A Study on an Unpressurized Medium-Temperature-Differential Stirling Engine Integrated with a New Spiral-Patterned Flat-Flame Burner and a New Spiral-Finned Hot-End Plate

,


Introduction
In the last few decades, the energy trend has gradually shifted toward renewable energy.The development in renewable energy is now growing rapidly mainly due to the urgency to address the climate change crisis caused by greenhouse gases like CO 2 and CH 4 and particulate matter produced by burning coal, petroleum, and natural gas through chemical reactions (EIA, Gawusu et al., and Zoungrana and Çakmakci [1][2][3][4]).Low-carbon energy technologies are critical for the near-and long-term global energy conservation and climate change mitigation (Dolf et al. and Yang et al. [5,6]).Additionally, due to a sudden increase in research effort aimed at combustion chemistry (such as measuring rate coefficients, laser/flash photolysis, discharge flow, macroscopic combustion, opposed jet, and low-pressure premixed flames), emission control has been enhanced, thus promoting the development of a low-emission energy conversion technology for power generation (Beér et al. [7,8]).Energy conversion technology based on combustion requires the development of combustors that are not only capable of releasing heat with low emissions but also flexible in handling various types of low-grade fuels with a wide air/fuel ratio to achieve higher fuel efficiency (Wu et al., Malik et al., and Ellzey et al. [9][10][11]).Among those techniques that satisfy the above demands, lean premixed combustion has come into the spotlight and has been commonly employed in lowtemperature combustion, which can effectively reduce NOx and CO emissions.Yet, premixed types of flames often encounter flame instability issues due to the controllability of various key operating parameters such as equivalence ratio and initial mixing rate (Sherif et al. [12], Wu et al. [13], and Yu and Wu [14]).
A well-controlled flat-flame burner can achieve high efficiency and cleaner combustion compared to traditional Bunsen burners.Adding a porous metal medium or arrays of tiny tubes on a flat burner exit surface can stabilize flame combustion to generate a radially distributed flame (Li et al. [15]).The metal medium acts as a flame stabilizer and prevents flashback into the flammable premixed chamber.Flat-flame burners can perform better than the Bunsen burners in terms of operating range, turndown ratio, and pollution mitigation.Additionally, they generate a more uniform temperature distribution at the radial location, which yields higher heat-transfer efficiency over a wider area.Wu et al. [16] conducted an experiment on a porous burner, and the results showed that fluctuations in axial temperature distribution of the flat flame were negligible.This promised an intensive rate of heat transfer from the flame to the heat loading.Conversely, in a jet flame, temperature changes are significant in the axial direction with the maximum at the tip of the flame cone (Chao and Wu [17], Yu et al. [18], and Ladislav et al. [19]).Various types of flat-flame burners have been extensively studied in flame-related research, and one of their active applications is laser calibration for combustion diagnostics (Waruna et al. [20], Migliorini et al. [21], Bosschaart and De Goey [22], and Brundage et al. [23]).Numerous studies and developments have been carried out on flame reactors with the aim of reducing pollution emissions and increasing combustion efficiency.Some review studies have focused on a burner-type evolutionary approach and flame synthesis since the 1970s (Ulrich [24], Pratsinis [25], and Wooldridge [26]).They have concluded that flat-flame burners are clean, highly efficient, and superior to Bunsen burners in terms of operating range, turndown ratio, and pollution emission.A flat-flame burner can be realized in several different methods, for example, the Mckenna burner, Hencken burner, radiant furnace, and porous medium burners.Operated under the combustion conditions of lean and near-to-stoichiometric, the McKenna burner is widely used due to its ability to produce flat premixed flames, which are thought to exist in a single dimension and are regarded as a benchmark.In many laboratories, such burners have been used for developing and calibrating various optical diagnostic techniques.The McKenna burner is typically constructed with a gravitysintered bronze plug that is enclosed in a stainless-steel sleeve and sealed by O-rings to prevent leakage.In other situations, the plug may also be made of brass.A premixed flame that is stable and radially uniform is produced at a height of approximately 1.5 mm above the surface of the burner.The Hencken flat-flame burner, normally operated in a diffusion flame mode, has been widely employed in the community of combustion researchers to calibrate both optical and physical sensors (e.g., laser diagnostics and thermocouples).The surface-mixing Hencken burner comprises a ceramic honeycomb that holds hundreds of tubes made of stainless steel.The interior diameters of these tubes are very small, ranging from 0.5 to 1.5 mm.The burner produces hundreds of multielement diffusion flamelets simulta-neously, which lead to a scalar profile that is radially flat, uniform, steady, and practically adiabatic when running under optimal flow conditions.The Hencken burner's global "lean" and "rich" flammability limitations are much wider than those of McKenna burners.The flat-flame burner's features and wide range of applications highlight its importance in flame synthesis studies, and they have great potential in the development of advanced combustion technology and energy conversion devices (Li et al. [27]).
In recent years, dimethyl ether (DME) has been recognized as a clean, nonpetroleum-based renewable fuel and has attracted considerable attention.The potential of DME as a hydrogen carrier made it an excellent alternative clean fuel that produces low CO and NOx emissions during combustion.It can be produced from various feedstocks such as natural gas, coal, or biomass, and it can be further converted into hydrogen products as future energy sources (Kanuri et al. [28][29][30]).Due to its high cetane number (between 55 and 60), DME has been investigated for being a potential substitute for diesel fuel in compression ignition engines.In several studies, an ignition stimulant mainly composed of DME was used to light a fuel with a low cetane number and achieve smokeless combustion (Shudo and Yamada [31] and Liang et al. [32]).DME is a volatile substance that can be liquidized at a pressure greater than 0.5 MPa; hence, it is often stored in a liquidous state.Even though DME only contains C-H and C-O bonds and no C-C bonds, it is safe for handling and storage because it does not produce explosive peroxides.Additionally, due to the fact that it contains around 35% oxygen, the by-products of its combustion, including carbon monoxide and unburned hydrocarbons, are significantly lower than those produced by natural gas (Tokay et al. [33]).
Currently, DME for the use as a domestic fuel is produced by synthesis gas (syngas).Regarded as an alternative renewable energy source, syngas can be produced from pyrolysis or gasification processes using biomass residues (Yang et al. [34]).It is further transformed by a two-step synthesis to produce DME, first with methanol in the presence of catalysts and then via traditional bimolecular dehydration from methanol catalyzed using various solid acids.The process also produces several useful by-products, including alumina or phosphoric acid-modified γ-Al 2 O 3 .In large-scale industrial operations, the methanol production and dehydration processes are merged in a single reactor, i.e., a single-step method.This step is called the indirect synthesis method: Furthermore, a process that combines the synthesis of methanol dehydration to produce DME has been developed, with water and DME both acting as reaction inhibitors (Barbarossa et al. [35], Palomo et al. [36], Lima et al. [37], and Said et al. [38]).In other approaches, direct synthesis methods using CO 2 and H 2 through bifunctional catalysts have also been investigated (Zhang et al. [39], Bonura et al.

2
International Journal of Energy Research [40], and Witoon et al. [41]).There are two basic methods for direct DME production from syngas, represented by equations ( 3) and ( 4), and they result in water and carbon dioxide as by-products: Between the two methods of producing DME, the direct methods offer the benefit of lowering the production cost compared to the indirect methods.Since DME and propane chemical properties are similar, it can be regarded as an environmentally friendly biobased energy carrier that is suitable for use in heating and power generation.Additionally, DME can be utilized to replace LPG in domestic and industrial applications (Wu et al. [42]).
The Stirling engine is a reciprocating engine that comprises a hot component and a cold component that are, respectively, heated and cooled continuously.They are commonly referred to as the hot end and cold end, respectively.According to their operation temperature, Stirling engines can be categorized into three types, namely, lowtemperature differential (LTD), moderate-temperature differential (MTD), and high-temperature differential (HTD) Stirling engines.The LTD Stirling engine often operates in unpressurized conditions with a small temperature difference of around 100 °C.The MTD Stirling engine works with a charge pressure between 1 and 4 bar and a higher temperature difference ranging between 200 °C and 400 °C.An engine with an operative temperature differential larger than 400 °C can be categorized as an HTD Stirling engine.The temperature differential is also indicative of the power output.Generally, HTD Stirling engines can produce more power but require high-intensity and high-temperature heat sources.In contrast, the LTD and MTD Stirling engines produce less power but greatly benefit from tapping into the abundance of inexpensive medium-or low-temperature heat sources.This makes it possible to recycle waste heat energy, thus improving the overall system efficiency of an energy conversion system.Conventional Stirling engines come in three basic configurations, namely, α, β, and γ types.The first two types of engines are normally HTD engines, while the last type of engine is often an MTD or LTD engine [43].
Stirling engines operate in a closed cycle (Ahmed et al. [44]).A confined volume of gas is expanded at the expansion chamber (near the hot end) of a Stirling engine where the engine continuously absorbs heat from the heat source; it is then recompressed in the compression chamber (near the cold end) where waste heat is rejected to the heat sink (Farret [45]).The heat necessary to run a Stirling engine is transferred to the engine externally; therefore, it can operate using a great variety of heat sources.Since the heating system is separated from the engine, it is easier to manage emissions and increase combustion efficiency.Furthermore, there is no need to incorporate a camshaft to drive valves or an ignition system, both of which consume the engine's energy output.In recent decades, Stirling engine technology has experienced a renaissance due to its many benefits in serving the purpose of energy conversion.These advantages include simple construction, low noise level, durability, and, most importantly, flexibility on the use of various heat  Stirling engines can utilize solid biomass, industrial waste heat, and even solar energy, making them promising prime movers for combined heat and power systems.Furthermore, they are simple and affordable and are good to be used as small-to medium-sized power generators driven by lowor medium-temperature heat sources (Marra et al. [46] and Chen et al. [47]).One of the important applications of the Stirling engine is to serve as the prime mover in a domestic micro-CHP system to satisfy the energy demands, including electricity, heating, and hot water, in a household.Aunon-Hidalgo et al. [48] proposed a combined solar photovoltaic and thermal and a Stirling engine micro-CHP system for domestic energy usage.The system included several solar photovoltaic panels and solar thermal collectors, a Stirling engine micro-CHP device, and a Li-ion battery with 20 kWh capacity.The results indicated that the system not only can meet all the energy consumption in a typical household but also produces surplus electricity, amounting to 31.8% of total generated electricity, to export to the electric grid.Incili et al. [49] also proposed a photovoltaic and Stirling engine-assisted micro-CHP system.The system used a coal-fired boiler as the heat source to produce hot water and power a beta-type Stirling engine for electricity generation, while additional electricity was generated by a set of solar photovoltaic panels.The system was reported to generate average electricity and heat productions of 3.126 kWh and 985.97 kWh, respectively.Jiang et al. [50] conducted a numerical optimization study to improve the performance of a micro-CHP system incorporated with a free-piston Stirling engine.A numerical model to analyze the performance of a free-piston Stirling engine was developed and used to optimize some geometrical and operational parameters of the Stirling engine.The optimized system was shown to achieve 95.7% of CHP efficiency and produce 4.03 kW of electric power.The above literature review highlights a growing interest in Stirling engine-based domestic micro-CHP systems; hence, the study to improve the performance of small Stirling engines for domestic applications is increasingly important.
The present study is aimed at investigating the performance of an alternative power generation system consisting of an innovative flat-flame burner and an unpressurized γtype MTD Stirling engine.The combustion and the operating range of the burner were evaluated using two different gaseous fuels, DME as a renewable energy fuel and propane as a traditional domestic fuel.The performance of the burner was tested by using it to power the Stirling engine in conjunction with a generator and some LED light bulbs which served as a mean to measure the electrical power generated by the system.This allows the performance of the system to be evaluated by electric power generation and thermal to electric efficiency which is the ratio of the electric power generated to the input fuel heat power.

The Present Stirling Engine. The nonpressurized, γ-type
Stirling engine in the current study is almost identical to the engine reported in Huang and Chen [51] and Wu et al. [52].The configuration of the Stirling engine is shown in Figure 1, and the dimensions of some important geometrical parameters are listed in Table 1.Most of the engine's linkage bars and plates are made of aluminum.The power cylinder is made of brass, and the crankshaft and flywheel are made of steel.A photo of the engine is given in Figure 2.
Table 1: The values of the geometrical parameters of the current Stirling engine.The movements of the displacer drive the heat-transfer events in the Stirling cycle; hence, the displacer is a vital component for a Stirling engine.The height and diameter of the displacer are 50 mm and 220 mm, respectively.As shown in Figure 3, the displacer also accommodates the regenerator, which is composed of 10 layers of thin copper screens separated by 10 layers of honey-cone aluminum sheets.The copper screen is so-called "80 scale," meaning that there are 80 copper wires within a distance of 1 inch.The upper and lower plates of the displacer have 75 holes each, allowing working gas to flow in and out of the displacer to perform heat exchange with the regenerator for storing or extracting heat.
Since the Stirling engine operates based on the temperature difference between hot and cold ends, the heat-transfer rates at both hot and cold ends and the ability to maintain the temperature difference between them are critical for the engine's performance.The bottom plate of the displacer cylinder is the hot end which was heated by the burner, and the upper plate of the displacer cylinder is the cold end which was cooled by cooling water.As shown in Figure 4, there were two types of hot-end plates investigated in this study.The external wall of one plate, termed the conventional hot-end plate, is just a flat surface (Figure 4(a)) that is commonly adopted by unpressurized Stirling engines, and the other one, termed the new hot-end plate, is equipped with 16 spiral fins for heat-transfer enhancement between the hot-end plate and the hot flue gas (Figure 4(b)).The internal walls of both plates are machined with 1963 small pin fins (Figures 4(a) and 4(b)) for enhanc-ing the heat transfer between the working gas and the inner walls of hot-end plates.These pin fins are 2 mm in diameter and 3 mm in height.Together, they increase the internal heat-transfer area by 1.956-folds.The spiral fins of the new hot-end plate are of Fermat spiral shape, and they serve three purposes.First, they form several elongated channels that prolong the time for the hot flue gas to transfer heat to the hot-end plate before it escapes from the exit holes on the edge of the plate.Second, these fins themselves increase the heat-transfer area between the hot-end plate and the flue gas.Third, they can strengthen the structure of the hot-end plate, allowing reduction in the wall thickness of the hot-end plate.In the present engine, the wall thickness of the new hot-end plate is only 2 mm.On the contrary, the wall thickness of the conventional hot-end plate is 6 mm.The thinner the hot-end plate wall is, the smaller the thermal resistance to the heat transfer through the solid hot-endplate material will be.With these advantageous features, the new hot-end plate is expected to perform better than the convention counterpart.To what extent the improvement would achieve will be discussed in the Results and Discussion.
2.2.The Flat-Flame Burner.The design of the new flat-flame burner is shown in Figure 5.Its outer diameter and the original height are 230 mm and 91 mm, respectively.There are 480 exit holes on the burner's top plate, and they are arranged based on Fermat's spiral pattern, which can be expressed as r = a ffiffi ffi θ p in a polar coordinate system.The diameter of those holes is 2.5 mm, and the thickness of the  5 International Journal of Energy Research top plate is 8.1 mm.The burner is made of aluminum.A stainless-steel wire mesh is installed under the burner exit plate to stop flashback flames from going straight into the mixing chamber and improve the spread of the fuel mixture inside the mixing chamber.The burner is supported by three adjustable screws; hence, the overall height of the burner can be adjusted to calibrate an adequate distance between the burner and the heated object.

Experimental Setup
A schematic of the setup for the present experiment is shown in Figure 6.The setup includes one Stirling engine, one flat-flame burner, a DC generator, a gear-and-chain transmission system, a DC-to-DC converter, 40 LED light bulbs for electric loading, two PT-100 temperature sensors, one tachometer, and a gas analyzer.The Stirling engine and the flat-flame burner are the main energy conversion devices that convert the heat from burning fuel to mechanical work.The mechanical work of the engine is further converted into electric energy through a transmission system and a DC generator.The gear ratio between the DC generator and the Stirling engine is 5.The Stirling engine's rotation speed varies with the magnitude of electric load, resulting in the generator producing electricity of unstable voltage.Therefore, the electricity from the generator must be further    International Journal of Energy Research processed by a DC-to-DC converter to deliver stable 5-volt electricity for the consumption of the electric loading.The DC-to-DC converter is an XLSEMI type-XL4005 with a tested conversion efficiency of between 73% and 90%, depending on the voltage of the input electricity.It has a built-in voltage meter and ampere meter, which enable the calculation of the output electric power from the converter.The electric loading consists of forty 5-volt LED light bulbs.Each light bulb consumes approximately 1 watt of electric power; hence, the system can measure electric power up to 40 watts.Every LED light bulb has its own switch so that it can be turned on or off individually to adjust to the magnitude of the total electric load, making the task of tuning the electric load magnitude to match the Stirling's power output much easier.The two PT-100 temperature sensors are for measuring the temperature difference between the hot-end plate and the cold-end plate.The cold-end plate is cooled by a water tank filled with water and ice cubes.The latent heat of those ice cubes can limit the water temperature variation at the cold end to a small range.The tachometer is an UT371 model for measuring the rotation speed of the Stirling engine.
The experiment was conducted in an air-conditioned lab with temperature set to 26 °C.The experimental procedure began with the heating of the Stirling engine by the flatflame burner.The burner produced premixed flame by burning a constant-ER mixture, and the input fuel power was set to a certain magnitude by controlling the mass flow rate of the mixture.During the experiment, the ice cubes in the cooling tank gradually melted into water.The water was constantly drained, and new ice cubes were regularly replenished to the cooling tank to maintain a low temperature at the cold end.Without electrical load, the Stirling engine started running at a temperature difference of about 70 °C.Over time, the temperature difference of the engine was gradually rising until it reached a certain stable value when there was a balance between the input fuel power and the output electric power.Then, important data, such as electric power, hot-end and cold-end temperatures, and engine rpm, were recorded for analysis.Figure 7 shows a snapshot of the experiment.
One of the most important performance parameters of this power generation system is the overall thermal-toelectric efficiency η sys , termed system efficiency for short, based on the ratio of the generated electric power to the input fuel power.Here, η sys can be evaluated by where EP is the electric power generated and IP is the input fuel power.Since the Stirling engine converted the heat from burning fuel into mechanical work, which was then converted into electrical energy, many forms of energy losses in these energy-conversion processes occurred.Those losses included incomplete combustion of the burner, heat loss due to early escape of the hot flue gas, friction that occurs between moving components of the Stirling engine, and energy losses in the generator and the DC-to-DC converter.
Consequently, the overall thermal-to-electric efficiency of the system would be much lower than the Stirling engine's thermal efficiency, which is the ratio of the engine's mechanical work to the input thermal energy.
Another important performance parameter is the emission index (EI), which is used to determine the pollutant content and the level of emissions.The sample of EI pollutant species in this experiment was measured using the MRU VARIO plus gas analyzer, which can detect several species such as O 2 , CO, CO 2 , NOx, and HC.Each chemical species of the pollutant is denoted as EI i .The EI unit is a dimensionless quantity and is expressed in g/kg, which is the ratio of the mass of the pollutant species (m i,emitted ) to the mass of the fuel burned ðm f ,burned Þ.The results of EI i are calculated using dry mole fractions as follows (Wu et al. [42]): where M i is the molecular mass of the pollutant species; x i is the measured volume fraction of the flue gas; and α and M f are, respectively, the number of moles of carbon in one mole of fuel and the mass of the fuel molecules.It is generally recognized that CO 2 , CO, and unburned hydrocarbons are the major products of combustion, and all other species can be ignored.Since CO 2 is the final product of complete oxidation of fuels containing carbon, it can be used to evaluate the combustion efficiency (CE) against a known mass of fuels.Combustion efficiency can be estimated by the ratio of the CO 2 emission index measured at the time of combustion to the CO 2 emission index measured in the stoichiometric chemical reaction of the fuel/air mixture as

Results and Discussion
In this study, two different kinds of fuel, DME and propane, for the burner were tested.DME represents renewable  Before testing the flat burner on the Stirling engine, we need to find the burner's operation range which stable flame can sustain.Since complete combustion is more likely to occur under lean combustion conditions, we only tested the burner with an equivalent ratio (ER) less than unity.

Operation Range and Flame Stability of Burning DME.
Figure 8 shows the operation of the burner without any heated apparatus, and the ER range was 0.6 to 0.8.The flame tended to blow off at ER = 0:6, suggesting that this condition is close to the minimum burning limit for the burner (Figure 8(a)).At ER = 0:7, the flame spread almost all over the burner's top plate, and the flame was stable (Figure 8(b)).This was the most stable condition among the tested equivalent ratios.At ER = 0:8, the flame was stable only for a short moment, and then, a flashback occurred that blew off the flame (Figures 8(c) and 8(d)).
Later, we tested the burner under the conditions of fixed ER = 0:7 and various premixed gas flow rates, which were represented by the values of the fuel's heating power.The heating power varied from 1357 W to 2036 W, and the flame remained stable and spread evenly on the top plate under all conditions.However, flamelets did not appear on some exit holes near the edge of the top plate, which suggested that either fuel mixture gas did not reach these holes or the mix-ture gas wasn't ignited there.Figure 8 shows the flame with a heated apparatus, which was a cylindrical heat exchanger placed some distances, varying from 10 mm to 35 mm, above the burner's top plate.It is obvious that the flame spread more evenly, and flamelets appeared on all exit holes.This implied that the flame would be more stable when the Stirling engine is placed on the burner.Since the distance between the burner top plate and the heated apparatus is significant for flame stability and it can affect the heat loss of the hot flue gas during heating of the heated component, this distance can be an important factor affecting the system's performance.To enhance heat transfer between the flue gas and the Stirling engine, the distance between the two surfaces should not be too far away.Hence, it is necessary to find a minimum distance that can still sustain stable flame.We tested different distances ranging from 10 mm to 35 mm.At a distance of 25 mm or above, the flame was stable, and it spread evenly all over every burner exit hole as shown in Figures 9(a)-9(c).From Figures 9(d)-9(f), at a heating distance of 20 mm or less, the flame was slightly stretched and became more unstable.As the heating distance was reduced to 10 mm, the flame was very unstable, and it quenched at the conditions of ER = 0:7 and 2036 W of input power.The above experiment suggests that the distance of 25 mm is an appropriate distance to sustain stable flame; hence, it was used for the experiment with the Stirling engine.

Operation Range and Flame Stability of Burning
Propane.By burning propane, the flame behaved similarly to burning DME.At a thermal power of 2055 W, stable flame could be sustained only at ER = 0:6 and 0.7 as shown in Figures 10(a

International Journal of Energy Research
In terms of the heating distance investigation, the distance range was the same as that in the test of burning DME.Figures 11(a)-11(f) illustrate the flame conditions under different heating distances.ER and input power were fixed at 0.7 and 2055 W, respectively.It is noticeable that the flame was stable at all heating distances, even at a very close distance of 10 mm (Figure 11(f)).This suggests that propane combustion is more stable than DME combustion.

4.2.
Flat-Flame Burner Temperature Profiles.One of the advantages of a flat-flame burner is to produce a uniform temperature distribution on the burner surface over a wide area.To verify such performance in the present flat-flame burner, the temperature profiles of the flame produced by the burner were measured along radial and axial directions.Figure 12 shows the flame temperature profiles of DME with input powers of 1448 W (Figure 12 Figure 13 shows temperature profiles of the flame by burning propane with thermal powers of 2055 W (Figure 13(a)) and 2377 W (Figure 13(b)).The temperature level of the propane flame is higher than that of the DME flame.The most uniform temperature profile occurred at an axial distance of 25 mm at both power inputs.At the ±50 mm radial position, the thermal powers of 2055 W and 2377 W, respectively, generated maximum temperatures of 958 °C and 1043 °C.At an axial position of more than 35 mm and beyond, the temperature distribution is similar to that of DME, and there was a decrease in temperature at a radial position of ±80 mm.The temperature profiles shown in Figures 12 and 13 verify that the present flatflame burner can generate uniform temperature distribution over a wide area by burning DME or propane.

Flat-Flame Burner Emission Content
Analysis.The flue gas from the flat-flame burner is analyzed by a gas analyzer to understand the system's performance in terms of pollutant emissions.Evaluation of the emission quantity, in the form of the emission index (EI i ), was conducted on CO, NOx, and unburned hydrocarbon (UHC) specimens in each case.The combustion efficiency is also calculated to assess the combustion efficiency of the present flat-flame burner.
Figure 14 shows the emission indices of CO, NOx, and UHC versus the input power of DME.The sample emission index at each input fuel power is estimated via equation (6).The EICO and EINOx can be determined by the amount of CO and NOx detected in the flue gas, and the emission index for UHC is determined by the amount of CH 4 .
The estimated EICO results for each input power appear erratic.The lowest EICO was generated at 1538 W of input power with a value of 0.01888 g-CO/g-fuel, while the highest EICO of 0.02073 g-CO/g-fuel occurred at 1629 W of input power.The fluctuations could be associated with the fact that not all of the fuel mixture in the mixing chamber was burned at the exit holes.The EINOx is seen to be related to EIUHC, where an increase in input power resulted in lower EINOx.This happened because the burner also released a higher UHC in the flue gas.EINOx is a chemical compound that is related to the combustion temperature.At IP = 1357 W, the ratio of EINOx to the fuel burned was 0.00063 g-NOx/g-fuel, whereas it was 0.00048 g-NOx/g-fuel at IP = 1810 W. The EIUHC calculation estimates 0.05965 g-UHC/g-fuel at IP = 1357 W and 0.12991 g-UHC/ g-fuel at IP = 1810 W. This suggests that the higher the EIUHC value, the lower the combustion efficiency (CE).The CE value at IP = 1357 W was 98.22%, while it was 97.98% at IP = 1810 W. The CO and UHC emission indices were also high, a consequence of lean premixed combustion.Meanwhile, the NOx emission index was quite low.
Propane is natural gas and is one of the main compounds of LPG fuel, which is widely used in various dailylife applications.Figure 15 shows the emission index produced by burning propane with various input powers.The correlation between EICO, EINOx, EIUHC, and combustion efficiency in each case is the same as that for DME.The lowest EICO was produced at 2237 W input power with a value of 0.00158 g-CO/g-fuel, while the highest EICO was 13 International Journal of Energy Research 0.00162 g-CO/g-fuel produced at 2055 W input power, suggesting that increasing input power would result in lower EINOx and higher EIUHC.The ratio of EINOx to fuel burned at the input power of 2055 W was 0.00019 g-NOx/ g-fuel and 0.00015 g-NOx/g-fuel at the input power of 2377 W. Meanwhile, the EIUHC generated at the input power of 2055 W and 2377 W was, respectively, 0.00278 g-UHC/g-fuel and 0.01267 g-UHC/g-fuel.The values of combustion efficiency, more than 99%, were higher in all cases than those cases of DME.The highest combustion efficiency occurred at an input power of 2237 W with a value of 99.685%.However, the emission performance of propane was significantly poorer than DME in terms of EICO, EINOx, and EIUHC.The NOx content produced by propane was generally higher than that by DME.Yet, burning propane produced a very low UHC content compared to DME, leading to the overall emission index ratio being lower than that of DME.In addition, cases with higher thermal input power of propane produced a more stable flame than those of DME.
4.4.Flat-Flame Burner Relative Thermal Efficiency. Figure 16 shows the experimental setup for estimating the percentage of the input fuel energy that was absorbed by a heated component, and such estimation is manifested by relative thermal efficiency.Here, an alumina heat exchanger, which is 30 mm in height and 210 mm in diameter, was used as the heated component, and water served as the coolant for evaluating the relative thermal efficiency.The water flowed into the heat exchanger and absorbed heat from the burner with a fixed flow rate of 1 liter/min.The distance between the burner and the heat exchanger was fixed at 25 mm.K-type thermocouples were installed to record the temperatures of the inlet and the outlet water.The performance of relative thermal efficiency η rel of the burner to the heat exchanger can be estimated by the following expression: where _ m represents the mass flow rate of water, C p is the specific heat transfer of water, _ Q fuel specifies the mass flow rate of fuel, and LHV fuel represents the low heating value of fuel.The measured data of the experiment by using DME and propane are listed, respectively, in Tables 2 and  3.The input power of DME was in the range of 2010 W to 3350 W, and the range of propane was from 1996 W to 3137 W. The results indicate that burning propane yielded higher relative thermal efficiency than burning DME.The relative thermal efficiency of DME was between 32.13% and 33.60%, whereas that of propane was between 33.67% and 39.27%.The maximum relative burning efficiency was 39.27% when burning propane with the heat input power of 3137 W. 4.5.System Performance.The performance of the system was evaluated by two quantities, electrical power generation and thermal-to-electric efficiency (or system efficiency η sys ).Test results were recorded after the engine was running stably under some specific input fuel power.

System
Performance by Burning DME.The results discussed in this subsection were obtained by burning DME.There were five different input power levels, 2010 W, 2345 W, 2680 W, 3015 W, and 3350 W. The variations of system efficiency (η sys ) produced by the conventional and the new hot-end plates versus various input powers are shown in Figure 17.Meanwhile, the variations of those two quantities versus temperature difference between hot and cold ends, termed temperature difference for short, are illustrated in Figure 18.From Figure 17, the results show that in general, both electric power and system efficiency increased  as input power increased.As expected, the new hot-end plate performed much better than conventional hotend plate.In this group of cases, the electric power produced by using the new hot-end plate increased by 18% to 36% compared to that by using the conventional hot-end plate.
The minimum and maximum electric power produced by the conventional hot-end plate was 6.8 W and 18.0 W, respectively, whereas, those produced by the new hot-end plate were 9.2 W and 22.0 W, respectively.Since the system efficiency is the ratio between electric power and input power, the behavior of this quantity is expected to be similar to that of electric power.This can be observed by comparing Figure 17(a) with Figure 17(b).In Figure 17(b), the system efficiency of employing the conventional hot-end plate varies from 0.34% to 0.54%, whereas it varies from 0.46% to 0.66% by using the new hot-end plate.From Figures 18(a) and 18(b), one noticeable phenomenon is that under the same input power, the new hot-end plate achieved a higher temperature difference than the conventional hot-end plate.For example, under an input power of 3350 W, the temperature differences achieved by the conventional and the new hot-end plates were 319 °C and 356 °C, respectively.This clearly proved the effectiveness of the new hot-end-plate design on enhancing the heat-transfer rate at the hot end.Those fins on the new hot-end plate formed curved channels to trap flue gas and prolong the flue gas's resident time at the hot end.Additionally, they increased the external heattransfer area of the hot-end plate, thus promoting the heattransfer rate between the flue gas and the hot-end plate.
Compared to the conventional hot-end plate, the increase in temperature difference by using the new hot-end plate was within the range of 8 °C to 36 °C.The plots also show that both electric power (Figure 18(a)) and system efficiency (Figure 18(b)) increased as temperature difference increased.The electric power data suggest that the magnitude of electric power was strongly dependent on temperature 15 International Journal of Energy Research difference because the data from both the conventional and new hot-end plates almost fall on the same curve.The maximum electric and system efficiency in this group of cases were 22.0 W and 0.66%, respectively, by using the new hot-end plate and under an input power of 3350 W.
The system efficiency data indicate that even with the employment of the new hot-end plate, system efficiency is still quite low.This is caused by a number of factors including energy losses of incomplete combustion in the burner, the heat loss due to the flue gas's premature escape from the engine's hot end, the mechanical friction in the Stirling engine, the inherent poor efficiency of an unpressurized Stirling engine, and the losses in the energy conversion processes of mechanical energy to electrical energy.Among them, the relative thermal efficiency measured in Section 4.4 suggested that the heat loss due to the premature escape of flue gas should be the most prominent energy loss.The flue gas temperature was still much higher than the hotend temperature when it was vented away from the hot end.This means that there was still much unused energy in it as it escaped; hence, there was only a fraction of heat from fuel combustion absorbed by the Stirling engine.The estimated η rel data in Table 2 suggest that the wasted heat was about 67% to 68% of the total heat input.The poor efficiency associated with an unpressurized Stirling engine is another primary factor responsible for poor system efficiency.In literature, the reported percentage of an unpressurized Stirling engine's thermal efficiency is generally in the single digit (Barbarossa et al. [35]).Employing a pressurized Stirling engine can drastically improve the engine's thermal efficiency.The energy conversion from mechanical work to electric energy is probably the third major factor responsible for low system efficiency.The study of Palomo et al. [36] estimated that the mechanical-to-electric efficiency in the present experimental setup is about 60%.

System
Performance by Burning Propane.In this group of cases, the fuel was propane, and there were also five input    19(a), it is found that electric power almost increased linearly with input power except the case with the new hotend plate under the highest input power level.With this high level of input power, the output electric power seemed to be less than expected as the slope of the curve slightly dropped at this point.The engine's rotational speed of this case was about 520 rpm, and we noticed that the engine vibration was more significant than in other cases.Therefore, this was probably caused by the increase in friction loss due to high rotational speed and a higher level of vibration.The results in Figure 19 clearly indicate that again, the performance of the new hot-end plate was much better than that of the conventional hot-end plate.The minimum and maximum electric power of using the new hot-end plate was 11.8 W and 24.6 W, respectively, whereas those of using the conventional hot-end plate were 7.2 W and 16.8 W, respectively.Overall, the electric power produced by using the new hot-end plate increased by 46% to 63% compared to that produced by using the conventional hot-end plate.Furthermore, compared with the results of burning DME, the margin of increase in electric power by using propane is more significant than that by using DME.
From Figure 19(b), the system efficiency shares a similar linear tendency to electric power.However, there is a slight drop in system efficiency when using the new hot-end plate under the highest input power level.This is associated with the reduction in electric power discussed above.The minimum and maximum system efficiencies of using the new hot-end plate are 0.59% and 0.81%, respectively, whereas those of using the conventional hot-end plate are 0.36% and 0.55%, respectively.This further confirms the augmentation in the margin of performance improvement by the change from using the conventional hotend plate to using the new hot-end plate when burning propane.
The data in Figures 20(a) and 20(b) show that again, using the new hot-end plate achieved a higher temperature difference than using the conventional hot-end plate.Compared to the results of using the conventional hot-end plate, the increase in temperature difference by using the new hotend plate was between 24 °C and 60 °C in this group of cases.The maximum temperature differences achieved by using the conventional and new hot-end plates were 344 °C and 404 °C, respectively.It is noticeable from Figure 20(a) that the electric power is almost linearly proportional to the temperature difference.Therefore, it can be readily realized that the prominent improvement of using the new hot-end plate over using the conventional hot-end plate was closely associated with the former's ability to increase the hot-end temperature, thus giving rise to a much higher temperature difference to promote electric power and efficiency.From Figure 20(b), system efficiency is observed to behave similarly to electric power.The results in this group of cases further demonstrated the effectiveness of the new hot-end-plate design over the conventional hot-end-plate design.
The Beale number and the West number are dimensionless parameters commonly used for assessing the perfor-mance of a Stirling engine.The Beale number is used to estimate the power output of a Stirling engine.The West number serves a similar purpose to the Beale number, but it further takes temperature difference between the engine's hot and cold ends into account; hence, it also reflects the level of thermal efficiency.The higher these two numbers are, the better the performance of the engine.They are defined as where p is the cycle average pressure, V is the swept volume of the engine, f is the engine's rotation rate in frequency, and _ W is the mechanical output power.Based on the maximum electric power in this group of cases and the reported mechanical-to-electric conversion efficiency of 60% (Palomo et al. [36]), its Beale number is about 0.92 and its West number is about 0.22.These numbers indicate good performance in terms of the unpressurized Stirling engine standard.
Finally, there is another clear piece of evidence for supporting the superior performance of the present system by burning propane to DME.The power generated by using the new hot-end plate and with a propane input power of 3137 W was even higher than the case with the DME input power of 3350 W. In this case, it was 24.6 W versus 22.0 W. In terms of the system efficiency, it was 0.78% versus 0.66%.However, from the environmental point of view, DME is a kind of renewable energy source and could serve the purpose of mitigating climate-change problems.Propane, on the other hand, is a fossil fuel and is harmful to the environment.

Conclusions
This study investigated a power generator based on an MTD γ-type Stirling engine combined with a new flat-flame burner with a new spiral-finned hot-end plate.System performance was measured in terms of electric power output and thermal-to-electric efficiency and compared against a conventional flat hot-end plate.Two types of fuel were employed, fossil (propane) and renewable (DME).It can be concluded that (1) Flame remains stable for an equivalent ratio of approximately 0.7, and flashback occurs at the equivalent ratio of 0.8.With respect to DME, propane combustion can be sustained for a smaller distance between the burner and the heated apparatus (2) The new flat-flame burner enhanced temperature uniformity in both radial and vertical directions.Such uniform temperature distribution gives rise to an evenly heated hot end that is beneficial for the operation of the Stirling engine (3) There exists a close correlation among the characteristics of EICO, EINOx, and EIUHC by burning DME International Journal of Energy Research and propane.Overall, DME emission indices are slightly higher than those of propane due to flame instability, incomplete combustion, and heat (4) The measurement on the burner conversion ratio, represented by combustion efficiency (CE), indicates that propane allows for a higher combustion efficiency with respect to DME, thus resulting in a higher specific thermal energy (5) Since the combustion efficiencies of both fuels are higher than 98%, both produce very few emissions.
From an environmental protection's point of view, the benefit of DME being a renewable fuel outweighs propane's benefit of slightly better combustion performance than DME (6) The new hot-end plate results in far superior performance with respect to the conventional hot-end plate.When heated by burning DME, the former produced, respectively, maximum electric power and efficiency of 22 W and 0.66%, and it produced, respectively, maximum electric power and efficiency of 24.6 W and 0.81% when heated by propane.On the contrary, the latter only generated maximum electric power and efficiency of 18.0 W and 0.54%, respectively, when heated by DME, and these quantities were 16.8 W and 0.55% when heated by propane.The new hot-end plate yielded a maximum system efficiency of 0.81% burning propane (and 0.66% burning DME).Among those cases in this study, the increase in system efficiency is 15% to 47% higher with respect to using the conventional hot-end plate.The results have proven the improvement of the new hot-end-plate design over the conventional hot-end-plate design.The high-level electric power generation also proved the effectiveness of the integration of the new hot-end plate and the new flat-flame burner on boosting the power output of an unpressurized Stirling engine (7) The enhancement in performance by using the new hot-end plate is similar for both propane (fossil fuel) and DME (renewable fuel); thus, this new design could serve the purpose of mitigating the global warming problem when using DME

Figure 1 :
Figure 1: Configuration and geometric parameters of the current Stirling engine.

3
International Journal of Energy Research sources, so it can be operated almost anywhere and anytime.

Figure 2 :
Figure 2: A photo of the current Stirling engine.

Figure 4 :
Figure 4: Typical sample of (a) conventional hot-end plate and (b) new hot-end plate.

Figure 5 :
Figure 5: The schematic and design plan of the new innovative flat-flame burner.

Figure 6 :
Figure 6: A schematic of the experimental setup.

Figure 7 :
Figure 7: A snapshot of the experiment.

Figure 16 :
Figure 16: Experimental setup of relative thermal efficiency.

Figure 17 :Figure 18 :
Figure 17: The variations of electric power and thermal-to-electric efficiency versus input power using DME.

Figure 19 :
Figure 19: The variations of electric power and efficiency versus input power using propane.

Figure 20 :
Figure 20: The variations of electric power and efficiency versus temperature difference using propane.

Nomenclaturea: 1 : 1 : 2 : 1 :
A scaling parameter in Fermat's spirals f : Rotation frequency of Stirling engine (s -1 ) L p : Length of power piston (m) l Length of the power piston linkage bar (m) l 2 : Length of the power piston connection rod (m) l 3 : Length of the displacer linkage bar (m) l 4 : Length of the displacer connection rod (m) l d : Length of displacer (m) m i : Mass of species i emitted (g) m f : Mass of fuel burned (g) M i : Molecular mass of species i (g/mol) M f : Molecular mass of fuel (g/mol) p: Average pressure of Stirling engine (Pa) Q: Heat-transfer rate (W) R Outer radius of the power piston (m) R Inner radius of the displacer cylinder (m) R d : Outer radius of the displacer (m) r: Radius r Crank radius of the power piston (m) r 2 : Crank radius of the displacer (m) T H : Hot-end temperature of Stirling engine ( °C) T L : Cold-end temperature of Stirling engine ( °C) V: Swept volume of Stirling engine's power piston (m 3 ) _ W: Shaft power of Stirling engine (W) x i : Volume fraction of species i in flue gas (-).Greek α: The number of moles of carbon in 1 mole of fuel (-) η rel : Relative thermal efficiency of the flat-flame burner (-) η sys : Thermal-to-electric efficiency of the system (-) ΔT: Temperature difference between Stirling engine's hot and cold end ( °C) θ: Radians (-).

Table 2 :
Relative thermal efficiency of dimethyl ether at ER 0.7.

Table 3 :
Relative thermal efficiency of propane at ER 0.7.