CN110826265B - Heat stealth cloak based on heat radiation and heat conduction conversion theory design - Google Patents
Heat stealth cloak based on heat radiation and heat conduction conversion theory design Download PDFInfo
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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
Technical Field
The invention belongs to the technical field of energy and infrared, and particularly relates to a thermal stealth cloak designed based on a theory of changing heat radiation and heat conduction.
Background
The heat energy transport mainly comprises three modes: heat conduction, heat convection, and heat radiation. Corresponding conversion theory has been developed in the last decade for controlling heat conduction and convection, but conversion theory for heat radiation has not been proposed at a later time. This greatly limits the practical application because any object with a non-zero temperature emits thermal radiation. It can be said that there is heat radiation everywhere in human life: the working principle of the night vision device is to detect heat radiation; heat radiation is also utilized in military countermeasures, so that if heat radiation can be freely regulated, practical application in these fields will be greatly promoted.
In order to solve the problem, realize the free regulation and control of heat radiation and promote practical application, the patent proposes a method for realizing a heat stealth cloak by utilizing coordinate transformation. The thermally stealth cloak can be such that internal objects do not affect the temperature distribution outside the cloak as if the intermediate objects were not present. However, the conventional heat stealth cloak is designed based on heat conduction, and the heat radiation is lack of regulation and control capability, so that the invention aims to solve the problem, expand the transformation theory from pure heat conduction to heat radiation, and further design the heat stealth cloak capable of treating the heat radiation problem. This has an important role in the field of high temperature thermal protection. This is because heat radiation is the primary means of thermal energy transport at high temperatures, so if devices that only consider the heat conduction effect, without considering the heat radiation effect, fail at high temperatures, losing the ability to thermally protect. The proposal of the technology can simultaneously treat the heat protection problem aiming at heat conduction and heat radiation, thereby having important effect on practical application.
Disclosure of Invention
The invention aims to provide a thermal stealth cloak designed based on the theory of transformation heat radiation and heat conduction, so that any object placed in the cloak cannot be found by external infrared detection.
The thermal stealth cloak designed based on the theory of transformation heat radiation and heat conduction adopts a coordinate transformation method to establish the connection between space change and material change, namely, a circular area is compressed from a circle center into an annular area through the coordinate change, the space change is further converted into the material change, the material parameters of the thermal stealth cloak are determined, the stealth cloak is obtained, and the thermal stealth function is realized, wherein any object placed in the thermal stealth cloak cannot be found by external infrared detection.
According to the invention, based on a coordinate transformation theory, heat conduction and heat radiation can be regulated and controlled simultaneously, so that a heat stealth function is realized.
In the present invention, the heat radiation is approximated by Rosseland diffusion, and the heat conduction is approximated by Fourier's law.
The thermal stealth cloak provided by the invention can be suitable for two-dimensional situations and three-dimensional situations; it can be applied to steady state heat conduction situations as well as transient heat conduction situations.
The following further derives the conditions for the thermal cloaking of the thermal cloak:
considering the transient heat transport process of heat radiation and heat conduction, its thermodynamic evolution process is determined by the following formula (1):
wherein ρ and C represent the density and heat capacity of the material, respectively, T represents the temperature, T represents the time,
is a laplace operator. J (J) rad For radiant heat flow, equation (2) is given by the Rosseland diffusion approximation:
where β is the Rosseland average extinction coefficient, n is the relative refractive index, σ is the Stefan-Boltzmann constant (which is equal to 5.67×10 -8 Wm -2 K -4 )。J con To conduct heat flow, equation (3) is given by Fourier's law:
wherein, κ is the material thermal conductivity.
Considering the two-dimensional case, the coordinate from the virtual space (r, θ) to the physical space (r ', θ') changes 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 a ring shapeAn area. The Jacobian transformation matrix a of the coordinate transformation is shown in formula (5):
by means of the Jacobian variation matrix a, a corresponding material variation can be obtained. Since the range of the relative refractive index of the natural material is not wide, the invention assumes that the transformed relative refractive index n is unchanged, namely as shown in formula (6):
n′＝n， (6)
where n' is the transformed relative refractive index. Correspondingly, for the Rosseland average extinction coefficient β, the thermal conductivity κ, the density and the heat capacity (ρC) are transformed, specifically:
the transformed Rosseland average extinction coefficient β' is determined by equation (7):
wherein detA is determinant of Jacobian transformation matrix, A τ Is a transpose of the 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):
to this end, four key parameters for designing thermal radiation cloaking have been determined, namely: equation (6) -equation (9). These parameters are all expressed in a cylindrical coordinate system.
The invention can be generalized to three-dimensional situations, for a slave virtual space
To physical space
The coordinate change of (2) is represented by the equation (4) to the equation (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;
jacobian transformation matrix A of equation (4-1) is transformed directly from equation (5) to equation (10)
The three-dimensional case is different from the two-dimensional case only in that the Jacobian transformation matrix a, and the algorithms of the rest and the two-dimensional cases are identical, namely, the transformation of the relative refractive index n, rosseland average extinction coefficient β, thermal conductivity κ, density and heat capacity (ρc) are also shown in formulas (6) - (9).
Because the thermal stealth cloak designed by the transformation theory is nonuniform, anisotropic and even peculiar, the practical design is difficult, and therefore, the invention further designs a multi-layer structure which is equivalent to the thermal stealth cloak, and the material is specifically designed as follows: two materials are alternately arranged in a ring shape to form a multi-layer structure, so that the effect of thermal stealth is equivalently realized; specifically, assume that the properties of material a are: 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 need to meet: beta A β B ＝β 2 And kappa (K) A κ B ＝κ 2 Extinction in which beta and kappa are the backgroundCoefficient and thermal conductivity. The two materials are alternately arranged in a layer-like structure in a ring shape (wherein the smaller the width of each layer ring is, the better the effect), whereby the function of achieving anisotropy with two uniformly isotropic materials can be achieved.
The invention has the advantages that:
(1) The method provided by the invention has universality, and can flexibly regulate and control the heat radiation through coordinate change;
(2) The method provided by the invention is suitable for two-dimensional and three-dimensional conditions;
(3) The method provided by the invention is suitable for steady state and transient state.
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.
Drawings
FIG. 1 is a two-dimensional schematic view of a thermal stealth cloak. The annular area corresponding to the inner diameter and the outer diameter is the thermal stealth cloak, and any object can be placed in the middle white area.
FIG. 2 is a two-dimensional transient simulation of a thermal stealth cloak. Wherein, (a) - (d) are transient evolution processes mainly conducted in a low-temperature region (300-320K). (e) - (h) is a transient evolution process equivalent to radiation conduction in the intermediate temperature range (300-1000K). (i) - (l) is the transient evolution process of the radiation of the high temperature region (300-4000K).
FIG. 3 is a structural and simulated view of a thermal stealth cloak utilizing two homogeneous isotropic materials. Wherein, (a) is a schematic structural diagram, and (b) is a simulation result of the structure in a temperature range (300-1000K).
FIG. 4 is a three-dimensional steady-state simulation of a thermal stealth cloak. Wherein, (a) - (d) are steady-state results of conduction predominately in the low temperature range (300-320K). (e) - (h) is a steady state result of radiation conduction equivalent in the intermediate temperature range (300-1000K). (i) - (l) is a steady state result of radiation in the high temperature range (300-4000K).
Detailed Description
The present invention will be described in detail with reference to specific embodiments and drawings, but the present invention is not limited thereto.
A two-dimensional schematic of a thermal cloak is shown in fig. 1, wherein the annular region between the inner and outer diameters is the thermal cloak, and any object can be placed in the middle white region. The cloak can simultaneously treat the problems of heat conduction and heat radiation, so that the thermal protection function under two heat energy transportation modes can be realized.
To demonstrate the correctness of theory, the present invention utilizes finite element modeling software COMSOL Multiphysics for verification. The results of the simulation of the two-dimensional transient are shown in fig. 2, among others. In the simulation process, the left and right boundaries are respectively set as a high-temperature heat source and a low-temperature cold source, and the upper and lower boundaries are both insulated. Wherein, (a) - (d) are transient evolution processes mainly conducted in a low-temperature region (300-320K). (e) - (h) is a transient evolution process equivalent to radiation conduction in the intermediate temperature range (300-1000K). (i) - (l) is the transient evolution process of the radiation of the high temperature region (300-4000K). The simulated size is 10X 10cm 2 ,r 1 ＝2.4,r 2 =3.6 cm. The background parameter is ρc=10 6 Jm -3 K -1 ,n＝1,β＝100m -1 ,κ＝1Wm -1 K -1 . The parameter settings for the thermal cloak are designed according to equations (6) - (9), where the Jacobian matrix is determined by equation (5). White lines represent isotherms. 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 cannot learn any information of the middle white area, thereby achieving the stealth effect.
Since the material obtained by the design of the transformation theory is heterogeneous, anisotropic, or even singular, the present invention has devised a multi-layered structure as shown in fig. 3 in order to solve this problem. Wherein, (a) is a schematic structural diagram, and (b) is a simulation result of the structure in a temperature range (300-1000K). Material a: beta A ＝1000m -1 ,κ A ＝0.1Wm -1 K –1 The method comprises the steps of carrying out a first treatment on the surface of the Material B: beta B ＝10m -1 ,κ B ＝10Wm -1 K –1 . There are 20 layers of material, each layer having a thickness of 0.6mm. Simulation results show that: the background isotherm is indeed not distorted, thus achieving the stealth effect.
The present invention also performed a three-dimensional steady state simulation, where the thermal cloak was a three-dimensional shell, the results of which are shown in fig. 4. The left and right boundaries of the heat source are respectively a high-temperature heat source and a low-temperature cold source, and the other four surfaces are heat-insulating boundary conditions. In the figure, (a) - (d) are steady-state results of conduction in the low temperature range (300-320K). (e) - (h) is a steady state result of radiation conduction equivalent in the intermediate temperature range (300-1000K). (i) - (l) is a steady state result of radiation in the high temperature range (300-4000K). Analog size is 10 multiplied by 10cm 3 ,r 1 ＝2.4,r 2 =3.6 cm. The background parameter is ρc=10 6 Jm -3 K -1 ,n＝1,β＝100m -1 ,κ＝1Wm -1 K -1 . The parameter settings for the thermal cloak are designed according to equations (6) - (9), where the Jacobian matrix is determined by equation (10). White lines represent isotherms. For convenience of presentation, the invention is viewed with a section taken in the middle. Similar to the two-dimensional results, the background isotherms remain untwisted, exhibiting excellent stealth.
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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| CN113688495B (en) * | 2021-07-01 | 2024-04-26 | 复旦大学 | Thermoelectric converter based on temperature-dependent transformation thermoelectric field theory and design method thereof |
| CN113656993B (en) * | 2021-07-01 | 2023-10-03 | 复旦大学 | Thermoelectric stealth cloak based on temperature-dependent transformation thermophysics design |
| CN113656991A (en) * | 2021-07-01 | 2021-11-16 | 复旦大学 | Temperature-tunable thermoelectric cloak based on phase-change material and design method thereof |
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