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The design and simulation of a two-stroke free-pistoncompression ignition engine for electrical power generation

R. Mikalsen, A.P. Roskilly *

School of Marine Science and Technology, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, United Kingdom

Received 9 December 2006; accepted 16 April 2007Available online 1 May 2007

Abstract

Free-piston engines are under investigation by a number of research groups worldwide due to their potential advantages in terms offuel efficiency and engine emissions. Some prototypes have emerged, mainly aimed for vehicle propulsion, and have reported favourableperformance compared to conventional technology. This paper describes the design of a modular compression ignition free-piston enginegenerator, applicable to electric power generation in large-scale systems. The development of a full-cycle engine simulation model isdescribed, and extensive simulation results are presented, giving insight into engine operating characteristics and performance. The oper-ating characteristics of the free-piston engine was found to differ significantly from those of conventional engines, giving potential advan-tages in terms of fuel efficiency and emissions formation due to fast power stroke expansion. Effects of varying engine stroke length andcompression ratio were not found to give any large advantages. 2007 Elsevier Ltd. All rights reserved.

Keywords: Free-piston; Two-stroke; Diesel; Linear combustion engine generator

1. Introduction

In light of the increased interest in the all-electric shipconcept and with the aim of increasing engine efficiencyand reducing exhaust emissions, work on the more electricengine concept was started in 1999 within the School ofMarine Science and Technology, at the University of New-castle upon Tyne. This work was subsequently supported byBAE Systems, Engineering and Physical Sciences ResearchCouncil (EPSRC) and The Institute of Marine Engineering,

Science and Technology (IMarEST), and resulted in asmall-scale prototype system being developed. Currently amore detailed and comprehensive design study is being con-ducted to investigate potential large-scale applications.

The more electric engine concept is based on a free-piston internal combustion engine coupled to a linearelectric machine. Free-piston engines have received moreinterest in recent years after being practically abandoned

since the 1960s. The modern developments include electricgenerators aimed for hybrid-electric automotive vehiclesand hydraulic pumps aimed for off-highway vehicles withhigh hydraulic loads. Some prototypes of these machineshave reported favourable performance compared to con-ventional technology.

1.1. The free-piston engine

The free-piston engine concept was first presented by

Pescara[1] in 1928, and since then a number of free-pistondesigns have been proposed. Common for these is that thepiston motion is not restricted by the motion of a rotatingcrankshaft, as known from conventional engines, but thatthe piston is free to move between its endpoints, only influ-enced by the gas and load forces acting upon it. This givesthe free-piston engine some distinct characteristics, mostimportantly variable stroke length and high controlrequirements.

Only a handful of successful free-piston engines beenreported, despite a high interest in the concept for a

1359-4311/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2007.04.009

* Corresponding author.E-mail address:[email protected](A.P. Roskilly).

www.elsevier.com/locate/apthermeng

Available online at www.sciencedirect.com

Applied Thermal Engineering 28 (2008) 589600
mailto:[email protected]:[email protected]

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number of years. Free-piston air compressors developed bythe German company Junkers were used by the Germannavy during World War 2, supplying compressed air forlaunching torpedoes [2]. In the 1940s, free-piston enginesfound use as gas generators, feeding hot gas to a power tur-bine. This concept was employed in marine and stationary

powerplants, most successful being a model developed bySociete Industrielle Generale de Mecanique Appliquee(SIGMA) in France [3]. Both Ford and General Motorslater developed prototype vehicles with small-scale free-pis-ton gas generators as prime movers, but none of thesemade it past the prototype stage [4,5]. As the technologyof both conventional engines and gas turbines matured,the interest in the free-piston engine vanished in early1960s.

With the introduction of modern, microprocessor-basedcontrol methods, the free-piston engine has again caughtinterest among present-day engineers seeking to reduceengine emissions and increase efficiency. Most promising

at the moment appears to be the hydraulic free-pistonengine, where among others the Dutch company InnasBV has reported performance advantages over conven-tional technology[6]. A number of other research groupsare also working on this type of engine, which is mainlyaimed for off-highway vehicles such as forklift trucks andearth-moving machines. The coupling of a free-pistonengine to a linear electric generator is also being investi-gated, amongst others by researchers at University of WestVirginia [7]. The main application for such units arehybrid-electric vehicles.

A more comprehensive background study on the history

and potential advantages of the free-piston engine was pre-sented by Mikalsen and Roskilly[8].

Potential advantages of the free-piston engine conceptinclude: vibration-free operation; lower production andmaintenance costs and reduced frictional losses due tomechanical simplicity; reduced heat transfer losses andNOxemission production due to faster power stoke expan-sion; higher part load efficiency and multi-fuel possibilitiesdue to combustion optimisation flexibility (variable com-pression ratio and electronically controlled valve operationand fuel injection timing). This paper presents the design ofthe more electric engine and investigates the general per-formance of the unit. It aims to identify some of the poten-tial advantages of free-piston engines over conventionaltechnology through a full-cycle engine simulation model.

2. Engine design

2.1. A brief description of the engine configuration

An engine as shown in Fig. 1 is proposed. The mainparts of the engine are a combustion cylinder, a bouncechamber cylinder and a linear electric machine. The enginewill have only one moving part, rigidly connecting the twopistons and the translator of the linear alternator. The pis-

ton will move freely between its two endpoints, its motion

being determined by the instantaneous balance of cylindergas forces, electric machine force and frictional forces.

Fig. 1shows the proposed engine design, with:

r Exhaust poppet valves.s Scavenging ports.

t Common rail fuel injection.u Linear alternator.v Bounce chamber.w Bounce chamber pressure control valves.x Turbocharger compressor.y Turbocharger turbine.

The engine will operate on a turbocharged two-strokediesel cycle with direct injection and electronically con-trolled fuel injection, utilising modern common rail tech-nology. Scavenging is provided through scavenging portsin the cylinder liner and electronically controlled exhaustpoppet valves in the cylinder head.

The bounce chamber will be a closed cylinder with pres-sure control valves to regulate the amount of gas trapped inthe bounce chamber, and thereby the gas pressure force onthe piston. Pressurised air will be provided to the pressurecontrol valves to allow control of the bounce chamber pres-sure at all operating conditions.

The linear electrical machine is assumed to be a perma-nent magnet machine, as suggested by Arshad et al. [9].Appropriate power electronics will be employed to allowcontrol of the electric load force and to allow operationof the electric machine as a motor for starting purposes.

The engine is intended to be modular in the way that a

number of such cylinders can be operated in parallel to

Fig. 1. Free-piston engine.

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achieve power outputs required in large-scale applications.A computer control system is to control the engines forperformance optimisation and synchronisation of pistonmotions to cancel out vibrations. Operation of a numberof cylinders on a common turbocharger is possible.

2.2. Engine control

The piston motion in conventional engines is controlledby the crankshaft, ensuring a sufficient compression ratiofor autoignition in one end and sufficient time for scaveng-ing in the other. The lack of this mechanism gives the free-piston engine the possible advantageous feature of variablecompression ratio, but requires a piston motion controlsystem to be established.

In addition, for the engine to be feasible in a large scale,it must be balanced. A great advantage of the free-pistonengine is that vibrations can be completely cancelled outby making two identical pistons operate in opposite phases.

The opposed piston free-piston engines developed in themid-20th century had mechanical linkages rigidly connect-ing two pistons operating with a common combustionchamber. The present design, however, seeks to use elec-tronic control to synchronise pairs of engine units to cancelout vibrations.

2.2.1. Control objectives

The primary control objectives for the free-piston engineincludes the control of top dead centre (TDC) and bottomdead centre (BDC) positions. The TDC position must becontrolled within tight limits, as overshoot may lead to

mechanical contact between the piston and the cylinderhead, which may be fatal for the engine. In addition to this,control of engine speed is required in order to synchronisethe operation of multiple engines to minimise vibrations.

Control variables available are the mass of injected fuel(fuel rack position), and bounce chamber pressure. Theelectric load force is considered a disturbance input,although the implementation of appropriate power elec-tronics may allow some control of this variable. (Fuel injec-tion timing proved in the simulations to only have a minorinfluence on the main control objectives, Pand this variablewas therefore saved for operation optimisation purposes.)

Secondary control objectives include the control of valvetimings, fuel injection timing and compression ratio, thelatter to provide the TDC setpoint to the primary control-lers, in order to optimise engine operation for all operatingconditions.

2.2.2. Control strategy

Johansen et al.[10]propose a control strategy for a free-piston gas generator with some similarities to the enginepresented here. Mass of fuel per injection and mass of airin the bounce chamber are used to control BDC positionand TDC position respectively, whereas engine speed con-trol is achieved by changing engine stroke length by adjust-

ing TDC and BDC setpoints. They further present

experimental results showing the feasibility of thisapproach.

In this study, a somewhat similar control approach havebeen tested using the simulation model described below,and appears to be feasible. Further work on engine controltopics is currently in progress, and for the purpose of the

work presented here it is assumed that a satisfactory enginecontrol system can be realised.

3. Modelling

The amount of research specifically addressing the mod-elling of free-piston engines is small and most authors tendto use well-known models used in conventional engine mod-elling to model free-piston engines. The engine processes aresimilar, but the free-piston engine does have some specificoperating characteristics compared to the conventionalengine, which need to be treated with some caution. Thisrelates in particular to the combustion process, but the par-

ticular piston motion profile of the free-piston engine is alsolikely to influence in-cylinder heat transfer and scavenging.

In this section, the modelling of the free-piston enginegenerator is presented, and the feasibility of the imple-mented models is discussed.

3.1. Piston dynamics

The piston motion can be derived from Newtons 2ndlaw, giving

FC FL Ffr FR mpd2x

dt2; 1

where x is piston position, mp is moving mass, FC is gasforce from combustion cylinder, FR is gas force frombounce chamber, FL is electric load force, Ffr is frictionforce.

3.2. Diesel engine submodels

The submodels for the simulation of the combustion cyl-inder are based on existing single-zone models commonlyused in the modelling of conventional diesel engines.

3.2.1. Ignition delay

Correlations for ignition delay based on the Arrheniusequation for reaction rate are widely used in internal com-bustion engine modelling and a correlation of this typedescribed by Stone[11]has been used:

tid 3:52exp2100=T

p1:022 ; 2

wheretidis ignition delay (ms), p is in-cylinder gas pressure(bar), Tis in-cylinder gas temperature (K).

The variables p and Tare the mean values during theignition delay, and to account for the changing conditionsin the ignition delay period the following correlation needs

to be satisfied:

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Z tsitidtsi

1

s

dt 1; 3

where tsiis the time of start of injection (ms), s is the igni-tion delay at time t (ms).

3.2.2. Combustion

The modelling of the heat release in the free-pistonengine is one of the factors with the highest degree ofuncertainty in the simulation model. The piston motionin the free-piston engine differs significantly from that ofconventional engines, and very little research exists onhow this influences the combustion process.

Some reports have indicated that the heat release rate issignificantly higher in the free-piston engine compared toconventional engines. Somhorst and Achten [12] presentmeasurements of heat release rate taken in the Innas free-piston engine and state that the pressure gradient reachesvalues two to five times higher than in comparable conven-

tional engines. Tikkanen et al. [13] present similar experi-mental results, and both groups indicate that combustiontakes place predominantly in one pre-mixed phase in thefree-piston engine.

A faster combustion is, however, usually an uncondi-tional advantage for engine performance. Hence, shouldthe models used in this work under-predict the heat releaserate, they will represent the more pessimistic predictions.

A single-zone combustion model described by Heywood[14]has been used:

mbt bf1t 1 bf2t; 4

where mb is mass fraction burned[1],t is time, non-dimen-sionalised by total time for combustion[1], b is fraction offuel burned in the pre-mixed phase [1].

f1is the pre-mixed burning function, given as

f1 1 1 tK1

K2 5

and f2is the diffusion burning function

f2 1 expK3tK4: 6

The fraction of fuel burned in the pre-mixed phase, b, is afunction including the ignition delay:

b 1 a/b=tcid; 7

where /is the fuelair equivalence ratio[1].K1, K2, K3, K4,a,b and c are empirical coefficients. Val-

ues of these based on experimental data from a truckengine are presented by Heywood[14], and these have beenimplemented in the model. Total time allowed for combus-tion is set to 5 ms based on experimental results obtainedfrom the engine against which the model was validated(see also Section4.1).

3.2.3. Scavenging

Accurate modelling of the scavenging process is not pos-sible in an early design phase, as this depends on design

details. Estimating the scavenging performance is, how-

ever, of high interest to investigate its influence on engineperformance, particularly due to the variable stroke whichmay have effects on scavenging performance.

A simple scavenging model is used to estimate the gasflows in and out of the cylinder. Exhaust blowdown ismodelled at the parts of the cycle where exhaust valves

are open but the scavenging ports have not yet been uncov-ered. The process is modelled as a polytropic expansion ofthe in-cylinder gas down to the exhaust back pressure, withmass flow through the exhaust valves modelled as flowthrough nozzles, with appropriate valve discharge coeffi-cients[14].

Scavenging is modelled with a perfect displacementmodel. During scavenging the cylinder is assumed to com-prise of two zones; one zone containing fresh air displacesthe other zone with combustion products. The zones do notexchange mass or heat and only when all the combustionproducts have been fully displaced will fresh air flow outthrough the exhaust ports. Gas temperatures are calculated

as the instantaneous mass-weighted average of fresh airand residual products in the cylinder. The thermodynamicconsequences of poor scavenging on the next cycle aretaken into account to allow simulation of engine transientoperation.

3.2.4. Turbocharger

The turbocharger model relates the boost pressure andtemperature to the exhaust temperature and exhaust backpressure. It receives as inputs: ambient conditions (inletair temperature and atmospheric pressure), compressorand turbine efficiencies, and exhaust back pressure, all

defined by the user. Using these together with exhaustgas temperature from the engine model, the turbochargermodel predicts boost air temperature and pressure.

Standard equations for isentropic state changes,allowing isentropic efficiency losses, are used in thecalculations (the calculation procedure can be found innumerous textbooks, including Stone [11]). Turbochargertransient response to changes in engine operation is notmodelled.

3.2.5. Heat transfer

In-cylinder heat transfer is modelled according to

Hohenberg[15]:_Q aAsT Ts; 8

where _Qis heat flow rate (J/s), a is heat transfer coefficient(W/m2K),Asis in-cylinder surface area in contact with thegas (m2), Ts is average temperature of the in-cylinder sur-face area (K).

The heat transfer coefficient, a, is given by

a 130V0:06 p

105

0:8T0:4vp 1:4

0:8; 9

where Vis instantaneous cylinder volume (m3),vp is mean

piston speed (m/s).


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Stone[11]suggests a average in-cylinder surface temper-ature, Ts, of 350 K, and this value is used in thesimulations.

3.2.6. Gas properties

Having the instantaneous heat transfer rate to/from the

in-cylinder gases (heat release from fuel burning minus heattransfer losses), cylinder pressure and temperature are cal-culated by applying the 1st law of thermodynamics on thecylinder charge:

dU

dt

dQ

dt

dW

dt ; 10

where Uis internal energy (J), Q is heat transferred to thegas (J), W is work done by the gas (J).

Assuming that the cylinder charge will behave as a idealgas, the internal energy is a function of temperature only,giving

U U0 mCvT T0; 11where m is mass of the in-cylinder gases (kg), Cvis specificheat capacity at constant volume (J/kg K).

Further, the gas will follow the ideal gas law

pV mRT; 12

where R is the gas constant (J/kg K).Assuming that mass, specific heat, Cv and the gas con-

stant, R, are constant, and letting R/Cv= (c 1), the fol-lowing correlations can be derived from Eqs. (10)(12):

dp

dt

1

V

c 1dQ

dt

pcdV

dt ; 13

dT

dt

1

mCv

dQ

dtp

dV

dt

; 14

where c is ratio of specific heats [1].

3.2.7. Friction

Friction losses in the free-piston engine are expected tobe lower than for the conventional internal combustionengine due to the elimination of the crank mechanism. Thisremoves a source of frictional losses, but also pistoncylin-der friction is reduced since no side forces act on the pistonin the free-piston engine.

A breakdown of engine friction mechanisms in four-stroke spark ignition and diesel engines is presented byHeywood [14]. This data is used, with the followingadjustments:

Pumping work is left out as the cycle is two-stroke. Compression and gas load are left out as their effects are

accounted for elsewhere in the simulation model. Crankshaft friction is left out as it is non-existent in the

free-piston engine.

This leaves frictional losses from the piston itself and the

piston rings, along with valve gear and auxiliaries, giving a

friction mean effective pressure (fmep) of around 120 kPa.Using this, a friction force is found. The friction force isassumed to be constant over the full stroke, an acceptablesimplification since the magnitude of the friction forces willbe significantly lower than the other forces that act on thepiston and will not have a large effect on the engine

dynamics.

3.3. Linear alternator

The design of the electric machine will have a high influ-ence on the performance of the free-piston engine genera-tor since the alternator translator forms a part of themoving mass. For the engine to be feasible and for it tobe a realistic alternative to conventional technology, it isessential that a translator with sufficiently low weight canbe found. Increasing moving mass reduces the bouncingfrequency of the system and thereby the power to weightratio.

Some reports have been published investigating thedesign of linear electric machines for use with free-pistonengines. Arshad et al. [9] indicate, having undertaken anextensive study resulting in a number of publications, thatan electric generator with 50 kW power output with effi-ciency of above 90% and a moving mass of less than10 kg can be realised with the use of a transverse flux, per-manent magnets machine. Similar longitudinal fluxmachines are reported to have moving masses in the order1015 kg.

In this study, a simple design procedure was developedto estimate the required magnet mass for a given free-pis-

ton engine generator, using basic magnetic circuit calcula-tions. The predictions showed reasonable agreement withthe data reported by Arshad et al., and, based on this, anestimation of magnet mass for the free-piston engine inves-tigated in this study has been made. As will be shownbelow, the mass requirements for the electric machine areless stringent in a turbocharged diesel-powered free-pistonengine compared to SI engines, due to the higher operatingpressures giving increased operating frequencies.

The load force of the electric machine is assumed to beproportional to translator speed, however the simulationmodel allows the user to define any load force profile tobe investigated.

3.4. Bounce chamber

The bounce chamber is modelled as a reversible isentro-pic compression and expansion of the air trapped withinthe bounce chamber cylinder. The force from the bouncechamber is proportional to the bounce chamber pressure,which is found using a user-defined start-of-compressionpressure and the instantaneous bounce chamber compres-sion ratio. The amount of air in the bounce chamber isallowed to vary by varying the given start-of-compressionpressure, and using this the operating characteristics of

the bounce chamber can be varied.


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The frictional losses in the bounce chamber are likely tobe lower than for the combustion cylinder since the bouncechamber is working with lower pressures and the sealingrequirements are less stringent. A value of half the frictionlosses of the combustion cylinder was used for the bouncechamber.

4. Simulation results and discussion

A simulation program was written using the numericalcomputation software Matlab to investigate the influenceof design parameters and engine input variables. Eq. (1)is solved using standard forward Euler numerical integra-tion to give piston speed and position, with the dieselengine submodels and the correlations for alternator loadforce and bounce chamber pressure being solved at eachsimulation step. The program allows investigation intoboth steady state outputs and transient response of engineperformance.

The code takes the following input variables:

cylinder bore; moving mass; nominal stroke and compression ratio; ambient conditions; exhaust back pressure and turbocharger isentropic

efficiencies; number of exhaust valves, dimensions and valve timing; scavenging ports height and width; fuel calorific value, mass of fuel per injection and injec-

tion timing;

linear alternator force function.

It predicts a number of variables, including:

speed; stroke; generator power output; cylinder temperature and pressure history; exhaust gas temperature and boost air pressure and

temperature; fuelair equivalence ratio; scavenging efficiency; predicted ignition delay, fuel burn rate and heat transfer

rate; engine efficiency.

4.1. Model validation

The output of the simulation model was compared todata from a Volvo TAD1240 six-cylinder, turbochargeddiesel engine located at the Jones Engine Laboratory, Uni-versity of Newcastle upon Tyne. The comparison was donewith the aim of verifying that the model produces realisticresults, and that it is able to predict real trends for varying

engine operating conditions.

4.2. Engine specifications

A number of simulations were run with varying inputvariables, and the results are presented in the following sec-tions. The engine specifications were chosen to be similar tothose of the engine against which the simulation model was

validated.Table 1shows the main engine specifications.Both the exhaust valve timing and fuel injection timingare variable in order to optimise engine performance, andcontrollers within the simulation model adjust these duringoperation. The exhaust valve opening timing is adjusted sothat the in-cylinder pressure at the time when the scaveng-ing ports are uncovered is equal to the boost pressure. Thismaximises the work done on the piston and prevents back-flow of exhaust gases into the intake manifold. The exhaustvalves close at the same time as the piston covers the scav-enging ports in the compression stroke. Fuel injection tim-ing is set to its optimum value for high efficiency in all thesimulated cases.

4.3. Basic performance

The basic performance parameters of the free-pistonengine are summarised inTable 2. The engine is operatingat a fuelair equivalence ratio of 0.60. The efficiency valuespresented below refer to the shaft fuel efficiency of thecombustion engine, and losses in the electric machine aretherefore ignored.

Fig. 2 shows the simulated in-cylinder pressure of thecombustion cylinder and bounce chamber for one enginecycle. The predicted combustion is seen to be close to a

constant volume process. The bounce chamber is modelledas a reversible isentropic compression, as can also be seenfrom the figure.

Fig. 3shows the predicted piston dynamics of the free-piston engine. Fig. 3a shows the simulated piston motionfor one engine cycle, compared to a conventional engine

Table 1Free-piston engine specifications

Design stroke 0.150 mBore 0.131 mScavenging ports height 0.022 mNominal compression ratio 15:1Piston mass 22 kgBounce chamber bore 0.150 mBounce chamber compression ratio 15:1Exhaust back pressure 1.5 105 Pa

Table 2Simulated engine basic performance

Speed 30 HzOutput power 44.4 kWMean piston speed 9 m/sScavenging efficiency 0.90Boost pressure 1.68 105 Pa

Engine efficiency 0.42


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(with crankshaft radius to connecting rod length ratio of

0.3) running at the same speed. Significant differences canbe seen, the most important being that the free-pistonengine spends shorter time around TDC, where the gaspressure and temperature are at their highest. This is

emphasised inFig. 3b, which shows the piston motion inthe area close to TDC, normalised around the TDC posi-tion. It is seen that the expansion just after TDC is signif-icantly faster for the free-piston engine.

It can also be seen from the piston motion trajectorythat the free-piston engine motion is asymmetrical around

TDC, and the engine spends more time in the compressionthan in the expansion phase of the cycle.Fig. 3c shows simulated piston speed in the free-piston

engine and the piston speed profile of a conventionalengine. It is seen that the peak piston speed is lower forthe free-piston engine, and that the speed profile is signifi-cantly different. Compared to the conventional engine, thefree-piston engine has a speed profile resembling a saw-tooth wave, with rapid speed changes and periods of closeto constant speed.

Fig. 3d shows piston acceleration in the free-piston andconventional engine. As above, significant differences canbe seen, particularly just after ignition where the unrestricted

motion of the piston in the free-piston engine gives a veryhigh acceleration when the in-cylinder pressure is high. Pre-dicted peak piston acceleration in the free-piston engine isaround 60% higher than in the conventional engine.

0 0.05 0.1 0.150

20

40

60

80

100

120

140

Piston position [m]

Pressu

re[bar]

Combustion cylinder

Bounce chamber

Fig. 2. Simulated combustion cylinder and bounce chamber pressure forone engine cycle (TDC at piston position 0).

0 5 10 15 20 25 30 35

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time [ms]

Pisto

npos

ition

[m]

ConventionalFreepiston

8 10 12 14 16 18 20 22 24

0

0.01

0.02

0.03

0.04

0.05

Time [ms]

Piston

pos

ition

[m]


0 5 10 15 20 25 30 3515

10

5

0

5

10

15

Time [ms]

Pistonspeed

[m/s]


0 5 10 15 20 25 306000

4000

2000

0

2000

4000

6000

8000

Time [ms]

Pistonacce

lera

tio

n[m/s

2]


a b

c d

Fig. 3. Predicted piston dynamics of the free-piston engine. (a) Simulated piston motion for the free-piston engine compared to a conventional enginerunning at the same speed. (Piston position shown as distance below TDC.) (b) Simulated piston motion close to TDC for a free-piston engine and aconventional engine, normalised around TDC position. (c) Simulated piston speed profile for the free-piston engine compared to a conventional engine

running at the same speed. (d) Simulated piston acceleration profile of the free-piston engine compared to a conventional engine running at the same speed.


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A curiosity of the free-piston engine is that, since theacceleration is directly proportional to in-cylinder pressure,events in the combustion chamber can be found on theacceleration graph. Both the fuel injection and the exhaustvalve opening can be seen on the graph in Fig. 3d, ataround t = 18 ms and t = 27 ms respectively.

4.4. Engine geometry and design

In an engine design process, knowledge of the influenceof different engine geometric variables is of high impor-tance. Although the influence of the main design parame-ters can be predicted based on experience fromconventional engines, their effects on overall engine perfor-mance may be different in the free-piston engine due to theparticular operating characteristics of this type of engine.This section investigates the influence of the main enginedesign parameters in the free-piston engine.

All the design and operational parameters in the free-

piston engine are highly interconnected, and the systembecomes more complicated in this sense than the conven-tional engine. For example, an increase in moving mass willnot only lead to lower engine speed, it will also have effectson the stroke length which influences both the scavengingprocess and the compression ratio. Changing operationalvariables, such as fuel mass flow or boost pressure, willhave the same effects. Due to this, a parametric study ofthe free-piston engine design and operational variables isnot straight-forward. A number of prerequisites must bedecided upon before such investigations can be undertaken.

In the simulations below, TDC and BDC positions are

controlled to their nominal values by changing the bouncechamber pressure and fuel flow rate respectively. To ensurethat the comparison is done on the same relative engineload, the electric load force is adjusted to achieve a fuelair equivalence ratio of 0.60 for all cases. The height ofthe scavenging ports is further adjusted to achieve a scav-enging efficiency of 0.90 to ensure that realistic enginedesigns are compared. Finally, the exhaust valve openingtiming and fuel injection timing are optimised as describedabove.

4.4.1. Moving mass

The engine resembles a springmass system, and themoving mass is therefore of high importance to engine per-formance. A low moving mass is expected to give highengine speeds and vice versa. A reported concern withthe free-piston engine generator is finding an electricmachine with sufficiently low weight, and it is clear thatif this cannot be found the engine will not achieve anacceptable power to weight ratio.

It is expected that a high moving mass leads to lowerengine speed, which again leads to more time availablefor scavenging, allowing lower scavenging ports height,and closer to constant volume combustion, both increasingefficiency. It will, however, at the same time lead to higher

peak temperatures and pressures, which increase heat

transfer losses. An optimal engine speed for high efficiencymay therefore be expected.

Fig. 4 shows the predicted effects of varying mass onengine performance. It is seen that the springmass analogyis valid, as increasing mass leads to a decrease in enginespeed and power output.

The results for engine efficiency show that the predictedoptimum moving mass for efficiency is relatively high. Thisindicates that the requirements of a low-mass electricmachine are less stringent in a turbocharged diesel-poweredfree-piston engine, and that acceptable mean piston speedsand high efficiency can be achieved even for a high movingmass.

4.4.2. Compression ratio

The compression ratio is changeable during operation inthe free-piston engine, but the nominal value must bedecided on a design stage. Although a higher compressionratio gives higher theoretical cycle efficiency, it increases in-cylinder temperatures and pressures, increasing heat trans-fer losses and mechanical stress, and these effectively deter-mine the maximum possible compression ratio.

Fig. 5 shows the effects of variations in the nominalcompression ratio of the free-piston engine. The simula-tions predict that an optimal compression ratio can befound, but only minor effects on engine efficiency are foundfor compression ratios between 15 and 25.

An effect that is not obvious is the decrease in enginepower output together with increased engine speed. Thelatter is a result of the combustion cylinder gas springbeing stiffer, which increases the bouncing frequency in

the massspring system. The reduced power output is dueto the fact that an increased compression ratio leads toan increased expansion ratio, which reduces the internalenergy in the exhaust gases. While this may increase engineefficiency, it reduces the boost pressure and therefore alsoengine power output since the simulations are run withconstant fuelair equivalence ratio. In the simulations,the exhaust gas temperature drops by around 8% between

5

10

15

Moving mass [kg]Meanp

iston

spee

d[m/s]

15 20 25 30 35 4030

40

50

Power

[kW]

15 20 25 30 35 400.415

0.42

0.425

0.43

Moving mass [kg]

Efficiency

[1]

Fig. 4. Effects of changes in moving mass on engine performance.


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compression ratios of 15 and 25, giving a reduction inboost pressure by around 4% in the same interval.

4.4.3. Exhaust back pressure

The exhaust back pressure of an engine is determined bythe size of the turbocharger. The effects of varying exhaustback pressure on engine performance are investigatedbelow, with the assumption that the turbocharger efficien-cies are constant for all conditions.

An increase in exhaust back pressure is assumed to givehigher engine speed, since the pressure forces increase. In

addition, significantly higher power output is expected withhigher boost pressure, since the engine is running at a con-stant fuelair equivalence ratio.

Fig. 6shows the effects of varying exhaust back pressureon engine performance with constant equivalence ratio. Itis seen that, along with the predicted increase in enginepower output and speed, the efficiency improves withincreasing exhaust back pressure. This is due to the fact

that the contribution from frictional losses decreases athigher engine power outputs.

Engine performance with higher exhaust back pressuresare not investigated as the upper range of the investigatedvalues produced very high peak cylinder pressures(approaching 20 MPa). Operation on higher exhaust back

pressures with constant fuelair equivalence ratio is there-fore not realistic. Further investigations to compare theperformance of a highly turbocharged engine running ata low equivalence ratio compared to a moderately turbo-charged engine running at high equivalence ratios may beworthwhile.

4.4.4. Stroke to bore ratio

The stroke to bore ratio is one of the core design vari-ables in internal combustion engines, relating combustionchamber surface area to its volume and piston area tostroke length. Conventional engines with high stroke tobore ratios, such as those found in marine and stationary

powerplants, are characterised by high efficiency but poorpower density. Low stroke to bore ratios, commonly foundin small-scale engines e.g. in automotive applications, allowhigher engine speeds which increase power to weight ratio,but at the cost of higher fuel consumption.

Fig. 7shows the effects of varying stroke to bore ratioon engine performance with engine swept volume kept con-stant. Higher efficiencies are as expected obtained with anincreasing stroke to bore ratio. Despite an increase in meanpiston speed the engine output power is slightly reducedwith increasing stroke to bore ratio due to a reduction inengine speed.

4.5. Effect of variable stroke

The free-piston engine has the potentially valuable fea-ture of variable stroke. This means that the compressionratio of the engine can be altered during operation, to opti-mise engine performance for any operating condition. This

130 140 150 160 170 1808

9

10

Exhaust back pressure [kPa]Meanp

istonspee

d[m/s]

130 140 150 160 170 18020

40

60

Powerou

tpu

t[kW]

130 140 150 160 170 1800.4

0.41

0.42

0.43

0.44

Exhaust back pressure [kPa]

Efficiency

[1]

130 140 150 160 170 180140

160

180

200

220

Boos

tpressure

[kPa

]

Fig. 6. Effects of changing exhaust back pressure on engine operation.

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.88.5

8.75

9

9.25

9.5

Stroke to bore ratio [1]Meanpis

tonspee

d[m/s]

40

41

42

43

44

Power

[kW]

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80.42

0.43

0.44

0.45

Stroke to bore ratio [1]

Efficiency

[1]

Fig. 7. Effects of varying free-piston engine stroke to bore ratio with

constant swept volume and constant equivalence ratio.

12 14 16 18 20 22 24 26 288

9

10

M

eanp

istonspee

d[m/s]

12 14 16 18 20 22 24 26 2835

40

45

Compression ratio [1]

Power

[kW]

12 14 16 18 20 22 24 26 280.4

0.41

0.42

0.43

0.44

Compression ratio [1]

Efficiency

[1]

Fig. 5. Effect of varying nominal compression ratio on engineperformance.


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has been mentioned by a number of authors, and suggestedadvantages include increased part load efficiency and multi-fuel operation possibilities.

Fig. 8shows the effect of changing the TDC setpoint forthe engine (the figure shows the corresponding effectivecompression ratio) on engine efficiency at different loads.

The simulations show that the optimum compression ratiovaries only slightly with load and no advantage of increas-ing the compression ratio on low loads was found. Forhigh loads a small increase in efficiency can be seen withincreasing compression ratio, but in these cases the peakcylinder pressure will limit the maximum compressionratio. The compression ratios where peak cylinder pressureexceeded 18 MPa are shown.

Similar simulations were performed for BDC position,but varying the BDC setpoint produced no noticeable effecton engine performance.

4.6. Effect of fuel burn rate

As discussed above, some uncertainty exists regardingthe accuracy of the combustion modelling as some authorshave reported an increased fuel burn rate in free-pistonengines. Furthermore, one of the claimed advantages ofthe free-piston engine is its multi-fuel possibilities, and itis therefore worthwhile to investigate how fuel burn rateinfluences engine performance.

Fig. 9 shows the effect of changing fuel burn rate onengine performance. In addition to changing the total timeallowed for combustion (but not the fuel burn pattern) inEq.(4), the effect of assuming that all the fuel burns in a

single pre-mixed phase is shown. Such an approach wasadopted by Tikkanen et al. [16] and was supported bythe experimental results of the same research group andthose of Somhorst and Achten[12].

Some influence on engine performance is seen, and amore rapid combustion will, as expected, improve engineperformance. It is further seen that the optimum compres-sion ratio does not change significantly with varying fuel

burn rate, indicating that the changeable the compressionratio is less beneficial than expected. It should, however,

be noted that changing the compression ratio will lead toother effects that the current engine model is unable toidentify, such as changes in squish effects, which may influ-ence combustion.

The simulations showed that for high load (fuelairequivalence ratio of 0.70), most of the fuel has been burnedwithin around 2 ms with total time for combustion in Eq.(4) is set to 5 ms. With total time for combustion set to3 ms most of the fuel burns in around 1.5 ms. Somhorstand Achten [12] report fuel burn rates even higher thanthis, stating that 90% of the combustion in their free-pistonengine finishes within 1 ms.

4.7. Comparison to conventional engines

To investigate the effects of the particular operatingcharacteristics of the free-piston engine compared to con-ventional engines, a crankshaft engine simulation subrou-tine was implemented in the simulation model. Thesubroutine uses the simulation results for a given free-pis-ton engine configuration and runs a subsequent simulationfor an engine with the same configuration and operationalvariables (bore, stroke, boost pressure, injected fuel mass,etc.), but with a piston motion equal to that of a conven-tional engine (i.e. a crankshaft-driven motion that is notinfluenced by the in-cylinder pressure and is described bya function of sine and cosine factors). Using such anapproach, some insight into the differences in performancebetween the free-piston and conventional engines can begained.

The optimum point of fuel injection differs between thetwo engines due to the differences in piston motion profile,and in order to obtain a realistic comparison each engine isrun with the injection timing giving best fuel efficiency.These optimum values were identified through simulationsand it was found that the free-piston engine requires aslightly advanced injection timing compared to the conven-

tional one.

12 14 16 18 20 22 24 26 280.34

0.36

0.38

0.4

0.42

0.44

0.46

Effective compression ratio [1]

Eng

inee

fficiency

[1]

P=50kW

P=35kW

P=20kW

pmax>180bar

Fig. 8. Effect of changing effective compression ratio during engine

operation at constant load.

12 14 16 18 20 22 24 26 28

0.415

0.42

0.425

0.43

0.435

0.44

Effective compression ratio [1]

Eng

inee

fficiency

[1]

TTFC=5msTTFC=3msPremixed

Fig. 9. Effect of total time for combustion (TTFC) on engine performancepredictions.


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Fig. 10shows the simulated efficiency of the free-pistonengine compared to an identical conventional engine forvarying engine load. Since no assumptions have been madefor the mechanical efficiency of conventional engines, thecomparison is done on the basis of indicated (in-cylinder)values. A slight fuel efficiency advantage is predicted for

the free-piston engine over the full load range, and it willbe shown below that this is due to reduced heat transferlosses. In addition to this come the potentially lower fric-tional losses in the free-piston engine.

4.7.1. In-cylinder gas temperature

The fast power stroke expansion of the free-pistonengine reduces the time which the gases spend in thehigh-temperature parts of the cycle, and this possiblyreduces in-cylinder heat transfer losses and temperature-dependent emissions formation. Using the simulationmodel, the predicted heat transfer rate from the cylinder

and in-cylinder gas temperature was compared for thefree-piston engine and for a similar conventional engine.Fig. 11shows the simulated in-cylinder gas temperature

and the total heat lost to in-cylinder heat transfer for onecycle, the latter shown as a fraction of the injected fuelheat. The graphs are synchronised around the start of com-bustion. It can be seen that both peak temperature andtemperature levels during expansion is lower in the free-pis-ton engine, and that this results in lower heat transferlosses. The simulations predict that in the free-pistonengine, 17.4% of the fuel heat is lost to in-cylinder heattransfer. For the conventional engine this value is 18.7%.

The simulations further show that the fast expansion of

the free-piston engine makes it spend less time in the partsof the cycle where the in-cylinder gas temperatures arehigh. The amount of time per cycle that the gases in thefree-piston engine hold a temperature of above 1500 K is89% of that in the conventional engine. (This time periodis equal to 10.1% of the cycle time in the free-piston engineand 11.3% in the conventional engine.) For temperatures ofabove 2000 K, this value is 83% (with such temperatures

levels occurring for 4.5% and 5.4% of the cycle time respec-tively). In addition to reducing heat transfer losses, thisparticular feature of the free-piston engine may lead to areduction in the formation of temperature-dependent emis-sions, most importantly nitric oxides.

4.7.2. Limitations of the simulation model

It should be noted that the existing simulation model,being a single-zone model, is unable to identify some fac-tors that will influence engine performance and the predic-tions shown above. Differences in in-cylinder gas motion,in particular squish effects, due to the piston motion profileand varying compression ratio, will not have been identi-fied, but such effects will undoubtedly have influence onboth the combustion process and formation of emissions.Further research is therefore necessary to be able to iden-tify the details of these effects, and these limitations shouldbe kept in mind while reading the results presented above.

5. Conclusions

The design of a free-piston diesel engine generator waspresented. A detailed simulation model was derived andextensive simulation results were presented, giving insightinto the basic performance of the engine and effects ofengine design parameters and operational variables onengine performance.

The performance parameters of the free-piston engineare highly interconnected, and changing one design param-eter will influence many operational variables. The massrequirements for the electric machine, discussed by otherauthors, were found to be less stringent in the currentdesign, due to higher operating pressures.

It was found that the free-piston engine has potentialadvantages over conventional technology in terms of fuelefficiency as a result of mechanical simplicity and fasterpower stroke expansion. Lower temperature levels mayreduce the formation of emissions. The flexibility of the

variable stroke was not found to give any large advantages

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750.45

0.46

0.47

0.48

0.49

0.5

0.51

0.52

Fuelair equivalence ratio [1]

Indica

tede

fficiency

[1]

FreepistonConventional

Fig. 10. Efficiency of the free-piston engine compared to a conventional

engine for varying loads.

0.01 0.015 0.02 0.025 0.03

0

500

1000

1500

2000

2500

Time [s]

Gaste

mperature[K]

0

0.1

0.2

Heattransferlosses[1]

0

0.05

0.1

0.15

0.2

Freepiston

Conventional

Fig. 11. In-cylinder gas temperature and heat transfer losses in free-pistonand conventional engines.


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for normal engine operation, a result that was somewhatunexpected.

Much development work remains before the free-pistonengine can become a realistic alternative to conventionaltechnology. Most importantly, further research into enginecontrol and free-piston engine combustion must be under-

taken. Work on these topics is currently underway at theSchool of Marine Science and Technology at Universityof Newcastle upon Tyne.

References

[1] R.P. Pescara, Motor compressor apparatus. US Patent 1,657,641,1928.

[2] W.T. Toutant, The WorthingtonJunkers free-piston air compressor,Journal of the American Society of Naval Engineers 64 (3) (1952)583594.

[3] R. Huber, Present state and future outlook of the free-piston engine,Transactions of the ASME 80 (8) (1958) 17791790.

[4] A.F. Underwood, The GMR 4-4 HYPREX engine A concept of

the free-piston engine for automotive use, SAE Transactions 65(1957) 377391.

[5] O.B. Noren, R.L. Erwin, The future of the free-piston engine incommercial vehicles, SAE Transactions 66 (1958) 305314.

[6] P.A.J. Achten, J.P.J. van den Oever, J. Potma, G.E.M. Vael,Horsepower with brains: The design of the Chiron free piston engine,SAE Paper 2000-01-2545, 2000.

[7] N. Clark, S. Nandkumar, C. Atkinson, R. Atkinson, T. McDaniel, S.Petreanu, et al., Modelling and development of a linear engine,ASME Spring Conference, Internal Combustion Engine Division 30(2) (1998) 4957.

[8] R. Mikalsen, A.P. Roskilly, A review of free-piston engine historyand applications, Applied Thermal Engineering 27 (1415) (2007)23392352.

[9] W.M. Arshad, P. Thelin, T. Backstrom, C. Sadarangani, Alternativeelectrical machine solutions for a free piston generator, in: The SixthIntl Power Engineering Conference (IPEC2003), Singapore, 2003.

[10] T.A. Johansen, O. Egeland, EAa Johannesen, R. Kvamsdal, Free-piston diesel engine timing and control towards electronic cam and crankshaft, IEEE Transactions on Control Systems Technology10 (2002) 177190.

[11] R. Stone, Introduction to Internal Combustion Engines, MacMillianPress Ltd., 1999.

[12] J.H.E. Somhorst, P.A.J. Achten, The combustion process in a DIDiesel hydraulic free piston engine, SAE Paper 960032, 1996.

[13] S. Tikkanen, M. Lammila, M. Herranen, M. Vilenius, First cyclesof the dual hydraulic free piston engine, SAE Paper 2000-01-2546,2000.

[14] J.B. Heywood, Internal Combustion Engine Fundamentals,McGraw-Hill, Inc., 1988.

[15] G.F. Hohenberg, Advanced approaches for heat transfer calculations,SAE Special Publications, SP-449, 1979, pp. 6179.

[16] S. Tikkanen, M. Herranen, R. Savela, M. Vilenius, Simulation of ahydraulic free piston engine: A dual piston case, in: Proceedings ofSixth Scandinavian International Conference on Fluid Power, 1999,pp. 339349.


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