Leg Geometry Research Articles

A Three-Dimensional Analysis of Homogeneous and Functionally Graded Thermoelectric Cylinders

This paper analyzes a homogeneous thermoelectric (TE) circular cylinder as well as an exponentially graded TE cylinder under three-dimensional (3D) conditions. Analytical solutions of the temperature fields are obtained using an eigenfunction expansion method. The energy conversion efficiencies are determined and the material property gradation and leg geometry effects are examined. For the homogeneous TE material, it is found that the efficiency of the TE cylinder is almost the same as that of the cuboid TE leg with the side 2 W equal to the diameter 2R of the cylindrical leg. The efficiency of the cylindrical leg, however, is slightly higher than that of the cuboid leg if the two legs have the same length and cross-sectional area. In this case, the difference in energy efficiency between the two leg geometries depends on the ratio of the lateral dimension to the leg length and vanishes when the lateral dimension goes to infinity. For the exponentially graded TE cylinder, the numerical examples show that the efficiency is increased by appropriate material property gradations but is decreased by the 3D effects. Finally, the analytical solution indicates that besides the figure of merit, the two dimensionless parameters R/L and hL/k, where L is the leg length, h is the surface heat transfer coefficient, and k is the thermal conductivity, are also important factors that influence the energy efficiency of TE cylinders in 3D.

Shape optimization of square weld nut in projection welding

This study provides an optimal shape of square nut for better projection welding performance. Both experimental design method and electrical-thermal-mechanical finite element analysis (FEA) are used to investigate the effects of nut shape parameters on the height decrease of nut leg, called setdown. The relationship between the setdown and weld strength is then analyzed. Also, welding time to reach 50% of setdown tset is introduced as another objective function for better welding performance. The optimal nut shape parameters are determined to maximize the setdown, and minimize the tset at the same time via Taguchi method. The difference of setdown values between experiments and FEA is within 12%, which verify the reliability of the FE model. The gap between DIN928 standard for nut leg geometry and the optimized nut leg shape is less than 0.2 mm. The differences of setdown and tset values for two nut shapes are 6% and 9%, respectively.

Performance comparison of TEGs for diverse variable leg geometry with the same leg volume

The product development process consists of all the steps required to transform a product from concept to market availability. The volume used to make a product is one of the most important factors affecting the final price of a product and has to be taken into account in the design stage. In this context, a study based on the finite element method was carried out using different geometrical shapes of the same volume by considering the five following shapes: rectangle, I-leg, X-leg, trap-leg, and Y-leg. To achieve this, two cases were examined. In the first case, all five shapes of the same volume (47.915 mm3) were studied by considering an identical length of X-leg (6 mm) and the variable cross-sectional area of the hot ceramic junction. The results obtained show that the rectangular leg model generates the highest efficiency and output power with 5.482% and 0.041 W respectively. In the second case, all shapes of identical volume (47.915 mm3) were analyzed by condensing a variable leg length and a fixed cross-sectional area of the hot ceramic junction of X-leg. The results also show that the rectangular leg model generates the highest output power, which is approximately 0.114 W. In addition, in order to optimize the best model found, the length of the legs allowing to obtain the optimal internal resistance and thermal conductivity has been determined. The findings indicate that the rectangular leg model with a leg length of 6 mm gives the best performance.

Optimization of Power and Efficiency in a segmented legs STEG using the Taguchi method

In the recent times, many researchers have concentrated on the development of thermoelectric materials with higher values of figure of merits to enhance the conversion efficiency. It have been observed in some of the previous studies that the figure of merit and hence, the performance of thermoelectric modules can be enhanced using the module with segmented legs of two or more thermoelectric materials. In this study, the application of segmented thermoelectric modules in a solar assisted thermoelectric generator have been presented. PbTe and BiTe alloys are used in the segmented module. Except the figure of merit, the performance of thermoelectric generator is also dependent on temperatures across modules, load resistance and various design parameters such as leg geometries, cross sectional area of legs etc. So, Taguchi method of optimization was employed using five factors and five levels design to optimize the power and conversion efficiency. The power and efficiencies are mathematically calculated at different combinations according to L25 orthogonal array. The maximum power output is predicted up to 31.52 W and conversion efficiency up to 14.61% using The Taguchi analysis. Analysis of Variance method is also used to analyze general linear model which results into the estimation of contribution percentages of each factor on the power and efficiency.

High Performance Solar Thermoelectric Generator Using Asymmetrical Variable Leg Geometries

This paper presents a computational study of the combined effects of variable geometry and asymmetry in the legs of thermocouples of thermoelectric modules used in solar thermoelectric generators (STEGs). Six different models were considered for the thermocouples in each module, namely: rectangular-rectangular legs, rectangular-trapezoidal legs, rectangular-X legs, trapezoidal-trapezoidal legs, trapezoidal-X legs, and X-X legs. Simulations of the six different modules under the same heat flux was carried out in ANSYS 2020 R2 software. Temperature and voltage distributions were obtained for each model and the results indicate significant variations due to the utilization of varying leg geometries. Results show that the X-X leg module generated the highest temperature gradient and electric voltage. In comparison, a temperature gradient and electric voltage of 297 K and 16 V, respectively were achieved with the X-X leg module as against 182 K and 8.4 V, respectively, achieved in a conventional rectangular leg module. This suggests a 63.2% and 90.5% increase in the temperature gradient and electric voltage of the conventional TE module. Therefore, this study demonstrates that X geometry gives the best performance for thermoelectric modules and STEGs.

Performance Evaluation of a Nanomaterial-Based Thermoelectric Generator with Tapered Legs

A thermoelectric generator (TEG) converts thermal energy to electricity using thermoelectric effects. The amount of electrical energy produced is dependent on the thermoelectric material properties. Researchers have applied nanomaterials to TEG systems to further improve the device’s efficiency. Furthermore, the geometry of the thermoelectric legs has been varied from rectangular to trapezoidal and even X-cross sections to improve TEG’s performance further. However, up to date, a nanomaterial TEG that uses tapered thermoelectric legs has not been developed before. The most efficient nanomaterial TEGs still make use of the conventional rectangular leg geometry. Hence, for the first time since the conception of nanostructured thermoelectrics, we introduce a trapezoidal shape configuration in the device design. The leg geometries were simulated using ANSYS software and the results were post-processed in the MATLAB environment. The results show that the power density of the nanoparticle X-leg TEG was 10 times greater than that of the traditional bulk material semiconductor X-leg TEG. In addition, the optimum leg geometry configuration in a nanomaterial-based TEG is dependent on the operating solar radiation intensity.

The Influence of Leg Shape on Thermoelectric Performance Under Constant Temperature and Heat Flux Boundary Conditions

Global energy resource consumption is increasing rapidly, and wasted energy (the portion not used for useful services) comprises a significant fraction of the energy consumed. Much of the wasted energy is in the form of heat. Thermoelectric devices offer the potential to convert this wasted heat into electricity, and they can be used for thermal management by pumping heat. The shape of thermoelectric devices, particularly the active semiconducting material units (or thermoelectric legs) within the device, has remained largely unchanged. However, the advent of new manufacturing techniques such as additive manufacturing enables customizable device shapes. Given these new manufacturing capabilities, exploring atypical, or non-rectangular, leg geometries becomes increasingly relevant. This work focuses on understanding the effect of different thermoelectric leg designs on thermoelectric device performance. Various leg shapes were studied for their thermal and electrical performance under different thermal boundary conditions. The shapes studied include rectangular prisms, rectangular prisms with interior hollows, trapezoids, hourglass, and Y-shapes. Temperature gradients and the electrical potentials of the thermoelectric legs are determined using the COMSOL Multiphysics Thermoelectric Module. Both fixed temperature and fixed heat flux boundary conditions were examined numerically. Among the geometries investigated, the hourglass-shaped thermoelectric leg, subjected to a fixed temperature boundary condition, is found to have the best thermal and electrical performance. The hourglass-shaped leg results in more than double the electrical potential and maximum power compared to the conventional rectangular shape when the cold side experiences a natural convection boundary condition. Under a fixed heat flux boundary condition on the hot side, a trapezoid-shaped leg results in almost double the electrical potential and a 50% increase in the power output compared to the conventional leg shape. Varying boundary conditions, which reflect different device operating conditions, result in different performance values for the same leg shapes. These findings underscore the importance of leg geometry on electrical and thermal performance of a thermoelectric leg, as well as the importance of considering the device operating condition when selecting the best leg shape.

Fuel-burning thermoelectric generators for the future of electric vehicles

Ragone plot showing power density (kW/kg) and energy density (kWh/kg) is widely used for batteries, fuel cells and other energy conversion technologies. This is particularly useful for transportation and mobile applications where the weight is a key limiting factor. Here, we present for the first time, Ragone plot for scalable fuel-burning thermoelectric power generators. Optimizing thermoelectric leg geometry, the highest power and energy densities nearly scale with the square root of the material figure-of-merit (ZT). Internal heat recovery can improve fuel economy by 350% (reaching an efficiency >20% for a temperature independent ZTavg ~0.5), however, there is a trade-off due to the additional mass of heat exchanger hence the reduced power density. Prospects for electrification of particularly compact and unmanned vehicles are discussed. We foresee the potential of using fuel to drive fully-electric vehicles with high temperature thermoelectric generators. Development of the technologies for high heat transfer, reliable and robust contacts, and high ZT over a wide temperature range presents opportunities in the future energy landscape for mobile applications.

Quad-Trapezoidal-Leg Orthoplanar Spring with Piezoelectric Plate for Enhancing the Performances of Vibration Energy Harvester

To validate the potentials of unequal-length section-varied geometry in developing a orthoplanar spring-based piezoelectric vibration energy harvester (PVEH), a modified spring with quad-trapezoidal-leg configuration is designed, analyzed, and fabricated. A basic quad-trapezoidal-leg orthoplanar spring (QTOPS) is theoretically analyzed, and the structural effective stress and eigenfrequency are formulated to determine the main dimension parameters. Then, an improved QTOPS with additional intermediations is constructed and simulated. Porotypes with different leg geometries and mass configurations are fabricated and tested. The results of QTOPS and a conventional rectangular-shaped spring are compared. It is verified that the proposed approach provides the structure with an enlarged effective stress and lower resonant frequency, which makes it more suitable to construct a high-performance PVEH than the orthoplanar spring with equal-length or rectangular legs.

Device modeling and performance optimization of thermoelectric generators under isothermal and isoflux heat source condition

Thermoelectric generator (TEG) is considered as promising way of clean energy generation by recycling waste heat, but its poor performance due to several kinds of energy losses impedes wide scale commercialization. Since, most of the waste heat sources have constant heat flux (isoflux) conditions it is necessary to evaluate the performance of TEG under such conditions. Here, various kinds of parasitic heat losses such as conduction, and radiation along with energy losses through contacts are numerically simulated in order to predict the performance of TEG for both isothermal and isoflux heat source conditions. Further, optimizations of controlling parameters of TEG such as leg geometry, leg length, cross sectional area, and external load resistance are done to maximize the efficiency and power output of TEG. To overcome the cumbersome optimization process by experimental trials, Taguchi and ANOVA methods are employed to optimize all the device parameters for both types of operating conditions i.e. isothermal and isoflux. Under optimized conditions, maximum power of ~48 W (an increase of 52%) is predicted under isothermal condition for cylindrical legged TEG and 10.6 W (an increase of 100%) is obtained under constant heat flux of 63 kW/m2 for pyramid legged TEG.

Optimization of All-Oxide 2D Layered Thermoelectric Device Fabricated by Plasma Spray

Harvesting waste energy using thermoelectric (TE) principles is a key technology that increases overall power conversion and efficiency from combustion-based energy generation systems. However, design restrictions of commercially available thermoelectric devices and toxicity of commercial thermoelectric materials currently limit large-scale deployment. Additive and multilayered design and manufacturing of thermoelectric modules are a potential pathway to overcome current design restrictions as it enables to implement the device directly to the engineering structures with direct access to waste heat. Plasma spray is the chosen technology in this work to fabricate such patterned and layered TE devices, using as p-type Ca2Co2O5 and the n-type material TiO2-x. The optimization of thermoelectric leg geometry results in a maximum power density output of 1.9 × 10−4 W/cm2 per couple and efficiency of 1.1% at 750 K. An important aspect of this TE device design is that it allows direct p-n contact, whereas the proportionality between p-n contact area and power output is demonstrated. A correlation between the coating thickness and nonlinear behavior of the thermoelectric voltage is also discussed, which is associated with the anisotropy degree of the n-type coating.

Comprehensive modeling for optimized design of a thermoelectric cooler with non-constant cross-section: Theoretical considerations

With the popularization of electric vehicles, a thermoelectric cooler can be a promising battery thermal-management device that achieves the heat dissipation and uniform heating of a battery pack to improve its performance. In this study, a three-dimensional numerical model was established in order to qualitatively and quantitatively analyze the factors affecting the cooling performance for a thermoelectric cooler with a non-constant cross-section via the finite element method, and a one-dimensional mathematical model was constructed in order to explain the working mechanism of the influencing factors. The optimization included the geometric structure, temperature difference, leg geometry, and contact layers. The results show that compared with a thermoelectric cooler with a constant cross-section, the cooling capacity and the coefficient of performance of an optimized thermoelectric cooler with a non-constant cross-section were improved by 35.73% and 21.59%, respectively. Compared with the thermoelectric cooler with a non-constant cross-section before optimization, the cooling capacity and the coefficient of performance after optimization increased by 20.98% and 20.52%, respectively.

Power Generation, Efficiency and Thermal Stress of Thermoelectric Module with Leg Geometry, Material, Segmentation and Two-Stage Arrangement

The objective of this study was to investigate the power generation, efficiency, and thermal stress of a thermoelectric module with leg geometry, material, segmentation, and two-stage arrangement. The effects of leg geometry, material, segmentation, and two-stage arrangement on maximum power, maximum efficiency, and maximum stress under various temperature differences and voltage load conditions were investigated. The performance parameters of the thermoelectric module were evaluated based on a numerical approach using ANSYS 19.1 commercial software. An analytical approach based on theoretical equations of the thermoelectric module was used to verify the accuracy and reliability of the numerical approach. The numerically predicted values for maximum power and maximum efficiency of the thermoelectric module were validated as ±5% and those for the maximum thermal stress of the thermoelectric module as ±7% with the corresponding calculated theoretical values. In addition, the predicted values of maximum power and maximum stress of the thermoelectric module were validated as ±2% and ±5%, respectively, with studies reported by Ma et al. and Al-Merbati et al. Of all the combinations, the single stage segmented arrangement with cylindrical leg geometry and SiGe+Bi2Te3 material was suggested as the best combination with maximum power of 0.73 W, maximum efficiency of 13.2%, and maximum thermal stress of 0.694 GPa.

Analysis of thermoelectric geometry in a concentrated photovoltaic-thermoelectric under varying weather conditions

This study presents a detailed three-dimensional numerical investigation of the optimum thermoelectric geometry in a hybrid concentrated photovoltaic-thermoelectric system under varying weather conditions. Four different thermoelectric leg geometries are considered and their effects on the performance of the hybrid system are studied. The effects of thermoelectric leg height, cross-sectional area and ceramic height on the hybrid system performance are investigated. Furthermore, the effect of convective heat transfer coefficient on the hybrid system performance is studied. The performance of the hybrid system with optimized thermoelectric geometry is compared with that of the hybrid system with original geometry for summer climatic conditions in London, United Kingdom for a duration of 24 h. Results show that thermoelectric geometry optimization can reduce significantly, the negative impacts of the variable weather conditions on the hybrid system performance. Furthermore, results show that the maximum hybrid system power output density with the optimized thermoelectric geometry decreased by 48.29% when the original geometry is used. This study will provide useful insights into thermoelectric geometry optimization in a hybrid system and optimum thermoelectric geometry for performance enhancement.

A Bird-Inspired Perching Landing Gear System1

Abstract The design, modeling, simulation, and testing of a landing gear system that enables a UAV to perch on an object or surface is presented here. The working principle of the landing gear is inspired by the anatomy of birds that grasp and perch as tendons in their legs and feet are tensioned. In a similar fashion, as the UAV sets down on a structure, its weight tensions a cable which actuates opposing, flexible, multi-segment feet to enclose the target. To analyze the grasping capability of the design, a hybrid empirical–computational model is developed that can be used to simulate the kinematics of the system as it grasps objects of various cross-sectional shapes and sizes. The model relates the curvature of the feet to the displacement and tension of the cable tendon. These quantities are then related to the weight of the UAV through the leg geometry. It also evaluates enclosure and calculates contact forces to quantitatively characterize the grasp. Results demonstrate how the model can be used by designers to determine how a UAV can perch upon a structure of a given shape and size. If perched, the minimum weight required to maintain its position is calculated. A prototype system was fabricated, analyzed, and tested on a radio-controlled hexacopter. Experiments show that the landing gear enables the hexacopter to land, perch, and takeoff from a variety of objects. Finally, we begin to investigate the scalability of the concept with a smaller, lighter design.

The impact of thermoelectric leg geometries on thermal resistance and power output

Thermoelectric devices enable direct, solid-state conversion of heat to electricity and vice versa. Rather than designing the shape of thermoelectric units or legs to maximize this energy conversion, the cuboid shape of these legs has instead remained unchanged in large part because of limitations in the standard manufacturing process. However, the advent of additive manufacturing (a technique in which freeform geometries are built up layer-by-layer) offers the potential to create unique thermoelectric leg geometries designed to optimize device performance. This work explores this new realm of novel leg geometry by simulating the thermal and electrical performance of various leg geometries such as prismatic, hollow, and layered structures. The simulations are performed for two materials, a standard bismuth telluride material found in current commercial modules and a higher manganese silicide material proposed for low cost energy conversion in high-temperature applications. The results include the temperature gradient and electrical potential developed across individual thermoelectric legs as well as thermoelectric modules with 16 legs. Even simple hollow and layered leg geometries result in larger temperature gradients and higher output powers than the traditional cuboid structure. The clear dependence of thermal resistance and power output on leg geometry provides compelling motivation to explore additive manufacturing of thermoelectric devices.

Influence of Scavenge Leg Geometry on Inertial Particle Separator Performance

An inertial particle separator (IPS) is a particulate removal device typically installed at the inlet of a gas turbine to mitigate effects of sand ingestion on the engine. This system can minimize particulate ingestion during helicopter landings in austere brownout conditions so as to increase engine life. Typically, IPS systems have lower engine power losses than alternative engine inlet filtration technologies. The present study investigates the effect of IPS particle removal and power losses as a function of scavenge leg geometry. Performance was evaluated based on particle separation efficiency, particle image velocimetry, and surface flow visualization, as well as power loss and mass flow rate variations. Of the various scavenge geometries considered, it was found that flow constriction with a hub-side ramp most improved separation efficiency, while also stabilizing mass flow rates and generally reducing power loss. This is attributed to a reduction in the level of flow separation by the addition of a favorable pressure gradient and geometry changes downstream of the attached flow region.

Modelling and comprehensive analysis of TEGs with diverse variable leg geometry

Exhaustive numerical modelling and performance evaluation of numerous forms of variable thermoelectric legs were performed and critically examined under a steady state condition. The study encompasses geometries such as rect-leg, trap-leg, Y-leg, I-leg and X-leg depending on their respective shape structures. From the study, variable cross sectional inclusion was found to influence the performance of the convectional rect-leg significantly, such that the X-leg generated about 19.13% more power density than the convectional geometry (i.e. the rectangular leg) and relatively most efficient amidst all configurations. However, the Fourier conduction heat was seen to be the major contributor to the system irreversibilities in comparison to Thomson and Joule heating. In addition, the X-leg appear to have the highest generated entropy density in all conceptual models. The newly introduced geometry experienced lower thermal stresses than the conventional models, while the Y-leg and Trap-leg would possibly fail structurally before other models. Therefore, this study and executed simulation results can be utilized as effective and feasible reference for designing thermoelectric modules with diverse kinds of variable leg geometry.

Optimized high performance thermoelectric generator with combined segmented and asymmetrical legs under pulsed heat input power

In this study, a segmented asymmetrical thermoelectric generator (SASTEG) is numerically investigated to optimize its electrical performance and mechanical reliability under transient and steady state conditions. The thermal and electrical performance of the SASTEG and TEG under transient and steady state heating conditions are studied and compared. A three-dimensional numerical model is developed and solved using finite element method in COMSOL 5.3 Multiphysics software. Temperature dependent thermoelectric material properties are considered, and the elastoplastic behaviour of copper and solder is accounted for in the thermal stress analysis. The initial SASTEG geometry used in this study is subsequently optimized to reduce the maximum von Mises stress developed in its legs while maintaining its enhanced power output. Results obtained show that the optimized SASTEG provided a power output enhancement of 117.11% compared to that of the conventional TEG under rectangular pulsed heat condition. Also, the asymmetrical leg geometry used in the SASTEG n-type leg provided a reduced thermal stress of 39.21% in the lower segment (cold side) compared to the symmetrical leg geometry used in the p-type leg lower segment. This study will provide vital guidance in the design of high-performance TEG with improved mechanical reliability.

Energy Conversion by Nanomaterial-Based Trapezoidal-Shaped Leg of Thermoelectric Generator Considering Convection Heat Transfer Effect

Thermoelectric generators (TEGs) can harvest energy without any negative environmental impact using low potential sources, such as waste heat, and subsequently convert that energy into electricity. Different shaped leg geometries and nanostructured thermoelectric materials have been investigated over the last decades in order to improve the thermal efficiency of the TEGs. In this paper, a numerical study on the performance analysis of a nanomaterial-based (i.e., p-type leg composed of BiSbTe nanostructured bulk alloy and n-type leg composed of Bi2Te3 with 0.1 vol % SiC nanoparticles) trapezoidal-shaped leg geometry has been investigated considering the Seebeck effect, Peltier effect, Thomson effect, Fourier heat conduction, and surface to surrounding irreversible heat transfer loss. Different surface convection heat transfer losses (h) are considered to characterize the current output, power output, and thermal efficiency at various hot surface (TH) and cold surface (TC) temperatures. Good agreement has been achieved between the numerical and analytical results. Moreover, current numerical results are compared with previous related works. The designed nanomaterial-based TEG shows better performance in terms of output current and thermal efficiency with the thermal efficiency increasing from 7.3% to 8.7% using nanomaterial instead of traditional thermoelectric materials at h = 0 W/m2K while TH is 500 K and TC is 300 K.