energies

Article A Micro Swing Rotor Engine and the Preliminary Study of Its Thermodynamic Characteristics

Chen Xia, Zhiguang Zhang * , Guoping Huang, Tong Zhou and Jianhua Xu College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; [email protected] (C.X.); [email protected] (G.H.); [email protected] (T.Z.); [email protected] (J.X.) * Correspondence: [email protected]



Received: 3 September 2018; Accepted: 29 September 2018; Published: 9 October 2018


Abstract: The rapid progress in microelectromechanical system technology has facilitated great developments in micro heat engines, however, defects in these engines still need to be overcome. Thus, a novel four-stroke micro swing rotor engine (MSRE) that features the advantages of Wankel engine and the micro swing engine is proposed in this study. Kinematic and thermodynamic analyses of the MSRE were performed, and a preliminary experimental research was conducted. In the MSRE, the driver assembly was used to dominate the movements of the two rotors. By the design guideline adaptable to the engine operation principle, the volume of each chamber will vary in a sine-like waveform, which was validated by kinematic analyses. Then, a prototype in mesoscale was designed and fabricated. In consideration of the leakage effect, the thermodynamic characteristics of this engine were numerically investigated. Results indicate that the engine thermodynamic processes were seriously affected by leakage flow, especially when working at low frequencies. Gap height and operation frequency were the two dominant factors that affected engine performance. Under a certain gap height, the MSRE had to work at a specific frequency range and the corresponding optical values exist for engine efficiency and power. With a 20 µm height, the MSRE reached the maximum efficiency of 23.62% at 55 Hz and the maximum power of 3442 W at 95 Hz. Feasibility of the engine was further verified by an experimental test on the operation characteristics, including the cold state test with pressured air blow and the combustion test for engine operation at thermal state. This research lays a good foundation for future development of MSRE, which is of great practical significance for the progress in micro power systems.

Keywords: swing rotor engine; driving assembly with velocity difference; motion simulation; thermodynamic characteristics; leakage effect; experimental verification

1. Introduction Currently, microelectromechanical systems (MEMS) are widely applied to fabricate devices in micro and mesoscales, such as sensors, actuators, micro-airplanes, micro aerial vehicle (MAV), and micro-robots. However, battery systems are the main power sources for these applications. Unfortunately, even the most advanced lithium-ion batteries only have an energy density of approximately 1.2 kJ/g [1]. This value is so poor that increasing fractions of the mass and volume of the entire MEMS-based devices are being occupied by batteries, which have a short durable time and a limited number of rechargeable cycles. The lack of compact, efficient, instantly rechargeable power supply devices with high-specific energy (light weight, long duration) and power greatly limits the development of micro-systems for various applications [2,3]. As sustainable resources, the condensed HC fuels contain much higher energy density (typically 45 MJ/kg), and the internal combustion micro engine systems for power generation are far superior to battery-motor electrical systems in the 1–100 W

Energies 2018, 11, 2684; doi:10.3390/en11102684 www.mdpi.com/journal/energies Energies 2018, 11, 2684 2 of 25 range, even with thermal efficiencies as low as 4% [4–6]. Therefore, combustion-based micro heat engines have become the most promising alternative as commercial power supply for micro devices to conventional battery systems. Micro engines have attracted increasing attention nowadays because of their potential applications in power generation. During the last decades, great efforts have been exerted to promote the development in this field and different types of miniaturized engines have been manufactured, including micro gas turbine, micro free-piston engine, micro rotary (Wankel) engine, micro swing engine, etc. A series of theoretical and experimental works on this topic are available in the literature. The MIT Gas Turbine Laboratory has developed several advanced MEMS-based micro gas turbines for power generation and discussed relevant issues [7,8]. Composed of silicon-carbide material, the first concept heat engine was designed to produce 10–20 W power; the working volume was about 300 mm3 [7]. Since then, advanced air bearing has been improved, allowing turbines to work at a high rotation velocity. In cooperation with the IHI Corporation, a research group at Tohoku University designed a rotor working at 770,000 rpm in a micro high-speed bearing test rig [9]. Later, a 100 W class micro-scale gas turbine with a centrifugal impeller of 10 mm diameter and a rotor that rotates at 870,000 rpm was experimentally investigated [10]. When the turbine inlet temperature was 1050 ◦C, the compressor was kept below 170 ◦C. Subsequently, they demonstrated the world’s smallest class gas turbine engine that established the Brayton cycle [11], indicating its promising applications for mobile robots, personal vehicles, etc. With further progress in gas bearings [12], a MEMS-based turbocharger was designed, fabricated, and tested [13], to produce a micro-fabricated gas turbine engine for portable power applications. This turbine produced approximately 5 W of power. A liquid-fueled micro engine that burns JP8 fuel is proved to be an attractive portable power source [14], because the designed micro-combustor can increase thermal efficiency. Nowadays, the research on micro gas turbine is focused on the components. Miniaturization of the rotary Wankel engine was first conducted by a combustion laboratory at UC Berkeley. Several liquid hydrocarbon fueled rotary engines in different sizes were designed [15]. The output of a mesoscale rotary engine was about 30 W with a 12.9 mm-diameter rotor [16]. In the first stage work of a research project launched by the University of Birmingham, an advanced UC-lithography process was developed, and a CO2 micro Wankel engine was successfully fabricated [17]. Sprague et al. [18] developed and characterized four small-scale rotary engines for portable applications in the output range of 10–200 W. The highest performing engine produced 33 W of power with an efficiency of 3.9%; the combustion chamber had a volume of 1.5 cm3. Zhejiang University in China designed and fabricated a series of small-scale rotary engines by using electro discharge machining [19]. Their M2.4 rotary engine, with a swept displacement of 2600 mm3, showed a steady 150 W net power output at 15,000 rpm. They pointed out that micro combustion and seal are two of the most prominent questions for small-scale rotary engines. Considering that the scaling down of rotary Wankel engines is limited by various factors, Wang et al. [20] developed a phenomenological model to investigate the effects of engine speed, compression ratio, blow-by, and heat transfer, and thus, provided guidelines for the preliminary design of rotary engines. In fact, various rotary engines have been designed, and the Wankel engine is just one type of them. The Yo-Mobile Engine developed in Russia has been reportedly applied in hybrid cars. Pan et al. [21–23] have designed several twin-rotor piston engines. However, the mechanism was modified to be more and more complicated, rendering it unfit for miniaturization. To avoid the serious sealing problem in rotary engines, the Honeywell center first developed a mesoscale free-piston knock engine using homogeneous charge compression ignition (HCCI) of hydrocarbon fuels [24,25]. A series of single shot combustion experiments on the rapid compression expansion machine were carried out to investigate the free piston motion at Minnesota University [26,27]. Experiments showed that HCCI combustion could be successful even in spaces with 3 mm diameter and 0.3 mm length. Although the HCCI inter-combustion engines have developed rapidly, the smaller version design has many restrictions. Therefore, I. Sher et al. [2,28] proposed Energies 2018, 11, 2684 3 of 25 a phenomenological model to consider the relevant processes in the HCCI engine. The influences of friction losses and charge leakage on engine performance were studied and inter-relationships between them were postulated. An approximated analytical solution was proposed to yield the lower possible limits of scaling-down HCCI cycle engines. Jin Bai et al. [29] have studied the methane HCCI in a micro free-piston engine. A formula for the critical initial kinetic energy, especially affected by leakage, was proposed to guide the design of micro free-piston power devices. The simulation results from their team [30] revealed that catalytic combustion facilitates energy conversion efficiency and extends the ignition limit of methane-air mixture obviously, which can be attributed to the existence of a catalytic wall. At the University of Michigan, Mijit et al. [31,32] proposed the micro internal combustion swing engine (MICSE), a rotationally oscillating free-piston engine. In this engine, a center swing that moves back and forth divides the base cavity into four chambers. Thus, a four-stroke MICSE that could produce 20 W of electrical power was designed. A numerical investigation was conducted by Gu et al. [33] to examine premixed the flame propagation in a generic mesoscale combustion chamber for various injection and ignition configurations. Results indicated that the mean flow and turbulence must be matched to the combustion chamber geometry to minimize the overall combustion time. Based on the main working principle of the MICSE, Zhang et al. [34,35] developed a novel two-stroke cycle micro free-piston swing engine, with a simplified structure and control system. The feasibility was validated by the successful realization and operation of the theoretical prototype; some performance analyses were executed numerically. A constant-speed model for the four-stroke MICSE has been developed to control the engine accurately [36]. However, irreversible losses in the MICSE are still serious, especially the leakage effect. Zhou et al. [37] investigated the leakage mechanism in detail and found that the performance reduction for the mesoscale swing engine was small for gap heights within 6 µm but was large for gap heights over 10 µm. Since a large amount of energy is wasted through hot exhaust, the recuperation technology suitable for MICSE is indispensable to elevate the engine efficiency. Therefore, Xia et al. [38] have proposed a hybrid thermodynamic cycle with heat recovery process, which was validated by numerical simulation. At present, three phenomenological models have been developed to describe the engine working process; that is, the zero, quasi, and multi-dimensional combustion model. Compared to the other two models, the zero-dimensional combustion model is able to largely reduce the time and calculation cost, and meanwhile, offer creditable results [31]. Because the spatial distribution of physical parameters is not considered in this model, only several simple boundary and initial conditions are required. Consequently, it has been widely adopted to obtain the thermodynamic characteristics of micro engines. Given close analysis on the aforementioned literature, the high working temperature and rotation speeds have seriously constrained the application of micro gas turbines. Sealing and friction problems must be overcome to promote the application of micro rotary engines. The micro free-piston engine must operate at kilohertz frequencies under short ignition delay times to achieve reliable auto-ignition of the fuel. Although the free swing-arm in the MICSE moves simply, in a rotating motion with less vibration, the engine cannot run stably in constant compress ratio because of irreversible losses. Referring to the control method of constant compress ratio in a reciprocating piston engine, this study proposed a novel micro swing rotor engine (MSRE), which features the advantage for Wankel engine, i.e., great ratio of power to volume, and that for MICSE, i.e., good cavity structure without valves favorable to scaling down. The operation principle and structural components of this creative power device are thoroughly elaborated. Motion analysis is conducted through the MATLAB program along with the motion module of UG to validate the design method for a mesoscale prototype. In the following research, a thermodynamic investigation of the engine that works in steady state was performed. Thermal performance curves are discussed for the MSRE under different compress ratios. The leakage effect and rotating frequency considerably influence the overall thermal characteristics, and the mechanisms were observed. Hence, the results of this study are used as a basis for the performance estimation and the guideline of engine design. Lastly, an experimental platform for the Energies 2018, 11, 2684 4 of 25

Energies 2018, 11, x FOR PEER REVIEW 4 of 26 MSRE was designed and established. Preliminary test of the engine performance was implemented to verifylay a good the feasibility theory and of experimental this micro heat foundation engine. This for researchfurther development will lay a good of theoryMSRE, and which experimental is of great foundationpractical significance for further for development the progress of in MSRE, micro whichenergy is power of great systems. practical significance for the progress in micro energy power systems. 2. Operation Principle and Mechanical Design of the Micro Swing Rotor Engine 2. Operation Principle and Mechanical Design of the Micro Swing Rotor Engine 2.1. Working Principle for this Novel Engine 2.1. Working Principle for this Novel Engine The MSRE is a dual rotor piston engine. As shown in Figure 1, this engine is composed of a cylinderThe assembly MSRE is aand dual a driver rotor piston assembly. engine. In the As cylinder shown inbase, Figure two1, rotors, this engine which is are composed individually of a cylinderfixed on assemblythe two swing and alinks driver in assembly.the driver Inassembly the cylinder and powered base, two by rotors, the fuel which charged are individuallythrough the fixedinlet, onrotate the in two the swing same linksdirection. in the For driver the driver assembly components, and powered the principal by the fuel function charged is throughto constrain the inlet,the rotor rotate motion, in the samewhose direction. spindle Foris the the main driver output components, link of the principalengine. Since function each is rotor to constrain holds two the rotoropposite motion, blades whose (arms), spindle the base is the structure main output is divided link of into the engine.four independent Since each rotorclosed holds chambers two opposite by two bladesrotors, (arms),which are the coaxially base structure installed is divided in the MSRE. into four Rotations independent of the closedtwo rotors chambers are controlled by two rotors, by a whichspecially are designed coaxially external installed driving in the MSRE. mechanism, Rotations so ofthat the the two two rotors rotors are can controlled move in by differential a specially designedvelocities externalat any time driving for one mechanism, period once so that the theoutp twout spindle rotors can rotates move at in one differential certain speed. velocities Therefore, at any timethe volume for one periodof each once chamber the output varies spindle accordingly. rotates at Similar one certain to the speed. thermodynamic Therefore, the volumeprocess ofin each the chamberconventional varies four-stroke accordingly. internal Similar combustion to the thermodynamic (IC) engine, the process four inchambers the conventional work in four four-stroke strokes internalbut are in combustion a distinct (IC)four-stroke engine, process the four at chambers any time work. Vice in versa, four strokes once the but fuel are is in combusted a distinct four-stroke and then processexpands, at the any two time. rotors Vice versa,are driven once theto fueloutput is combusted power and and the then MSRE expands, will work the two continuously. rotors are driven The tointernal output energy power is and thus the converted MSRE will into work mechanical continuously. energy Thesuccessfully. internal energyTake one is thuschamber converted (Chamber into mechanicalA) for instance: energy the successfully.operation process Take one of MSRE chamber is de (Chambermonstrated A) in for Figure instance: 2 for the one operation rotation process period of MSREthe spindle. is demonstrated in Figure2 for one rotation period of the spindle.

Figure 1. Composition of the overall structure for the micro swing rotor engine (MSRE).

Energies 2018, 11, 2684 5 of 25 Energies 2018, 11, x FOR PEER REVIEW 5 of 26

Figure 2. OperationOperation process of the micro swing rotor engine.

2.2. Design of the Driving Mechanism and Kinematic Analysis The driving mechanismmechanism (i.e., (i.e., the the driver driver assembly) assembly) of of the the MSRE MSRE was was composed composed of a of planetary a planetary gear gearmechanism mechanism and twoand crank-rockertwo crank-rocker mechanisms, mechanisms, which which were coaxiallywere coaxially linked linked by two by groups two groups of planet of planetgear and gear crank and and crank share and the share same bracketsthe same (Figure brackets3). That(Figure is, the 3). planetThat is, carrier the ofplanet the planetarycarrier of gear the planetarymechanism gear was mechanism the support was bar the of the support crank-rocker bar of the mechanisms crank-rocker at the mechanisms same time. Moreat the importantly,same time. Moreit functioned importantly, as the outputit functioned spindle as for the the output driver assemblyspindle for and the even driver for theassembly engine. and The even two four-barfor the engine.linkages The were two installed four-bar on linkages the same were frame installed in the opposite on the same direction frame with in the a phase opposite divergence direction of πwith, and a phaseeach rocker divergence was fixedly of π, and connected each rocker to one was rotor. fixedly Thus, connected once the bracket to one rotatesrotor. Thus, at a certain once the speed, bracket one rotatespursue motionat a certain between speed, the one two pursue rotors ismotion realized. between Given the that two the sunrotors gear is wasrealized. fixed Given on the that engine the body sun gearframe was stationary, fixed on a one-degree-of-freedomthe engine body frame driving stationary, mechanism a one-degree-of-freedom was established. In cooperationdriving mechanism with the wasplanetary established. gear train, In cooperation the rotors were with constrained the planetary to rotate gear train, at a speed the rotors that fluctuates were constrained periodically, to rotate thereby at aresulting speed that in thefluctuates relative periodically, motion that thereby made the resultin includedg in anglethe relative between motion two armsthat made (chamber the included volume) anglevary periodically. between two The arms specially (chamber designed volume) driving vary mechanism periodically. was determined The specially by the designed bar lengths driving of the mechanismfour-bar linkages was determined and the transmission by the bar ratiolengths of planetaryof the four-bar gear train,linkages which and were the transmission calculated through ratio of a planetaryseries of reasonable gear train, approaches, which were includingcalculated the through closed a vectorseries methodof reasonable and the approaches, center of speed including method. the EnergiesclosedLastly, 2018 vector the, operation11, xmethod FOR PEER principle and REVIEW the ofcenter MSRE of wasspeed satisfied. method. Lastly, the operation principle of MSRE6 of was 26 satisfied. In view of the structure design of the complete engine, the requirements of the compression ratio ε and the arm thickness-angle β in the cylinder assembly had to be met. The relationship among the two factors and the bar-lengths are expressed as

22+−+()2 22+−()2 πβ() − ε − −−l ll14 ll 23 1 ll14 l 2 180 2 1 cos−= cos  (1) 223601ll ll ε + 14 14 Fn where l , l , l , and l represent the length of planet carrier, crank, connecting rod, and rocker, 1 2 3 4 F F respectively. t

1.1. sunsun gear; gear; 2,3. 2,3. planet planet gear; gear; 4,9. 4,9. crank; crank; 5,8. connecting5,8. connecting rod; 6,7. rod; rocker; 6,7. rocker; 10. planet 10. carrier. planet carrier.

FigureFigure 3. 3. SchematicSchematic of of the the driving driving mechanism. mechanism.

According to the design guideline of the aforementioned driving mechanism, Table 1 shows one group structure parameters of this engine, in which the compression ratio of MSRE is 6. Since this study is just in the first stage of our research, the principle prototype was designed in mesoscale for convenience.

Table 1. Design parameters of the micro swing rotor engine in mesoscale.

Parameters Value Compression ratio 6 Minimum transmission angle for crank-rocker mechanism/° 60 Arm thickness-angle/° 10

Relative lengths of four-bar linkage llll1234::: 3:0.5973:2.7402:1.2503 Arm-diameter/mm 60 Hinge-diameter/mm 30 Arm-height/mm 15

In accordance with the parameters in Table 1, a 3D modeling of the engine was established in UG software and the motion analysis has been investigated. Results from the MATLAB program agreed with the motion simulation of three-dimensional modeling conducted through UG. When the spindle rotated at a frequency of 100 Hz, the angular velocity curve of each rotor and the volume angle of one chamber could be obtained, as shown in Figures 4 and 5, respectively, for one quarter period. Figure 4 shows that the rotor velocity was always greater than zero. Unlike the conventional IC engines, no reciprocating piston motion existed in the MSRE, resulting in a lower impact load. In Figure 5, the included angle between two neighboring arms varied in a sine-like waveform from the minimum value of 22.85° to the maximum angle of 137.1°, which was consistent with the designed compression ratio and met the design requirements well.

Energies 2018, 11, 2684 6 of 25

In view of the structure design of the complete engine, the requirements of the compression ratio ε and the arm thickness-angle β in the cylinder assembly had to be met. The relationship among the two factors and the bar-lengths are expressed as ! ! l 2 + l 2 − (l + l )2 l 2 + l 2 − (l )2 π(180 − 2β) ε − 1 cos−l 1 4 2 3 − cos−1 1 4 2 = (1) 2l1l4 2l1l4 360 ε + 1 where l1, l2, l3, and l4 represent the length of planet carrier, crank, connecting rod, and rocker, respectively. According to the design guideline of the aforementioned driving mechanism, Table1 shows one group structure parameters of this engine, in which the compression ratio of MSRE is 6. Since this study is just in the first stage of our research, the principle prototype was designed in mesoscale for convenience.

Table 1. Design parameters of the micro swing rotor engine in mesoscale.

Parameters Value Compression ratio 6 Minimum transmission angle for crank-rocker 60 mechanism/◦ Arm thickness-angle/◦ 10 Relative lengths of four-bar linkage l1 : l2 : l3 : l4 3:0.5973:2.7402:1.2503 Arm-diameter/mm 60 Hinge-diameter/mm 30 Arm-height/mm 15

In accordance with the parameters in Table1, a 3D modeling of the engine was established in UG software and the motion analysis has been investigated. Results from the MATLAB program agreed with the motion simulation of three-dimensional modeling conducted through UG. When the spindle rotated at a frequency of 100 Hz, the angular velocity curve of each rotor and the volume angle of one chamber could be obtained, as shown in Figures4 and5, respectively, for one quarter period. Figure4 shows that the rotor velocity was always greater than zero. Unlike the conventional IC engines, no reciprocating piston motion existed in the MSRE, resulting in a lower impact load. In Figure5, the included angle between two neighboring arms varied in a sine-like waveform from the minimum value of 22.85◦ to the maximum angle of 137.1◦, which was consistent with the designed compressionEnergies 2018, 11 ratio, x FOR and PEER met REVIEW the design requirements well. 7 of 26

Time (Second)

Figure 4.4. Angular velocity of the two rotors.

Figure 5. Included angle between two arms.

3. Thermodynamic Characteristics of the Micro Swing Rotor Engine

3.1. Thermodynamic Model for the MSRE in Steady Operation State and the Solution Method Without regard for the details of the physical-chemical process in combustion and the inhomogeneous distribution of the working medium in space field [39,40], the single-dimensional combustion model was adopted to research the thermodynamic characteristics of the MSRE. Based on the fundamental thermodynamic processes in each chamber, differential equations are given to present the working processes for each stroke, and the time-variation process of each thermodynamic parameter is numerically solved.

3.1.1. Establishment of the Thermodynamic Model When the engine operated stably, the four chambers were in four distinct stroke processes in order at any moment. In combination with conservation equations, the gas equation of state, and the Wiebe function for heat release in combustion, the uniform single-dimensional thermodynamic governing model for each chamber at any stroke was established [31], in which the chamber was treated as an open thermal system. Accordingly, the temperature derivative T , the pressure derivative p , and the mass derivative m for the control volume are expressed as:

Energies 2018, 11, x FOR PEER REVIEW 7 of 26

Time (Second)

Energies 2018, 11, 2684 7 of 25 Figure 4. Angular velocity of the two rotors.

Figure 5. Included angle between two arms.

3. Thermodynamic Characteristics of the Micro Swing Rotor Engine

3.1. Thermodynamic Model for the MSRE in SteadySteady Operation State and the Solution MethodMethod Without regard for thethe detailsdetails ofof thethe physical-chemicalphysical-chemical process in combustioncombustion and the inhomogeneous distribution of the working medium in space fieldfield [[39,40],39,40], thethe single-dimensionalsingle-dimensional combustion model was adopted to research thethe thermodynamicthermodynamic characteristics of the MSRE. Based on the fundamental thermodynamic processes in each chamber, differential equations are given to present thethe working working processes processes for each for stroke,each andstroke the, time-variationand the time-variation process of each process thermodynamic of each parameterthermodynamic is numerically parameter solved. is numerically solved. 3.1.1. Establishment of the Thermodynamic Model 3.1.1. Establishment of the Thermodynamic Model When the engine operated stably, the four chambers were in four distinct stroke processes in order When the engine operated stably, the four chambers were in four distinct stroke processes in at any moment. In combination with conservation equations, the gas equation of state, and the Wiebe order at any moment. In combination with conservation equations, the gas equation of state, and the function for heat release in combustion, the uniform single-dimensional thermodynamic governing Wiebe function for heat release in combustion, the uniform single-dimensional thermodynamic model for each chamber at any stroke was established [31], in which the chamber was treated as an governing model for each chamber at any stroke was established. [31], in which the chamber. was open thermal system. Accordingly, the temperature derivative T, the pressure derivative p, and the treated as an open. thermal system. Accordingly, the temperature derivative T , the pressure mass derivative m for the control volume are expressed as: derivative p , and the mass derivative m for the control volume are expressed as: " . . # " # .   . RT . Rb − Ru hu − hb m V 1 . T = xb + + − + ∑ mi(hi − h) − Qw (2) Cv R RT m V mCv i

" . . . # .  R − R  T m V p = p x b u + + − (3) b R T m V . . . . m = min − mex + ml (4) . where Cv is the specific heat under constant volume; Qw is the heat transfer losses that cross system boundary; xb is the mass fraction burned, which is determined by the Wiebe function; subscripts u and b represent the fresh charge and the residual gas, respectively, and xb + xu = 1; h is the specific . . enthalpy of the mixture gas; min, mex are the instantaneous mass changes in the controlled volume caused by the mixture through the inlet and outlet, respectively, which can be calculated by the quasi . one dimensional isentropic flow equations [31]; and ml denotes the mass change caused by flow leakage from the neighboring chambers. For the MSRE working in steady state, the spindle speed was a certain number, and the volume of each chamber changed periodically with time in a sine-like waveform. Given the main structural Energies 2018, 11, x FOR PEER REVIEW 8 of 26

RR−− hh ˙ =++−+−−RTbbuu m V 1 () Tx b  mhhQii w (2) CRRTmVmCvvi RR− =++−buTmV ppx b  (3) R TmV =+− mmin m  ex m  l (4)

where Cv is the specific heat under constant volume; Qw is the heat transfer losses that cross

system boundary; xb is the mass fraction burned, which is determined by the Wiebe function; += subscripts u and b represent the fresh charge and the residual gas, respectively, and xxbu1;

h is the specific enthalpy of the mixture gas; m in , m ex are the instantaneous mass changes in the controlled volume caused by the mixture through the inlet and outlet, respectively, which can be

calculated by the quasi one dimensional isentropic flow equations [31]; and ml denotes the mass Energieschange2018 caused, 11, 2684 by flow leakage from the neighboring chambers. 8 of 25 For the MSRE working in steady state, the spindle speed was a certain number, and the volume of each chamber changed periodically with time in a sine-like waveform. Given the main structural parametersparameters forfor MSREMSRE inin Table1 1,, with with an an operation operation frequency frequency of of 100 100 Hz, Hz, the the volume volume of of eacheach chamberchamber (working(working volumevolume forfor thethe medium)medium) versusversus time over oneone spindle circle is given in Figure 66.. Moreover,Moreover, thethe timetime raterate ofof changechange forfor thethe chamberchamber volumevolume isis obtainedobtained atat anyany instantinstant ofof timetime fromfrom FigureFigure6 .6.

Figure 6. Time-varying process for each chamber volumevolume atat aa workingworking frequencyfrequency ofof 100100 Hz.Hz.

AA certaincertain gap gap should should be be maintained maintained between between the rotorsthe rotors and the and wall the surfaces wall surfaces inside the inside chamber the especiallychamber especially for engines for in microengines and in mesoscales, micro and so mesosc that theales, rotors so canthat rotate the rotors with less can friction. rotate However,with less forfriction. MSRE, However, because thefor working MSRE, fluidbecause in each the chamberworking isfluid influenced in each by chamber the neighboring is influenced two chambers by the throughneighboring leakage two flow, chambers the engine through performance leakage isflow, weakened the engine by the performance leakage effect is more weakened seriously. by Forthe eachleakage rotor effect arm ofmore the MSRE,seriously. the leakageFor each flows rotor exist arm in of three the interfacesMSRE, the between leakage the flows rotor andexist the in statorthree (Figureinterfaces7), thatbetween is, one the clearance rotor and on the top stator of the (Figure armand 7), that two is, clearances one clearance on both on top axial ofsides the arm of theand arm. two Withoutclearances consideration on both axial of the sides rarefaction of the effects,arm. Without the clearance consideration leakage can of bethe described rarefaction by theeffects, classical the Couette–Poisueilleclearance leakage can flow be with described no slip boundaryby the classical conditions Couette–Poisueille and the fluid velocity flow withu(y )noin slip stream boundary wise is givenconditions by [37 and]: the fluid velocity uy() in stream wise is given by [37]: 1 dp 2 2 1 y u(y) = (y − h0 ) + U(1 + ) (5) 2µ11dxdp222 h y uy()=−++ ( y h ) U (10 ) 22μ dx0 h (5) where h0 is the half of the gap height H, y is the coordinate across the0 gap, µ is the dynamic viscosity of the leakage flow, and U is the velocity of the rotor. μ where h0 is the half of the gap height. H , y is the coordinate across the gap, is the dynamic Thus, the leakage mass flow rate ml1 for the clearance on top of the arm can be obtained via: viscosity of the leakage flow, and U is the velocity of the rotor.

+h0 . Z ml1 = ρH u(y)dy (6)

−h0

. The leakage mass flow rate ml2 for the clearance on both axial sides of the arm is obtained via:

rout +h0 . Z Z ml2 = 2 · ρ u(y)dydr (7)

rin −h0 where rin is the hinge-radius, rout is the arm-radius. And the total leakage mass flow rate is given as:

. . . ml = ml1 + ml2 (8) Energies 2018, 11, x FOR PEER REVIEW 9 of 26

Thus, the leakage mass flow rate m l1 for the clearance on top of the arm can be obtained via:

+ h0 mHuydy= ρ ()  l1  (6) − h0

The leakage mass flow rate m l2 for the clearance on both axial sides of the arm is obtained via:

+ rhout 0 muydydr=⋅2 ρ ()  l 2  (7) − rhin 0

where rin is the hinge-radius, rout is the arm-radius. And the total leakage mass flow rate is given as: Energies 2018, 11, 2684 =+ 9 of 25 mmll12 m  l (8)

FigureFigure 7.7. Schematic of of the the leakage leakage model. model.

3.1.2.3.1.2. Solution Solution Method Method for for the the Thermodynamic Thermodynamic Model Model UnderUnder a stable a stable working working station, station, each of of the the four four chambers chambers in the inthe MSRE MSRE will willfinish finish a complete a complete four-strokefour-stroke process process during during one one spindlespindle circle, or or aa total total of of four four similar similar cycles. cycles. Figure Figure 8 shows8 shows the the thermo-statethermo-state of each of each chamber chamber at aat certain a certain moment, moment, in in which which chambers chambers A, A, B, B, C C and and D D are are about about to to intake, intake, compress, expand, and exhaust, respectively. Since each stroke takes the same time, the compress, expand, and exhaust, respectively. Since each stroke takes the same time, the combination of combination of four distinct thermodynamic processes for each chamber during one quarter of fourspindle distinct circle thermodynamic exactly matches processes a complete for four-strok each chambere process. during Therefore, one quarter the thermo-process of spindle circleshould exactly matchesbe simulated a complete in 1/4 four-stroke cycles to obtain process. a comprehens Therefore,ive theanalysis thermo-process of the thermodynamic should be characteristics simulated in 1/4 cyclesof the to obtainMSRE. The a comprehensive variable step Runge–Kutta analysis of method the thermodynamic (ode45, in Matlab) characteristics was adopted in of this the study MSRE. to The variablenumerically step Runge–Kutta solve the nonlinear method ordi (ode45,nary differential in Matlab) equations was adopted established in this above. study In to the numerically ode45 time solve the nonlinearintegration ordinary scheme, differentiala four-sub-step equations method established was used to above. provide In thethe ode45candidate time solution, integration and scheme,a a four-sub-stepfive-sub-step methodmethod to was control used the to calculation provide the erro candidater. As an adaptive solution, step and numerical a five-sub-step solution, method this to controlscheme the was calculation able to solve error. the As Nonstiff an adaptive differential step eq numericaluation with solution, rather high this accuracy scheme in wasa short able time. to solve We refer to the initial parameters taken in the simulation for the MICSE [31]; the parameters used in the Nonstiff differential equation with rather high accuracy in a short time. We refer to the initial this work are provided in Table 2. parameters taken in the simulation for the MICSE [31]; the parameters used in this work are provided Energiesin Table 20182. , 11, x FOR PEER REVIEW 10 of 26

FigureFigure 8. 8. WorkingWorking cycle cycle of of the the micro micro swing swing rotor rotor engine in steady state.

Table 2. Initial parameters of the micro swing rotor engine. Table 2. Initial parameters of the micro swing rotor engine.

InitialInitial Parameters Parameters Value Value Initial Initial Parameters Parameters Value Value EquivalenceEquivalence ratio ratio 0.8 0.8 ExhaustExhaust port port diameter/mm diameter/mm 10 10 Reactants C4H10, air Intake discharge coefficient 0.7 Reactants C4H10, air Intake discharge coefficient 0.7 Intake pressure/MPa 0.1 Exhaust discharge coefficient 0.7 IntakeIntake pressure/MPa temperature/K 0.1 300 Exhaust Compression discharge ratio coefficient 6 0.7 IntakeAmbient temperature/K pressure/MPa 300 0.1 Burn Compression duration /ms ratio 2 6 AmbientAmbient pressure/MPa temperature/K 0.1 300 Weibe Burnfunction duration parameters /ms [31] a = 5, m = 2 1 AmbientIntake temperature/ port diameter/mmK 300 10 Weibe function parameters [31] a = 5, m = 1 Intake port diameter/mm 10

3.2. Results of Thermodynamic Simulation for MSRE and Discussion Based on the designed prototype, a preliminary analysis on the basic thermodynamic characteristics was carried out, in which the heat transfer losses through walls were not considered. With a compression ratio of 6, the working frequency and clearance size were two dominant factors of the engine performance, the influences of which will be elaborated in the following part.

3.2.1. Basic Thermodynamic Characteristics of the MSRE As the most influential irreversible loss, the leakage effect reduces the engine performance drastically. The thermodynamic characteristics with and without consideration of the leakage effect using a gap height of 20 μm were compared. Figures 9–16 show the simulation results at the working frequency of 30 Hz and 100 Hz. As shown in Figure 9, for the MSRE at 30 Hz frequency, trends of the pressure change during one cycle with and without leakage effect were similar. The pressure of the working fluid continuously increased for the intake and compression processes, peaked at the end of combustion process, and slowed down during the expansion and exhaust strokes. However, compared to the results with no leakage flow, the pressure curve with leakage effect over the entire compression stroke was higher, however, that over the entire expansion stroke was lower. Because the gas with higher pressure and temperature in the combustion chamber could flow into the neighboring compression chamber through the clearance, the pressure in the compression chamber was raised and vice versa, the pressure in the combustion chamber was lowered. In comparison to the results in Figure 10 for the MSRE at 100 Hz frequency, the discrepancy caused by the leakage effect was more serious for the engine at lower frequency, in which the peak pressure was dramatically reduced. In other words, it was inferred that the leakage influence can be suppressed by higher working frequency.

Energies 2018, 11, 2684 10 of 25

3.2. Results of Thermodynamic Simulation for MSRE and Discussion Based on the designed prototype, a preliminary analysis on the basic thermodynamic characteristics was carried out, in which the heat transfer losses through walls were not considered. With a compression ratio of 6, the working frequency and clearance size were two dominant factors of the engine performance, the influences of which will be elaborated in the following part.

3.2.1. Basic Thermodynamic Characteristics of the MSRE As the most influential irreversible loss, the leakage effect reduces the engine performance drastically. The thermodynamic characteristics with and without consideration of the leakage effect using a gap height of 20 µm were compared. Figures9–16 show the simulation results at the working frequency of 30 Hz and 100 Hz. As shown in Figure9, for the MSRE at 30 Hz frequency, trends of the pressure change during one cycle with and without leakage effect were similar. The pressure of the working fluid continuously increased for the intake and compression processes, peaked at the end of combustion process, and slowed down during the expansion and exhaust strokes. However, compared to the results with no leakage flow, the pressure curve with leakage effect over the entire compression stroke was higher, however, that over the entire expansion stroke was lower. Because the gas with higher pressure and temperature in the combustion chamber could flow into the neighboring compression chamber through the clearance, the pressure in the compression chamber was raised and vice versa, the pressure in the combustion chamber was lowered. In comparison to the results in Figure 10 for the MSRE at 100 Hz frequency, the discrepancy caused by the leakage effect was more serious for the engine at lower frequency, in which the peak pressure was dramatically reduced. In other words, it was inferred Energies 2018that, 11 the, x leakageFOR PEER influence REVIEW can be suppressed by higher working frequency. 11 of 26

FigureFigure 9. Pressure 9. Pressure of ofworking working fluid fluid vs.vs. time time over over one one cycle cycle (30 Hz). (30 Hz).

Figure 10. Pressure of working fluid vs. time over one cycle (100 Hz).

The changing processes of working fluid mass over one cycle are given in Figures 11 and 12. Without leakage flow, the fluid mass in one certain chamber increased in the intake stroke, remained constant for compression and expansion stokes, and declined rapidly in the exhaust stroke. However, things were quite different when the leakage effect was considered. At the end of the intake process, since the pressure is higher, a small amount of the fresh fuel mixture was extruded to the neighboring exhaust chamber and the fluid mass slightly decreased. In the compression stroke, the fluid mass at the initial stage increased with the more reception of gas from the combustion chamber. But at the later stage, the pressure increased rapidly and more fluid flowed into the neighboring intake chamber. Thus, the fluid mass decreased until the end of the combustion process. Then, the fluid mass increased again because of the gas injection from the neighboring compression chamber. Certainly, this discrepancy is more serious for a lower working frequency where the amplitude of fluctuation will be much higher.

Energies 2018, 11, x FOR PEER REVIEW 11 of 26

Energies 2018, 11, 2684 11 of 25 Figure 9. Pressure of working fluid vs. time over one cycle (30 Hz).

FigureFigure 10. Pressure 10. Pressure of ofworking working fluid fluid vs. vs. time time over over one one cycle cycle (100Hz). (100 Hz).

The changing processes of working fluid mass over one cycle are given in Figures 11 and 12. TheWithout changing leakage processes flow, the fluidof working mass in onefluid certain mass chamber over increasedone cycle in are the intakegiven stroke, in Figures remained 11 and 12. Withoutconstant leakage for flow, compression the fluid and mass expansion in one stokes, certain and chamber declined rapidly increased in the in exhaust the intake stroke. stroke, However, remained constantthings for werecompression quite different and when expansion the leakage stokes, effect was and considered. declined At therapidly end of thein intakethe exhaust process, stroke. However,since things the pressure were isquite higher, different a small amount when of the the freshleakage fuel mixtureeffect was extruded considered. to the neighboringAt the end of the exhaust chamber and the fluid mass slightly decreased. In the compression stroke, the fluid mass at intake process, since the pressure is higher, a small amount of the fresh fuel mixture was extruded to the initial stage increased with the more reception of gas from the combustion chamber. But at the later the neighboringstage, the pressureexhaust increased chamber rapidly and and the more fluid fluid mass flowed slightly into the decreased. neighboring In intake the chamber.compression Thus, stroke, the fluidthe mass fluid massat the decreased initial untilstage the increased end of the combustion with the process.more reception Then, the fluid of massgas from increased the again combustion chamber.because But at of thethe gas later injection stage, from the the neighboringpressure in compressioncreased rapidly chamber. and Certainly, more this fluid discrepancy flowed is into the neighboringEnergiesmore intake serious 2018, 11, for chamber.x FOR a lower PEER REVIEW workingThus, the frequency fluid mass where de thecreased amplitude until of fluctuation the end of will the be combustion much12 higher. of 26 process. Then, the fluid mass increased again because of the gas injection from the neighboring compression chamber. Certainly, this discrepancy is more serious for a lower working frequency where the amplitude of fluctuation will be much higher.

Figure 11. Mass of working fluid fluid vs. time over one cycle (30 Hz).

Figure 12. Mass of working fluid vs. time over one cycle (100 Hz).

The temperature of the working fluid changes in accordance with pressure and the curves are expressed in Figures 13 and 14. Whether the leakage effect is considered or not, the fluid temperature changes in a similar trend, for a certain working frequency. However, influenced by this irreversible loss, the fluid remains heated for the entire cycle. The reason for the pressure changing process is given as follows.

Energies 2018, 11, x FOR PEER REVIEW 12 of 26

Energies 2018, 11, 2684 12 of 25 Figure 11. Mass of working fluid vs. time over one cycle (30 Hz).

Figure 12.12. Mass of working fluidfluid vs.vs. time over one cycle (100(100 Hz).Hz).

TheThe temperaturetemperature of thethe workingworking fluidfluid changeschanges in accordanceaccordance with pressure and thethe curvescurves areare expressedexpressed inin Figures Figures 13 and13 and 14. Whether14. Whether the leakage the leak effectage is effect considered is considered or not, the or fluid not, temperature the fluid changestemperature in a similarchanges trend, in a forsimilar a certain trend, working for a cert frequency.ain working However, frequency. influenced However, by this influenced irreversible by loss,this theirreversible fluid remains loss, heatedthe fluid for theremains entire heated cycle. The for reasonthe entire for the cycle. pressure The changingreason for process the pressure is given aschanging follows. process is given as follows. Because of the leakage gaps, the compression and exhaust chambers were continuously injected by the working medium with higher temperature from the adjacent combustion chamber, thereby resulting in their higher temperature. The heated exhaust process increased the initial temperature for the intake stroke, while the intake chamber was heated further by the leakage flow from the compression chamber. In addition, since the fuel combusted based on the temperature gained from the end of compression stroke, the temperature for the expansion stroke became higher accordingly. In conclusion, the progressive interactions between two neighboring chambers resulted in a higher temperatureEnergies 2018, 11 for, x FOR the PEER entire REVIEW cycle, which was, essentially, caused by the leakage effect. Similarly,13 of the 26 engine with a low working frequency was more seriously influenced by the leakage effect.

FigureFigure 13.13.Temperature Temperature of of working working fluid fluid vs. vs. time time over over one one cycle cycle (30 (30 Hz). Hz).

Figure 14. Temperature of working fluid vs. time over one cycle (100 Hz).

Because of the leakage gaps, the compression and exhaust chambers were continuously injected by the working medium with higher temperature from the adjacent combustion chamber, thereby resulting in their higher temperature. The heated exhaust process increased the initial temperature for the intake stroke, while the intake chamber was heated further by the leakage flow from the compression chamber. In addition, since the fuel combusted based on the temperature gained from the end of compression stroke, the temperature for the expansion stroke became higher accordingly. In conclusion, the progressive interactions between two neighboring chambers resulted in a higher temperature for the entire cycle, which was, essentially, caused by the leakage effect. Similarly, the engine with a low working frequency was more seriously influenced by the leakage effect. Due to the leakage effect, pressure for the compression process raised, while pressure in the expansion process did just the opposite. Consequently, the indicated work of the engine was decreased. The lower the working frequency was, the more remarkable the reduction in output work was (Figures 15 and 16). It can also be observed that the four-stroke process for the engine with a low frequency (30 Hz) was close to the Otto cycle, because the fuel combusted in a nearly constant volume. However, with a higher operation frequency (100 Hz), the engine cycle deviates from the Otto cycle, since the pressure in the combustion process increased gradually.

Energies 2018, 11, x FOR PEER REVIEW 13 of 26

Energies 2018, 11, 2684 13 of 25 Figure 13. Temperature of working fluid vs. time over one cycle (30 Hz).

Figure 14. Temperature of workingworking fluidfluid vs.vs. time over one cyclecycle (100(100 Hz).Hz).

DueBecause to the of the leakage leakage effect, gaps, pressure the compression for the compression and exhaustprocess chambers raised, were whilecontinuously pressure injected in the expansionby the working process medium did just with the opposite. higher temperature Consequently, from the the indicated adjacent work combustion of the engine chamber, was decreased. thereby Theresulting lower in the their working higher frequencytemperature. was, The the heated more exhaust remarkable process the increased reduction the in initial output temperature work was (Figuresfor the intake 15 and stroke, 16). while the intake chamber was heated further by the leakage flow from the compressionIt can also chamber. be observed In addition, that the since four-stroke the fuel process combusted for the based engine on withthe temperature a low frequency gained (30 from Hz) wasthe end close of to compression the Otto cycle, stroke, because the temperature the fuel combusted for the inexpansion a nearly stroke constant became volume. higher However, accordingly. with a higherIn conclusion, operation the frequency progressive (100 interactions Hz), the engine between cycle two deviates neighboring from the chambers Otto cycle, resulted since the in pressurea higher intemperatureEnergies the combustion 2018, 11 for, x FOR the process PEERentire REVIEW increasedcycle, which gradually. was, essentially, caused by the leakage effect. Similarly,14 of the 26 engine with a low working frequency was more seriously influenced by the leakage effect. Due to the leakage effect, pressure for the compression process raised, while pressure in the expansion process did just the opposite. Consequently, the indicated work of the engine was decreased. The lower the working frequency was, the more remarkable the reduction in output work was (Figures 15 and 16). It can also be observed that the four-stroke process for the engine with a low frequency (30 Hz) was close to the Otto cycle, because the fuel combusted in a nearly constant volume. However, with a higher operation frequency (100 Hz), the engine cycle deviates from the Otto cycle, since the pressure in the combustion process increased gradually.

FigureFigure 15.15. P-VP-V diagramdiagram overover oneone cyclecycle (30(30 Hz).Hz).

Figure 16. P-V diagram over one cycle (100 Hz).

3.2.2. Influence of Operation Frequency on the Engine Thermodynamic Characteristics The analysis reveals that, even with the same gap size, different working frequencies will result in influences of leakage effect with distinct levels on the engine. Therefore, the impact of operation frequency on the thermodynamic characteristics of the MSRE was investigated. With a gap height of 20 μm, simulation results for the engine at a series of frequencies (i.e., 30 Hz, 60 Hz and 100 Hz) are taken for this study (Figures 17–20). For the convenience of analysis, the dimensionless time τ is defined as

τ = t (9) Tcycle

where t is real time (s), Tcycle is the duration for one total cycle (s). With a burn duration time, the ratio of combustion time to one expansion stroke will be larger when the engine operates at a higher frequency. Thus, the pressure-rise effect resulting from combustion was further weakened by the pressure drop effect caused by volume expansion, that is, the peak pressure after combustion was cut down. As Figure 17 shows, for the studied three working conditions, the lower frequency, and the higher peak pressure. However, higher frequency

Energies 2018, 11, x FOR PEER REVIEW 14 of 26

Energies 2018, 11, 2684 14 of 25 Figure 15. P-V diagram over one cycle (30 Hz).

FigureFigure 16.16. P-V diagram overover oneone cyclecycle (100(100 Hz).Hz).

3.2.2.3.2.2. InfluenceInfluence ofof OperationOperation FrequencyFrequency onon thethe EngineEngine ThermodynamicThermodynamic CharacteristicsCharacteristics TheThe analysisanalysis revealsreveals that,that, eveneven withwith thethe samesame gapgap size,size, different workingworking frequenciesfrequencies willwill resultresult inin influencesinfluences ofof leakageleakage effecteffect withwith distinctdistinct levelslevels onon thethe engine.engine. Therefore,Therefore, thethe impactimpact ofof operationoperation frequencyfrequency on the thermodynamic characteristics characteristics of of the the MSRE MSRE was was investigated. investigated. With With a gap a gap height height of of20 20μm,µm, simulation simulation results results for for the the engine engine at a at series a series of frequencies of frequencies (i.e., (i.e., 30 Hz, 30 Hz, 60 Hz 60 Hzand and 100 100Hz) Hz)are aretaken taken for forthis this study study (Figures (Figures 17–20). 17–20 For). For the the co conveniencenvenience of ofanalysis, analysis, the the dimensionless dimensionless time time ττ isis defined as defined as t τ = (9) T τ = cyclet (9) where t is real time (s), Tcycle is the duration for oneTcycle total cycle (s). With a burn duration time, the ratio of combustion time to one expansion stroke will be largerwhere whent is real the enginetime (s), operates Tcycle is atthe a duration higher frequency. for one total Thus, cycle the (s). pressure-rise effect resulting from combustionWith a burn was furtherduration weakened time, the byratio the of pressure combustion drop time effect to causedone expansion by volume stroke expansion, will be larger that is,when the peakthe engine pressure operates after combustionat a higher was frequency. cut down. Thus, As the Figure pressure-rise 17 shows, foreffect the resulting studied threefrom workingcombustion conditions, was further the lowerweakened frequency, by the andpressure the higher drop peakeffect pressure.caused by However, volume expansion, higher frequency that is, usuallythe peak means pressure less timeafter allowed combustion for leak was flow, cut therebydown. playingAs Figure a certain 17 shows, role in for suppressing the studied leakage three effect.working Thus, conditions, the pressure the lower for engine frequency, at higher and frequency the higher will peak be lowerpressure. during Howe intakever, higher and compression frequency strokes, until after combustion. But it increases for the expansion and exhaust process, compared to the simulation results for lower-frequency cases. As a consequence, the difference between the pressure value for the intake end and that for the exhaustion end was narrowed. Therefore, the reduction value of the working fluid mass at the end of the intake process is lessened (Figure 18). Under the working frequency of 100 Hz, the mass reduction trend even disappeared entirely. Furthermore, the mass fluctuation caused by the leakage effect for the engine at a higher frequency was much smaller. As for the changing process of temperature shown in Figure 19, explanations for the pressure change are applicable here. Energies 2018, 11, x FOR PEER REVIEW 15 of 26 Energies 2018, 11, x FOR PEER REVIEW 15 of 26 usually means less time allowed for leak flow, thereby playing a certain role in suppressing leakage effect.usually Thus, means the less pressuretime allowed for forengine leak atflow, higher thereby frequency playing awill certain be rolelower in suppressingduring intake leakage and compressioneffect. Thus, strokes,the pressure until after for combustion.engine at higherBut it increases frequency for willthe expansionbe lower andduring exhaust intake process, and comparedcompression to strokes,the simulation until after results combustion. for lower-fr But itequency increases cases. for the As expansiona consequence, and exhaust the difference process, betweencompared the to pressurethe simulation value forresults the forintake lower-fr end equencyand that cases.for the As exhaustion a consequence, end was the narrowed.difference Therefore,between the the pressure reduction value value for of thethe workingintake end fluid and mass that at forthe endthe exhaustionof the intake end process was isnarrowed. lessened (FigureTherefore, 18). the Under reduction the working value of frequency the working of fluid100 Hz, mass the at mass the end reduction of the intake trend processeven disappeared is lessened entirely.(Figure 18).Furthermore, Under the the working mass flfrequencyuctuation ofcaused 100 Hz, by the leakagemass reduction effect for trend the engineeven disappeared at a higher frequencyentirely. Furthermore, was much smaller.the mass As fluctuation for the changing caused by process the leakage of temperature effect for the shown engine in atFigure a higher 19, frequency was much smaller. As for the changing process of temperature shown in Figure 19, Energiesexplanations2018, 11, for 2684 the pressure change are applicable here. 15 of 25 explanations for the pressure change are applicable here.

Figure 17. Changing process of pressure at different frequencies. FigureFigure 17.17. ChangingChanging processprocess ofof pressurepressure atat differentdifferent frequencies.frequencies.

Energies 2018, 11, x FOR PEERFigure REVIEW 18. Changing process of mass at different frequencies.frequencies. 16 of 26 Figure 18. Changing process of mass at different frequencies.

Figure 19. Changing process of temperature atat differentdifferent frequencies.frequencies.

Figure 20. Thermal performances of MSRE at different frequencies.

The overall engine performance at a series of operating frequencies is shown in Figure 20. Results show that the MSRE cannot function properly when the operating frequency was lower than 10 Hz, because both the engine efficiency and power are negative. For frequencies larger than 10 Hz, the maximum efficiency and power individually corresponded to an optimal frequency value. The reason is given as follows. As the working frequency increased from 10 Hz, although the leakage mass flow nearly remains the same, the available time for leakage was reduced, resulting in a weakened leakage effect, thereby improving the engine efficiency. In addition, the engine power increased accordingly, because the time ratio to output work per unit time increased. However, once the operating frequency grew excessively, the burn duration time could not be ignored, and the incomplete combustion could lead to more severe deterioration of the engine performance. As a consequence, two optimal values of frequency exist for engine performance and power. At an operating frequency of 55 Hz, the engine reached the optimum thermal efficiency (23.62%) with a power of 2458.18 W, which is approximately 4.72 times of the micro-turbine’s efficiency (5%). When the operating frequency is 95 Hz, it will reach the maximum power (3442 W) with a thermal efficiency of 18.96%. The corresponding power weight ratio is 1.72 kW/kg, about 5.21 times of that for the MICSE (0.33 kW/kg) and 3.44 times of that for conventional IC engines (0.5 kW/kg).

Energies 2018, 11, x FOR PEER REVIEW 16 of 26

Energies 2018, 11, 2684 16 of 25 Figure 19. Changing process of temperature at different frequencies.

FigureFigure 20. 20. ThermalThermal performances performances of of MSRE MSRE at at different different frequencies. frequencies.

TheThe overall overall engine engine performance performance at at a a series series of of operating operating frequencies frequencies is is shown shown in in Figure Figure 20. 20 . ResultsResults show show that that the the MSRE MSRE cannot cannot function function properly properly when when the operating the operating frequency frequency was lower was lowerthan 10than Hz, 10 because Hz, because both the both engine the engine efficiency efficiency and power and power are negative. are negative. For frequencies For frequencies larger larger than than10 Hz, 10 theHz, maximum the maximum efficiency efficiency and and power power individually individually corresponded corresponded to toan an optimal optimal frequency frequency value. value. The The reasonreason is is given asas follows.follows. As As the the working working frequency frequency increased increased from from 10 Hz,10 Hz, although although the leakagethe leakage mass massflow nearlyflow nearly remains remains the same, the thesame, available the available time for time leakage for wasleakage reduced, was reduced, resulting inresulting a weakened in a weakenedleakage effect, leakage thereby effect, improving thereby improving the engine the efficiency. engine efficiency. In addition, In addition, the engine the power engine increased power increasedaccordingly, accordingly, because thebecause time the ratio time to ratio output to output work perwork unit per time unit increased.time increased. However, However, once once the theoperating operating frequency frequency grew grew excessively, excessively, the burn the duration burn duration time could time not could be ignored, not be andignored, the incomplete and the incompletecombustion combustion could lead to could more lead severe to deteriorationmore severeof deterioration the engine performance. of the engine As performance. a consequence, As two a consequence,optimal values two of optimal frequency values exist of for frequenc engine performancey exist for engine and power.performance and power. AtAt an operatingoperating frequencyfrequency of of 55 55 Hz, Hz, the enginethe engine reached reached the optimum the optimum thermal thermal efficiency efficiency (23.62%) (23.62%)with a power with ofa 2458.18power of W, 2458.18 whichis W, approximately which is approximately 4.72 times of 4.72 themicro-turbine’s times of the micro-turbine’s efficiency (5%). efficiencyWhen the (5%). operating When frequency the operating is 95 frequency Hz, it will is reach 95 Hz, the it maximum will reach powerthe maximum (3442 W) power with a(3442 thermal W) withefficiency a thermal of 18.96%. efficiency The correspondingof 18.96%. The powercorresponding weight ratio power is 1.72 weight kW/kg, ratio about is 1.72 5.21 kW/kg, times about of that 5.21 for timesthe MICSE of that (0.33 for kW/kg)the MICSE and (0.33 3.44 timeskW/kg) of thatand for3.44 conventional times of that IC for engines conventional (0.5 kW/kg). IC engines (0.5 kW/kg). 3.2.3. Combined Effect of Gap Height and Operating Frequency Since the compression ratio of the engine has been designated as 6, working frequency and clearance size were the two parameters that determined the engine performance, and their combined effect should be investigated. Figure 21 shows the change process of engine efficiency with gap length for different gap heights. Under a certain gap height, as the gap depth increases linearly, the thermal efficiency rises, and the increase will gradually slow down. However, with the increase in gap height, the engine efficiency will be sharply reduced, especially for values larger than 20 µm. When the gap height is 50 µm and the gap depth is less than 8 mm, the engine efficiency will be less than zero, indicating that it is incapable of self-operation. Energies 2018, 11, x FOR PEER REVIEW 17 of 26

3.2.3. Combined Effect of Gap Height and Operating Frequency Since the compression ratio of the engine has been designated as 6, working frequency and clearance size were the two parameters that determined the engine performance, and their combined effect should be investigated. Figure 21 shows the change process of engine efficiency with gap length for different gap heights. Under a certain gap height, as the gap depth increases linearly, the thermal efficiency rises, and the increase will gradually slow down. However, with the increase in gap height, the engine efficiency will be sharply reduced, especially for values larger than 20 μm. When the gap height is 50 μm and the gap depth is less than 8 mm, the engine efficiency will be less than zero, indicating that it Energies 2018, 11, 2684 17 of 25 is incapable of self-operation.

FigureFigure 21. 21. EngineEngine efficiency efficiency vs. gap gap leng lengthth under under different different gap heights.

InIn considerationconsideration of of the the leakage leakage effect, effect, the optimal the op valuestimal ofvalues frequency of frequency exist for engine exist performancefor engine performanceand power. As and shown power. in FiguresAs shown 22 andin Figures 23, the 22 larger and the23, gapthe larger height the was, gap the height lower was, the corresponding the lower the correspondingoptimum efficiency optimum and power efficiency value and were. power Moreover, value thewere. feasible Moreover, range ofthe working feasible frequency range of working becomes frequencynarrower. Forbecomes example, narrower. when theFor gapexample, height when was largerthe gap than height 40 µ m,was the larger engine than could 40 μ onlym, the work engine at a couldfrequency only rangework ofat 55a frequency Hz to 135 Hz,range with of a55 maximum Hz to 135 efficiency Hz, with of a nomaximum more than efficiency 2.25%, and of no a power more thanlower 2.25%, than 350and W. a Inpower addition, lower the than maximum 350 W. In thermal addition, efficiency the maximum dropped thermal dramatically efficiency from 35%dropped for a dramatically10 µm gap height from to35% 2% for for a a 10 40 μµmm gap gap height height. to Under 2% for a certaina 40 μm gap gap height, height. the Under optimal a certain frequency gap height,value for the engine optimal efficiency frequency was valu lowere for than engine that forefficiency engine power.was lower Overall, than thethat optimal for engine frequencies power. Overall,increased the as optimal the gap frequencies height grew. increased as the gap height grew. The results indicate that, although affected by the working frequency and leakage, the engine performance was was dominated dominated by by the the leakage leakage effect effect when when it it worked worked at at a a low frequency. However, However, with thethe increaseincrease in in working working frequency, frequency, the leakage the leakage influence influence gradually gradually weakened. weakened. Once the Once frequency the frequencywas high enough,was high the enough, engine the performance engine performance approached approached that result that without result without leakage leakage effect; thateffect; is, thatthe workingis, the working frequency frequency became became the dominant the domina parameternt parameter for engine for engine performance. performance. For thatFor case,that Energiescase,the leakage the 2018 leakage, 11 can, x FOR be can neglected,PEER be neglected,REVIEW especially especially for a smallerfor a smaller gap height. gap height. 18 of 26

FigureFigure 22. 22. EngineEngine efficiency efficiency vs. vs. frequenc frequencyy under under different different gap gap heights. heights.

Figure 23. Engine power vs. frequency under different gap heights.

4. Preliminary Experiments on the Micro Swing Rotor Engine A prototype was designed and fabricated in mesoscale to validate the novel engine proposed in this study. Based on the established experimental platform, preliminary tests were carried out on the prototype for cold and thermal states, which could verify the feasibility of MSRE

4.1. Establishment of the Experimental Platform The experiment platform was composed of four parts, namely, the prototype system, the fuel supply system, the ignition control system, and the parameter acquisition and measurement system (Figure 24). As the main body of this platform, the prototype system output power by consuming hydrocarbon fuels, which was comprised of a prototype and a small generator. A gas-channel assembly, an air-channel assembly, and the pre-mixer made up the fuel supply system to provide combustible mixture for the engine. Consisting of a sparking plug, a high voltage coil, and a speed sensor (hall element), the ignition controller was responsible for the combustion of inflammable gas at high frequency (100 Hz). In cooperation with a group of thermocouples and dynamic pressure sensors, the computer control system made a parameter acquisition and measurement system to monitor the changing process of thermodynamic state in each chamber. In Figure 24, letters ‘P’ and ‘T’ represent the pressure and temperature measuring points, respectively.

Energies 2018, 11, x FOR PEER REVIEW 18 of 26

Energies 2018, 11, 2684 18 of 25 Figure 22. Engine efficiency vs. frequency under different gap heights.

FigureFigure 23. 23.Engine Engine power powervs. vs. frequencyfrequency under different different gap gap heights. heights.

4. Preliminary4. Preliminary Experiments Experiments on on the the Micro Micro SwingSwing RotorRotor Engine A prototypeA prototype was was designed designed and and fabricated fabricated inin mesoscalemesoscale to validate validate the the novel novel engine engine proposed proposed in in thisthis study. study. Based Based on on the the established established experimental experimental platform,platform, preliminary tests tests were were carried carried out out on on the the prototypeprototype for for cold cold and and thermal thermal states, states, which which could could verifyverify thethe feasibility of of MSRE MSRE

4.1.4.1. Establishment Establishment of of the the Experimental Experimental Platform Platform TheThe experiment experiment platform platform was was composedcomposed ofof four parts, namely, namely, the the prototype prototype system, system, the the fuel fuel supplysupply system, system, the the ignition ignition control control system, system, andand thethe parameterparameter acquisition acquisition and and measurement measurement system system (Figure(Figure 24 ).24). As As the the main main body body of of this this platform, platform, thethe prototypeprototype system system output output power power by by consuming consuming hydrocarbonhydrocarbon fuels, fuels, which which was was comprised comprised of a prototypeof a prototype and a and small a generator.small generator. A gas-channel A gas-channel assembly, anassembly, air-channel an assembly, air-channel and assembly, the pre-mixer and the made pre-mi upxer the made fuel supplyup the fuel system supply to provide system to combustible provide mixturecombustible for the mixture engine. for Consisting the engine. of Consisting a sparking of plug, a sparking a high plug, voltage a high coil, voltage and a speedcoil, and sensor a speed (hall element),sensor (hall the element), ignition controllerthe ignition was controller responsible was responsible for the combustion for the combustion of inflammable of inflammable gas at gas high at high frequency (100 Hz). In cooperation with a group of thermocouples and dynamic pressure frequency (100 Hz). In cooperation with a group of thermocouples and dynamic pressure sensors, sensors, the computer control system made a parameter acquisition and measurement system to the computer control system made a parameter acquisition and measurement system to monitor the monitor the changing process of thermodynamic state in each chamber. In Figure 24, letters ‘P’ and changing process of thermodynamic state in each chamber. In Figure 24, letters ‘P’ and ‘T’ represent ‘T’ represent the pressure and temperature measuring points, respectively. the pressure and temperature measuring points, respectively. Energies 2018, 11, x FOR PEER REVIEW 19 of 26

Figure 24. The experimental platform for MSRE. Figure 24. The experimental platform for MSRE.

With less than 2 kg weight, the prototype was designed to be in a high coaxial structure, especially for the driver and cylinder assemblies, with a main size of 75mm×× 75 mm 50 mm (Figure 25). A coupling was used to link the generator and the prototype body in the test rig; the overall prototype is shown in Figure 26. Butane and air were used as fuel reactants here. The scopes of mass flow controllers were 4 g/s and 0.5 g/s for the gas and air channels, respectively, with an accuracy of ±0.1% flow scope. The spiral rise mixing of counter flow occurred in the pre-mixer, so that the reactants were fully mixed in a certain proportion controlled by mass controllers.

Figure 25. Prototype of the MSRE with high coaxiality.

Energies 2018, 11, x FOR PEER REVIEW 19 of 26

Figure 24. The experimental platform for MSRE.

With less than 2 kg weight, the prototype was designed to be in a high coaxial structure, 75mm×× 75 mm 50 mm especiallyEnergies 2018 ,for11, the 2684 driver and cylinder assemblies, with a main size of (Figure19 of 25 25). A coupling was used to link the generator and the prototype body in the test rig; the overall prototype is shown in Figure 26. ButaneWith less and than air 2 were kg weight, used as the fuel prototype reactants was here. designed The scopes to be inof a mass high flow coaxial controllers structure, were especially 4 g/s andfor the0.5 driverg/s for and the cylindergas and assemblies,air channels, with respectively, a main size with of 75an mmaccuracy× 75 mmof ±0.1%× 50 flow mm (Figurescope. The25). Aspiral coupling rise mixing was used of counter to link theflow generator occurred and in the the pre-mixer, prototype bodyso that in the the reactants test rig; the were overall fully prototype mixed in ais certain shown proportion in Figure 26 controlled. by mass controllers.

Energies 2018, 11, x FOR PEER FigureFigureREVIEW 25. PrototypePrototype of of the MSRE with high coaxiality. 20 of 26

FigureFigure 26.26. PrototypePrototype system in in the the test test rig. rig.

ButaneThe micro and airthermocouples were used as (OMEGA) fuel reactants in K-Type here. with The scopesan end ofdiameter mass flow of 0.5 controllers mm were wereadopted 4 g/s andto0.5 measure g/s for the the chamber gas and temperature air channels, in respectively, the MSRE. withConnected an accuracy to a high-precision of ±0.1% flow data scope. acquisition The spiral risedevices mixing (Agilent of counter U2802A flow and occurred U2356A), in the the pre-mixer, maximum so sampling that the reactantsrate of the were thermocouples fully mixed was in a up certain to proportion500 kHz and controlled the measure by mass accuracy controllers. was ±0.02% of reading. Pressure in the chambers was measured byThe high micro frequency thermocouples dynamic pressure (OMEGA) sensors in K-Type (sqsensor, with anCYG502ASL) end diameter with of 0.5a maximum mm were sampling adopted to measurerate of the20 chamberkHz. The temperature measure scop ine the of MSRE.the sensor Connected was 500 to kPa a high-precision and the measurement data acquisition accuracy devices of (Agilent±0.25% U2802A of its scope. and U2356A),According theto the maximum circumferential sampling positions rate of of the the thermocouples dual-rotor in one was cycle, up to that 500 is, kHz andthe the changing measure process accuracy of one was certain±0.02% chamber of reading. distribution, Pressure six inmeasuring the chambers points was around measured the cylinder by high base were necessary to obtain the successive parameter change in one chamber for one complete frequency dynamic pressure sensors (sqsensor, CYG502ASL) with a maximum sampling rate of 20 kHz. cycle. Two groups of measuring points were designed for temperature and pressure; the The measure scope of the sensor was 500 kPa and the measurement accuracy of ±0.25% of its scope. circumferential distribution for the probes is presented in Figure 27. Take chamber A, for example: a According to the circumferential positions of the dual-rotor in one cycle, that is, the changing process complete operation mode or the selection principle for the six measuring points is elaborated in of one certain chamber distribution, six measuring points around the cylinder base were necessary Figure 28. For the other measuring parts shown in Figure 24, the pressure was tested by topressure-gauges, obtain the successive with a parameter scope of 200 change kPa and in onean accuracy chamber of for ±0.4% one FS. complete During cycle.the experiments, Two groups all of measuringthe measuring points conditions were designed had to forbe temperaturekept coincident, and so pressure; that the flow the circumferentialinterpretation was distribution affected as for thelittle probes as possible is presented [41]. in Figure 27. Take chamber A, for example: a complete operation mode or the Because the following analysis was conducted on the basis of pressure measurements, some pressure uncertainty estimation for this experiment was necessary [42]. The pressure measurement error in this study was determined by the high frequency dynamic pressure sensors with an accuracy of ±0.25% of its scope (500 kPa), that is ±0.0125 atm. In Figures 29 and 30, the measured pressures are in the range between 1 atm and 1.5 atm. Compared to the smallest value, the experimental error was controlled within ±1.25% and, compared to the highest value, the measurement error was within ±0.84%. Therefore, the experimental uncertainty was totally acceptable and could have little effect on the final test conclusion and explanations. That is why in Figures 29 and 30 the errors were not marked.

Energies 2018, 11, 2684 20 of 25 selection principle for the six measuring points is elaborated in Figure 28. For the other measuring parts shown in Figure 24, the pressure was tested by pressure-gauges, with a scope of 200 kPa and an accuracy of ±0.4% FS. During the experiments, all the measuring conditions had to be kept coincident, soEnergiesEnergies that 2018 the 2018, flow11, 11, x, FORx interpretation FOR PEER PEER REVIEW REVIEW was affected as little as possible [41]. 21 of21 26of 26

Figure 27. Distribution of parameter-measuring points. Figure 27. Distribution of parameter-measuring points.

FigureFigure 28.28. SelectionSelection principle of of the the six six measuring measuring points. points.

4.2.Because Cold State the Test following with Pressure-Air analysis Blow was conducted on the basis of pressure measurements, some Figure 28. Selection principle of the six measuring points. pressureDisregarding uncertainty pressure-ris estimatione, for brought this experiment out by the wascombustion necessary reaction, [42]. The the pressurecold state measurement tests were error4.2.performed Cold in this State studyby Test charging waswith determinedPressure-Air pressure-air byBlow into the highthe engine frequency through dynamic the spark-plug pressure sensorsport at the with time an accuracywhen ofcombustion±0.25% of itswas scope to occur. (500 kPa),A survey that of is pressure±0.0125 atm.changing In Figures process 29 was and obtained 30, the measuredto test the pressuresengine Disregarding pressure-rise, brought out by the combustion reaction, the cold state tests were performance in cold state, which was necessary for investigating the influence of unthermal factors, performed by charging pressure-air into the engine through the spark-plug port at the time when such as the leakage effect and mechanical friction. combustion was to occur. A survey of pressure changing process was obtained to test the engine With the flowing-in air at the pressure of 2.0 atm, a typical experimental result for the cold state performanceengine at 240 in rpmcold speed state, iswhich shown was in necessaryFigure 29 (infor relative investigating value). theSince influence the assembly of unthermal error for factors, this such as the leakage effect and mechanical friction.

With the flowing-in air at the pressure of 2.0 atm, a typical experimental result for the cold state engine at 240 rpm speed is shown in Figure 29 (in relative value). Since the assembly error for this

Energies 2018, 11, x FOR PEER REVIEW 22 of 26

prototype was controlled under 100 μm, the severe leakage caused a dramatic pressure loss; the peak value was just a little more than 0.5 atm. However, the pressure changing trend was similar to the simulation result, which could be used to demonstrate the structure feasibility of the MSRE.

Energies 2018, 11, 2684 21 of 25

Energies 2018, 11, x FOR PEER REVIEW 22 of 26 are in the range between 1 atm and 1.5 atm. Compared to the smallest value, the experimental error prototype was controlled under 100 μm, the severe leakage caused a dramatic pressure loss; the was controlled within ±1.25% and, compared to the highest value, the measurement error was within peak value was just a little more than 0.5 atm. However, the pressure changing trend was similar to ±0.84%. Therefore, the experimental uncertainty was totally acceptable and could have little effect on the simulation result, which could be used to demonstrate the structure feasibility of the MSRE. the final test conclusion and explanations. That is why in Figures 29 and 30 the errors were not marked.

Figure 29. Experimental pressures vs. time for cold state over one cycle.

4.3. Combustion Test for Engine Operation at Thermal State The mixture gas was charged into the prototype engine and combustion test was carried out. With an entrance pressure of 0.12 atm (relative value) just before the intake port, the complete combustion process in one chamber was obtained (Figure 31); the results of the measured pressure for the engine operating at 150 rpm are given in Figure 30. It is explicit that, influenced by other irreversible effects, especially the leakage flow, the prototype could not generate net power at the present low frequency, which was consistent with the simulation results. FigureFigure 29. Experimental29. Experimental pressures pressures vs. vs. timetime for cold state state over over one one cycle. cycle.

4.3. Combustion Test for Engine Operation at Thermal State The mixture gas was charged into the prototype engine and combustion test was carried out. With an entrance pressure of 0.12 atm (relative value) just before the intake port, the complete combustion process in one chamber was obtained (Figure 31); the results of the measured pressure for the engine operating at 150 rpm are given in Figure 30. It is explicit that, influenced by other irreversible effects, especially the leakage flow, the prototype could not generate net power at the present low frequency, which was consistent with the simulation results.

FigureFigure 30. Experimental30. Experimental pressures pressures vs. vs. time time forfor hot state state over over one one cycle. cycle. 4.2. Cold State Test with Pressure-Air Blow

Disregarding pressure-rise, brought out by the combustion reaction, the cold state tests were performed by charging pressure-air into the engine through the spark-plug port at the time when combustion was to occur. A survey of pressure changing process was obtained to test the engine performance in cold state, which was necessary for investigating the influence of unthermal factors, such as the leakage effect and mechanical friction.

With the flowing-in air at the pressure of 2.0 atm, a typical experimental result for the cold state Figure 30. Experimental pressures vs. time for hot state over one cycle. engine at 240 rpm speed is shown in Figure 29 (in relative value). Since the assembly error for this prototype was controlled under 100 µm, the severe leakage caused a dramatic pressure loss; the peak value was just a little more than 0.5 atm. However, the pressure changing trend was similar to the simulation result, which could be used to demonstrate the structure feasibility of the MSRE. Energies 2018, 11, 2684 22 of 25

4.3. Combustion Test for Engine Operation at Thermal State The mixture gas was charged into the prototype engine and combustion test was carried out. With an entrance pressure of 0.12 atm (relative value) just before the intake port, the complete combustion process in one chamber was obtained (Figure 31); the results of the measured pressure for the engine operatingEnergies at2018 150, 11,rpm x FOR are PEER given REVIEW in Figure 30. It is explicit that, influenced by other irreversible23 of 26 effects, especiallyIn the conclusion, leakage flow,though the creativeness prototype and could feasibility not generate of MSRE net were power proven at the in present this study, low frequency,deep whichworks was on consistent the prototype with design the simulation and fabrication results. are necessary to further improve its performance.

(a) initial ignition. (b) full ignition.

(c) full combustion. (d) full expansion.

(e) combustion end. (f) expansion end.

FigureFigure 31. 31.Combustion Combustion process process for for one one chamber. chamber.

Energies 2018, 11, 2684 23 of 25

In conclusion, though creativeness and feasibility of MSRE were proven in this study, deep works on the prototype design and fabrication are necessary to further improve its performance.

5. Conclusions As a potential system for power supply, great developments in the micro heat engine have been accomplished. In view of the defects (e.g., complex structure, difficultly in sealing, and low power-to-volume ratio) of existing engine types, the MSRE was proposed in this paper. Preliminary kinematic and thermodynamic analyses were conducted. The major conclusions are summarized as follows:

(1) The proposed MSRE in four-stroke is composed of cylinder assembly and driver assembly, which can make the best of advantages for the micro swing engine and other IC engines. Without any complex components, surface sealing is applicable and the working frequency of this engine is relatively low at approximately 100 Hz order. Since available volume in cylinder assembly is high, the power to weight ratio is remarkable. (2) In accordance with the operating characteristics of the MSRE, the design principle of the driver assembly was proven, so that the required periodical pursue motion of the two rotors was accomplished. In the prototype, the bar-length ratio of the crank-rocker mechanism was designed to be 3:0.5973:2.7402:1.2503; the rotor-thickness angle was 10◦. With a compression ratio of 6, the volume of each chamber in the MSRE varied in a sine-like waveform, meeting well the design requirements. (3) Considering leakage effect, the thermodynamic model for the engine in steady working cycle was established. Simulation results indicated that the engine performance suffers poorly due to the leakage influence, especially when working at low frequencies. Thus, the effect of leakage size was analyzed. As the gap height increased, the engine efficiency diminishes sharply. (4) Gap height and the operation frequency were demonstrated as the two dominant factors that affect the engine performance. Analyses show that, under certain gap height, the MSRE must work at a specific frequency range, and the corresponding optical values exist for engine efficiency and power. With a gap height of 20 µm, the MSRE will reach the maximum efficiency of 23.62% at 55 Hz and achieve its maximum power of 3442 W at 95 Hz. Compared to the Micro-turbine by IHI or MICSE, the MSRE has remarkable advantages in power weight ratio and efficiency. (5) An experimental platform has been established and a preliminary test on the engine operation characteristics was conducted. In the cold state test with pressure-air blow, the experimental pressure changing trend was similar to the numerical result. Moreover, the research on combustion for the MSRE at thermal state showed that a full combustion process of butane was realized when the engine worked at 150 rpm. (6) Theoretical feasibility and creativity of MSRE were validated primitively by simulation analysis, together with the experimental test in this study. This work contributes a lot to the development of micro power systems.

Author Contributions: C.X. performed the data analyses and wrote the manuscript; Z.Z. contributed significantly to analysis, experiment and manuscript preparation; G.H. proposed the conception of the study; T.Z. helped design the engine structure and perform the numerical simulations; J.X. helped perform the data analyses and manuscript preparation. Funding: This research was funded by the National Basic Research Program of China (grant number 2014CB239602) and the Funding of Jiangsu Innovation Program for Graduate Education (grant number KYLX15_0258). And The APC was funded by 2014CB239602. Acknowledgments: This work was supported by the National Basic Research Program of China (NO. 2014CB239602) and the Funding of Jiangsu Innovation Program for Graduate Education (NO. KYLX15_0258). Conflicts of Interest: The authors declare no conflicts of interest. Energies 2018, 11, 2684 24 of 25

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