Stirling Cycle Engines: Inner Workings and Design
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Appropriately designed, the Stirling engine promises high thermal efficiency, quiet operation and the ability to operate from a wide range of heat sources. Stirling Cycle Engines offers tools for expediting feasibility studies and for easing the task of designing for a novel application. Prime movers and coolers operating on the Stirling cycle are of increasing interest to industry, the military stealth submarines and space agencies.
Stirling Cycle Engines fills a gap in the technical literature and is a comprehensive manual for researchers and practitioners. In particular, it will support effort world-wide to exploit potential for such applications as small-scale CHP combined heat and power , solar energy conversion and utilization of low-grade heat. Organ, formerly of University of Cambridge, UK - now retired.
Before his retirement Allan J. Organ was a lecturer at the University of Cambridge, specializing in thermodynamics and gas dynamics of the Stirling cycle machine and regenerator. He has studied stirling cycle machines throughout his career and is a leading authority in the field. Permissions Request permission to reuse content from this site.
A considerable reduction in mortality rate from outbreaks of infectious diseases in developed and developing countries could be prevented with improved and safer sanitation systems . The Nano Membrane Toilet NMT is being developed to treat human waste into clean water and heat without the external supply of water, energy, and sewer.
This unit requires the development of new technologies for power generation, and the use of human faecal material as an energy source is one example.
The combined benefits of the novel systems embedded in this unit i. Conversion of thermal energy to electrical energy in medium-scale commercial environments is mostly associated with gas engines, Rankine engines, microturbines, fuel cells and Stirling engines in a cogeneration system . Heat recovery for power generation in household-scale applications can be accomplished with the use of an external combustion engine such as a Stirling engine that can function by using the heat generated from a gas stream at high temperature.
Stirling engines have been considered for cogeneration systems due to certain features that give them greater advantage over other reciprocating engines, such as low vibration, very low emissions, high efficiency and the ability to utilise different forms of energy . Stirling engines also operate in a closed, regenerative thermodynamic cycle  and they have been employed in various applications, such as combined heat and power CHP production, solar power generation, heat pumps, nuclear power for electricity generation, and geothermal energy .
The performance of the Stirling engine is based on its physical and geometrical features, the type and properties of the working gas, regenerator porosity and efficiency, dead volume, heat exchanger temperature, pressure drop, and heat and shuttle losses. In the case of the NMT unit, the primary aim of the integration of the combustor with the Stirling engine is to utilise the excess heat from the former to power the engine, and convert to electricity by connecting to an alternator.
The Stirling engine is considered over other options due to its compatibility with the micro-combustor of the NMT, high specific power and efficiency, and good performance at partial load; also due to features which are particularly advantageous for household applications such as simplicity, long-life cycle, low emission level, and low vibration and noise levels.
The disadvantages of Stirling engines are low compression ratio, working gas leakage and large volume. Certain approaches have been taken to increase the output power of the engines, such as the selection of the working gas, with the use of helium rather than hydrogen at high pressure, and increase in heat transfer surface area and internal heat transfer coefficient. Changes have also been made to the mechanical arrangements, such as the use of free piston Stirling rather than conventional Stirling engines; although the free piston Stirling engine has its own minimal disadvantages in connection with the stability of the mechanical elements, such as the damper and mechanical springs .
The application of a biomass energy conversion system using a Stirling engine is more flexible than the conventional biomass energy conversion with gas engines . In addition, there have been recent developments on biofuel powered Stirling engines.
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The utilisation of bioenergy with the application of Stirling engines has proved to be a promising technology . A comparison of the use of the Stirling engine and organic Rankine cycle turbine for electricity generation from poultry waste was carried out by Cotana et al. This gives the Stirling a greater advantage over internal combustion engines.
Recent investigations have been undertaken on the numerical and experimental analysis of Stirling engines powered by biomass combustion. An evaluation was carried out by Kuosa et al. Sato et al. The combustion and inlet gas temperature were optimised to develop a cleaning process for hot ash, due to the ash fouling that was observed in the heat exchangers of the engine. The study showed that the introduction of a filter system reduced the heat transfer between the burner and Stirling engine, and the power output was affected negatively.
Combustion tests were conducted by Nishiyama et al. The air-to-fuel ratio effect on the output performance of the engine in relation to the hot end was highlighted. An experimental observation was conducted by Thiers et al. The specified output performance of the manufacturer could not be achieved as the analysis resulted in high thermal losses, low power output and efficiency.
Alfarawi et al.
Also the usage of stored cold energy of LN2 to optimise the power output of the engine was presented. However, there has not been extensive research on the thermodynamic characteristics of the quasi steady state Stirling engine integrated with gasifier or combustor, with more detailed and accurate analyses of the output performance.
In order to recover energy from the micro-combustor, including the conversion of heat losses into useful work, the integration process requires the design of a small scale Stirling engine to run at quasi steady state. Hence, there is a need for further investigation into the thermodynamic performance of the Stirling engine with biomass combustion, especially the heat exchangers, thermal losses, pressure drops, output power and efficiency of the engine.
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This study examines the thermodynamic performance of the Stirling engine integrated with a self-sustaining sanitation technology for waste heat recovery and electrical power generation. The effect of different operating temperature profiles including the heater, the cooler, the flue gas and working gas temperatures on the thermal efficiency and power output are examined.
In addition, the results are compared with the outputs from similar analyses on micro-CHP technologies with biomass combustion.
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The performance of the NMT system is defined by the collective operation of each integrated component, such as settling tank, mechanical screw, dryer, feeder, micro-combustor, membrane, water settling tank and Stirling engine  ,  as described in Fig. In this system, human waste is received in the settling tank and separated into two streams: urine and faeces.
The supernatant fluid urine is heated up by the supernatant heater before it is transported to the hollow-fibre membrane for purification. The resultant water is collected in the water settling tank. The faeces are transported by the mechanical screw to the dryer. Hot air is supplied to the dryer from the combustor to remove the moisture in the faeces before they proceed into the feeder. Faeces are transported into the combustor from the dryer with the aid of the feeder, which controls the feed rate of dried material into the combustor.
The energy for the start-up of the combustor is supplied to the system via an air heater, which aids the increase of the operating temperature. The Stirling engine is integrated into the combustor and connected to an alternator for electricity power generation. The product and by-products include clean water from the purified supernatant fluid, ash from burnt faecal material and exhaust gases. The Stirling engine is conceptualised to be integrated as the heat recovery system of the NMT unit. The hot-side of the Stirling engine, known as the heater, is assumed to be attached directly to the outer cylindrical wall of the combustor as depicted in Fig.
This ensures that there is maximum heat surface area and heat transfer between the flue gas of the combustor and working gas in the Stirling engine. The recovered heat in the Stirling engine is then converted into electricity via an alternator. Therefore, the co-products of the NMT include electricity, clean water from the purified supernatant, and exhaust gases and ash from the combustion of faecal material.
Schematic illustration of the integration of the micro-combustor with the Stirling engine showing heat fluxes through the combustor walls. The performance of the energy conversion unit proposed for the NMT has been previously described based on an experimental investigation on a bench-scale downdraft combustor test rig using faeces, wood biomass and simulant faeces . This work focuses on the numerical investigation of the conceptualised heat recovery system of the NMT, using a quasi steady state model of the gamma type Stirling engine.
The major factors that determine the Stirling engine performance are its thermal efficiency and power output. Other factors that contribute to the effective performance of the engine include: i mean pressure, which is the average pressure in the engine; ii working gas characteristics, such as high specific heat capacity, density, viscosity and thermal conductivity that vary with gas types, all of which contribute to the output performance of the engine; iii regenerator effectiveness, which defines the rate of heat absorbed from the working gas and the heat returned to the working gas during the oscillatory movement between the heat exchangers; iv work space temperature, which defines the temperature of the expansion and compression spaces; and v the swept volume, which defines the actual working gas volume in the work spaces.
The higher the swept volume difference, the higher the power output from the pressure to volume P-V diagram. The heat transfer by conduction Q cond is determined from Eq. This rate determines the heat transfer from the flue gas to the working gas in the heater of the engine and plays a major role in the performance of the engine. T w and T wg are the temperature of the combustor wall assumed to be the temperature of the heater wall and temperature of the working gas respectively, and d is the thickness of the Stirling engine heater.
The control volume in the Stirling engine is divided into six parts, i. The analysis of the working gas volume in the two parts of the regenerator is important as the output and efficiency of the engine are determined by the performance of the regenerator. The numerical equations for the regenerator parts were applied to the thermodynamic modelling for accurate analysis of their performance in the engine. The pressure, temperature, mass flow and volumetric flow of the working gas across the work spaces and heat exchangers from the expansion space to the compression space, and the heat transfer in the heat exchangers, are exhibited in the diagram.
An ideal adiabatic model was applied for the numerical simulation of the gamma type Stirling engine. The equations used to determine the essential parameters for the numerical simulation can be found elsewhere  ,  and are given below. The derivatives of the gas temperatures in the compression and expansion spaces are calculated by means of Eqs. The working gas temperature across the boundary between the heater and the expansion space is determined by Eqs. The temperature of the gas stream flowing from the first part of the regenerator to the heater is described by Eqs.
The boundary condition for mass flow rates from the cooler to the second part of the regenerator is defined by Eqs. The mass flow rate for the boundary between the compression space to the cooler is given by Eqs. The application of the energy conservation equation to determine the control volumes can be defined by means of Eqs.
The regenerator is divided into two parts to investigate its performance based on its proximity to the heater and cooler. The parts of the regenerator are derived as Eqs. In the above equations, m k , m r and m h are the mass of working gas in the cooler, regenerator and heater, respectively kg , W c is the work in the compression space J , W e is the work in the expansion space J , Q cool , Q reg , Q heat are the heat transfer in the cooler, regenerator, and heater, respectively W , Q kdiss is the heat dissipation loss due to friction in the cooler W , Q r j diss is the heat dissipation loss due to friction in the two parts of the regenerator W , Q hdiss is the heat dissipation loss due to friction in the heater W.
The conservation of energy for each control volume is obtained by using the ideal gas state equation of the working gas Eq. The rate of heat transfer in the two parts of the regenerator is determined by means of Eq. For pressure drop in the heat exchangers, Eq. The shuttle loss accounted for in this study is given by Eq. The derivative for the total pressure in the engine is obtained by summing all the energy equations and losses as given by Eq.
The indicated work in the cycle and the indicated power of the engine are defined by Eqs. MATLAB was employed to write the codes for the numerical simulation using the mathematical equations stated and to determine the output performance and thermodynamic characteristics.
The initial input parameters for the Stirling engine were obtained from the design specifications listed in Table 1. The model is based on the concept of the working gas inside the Stirling engine heater being heated through conduction by the hot flue gas leaving the combustor. The heat transfer by conduction is calculated, and the heater temperature is provided as an input. The set of differential equations were solved and the unknown function that satisfies the initial conditions of the differential equations was the objective, which was computed for each of the output parameters.
The equations in the operating system were integrated through complete cycles to determine the pressure, displacement and velocity of the piston and displacer, the pressure drop and heat losses, and the volume of the expansion and compression spaces until the steady state operation of the engine was achieved.
The heat exchangers heater, regenerator and cooler were modelled with an infinite surface area similar to the ideal Stirling engine, and the steady state condition was achieved when the temperature of the expansion and compression space at the beginning of the cycle was the same as the temperature at the end of the cycle. The consecutive process of the computation for the numerical procedure is described by the flow chart in Fig.
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The assumptions listed next were made to obtain the mathematical model of the Stirling engine:. The temperature of the working gas changes with time in the surrounding wall in the engine compartment. The regenerator temperature is equal to the average temperature of the heater and cooler.
The quasi steady state model developed in this study was validated with the experimental results from the gamma type Stirling engine reported by Gheith et al. In order to validate the model the brake power of the Stirling engine was calculated by first establishing the total torque on the crankshaft. Equations obtained from  ,  were used for this calculation. The torque Tq from the piston and displacer is determined with Eq.
To account for the mechanical loss in the engine due to friction Tq b , Eq. The cyclic brake work is determined with Eq. And the cyclic brake power is determined with Eq. The values of the parameters used as input to the model for validation are presented in Table 2. The results for output power obtained from the model and presented in Gheith et al.
Input parameters of the gamma Stirling engine for model validation data collected from Gheith et al. Results from the validation of the numerical model of the gamma Stirling engine against the experimental output. The maximum and minimum heat flow rates correspond to the instances when the gas velocity is at the highest and lowest in the cycle. The variations in the heat flow rate in the heat exchangers occur when the displacer and pistons are at the top and bottom dead centre positions. The maximum heat flow rate in the heater is 6. The regenerator exhibits the highest values of the heat flow rate due to its effectiveness absorbing and rejecting heat from the working gas in the regenerator chamber.
The heat dissipation loss in the heat exchangers, as shown in Fig. These results show that the heat flow rate of the working gas in the heat exchangers varies with the displacement of the working gas volume. The highest pressure drop is observed in the regenerator at a value of 0.
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Description Some years after the original invention, internal design of a Stirling engine has come to be considered a specialist task, calling for extensive experience and for access to sophisticated computer modelling. The low parts-count of the type is negated by the complexity of the gas processes by which heat is converted to work.
Some years after the original invention, internal design of a Stirling engine has come to be considered a specialist task, calling for extensive experience and for access to sophisticated computer modelling. Design is perceived as problematic largely because those interactions are neither intuitively evident, nor capable of being made visible by laboratory experiment. There can be little doubt that the situation stands in the way of wider application of this elegant concept.
Stirling Cycle Engines re-visits the design challenge, doing so in three stages. Firstly, unrealistic expectations are dispelled: chasing the Carnot efficiency is a guarantee of disappointment, since the Stirling engine has no such pretentions. Secondly, no matter how complex the gas processes, they embody a degree of intrinsic similarity from engine to engine. Suitably exploited, this means that a single computation serves for an infinite number of design conditions.
Thirdly, guidelines resulting from the new approach are condensed to high-resolution design charts? Stirling Cycle Engines offers tools for expediting feasibility studies and for easing the task of designing for a novel application. The formulation throughout highlights what the thermodynamic processes of different engines have in common rather than what distinguishes them. Design by scaling is extended, corroborated, reduced to the use of charts and fully Illustrated.