Air Barriers Research Articles

A simulation-optimization integrated framework for subsurface air barrier strategies to mitigate seawater intrusion in a 3D coastal aquifer

Subsurface air barrier, owing to readily accessible and sufficiently clean of injected air, is a more attractive alternative for mitigating seawater intrusion (SWI) in arid and semi-arid coastal regions, compared to hydraulic barrier. Nevertheless, it remains an enormous challenge to recognize the appropriate layout scheme of air barrier system in a 3D coastal aquifer, including the spatial structure of air-injection zone and the adopted injection pressure, simultaneously considering the environmental and economic performances. This study established a simulation–optimization (S-O) integrated framework for determining the optimal air barrier scheme with minimizing total cost while effectively controlling the extent of SWI. Within the proposed S-O framework, the liquid–gas two-phase flow and solute transport (LGST) numerical model was linked with the micro-population genetic algorithm (mGA). Layout parameters of air barriers, salinity at constraint points and air injection rates were continuously exchanged between the LGST model and mGA at each optimization step. A hypothetical 3D confined aquifer was then employed to evaluate the stability of this S-O framework. The total cost of air barriers increasingly declines to a stable minimum value with the evolutionary processes. With the optimal scheme, there forms a complete and continuous air barrier system between adjacent air-boreholes, giving rise to the intrusive seawater decreasing by 69.7 % and the 0.5 isochlor retreating by 43.4 % at 365.0 day. Furthermore, the 3D aquifer system gradually reaches a quasi-steady state with time and the air injection rate cannot indefinitely increase in response to air injection. The proposed S-O framework can therefore provide a decision support system for designing subsurface air barrier with the least cost on the promise of controlling SWI in 3D coastal aquifers.

Topology optimization and parameter optimization hybridized by mesh smoothing for IPMSM design

PurposeTopology optimization (TO) methods have shown their unique advantage in the innovative design of electric machines. However, when introducing the TO method to the rotor design of interior permanent magnet (PM) synchronous machines (IPMSMs), the layout parameters of the magnet cannot be synchronously optimized with the topology of the air barrier; the full design potential, thus, cannot be unlocked. The purpose of this paper is to develop a novel method in which the layout parameters PMs and the topology of air barriers can be optimized simultaneously for aiding the innovative design of IPMSMs.Design/methodology/approachThis paper presents a simultaneous TO and parameter optimization (PO) method that is applicable to the innovative design of IPMSMs. In this method, the mesh deformation technique is introduced to make it possible to make a connection between the TO and PO, and the multimodal optimization problem can thereby be solved more efficiently because good topological features are inherited during iterative optimization.FindingsThe numerical results of two case studies show that the proposed method can find better Pareto fronts than the traditional TO method within comparable time-consuming. As the optimal design result, novel rotor structures with better torque profiles and higher reluctance torque are respectively found.Originality/valueA method that can simultaneously optimize the topology and parameter variables for the design of IPMSMs is proposed. The numerical results show that the proposed method is useful and practical for the conceptual and innovative design of IPMSMs because it can automatically explore optimal rotor structures from the full design space without relying on the experience and knowledge of the engineer.

Efficiency enhancing of the local capture hood due to air barriers

AbstractThis article is related to investigations of the capture hoods of the local exhaust ventilation. The purpose of the research: to increase the zone of action of local exhaust hoods and reduce the amount of air removed. It is equipped with two barriers for air: ring and cylindrical. The empirical dependences for air velocity determination near the suction zone are obtained. Graphs, chart and three-dimensional image visualizations of removed air jet velocity near capture hood with barriers for air are designed. The reduction of production energy consumption, material, and ventilation system maintenance costs due to the correction of the design of the capture hood are the main benefits of the new solution.

Application of experimental, numerical, and machine learning methods to improve drying performance and decrease energy consumption of tunnel-type food dryer

In this study, to distribute the drying air uniformly on the product surface, straight and trapeze air barriers were designed in the drying chamber of the existing tunnel dryer. The effects of air barriers on product surface temperature changes were investigated by computational fluid dynamics analysis (CFD). Drying time in the experiment without an air barrier decreased by 45% with the trapeze barrier and 20% with the straight barrier. Likewise, the trapeze barrier provided 53.9% energy savings, and the straight barrier 37.4% energy saving compared to the drying process carried out in the current system. Also, using the experimental data, mathematical equations that can calculate activation energy (Ea) in the drying process were produced with the help of regression-based artificial intelligence methods (Pace and Elastic.Net). With the help of these equations, the Ea values of the drying process performed under different experimental conditions were determined, and a 1.03% error value was calculated between the obtained Ea values and the experimental values.

An efficient combination of topology optimization and parameter optimization for electromagnetic devices

A novel hybrid optimization (HO) method efficiently combines parameter optimization (PO) and topology optimization (TO) is proposed. The novelty concerns introducing the mesh deformation technique for model regeneration to make a connection between the TO and PO, in this way, the geometric features can be inherited in iterative optimization to fasten the convergence. The proposed HO is applied to the optimal design of a baseline V-type permanent magnet synchronous machine (PMSM), in which the topology of air barriers and the layout parameters of permanent magnets (PMs) are simultaneously optimized, for torque property enhancement. Comparative numerical results show that the proposed HO is more efficient in optimal solution searching compared with traditional methods, as good topological features can be inherited in the iterative optimization. The numerical results also indicate that the proposed HO has good compatibility with different solvers, it can always provide good convergence to provide PMSM designs with excellent torque property when an evolutionary algorithm such as a genetic algorithm and evolution strategy is used as the solver.

Numerical study the effect of air barriers height inside the air conditioning ducting to satisfy the regulation of Indonesia Minister of Transportation number 69 of 2019

The Indonesian smart hybrid light train is a train under development by the government and will operate in Makassar-Parepare, Indonesia track. The authors conducted a numerical study on CFD to investigate the air flow distribution inside the air conditioning ducting and the air velocity and air temperature distribution on Motor Engine and Compartment (MEC) car to achieve the passenger comfort criteria based on the regulation standard of Indonesia Minister of Transportation Number 69 of 2019. This study was conducted by simulating 5 variations of air barriers height inside the supply ducts. The input of air into the ducting has the parameters of mass flow rate, static temperature, static pressure, and density with the values of 1 kg/s, 20 °C, 1 atm, and 1.2 kg/m 3 , respectively. The simulation results show that variation E is the best design which generated the average air velocity and air temperature distribution in the executive passenger cabin with the values of 0.25 m/s and 21.91 °C, respectively. Meanwhile, the other 4 variations did not satisfy the standard. The results also show that the ducting geometry can accommodate the air temperature difference on the MEC car that does not exceed 1.5 °C and the air supply is sufficient from the air conditioner unit to the driver room.

Impact of air barriers application in LCA and LCC of naturally ventilated dwellings in mild climate regions

Assessing singular elements that constitute the air barrier of a building envelope is quite unfeasible in Life Cycle Assessment (LCA). The study of these solutions through this particular scope is often overlooked. Two major aspects contribute to it: the complexity of the relationships between elements and the reduced embodied impact of these materials in the overall construction or retrofitting works. This work uses LCA and Life Cycle Costing (LCC) to study the viability of applying two envelope air barrier solutions in dwellings with excessive air change rates and equipped with different heating systems. The application of air barrier solutions resulted in average energy consumption savings in urban terrain, almost half of those in rural terrain during the heating season. Environmental performance and life cycle costs revealed mechanically (MECH) fastened air barriers to outperform fluid (FLUID) applied ones. The median annualized cost of adopting a FLUID solution was almost four times that of a MECH solution. Dwellings equipped with electric radiators ranked first in the shortest average Energy Payback Period (EPP) and the highest average Reference Service Life (RSL) savings. With the current analysis, the adoption of MECH solutions is recommended, independently of the heating system the dwelling is equipped with.

Comprehensive energy, exergy, enviro-exergy, and thermo-hydraulic performance assessment of a flat plate solar air heater with different obstacles

• Performance assessment of a solar air heater with different air barriers is performed. • Air obstacles can significantly enhance the system's energy and exergy efficiencies. • Vertical cylindrical obstacles have a greater performance compared to others. • Energy and exergy efficiencies can be enhanced up to 70% and 105%, respectively. • Relative CO 2 reduction potential is improved up to 170%. Although obstacles on the absorber surface of a solar air heater (SAH) can increase the thermal efficiency by creating turbulent conditions, they might reduce the system's exergy efficiency due to an increase in the pressure drop. In the present work, a 3-dimensional computational fluid dynamics (3D CFD) model is first developed to simulate conical obstacles, and the developed model is then validated using the available experimental data. To find optimal design features, obstacles with various shapes/geometries such as cylindrical, spherical, hemispherical, pyramidal, and cubical are investigated. To attain this goal, a comprehensive study is conducted by including energy, exergy, enviro-exergy, and thermo-hydraulic analyses. The results reveal that vertical cylindrical obstacles have better performance than other geometries as well as a flat absorber without obstacles. The average daily thermal efficiency of the system is increased by 69.16%, and the exergy efficiency of the system is increased by 103.16%. The relative CO 2 reduction potential (RCDRP) for a SAH with vertical cylinders is improved up to 168.7%. In addition, the vertical cylinder with a daily average thermo-hydraulic performance parameter of 1.2 shows the greatest thermo-hydraulic performance parameter (THPP) among other geometries, and the pyramidal obstacle with the THPP of 0.66 has the minimum performance.

An adaptive aerodynamic approach to mitigate convective losses from solar cavity receivers

We explore the potential for adaptive air barriers to mitigate convective heat losses from cavity receivers, especially at large tilt angles, using both suction and blowing nozzles. A heated scaled-down cylindrical cavity receiver was fitted with nozzles on four sides of the aperture, at 30° to the aperture plane. The tilted cavity receiver was mounted in a large wind tunnel to allow systematic variation of wind speed and direction. The effectiveness of different nozzle arrangements was calculated from the measured convective heat losses for a series of different mitigation strategies. The results reveal that a suction nozzle mounted at the bottom of the aperture is more effective than a blowing nozzle mounted at the top of aperture for tilt angles of θ= 45°, and under different wind speeds. The effectiveness ranged from 0 at a low suction flow rate to ~80% at a high suction flow rate. With the use of three suction nozzles, at the bottom and both sides of aperture, the effectiveness decreased markedly for both tilt angles and all wind speeds. For more challenging conditions of a 45° tilt angle and 45° yaw angle, the most effective approach is the use of suction through nozzles aligned diametrically opposite to the wind, while other nozzle combinations were ineffective in mitigating losses. Finally, the results highlight the need to apply an adaptive aerodynamic strategy that can respond to measured changes in the environmental conditions to achieve the highest thermal efficiency.

Elastic complementary meta-layer for ultrasound penetration through solid/liquid/gas barriers

Efficient ultrasound transmission is crucial in vast areas including noninvasive surgery, structural health monitoring, and underwater detection. However, extreme impedance contrast of interfering media spanning from solid to liquid and even gas seriously harms ultrasound transmission efficiency. Here, we propose a complementary meta-layer (CML) to “virtually cancel out” not only dissimilar solid but also liquid and gas barriers for highly enhanced transmission through the barriers in wave propagation perspective. Our proposition is apparently the first elastic CML and it is uniquely designed in a monolayer. The meta-atom forming a single meta-layer consists of spatially separated dipolar and monopolar resonators with completely independent tunability of effective negative properties. The proposed CML is capable of enhancing the ultrasound transmission by 593%, 1426%, and 3280% respectively for the polymer, water, and air barriers by numerical simulations. The proposed methodology to “cancel out” diverse barriers of highly dissimilar impedances can be groundbreaking in various ultrasound applications.

Thermal Conductive Encapsulation Enables Stable High-Power Perovskite-Converted Light-Emitting Diodes.

Significant progress has been achieved on perovskite nanocrystal (PNC)-converted light-emitting diodes (PcLEDs) with the development of surface encapsulations. However, achieving bright and long-living devices remains a challenge because the thermal isolation structure of the air barriers exacerbates heat accumulation inside PcLEDs. Here, we proposed a thermal conductive encapsulation for PNCs by embedding CsPbBr3 PNCs in layer-by-layer assembled boron nitride (BN) nanoplatelets through SiO2 crosslinking. This structure effectively suppresses the heat accumulation on PNCs and provides excellent air resistance, enabling the PNC-SiO2-BN composite to withstand 1000 h of photothermal annealing (under a 405 nm laser at 0.31 W cm-2, 80 °C in air) without showing obvious degradation. Green- and white-light PcLEDs were fabricated via on-chip encapsulation of PNC-SiO2-BN. The PcLEDs achieved the milestone in long-term stability (half-life time > 1000 h) at a high power density of ∼1.7 W cm-2 and displayed extradentary stability at ∼0.15 W cm-2 with constant light intensity within 1000 h of sustained illumination. The success in making thermal conductive composites will expedite the application of PNCs in LED backlights and other optoelectronic devices.

A Comparative Study of Air Flow Value over the Infant Radiant Warmer Bed

Radiant warmers are widely used in hospital neonatal care departments. Particular requirements for the basic safety and essential performance of infant radiant warmers are regulated by EN 60601-2-21:2009 + A1:2016. This standard doesn’t include the maximal air flow value over the infant bed while the standard 60601-2-19:2009 describes the maximal air flow values for incubators. This study shows fluctuation of the air flow over the infant bed and it leads to think, that a more preventive care of infants ambient is needed in the system. Authors have investigated the impact of air barriers on direct air flow value. Studies show that barriers can significantly decrease air flow over infant’s bed and potentially lower infant’s t heat losses by convection on infant bed.

Evaluating potential benefits of air barriers in commercial buildings using NIST infiltration correlations in EnergyPlus

According to the U. S. Department of Energy (DOE), infiltration accounts for 6% of the energy use and $11 billion in energy cost for U. S. commercial buildings. One strategy to reduce infiltration in commercial buildings is to provide more supply airflow than return and exhaust in order to “pressurize the building”. DOE has developed EnergyPlus models of several prototype buildings which assume that pressurization results in system-on infiltration rates that are 75% less than the system-off rates. However, airflow simulations of these buildings using the CONTAM multizone airflow software showed that pressurization reduced infiltration by an average of 44% only. To improve the infiltration rates calculated by the EnergyPlus models of prototype buildings, CONTAM infiltration rates were used to develop coefficients that can be input into EnergyPlus. CONTAM captures the effects of wind, temperature difference, and system operation on infiltration rates. Coefficients were developed for 11 prototype buildings, eight cities, and two levels of building envelope airtightness. Comparisons of the predicted infiltration rates were made between using the DOE prototype model inputs and the NIST infiltration correlations. Using the NIST correlations resulted in an average HVAC-EUI (HVAC-related energy use intensity) savings of 6% or 1.4 kBtu/ft2 due to airtightening. These results indicate that the effects of infiltration on HVAC energy use are important and that infiltration can and should be better accounted for in whole-building energy modeling.

Numerical assessment of compressed air injection for mitigating seawater intrusion in a coastal unconfined aquifer

Subsurface fluids injection is a viable alternative for controlling seawater intrusion in coastal regions, and freshwater is usually served for valid fluids to generate pressure ridge towards the ocean. But other fluids injection, such as compressed air, which presents clean and readily available, is a more attractive solution for repulsing the intruded seawater where freshwater is insufficient. In this study, the performance of compressed air injection (i.e., air barriers) for mitigating seawater intrusion in a coastal unconfined aquifer was quantificationally assessed using a coupled water-air two-phase flow and saltwater transport model. As compressed air is introduced into the aquifer at the toe of saltwater wedge, the seaward hydraulic gradient adjacent to the coast is produced driven by the generated airflow, thereby causing salt-freshwater interface to retreat to the ocean. The magnitude of air injection rate, related to the operational cost of air barriers, does not increases significantly given the progressively decreasing change rate. Compared to the workability of air barriers in the confined aquifer under similar conditions, the reduction in intruded seawater at 365.0 d in the unconfined aquifer reaches only about 0.45 times that in the confined aquifer, which indicates the significance of the boundary condition of aquifer top. The sensitivity analysis of the overlying unsaturated zone reveals that with its permeability decreasing or its thickness increasing, the performance of air barriers is enhanced owing to the blocking effect of the overlying layer on the escape of generated airflow and tends progressively to be stable. Particularly, the efficacy of air barriers in the confined aquifer, including the reduction in intruded seawater and the air injection rate, also can be achieved in an unconfined aquifer with an overlaying sufficient-semipermeable layer.

Slippery liquid‐infused porous surface via thermally induced phase separation for enhanced corrosion protection

AbstractSlippery liquid‐infused porous surface (SLIPS) is a rising star in corrosion protection owing to its outstanding corrosive medium resistance and self‐healing property. The large‐area and facile fabrication of SLIPS remains a challenge lying on the way of its practical application. Herein, we develop a novel SLIPS based on a porous polyvinylidene fluoride (PVDF) substrate fabricated by thermally induced phase separation. A sphere‐packing structure can be easily obtained by blade‐coating followed by cooling. The SLIPS exhibits an extremely low sliding angle of 5.8° so that it can resist the fouling of even the Chinese ink, ascribing to its slippery dynamic surface with low surface energy. We also evaluated the anti‐corrosion performance of the SLIPS and superhydrophobic PVDF coating by electrochemical impedance spectroscopy (EIS) and scanning Kelvin probe technique (SKP), both of which exhibited enhanced corrosion resistance in 3.5 wt% NaCl solution due to the physical oil and air barriers against the corrosive medium penetration. Nevertheless, the SLIPS coatings performed outstanding self‐healing properties because of the high fluidity of infused oil to recover the surface damages, and the self‐healing process was recorded by the SKP.

Mesophyll conductance: the leaf corridors for photosynthesis.

Besides stomata, the photosynthetic CO2 pathway also involves the transport of CO2 from the sub-stomatal air spaces inside to the carboxylation sites in the chloroplast stroma, where Rubisco is located. This pathway is far to be a simple and direct way, formed by series of consecutive barriers that the CO2 should cross to be finally assimilated in photosynthesis, known as the mesophyll conductance (gm). Therefore, the gm reflects the pathway through different air, water and biophysical barriers within the leaf tissues and cell structures. Currently, it is known that gm can impose the same level of limitation (or even higher depending of the conditions) to photosynthesis than the wider known stomata or biochemistry. In this mini-review, we are focused on each of the gm determinants to summarize the current knowledge on the mechanisms driving gm from anatomical to metabolic and biochemical perspectives. Special attention deserve the latest studies demonstrating the importance of the molecular mechanisms driving anatomical traits as cell wall and the chloroplast surface exposed to the mesophyll airspaces (Sc/S) that significantly constrain gm. However, even considering these recent discoveries, still is poorly understood the mechanisms about signaling pathways linking the environment a/biotic stressors with gm responses. Thus, considering the main role of gm as a major driver of the CO2 availability at the carboxylation sites, future studies into these aspects will help us to understand photosynthesis responses in a global change framework.

Mechanisms of Pulmonary Toxicity of Perfluoro-n-Alkane Pyrolysis Products with Consideration of the Structural Features of the Blood-Air Barriers.

Perfluoroisobutylene a is pulmonotoxic chemical generated during pyrolysis of perfluoro-nalkanes (polytetrafluoroethylene). The mechanisms of acute pulmonary toxicity induced by perfluoroisobutylene have not been studied yet. The analysis of tissues of brown frogs showed that the products of polytetrafluoroethylene pyrolysis induce typical inflammatory response in the lungs (fluid accumulation, erythrocyte stasis, desquamation of the epithelium, and capillary plethora in lung septa) and oropharyngeal cavity (degeneration of ciliated epithelium, hyperemia of underlying vessels with plasmatic imbibition of the connective tissue, and margination of segmented leukocytes and monocytes). The absence of surfactant is a specific feature of the blood-air barrier of the oropharyngeal cavity in frogs compared to the lungs. It can be hypothesized that toxic effects of perfluoroisobutylene are determined by its influence on epithelial (pneumocytes and cells of nonkeratinized stratified ciliated epithelium) and endothelial cells. Even though the effects of the agent on surfactant cannot be excluded, they do not determine the probability of development of inflammatory response.

Nanocellulose films as air and water vapour barriers: A recyclable and biodegradable alternative to polyolefin packaging

Synthetic polymer packaging is neither reprocessable, renewable nor biodegradable and is difficult to recycle into useful barrier materials. Cellulose fibre based packaging is renewable, easily reprocessable, recyclable and biodegradable, however, it is a poor barrier material both before and after recycling, especially against air and water vapour. Nanocellulose (NC), formed by breaking down cellulose fibres into nanoscale diameter fibres, is a renewable alternative to synthetic polymer packaging barrier layers. This research investigates the recyclability of virgin NC films. Nanocellulose films were recycled and prepared into films, using standard dispersion-based laboratory papermaking techniques through mixing and vacuum filtration of the resultant suspension. The recycled films retained ˜70% of the strength of the virgin films. Although the water vapour permeability (WVP) approximately doubled, increasing to 1.29 × 10−10 g.m−1.s−1 Pa−1, it is still comparable to synthetic polymer packaging materials such as Polyethylene(PE), Plasticized PVC, Oriented Nylon 6 and Polystyrene (PS). SEM micrographs reveal no fibre agglomeration and no damage to the fibres during the recycling process. The optical uniformity measurements of recycled NC film confirms a drop in uniformity of the film at smaller length scales and an increase in uniformity at larger length scales, compared with virgin NC film. The retained strength and barrier properties combined with easy reprocessability of the product promises a sustainable and recyclable alternative to conventional polyolefin packaging, providing a very attractive alternative for the packaging industry.

Effects of straw incorporation on desiccation cracking patterns and horizontal flow in cracked clay loam

Shrink-swell soil cracks upon dehydration, providing potentially preferential pathways for gravity-driven flow and contaminants transport. The process of crack-preferential flow is swelling-dependent, due to the dynamical changes in porous structure (cracks) in response to moisture variation. Incorporating straw into soils modifies the behavior of soil cracking, soil deformation characteristics and hydraulic properties, which has a possibility of inhibiting propagation of crack-preferential flow. The objectives of this study were to investigate the effects of straw incorporation on the crack patterns and preferential flow and to reveal how the swelling dynamics of cracked soils intervene the crack-preferential flow process. The soils were treated with three densities of straw incorporation. We investigated the horizontal infiltration in uncracked and cracked soils amended with straw and exposed to wetting-drying cycles. Horizontal flow patterns and the dynamics of crack closure were recorded with a digital camera mounted above the specimen. The propagation characteristics of the wetting front (WF) were quantified using digital image processing and morphological algorithms. The results showed that straw incorporation markedly inhibited the cracking degree and rendered the crack patterns more fragmented. Significant fluctuations in the infiltration rate were observed in cracked soils in the early stages of the infiltration process, and the straw incorporation attenuated the fluctuations of the infiltration rate. Normal crack apertures (perpendicular to the infiltration direction) blocked the continuous capillary-driven flow as air barriers and decelerated the infiltration rate in comparison to uncracked soils. The longitudinal cracks (along the infiltration direction) served as preferential pathways and facilitated the early-stage infiltration, but the duration of crack-preferential flow was dominated by the swelling rate of the aggregated soil clods. The tortuosity of the WF revealed that the flow regime transitioned from crack-preferential flow to matrix flow as the infiltration process progressed. Our results suggest that the crack-preferential flow becomes less pronounced as the cracks become progressively narrower, resulting from the swelling dynamics of the soil matrix. The fluctuations in the infiltration rate and the developing extent of crack flow can be attenuated by straw incorporation through restricting crack ratio and modifying crack morphology. Rice straw at a threshold density (experimentally determined) could be incorporated into soils to restrict the flow regime transition point (from crack preferential flow to matrix flow) to the depths of root zones, thus effectively precluding deep percolation induced by the cracks in shrink-swell soils.

Network modelling of dry-type transformer cooling systems

PurposeThe application of dry-type transformers is growing in the market because the technology is non-flammable, safer and environmentally friendly. However, the unit dimensions are normally larger and material costs become higher, as no oil is present for dielectric insulation or cooling. At designing stage, a transformer thermal model used for predicting temperature rise is fundamental and the modelling of cooling system is particularly important. This paper aims to describe a thermal model used to compute dry transformers with different cooling system configurations.Design/methodology/approachThe paper introduces a fast-calculating thermal and pressure network model for dry-transformer cooling systems, preliminarily verified by analytical methods and advanced CFD simulations, and finally validated with experimental results.FindingsThis paper provides an overview of the network model of dry-transformer cooling system, describing its topology and its main variants including natural or forced ventilation, with or without cooling duct in the core, enclosure with roof and floor ventilation openings and air barriers. Finally, it presents a formulation for the new heat exchanger element.Originality/valueThe network approach presented in this paper allows to model efficiently the cooling system of dry-type transformers. This model is based on physical principles rather than empirical assessments that are valid only for specific transformer technologies. In comparison with CFD simulation approach, the network model runs much faster and the accuracies still fall in acceptable range; therefore, one is able to utilize this method in optimization procedures included in transformer design systems.