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A Study of Simple Thermal Energy Conversion DeviceLai, Wei-ting 11 June 2009 (has links)
The main purpose of this research is to design a thermal energy conversion device, which is aimed to collect unused heat produced by nature. In order to achieve high-efficiency conversion, some novel devices will be studied to convert heat energy into mechanical power. A simple heat exchanger as well as heat engine device is proposed in this study. Dichloromethane is used as an important factor due to its physical properties. Finally, the concept of a tubular linear generator will be adopted to generate electric power.
The feature of the proposed simple thermal energy conversion device is that we can use unused heat sources as input, such as solar energy and waste heat from car engines. Besides, the system is capable to work under the condition of low-temperature difference
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Thermodynamic and economic feasibility analysis of a 20 MW ocean thermal energy conversion (OTEC) power plantUpshaw, Charles Roberts 30 July 2012 (has links)
Ocean Thermal Energy Conversion (OTEC) is the process of harnessing the temperature differential that exists in the equatorial oceans between the warm surface water and the cool water thousands of feet below to produce electricity. Due to the massive scale of the ocean thermal resources, OTEC power generation is appealing. The purpose of this thesis was to investigate OTEC and assess its potential viability as an energy source from both engineering and economic perspectives.
This thesis provides an introduction to the research, and outlines the scope of the project in Chapter 1. Chapter 2 proves an overview of OTEC, from the basic operation and viable locations, to information on some of the major components that make up the plant. Chapter 3 describes the thermodynamics, heat transfer, and fluid mechanics that govern the physical operation of the OTEC plant. Chapter 4 provides an analysis of different plant design parameters to examine effects different parameters have on plant operations and equipment sizing. Chapter 5 describes the cost estimation for an OTEC plant, and provides subsequent analysis by comparing the estimated cost with other technologies and electricity prices from four island communities.
The primary research of this thesis was the development of an integrated thermal fluids systems model of a closed-cycle OTEC power plant for the purpose of analyzing the effects of key design parameters on the plant performance. A simple Levelized Cost of Electricity (LCOE) economic model was also developed and integrated with the Thermal Fluid Systems model in order to assess the potential economic viability of a 20 MW OTEC power plant. The analyses from these models suggest that OTEC is definitely viable from an engineering standpoint, but economic viability for a 20 MW plant would likely be limited to small or remote island communities. / text
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Optimization Of Ocean Thermal Energy Conversion Power PlantsRizea, Steven Emanoel 01 January 2012 (has links)
A proprietary Ocean Thermal Energy Conversion (OTEC) modeling tool, the Makai OTEC Thermodynamic and Economic Model (MOTEM), is leveraged to evaluate the accuracy of finite-time thermodynamic OTEC optimization methods. MOTEM is a full OTEC system simulator capable of evaluating the effects of variation in heat exchanger operating temperatures and seawater flow rates. The evaluation is based on a comparison of the net power output of an OTEC plant with a fixed configuration. Select optimization methods from the literature are shown to produce between 93% and 99% of the maximum possible amount of power, depending on the selection of heat exchanger performance curves. OTEC optimization is found to be dependent on the performance characteristics of the evaporator and condenser used in the plant. Optimization algorithms in the literature do not take heat exchanger performance variation into account, which causes a discrepancy between their predictions and those calculated with MOTEM. A new characteristic metric of OTEC optimization, the ratio of evaporator and condenser overall heat transfer coefficients, is found. The heat transfer ratio is constant for all plant configurations in which the seawater flow rate is optimized for any particular evaporator and condenser operating temperatures. The existence of this ratio implies that a solution for the ideal heat exchanger operating temperatures could be computed based on the ratio of heat exchanger performance curves, and additional research is recommended.
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Ocean energy assessment : an integrated methodologyBanerjee, S. January 2011 (has links)
The huge natural energy resources available in the world’s oceans are attracting increasing commercial and political interest. In order to evaluate the status and the degree of acceptability of future Ocean Energy (OE) schemes, it was considered important to develop an Integrated Assessment Methodology (IAM) for ascertaining the relative merits of the competing OE devices being proposed. Initial studies included the gathering of information on the present status of development of the ocean energy systems on wave, OTEC and tidal schemes with the challenges faced for their commercial application. In order to develop the IAM, studies were undertaken for the development and standardization of the assessment tools focussing on: • Life Cycle Assessment (LCA) on emission characteristics. • Energy Accounting (EA) studies. • Environmental Impact Assessment (EIA) over different environmental issues. • Resource captures aspects. • Defining economy evaluation indices. The IAM developed from such studies comprised of four interrelated well defined tasks and six assessment tools. The tasks included the identification of the modus operandi on data collection to be followed (from industry) for assessing respective OE devices, and also advancing relevant guidelines as to the safety standards to be followed, for their deployment at suitable sites. The IAM as developed and validated from case studies in ascertaining relative merits of competing OE devices included: suitable site selection aspects with scope for resource utilisation capability, safety factors for survivability, scope for addressing global warming & energy accounting, the environmental impact assessment both qualitatively and quantitatively on different environmental issues, and the economic benefits achievable. Some of the new ideas and concepts which were also discovered during the development of the IAM, and considered useful to both industry and researchers are given below: • Relative Product Cost (RPC) ratio concept- introduced in making an economic evaluation. This is considered helpful in sensitivity analysis and making design improvements (hybridising etc) for the cost reduction of OE devices. This index thus helps in making feasibility studies on R&D efforts, where the capital cost requirement data and life span of the device is not well defined in the primary stages of development. • Determination of the threshold limit value of the barrage constant - considered useful in determining the efficacy of the planning process. The concept ascertained the relative efficiency achieved for various barrage proposals globally. It could also be applied to suggest the revisions required for certain barrage proposals and also found useful in predicting the basin area of undefined barrage proposal for achieving economic viability. • Estimations made on the future possibility of revenue earnings from the by-products of various OTEC types, including the scope of chemical hubs from grazing type OTEC plants. • Determination of breakeven point- on cost versus life span of wave and OTEC devices studied, which is useful in designing optimum life of the concerned devices. The above stated multi-criterion assessment methodology, IAM, was extended leading to the development of a single criterion model for ascertaining sustainability percent achievable from an OE device and termed IAMs. The IAMs was developed identifying 7 Sustainability Development Indices (SDI) using some the tools of the IAM. A sustainability scale of 0-100 was also developed, attributing a Sustainability Development Load Score (SDLS) percentage distribution pattern over each SDIs, depending on their relative importance in achieving sustainability. The total sum of sustainability development (SD) gained from each SDI gave the IAMs (for the concerned device), indicating the total sustainable percentage achieved. The above IAMs developed, could be applied in ranking OE devices alongside the unsustainable coal power station. A mathematical model of estimating the IAMs was formulated, in order to ascertain the viability to the sustainable development of any energy device. The instruments of IAM and IAMs which have been developed would be helpful to the OE industry in ascertaining the degree of acceptability of their product. In addition it would also provide guidelines for their safe deployment by assessing the relative merits of competing devices. Furthermore, IAM and IAMs would be helpful to researchers undertaking feasibility studies on R&D efforts for material development research, ‘hybridization studies’ (as also new innovations), cost reduction, the performance improvement of respective devices, and any economic gains. With future advancements in OE systems and the availability of field data from large scale commercial applications, the specific values/data of the IAM & IAMs may be refined, but the logic of the models developed in this research would remain the same.
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Étude de la production d'électricité à partir de l'énergie thermique des mers à l'île de la Réunion : modélisation et optimisation du procédé / Study of electricity production from the ocean thermal energy conversion to the Reunion Island : modelling and process optimizationSinama, Frantz 07 December 2011 (has links)
L’énergie thermique des mers (ETM) offre une alternative intéressante pour la réduction de l’utilisation des énergies fossiles. En utilisant le gradient de température présent entre l’eau de surface et l’eau en profondeur, il est possible de produire de l’électricité grâce à un cycle thermodynamique. Les expérimentations sont peu nombreuses à l’heure actuelle, en raison d’un coût relativement élevé. Une approche fondamentale est donc développée avec la création de modèles numériques en régime permanent et dynamique. Le modèle en régime statique a été développé à partir d’une description mathématique simplifiée des composants du cycle. Ce modèle permet une évaluation globale des performances du système, incluant le prélèvement et le rejet de l’eau de mer ainsi que le cycle thermodynamique. À partir de la modélisation statique, un modèle dynamique a été établi en appliquant la méthode des systèmes équivalents de Gibbs. Cet outil permet de décrire les phases de démarrage et d’arrêt, d’étudier la modulation de la puissance électrique délivrée au réseau et d’optimiser le cycle. Les résultats de simulations des différents modèles sont confrontés à la littérature et à des données expérimentales, afin d’avoir des éléments de validation. L’un des intérêts du modèle en régime dynamique est la possibilité d’effectuer une analyse de type « premier et second principe » du système. Une optimisation du fonctionnement du cycle est réalisée à partir de cette analyse. Des pistes d’améliorations sont proposées. L’optimisation est réalisée grâce au couplage du modèle dynamique avec l’outil Genopt. Les outils numériques développés permettront d’élaborer des stratégies de contrôle des installations. / Ocean Thermal Energy Conversion (OTEC) offers an interesting alternative for reducing the use of fossil fuels for energy generation. Using the temperature gradient present between the surface water and deep water, it is possible to produce electricity through a thermodynamic cycle. At present, the experiments are limited due to a relatively high cost. A fundamental approach is developed with the creation of numerical models in steady and dynamic state. The model in steady state has been developed from a simplified mathematical description of the components of the cycle. This model allows for an overall assessment of system performance including the withdrawal and discharge of the sea water, as well as the thermodynamic cycle. From the static model, a dynamic model was established using the method of the equivalent Gibbs systems. This tool is used to describe the start-up and shutdown, to study the modulation of the electrical power delivered to the network and to optimize the cycle. The simulation results of the different models are confronted with the literature and experimental data in order to have points of validation. One of the advantages of the model under dynamic conditions is the ability to perform an analysis of the "first and second principle" of the system. Optimization of the operation is carried out from this analysis. Possible improvements are proposed. An optimization of the cycle operation is carried out from this analysis. The optimization is done by coupling the dynamic model with the tool Genopt. The numerical tools developed will permit in addition to develop strategies to control of the power plants.
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Métodos analíticos para o cálculo de desempenho de motores termomagnéticos do tipo tesla. / Analytical methods for the performance calculation of tesla type thermomagnetic motors.Bessa, Carlos Vinicius Xavier 08 June 2018 (has links)
Motores termomagnéticos são dispositivos capazes de converter calor em energia mecânica através do efeito termomagnético, e são uma alternativa para a conversão de energia de rejeitos térmicos de baixa e baixíssima qualidade. Neste trabalho é proposta uma classificação dos motores termomagnéticos como sendo de dois tipos, os motores tipo Edison e os motores tipo Tesla. Feita a classificação, diferenciou-se o comportamento de operação e os ciclos termodinâmicos desenvolvidos pelos dois tipos de motores, mostrando que motores do tipo Tesla desenvolvem um ciclo termodinâmico que pode ser aproximado por um ciclo Brayton magnético, já motores do tipo Edison descrevem um ciclo mais complexo, não podendo ser aproximado por um ciclo Brayton. Compararam-se os parâmetros de interesse para ambos os motores através de análises termodinâmicas, onde se concluiu que motores do tipo Tesla apresentam melhores respostas de trabalho e eficiência que motores do tipo Edison, quando são consideradas as mesmas condições de operação. Além disso, identificou-se que a equação de força de Kelvin é a equação que corretamente descreve o comportamento da força magnética em um motor termomagnético, essa contribuição é importante, pois vários trabalhos publicados na literatura utilizam equações que não descrevem corretamente o comportamento da força magnética. Mostrou-se que o trabalho produzido em um motor termomagnético é igual ao trabalho produzido pela força magnética resultante no dispositivo. Foi desenvolvida e validada uma metodologia para o cálculo do trabalho específico produzido em um motor do tipo Tesla. Utilizando as metodologias validadas, verificou-se como a temperatura, o campo magnético aplicado, o fator de desmagnetização e o tipo de transição influenciam o comportamento dos motores termomagnéticos tipo Tesla, o que abre caminho para o desenvolvimento de dispositivos mais interessantes do ponto de vista termodinâmico. / Thermomagnetic motors are devices capable of converting heat into mechanical energy through the thermomagnetic effect. These devices are able to operate using low or very low quality thermal waste, being an alternative to avail that range of thermal energy. This work classifies the thermomagnetic motors in two types: The Tesla type and the Edison type thermomagnetic motors, differentiating the operational behavior and the thermodynamic cycles developed in each type. By using thermodynamic approaches, it is shown that the Tesla type thermomagnetic motors have best response in terms of work and efficiency than the Edison type thermomagnetic motors, when the same operating conditions are considered. In addition, an experimental approach is presented, proving that the Kelvin force equation describes the behavior of the force in thermomagnetic motors, and the work produced in a motor is the same that the work produced by the resultant magnetic force in the system. It was developed and validated a method to estimate the work produced by cycle in a Tesla type thermomagnetic motor, and using thermodynamic approaches, the relevance of the temperature, applied magnetic field, demagnetizing factor and transition type in the Tesla type thermomagnetic motor were verified.
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Métodos analíticos para o cálculo de desempenho de motores termomagnéticos do tipo tesla. / Analytical methods for the performance calculation of tesla type thermomagnetic motors.Carlos Vinicius Xavier Bessa 08 June 2018 (has links)
Motores termomagnéticos são dispositivos capazes de converter calor em energia mecânica através do efeito termomagnético, e são uma alternativa para a conversão de energia de rejeitos térmicos de baixa e baixíssima qualidade. Neste trabalho é proposta uma classificação dos motores termomagnéticos como sendo de dois tipos, os motores tipo Edison e os motores tipo Tesla. Feita a classificação, diferenciou-se o comportamento de operação e os ciclos termodinâmicos desenvolvidos pelos dois tipos de motores, mostrando que motores do tipo Tesla desenvolvem um ciclo termodinâmico que pode ser aproximado por um ciclo Brayton magnético, já motores do tipo Edison descrevem um ciclo mais complexo, não podendo ser aproximado por um ciclo Brayton. Compararam-se os parâmetros de interesse para ambos os motores através de análises termodinâmicas, onde se concluiu que motores do tipo Tesla apresentam melhores respostas de trabalho e eficiência que motores do tipo Edison, quando são consideradas as mesmas condições de operação. Além disso, identificou-se que a equação de força de Kelvin é a equação que corretamente descreve o comportamento da força magnética em um motor termomagnético, essa contribuição é importante, pois vários trabalhos publicados na literatura utilizam equações que não descrevem corretamente o comportamento da força magnética. Mostrou-se que o trabalho produzido em um motor termomagnético é igual ao trabalho produzido pela força magnética resultante no dispositivo. Foi desenvolvida e validada uma metodologia para o cálculo do trabalho específico produzido em um motor do tipo Tesla. Utilizando as metodologias validadas, verificou-se como a temperatura, o campo magnético aplicado, o fator de desmagnetização e o tipo de transição influenciam o comportamento dos motores termomagnéticos tipo Tesla, o que abre caminho para o desenvolvimento de dispositivos mais interessantes do ponto de vista termodinâmico. / Thermomagnetic motors are devices capable of converting heat into mechanical energy through the thermomagnetic effect. These devices are able to operate using low or very low quality thermal waste, being an alternative to avail that range of thermal energy. This work classifies the thermomagnetic motors in two types: The Tesla type and the Edison type thermomagnetic motors, differentiating the operational behavior and the thermodynamic cycles developed in each type. By using thermodynamic approaches, it is shown that the Tesla type thermomagnetic motors have best response in terms of work and efficiency than the Edison type thermomagnetic motors, when the same operating conditions are considered. In addition, an experimental approach is presented, proving that the Kelvin force equation describes the behavior of the force in thermomagnetic motors, and the work produced in a motor is the same that the work produced by the resultant magnetic force in the system. It was developed and validated a method to estimate the work produced by cycle in a Tesla type thermomagnetic motor, and using thermodynamic approaches, the relevance of the temperature, applied magnetic field, demagnetizing factor and transition type in the Tesla type thermomagnetic motor were verified.
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Thermodynamic Analysis And Simulation Of A Solar Thermal Power SystemHarith, Akila 01 1900 (has links) (PDF)
Solar energy is a virtually inexhaustible energy resource, and thus, has great potential in helping meet many of our future energy requirements. Current technology used for solar energy conversion, however, is not cost effective. In addition, solar thermal power systems are also generally less efficient as compared to fossil fuel based thermal power plants. There is a large variety of systems for solar thermal power generation, each with certain advantages and disadvantages. A distinct advantage of solar thermal power generation systems is that they can be easily integrated with a storage system and/or with an auxiliary heating system (as in hybrid power systems) to provide stable and reliable power. Also, as the power block of a solar thermal plant resembles that of a conventional thermal power plant, most of the equipment and technology used is already well defined, and hence does not require major break through research for effective utilisation. Manufacturing of components, too, can be easily indigenized.
A solar collector field is generally used for solar thermal energy conversion. The field converts high grade radiation energy to low grade heat energy, which will inevitably involve energy losses as per the laws of thermodynamics. The 2nd law of thermodynamics requires that a certain amount of heat energy cannot be utilised and has to be rejected as waste heat. This limits the efficiency of solar thermal energy technology. However, in many situations, the waste heat can be effectively utilized to perform refrigeration and desalination using absorption or solid sorption systems, with technologies popularly known as “polygeneration”.
There is extensive research done in the area of solar collectors, including but not limiting to thermal analysis, testing of solar collectors, and economic analysis of solar collectors. Exergy and optimization analyses have also been done for certain solar collector configurations. Research on solar thermal power plants includes energy analysis at system level with certain configurations. Research containing analysis with insolation varying throughout the day is limited. Hence, there is scope for analysis incorporating diurnal variation of insolation for a solar thermal power system.
This thesis centres on the thermodynamic analysis at system level of a solar thermal power system using a concentrating solar collector field and a simple Rankine cycle power generation (with steam as the working fluid) for Indian conditions. The aim is to develop a tool for thermodynamic analysis of solar thermal power systems, with a generalised approach that can also be used with different solar collector types, different heat transfer fluids in the primary loop, and also different working fluids in the secondary loop.
This analysis emphasises the solar collector field and a basic sensible heat storage system, and investigates the various energy and exergy losses present. Comparisons have been made with and without a storage unit and resulting performance issues of solar thermal power plants have been studied. Differences between the system under consideration and commercially used thermal power plants have also been discussed, which brought out certain limitations of the technology currently in use. A solution from an optimization analysis has been utilized and modified for maximization of exergy generated at collector field.
The analysis has been done with models incorporating equations using the laws of thermodynamics. MATLAB has been used to program and simulate the models. Solar radiation data used is from NREL’s Indian Solar Resource Data, which is obtained using their SUNY model by interpreting satellite imagery.
The performance of the system has been analysed for Bangalore for four different days with different daylight durations, each day having certain differences in the incident solar radiation or insolation received. A particular solution of an optimization analysis has been modified using the simulation model developed and analysed with the objective of maximization of exergy generated at collector field.
It has been found that the performance of the solar thermal power system was largely dependent on the variation of incident solar radiation. The storage system provided a stableperformance for short duration interruptions of solar radiation occurred on Autumn Equinox (23-09-2002).The duration of the interruption was within the limits of storage unit capacity. The major disruption in insolation transpired on Summer Solstice (21-06-2002) caused a significantly large drop in the solar thermal system performance; practically the system ceased to function due to lack of energy resource. Hence, the use of an auxiliary heating system hasbeen considered desirable.
The absence of a storage unit has been shown to cause a significant loss in gross performance of the power system. The Rankine cycle turbine had many issues coping with a highly fluctuating energy input, and thus caused efficiency losses and even ceased power generation. A storage unit has been found to be ideal for steady power generation purposes. Some commercial configurations may lack a storage system, but they have been compensated by the auxiliary heating system to ensure stable power generation.
The optimization of the solar collector determines that optimal collector temperatures vary in accordance to the incident solar radiation. Hence, the collector fluid outlet temperature must not be fixed so as to handle varying insolation for optimal exergy extraction. The optimal temperatures determined for Bangalore are around 576 K which is close to the values obtained by the simulation of the solar thermal power system.
The tools for analysis and simulation of solar thermal power plants developed in this thesis is fairly generalised, as it can be adapted for various types of solar collectors and for different working fluids (other than steam), such as for Organic Rankine Cycle (ORC). The model can also be easily extended to other types of power cycles such as Brayton and Stirling cycles.
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Konceptstudie för omvandling av termisk energi till elektrisk samt mekanisk energi i en autonom undervattensfarkost / Concept Study Regarding the Conversion of Thermal Energy into Electrical and Mechanical Energy in an Autonomous Underwater VehicleWodlin, Jakob January 2016 (has links)
Rapporten avhandlar en konceptstudie för omvandling av termisk energi till elektrisk samt mekanisk energi, i den autonoma undervattensfarkosten SAPPHIRES. Inledningsvis utreds vilka förväntningar och krav som finns på konceptet för energiomvandling samt om där finns någon publicerad litteratur som redan gjort ansträngningar för att lösa det aktuella problemet. Allmän teori kring värmemotorer och en bred, systematisk litteratursökning inkluderas även i det arbetet. Energiomvandlingen antas kunna ske enligt två fall kallade ”hög-prestanda” och ”låg/medel-prestanda”, vilka innebär att mekanisk samt elektrisk effekt, respektive endast elektrisk effekt ska kunna levereras av konceptet. De mekaniska samt elektriska effekterna ska, vidare, kunna levereras om maximalt 600, respektive 6 kW, och konceptet ska åtminstone kunna uppfylla ett av energiomvandlingsfallen. Den faktiska konceptstudien utgörs av två iterationer av konceptgenereringar, -utvärderingar och -val och de visar att ett koncept kallat ”Öppet system inspirerat av nukleär värmeframdrivning” förefaller vara det bästa sättet att omvandla termisk energi i SAPPHIRES. Därtill indikerar en mer detaljerad analys, bestående av bland annat matematisk modellering och konceptuell konstruktion, att konceptet möjligen skulle kunna uppfylla så kallad ”hög-prestanda” och sedermera leverera både mekanisk och elektrisk effekt om 600, respektive 6 kW. Mer specifikt visar en matematisk analys, med hjälp av vissa antaganden rörande konceptets funktion, att ett ”Öppet system inspirerat av nukleär värmeframdrivning” skulle kunna leverera en mekanisk effekt om 1025 kW samt en elektrisk effekt om 141 kW. En grov, konceptuell konstruktion bekräftar också att konceptets vitala, ingående komponenter faktiskt kan rymmas inom de specificerade dimensionskraven (en cylinderformad volym med en längd och diameter om 1,7, respektive 0,5 m.). Det står dock klart att de möjliga koncepten för energiomvandling kraftigt begränsas av deras möjligheter att leverera tillräcklig mekanisk effekt, för att uppnå ”hög-prestanda”. Om endast ”låg/medel-prestanda” ska uppfyllas tillåts fler av de möjliga koncepten och i ett sådant fall skulle faktorer som underhåll, miljöpåverkan och SAPPHIRES signatur kunna prioriteras i högre utsträckning. / The report discusses a concept study regarding the conversion of thermal energy into electrical and mechanical energy, in the autonomous underwater vehicle SAPPHIRES. First, the requirements and expectations regarding the concept of energy conversion are investigated and efforts are made to identify any published literature, which has already made attempts of solving the issue. General theory regarding heat engines and an extensive literature study are also included in this work. The energy conversion is assumed to perform according to two cases called "high-performance" and "low/medium-performance", meaning mechanical and electrical energy or electrical power should be delivered by the concept, respectively. More specifically, the mechanical and electrical powers should be delivered of a maximum of 600 and 6 kW, respectively and the concept should at least fulfill one of the performance settings. The actual concept study comprises of two iterations of concept generations, evaluations and selections and shows that a concept called "Open system inspired by nuclear thermal propulsion" seems to be the best way of converting thermal energy on-board SAPPHIRES. Moreover, a more detailed analysis, comprising of, inter alia, mathematical modelling and conceptual design, indicates that the concept possibly can meet the so-called "high-performance" and thus, deliver both mechanical and electrical powers of 600 and 6 kW, respectively. More specifically, a mathematical analysis, based on some assumptions regarding the concept's functionality, shows that an "Open system inspired by nuclear thermal propulsion" could deliver a mechanical power of 1025 kW and an electrical power of 141 kW. Rough conceptual design also shows that the vital parts of the concept could fit within the specified maximal dimensions (a cylinder-shaped volume with a length and diameter of 1.7 and 0.5 m, respectively). However, it is clear the possible concepts of energy conversion are severely limited by their capacities of delivering enough mechanical energy, to meet the "high-performance" demands. Assuming only the "low/medium-performance" has to be met, more possible concepts becomes available and in that case, factors such as maintenance, environmental impact and signature of SAPPHIRES could be considered to a greater extent.
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