer structure, which is equivalent to the material of the thermal cloak. The specific design is as follows: two materials are arranged alternately in a ring to form a multi-layer structure, which is equivalent to the thermal stealth effect; specifically, it is assumed that the properties of material A are: extinction coefficient β _A , thermal conductivity κ _A ; the properties of material B are: extinction coefficient β _B , thermal conductivity κ _B ; these two materials need to meet: β _A β _B = β ² and κ _A κ _B = κ ² , where β and κ are the extinction coefficient and thermal conductivity of the background. The two materials are arranged alternately in a ring to form a layered structure (the smaller the width of each layer of the ring, the better the effect), thereby realizing the anisotropic function of using two uniform isotropic materials.

Advantages of the present invention:

(1) The method proposed in the present invention is universal and can flexibly control thermal radiation by changing coordinates;

(2) The method proposed in the present invention is applicable to two-dimensional and three-dimensional situations;

(3) The method proposed in the present invention is applicable to both steady state and transient state.

The present invention provides a new solution for regulating thermal radiation, which can be used in the fields of deceiving infrared detection, thermal protection, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a two-dimensional schematic diagram of a thermal cloak. The annular area corresponding to the inner and outer diameters is the thermal cloak, and any object can be placed in the white area in the middle.

Figure 2 is a two-dimensional transient simulation diagram of the thermal cloak. Among them, (a)-(d) are transient evolution processes dominated by conduction in the low temperature range (300-320K). (e)-(h) are transient evolution processes dominated by radiation conduction in the intermediate temperature range (300-1000K). (i)-(l) are transient evolution processes dominated by radiation in the high temperature range (300-4000K).

Figure 3 shows the structure and simulation diagram of a thermal cloak using two homogeneous isotropic materials, where (a) is a schematic diagram of the structure and (b) is the simulation result of the structure in the temperature range (300-1000K).

Figure 4 is a three-dimensional steady-state simulation diagram of the thermal cloak. Among them, (a)-(d) are steady-state results dominated by conduction in the low temperature range (300-320K). (e)-(h) are steady-state results dominated by radiation conduction in the intermediate temperature range (300-1000K). (i)-(l) are steady-state results dominated by radiation in the high temperature range (300-4000K).

DETAILED DESCRIPTION

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

The two-dimensional schematic diagram of the thermal cloak is shown in Figure 1, where the annular area between the inner diameter and the outer diameter is the thermal cloak, and any object can be placed in the middle white area. The cloak can handle both heat conduction and heat radiation problems at the same time, thus achieving thermal protection functions under two forms of heat energy transport.

In order to demonstrate the correctness of the theory, the present invention uses the finite element simulation software COMSOL Multiphysics for verification. The results of the two-dimensional transient simulation are shown in Figure 2. During the simulation, the left and right boundaries are set as high-temperature heat sources and low-temperature cold sources, respectively, and the upper and lower boundaries are adiabatic. (a)-(d) are transient evolution processes dominated by conduction in the low temperature range (300-320K). (e)-(h) are transient evolution processes dominated by radiation conduction in the intermediate temperature range (300-1000K). (i)-(l) are transient evolution processes dominated by radiation in the high temperature range (300-4000K). The simulation size is 10×10cm ² , r ₁ =2.4, r ₂ =3.6cm. The background parameters are ρC=10 ⁶ Jm ^-3 K ^-1 , n=1, β=100m ^-1 , κ=1Wm ^-1 K ^-1 . The parameter setting of the thermal cloak is designed according to formula (6)-(9), where the Jacobian matrix is determined by formula (5). The white line represents the isotherm. By observing the simulation results, it can be found that during the temperature evolution process, the isotherm of the background is always straight and not distorted, which means that the external infrared detection cannot obtain any information about the white area in the middle, thus achieving the stealth effect.

Since the material designed by the transformation theory is non-uniform, anisotropic, and even singular, in order to solve this problem, the present invention designs a multilayer structure, as shown in Figure 3. Wherein, (a) is a schematic diagram of the structure, and (b) is the simulation result of the structure between the temperature range (300～1000K). Material A: β _A ＝1000m ^-1 ,κ _A ＝0.1Wm ^-1 K ^–1 ; Material B: β _B ＝10m ^-1 ,κ _B ＝10Wm ^-1 K ^–1 . There are 20 layers of material in the figure, and the thickness of each layer is 0.6mm. The simulation results show that the background isotherm is indeed not distorted, thereby achieving the stealth effect.

The present invention also performs a three-dimensional steady-state simulation, in which the thermal cloak is a three-dimensional shell, and the results are shown in Figure 4. The left and right boundaries are high-temperature heat sources and low-temperature cold sources, respectively, and the remaining four faces are adiabatic boundary conditions. In the figure, (a)-(d) are steady-state results dominated by conduction in the low-temperature range (300-320K). (e)-(h) are steady-state results dominated by radiation conduction in the intermediate temperature range (300-1000K). (i)-(l) are steady-state results dominated by radiation in the high-temperature range (300-4000K). The simulation size is 10×10×10cm ³ , r ₁ =2.4, r ₂ =3.6cm. The background parameters are ρC=10 ⁶ Jm ^-3 K ^-1 , n=1, β=100m ^-1 , κ=1Wm ^-1 K ^-1 . The parameter setting of the thermal stealth cloak is designed according to formula (6)-(9), where the Jacobian matrix is determined by formula (10). The white line represents the isotherm. For the convenience of display, the present invention intercepts a cross section in the middle for observation. Similar to the two-dimensional results, the background isotherm is still not distorted, showing excellent stealth capability.

Claims (2)

1. The thermal stealth cloak designed based on the theory of transformation heat radiation and heat conduction is characterized in that a coordinate transformation method is adopted to establish the connection between space change and material change, namely, a circular area is compressed from the center of a circle to an annular area through the coordinate change, the space change is further converted into the material change, and the material parameters of the thermal stealth cloak are determined to obtain the stealth cloak; wherein, the heat conduction and the heat radiation can be regulated and controlled simultaneously, and the heat stealth function is realized;

the radiant heat flow J of the heat radiation _rad Given by Rosseland diffusion approximation formula (2):

the heat conduction heat flow J _con Given by equation (3) according to Fourier's law:

wherein ρ and C represent the density and heat capacity of the material, respectively, T represents the temperature, T represents the time,

is a Laplacian operator; beta is Rosseland average extinction coefficient, n is relative refractive index, sigma is Stefan-Boltzmann constant, and kappa is material thermal conductivity;

the circular area is compressed into an annular area from the center of a circle through coordinate change, and the circular area is specifically as follows:

for the two-dimensional case, the coordinates from the virtual space (r, θ) to the physical space (r ', θ') change as shown in equation (4):

wherein r is ₁ And r ₂ The inner diameter and the outer diameter of the thermal stealth cloak are respectively, namely the thermal stealth cloak is composed of a radius r ₁ And r ₂ An annular region defined by two concentric circles; 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 shown in formula (5):

for three-dimensional situations, from virtual space

To physical space->

As shown in the formula (4-1):

wherein r is ₁ And r ₂ The inner diameter and the outer diameter of the thermal stealth cloak are respectively, namely the thermal stealth cloak is composed of a radius r ₁ And r ₂ An annular area surrounded by two concentric spheres;

the Jacobian transformation matrix a of the coordinate transformation is shown in formula (10):

the spatial change is converted into the material change, and the material parameters of the thermal stealth cloak are determined, specifically as follows:

the relative refractive index n is unchanged, i.e., as shown in equation (6):

n′＝n (6)

wherein n' is the transformed relative refractive index;

for the Rosseland average extinction coefficient β, the thermal conductivity κ, density and heat capacity (ρC) were transformed, specifically:

the transformed Rosseland average extinction coefficient β' is determined by equation (7):

wherein detA is determinant of Jacobian transformation matrix, A ^τ Transpose of Jacobian transform matrix;

the transformed thermal conductivity κ' is determined by equation (8):

the transformed density and heat capacity (ρc)' are determined by equation (9):

2. the thermal stealth cloak of claim 1 wherein two materials are alternately arranged in a ring-like fashion in a multi-layered configuration to equivalently achieve thermal stealth; specifically, let the properties of material a be: extinction coefficient beta _A Thermal conductivity κ _A The method comprises the steps of carrying out a first treatment on the surface of the The properties of material B are: extinction coefficient beta _B Thermal conductivity κ _B The method comprises the steps of carrying out a first treatment on the surface of the These two materials satisfy: beta _A β _B ＝β ² And kappa (K) _A κ _B ＝κ ² Wherein β and κ are the extinction coefficient and thermal conductivity of the background; the two materials are alternately arranged in a layer-shaped structure in a ring shape, and the anisotropic function can be realized by using the two uniformly isotropic materials.

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