Figure 26- - uploaded by Maxwell H. Briggs
Content may be subject to copyright.
Sinusoidal, ideal, and optimal piston and displacer motion The results in this section are specific to this engine design and should not be
Source publication
![Figure 16-Conceptual layout of an adiabatic Stirling convertor [24]...](profile/Maxwell-Briggs/publication/281590001/figure/fig5/AS:669299815501849@1536584919907/Conceptual-layout-of-an-adiabatic-Stirling-convertor-24-Reprinted-with-permission_Q320.jpg)
Analyses and experiments demonstrate the potential benefits of optimizing piston and displacer motion in a free piston Stirling Engine. Isothermal analysis shows the theoretical limits of power density improvement due to ideal motion in ideal Stirling engines. More realistic models based on nodal analysis show that ideal piston and displacer wavefo...
Similar publications
The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine mod...
Stirling engines have a high potential to produce renewable energy due to their ability to use a wide range of sustainable heat sources, such as concentrated solar thermal power and biomass, and also due to their high theoretical efficiencies. They have not yet achieved widespread use and commercial Stirling engines have had reduced efficiencies co...
Citations
... Červenka [20] reported a power drop by 82% when pistons move in sinusoidal motion compared to the discontinuous motion of the ideal cycle. Briggs [21] achieved 14% power increase by manipulated electrically the sinusoidal volume change of a free-piston Stirling engine. By using a linear electric motor Gopal [22] reported a 15% increase in efficiency. ...
This paper uses a simple model to estimate the power output of Stirling engine when giving the pistons a continuous motion with a prescribed pattern, fixed frequency, and a variable phase shift for different operational temperature ratios. Two continuous motions patterns, sinusoidal and modified sinusoidal, have been examined against the discontinuous motion of the ideal cycle. The power produced from engines having continuously moving pistons is lower than the power produced from the ideal cycle. The power ratio decreases as the temperature ratio increases. the highest produced power with a temperature ratio of 1.5, is 97% of the ideal cycle and it occurs at a phase-shift of 81o. Operating at ±10o off the highest power phase shift condition reduces the output power by 5-7%. For modified sinusoidal motion, the highest output power is 88% when the phase shift is 55o. Operating at ±10o off the maximum power phase shift condition reduces the output power by 2%. Moreover, at the highest output phase shift condition, the power output ratio drops from 97% to 93%, for sinusoidal motion as the cycle temperature ratio changes from 1.5 to 3. For modified sinusoidal motion, the output power drops from 88% to 78% at the highest phase shift condition.
... To attain the Carnot efficiency, it is critical for the practical engine configurations to reproduce these processes precisely. Typical commercial Stirling engine configurations use pistons connected to a crankshaft or a free piston arrangement, both of which result in continuous sinusoidal movement with a phase angle difference between the pistons [8][9][10]. This arrangement deviates from the theoretical Stirling cycle since the pistons do not adequately dwell and isolate the working fluid in either the hot or cold cylinder(s) during the expansion and compression processes respectively. ...
... Alfarawi et al. [23] presented the development and validation of a CFD model on a gamma-type Stirling engine to demonstrate the effects of a variety of phase angles on power output. Briggs [9] showed that power density could be increased by modifying the sine wave for prolonged dwell in a free-piston Stirling arrangement, and found that efficiency was reduced. These works have all developed their analyses considering sinusoidal motion of the pistons, which deviates from the ideal Stirling cycle; however, there have been no studies that calculate and analyze the deviation in efficiency between the ideal Stirling cycle and the cycle resulting from sinusoidal motion. ...
... Engine cycles can be visualized on P-v and T-s diagrams to illustrate their performance characteristics [1]. The cycle resulting from sinusoidal motion is plotted on P-v and T-s diagrams in Figure 2, using Equations (5), (6), (8) and (9). The ideal Stirling cycle is plotted using the same equations but fixing the variables to achieve the four ideal processes: isochoric heat addition (regeneration), isothermal expansion, isochoric heat rejection (regeneration), and isothermal compression. ...
Stirling engines have a high potential to produce renewable energy due to their ability to use a wide range of sustainable heat sources, such as concentrated solar thermal power and biomass, and also due to their high theoretical efficiencies. They have not yet achieved widespread use and commercial Stirling engines have had reduced efficiencies compared to their ideal values. In this work we show that a substantial amount of the reduction in efficiency is due to the operation of Stirling engines using sinusoidal motion and quantify this reduction. A discrete model was developed to perform an isothermal analysis of a 100cc alpha-type Stirling engine with a 90 ∘ phase angle offset, to demonstrate the impact of sinusoidal motion on the net work and thermal efficiency in comparison to the ideal cycle. For the specific engine analyzed, the maximum thermal efficiency of the sinusoidal cycle was found to have a limit of 34.4%, which is a reduction of 27.1% from Carnot efficiency. The net work of the sinusoidal cycle was found to be 65.9% of the net work from the ideal cycle. The model was adapted to analyze beta and gamma-type Stirling configurations, and the analysis revealed similar reductions due to sinusoidal motion.
With the increasing ambition of space agencies and the private sector, space missions are increasingly daring and focus on deep space missions, aiming to reach planets like Mars and Jupiter. For missions with these objectives to be viable, the spacecraft must have a high availability of energy to carry out the mission safely. Although solar conversion systems are well established for space application, they have a number of limitations such as the low solar incidence on more distant planets would make it impossible to apply a photovoltaic system. In this scenario, nuclear power generation systems are an alternative, as they can operate for long periods providing a high amount of energy. However, for these systems to become applicable, an energy conversion system with high efficiency and low mass must be applied. Dynamic conversion cycles, especially the Stirling cycle, is one of the best options, however, several components considerably increase the system mass, especially the radiator. This component used for heat rejection, can be responsible for more than 1/3 of the entire system mass. Considering this perspective, this work performed a finite time thermodynamic modeling of a Stirling cycle and an exergy analysis to evaluate the radiator impact on the system. With the model, it was possible to evaluate the impact of the radiator area on the cycle energy and exergy efficiency, map the radiator irreversibility; find the ratio of the increase in radiator mass to the increase in panel area; and through a figure of merit to find the best kg/kW system ratio that provides the greatest efficiency. With the results it was possible to identify that with approximately 70 m² of radiator area the system finds the best kg/kW ratio. These results may provide valuable theoretical insight into the future development of radiators for space nuclear power conversion systems.
The new space age that humanity is living in is constantly expanding the limit of human presence in the solar system. New missions are being planned by space agencies and private companies to take the man to planets like Mars. However, for missions like this to be possible, high-efficiency power generation systems are needed. From this perspective, nuclear power generation systems are an excellent option, as they are able to supply energy for a long period in a constant way. For systems like this to become viable, high-efficiency, low-mass energy conversion systems must be used. In this scenario, the dynamic Stirling conversion cycle proves to be an excellent option. However, these systems have several components that can make them very heavy, which could prevent their application, given the need for the system to have good compatibility and low mass to allow it to be launched into space. Among these components, the heat pipe-radiator assembly is the one that has the greatest participation in the size and total mass of the system, reaching more than 1/3 of the total mass. With this in mind, this work carried out thermodynamic modeling of the Stirling cycle together with an asymmetrical heat pipe model, to evaluate the dimensional impact of low-temperature heat pipes on the system's total mass. With the model, it was possible to identify that the reduction of the engine cold side temperature considerably increases the system mass, due to the need to use a greater heat-pipe-radiator system. Taking into account the configuration of the cold heat pipes, it was possible to conclude that increasing the number of heat pipes provides the greatest increase in mass for the rejection system in relation to the increase in the length and diameter of the cold heat pipes. The results also indicated that an optimization between the number of heat pipes, heat pipes diameter, and length is necessary to reach an optimal value of the heat rejection system mass.
Recent work suggests that Stirling device performance can be improved using a decoupled, actively controlled displacer piston to directly shape the device’s thermodynamic behavior. In this paper, the authors validate the controlled displacer concept using a low-frequency thermocompressor platform whose displacer and power output mechanisms are not kinematically coupled. As a little-known class of Stirling devices whose work output is pneumatic rather than mechanical, the thermocompressor presents new challenges for modeling and experimental validation because few devices have actually been built and tested. The device presented here is currently the highest pressure experimental research platform of a Stirling thermocompressor known to the authors. A third-order dynamic model is derived using first principles and is validated against experimental results. The model contains parameters that are known and/or measurable and as such is not a “fitted” model. This first-principles model is used to explore the influence of different displacer motion profiles on the output of the thermocompressor. The model is able to incorporate an arbitrarily-specifiable displacer motion profile. Using a controlled displacer piston profile, we experimentally demonstrate 1.45X higher peak cycle power and 3.6X higher work output, compared to a traditional sinusoidal displacer motion. This model is appropriate for optimizing the control of the displacer motion with respect to desired thermocompressor power, efficiency, or other performance metrics for any general Stirling thermocompressor.
As the new space era advances, there is an increasing demand for long-term missions beyond Earth’s orbit, such as on Mars and the Moon. The level of complexity of these missions is higher than conventional missions in terms of duration, particularly the energy demand required. To become viable, power generation systems must have a high power density, that is, high power associated with low mass. From this perspective, dynamic nuclear power generation systems coupled with electric propulsion are considered the most promising systems for deep-space exploration and colonization missions. Thus, to provide valuable information for the development of a dynamic energy conversion system for space, this study carried out thermodynamic modeling of a nuclear-powered Stirling cycle coupled with a dynamic engine model for space purposes. By means of numerical modeling, the constructive parameters of the Stirling engine, such as regenerator efficiency, compression ratio, heat exchanger thermal conductance, engine frequency, piston stroke, and area, are varied to understand the impact of these parameters on the final system performance. The results show that the regenerator efficiency can provide significant gains in the engine efficiency. However, a very high regenerator efficiency reduces the power of the cycle. The engine compression ratio tends to increase the engine efficiency, but a compression ratio above six provides marginal gains for cycle efficiency. From the results obtained, the best parameters yielded a system with a power output of 260.5 kW and a power density of 35.38 kg∙kW-1. This study can serve as a theoretical guideline for the future design of nuclear-powered Stirling engines for space applications, providing insight into the constructive parameters that influence the overall performance of the system.
The ideal Stirling cycle provides a clear control strategy for the piston paths of ideal representations of Stirling cycle machines. For non-equilibrium Stirling cycle machines however, piston paths aiming to emulate the ideal cycle’s four strokes will not necessarily yield best performance. In this contribution, we ask the question: What are the COP -optimal piston paths for specific non-equilibrium Stirling cryocoolers? To this end, we consider a low-effort Stirling cryocooler model that consists of a set of coupled ordinary differential equations and takes several loss phenomena into account. For this model and an exemplary parameter set, piston path optimizations are done with an indirect iterative gradient method based on optimal control theory. The optimizations are repeated for two different kinds of volume constraints for the working spaces: one representing an alpha-Stirling configuration, the other a beta-Stirling configuration. Compared to harmonic piston paths, the optimal piston paths lead to significant improvements in COP of ca. 88 % for the alpha-Stirling and ca. 117 % for the beta-Stirling at the maximum- COP operational frequency. Additionally—and even though the optimizations were performed for maximum COP —cooling power was increased with even lager ratios.
In recent years, the interest of space agencies and private companies in space exploration has increased, mainly in deep space missions. This type of mission poses great challenges due to the high energy level demanded from the power systems, requiring a more efficient and compact energy conversion system. Thus, this work carried out a finite-time thermodynamic model and exergy analysis of a Stirling cycle for nuclear space power generation. The thermodynamic model was coupled to a simple dynamic Stirling engine model and takes into account several aspects such as the thermal losses between the hot and cold side of the Stirling cycle, finite-time regeneration, temperature drop along heat pipes, and variable compression ratio. The system performance and component irreversibilities were evaluated by varying the nuclear core temperature and the cold side temperature of the cycle. Then, the figure of merit mass per power output (kg.kW-1) of the energy conversion system was computed, enabling the model to find temperature conditions for a system that aligns high efficiency and compactness. The results showed that the component with the greatest irreversibility is the reactor core with a value of 496.14 kJ, representing 68.18% of the total irreversibility. The exergy analysis showed that only 5.15% of the total exergy is used for power generation and 24.33% is rejected to space. Moreover, the cold side temperature of 352 K provided the system with the lowest value of mass per power output (87.69kg.kW-1).
View Video Presentation: https://doi.org/10.2514/6.2021-3605.vid This paper discusses the concept of a Minimally-Intrusive Power generation System (MIPS) for use in transport vehicles which use Nuclear Thermal Propulsion (NTP). A MIPS could take the waste heat produced by the reactor in idle mode and removed by the hydrogen coolant loop and convert it into usable electrical power for the vehicle. MIPS differs from bimodal Nuclear Thermal Propulsion in the sense that MIPS aims for adequate power generation and bimodal aims for maximum power generation. The goal of the MIPS is to provide adequate usable power to the vehicle while reducing total system mass and addressing fuel embrittlement concerns.
