Thermal Modeling of a Hybrid Thermoelectric Solar Collector with a Compound Parabolic Concentrator

In this study radiant light from the sun is used by a hybrid thermoelectric (TE) solar collector and a compound parabolic concentrator (CPC) to generate electricity and thermal energy. The hybrid TE solar collector system described in this report is composed of transparent glass, an air gap, an absorber plate, TE modules, a heat sink to cool the water, and a storage tank. Incident solar radiation falls on the CPC, which directs and reflects the radiation to heat up the absorber plate, creating a temperature difference across the TE modules. The water, which absorbs heat from the hot TE modules, flows through the heat sink to release its heat. The results show that the electrical power output and the conversion efficiency depend on the temperature difference between the hot and cold sides of the TE modules. A maximum power output of 1.03 W and a conversion efficiency of 0.6% were obtained when the temperature difference was 12°C. The thermal efficiency increased as the water flow rate increased. The maximum thermal efficiency achieved was 43.3%, corresponding to a water flow rate of 0.24 kg/s. These experimental results verify that using a TE solar collector with a CPC to produce both electrical power and thermal energy seems to be feasible. The thermal model and calculation method can be applied for performance prediction.     

Performance Study of Thermoelectric Solar-Assisted Heat Pump with Reflectors

The simultaneous conversion of solar radiation into thermal and electrical energy in a thermoelectric (TE) solar-assisted heat pump is, for the purposes of this study, referred to as hybrid conversion. To capture more thermal and electrical energy, flat-plate reflectors have been mounted on a TE solar collector. To obtain higher solar radiation intensity on the TE solar collector, the position of the reflectors has been changed and the optimal position of the reflectors determined by both experimental measurements and numerical calculation so as to obtain maximal concentration of solar radiation intensity. The calculated values have been found to be in good agreement with measured ones. Improvements to the thermal energy and electrical power outputs of the system can be achieved by the use of the TE solar-assisted heat pump with reflectors. For the optimum position of the reflectors, the coefficient of performance (COP) of the system formed from a TE solar collector integrated with a heat pump (TESC-HP) was 5.60. The power output and conversion efficiency of the TE modules can reach 10.09 W and 2.40%, respectively, being improved by 34.5% and 18.2%, respectively, compared with the TESC-HP without reflectors.     

Cost–Performance Analysis and Optimization of Fuel-Burning Thermoelectric Power Generators

Energy cost analysis and optimization of thermoelectric (TE) power generators burning fossil fuel show a lower initial cost compared with commercialized micro gas turbines but higher operating cost per energy due to moderate efficiency. The quantitative benefit of the thermoelectric system on a price-per-energy ($/J) basis lies in its scalability, especially at a smaller scale (<10 kW), where mechanical thermodynamic systems are inefficient. This study is based on propane as a chemical energy source for combustion. The produced heat generates electric power. Unlike waste heat recovery systems, the maximum power output from the TE generator is not necessarily equal to the economic optimum (lowest $/kWh). The lowest cost is achieved when the TE module is optimized between the maximum power output and the maximum efficiency, dependent on the fuel price and operation time duration. The initial investment ($/W) for TE systems is much lower than for micro gas turbines when considering a low fractional area for the TE elements, e.g., 5% to 10% inside the module. Although the initial cost of the TE system is much less, the micro gas turbine has a lower energy price for longer-term operation due to its higher efficiency. For very long-term operation, operating cost dominates, thus efficiency and material ZT become the key cost factors.     

Numerical Simulation of Performance and Thermomechanical Behavior of Thermoelectric Modules with Segmented Bismuth-Telluride-Based Legs

The approach of using segmented legs to build thermoelectric (TE) modules can enhance the performance of TE generators. This approach is based on the selection of materials for different segments that are optimized in terms of their TE properties with respect to the temperature range to which they are exposed during module operation. For this purpose, by carefully controlling the chemical composition of ternary and quaternary bismuth-telluride-based alloys, we have optimized the figure of merit ZT of p-type and n-type alloys implemented by a powder technology approach. The alloys were prepared by mechanical alloying followed by hot extrusion, and their mechanical and TE properties were fully characterized as a function of temperature, which gave us a solid database for simulation of modules containing these materials. Finite-element numerical simulation was applied to evaluate the impact of TE materials properties on the level of mechanical stresses generated by thermal gradients in modules made of segmented legs. Keeping the same total length of two-segment p- and n-type legs, the relative length of each segment was varied to obtain an 8% relative increase of generated electrical power compared with homogeneous legs of the same total length. Under these conditions, the presence of solder interface between the two segments and between the segments and the copper conductors of the module concentrates plastic strain, leading to a significant reduction of the stress level in the TE materials compared with that resulting from using nonsegmented legs. Leg segmentation not only leads to improved TE performance but could also significantly modify the maximum values and distribution of thermomechanical stresses in the modules, depending on how it is realized. The study presents how this numerical simulation tool can be used to optimize the design of segmented modules.     

Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates

This paper presents the design of a compact (~1 cm³) thermoelectric (TE) generator intended to generate power locally for sensor/electronic device applications using hot gases (~100°C to 400°C). The design employs 13-mm-diameter, ~0.36-mm-thick (48 mm³) silicon-micromachined TE modules that are stacked to form a cylindrical, finned heat exchanger. The stacked structure is intended to establish a large, uniform temperature gradient across radially oriented thermopiles in each module. Analytical heat transfer and electrical circuit models are used to design and optimize the thermopile for maximum output power under microfabrication and system-level constraints. Optimized structures using PbTe and Bi₂Te₃ thin films are predicted to achieve output power levels of 1.3 mW per module (26.7 mW/cm³) and 0.83 mW per module (17.4 mW/cm³), respectively, for hot gas at 400°C.     

Validating Steady-State and Transient Modeling Tools for High-Power-Density Thermoelectric Generators

Steady-state and transient models have been created in a MATLAB/Simulink environment for high-power-density thermoelectric generators (TEG). These numerical models, comprising simultaneously solved, nonlinear, energy balance equations, simulate novel TEG architectures, such as a cylindrical TEG with gas/liquid heat exchangers. Model validation studies, including component-level testing of thermoelectric (TE) subassemblies, interface thermal resistance tests, and full-scale TEG tests, were performed under different operating conditions and designs. Targeted finite-element analysis studies were also conducted. A full-scale cylindrical-shaped TE generator was built using high-power-density, segmented TE elements and tested on a test-bench with hot air and cold water with maximum power output of 608?W. Measured performance data from these tests were used in model validation. Process outlet temperatures, pressure drops, hot and cold shunt temperatures along the length of the TEG, TEG voltage, and TEG current are some of the performance variables included in the model validation. The validated model is now being used with more confidence to optimize new TEG designs for different applications.     

热容激光器激光输出特性的数值模拟

热容激光器在激射过程中，激光介质的温度快速升高，导致了热容激光器具有特殊的激光输出特性。通过理论分析、数值模拟和实验研究等方法，对热容激光器的激光输出特性进行研究，掌握热容激光器工作的基本规律，为热容激光器的设计、实验提供了重要的参考。建立了描述热容激光输出特性的理论模型，给出了输出功率随激光介质温升及工作时间的变化关系。数值模拟研究结果表明。激光介质的温度从300K升高到400K过程中，阈值功率密度从2．6W／cm^3增加到33．6W／cm^3，输出功率下降7％。利用建立的热容激光器实验装置．测量了不同占空比情况下的输出功率，占空比越高输出功率随时间下降得越快，与数值模拟结果相符。在低占空比时，数值模拟和测量结果吻合较好；在高占空比时出现误差，而且占空比越高误差越大。     

Heat-Pipe-Associated Localized Thermoelectric Power Generation System

The present study focused on how to improve the maximum power output of a thermoelectric generator (TEG) system and move heat to any suitable space using a TEG associated with a loop thermosyphon (loop-type heat pipe). An experimental study was carried out to investigate the power output, the temperature difference of the thermoelectric module (TEM), and the heat transfer performance associated with the characteristic of the researched heat pipe. Currently, internal combustion engines lose more than 35% of their fuel energy as recyclable heat in the exhaust gas, but it is not easy to recycle waste heat using TEGs because of the limited space in vehicles. There are various advantages to use of TEGs over other power sources, such as the absence of moving parts, a long lifetime, and a compact system configuration. The present study presents a novel TEG concept to transfer heat from the heat source to the sink. This technology can transfer waste heat to any location. This simple and novel design for a TEG can be applied to future hybrid cars. The present TEG system with a heat pipe can transfer heat and generate power of around 1.8 V with T _TEM = 58°C. The heat transfer performance of a loop-type heat pipe with various working fluids was investigated, with water at high heat flux (90 W) and 0.05% TiO₂ nanofluid at low heat flux (30 W to 70 W) showing the best performance in terms of power generation. The heat pipe can transfer the heat to any location where the TEM is installed.     

Modeling and Optimization of Thermoelements by a Combined Analytical and Numerical Method

A combined analytical and numerical process has been developed to model and optimize thermoelements. In this way, the performance of commercial n- and p-type thermoelectric materials can be optimized to deliver the maximum output power and conversion efficiency. The validity of the method is demonstrated using a silicon germanium unicouple.     

Multi-parameter Optimization of a Thermoelectric Power Generator and Its Working Conditions

The global optimal working conditions and optimal couple design for thermoelectric (TE) generators with realistic thermal coupling between the heat reservoirs and the TE couple were studied in the current work. The heat fluxes enforced by the heat reservoirs at the hot and the cold junctions of the TE couple were used in combination with parameter normalization to obtain a single cubic algebraic equation relating the temperature differences between the TE couple junctions and between the heat reservoirs, through the electric load resistance ratio, the reservoir thermal conductance ratio, the reservoir thermal conductance to the TE couple thermal conductance ratio, the Thomson to Seebeck coefficient ratio, and the figure of merit (Z) of the material based on the linear TE transport equations and their solutions. A broad reservoir thermal conductance ranging between 0.01  W/K and 100 W/K and TE element length ranging from 10^-7 m to 10^-3 m were explored to find the global optimal systems. The global optimal parameters related to the working conditions, i.e., reservoir thermal conductance ratio and electric load resistance ratio, and the optimal design parameter related to the TE couple were determined for a given TE material. These results demonstrated that the internal and external electric resistance, the thermal resistance between the reservoirs, the thermal resistance between the reservoir and the TE couple, and the optimal thermoelement length have to be well coordinated to obtain optimal power production.     

Improvement in the Durability and Heat Conduction of uni-leg Thermoelectric Modules Using n-type Mg2Si Legs

We have fabricated several kinds of uni-leg thermoelectric (TE) modules using Sb-doped n-type Mg₂Si. In order to evaluate the influence of the structure of the modules on their durability with respect to heat-cycling, modules of two different types were evaluated. One was a conventional-structured module, in which the upper and lower surfaces of the legs were each fixed to a ceramic substrate. The other was a ‘half skeleton’ module, in which the ‘cold-side’ substrate was removed and a thermal-conductive sheet was used instead of a ceramic plate for the cold-side insulator. From the result of this evaluation, it was confirmed that, although some variation in the output power was observed for the ‘half-skeleton’ module, the power variation was markedly less than for the conventional-structured module. Additionally, to improve the output power of the module, we replaced the Al₂O₃ substrate with Si₃N₄, which has a higher thermal conductivity than the Al₂O₃ substrate. The observed output power of a module (25 mm × 24 mm × 8.3 mm) fabricated using the Si₃N₄ substrate was 1,293 mW at ΔT = 500 K. The output value of the module using the Si₃N₄ plate was improved by 29 % compared with the output value of the module using the Al₂O₃ substrate. Moreover, based on the structures of these modules, a 36 mm × 41 mm × 8.3 mm module was fabricated. The expected value of the output power of the module was 1.9 W at ΔT = 500 K.     

Solid state thermal control for spacecraft

The steady state heat pumping capabilities of thermoelectric devices are examined for spacecraft in Earth orbit, using a simple model. Thermoelectric parameters for a standard Bi₂Te₃ alloy are fitted with fourth order polynomials in temperature. Parameters are used which are the average for the temperature difference across the p?n couple. Internal spacecraft temperatures are varied from 270 to 330°K, and absorbed incident radiation fluxes are varied from zero to 700 W/m². It is found that heat rejection can be optimized with respect to thermoelectric device and radiator fin geometries, as well as with respect to input electrical power and that these devices are most useful on the surfaces with highest incident radiant power. Maximum heat fluxes which can be pumped out of the spacecraft are on the order of 50–160 W/m² for the various thermal environments examined. Input electrical powers corresponding to these maximum heat fluxes range from about 50–300 W/m². However, efficiency is greatly improved by operation at lower input power levels.     

Examination of a Thermally Viable Structure for an Unconventional Uni-Leg Mg2Si Thermoelectric Power Generator

We have fabricated an unconventional uni-leg structure thermoelectric generator (TEG) element using quad thermoelectric (TE) chips of Sb-doped n-Mg₂Si, which were prepared by a plasma-activated sintering process. The power curve characteristics, the effect of aging up to 500?h, and the thermal gradients at several points on the module were investigated. The observed maximum output power with the heat source at 975?K and the heat sink at 345?K was 341?mW, from which the ??T for the TE chip was calculated to be about 333?K. In aging testing in air ambient, a remarkable feature of the results was that there was no notable change from the initial resistance of the TEG module for as long as 500?h. The thermal distribution for the fabricated uni-leg TEG element was analyzed by finite-element modeling using ANSYS software. To tune the calculation parameters of ANSYS, such as the thermal conductance properties of the corresponding coupled materials in the module, precise measurements of the temperature at various probe points on the module were made. Then, meticulous verification between the measured temperature values and the results calculated by ANSYS was carried out to optimize the parameters.     

Effects of Fluid Directions on Heat Exchange in Thermoelectric Generators

Thermal fluids can transport heat to the large surface of a thermoelectric (TE) panel from hot and/or cold sources. The TE power thus obtainable was precisely evaluated using numerical calculations based on fluid dynamics and heat transfer. The commercial software FLUENT was coupled with a TE model for this purpose. The fluid velocity distribution and the temperature profiles in the fluids and TE modules were calculated in two-dimensional space. The electromotive force was then evaluated for counter-flow and split-flow models to show the effect of a stagnation point. Friction along the fluid surface along a long, flat path was larger than that along a short path split into two parts. The power required to circulate the fluids along the flow path is not negligible and should be considered in TE generation system design.     

Analysis of Annular Thermoelectric Couples with Nonuniform Temperature Distribution by Means of 3-D Multiphysics Simulation

Thermoelectric (TE) modules with annular geometry are very attractive for waste heat recovery within the automotive world, especially when integrated as stacks into tubular heat exchangers. The required temperature difference is built up between the coolant, which flows inside an inner tube, and the exhaust gas, which flows around an outer tube. The flow pattern of the exhaust gas can be axial or circumferential, which can lead to higher heat transfer coefficients on the outer surface of the tube. However, this multidimensional construction in combination with a complex flow pattern can lead to a nonuniform heat flux. Additionally, the system experiences a nonuniform temperature distribution which consequently leads to complex conditions regarding the electrical potential. The relevant effects are investigated using a three-dimensional (3-D) numerical model implemented in the computational fluid dynamics (CFD) simulation environment Star-CCM+. The model supports temperature-dependent characteristics of the materials, contact resistances, and parasitic effects in the TE module. Furthermore, it involves techniques to quickly find the exact maximum power point of the TE module with the given boundary conditions. Using the validated model the influence of the nonuniform temperature distribution is investigated with emphasis on the electrical output and TE efficiency.     

Novel Heat Controller for Thermogenerators Working on Uncontrolled Stoves

This paper describes the development of a thermogenerator designed for uncontrolled firewood household stoves. It was built on BiTe thermoelectric (TE) modules, and it uses a water pot as a cooling device that also serves as a hot water source. An original heat controller was developed; it has low thermal resistance (R) during low-power operation, but its R can be continuously increased according to the stove temperature so that the TE never overheats while its power generation is optimized.     

Geometry Optimization of a Segmented Thermoelectric Generator Based on Multi-parameter and Nonlinear Optimization Method

As no single thermoelectric material has presented a high figure-of-merit (ZT) over a very wide temperature range, segmented thermoelectric generators (STEGs), where the p- and n-legs are formed of different thermoelectric material segments joined in series, have been developed to improve the performance of thermoelectric generators. A crucial but difficult problem in a STEG design is to determine the optimal values of the geometrical parameters, like the relative lengths of each segment and the cross-sectional area ratio of the n- and p-legs. Herein, a multi-parameter and nonlinear optimization method, based on the Improved Powell Algorithm in conjunction with the discrete numerical model, was implemented to solve the STEG’s geometrical optimization problem. The multi-parameter optimal results were validated by comparison with the optimal outcomes obtained from the single-parameter optimization method. Finally, the effect of the hot- and cold-junction temperatures on the geometry optimization was investigated. Results show that the optimal geometry parameters for maximizing the specific output power of a STEG are different from those for maximizing the conversion efficiency. Data also suggest that the optimal geometry parameters and the interfacial temperatures of the adjacent segments optimized for maximum specific output power or conversion efficiency vary with changing hot- and cold-junction temperatures. Through the geometry optimization, the CoSb₃/Bi₂Te₃-based STEG can obtain a maximum specific output power up to 1725.3 W/kg and a maximum efficiency of 13.4% when operating at a hot-junction temperature of 823 K and a cold-junction temperature of 298 K.     

Development of an Mg2Si Unileg Thermoelectric Module Using Durable Sb-Doped Mg2Si Legs

Mg₂Si unileg structure thermoelectric (TE) modules, which are composed only of n-type Mg₂Si legs, were fabricated using Sb-doped Mg₂Si. The Mg₂Si TE legs used in our module were fabricated by a plasma-activated sintering method using material produced from molten commercial doped polycrystalline Mg₂Si, and, at the same time, nickel electrodes were formed on the Mg₂Si using a monobloc plasma-activated sintering technique. The source material used for our legs has a ZT value of 0.77 at 862 K. The TE modules, which have dimensions of 21 mm × 30 mm × 16 mm, were composed of ten legs that were connected in series electrically using nickel terminals, and the dimensions of a single leg were 4.0 mm  × 4.0 mm × 10 mm. From evaluations of the measured output characteristics of the modules, it appeared that the electrical resistance of the wiring that is used to connect each leg considerably affects the power output of the unileg module. Thus, we attempted to reduce the wiring resistance of the module and fabricated a module using copper terminals. The observed values of the open-circuit voltage and output power of the Sb-doped Mg₂Si unileg module were 496 mV and 1211 mW at ΔT = 531 K (hot side: 873 K; cool side: 342 K).     

Encapsulated Thermoelectric Modules for Advanced Thermoelectric Systems

An encapsulated thermoelectric (TE) module consists of a vacuum-tight stainless-steel container in which an SiGe or BiTe TE module is encapsulated. This construction enables maximum performance and durability because: the thermal expansion mismatch between the hot and cold sides of the container can be accommodated by a sliding sheet in the container; the TE module inside is always kept in a vacuum environment, therefore no oxidation can occur; and the pressure difference between the inside and outside of the container reduces thermal contact resistance inside the container. Our encapsulated SiGe module features higher operating temperature—up to 650°C for both hot and cold sides. Other high-temperature modules and conventional BiTe modules, including both-sides and one-side skeleton types, have been encapsulated. Several variants of the encapsulated module are available. Encapsulated thermoelectric modules with integrated coolers contain cooling panels through which water can pass. If the module hot side is heated by a radiating heat source (radiation coupling) or convection of a hot gas or fluid (convection coupling), no pressing force on the module is necessary. It therefore features minimum contact resistance with the cooling duct, because no pressure is applied, maximum TE power, and minimum installation cost. Another, larger, variant is a quadruple flexible container in which four modules (each of maximum size 40 mm × 40 mm) are encapsulated. These encapsulated modules were used in a powder metallurgy furnace and were in use for more than 3000 h. Application to cryogenic temperatures simulating the liquid nitrogen gas vaporizer has been also attempted.     

Evaluation of the Thermoelectric Module Consisting of W-Doped Heusler Fe2VAl Alloy

Power generation performance of a thermoelectric module consisting of the Heusler Fe₂VAl alloy was evaluated. For construction of the module, W-doped Fe₂VAl alloys were prepared using powder metallurgy process. Power generation tests of the module consisting of 18 pairs of p–n junctions were conducted on a heat source of 373–673 K in vacuum. The reduction of thermal conductivity and improvement of thermoelectric figure of merit by W-doping enhanced the conversion efficiency and the output power. High output power density of 0.7 W/cm² was obtained by virtue of the high thermoelectric power factor of the Heusler alloy. The module exhibited good durability, and the relatively high output power was maintained after temperature cycling test in air.