Virtual Heat Source Research Articles

Development of Fourier Transform Ultrafast Laser Flash Method for Simultaneous Measurement of Thermal Diffusivity and Interfacial Thermal Resistance

The thermoreflectance technique is one of the few methods which can measure thermal diffusivity of thin films as thin as 100 nm or thinner in the cross-plane direction. The thermoreflectance method under rear-heat front-detect configuration is sometimes called ultrafast laser flash method because of its similarity to laser flash method. Up to now it has typically only been possible to attempt to evaluate the interfacial thermal resistance between the thin films by preparing and measuring several samples with different thicknesses. In this study, a method to directly determine interfacial thermal resistance by a single measurement of a thin film on substrate is represented, by analyzing the shape of thermoreflectance signals with analytical solutions in frequency domain and time domain. Thermoreflectance signals observed from metallic thin films on sapphire substrate with different thickness steps were analyzed by Fourier analysis and fitted by analytical equations with four parameters: heat diffusion time across the first layer, ratio of virtual heat sources, characteristic time of cooling determined by interfacial thermal resistance and relative amplitude of the signal. Interface thermal resistance between the thin film and substrate was able to be determined reliably with smaller uncertainty.

Improved inherent strain extraction algorithm based analytical surface modeling for Ti-6Al-4V and SS316L selective laser melting part

Selective laser melting (SLM) is one of the most popular metal additive manufacturing (AM) techniques relied on powder bed and has been widely used in numerous fields. Printing surface modeling is a critical step for product development and quality control of SLM parts as the surface profile has a great impact on the structure and functional performance of printed parts. However, it is still a challenge to predict the printing surface geometry of the SLM part accurately and quickly due to the complex physical processes and thermomechanical behaviors in SLM. To address this barrier, a comprehensive bottom-up modeling approach based on an improved inherent strain method (ISM) is proposed to estimate the surface fluctuation between designed and printed parts and further predict the printing surfaces of SLM parts. The improved inherent strain is extracted from multi-physics analytical calculation considering the thermal influences of in-plane scanning tracks, interlayer re-melting and interlayer strain accumulation. Specifically, temperature filed is obtained from the quasi-static heat analytical model integrating residual temperature involving the heat contribution of in-plane scanning tracks via virtual heat source technique. The interlayer strain accumulation and interlayer re-melting effects are embedded into the inherent strain terms through the layer-lever fluctuation superposition and re-melted depth parameter respectively. Strain compositions are solved through thermo-elastic Green function models and modified elastic-plastic McDowell analytical models, where temperature-dependent material properties are employed. The proposed method has been validated by experimental observations from the literature via two SLM parts using two distinct materials (Ti-6Al-4 V and SS316L).

Evaluation of defect depth in CFRP composites by long pulse thermography

Long pulse thermography (LPT) is an emerging non-destructive technique that has been used for rapid, cost-effective and accurate damage assessment of composite materials. This paper proposes three analytical models for the in-depth evaluation of defects in a carbon fibre-reinforced plastic (CFRP) specimen by long pulse thermography. The first two models rely on the estimate of the peak temperature-contrast and the peak temperature-contrast slope from the thermal data recorded by an infrared (IR) camera. Both the analytical and experimental results showed that the arriving time of the peak temperature-contrast depends on both the depth and the diameter of defects, whilst the contrast time slope is mainly proportional to the square of the damage depth. The third model here proposed consists of a two-dimensional (2D) axisymmetric heat conduction model based on virtual heat sources. Compared to previously reported analytical models, the proposed 2D one showed higher accuracy on the depth estimation.

Illusion thermotics with topology optimization

Illusion thermotics, which aims at creating temperature fields to mislead a thermal detector, encompasses many thermal functionalities. It has attracted significant attention due to the increasing number of promising applications. Transformation thermotics and scattering cancellation methods are frequently adopted for illusion devices, though they have inherent defects such as anisotropic thermal properties and complicated fabrication methods. Here, we present a general framework for topology optimization, which can be used to design the structure of an illusion device automatically. The optimized configuration can camouflage the thermal exterior of an illusion device so that it is identical to a reference. The original heat source can drive the virtual heat source despite the structure being simply composed of natural materials. To establish an effective topology optimization model, a volume constraint was imposed on the total volume of iron and a prescribed objective function was used to evaluate the difference between the reference temperature and the temperature field during the topology optimization. The flexibility of the method presented was successfully validated by changing the total volume of iron, the number and locations of the thermal illusions, the types of composite materials, and the original heat sources. Topology optimization is a new and flexible approach for designing thermal metamaterials and metadevices for diverse thermal functionalities and beyond.

The detection and evaluation for the internal defection in industrial pipeline based on the virtual heat source temperature field

Industrial pipelines work in high temperature and are corrosive, and this causes corrosion and shedding of the inner walls. Therefore, it is a realistic engineering problem to detect the defect information of pipeline accurately. In the paper, according to the characteristics of pipeline and heat conduction theory, the temperature field is equivalent to a composite model. Utilizing the three-dimensional heat conduction equation, the heat dissipation temperature field model of no-defects pipeline is established. Taking the medium temperature as the boundary condition, the model is solved by variables separation method and Bessel function. Secondly, based on the principle of microelement integration and finite element, considering the uncertainty of the defect boundary, the boundary information is expressed by the geometric variable factors of virtual heat source. And heat source temperature field model is obtained. Then, using the defect radius as the variable, the boundary function of the defect is established. Thirdly, considering the temperature field function and the maximum allowable pressure of the pipeline, the effective temperature evaluation model of pipeline defects is constructed. Finally, using the experiments and the Simulation of Software COMSOL, the feasibility of the pipeline models is verified. The relationship between the defect boundary and the temperature can be analyzed by mathematical methods. Internal defects in pipes are quantitatively analyzed and evaluated. This provides a theoretical basis for ensuring the quality and operation of the pipeline.

An Analytical Computation of Temperature Field Evolved in Directed Energy Deposition

This paper presents an analytical computation of temperature field evolved in a directed energy deposition process, using single-bead walls as illustrating examples. Essentially, the temperature field evolution during the deposition of a wall is computed by super-position of the temperature field generated by the laser source depositing the current bead and that induced from each of the past beads (layers). First, the transient solution to a point heat source in a semi-infinite body is applied to describe each individual temperature field. Then, to better describe temperature contribution from a past bead, a pair of virtual heat sources with positive and negative powers is assigned for each past bead to compute the temperature field under cooling. In addition, mirrored heat sources through a reflexion technique are introduced to define adiabatic boundaries of the part and to account for substrate thickness. In the end, three depositions of Ti-6AL-4V walls with different geometries and interlayer dwell times on an Optomec® laser engineering net shaping (LENS) system are used to validate the proposed analytical computation, where predicted temperatures at several locations of the substrate show reasonable agreement with the in situ temperature measurements with prediction error rate ranging from 12% to 27%. Furthermore, temperature distributions predicted by the proposed model are compared to finite element simulations. The proposed analytical computation for temperature field could be potentially used in model-based feedback control for thermal history in the deposition, which could affect microstructure evolution and other properties of the final part.

Three dimensional temperature field of thermoelectric radiant panel system: Analytical modeling and experimental validation

Thermoelectric radiant panel (TERP) system is a new prototype of radiant system with fast cooling/heating speed, stable operation, and easier system control. The full and deeper understanding of heat transfer of TERP could be beneficial for system design, operation and control. The purpose of this paper is to establish a three-dimensional analytical model of TERP in both steady and dynamic state which could be used as a useful tool for further research. The method of mirror virtual heat sources was adopted to transform original heat conduction problem to the superposition of temperature solutions of radiant panel in infinite plane. In addition, this method can offer a highly flexible treatment on boundary conditions. The basic conduction problem was solved by the method of separation of variables and the temperature field subjected to non-functional finite-plane heat source was modeled by Duhamel theorem in simulation algorithm. Thermal network RC model for TEM and copper cube was integrated with the analytical model of radiant panel for simulation of TERP. The simulation accuracy of three-dimensional temperature field of TERP was verified by comparing with experimental results in both steady and dynamic state. In order to understand the simulation difference between the previous 2-D and new 3-D model, a comparative study was implemented under different model parameters arrangements. This numerical comparative investigation can provide a basic guidance on the application of 2-D and 3-D model. And this study offered a solid and sophisticated system model for TERP.

仮想的な物理モデルに基づく幾何学的制約付きトポロジー最適化（型成形及びフライス加工のための幾何学的制約法）

This paper proposes a scheme for imposing geometrical constraints in topology optimization for molding and milling so that optimal configurations that guarantee manufacturability can be obtained, based on the fictitious physical model. First, a level set-based topology optimization method is briefly described, and geometrical requirements for molding and milling are clarified. In molding, molded products must embody certain geometrical features so that mold parts can be separated, and milling cannot proceed unless the desired shape allows tool cutting faces to reach the workpiece. A fictitious physical model described by a steady-state advection-diffusion equation is then constructed based on the requirements. In the fictitious physical model, material domains are represented as virtual heat sources and an advection direction is aligned with a prescribed direction, along which mold parts are moved, or attitude in the case of a milling tool. Void regions, where the value of the fictitious physical field is high, represent either undercut geometries which would prevent the mold from being parted, interior voids that cannot be manufactured, or regions that a milling tool cannot reach. Next, a geometrical constraint is formulated based on the fictitious physical model. An optimization algorithm is then constructed. Finally, in the numerical examples, the proposed method yields manufacturable optimal configurations, confirming the validity and the utility of the proposed method.

Hydraulic modeling and experimental study of three heat sources and three rings heating networks

For the further research on the hydraulic characteristics of multi-source and multi-ring heating network polycyclic, this paper based on the fluid network analysis, the hydraulic intersection user virtual segmentation, at the ends of common pipe set virtual users or virtual heat source modeling method, the hydraulic simulation model of three heat sources and three rings of a heating pipe network is established by using MATLAB platform. Based on the experimental platform of the multi-source heat supply network, the three heat sources and rings ideal working conditions and the variation of the two working conditions are simulated and experimentally studied. The results show that under the 3 different conditions, the maximum absolute value of relative error of simulation data and the experimental data were 1.30%, 1.26% and 1.09%, to verify the validity of the simulation method proposed in this paper and the simulation model and the accuracy of.

Solving the multi-domain variable coefficient heat conduction problem with heat source by virtual boundary meshfree Galerkin method

Virtual boundary meshfree Galerkin method (VBMGM) is developed to solve the multi-domain variable coefficient heat conduction problem with heat source. Both the virtual source function on the virtual boundary and heat source within each subdomain are approximate by the radial basis function interpolation. The equation of the proposed technique is derived by one of the weighted residual methods, namely the Galerkin method, for multi-domain variable coefficient heat conduction problem with heat source. Therefore, VBMGM simultaneously possesses the merits of Galerkin method, boundary element method and meshfree method. And the numerical meanings of the weighted values are definite, such as the partial derivative heat source expressions, the temperature, the heat flux and the continuity conditions, in VBMGM for multi-domain variable coefficient heat conduction problem with heat source. The specific and detailed equation of VBMGM is obtained for multi-domain variable coefficient heat conduction problem with heat source. The accuracy and the stability of the proposed technique are validated by two numerical examples for multi-domain variable coefficient heat conduction problem with heat source.

Modeling of the surface temperature field of a thermoelectric radiant ceiling panel system

Thermoelectric radiant ceiling panel system (TE-RCP) is a novel and promising system which combines the advantages of thermoelectric cooling/heating and conventional radiant ceiling panel system. The experimental investigations and case studies of TE-RCP have been carried out. But there is short of theoretical analysis and heat transfer model to provide a basis for the deeper and further investigation about TE-RCP. By solving the governing equation of the TE-RCP and using virtual heat source method to simulate the boundary conditions, the surface temperature field of TE-RCP under constant heat source intensity can be calculated. The dynamic-state model under variable heat source intensity is developed by adopting the idea of superposition principle and step load theory. The calculated temperature on the surface of radiant panel and hot/cold side of TE modules are in agreement with the experimental values. A system coefficient of performance (COP) is proposed based on the steady state model of TE-RCP to analyze the impact of working current of TE modules on the system performance. The simulations indicate that in cooling mode the system cooling capacity ranges between 48.6W/m2 and 104.1W/m2 and the corresponding system COP ranges between 1.06 and 2.29 under the working current from 1A to 2A. In heating mode, the system heating capacity ranges between 165.6W/m2 and 343W/m2 and the corresponding system COP ranges between 1.51 and 1.8 under the working current from 2A to 3A. This proposed model can provide a solid foundation for the further design, optimization, and system control of TE-RCP.

Direct-Forcing Immersed Boundary Method for Mixed Heat Transfer

AbstractA direct-forcing immersed boundary method (DFIB) with both virtual force and heat source is developed here to solve Navier-Stokes and the associated energy transport equations to study some thermal flow problems caused by a moving rigid solid object within. The key point of this novel numerical method is that the solid object, stationary or moving, is first treated as fluid governed by Navier-Stokes equations for velocity and pressure, and by energy transport equation for temperature in every time step. An additional virtual force term is then introduced on the right hand side of momentum equations in the solid object region to make it act exactly as if it were a solid rigid body immersed in the fluid. Likewise, an additional virtual heat source term is applied to the right hand side of energy equation at the solid object region to maintain the solid object at the prescribed temperature all the time. The current method was validated by some benchmark forced and natural convection problems such as a uniform flow past a heated circular cylinder, and a heated circular cylinder inside a square enclosure. We further demonstrated this method by studying a mixed convection problem involving a heated circular cylinder moving inside a square enclosure. Our current method avoids the otherwise requested dynamic grid generation in traditional method and shows great efficiency in the computation of thermal and flow fields caused by fluid-structure interaction.

The interplay between the measured dimension and temperature of hot large forgings

During the forming process of hot forgings, the dimension and temperature are key parameters for improving the forging technology. In the paper, based on the mathematical physics methods, a mutual relationship model between the measured dimension and the temperature is proposed. This relationship model is displayed by the temperature field model and the dimensional model. Firstly, according to the law of conversation of energy, using the Dirichlet function and the measured dimension, the power-transfer function of heat source is established. Taking the measured temperatures as the boundary conditions, the temperature field model influenced by the dimensional change is established using the method of the moving virtual heat source. Secondly, based on the variation characteristics between the mesoscopic structure and the stress, using the function of the deformation energy is analyzed. Using the differential calculus of the pluralistic function, the dimensional change model influenced by the measured temperature is established. Based on the temperature field model and the dimensional model, this mutual relationship of the two ones can be clearly and directly displayed. Finally, the verifiable experiments and simulations are obtained using the forging experiments and the Deform-3D. Using the contrastive analysis method, the feasibility of the two relationship models is verified and the change trends of the dimension and temperature are analyzed. Combining the parameters of the forging technology in the thermal forming process, the application and the practical significance of the model are further cleared. The mutual relationship model provides a theoretical basis for improving the forging technology.

J113013 VR用匂い提示装置の開発 : 仮想的な匂い源と熱源の同時提示([J113]設計における知識マネジメント・情報共有)

This paper reports on a new display system that can present a virtual odor and/or heat source at an arbitrary position on a two-dimensional screen. By releasing a smell of coffee in a warm airflow while showing a cupful of coffee on an LCD monitor, for example, the system can make the user feel as if warm savory steam is emanating from the coffee. In the proposed system, airflows generated by four fans are made to change their courses multiple times by making them collide with each other. Finally, an airflow directed toward the user from a certain position on the screen is generated. By introducing odor vapor and/or heat into the airflows, the odor/temperature distribution is generated as if the odor/heat were spreading from the specific position on the screen. The position of this virtual odor/heat source can be shifted to an arbitrary position on the two-dimensional LCD monitor screen by changing the speeds of the four fans. The proposed system can be used to make attractive digital signage.

Determination of Defect Depth and Size Using Virtual Heat Sources in Pulsed Infrared Thermography

The determination of defect depth and size using Pulsed Infrared Thermography is a critical problem. The problem of defect depth estimation has been previously studied using 1D heat conduction models. Unfortunately, 1D heat conduction based models are generally inadequate in predicting heat flow around defects. In this study, a novel approach based on virtual heat sources is proposed to model heat flow around defects accounting for 2D axisymmetric heat conduction. The proposed approach is used to quantitatively determine the defect depth and size. The validity of the model is established using experiments performed on a stainless steel plate specimen with flat bottom holes at different depths.

Analysis of One-dimensional Heat Diffusion after Light Pulse Heating by the Response Function Method

To measure thermal diffusivity across thin films, the laser flash method has been improved by using ultrafast lasers and thermoreflectance temperature detection. These light pulse heating methods allow observation of one-dimensional heat diffusion from the heated face to the detected face of a specimen across a well-defined length of specimen thickness following the light pulse heating. Since most electronic devices, storage media, displays, and so forth have a multilayered structure of thin films, information about heat diffusion across multilayers, thermophysical properties of constituent single layers, boundary thermal resistance between the layers, and effective thermophysical properties of the multilayered structure as a whole are required for improved thermal design of devices and development of materials. To meet these requirements, a generally applicable approach to analyze one-dimensional heat diffusion across multilayers has been developed on the basis of the virtual heat source method and response function method. These methods of analysis can be applied over a timescale ranging from picoseconds, as observed by the picosecond thermoreflectance method, to more than 10 seconds, as observed by the laser flash method.

1063 熱画像の逆解析によるコンクリート構造物の表層部欠陥診断(J09 逆問題解新手法の開発と最新応用,ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

In this paper, a method to identify the geometrical shape and the location of the defect embedded in a concrete structure by processing the thermal image of the structural surface acquired by infrared thermography is presented. In the proposed method, the structure is modeled as a homogeneous infinite plate whose boundary condition on the observed surface is known. A layer-by-layer inverse analysis using a regularized interlayer transfer matrix based on 2D Fourier transform is carried out to obtain the sharper image of the defect as well as the depth of the damaged layer. The estimated depth information mapped on the image plane has resulted in a depth image which can display the shape of the defects as well as their depth simultaneously. An improved method introducing equivalent virtual heat sources that prevent the "boundary artifact" caused by the heat flux across the image boundary is presented.

Theoretical Analysis of the Coincident Wire-Powder Laser Deposition Process

The process of coincident wire and powder deposition by laser has recently emerged in research work as a layered manufacturing method with a higher deposition rate than the established laser direct metal deposition technique and as a means of creating functionally graded metallic surface layers in a single pass. This work analytically models the process by accounting for the incoming wire and powder as virtual negative heat sources. The major assumptions of the model are confirmed experimentally and the predicted temperature profiles compared with values measured using contact and pyrometric methods. Model accuracy outside the molten zone is excellent, but this solution does not account for latent heat and intrapool circulation effects so it gives only moderate precision when extrapolated to within the melt pool. Increasing the mass feed rate to the melt pool reduces its depth and the temperature surrounding it—these effects can be quantified in three dimensions by the model.

Transient conduction and convection heat transfer across a multi-layer floor subjected to multiple heat sources

This paper analyses the transient heat transfer across multi-layer floors subjected to multiple heat sources. The formulation that is proposed to solve this problem uses analytical expressions handling both conduction and convection phenomena. The Green's functions (analytical expressions) for the layered formation are established by imposing the continuity of temperatures and heat fluxes at the medium interfaces between the various layers. The heat field inside a layer is obtained by adding the contribution of the direct heat incident field, generated as in an unbounded medium, to the heat produced by a set of virtual surface heat sources, that take into account the presence of the interfaces. The technique used to deal with the unsteady state conditions consists of first computing the solution in the frequency domain and then applying (fast) inverse Fourier transforms into space-time.

Three-dimensional unsteady thermal stress analyses by means of the thermoelastic displacement potential and the boundary element method.

The boundary element method (BEM) has been used in various fields because it is convenient in comparison with FEM. BEM does not need a volume integral in three-dimensional elastic problems without body forces, but generally in unsteady three-dimensional thermoelastic problems, the volume integral is necessary. Recently, a method transforming the volume integral in BEM for three-dimensional problems of unsteady thermoelasticity has been reported. However, the time integral was not carried out analytically and a numerical example was not shown in that report. This paper describes the three-dimensional problem of unsteady thermoelasticity can be easily solved without a volume integral by means of a thermoelasticity displacement potential and the boundary element method. It is also shown that the time integral can be carried out analytically and a singularity problem caused by imposing virtual heat sources on the boundary element can be easily solved. Some numerical examples are shown for investigating the accuracy of this method.