Research ArticleParametric Investigation of Combustion and Heat TransferCharacteristics of Oscillating Linear Engine Alternator

Mehar Bade ,1 Nigel N. Clark ,1 Matthew C. Robinson,1 and Parviz Famouri2

1Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV, USA2Lane Department of Computer Science & Electrical Engineering, West Virginia University, Morgantown, WV, USA

Correspondence should be addressed to Nigel N. Clark; nigel.clark@mail.wvu.edu

Received 31 January 2018; Revised 30 April 2018; Accepted 21 May 2018; Published 28 June 2018

Academic Editor: Sotirios Mamalis

Copyright © 2018 Mehar Bade et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An Oscillating Linear Engine Alternator (OLEA) has the potential to overcome the thermal, mechanical, and combustioninadequacies encountered by the conventional slider-crank engines.The linear engines convert the reciprocating pistonmotion intoelectricity, thereby eliminating needless crankshaft linkages and rotational motion. As the dead center positions are not explicitlyidentified unlike crankshaft engines, the linear engine exhibits different stroke and compression ratio every cycle and shouldmanagethe unfavorable events like misfire, rapid load changes, and overfueling without the energy storage of a flywheel. Further, theapparatus control and management strategy is difficult for OLEA when compared to conventional engines and depends on thecombustion event influencing the translator dynamics. In this research paper, theMATLAB�/Simulink numerical model of a singlecylinder, mechanical spring assisted, 2-stroke natural gas fueled, spark-ignited OLEA was investigated to enhance the perceptionof the coupled system.The effect of combustion and heat transfer characteristics on translator dynamics and performance of OLEAwere analyzed by usingWiebe form factors, combustion duration, and heat transfer correlations. Variation in theWiebe form factorsrevealed interesting insights into the translator dynamics and in-cylinder thermodynamics of a coupled system. High translatorvelocity, acceleration, and higher heat transfer rate were favored by low combustion duration.

1. Introduction

Tightening exhaust emissions and greenhouse gas regulationsplace great strain on the engine manufacturers to meetregulatory and consumer demands. Further, the limitedresources of fossil fuels and rising energy prices necessitatethe investigation of highly efficient alternative engine tech-nology [1]. Considering these setbacks, the most desirableengine should be highly productive, durable, inexpensive,and socially acceptable, while marginal improvements likesophisticated control, increased compression ratio, variablevalve compression, and high-pressure fuel injection are avail-able. These cutting-edge technologies may not characterizethe level of improvement required to sustain the range ofdemands. Even though many researchers believe that hybridelectric vehicles are a satisfactory solution to the problem,they still depend upon the power density and reliability ofconventional crankshaft engine technology [2].

In the interest of engine efficiency, fuel flexibility, cost,and complexity, it is advisable to go for a new technologythat can fulfill power and consumer demands. An OscillatingLinear Engine Alternator (OLEA), which converts the recip-rocating motion of the piston to electricity, is considered asa viable alternative to fulfill power and consumer demands.The motion of the translator rod is decided merely by theforces acting on it [3]. Furthermore, the OLEA operates onlyon a few moving parts, that is, translator rod and mechanicalsprings. The elimination of crankshaft linkages in the designallows unrestricted piston motion, thereby exhibiting differ-ent stroke and variable compression ratio every cycle [4, 5].

The reasons for the rapid pace and growing interest in theOLEA investigations among the engine research communityare stated below:

(i) Structural simplicity: the mechanical linkages torestrict the piston motion in the conventional slider-crank engines are eliminated in the design of OLEA,

HindawiJournal of CombustionVolume 2018, Article ID 2907572, 16 pageshttps://doi.org/10.1155/2018/2907572

2 Journal of Combustion

thereby reducing the number of moving parts andcomplexity in the design

(ii) Low frictional losses: the reduction in the number ofmoving parts in OLEA design lessens the frictionallosses in the device. Furthermore, the ideal OLEAdesign has no piston side forces induced by the slider-crank mechanism. A greater percentage of the fric-tional losses is attributed to piston ring frictionallosses [6]

(iii) Fuel flexibility: a wide variety of alternative fuels isused for combustion in OLEA with minor hardwarealterations [3]

(iv) High thermal efficiency: relative to the slider-crankengine, the OLEA has higher thermal efficiency andhigher power density due to reduced weight. Further-more, the short residence of the piston at the TopDead Center (TDC) and a faster expansion stroke arebeneficial for reducing heat transfer losses, therebyimproving the thermal efficiency [7]

(v) Minimal vibration: elimination of crankshaft mech-anical linkages reduces the associated forces andmoments in the OLEA system, thereby cutting backthe vibrations in the OLEA systemwhen compared tocrankshaft engine. However, of all the OLEA configu-rations, the opposed piston configuration with equalpiston masses enjoys the benefits of minimal vibra-tions, whereas single cylinder OLEA is more prone tothe vibrations [5, 7]. The vibrations of the dual cylin-der configuration lie in between the single cylinderand opposed piston configuration. However, for thesingle piston and dual piston OLEA configurations,balancing issues due to mounting the engine need tobe addressed

Though OLEA technology is considered as a viable optionto replace the crankshaft technology, there are certain chal-lenges associated with this technology:

(i) Starting: the OLEA cannot be cranked just likeconventional crankshaft engines and requires specialmethods for startup. Most OLEA devices are startedby running the alternator as a motor until desiredcompression ratio is reached [5]

(ii) Misfiring: due to the absence of flywheel, the rapidload changes and misfires will affect the translatordynamics for the upcoming stroke and eventuallyresult in the stopping of the engine [8]

(iii) Device control: as the OLEA exhibits cycle to cyclevariability, the mistiming of fuel injection and igni-tion results in the development of unfavorable eventslike misfires and stalls [7]

Grounded on the above-mentioned plusses and minuses ofOLEA, a number of investigations of both single and dualcylinder types have been published [3, 5, 7–9]. In the presentinvestigation, single cylinder design assisted by mechanicalsprings is investigated using numerical simulation.

Figure 1: Illustration of experimental rig of free piston engine atWVU in 1998 [14].

2. Reported OLEA Prototypes

The idea of the development of free piston engines is orig-inally credited to Pescara who started his work in 1922 anddeveloped the first Pescara compressor based on SI combus-tion in 1925 and the second Pescara compressor based on CIcombustion in 1928 [10, 11]. For an extensive understandingon the development of OLEA technology in the 20th century,Aichlmayr compiled a complete timeline of events [12].

In 1995, Callahan et al. from theUniversity of Texas evalu-ated the scope of free piston engine as a supplementary powersource for a hybrid electric vehicle with different engineand alternator configurations [13]. As per their findings, animprovement in the efficiency was observed for the tailoredalternator generator based on the translator velocity profile.In 1998, Nigel Clark et al. from West Virginia University(WVU) published two research papers involving fundamen-tal analysis of a linear engine and experimental verification.The first paper described themodeling of translator dynamicsusing Newton’s second law with instantaneous heat rejectionand addition using an Otto cycle [5]. The final second-orderdifferential equation was solved to analyze the piston motionand velocity, revealing important insights into the translatordynamics. The illustration of the successful prototype devel-oped by WVU research group in 1998 is shown in Figure 1.

The second publication describes the prototype modelbuilt from off-the-shelf components and operated on two-stroke, Spark Ignition combustion cycle permitted for a max-imum compression ratio of 8:1. A useful power output of 316Wwas developed through stable operation of the engine [14].

At the same time,VanBlarigan et al. fromSandiaNationalLaboratories (SNL) investigated the usage of HomogeneousCharge Compression Ignition (HCCI) with an extensiverange of fuels for different stoichiometric ratios and initialtemperatures [15].The significant performance improvementwas observed in HCCI case. Following the same line ofresearch, HCCI combustion for hydrogen fuel was modeledusing a single zone chemical kinetics [16]. Iterative simu-lations showed rapid HCCI combustion with improvementin thermal efficiency and reduction in NOx emissions whencompared to conventional crankshaft engines.

In the year 2000, a German company, FEV EngineTechnology, explored several auxiliary power sources for

Journal of Combustion 3

hybrid powertrains and identified that the OLEA engines area viable option to substitute for fuel cells with reference tocost and efficiency [17]. In 2002, Shoukry fromWVUworkedon the concept of four-stroke OLEA by building a detailedmodel.The comprehensivemodel analyzed the importance ofstoichiometric ratio, friction, translatormass, geometry of thesystem, and injection timingwith respect to engine frequencyand thermal efficiency [18]. In 2002, Van Blarigan fromSNL research team developed a loop-scavenged system inKIVA software and aimed at the optimization of scavengingparameters for maximized performance [19].

In the year 2003, the Australian company PempekSystems Pty. Ltd. presented their third prototype enginegenerator FP3. Their publications reported a 25 kW freepiston systemwith 50% thermal efficiency and 93% alternatorconversion efficiency. Furthermore, their design includesspecial gas exchange passages unlike conventional portdesign [20].

Starting in 2007, Mikalsen and Roskilly from New CastleUniversity published an article depicting a broad review ofthe history, development, and the applications of free pistonengine generator [21]. In the year 2009, the same groupfrom Newcastle University developed a Computational FluidDynamics (CFD) model to calculate the engine out exhaustemissions from the linear device and assessed them with anequally scaled diesel engine. In the year 2010, they presentedtheirwork in regulating the pistonmotionusing feed-forwardprediction of the TopDeadCenter position in order to governthe fuel flow [22, 23].

Toyota is currently developing a single cylinder, 10 kW,gas spring assisted, opposed piston engine as an auxiliarypower source in a hybrid electric vehicle. The accompany-ing publications reported by Toyota are presented here assupplemental information [9, 24]. Another LEA has beenconstructed by Tatarnikov et al. from Moscow PolytechnicUniversity and has produced 16.87 kW [25].

Beginning in 2014, researchers at WVU began a newexamination aimed at the development of high frequency,spring assisted prototype used as aCombinedHeat andPower(CHP) generator at home level [26]. The working prototypeis based on a two-stroke, natural gas fueled, spark-ignitedsingle cylinder engine assisted with mechanical springs. Theillustration of the prototype under development at WVU isshown in Figure 2.

Most of the OLEA prototypes mentioned here employa two-stroke thermodynamic cycle. In 2002, Van Blari-gan from SNL research team developed a loop-scavengedsystem in KIVA software and aimed at the optimizationof scavenging parameters for maximized performance [19].Different options were analyzed and compared for loop,hybrid-loop, and uniflow scavenging methods with differentdelivery options. The CFD results indicated that the uniflowscavenging geometry with low intake pressure attains bestengine efficiency and emission characteristics [27]. In 2011,Mao et al. discussed the scavenging performance of the freepiston engine by varying engine effective stroke, valve timing,and intake pressure. Their simulation findings suggested thathigher trapping and scavenging efficiencies were obtainedfor a combination of low bore to stroke aspect ratio engine

Figure 2: Illustration of experimental rig of OLEA at WVU.

with low intake pressure and long valve overlapping timing[28].

In this investigation, the gas exchange process is achievedby using scavenging and exhaust ports [29]. The scavengingprocess is employed by opening and closing of scavengingport, whereas exhaust blowdown process is achieved by usingopening and closing of the exhaust port. These scavengingand exhaust ports are opened and closed according to thelocation of translator position. The location and the geomet-ric dimensions of these ports are provided as an input tothe numerical model. The mass flow rates for the scavengingand exhaust gas process are modeled by using perfect gasmixingmodel based on pressure differential method [26] andtheir respective intake and exhaust enthalpies are provided inthe numerical model section of this paper. The inefficienciesdue to scavenging gas exchange process are categorized intofuel energy losses. Although there exist slight variations inthese losses for the concepts presented in this paper, they arenot significant enough when compared to other losses in theengine.

3. Fundamental Physics-Based Model

Similar to the fundamental analysis of the dual cylindersystem [8], the basic model with simplified assumptions isused to analyze the single cylinder linear engine system. Theschematic diagram of the single cylinder Oscillating LinearEngine Alternator (OLEA) under study is shown in Figure 3.

An Oscillating Linear Engine Alternator (OLEA) inFigure 3 consists of four major components: internal com-bustion engine, linear electric machine, translator rod, andmechanical springs. It works on the principle of convertingthe linear piston motion to electricity by using a centrallymounted linear electric machine. Further, the translator rodand springs are the only moving parts in the system andthe motion of the translator rod is decided merely by thesummation of forces acting on it. Let Lc represent the lengthfrom alternator housing midpoint to the cylinder head,whereas Lp represents the length from alternator housingmidpoint to the engine piston crown [8]. Assuming that thetranslator rod moved the distance x towards left, at any time

4 Journal of Combustion

Figure 3: Schematic diagram of OLEA.

instance, the instantaneous engine cylinder volume (𝑉𝑐𝑦𝑙) canbe found out using geometrical parameters defined above.

𝐿 = 𝐿𝑐 − 𝐿𝑝 (1)

𝑉𝑐𝑦𝑙 = 𝜋𝑏24 (𝐿 + 𝑥) (2)

Assuming that the pressure in the engine cylinder is Pmpwhen the translator zero matches the alternator housingmidpoint (i.e., x = 0) and by modeling the expansion andcompression, using polytropic equation yields in-cylinderpressure and cylinder pressure forces as shown in the follow-ing equations:

𝑃𝑐𝑦𝑙,𝑖 = 𝑃𝑚𝑝 { 𝐿𝐿 + 𝑥}

𝛾

(3)

𝐹𝑐𝑦𝑙,𝑖 = 𝜋𝑏24 𝑃𝑚𝑝 { 𝐿

𝐿 + 𝑥}𝛾

(4)

In (3) and (4), the subscripts mp and cyl represent midpointand cylinder, whereas the terms 𝛾, b, and x denote specificheat ratio, cylinder bore, and translator displacement, respec-tively.

Similarly, the spring force is provided by the followingrelationship:

𝐹𝑠𝑝𝑟,𝑙 = 𝑘 (𝐿𝑓𝑙 − (𝑥 + 𝐿𝑝))𝐹𝑠𝑝𝑟,𝑟 = 𝑘 (𝐿𝑓𝑙 + (𝑥 − 𝐿𝑝))

(5)

In (5), the subscripts l, r, spr, and fl represent left and rightrelative to the midpoint of alternator housing, springs, andfree length of the springs, whereas k denotes springs stiffness.For basic understanding of the system, the engine follows theOttoCombustion cycle.The following assumptions are incor-porated to the fundamental model owing to the complexity:

(i) Addition and rejection of heat take place instanta-neously at top and Bottom Dead Centers.

(ii) Cylinder gases are presumed to undergo polytropiccompression and expansion.

(iii) Work output is merely characterized as a spatiallydependent profile that is influenced by the translatorrod dynamics.

While the instantaneous heat addition and heat rejection areonly for the basic understanding of translator dynamics, thenumerical model in the upcoming section considers a moredetailed version of heat addition and heat rejection. Highertranslator velocity, in-cylinder pressure, and system efficiencyare favored by the assumption of instantaneous heat addition.

With the assumptions mentioned above, when the pistonreverses its direction at the TopDeadCenter (TDC) of enginecylinder, constant volume heat addition occurs. By using thefirst law of thermodynamics for a closed system and idealgas equation, the heat addition is shown in the followingequations:

𝑄𝑖𝑛 = 𝑚𝑐𝑦𝑙𝑔𝑎𝑠𝐶V (𝑇𝑐𝑦𝑙,𝑓 − 𝑇𝑐𝑦𝑙,𝑖) (6)

𝑄𝑖𝑛 = 𝑚𝑐𝑦𝑙𝑔𝑎𝑠𝐶V ( 𝑃𝑐𝑦𝑙,𝑓∗𝑉𝑐𝑦𝑙,𝑓𝑚𝑐𝑦𝑙𝑔𝑎𝑠∗𝑅𝑐𝑦𝑙𝑔𝑎𝑠 −

𝑃𝑐𝑦𝑙,𝑖∗𝑉𝑐𝑦𝑙,𝑖𝑚𝑐𝑦𝑙𝑔𝑎𝑠∗𝑅𝑐𝑦𝑙𝑔𝑎𝑠)

𝑄𝑖𝑛 = 𝐶V𝑉𝑐𝑦𝑙,𝑖𝑅𝑐𝑦𝑙𝑔𝑎𝑠 (𝑃𝑐𝑦𝑙,𝑓 − 𝑃𝑐𝑦𝑙,𝑖)

(7)

In (6) and (7), the terms 𝑄𝑖𝑛, 𝑚𝑐𝑦𝑙𝑔𝑎𝑠, 𝐶V, P, V, T, and Rdenote heat energy input, mass of cylinder contents, specificheat at constant volume, pressure, volume, temperature, andgas constant, respectively. Since the heat addition occurs atconstant volume, the initial and final volumes are equal.

𝑉𝑐𝑦𝑙,𝑖 = 𝑉𝑐𝑦𝑙,𝑓 = 𝜋𝑏24 (𝐿 + 𝑥𝑟) (8)

where 𝑥𝑟 represents the distance translator that moved toreach the Top Dead Center of the engine cylinder.

Substituting (8) into (7) and reorganizing for final pres-sure yield the following equation:

𝑃𝑐𝑦𝑙,𝑓 = 4𝑄𝑖𝑛𝜋𝑏2 (𝛾 − 1𝐿 + 𝑥𝑟) + (𝑃𝑚𝑝 {

𝐿𝐿 + 𝑥}

𝛾) (9)

By using polytropic relationships and the in-cylinder pressureat Top Dead Center, the pressure in the in-cylinder for anytranslator position and cylinder pressure force are given inthe following equations:

𝑃𝑐𝑦𝑙,𝑓𝑉𝛾𝑐𝑦𝑙,𝑓 = 𝑃𝑐𝑦𝑙𝑉𝛾𝑐𝑦𝑙𝑃𝑐𝑦𝑙= (4𝑄𝑖𝑛𝜋𝑏2 (

𝛾 − 1𝐿 + 𝑥𝑟) + (𝑃𝑚𝑝 {

𝐿𝐿 + 𝑥}

𝛾))(𝐿 + 𝑥𝑟𝐿 + 𝑥 )𝛾

(10)

𝐹𝑐𝑦𝑙 = 𝑄𝑖𝑛 (𝛾 − 1) (𝐿 + 𝑥𝑟)𝛾−1(𝐿 + 𝑥)𝛾 + 𝜋𝑏24 𝑃𝑚𝑝 { 𝐿𝐿 + 𝑥}

𝛾

(11)

By using Newton’s second law of motion, the second-orderdifferential equation for force balance is written as follows:

𝐹𝑐𝑦𝑙 − 𝐹𝑠𝑝𝑟 − 𝐹𝑤 = 𝑚�� (12)

Journal of Combustion 5

The term𝐹𝑤 includes both frictionwork and useful alternatorwork output. The simple compression and expansion springforce 𝐹𝑠𝑝𝑟 are comprised of both left and right spring force.The equations for 𝐹𝑠𝑝𝑟 and 𝐹𝑤 are presented as follows:

𝐹𝑤 = 𝐹𝑎𝑙𝑡 + 𝐹𝑓𝑟𝑖𝑐𝐹𝑠𝑝𝑟 = 𝐹𝑠𝑝𝑟,𝑟 − 𝐹𝑠𝑝𝑟,𝑙 (13)

The frictional force includes piston ring frictional force andviscous damping force. The piston ring frictional force isassumed as a function of pressure differential above andbelow the ring.The corresponding equation for the frictionalforce is provided as follows:

𝐹𝑓𝑟𝑖𝑐 = 𝑐𝑓�� + 𝑐𝑓 (𝐹𝑟𝑔 + 𝜋𝑇𝑟𝑔𝑏 (𝑃𝑐𝑦𝑙 − 𝑃𝑟𝑔)) (14)

The terms 𝑃𝑟𝑔, 𝐹𝑟𝑔, 𝑇𝑟𝑔, b, and �� represent pressure belowthe piston ring, piston ring stiffness force, axial thickness ofpiston ring, engine cylinder bore, and translator rod velocity,respectively. The friction coefficient 𝑐𝑓 is calculated basedon Blair’s relationship depending on engine operation andgeometry.

𝐶𝑓 = 12𝐶𝑉𝑠𝑤 (60𝑓) (15)

The terms C, 𝑉𝑠𝑤, and 𝑓 characterize leading coefficient,swept volume, and average engine frequency in Hz. Theleading coefficient in the present investigation is assumed as0.06 based on the research findings of German AerospaceCenter (DLR) [30].

The alternator work output is assumed as spatial profilethat depends upon the translator rod velocity. Aichlmayr inhis dissertation proposed standard alternator work profilesfor a free piston linear engine [12]. The work profile of thefollowing form is selected for the present investigation.

𝐹𝑎𝑙𝑡 = 𝐴 cos(𝜋𝑥2𝐿 ) (16)

The work amplitude (A) is calculated by matching the engineoutput with the alternator load. Combining all the equationsand substituting them in (12) yield (17).The second-order dif-ferential equation for the force balance (17) is solved to obtaina closed-form solution for translator dynamics (i.e., relationsbetween translator position, velocity, and acceleration). Thechanges in the combustion parameters are explained in adetailed manner in Numerical Model Description.

𝑄𝑖𝑛 (𝛾 − 1) (𝐿 + 𝑥𝑟)𝛾−1(𝐿 + 𝑥)𝛾 + 𝜋𝑏24 𝑃𝑚𝑝 { 𝐿𝐿 + 𝑥}

𝛾

− 2𝑘𝑥−𝑐𝑓�� − 𝑐𝑓 (𝐹𝑟𝑔 + 𝜋𝑇𝑟𝑔𝐵 (𝑃𝑐𝑦𝑙 − 𝑃𝑟𝑔))− 𝐴 cos(𝜋𝑥2𝐿 ) = 𝑚�� = 𝑚��

𝑑��𝑑𝑥

(17)

4. Numerical Model Description

The interpretation of management and control of OLEAdepends upon the sophisticated numerical simulations.

Although there aremultiple approaches formodeling a singlesubmodel, the total time needed to simulate multiple cyclesof operation is not feasible owing to high-speed computingand costs associated. For example, one can model the fric-tional characteristics of piston rings in different ways. Onepossible approach is to employ the use of iteration-basedReynolds hydrodynamic equation applied across multiplezones around piston rings. However, this method is compu-tationally expensive and time-consuming. To overcome thehindrances, many researchers simply assume the frictionalforces as a function of piston velocity and pressure differ-ential between in-cylinder and interring pressure. Similarly,substantial effort has been made to incorporate a robustand sophisticated combustion model without restricting theattempt of extreme computational needs.

Even though the fundamental-physics-based modeloffers valuable perception into the operation and behaviorof OLEA, more realistic simulation includes highlysophisticated heat addition, heat rejection, and alternatormodels. Since closed-form solutions are unlikely to existfor more detailed modeling, MATLAB/Simulink time-based model was developed to understand the behavioralcharacteristics of linear engine.

Just as in the physics-based model presented above,Newton’s second law of motion is used to define translatordynamics. To accommodate more accurate heat additionand heat transfer in the numerical analysis, the in-cylinderpressure is expressed by a first-order differential pressureequation that is shown as follows:

𝑑𝑃𝑑𝑡= −𝑃𝛾

𝑉𝑑𝑉𝑑𝑡

+ (𝛾 − 1𝑉 )(𝑑𝑄𝐻𝑅𝑑𝑡 − 𝑑𝑄𝐻𝑇𝑑𝑡 + 𝑑𝐻𝑖𝑛𝑑𝑡 − 𝑑𝐻𝑜𝑢𝑡𝑑𝑡 )(18)

The terms P, V, 𝛾, 𝑄𝐻𝑅, 𝑄𝐻𝑇, 𝐻𝑖𝑛, 𝐻𝑜𝑢𝑡, and 𝑡 representpressure, volume, ratio of specific heats, heat released dueto combustion, heat transfer between the cylinder walls andgas, inlet enthalpy, outlet enthalpy, and time, respectively.The inlet and outlet enthalpies depend upon the mass flowrates due to scavenging and exhaust blowdown process,temperatures, and specific heats.The scavenging and exhaustblowdownmass flow rates are calculated using perfectmixingmodel that is based on the pressure differential [26]. Theblow-by losses are also included in the enthalpy losses flowingout of the cylinder.

Compressed Natural Gas (CNG) is selected as a fuelfor this investigation. The specific heats at constant pressureand constant volume for all the natural gas constituentsare dependent on temperature and are defined according tothe tables. The composition of natural gas selected for thisinvestigation is shown in Table 1.

The first-order differential equation for heat transferfrom the engine cylinder takes the form shown in (19).The term 𝑇𝑤 denotes wall temperature and it is assumedthat the temperature is the same over the piston crown,

6 Journal of Combustion

Table 1: Composition of natural gas used in this investigation.

Component % of composition by volumeMethane 90%Ethane 9%Propane 1%

wall, and cylinder head. The wall temperature in the currentinvestigation is adapted from a slider-crank test rig availableat WVU.

𝑑𝑄𝐻𝑇𝑑𝑡 = ℎ𝐴 (𝑇 − 𝑇𝑤) (19)

The convective heat transfer coefficient (ℎ) can be evaluatedusing several empirically associated formulae defined byHohenberg [31, 32], Woschni [33], and Annand [34]. Thecorrelations presented above are for slider-crank drivenengines. Empirical models for variable and unusual motionof linear engine are not available, but the slider-crank modelscan be adapted with some confidence. For the base case,the Hohenberg heat coefficient formulation was used, whilethe Woschni and the Annand formulae were employed inthe investigation for comparison. A similar comparison wasemployed by Robinson for dual cylinder and is repeated herefor the single cylinder device [35]. Hohenberg’s convectiveheat transfer coefficient relationship with geometrical andoperational parameters is provided in the following equation:

ℎ = 𝑎𝑉𝑏𝑇𝑐𝑃𝑑 (𝑉𝑝 + 1.4)𝑒 (20)

In (20), 𝑉, 𝑇, 𝑃, and 𝑉𝑝 denote volume in 𝑚3, temperaturein K, pressure in bar, and average piston speed in m/s,respectively.The terms 𝑎, 𝑏, 𝑐, 𝑑, and 𝑒 are empirical constantsand their values are 130, -0.06, -0.4, 0.8, and 0.8 in that order.

Heat addition in the combustion chamber depends uponcomplex pressure wave dynamics, flame front propagation,quenching, preignition, and knock characteristics of workingfluid. Linear engine simulations with detailed chemical kinet-ics cannot give accurate results in reasonable computationaltimes. Further, for a coupled systemwithmultiple subsystemsand multicycle modeling, it is not feasible to use detailedchemical kinetics model considering the computational timeand costs. To overcome the hindrances in the computationaltime and costs associated, a time-based empirical Wiebefunctionmodel was used formodeling the rate of combustionin the present investigation [36]. Furthermore, the potentialfor preignition and knock is neglected.

𝜒 (𝑡) = 1 − exp[−𝑎(𝑡 − 𝑡𝑠𝑜𝑐𝑡𝑐𝑑 )𝑏+1]𝑑𝑄𝐻𝑅𝑑𝑡 = }𝑐𝑜𝑚𝑏𝐻𝑉𝑓𝑢𝑒𝑙 𝑑𝜒 (𝑡)𝑑𝑡

(21)

The combustion efficiency (}𝑐𝑜𝑚𝑏) is provided as an inputvariable that is tuned from crankcase test rig. This combus-tion efficiency of 95% is realistic for the natural gas and wasobtained from the similar size crankcase test rig experiments.

The combustion efficiency is influenced by many factorswithin the free piston engine system, so modeling }𝑐𝑜𝑚𝑏 isout of this research paper’s scope. Further, the variations inthe Wiebe form factors and combustion duration are notaccompanied by the changes in the combustion efficiencyas the effect of combustion efficiency deviation was foundto be small based on the crankcase investigation of similarsize. The form factors ”a” and ”b” in the time-dependentWiebe function are set to 5 and 2, respectively [36]. Theterm ”𝑡𝑐𝑑” denotes the combustion duration that is set to 1ms for base case. However, the variations in the combustionduration are examined in the upcoming section of this paperfor comparison. The total heat value (HV) of combustioncharge relies upon the fuel and equivalence ratio of mixtureinside the combustion chamber.

The important variable in a time-based Wiebe functionis the prediction of start of combustion (SOC). Since theOLEA system in the current exploration is modeled forSpark Ignition combustion cycle, the start of combustionis predicted by using spark generation signal that acts as atrigger to activate the ignition system. The spark controllersignal is generated when the translator rod velocity exceedsa threshold value. The threshold velocity is provided asan input variable to the controller and can be modifiedto achieve either early ignition or late ignition or optimalignition according to the experiments. Once the spark istriggered, the combustion occurs according to theWiebe heatrelease correlation based on the form factors and combustionduration defined earlier.

The numerical model follows the samemodel for the fric-tional losses as explained earlier in the fundamental-physics-based analysis section. A linear alternator generator designedwith permanent magnets is coupled to the translator rod inorder to generate electricity from the reciprocating motioncaused by the combustion of fuel. An equivalent circuit alter-nator coil approach is used to define the energy output fromthe linear alternator. The alternator force comprises bothelectromagnetic and cogging forces. The electromagneticforce is modeled as a function of translator velocity, whereasthe cogging force is the thrust force from the alternator thatis needed to overcome the interaction of magnetic fields frompermanent magnets. It is provided as an input table obtainedfrom finite element analysis for different translator positions.The relationship for the alternator electromagnetic force ispresented in the following equation [37]:

𝐹𝑤 = 𝐶𝑎𝑙𝑡𝑊𝑐�� (22)

The term 𝐶𝑎𝑙𝑡 denotes constant flux change depending ontranslator rod position. The weight of the controller (𝑊𝑐)scales the alternator force according to the variation in thecompression ratio. If the compression ratio of the engineis increased, higher alternator force is applied, whereas thealternator load is reduced for corresponding reduction incompression ratio. This controller weight forces the OLEAsystem to operate within certain limits of target compressionratio, thereby ensuring steady-state operation.

The stability of OLEA is determined by governing loadequation for translator dynamics in tandemwith themanage-ment of the combustion events. If more net energy is released

Journal of Combustion 7

0 0.005 0.01 0.015 0.02Position (m)

−6

−4

−2

0

2

4

6

Velo

city

(m/s

)

Figure 4: Translator dynamics for base case. The fairly egg shapevariation in the translator velocity suggests the domination ofcombustion forces from single cylinder.

−3000−2000−1000

0100020003000400050006000

42 60−4 −2−6Velocity (m/s)

Acc

eler

atio

n (m

/s2 )

Figure 5: Translator dynamics for base case (clockwise). The peakin the acceleration of the translator corresponds to the peak in thein-cylinder pressure due to heat release.

in the course of combustion than is consumed by lossesand the alternator, with all else being equal, the engine willachieve higher compression ratio on the subsequent cycle. Ifthis process continues, additional energy will be gained inthe system and the translator velocity at mid-stroke will behigher in contrast to prior cycles. This is analogous to thestorage of more energy, as higher speed of the reciprocatingcomponents and flywheel in a conventional engine, if thedelivered power exceeds the applied load.

Similarly, if inadequate fuel is delivered to the engineor if combustion efficiency is poor, the heat released duringcombustion is reduced and the compression ratio decreasesin successive cycles. However, the actual operation, manage-ment, and stability of such a variable compression ratio linearengine depend upon the numerous events taking place in thewhole alternator-engine-springs system. Optimized controlfor stable operation of linear engines is a subject warrantingmore research.

5. MATLAB/Simulink Model Results

The modeling results presented in this paper exhibit thechange in the operation of OLEA as Wiebe form factors,combustion duration, and heat transfer parameters are mod-ified. To begin with, the simulation results for a base case arepresented in Figures 4–9. For the base case, the heat release

AlternatorSpring

FrictionPressure

−1000

0

1000

2000

3000

4000

5000

Forc

es (N

)

59.9759.96559.96Time (s)

59.975 59.98559.98

Figure 6: The breakdown of forces acting on the translator rod atsteady-state operation of OLEA. The term ”pressure” represents thein-cylinder pressure forces acting on the translator rod.

84 62 100 14 16 18 2012Volume (cc)

01020304050607080

Pres

sure

(bar

)

Figure 7: Variation of in-cylinder pressure as a function of volume.

and heat transfer were modeled by using time-based Wiebefunction andHohenberg’s correlation, respectively.The inputand steady-state parameters for base case are listed in Table 2.

Figures 4 and 5 explain the dynamic characteristics ofsingle cylinder linear engine alternator system. Figure 4 rep-resents the variation in the translator rod velocitywith respectto translator displacement. The nonsymmetrical characteris-tic of translator velocity in Figure 4 is due to the dominanteffect of in-cylinder combustion forces over the translatordynamic system. Towards the right of velocity profile, thevelocities are fairly small due to the absence of combustionforces. The steep nature of the velocity profile at the deadcenter is an explanation for the short residence of the pistonat the dead centers in OLEA. Figure 5 shows the variation inthe acceleration with respect to translator velocity. The steeprise in the acceleration at the Top Dead Center is due to theinitiation of combustion once the translator velocity exceedsthe threshold spark timing velocity.

The various forces acting on the translator rod wereplotted against time in Figure 6. The term ”pressure” in thelegend represents the cylinder pressure forces acting on thetranslator rod. It is evident that the cylinder combustionforces dominate the next peak forces (i.e., mechanical springforces) by a factor of 4-5. The odd-looking alternator forcesin Figure 6 are due to the juxtaposition of poles. Since the

8 Journal of Combustion

59.966 59.968 59.97 59.972 59.974 59.976 59.978 59.98 59.982500

1000

1500

2000

Tem

pera

ture

(K)

59.966 59.968 59.97 59.972 59.974 59.976 59.978 59.98 59.982

Time (s)

0

Hea

t flux

(W/m

)

−3500−3000−2500−2000−1500−1000

−500

Figure 8: Top: variation of in-cylinder temperature against timefor one steady-state cycle of operation. Bottom: variation of heatflux modeled using Hohenberg correlation. The secondary peak inthe temperature curve denotes the gas exchange process from theexhaust.

2%6%

22%

16%

< 1% 9%

39%

6%

Combustion lossesFuel energy lossesHeat transfer lossesAlternator work

Alternator lossesFrictionExhaust heatBlow-by

Figure 9: Distribution of combustion energy pathways duringsteady-state operation. Fuel energy losses represent the flow lossesdue to pressure differential in the intake and exhaust system.

mechanical flexures are considered as simple compressiblesprings, the spring forces are sinusoidal in nature. The PVdiagram for the base case is presented in Figure 7.

To supplement the plots presented above, the variation ofheat flux with in-cylinder temperature is shown in Figure 8.A closer look at heat flux in Figure 8 shows that the rapidincrease in the heat flux is due to rise in cylinder temperatureassociated with combustion heat release. The heat transfer

Table 2: Input and steady-state parameters for fundamental caselinear engine.

Cylinder bore 31.02 mmMaximum cylinder stroke 24.97 mmEngine displacement volume 18.87 ccEquivalence ratio 1.02Exhaust port location from head 15.5 mmTranslator frequency 88.25 HzLHV of natural gas 49.5 MJ/kgIntake temperature 300 KIntake pressure 100 kPaAlternator efficiency 95 %Combustion efficiency 95 %Max in-cylinder pressure 77.4 barMax in-cylinder temperature 2368 KCompression ratio 15Translator mass 1.2 kgWall temperature 450 KSpring stiffness 30180 N/mNumber of springs 6System efficiency 16.48 %

flux that depends upon the instantaneous area available, in-cylinder temperature, and cylinder wall temperature fallsduring the expansion stroke due to increase in the instan-taneous area. Further, the temperature that decides the heattransfer also follows the same trend until the commencementof exhaust and recharging process.

Figure 9 shows the breakdown of steady-state OLEAenergy balance for a set of operating variables.Theoverall sys-tem efficiency is approximated at 16.48% with 22% and 39%of the input fuel energy lost to in-cylinder heat transfer andexhaust heat, respectively. The cylinder heat transfer beingthe second major energy loss has significant influence on thetranslator dynamics andOLEA system efficiency importantly.The fuel energy losses represent the flow losses in the intakesystem due to pressure differential in the intake and enginecylinder, whereas combustion losses represent the lossesrelated to combustion inefficiency. If the in-cylinder pressureis greater than crankcase pressure, then fuel air mixture flowsinto the crankcase, which is referred to as blow-by losses.These blow-by losses are calculated based on the pressure dif-ferential method after the closure of exhaust and intake ports.

5.1. Variation in Wiebe form Factors. An investigation iscarried out to understand the variation in the translatordynamics and performance for different Wiebe form factorswhile maintaining all other parameters constant [36]. Fur-ther, it is of utmost importance to examine various values ofform factor in order to get a goodmatch for the experimentalin-cylinder pressure traces. The mass fraction of the fuelburned defined by time-based Wiebe function will neverreach unity. At a given time equal to combustion duration,theMFB is less than unity by a factor 𝑒−𝑎. For instance, at timeequal to combustion duration, if the value of ”a” is assumed as

Journal of Combustion 9

a = 5.5a = 5

a = 4.5a = 4

−6

−4

−2

0

2

4

6Ve

loci

ty (m

/s)

0.005 0.01 0.015 0.02 0.0250Position (m)

4 4.5 5 5.5 63.5Wiebe a value

55.15.25.35.45.55.65.75.85.9

6

Max

vel

ocity

(m/s

)

Figure 10: Variation in translator velocity with respect to position for different values of Wiebe parameter ”a.”

b = 1.5b = 2b = 2.5

Max

vel

ocity

(m/s

)

0.005 0.01 0.015 0.02 0.0250Position (m)

−6

−4

−2

0

2

4

6

Velo

city

(m/s

)

44.24.44.64.8

55.25.45.65.8

6

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 31Wiebe b value

Figure 11: Variation in translator velocity with respect to position for different values of Wiebe parameter ”b.”

5, the amount of MFB corresponds to 0%-99.32%; similarly,for a = 4, the amount of MFB corresponds to 0%-98.16%.The change in the form factor ”a” is not accompanied bythe change in the combustion efficiency. As the combustionefficiency is prescribed in the model, the changes in the heatrelease rate are taken care of by using mass fraction burnt.The form factor parametric sweep results provided interestinginsights into the translator rod dynamics and performance ofOLEA system.

Figures 10–17 show the modeling results for differentcases of form factors variation. Figures 10 and 11 represent thevariation in the translator velocity profile for form factor ”a”variation and form factor ”b” variation. Increasing the formfactor ”a” increased the translator velocity due to increase inthe mass fraction burned closer to unity, thereby increasingthe in-cylinder pressure forces. On the other hand, anincrease in the form factor ”b” reduced the translator velocity.This is due to the fact that, at any time step, the mass fractionburnt will be higher for lower form factor ”b.” It is evidentfrom themass fraction burned (MFB) profile plot for differentvalues of form factor ”b” which is shown in Figure 12. Forexample, at 150th time step, 63.3% of mass fraction is burntfor form factor ”b” value of 1.5, 62.1% ofmass fraction is burnt

for value of 2.0, and 60.2% of mass fraction is burnt for valueof 2.5, respectively. These variations in the MFB caused thevariations in the in-cylinder pressures and heat release rate.

As the translator acceleration is obtained from the time-based differentiation of velocity, the translator accelerationalso follows the same trend. The variation in the in-cylinderpressure traces for different values of form factors ”a” and”b” is shown in Figures 13 and 14. As the mass faction burntbecomes closer to the unity, the heat release input increaseswith an increase in the form factor, thereby causing theincrease in the pressure and in-cylinder temperature. Thetemperature that decides the heat flux causes the heat flux tofollow the same trend and is evident fromFigure 15. Similarly,increasing the form factor ”b” reduced the value of massfraction burnt at any time step when compared to lowervalues of form factor ”b.” Further, the gradual rise in theMFB burnt at higher form factor ”b” reduced the heat releaserate, thereby reducing the in-cylinder pressures at higherform factors. The heat flux also follows the same trend and isprovided in Figure 16. The major losses in the OLEA systemfrom the parametric sweep studies of Wiebe form factors arepresented in Figure 17. The heat transfer losses are increasedby increasing the form factor ”a” due to high temperatures

10 Journal of Combustion

b = 1.5b = 2b = 2.5

500 150 200 250100Time step

0.10.20.30.40.50.60.70.80.9

1

Mas

s fra

ctio

n bu

rned

Figure 12: Mass fraction burnt profile for different values of Wiebe parameter ”b.” At any time instant, the mass fraction burnt (MFB) ishigher for low value of ”b.”

a = 5.5a = 5

a = 4.5a = 4

161412 18 208642 100Volume (cc)

01020304050607080

Pres

sure

(bar

)

4 4.5 5 5.5 63.5Wiebe a value

50556065707580859095

100M

ax p

ress

ure (

bar)

Figure 13: Variation in in-cylinder pressure with respect to volume for different values of Wiebe parameter ”a.” The rise in the pressure withform factor ”a” is due to MFB becoming closer to unity for high form factor value.

20

b = 1.5b = 2b = 2.5

2 4 6 8 10 12 14 16 180Volume (cc)

01020304050607080

Pres

sure

(bar

)

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 31Wiebe b value

0102030405060708090

100

Max

pre

ssur

e (ba

r)

Figure 14: Variation in in-cylinder pressure with respect to volume for different values of Wiebe parameter ”b.” The fall in the pressure withform factor ”b” is due to the shape of MFB profile.

Journal of Combustion 11

a = 5.5a = 5

a = 4.5a = 4

a = 5.5a = 5

a = 4.5a = 4

1000 1500 2000500Time steps

−3500−3000−2500−2000−1500−1000

−5000

Hea

t flux

(W/m

)

1000 1500 2000 2500500Time steps

010203040506070

Pres

sure

(bar

)

Figure 15: In-cylinder pressure traces and heat flux variation with form factor ”a.” The higher the value of ”a,” the higher the heat flux due tohigh in-cylinder temperatures.

b = 1.5b = 2b = 2.5

b = 1.5b = 2b = 2.5

01020304050607080

Pres

sure

(bar

)

1000 1500 2000 2500 3000500Time steps

−4000−3500−3000−2500−2000−1500−1000

−5000

Hea

t flux

(W/m

)

1000 1500 2000 2500 3000 3500500Time steps

Figure 16: In-cylinder pressure traces and heat flux variation with form factor ”b.”

Exhaust heatHeat transfer

FrictionSystem efficiency

Exhaust heatHeat transfer

FrictionSystem efficiency

0

10

20

30

40

50

60

Perc

enta

ge o

f fue

l ene

rgy

(%)

4 4.5 5 5.5 63.5Wiebe a value

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 31Wiebe b value

05

101520253035404550

Perc

enta

ge o

f fue

l ene

rgy

(%)

Figure 17: Major energy losses comparison for different values of Wiebe form factors.

associated at higher values of ”a.” Further, a slight increase inthe system efficiencies is observed with increasing the Wiebeform factors.

5.2. Variation in Combustion Duration. The combustioncharacteristics in this investigation are characterized by using

Wiebe form factors and combustion duration. Further, thechanges in the combustion duration are not accompanied bythe changes in the combustion efficiency. It is presumed thatthe decrease in the combustion duration causes the imme-diate heat release, thereby improving system efficiency. Justlike steady-state parameters presented in Table 2, many stable

12 Journal of Combustion

0 0.005 0.01 0.015 0.02 0.025Position (m)

−6

−4

−2

0

2

4

6Ve

loci

ty (m

/s)

0 0.5 1 1.5 2 2.5Combustion duration (ms)

44.24.44.64.8

55.25.45.65.8

6

Max

vel

ocity

(m/s

)

Ｎ＝ = 0.5 msＮ＝ = 1 ms

Ｎ＝ = 1.5 msＮ＝ = 2 ms

Figure 18: Translator velocity profiles for different combustion durations. Higher velocities are attained at lower combustion duration due toinstantaneous in-cylinder forces.

2 4 6 8 10 12 14 16 18 200Volume (cc)

0102030405060708090

100

Pres

sure

(bar

)

Ｎ＝ = 0.5 msＮ＝ = 1 ms

Ｎ＝ = 1.5 msＮ＝ = 2 ms

0

20

40

60

80

100

120

Max

pre

ssur

e (ba

r)

0.5 1 1.5 2 2.50Combustion duration (ms)

Figure 19: In-cylinder pressure traces from the combustion chamber for different combustion duration. Higher pressures are favored bylower combustion due to instantaneous heat addition.

solutions are possible for successful operation of OLEA; onesuch solution is presented here. Figures 18–22 present thesimulation results for different combustion durations.

Figure 18 shows the variation in the velocity profilefor different combustion durations. Higher velocities areachieved at lower combustion durations. This is due to theinstantaneous heat addition that caused the rapid rise inthe pressure at almost constant volume at lower combustionduration. For higher combustion duration, the rise in theheat release rate is gradual rather than instantaneous. Withinstantaneous heat addition, higher pressures are achieved atlower combustion duration and are evident from Figure 19.Higher translator rod frequencies are observed at lowercombustion duration, which is evident from Figure 20.

Similarly, higher temperatures are attained due to reduc-tion in combustion duration causing greater heat transferrate, which is shown in Figure 21. Figure 22 shows thedistribution ofmajor losses ofOLEA for different combustiondurations. Due to higher in-cylinder temperatures attainedfor lower combustion duration, the heat transfer losses arehigher for low combustion duration. Further, the instanta-neous heat addition due to low combustion duration reduced

the exhaust thermal energy losses, whereas increasing thecombustion duration increased the exhaust thermal energylosses as the exhaust blow down occurred later in the stroke.The frictional losses that are modeled as a function of trans-lator velocity reduced with an increase in the combustionduration. From Figure 22, it is evident that the decrease in thecombustion duration increased the overall system efficiencyto a certain extent. Reducing the combustion efficiencyeven further reduced the overall system efficiency due topronounced effect of heat transfer losses when compared toother losses. At higher combustion duration, the exhaust heatlosses are more prominent even though the heat transfer andfrictional losses are reduced. This obvious effect of exhaustheat losses reduced the overall system efficiency for highercombustion duration.

5.3. Variation in Heat Transfer Correlation. Figures 23 and 24show the effect of different heat transfer correlations used todefine the heat losses in OLEA system. In these three cases,higher system efficiency and lower heat losses are observedfor Hohenberg correlation, while high heat losses andlower efficiency are obtained with Annand correlation. The

Journal of Combustion 13

0.5 1 1.5 2 2.50Combustion duration (ms)

80828486889092949698

100

Max

freq

uenc

y (H

z)

Figure 20: Variation in the translator frequency for different combustion durations. The reason for the higher frequencies is the greaterdominance of in-cylinder pressure forces at low combustion duration.

Ｎ＝ = 0.5 msＮ＝ = 1 ms

Ｎ＝ = 1.5 msＮ＝ = 2 ms

500 1000 1500 2000 25000Time steps

102030405060708090

100

Pres

sure

(bar

)

1000 1500 2000 2500500Time steps

−5000

−4000

−3000

−2000

−1000

0

Hea

t flux

(W/m

)

Ｎ＝ = 0.5 msＮ＝ = 1 ms

Ｎ＝ = 1.5 msＮ＝ = 2 ms

Figure 21: Variation of in-cylinder pressures and heat transfer flux for different combustion durations. Higher heat flux is attained due torapid rise in the cylinder temperature for low duration of combustion.

difference in the heat losses is associated with thermody-namic relationships, dissimilarities in in-cylinder pressuredomain, and subtle variations in translator dynamics.

6. Summary/Conclusions

The Oscillating Linear Engine Alternator (OLEA) has beeninvestigated relentlessly for few decades owing to the ben-efits offered by it over conventional crankshaft engines.To augment the understanding of OLEA operation andmanagement, the fundamental physics-basedmodel has beendescribed. With the assistance of well-built numerical simu-lation, a parametric exploration has been carried out to studythe effect of combustion and heat transfer characteristics onthe translator dynamics and performance of OLEA.

The combustion characteristics are characterized by usingWiebe form factors and combustion duration. Increase in theform factor ”a” increased the mass fraction burned closer tounity, which further increased the translator velocity, cylinderpressure, temperature, and heat transfer rate. On the samenote, low value of form factor ”b” resulted in the maximumamount of mass fraction burned at any time step whencompared to higher values of ”b” and thereby exhibited sharprise in the pressure and heat transfer rate. Further, a slight

increase in the system efficiencies is observed with increasingthe Wiebe form factors.

Combustion duration had a strong effect on the translatordynamics, in-cylinder pressure, and OLEA behavior. Hightranslator velocity, high acceleration, and rise in maximumcombustion chamber pressure were favored by low com-bustion duration. The decrease in the combustion durationincreased the system efficiency to a certain extent. Reducingthe combustion efficiency even further reduced the systemefficiency due to pronounced effect of heat transfer losseswhen compared to other losses. At higher combustionduration, the exhaust heat losses are more prominent eventhough the heat transfer and frictional losses are reduced.This obvious effect of exhaust heat losses reduced the systemefficiency for higher combustion duration.

Variation in the heat transfer calculations was modeledby using Hohenberg, Woschni, and Annand’s correlations.Moderate variations in heat transfer, in-cylinder pressure,and gas temperature were observed as all the correlations aredependent upon the combustion heat release that is furtherdependent upon the combustion timing and duration.

Although there exists only one correct MFB curve thatrepresents the experimental in-cylinder pressure traces for aspecific spring stiffness, it is of utmost importance to examine

14 Journal of Combustion

Exhaust heatHeat transfer

FrictionSystem efficiency

05

101520253035404550

Perc

enta

ge o

f fue

l ene

rgy

(%)

0.5 1 1.5 2 2.50Combustion duration (ms)

1 1.5 20.5Combustion duration (ms)

11

12

13

14

15

16

17

Ove

rall

syste

m effi

cien

cy (%

)

Figure 22: Major energy losses comparison for different combustion duration. Heat transfer and frictional losses decreased with increase incombustion duration, while exhaust heat increased with an increase in combustion duration.

HohenbergWoschniAnnand

010203040506070

Pres

sure

(bar

)

1000 1500 2000 2500500Time steps

−4500−4000−3500−3000−2500−2000−1500−1000

−5000

Hea

t flux

(W/m

)

1000 1500 2000 2500500Time steps

HohenbergWoschniAnnand

Figure 23: Variation in pressure and heat flux for different heat transfer correlations.

Hohenberg Woschni Annand

Exhaust heatHeat transfer

FrictionSystem efficiency

05

101520253035404550

Perc

enta

ge o

f fue

l ene

rgy

(%)

Figure 24: Distribution of major losses in OLEA system for different heat transfer correlations. Lower heat loss and higher efficiency areobserved for Hohenberg correlation.

various values of form factor in order to get a good matchfor the experimental traces. Further, if the spring stiffness ofthe specially designed mechanical flexures is varied, the in-cylinder pressure traces will vary, and the results obtainedfrom this study will be useful for matching the in-cylinder

pressure curves. Even without the access to the experimentaldata at this moment, it is believed that this investigation willadd some value for those who are investigating the higherfrequency OLEA system running at frequencies above 80 Hzwhich are not yet explored by many researchers.

Journal of Combustion 15

7. Future Research Scope

The utmost and useful direction in understanding the oper-ation and strategic control of OLEA is the experimental val-idation of data obtained from numerical simulation. This isthe main motto of linear engine researchers at West VirginiaUniversity. The combustion and heat transfer informationwill be collected fromOLEA test rig and it is used for studyingthe deviations and discrepancies in the conventional slider-crank-based empirical models used in modeling. Finally, thesuperiority of the heat transfer and combustion study stem-ming from this investigation will be improved by developingmore robust, realistic, and sophisticated numerical model.

Appendix

See Figures 4–24.

Abbreviations

OLEA: Oscillating Linear Engine AlternatorSI: Spark gnitionCI: Compression gnitionWVU: West Virginia UniversitySNL: Sandia National LaboratoriesHCCI: Homogeneous Charge Compression IgnitionCFD: Computational Fluid DynamicsCHP: Combined Heat and PowerTDC: Top ead enterBDC: Bottom ead enterDLR: German Aerospace CenterMFB: Mass raction of fuel urnedLHV: Lower Heating.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

This researchwas conducted underWestVirginiaUniversity’sOscillating Linear Engine Alternator (OLEA) project. It wasfunded by DOE ARPA-E GENSETS program to the WestVirginia University (DE-AR0000608). The authors gratefullyacknowledge the support of DOE ARPA-E for funding thiswork.The authors also acknowledge the support and fundingfrom the WVU George B. Berry chair endowment.

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