Design of square-shaped heat flux cloaks and concentrators using method of coordinate transformation

A square-shaped heat flux cloak and a square-shaped heat flux concentrator have been designed theoretically according to the invariance symmetry of steady state thermal conductive equation. The direction of heat flux in these devices can be modulated as desired. Using the method of coordinate transformation, the inhomogeneous and anisotropic thermal conductivity in the transformation region have been acquired. Two-dimensional finite element simulations were performed to confirm the theoretical results.     

基于变换热力学的任意形状热集中器研究与设计

如何灵活地控制和操纵热流是目前研究的热点.本文根据变换热力学方法,导出了具有任意横截面形状热集中器的材料参数表达式,并在此基础上设计了具有圆形、椭圆形、正五边形等规则横截面形状的热集中器和具有共形、非共形任意横截面形状的热集中器.全波仿真结果表明,这些热集中器使等温线和热通量向其压缩区弯曲,靠近热源的一侧热扩散加快而相反的一侧热扩散减慢,在很小的区域内表现出对热量的集中作用,这一特点在热能工程中有潜在应用.此外,研究了圆柱形热集中器的层化实现方法.结果显示,热集中器可通过将同性材料沿角向分层交替填充来实现.这项工作对热集中器的设计及制备具有指导意义.     

基于变换热力学的三维任意形状热斗篷设计

在变换热力学的基础上,通过坐标变换的方法,推导出三维任意形状热斗篷导热系数的通解表达式,并进行了全波仿真验证.结果表明:热流均能绕过保护区域流出,保护区域的温度保持不变,而且热斗篷外的温度场并没有破坏,具有很好的热保护和热隐身的效果.这一方法把变换热力学从二维拓展到三维,具有普遍的适用性.同时,这种技术为热流流动路径和目标温度场的控制奠定了理论基础,在微芯片、电动机的保护以及目标热隐身上有潜在应用.     

非均匀背景中任意柱状热斗篷的研究与设计

在变换热力学的基础上,通过坐标变换的方法严格推导出在层状背景和渐变背景下二维任意形状热斗篷导热系数的通解表达式,并在此基础上设计出非均匀背景下二维非共形热斗篷.全波仿真结果表明:在不同背景下,热流均能绕过保护区域流出,保护区域的温度保持不变,而且热斗篷外的温度场并没有破坏,具有很好的热保护和热隐身的效果.这一方法考虑到背景的复杂性,更加贴近工程实际应用,为未来灵活控制热流传递提供了一种可行的方法,对目标热隐身和热保护具有重要借鉴意义.     

While rotating while cloaking

Invisible optical and thermal cloaking have been explored as the typical demonstrations of the transformation optics and thermotics theory. However, the existing cloaks are realized by only one-coordinate transformation, and the cloaking layout, i.e. the form of electromagnetic wave/heat passing around the invisible region, is single for a long time. Here, we propose a new rotated thermal cloak which can unify the conventional cloaking and rotating together, and realize the while-rotating–while-cloaking effect. The required anisotropic thermal conductivity tensor is deduced from the new geometric mapping. Though rotated, the heat flux can be tuned around the central invisible region perfectly by the proposed rotated thermal cloak. The underlying physics is explored by comprehensive analysis of the distribution of the thermal conductivity tensor, which is further compared with those of the conventional cloak and rotator. The experimental feasibility is also discussed by validating the practical while-rotating–while-cloaking effect through a proof-of-concept design. The proposed rotated thermal cloak is expected to extend the possibility of cloaking scheme, and open avenues for the multiple coordinate transformation in counterpart physical fields, like optics, electrics, acoustics, magnetics, mechanics, etc.     

任意横截面柱形热斗篷研究与设计

基于变换热力学,导出了具有非共形任意横截面的柱形热斗篷热导率表达式,并在此基础上设计了具有非共形横截面的柱形热斗篷.全波仿真结果表明,热斗篷迫使外部热流绕过斗篷,导致隐身区域热通量为零,从而具有热保护功能;同时,热流绕过斗篷后将恢复原来的温度场分布,使其具有完美热隐身功能.此外,基于所导出的变换媒质热导率表达式,设计并求解了具有规则共形和非规则共形横截面的柱形热斗篷,发现它们同样具有热保护和完美热隐身功能.这表明通过选择适当的边界函数,所得变换媒质热导率表达式可用于设计任意横截面柱形热斗篷,具有普遍的适用性,这种技术在计算机芯片、卫星和航天器等的热保护中有潜在应用.     

热超构材料：几何结构、工作机制与新奇性质

因为在热保护、热探测和热管理领域存在重要的应用价值,自由操控宏观热流一直是人类的 一个梦想。热超构材料正是为此目的应运而生,它是电磁超构材料在热学领域的延伸。在此,我将 综述该领域自2008 年诞生以来取得的若干研究进展,其将主要包括以下新奇热现象或功能器件： 热隐身;热聚集;热旋转;宏观热二极管;热伪装;热透明;热晶体;环境温差中零能耗保温;宏 观热网络中反常热传导;热对流隐身、聚集、伪装;热辐射制冷。我将介绍与之相关的微观或宏观 传热机制,这些机制可以通过以下理论或方法来理解或阐述：变换热学理论、Laplace 方程、热声 子能带理论、相变理论、变换热对流理论、热辐射制冷理论。我也将介绍这些材料从基础研究到工 业应用的发展前景。     

一种适用于对称截面的主动式热斗篷的研究

直接求解导热方程对具有自适应热源的可控式热隐身技术进行数值研究，探索热流控制方法及隐身效果，推导出均匀背景下二维对称截面热斗篷热隐身区域自适应热源分布的通解.仿真结果表明：对于任意对称截面斗篷，自适应热源都能使得扰动后的温度场很好地恢复到背景温度场，达到热隐身的目的.     

Nanoscale thermal cloaking by in-situ annealing silicon membrane

With the advent of thermal metamaterials, many new thermal functionalities have been proposed, like thermal cloaking, concentrating, etc. However, these thermal functionalities are based on the transformation thermotics or scattering cancellation technique, which, derived from Fourier's law, cannot apply to the micro-/nanoscale counterparts. In this paper, we design a nanoscale thermal cloak based on a crystalline silicon (Si) membrane and investigate the in-plane phonon transport via non-equilibrium molecular dynamics (NEMD) simulation by in-situ tuning the thermal conductivity of the thermal cloak from crystalline Si to amorphous Si. The two-dimensional temperature profile is obtained, and the thermal cloaking effect is evaluated by the ratio of heat flux. By analyzing the phonon density of state (PDOS) and the mode participation ratio (MPR), the mechanism can be attributed to the phonon localization in the annealed cloaking region. The proposed nanoscale thermal cloak by in-situ tuned thermal conductivity, may trigger the development of nanoscale thermal functionalities and open avenues for and thermal management for nano-photonics and nano-electronics.     

基于拉普拉斯方程的任意形状热斗篷研究与设计

如何灵活地控制和操纵热流是目前研究的热点.本文基于拉普拉斯方程提出了一种设计任意形状热斗篷的方法.对于形状规则的热斗篷,在特定边界条件下求解拉普拉斯方程得到了斗篷区域材料的热导率分布解析表达式;对于不规则形状的热斗篷,通过数值求解拉普拉斯方程得到了斗篷区域材料的热导率参数分布.全波仿真结果表明,所设计的二维和三维任意形状热斗篷内部隐身区域的热通量为零,从而具有热保护功能;同时,热流绕过斗篷后温度场恢复原来的分布,实现了完美隐身功能.这项研究为解决热斗篷内外边界非共形问题提供了一种可行的方法,对热保护器件的设计和制备有指导意义.     

Performance investigation of nanoscale thermal cloak by the perforated silicon film

In recent years, nanoscale thermal cloak, as a representative of nanoscale heat flux regulation devices, has attracted a lot of attention from researchers. However, the existing design methods are relatively complicated and all adopt constant temperature boundaries, the temperature changes constantly in the real environment, which greatly hinders its engineering applications. In this paper, inspired by phonon localization theory, we construct a nanoscale thermal cloak by a perforated silicon membrane and evaluate its cloaking performance and dynamic response. Results show that when the perforated area is fixed, the more the number of holes, the better the cloaking performance. In addition, the nanoscale thermal cloak still exhibits good cloaking performance in the dynamic environment. Finally, the cloaking mechanism is analyzed by calculating the phonon density of states (PDOS) and mode participation rate (MPR), and the reduction of thermal conductivity in the functional region is attributed to phonon localization.     

Controlling Thermal Conduction by Graded Materials

Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded materials designed according to coordinate transformation approaches, and their effective thermal conductivity is equal to that of the host medium outside the cloak or concentrator. Here we attempt to investigate a more general problem: what is the effective thermal conductivity of graded materials? In particular, we perform a first-principles approach to the analytic exact results of effective thermal conductivities of materials possessing either power-law or linear gradation profiles. On the other hand, by solving Laplace's equation, we derive a differential equation for calculating the effective thermal conductivity of a material whose thermal conductivity varies along the radius with arbitrary gradation profiles. The two methods agree with each other for both external and internal heat sources, as confirmed by simulation and experiment. This work provides different methods for designing new thermal metamaterials (including thermal cloaks and concentrators), in order to control or manipulate the transfer of heat.     

Three-dimensional thermal illusion devices with arbitrary shape

Since the concept of invisible cloak was proposed by Pendry and Leonhardt in 2006, many researchers have applied the theory of coordinate transformation to thermodynamics and overcome the complexity of inhomogeneous and anisotropic of material parameters. However, only two-dimensional(2 D) thermal illusion devices are researched recently. According to this situation, our study focuses on three-dimensional(3 D) thermal illusion devices including shrinker(or invisible cloak),concentrator, amplifier, reshaper, and rotator with arbitrary shape in a general way. In this paper, the corresponding material parameters of thermal illusion devices mentioned above are derived based on the theory of transformation thermodynamics and the simulated results agree well with the theoretical derivations. In addition, the conventional invisible cloak just controls the temperature gradient rather than the temperature value which is more concerned in physical applications. Here,we find that the temperature value of the cloaked object can be controlled by adjusting the location of the original point of the coordinate system.     

Soft X-ray concentrators fabricated by the glass thermoplastic deformation technique

The technique of thermoplastic deformation of a glass has been adapted to the problem of fabrication of an axisymmetric X-ray concentrator. The FOKON-2 facility implementing this technique enables fabrication of ellipsoidal, parabolic and toroidal specimens with geometrical parameters up to 500 mm in length and 30 mm in diameter. The focusing properties of some ellipsoidal concentrators have been investigated. The maximum gain of soft X-rays flux density with wavelength 4.47 nm achieves 370 in the concentrator focal plane.     

圆柱形热集中器理论、仿真和实现

作为一种高效的热能收集与俘获技术,热集中器最近引起了研究者的关注.本文从热传导方程和坐标变换关系出发,导出了圆柱形热集中器温度分布的解析表达式,并通过与COMSOL数值仿真结果比较证实了表达式的正确性.分析了热集中器性能与材料各向异性和器件几何结构二者之间的联系,结果表明,包层热超材料的各向异性越大,集中器的热集中性能越好;包层与内核的半径比越大,集中器的热聚焦能力越强.利用包层与背景媒质之间的温度关系,进一步研究了用常规材料实现热集中器的方法,通过将两种常见的天然材料沿角向按周期交替排列并调整各自面积的大小,可观察到不同程度热集中现象.     

基于超材料的定向传热结构研究与设计

在热斗篷研究的基础上, 提出定向传热结构的研究. 基于变换热力学, 采用坐标斜变换推导了定向传热结构热导率分布的表达式. 数值计算结果表明, 外部热流流经定向传热区域时, 热流向设计的高温面流动, 而设计的低温面温度较低. 此外, 在导出的热导率分布表达式的基础上, 进一步进行坐标旋转变换, 得到的热导率表达式只有相互垂直的两个分量. 计算结果表明, 沿高温面法向的热导率增大时, 传热效率提高, 而且经过坐标旋转变换后, 高温面与低温面的温差增大. 定向传热在红外隐身、热防护领域具有潜在的应用价值.     

Quasi-invisible thermal cloak based on homogenous materials

Invisible thermal cloak, which cancels distortions of temperature distribution caused by objects, has many potential applications in thermal engineering. In this letter, we theoretically proposed and simulatively verified a new design method for quasi-invisible thermal cloak. Different from conventional transformation thermodynamics that focus on complete invisibility, our method only decreases the effective scale of objects to small enough and realizes a quasi-invisible cloaking effect in thermal conduction regime. However, this quasi-invisible cloak has the same effect as that of invisible thermal cloak in practical engineering. More important, our cloak is easy to construct by natural materials due to its homogenous thermal properties and can cloak objects with different shapes and properties. These characters make the clock more comfortable for engineering applications.     

A solar concentrator with two reflection mirrors designed by using a ray tracing method

Solar concentrators with two reflection mirrors are numerically designed by using a ray-tracing method to obtain higher concentration ratio when the concentrator tracing error is existed. The primary reflection mirror adopts paraboloidal mirror; the secondary mirror adopts hyperboloidal or ellipsoidal mirror. The optimal designed shape parameters for hyperboloidal and ellipsoidal cases are obtained, respectively. It is found that, when the concentrator tracing errors are 0°, 0.5° and 1°, the concentration ratios for hyperboloidal case are about 5837, 1954 and 1127 at f-number₁=0.22 and NA₂=0.62 and the one for ellipsoidal case are about 5860, 1993 and 1193 at f-number₁=0.25 and NA₂=0.62, respectively. Obviously, the concentrator with the ellipsoidal mirror is slightly better than the one with the hyperboloidal mirror.     

Analysis of elliptical thermal cloak based on entropy generation and entransy dissipation approach

In this work, we designed the elliptical thermal cloak based on the transformation thermotics. The local entropy generation rate distribution and entransy dissipation rate distribution were obtained, and the total entropy generation and entransy dissipation of different types of elliptical cloaks were evaluated. We used entropy generation approach and entransy dissipation approach to evaluate the performance of the thermal cloak, and heat dissipation analysis was carried out for models with different parameters. Finally, the optimized elliptical thermal cloak with minimum entropy generation and minimum entransy dissipation is found, and some suggestions on optimizing the structure of elliptical thermal cloak were given.     

TE波辐射下超材料椭圆柱电磁斗篷特性分析

 利用有限元方法分析了TE波辐射下,超材料椭圆柱斗篷的电磁特性。研究发现：当超材料的介电常数、磁导率和电导率偏离理论值0.5%时,斗篷外的电场发生了明显变化;当材料的介电常数、磁导率和电导率为理论值时,不论在斗篷内放置什么特性的材料,也不论斗篷内壁上的边界条件如何,超材料椭圆柱斗篷都具有隐形作用。