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Parametric Study of an Air Charged Franchot Engine with Novel Hot and Cold Isothermalizers

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Parametric Study of an Air Charged Franchot Engine with Novel Hot and Cold Isothermalizers inventions Article Parametric Study of an Air Charged Franchot Engine with Novel Hot and Cold Isothermalizers Jafar M. Daoud ID and Daniel Friedrich * ID School of Engineering, Institute for Energy Systems, University of Edinburgh, Edinburgh EH9 3DW, Scotland, UK; [email protected] * Correspondence: [email protected] Received: 19 October 2017; Accepted: 1 December 2017; Published: 5 December 2017 Abstract: The Stirling engine is an external combustion engine that uses heat exchangers to enhance the addition and removal of energy. This makes the engine power-dense but expensive, less efficient and complicated. In this contribution, the Stirling engine based on the Franchot engine has novel cylindrical fins working as isothermalizers to improve heat transfer without the complications of heat exchangers. Enhancing the power density by isothermalizing work spaces is compared to the bare cylinder optimized by varying the phase angle. The theoretical analysis shows that both the adiabatic and isothermal fins increase the power and efficiency, achieving the Curzon and Ahlborn efficiency at the maximum power point. In comparison to the phase angle method, the finned engine resulted in much lower gas mass flow rate, which leads to a reduction in the regenerator pumping and enthalpy losses. Thus, the Stirling engine has the potential to be simple, cheap, efficient and power-dense, and thus can be used effectively for different applications. Keywords: Franchot engine; double acting Stirling engine; isothermalizer; heat transfer; phase angle 1. Introduction In internal combustion engines, air and fuel are mixed and burned inside the working cylinders and thus, the temperature of the mixture rises very fast. The exhausted gas is discharged to the atmosphere requiring no heat exchanger. In contrast, Stirling engines exchange the heat with the working gas through finite surfaces, which limits the heat transfer. Many techniques have been used to increase the heat transfer and are classified as follows. 1.1. Plain Cylinder In plain cylinder Stirling engines, heat is exchanged through displacer cylinder end plates [1–3]. A light displacer that has low thermal conductivity shuttles the gases between the hot and cold sides. However, the cold side has a larger surface area because the power cylinder wall is located on the cold side. The heat transfer can be enhanced by increasing the end plate areas of the displacer-containing cylinder. This will increase the size of the engine, limiting its applications to low-power applications. Enhancing the power by increasing the temperature difference is possible but requires an increase of the displacer length. Accordingly, high-temperature high-power engines have the large wall area of the displacer-containing cylinder, which is not participating in heat addition or rejection. Moreover, a long displacer increases the volume and weight of the Stirling engine. Low-temperature difference (LTD) engines reported by Kongtragool et al. [4] effectively reduce the wall area by using a short displacer with relatively large diameter. Hence the plain cylinder method is suitable for low-temperature low-power engines, which are characterised by small displacer stroke, low operating speed, simplicity and low-cost technologies and materials [5]. However, the advantages of LTD Stirling engines are balanced by lower efficiencies and power densities. The moderate temperature difference (MTD) Inventions 2017, 2, 35; doi:10.3390/inventions2040035 www.mdpi.com/journal/inventions Inventions 2017, 2, 35 2 of 13 Stirling engineInventions reported 2017, 2, 35 by [6] has low heat transfer area and a long displacer. It needs concentrated2 of 14 heating and cooling in small areas, which reduces the in-cylinder heat transfer. Figure1 shows the needs concentrated heating and cooling in small areas, which reduces the in-cylinder heat transfer. geometry differencesFigure 1 shows between the geometry a gamma differences type between LTD and a gamma MTD type with LTD plain and MTD cylinders. with plain cylinders. Inventions 2017, 2, 35 2 of 14 needs concentrated heating and cooling in small areas, which reduces the in-cylinder heat transfer. Figure 1 shows the geometry differences between a gamma type LTD and MTD with plain cylinders. Figure 1. Heat transfer area in the low-temperature difference (LTD) and moderate temperature Figure 1. Heat transfer area in the low-temperature difference (LTD) and moderate temperature difference (MTD) gamma type Stirling engine. difference (MTD) gamma type Stirling engine. Daoud and Friedrich [7] reported a novel Franchot engine design in which the heat transfer area Daoudwas and extended Friedrich to the whole [7] reported cylinder wall a novel area, which Franchot allows engine the use of design high temperatures. in which In the addition, heat transfer they increased the phase angle to allow faster speeds and hence increased the heat transfer. area was extended to the whole cylinder wall area, which allows the use of high temperatures. Unfortunately,Figure 1. Heat the transfer increase area in inthe the heat low-temperatur transfer is note difference in the same (LTD) order and as moderate the increase temperature in the speed. In addition, theydifference increased (MTD) gamma the phase type Stirling angle engine. to allow faster speeds and hence increased the heat transfer. Unfortunately,1.2. Heat the Exchanger increase in the heat transfer is not in the same order as the increase in the speed. DaoudIn general, and Friedrich the Stirling [7] machinereported with a novel bare Franchot cylinders en hasgine poor design heat in transfer which the [8–10]. heat To transfer increase area the 1.2. Heat Exchangerwasheat extended transfer, to additional the whole heatcylinder exchangers wall area, that which are allowsconnected the usein series of high to temperatures. the gas circuit In are addition, needed they[11]. increased The heat exchangersthe phase increaseangle to the allow heat transferfaster speeds area and and make hence it possible increased to operate the heat at high transfer. power In general,Unfortunately,densities. the In Stirling reality, the increase machinethey are in theresponsible with heat transfer bare for cylinders increasingis not in the hasgas same poorfriction order heat losses as transferthe and increase dead [8 –involume,10 the]. speed. To which increase the heat transfer,should additional ideally be heat zero [12]. exchangers The heat exchangers that are connected are particularly in series responsible to the for gas increasing circuit the are Stirling needed [11]. 1.2. Heat Exchanger The heat exchangersengine complexity increase and cost the [8]. heat The transfer most commonl areay and used make heat exchangers it possible with to Stirling operate engines at high are power densities. Inreported reality,In general, in [13–15]. they the Stirling are However, responsible machine additional with for bare heat increasing cylinders exchangers has gas do poor frictionnot heat lead transfer to losses an increase [8–10]. and in deadTo the increase maximum volume, the which heatpower transfer, efficiency additional [16]. heat exchangers that are connected in series to the gas circuit are needed should ideally be zero [12]. The heat exchangers are particularly responsible for increasing the [11]. TheA Stirlingheat exchangers engine with increase heat the exchangers heat transfer has areaa th ermodynamicand make it possible cycle that to operate differs at from high the power ideal Stirling enginedensities.one. As complexity Inthe reality, speed theyincreases, and are costresponsible the [ 8isothermal]. The for increasing most expansion commonly gas and friction compression used losses heat and processes dead exchangers volume, become which with more Stirling engines areshouldadiabatic reported ideally [8,13,17],in be [zero13 –which 15[12].]. The However,produces heat exchangers lower additional cycle are work particularly heat and exchangers efficiency responsible than do for notthe increasing isothermal lead to the an processes Stirling increase in the maximumengine[9,18,19]. power complexity efficiencyThe efficiency and [ 16cost is]. [8].even The worse most than commonl the idealy used adiabatic heat exchangers efficiency with due Stirlingto the non-adiabatic engines are A Stirlingreportedcylinders engine in and[13–15]. non-isothermal with However, heat exchangers additional heat exchangers heat has exchangers athat thermodynamic increase do not the lead irreversibilities to cyclean increase that [20–22]. in differs the maximum Hence from the the ideal powerthermodynamic efficiency [16]. processes are better described by polytropic processes. Figure 2 clearly shows the one. As thedifferencesA speed Stirling between increases, engine the with isothermal the heat isothermal exchangers and adiabatic has expansion a processesthermodynamic and on the compression cycle work.that differs processes from the become ideal more adiabatic [one.8,13 As,17 the], which speed produces increases, lowerthe isothermal cycle work expansion and efficiency and compression than the processes isothermal become processes more [9,18,19]. The efficiencyadiabatic is even [8,13,17], worse which than produces the ideal lower adiabatic cycle work efficiency and efficiency due tothan the the non-adiabatic isothermal processes cylinders and [9,18,19]. The efficiency is even worse than the ideal adiabatic efficiency due to the non-adiabatic non-isothermal heat exchangers that increase3 the irreversibilities [20–22]. Hence
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