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Multi-dimensional scavenging analysis of a free-piston linear alternator based

on numerical simulation

Jinlong Mao⇑, Zhengxing Zuo, Wen Li, Huihua Feng

School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

a r t i c l e i n f o

Article history:Received 11 November 2009

Received in revised form 25 September

2010

Accepted 5 October 2010

Available online 30 October 2010

Keywords:

Free-piston

Linear alternator

Two-stroke

Scavenging process

Numerical simulation

Computational fluid dynamics

a b s t r a c t

A free-piston linear alternator (FPLA) is being developed by the Beijing Institute of Technology to improvethe thermal efficiency relative to conventional crank-driven engines. A two-stroke scavenging process

recharges the engine and is crucial to realizing the continuous operation of a free-piston engine. In order

to study the FPLA scavenging process, the scavenging system was configured using computational fluid

dynamics. As the piston dynamics of the FPLA are different to conventional crank-driven two-stroke

engines, a time-based numerical simulation program was built using Matlab to define the piston’s motion

profiles. A wide range of design and operating options were investigated including effective stroke length,

valve overlapping distance, operating frequency and charging pressure to find out their effects on the

scavenging performance. The results indicate that a combination of high effective stroke length to bore

ratio and long valve overlapping distance with a low supercharging pressure has the potential to achieve

high scavenging and trapping efficiencies with low short-circuiting losses.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

As oil prices rise and the debate on fossil fuels and environmen-

tal legislation intensifies, alternative drivetrains and engines are

gaining in interest. The FPLA is an alternative engine with the po-

tential to be both environmental friendly and efficient. The FPLA is

a combination of a free-piston engine and a linear electrical ma-

chine. This type of energy converter has many advantages such

as high efficiency, low fuel consumption and low emissions which

makes it suitable for a series hybrid vehicle [1]. Other significant

potential advantages of the FPLA, such as reduced heat transfer

losses, variable compression ratio and combustion optimization

flexibility, etc. were presented by Mikalsen and Roskilly [2].

Multi-dimensional computational fluid dynamics (CFD) codes

are widely used in the design and development of internal com-bustion engines due to their ability to investigate variables which

are difficult or costly to measure in experimental tests [3]. CFD of-

fers an expedient means for investigating the flow, gas exchange

and combustion processes under realistic engine operating condi-

tions, and the identification of the important features and major

underlying interactions between them.

The approach by the Beijing Institute of Technology (BIT) uses a

loop scavenged, carbureted free-piston, double-ended cylinder

arrangement with a linear alternator integrated directly into the

cylinder’s center position, as illustrated in Fig. 1. The combustion

at opposing cylinder ends is used to drive coils fixed to the piston

back and forth through the alternator’s magnetic field. The alterna-

tor generates electrical power and controls the piston’s motion by

dynamically varying the rate of electrical generation. Engine start-

up is also achieved using the alternator. Some experiments have al-

ready been done using the FPLA prototype and the results showed

that the engines could not work continuously for several cycles.

According to the in-cylinder pressure data collected, the engine

misfired every one or two strokes and the device would power

down without the aid of the linear alternator. Based on part load

characteristics of two-stroke engines, there must be something

inappropriate with the BIT engine’s gas exchange system.

The paper provides some insights into the multi-dimensional

gas flows in the scavenging process of a FPLA using commercialCFD software AVL_FIRE based on numerically simulated piston

motion profiles and evaluates the scavenging performance using

different design and operating options. The experimentally mea-

sured in-cylinder and scavenge case pressures were used to define

the boundary conditions.

2. Free-piston engines

2.1. Literature review

The free-piston engine concept was first introduced in the

1920s, and since then there have been many attempts to use this

0306-2619/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.apenergy.2010.10.003

⇑ Corresponding author. Tel./fax: +86 10 68911062.

E-mail address: [email protected] (J. Mao).

Applied Energy 88 (2011) 1140–1152

Contents lists available at ScienceDirect

Applied Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p e n e r g y

http://dx.doi.org/10.1016/j.apenergy.2010.10.003mailto:[email protected]://dx.doi.org/10.1016/j.apenergy.2010.10.003http://www.sciencedirect.com/science/journal/03062619http://www.elsevier.com/locate/apenergyhttp://www.elsevier.com/locate/apenergyhttp://www.sciencedirect.com/science/journal/03062619http://dx.doi.org/10.1016/j.apenergy.2010.10.003mailto:[email protected]://dx.doi.org/10.1016/j.apenergy.2010.10.003

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kind of engine for automobile and power generation applications.

These engines were in commercial use in the 1930–1960s as aircompressors in naval applications and air generators feeding hot

gases to power turbines. As conventional internal combustion en-

gine and gas turbine technology matured, the free-piston engine

concept was abandoned in the 1960s because of issues such as con-

trol problems and low power densities [4].

As modern microprocessor-based control methods became

available, the free-piston engine concept again stimulated interest

among research groups. Many papers on FPLA have been published

in the past two decades and among these West Virginia University

have demonstrated the stable operation of a spark ignited FPLA

prototype with a bore of 36.5 mm, a maximum possible stroke of

50 mm producing 316 W output power at 79 V while working at

full load [5,6]. Subsequently, a numerical parametric study of a

compression ignition FPLA was done by Shoukry et al. [7] in whichseveral parameters were modeled to predict the behavior of the

engine over a wide operating range. Petreanu [8], in his doctoral

dissertation, presented a conceptual design for a four-stroke com-

pression ignition linear engine based on a numerical simulation of

the operation of this type of linear engine.

Dr. Peter Van Blarigan at Sandia National Laboratory carried out

a series of single shot combustion experiments on a rapid compres-

sion expansion machine to simulate a free-piston’s performance

and undertook a numerical study of a free-piston engine operating

on homogenous charge compression ignition combustion [9]. The

engine operated at a high compression ratio (30:1) and a very

lean (fuel/air equivalence ratio of 0.35) fuel/air mixture to

Nomenclature

a shape factor of Wiebe function A top area of the piston (m2) At heat transfer area (m

2)b shape factor of Wiebe functionB magnetic induction intensity (m)

c V constant volume specific heat (J/(kg K))D cylinder diameter (m) f frequency (Hz)F e electromagnetic force (N)F f friction force (N) g air gap length (m)h heat transfer coefficient (J (m2 K)1)hm thickness of the permanent magnet (m)H length of coil cutting magnetic lines (m)H c magnetic field strength (A/m)_H e enthalpy output (J/s)_H i enthalpy input (J/s)iL current in the load circuit (A)L induction (mH)Leff effective stroke length (m)

Ltot total stroke length (m)Loverlap valve overlapping distance (m)m moving translator mass (kg)min mass of the charge (kg)M load coefficient (N/(m s1)1)M F mean magneto motive force (A)N coil number of turns in the coil p in-cylinder absolute pressure (Pa) p0 scavenge pressure (Pa) pL pressures in the left cylinder (Pa) pR pressures in the right cylinder (Pa)

ps pressure in scavenge case (Pa) psL pressure in left scavenging case (Pa) psR pressure in right scavenging case (Pa)Q energy (J)Q c heat released in combustion (J)

Q h heat transfer (J)Q in total input energy (J)R gas constant (J/(kg K))Rs internal resistance of coils (X)RL load resistance (X)t time (s)t 0 time combustion begins (s)t c combustion duration (s)T temperature (K)T w wall temperature (K)U internal energy (J)U mean piston speed (m/s)V displaced volume of the cylinder (m3)V n volume of free blow-down (m

3)V s volume of scavenge case (m

3)

W work done (J) x displacement of the translator (m) xign translator ignition position (m)c specific heat ratioeind induced voltage (V)U flux passing through the coil (Wb)k total flux passing through the coil (Wb)l0 vacuum permeability (H/m)s pole pitch (m)sp width of PM (m)

Fig. 1. FPLA configuration.

J. Mao et al. / Applied Energy 88 (2011) 1140–1152 1141

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approach the ideal Otto cycle performance. The experiments

demonstrated a thermal efficiency of 56% with low emissions.

Goldsborough investigated a wide range of design options of scav-

enging systems using CFD. The computational results indicated

that a stratified scavenging scheme employing uniflow geometry

and supplied by a stable, low temperature/pressure charge best

optimized the efficiency and emissions characteristics of the en-

gine [10].The European Union has been researching the subject of Free-

piston Energy Converter (FPEC) aimed at developing an efficient

new technology suitable for vehicle propulsion, auxiliary power

units and distributed power generation since 2002. Simulations

of the combustion system (two cylinders, two-stroke, and HCCI

combustion) showed an indicated efficiency of 51% at 23 kW

power output (effective efficiency around 46%) [11].

The Czech Technical University has recently successfully devel-

oped a direct injection FPLA prototype, with steady operation being

realized based on precise motion control. When the prototype was

running at a frequency of 27 Hz and compression ratio of 9, the

average power output was approximately 350 W, but the efficiency

was not reported [12].

Mikalsen and Roskilly proposed a design of a single cylinder

free-piston engine generator with gas-filled bounce chamber then

simulated its working process and discussed the effects of chang-

ing parameters over a wide operating range, with different mass

and compression ratios, on the FPLA performance [13]. A novel ap-

proach to modeling the free-piston engine through the introduc-

tion of a solution-dependent mesh motion using the engine CFD

toolkit OpenFOAM was also presented [14].

Bergman and Fredriksson et al. recently presented a CFD based

optimization of a diesel–fueled, uniflow scavenged, free-piston en-

gine. The piston dynamics, combustion process and intake and ex-

haust system dynamics were solved using Matlab/Simulink, KIVA-

3V and GT-Power respectively. Since there was no coupling be-

tween them, an iterative procedure was used for these models.

The effects of varying parameters such as compression ratios,

power supplied to the compressor, fuel injection timings and injec-tion pressures were studied in both conventional and HCCI modes

[15,16].

Free-piston engines are commonly modeled by most research-

ers using zero-dimensional, single zone models developed for con-

ventional engines. While such models can be useful for

investigating basic engine performance and piston dynamics, they

are unable to identify details of the engine operation such as in-

cylinder gas motion and emissions formation.

2.2. Operating characteristics of free-piston engines

Free-piston engines are crankless engines in which the output

power is extracted by a linear load device directly coupled to the

moving piston. Because energy transfer for the to-and-fro motionof the free-piston is complete, cycle-to-cycle energy storage is

not possible. Consequently, energy to power the separate intake

and exhaust strokes is not available and free-piston engines must

execute a two-stroke engine working mode with intake and ex-

haust processes typically conducted through ports coverage and

un-coverage by the piston. However, conventional two-stroke en-

gines are plagued by problems of insufficient charging and high

short-circuit losses over their part operating regimes due to the

wide range of speeds and power outputs over which the engines

operate. The free-piston engine, however, uses a much narrower

range of operating speeds due to the electrical generating scheme

employed by the device [9].

Although discussed briefly by some free-piston engine

researchers, only a few studies investigating the details of thethree-dimensional gas flows in the scavenging process in free-pis-

ton engines have been reported. The motion of a free-piston is not

mechanically prescribed but is rather a result of the balance of in-

cylinder pressures, inertia forces, friction forces and the applied

load. The differences in the piston motion profiles between the

free-piston engine and conventional engine have been docu-

mented by a number of authors, and the free-piston engine is

known to have higher piston acceleration around its end pointsand a significantly faster power stroke expansion [14]. These may

influence the in-cylinder gas dynamics and consequently the per-

formance of the engine.

2.3. Parameter definitions

Effective stroke length: the distance between the upper edge of

the exhaust port and the cylinder head.

Valve overlapping distance: the distance the translator can travel

when the exhaust ports of both cylinders are closed. Total stroke length: the distance the translator can travel from

cylinder head to cylinder head. Since the effective stroke length

is defined by the geometry of the cylinder, it is altered by

changing the valve overlapping distance. Scavenging efficiency: the ratio of the trapped fresh charge to the

total trapped mass of the cylinder during the scavenging pro-

cess [17].

Trapping efficiency: the ratio of the trapped fresh charge in the

cylinder to the total delivered fresh charge [17]. The trapping

efficiency is a measure of how much fuel flows directly into

the exhaust system (short-circuiting) and how much mixing

there is between the exhaust residual and the fresh charge.

The geometric parameters of FPLA are shown in Fig. 2. The rela-

tionships of effective stroke length, total stroke length and valve

overlapping distance can be expressed by the following equation:

Ltot ¼ 2Leff Lov erlap ð1Þ

3. Numerical simulation

As the piston motion profile of FPLA is different to conventional

engines, existing work on the CFD modeling of free-piston engines

uses piston motion profiles obtained from a dynamic engine mod-

el, which are expressed mathematically as a function of time and

implemented in the CFD code [3,9,15]. The same method is used

in this paper and the time is transferred to the equivalent crank an-

gle according to the frequency of the translator.

The FPLA represents both a dynamic and a thermodynamic de-

vice and the approach uses a series of dynamic and thermody-

namic equations to follow different events such as compression,combustion, expansion and scavenging over a full stroke.

Fig. 2. Geometric parameters of FPLA.

1142 J. Mao et al./ Applied Energy 88 (2011) 1140–1152

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3.1. Dynamic modeling

The piston dynamics are determined by analyzing the forces

acting on the free-piston and these include the pressures from each

cylinder, pressures from each scavenge case, friction force and the

electromagnetic force introduced by the linear alternator, as can be

seen in Fig. 3.

Applying Newton’s second law:

md

2 x

dt 2

¼ ð pL pRÞ A þ ð psR psLÞ A F f F e ð2Þ

Considering that the free-piston is free of side loads from the con-

necting rod, the friction force is small compared to the magnetic

force [18]. It was taken to be a constant in the dynamic model.

3.2. Modeling of the linear alternator

The linear alternator consists of two main components, a stator

and a translator. The permanent magnets are mounted on the sta-

tor and the translator which is made up of coils is the moving por-

tion of the machine. A schematic of a three-phase, ‘‘U” shaped

linear alternator with permanent magnet (PM) excitation is shownin Fig. 4.

The FPLA operates on the same basic physical principles as con-

ventional rotary alternators. The principle that governs the voltage

generating operation of the alternator is Faraday’s law expressed as

[19]:

eind ¼ dk

dt ¼ N coil

d/

dt ð3Þ

The permanent magnets create a magneto motive force (MMF)

in the air gap between the stator and the winding coils as shown in

Fig. 5, and the magneto motive force can be described by the fol-

lowing mathematical equation:

M F ð xÞ ¼

0 0 >><>>>>>>>:

ð4Þ

where M p = H c hm.

The mean value of the MMF can be obtained from the single-or-

der truncated Fourier series [20]:

M F ð xÞ ¼a02

þ a1 cos p xs

þ b1 sin

p xs

ð5Þ

where a0 ¼1

s

Z 2s0

M F ð xÞdx ¼ 0

a1 ¼1

s

Z 2s0

M F ð xÞ cos p xs

dx ¼ 0

b1 ¼1

s

Z 2s0

M F ð xÞ sin p xs

dx ¼

4

pM p sin

ps p2s

Then M F ð xÞ ¼ 4

pM p sin

ps p2s

sin

p xs

:

So the flux density in the air gap due to PM excitation is:

Bð xÞ ¼l0 g

M F ð xÞ ¼l0 g

4

pM p sin

ps p2s

sin

p xs

¼ Bm sin

p xs

ð6Þ

where Bm ¼

l0 g

4

pM p sin

ps p2s

:

Both experimental measurements and numerical calculation

using the finite element method showed that the flux in the air

gap of the PM-exited linear alternator in Fig. 5 could be assumed

to be sinusoidal, supporting the above result [21].

Therefore, the flux contained in the differential element dx is:

d/ ¼ Bð xÞdA ¼ Bð xÞHdx ð7Þ

Then the total flux contained in the coil of one phase at a ran-

dom position x is described by the following equation:

kð xÞ ¼

Z x xs

N coilHBð xÞdx ¼ sHN coilM pl0 g

8

p2 sin

ps p2s

cos

ps

x

ð8Þ

Thus, the induced electromotive force produced in the coil of one phase is:

e ¼ dk

dt ¼ HN coilM p

l0 g

8

p sin

ps p2s

sin

ps

x dx

dt ð9Þ

The induced current in the load circuit can be derived from the

following equations:

eðt Þ ¼ ðRs þ RLÞiLðt Þ þ LdiLðt Þ

dt ð10Þ

iLðt Þ ¼ eðt ÞRs þ RL

1 eRsþRL

L t

ð11Þ

The magnetic force has the opposite direction to the direction of

the translator’s movement. According to Ampere’s law, it is de-

scribed by the following equation:

F e ¼ 2N coilBð xÞiLH ¼ 4H 2N 2coilB

2m

1 eRs þRL

L t

Rs þ RL

sin2 p x

s

dxdt

ð12ÞFig. 3. Free body diagram for FPLA.

Fig. 4. Schematic of a U shaped three-phrase linear alternator.


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When it comes to the three-phase linear alternator, the third

phase is derived from the other two phases according to the fol-

lowing equation [22]:

sinu ¼ sin u þ2

3p

sin u

2

3p

ð13Þ

So the total electromagnetic force produced by a three-phase

linear alternator is:

F e ¼ 4H 2N 2coilB

2m

1 eRs þRL

L t

Rs þ RL

dx

dt

sin2 p x

s

2

3

p þ sin

2 p xs

þ sin

2 p xs

þ2

3p

¼ 6H 2N 2coilB2m 1 e

RsþRL

L t

1Rs þ Rl

dx

dt ¼ M 1 e

Rs þRLL

t dx

dt ð14Þ

where

M ¼ 6H 2N 2coilB2m

1

Rs þ Rl:

3.3. Thermodynamic modeling

The zero-dimensional, single zone model is used to describe the

thermodynamic process in the cylinder and the important assump-tions are:

At any instant of time there is thermodynamic equilibrium of

the temperature and pressure in the cylinder.

The working gas in the cylinder obeys the ideal gas law.

The effects of vaporizing liquid droplets, fluid flow, combustion

chamber geometry or spatial variations of the mixture’s compo-

sition are ignored.

The kinetic energy of the working gas is negligible.

The combustion process is assumed to be perfect and no com-

bustion loss is considered.

The thermodynamic model is derived based on the first law of

thermodynamics and the ideal gas law. It includes the calculation

of the processes of scavenging, compression, combustion, expan-

sion and exhaust. The zero-dimensional, single zone model is used

to describe the thermodynamic process [5–7,9,13].

Appling the first law of thermodynamics and the ideal gas law

on the cylinder as an open thermodynamic system, shown in

Fig. 6, and assuming that the specific heat c V and the gas constant

R are constant, then:

dU

dt ¼ p

dV

dt þ

dQ

dt þ _H i _H e ð15Þ

In the case of the compression and expansion processes,

neglecting crevice flow and leakage, the first law of thermodynam-

ics applied to the cylinder content becomes:

mindðc V T Þ

dt ¼ pdV

dt þdQ

dt ð16Þ

Considering the cylinder content is an ideal gas, then at every

instant the ideal gas law is satisfied as:

pV ¼ minRT ð17Þ

Substitution and mathematical manipulation yield the follow-

ing equation which is used to calculate the in-cylinder pressure

at each time step.

dpdt

¼ c 1V

dQ dt

c pV

dV dt

ð18Þ

In the combustion model, since the engine is crankless, a time-

based Wiebe function (as opposed to a conventional crank-angle

based approach) is used to express the mass fraction burned in

the combustion process as [6]:

vðt Þ ¼ 1 exp a t t 0

t c

1þb ! ð19Þ

dQ c dt

¼ Q indvðt Þ

dt ð20Þ

The in-cylinder heat transfer effect is modeled according to

Hohenberg [23]:

dQ hdt

¼ hAt ðT T wÞ ð21Þ

and the in-cylinder temperature is calculated according to the ideal

gas law:

T ¼ pV

minR ð22Þ

The heat transfer coefficient h is given by:

h ¼ 130V 0:06 p

105

0:8T 0:4ðU þ 1:4Þ

0:8ð23Þ

So the amount of the total heat input used to increase the in-

cylinder pressure is:

dQ

dt ¼

dQ c

dt

dQ h

dt ð24Þ

Exhaust blow-down is modeled to be a polytrophic expansion

process while the exhaust port is opening and the scavenging ports

are still covered by the piston [13]

dp

dt ¼

c 1V n

dQ

dt c

p

V n

dV ndt

ð25Þ

When the scavenging ports and intake port are covered by the

piston, the fuel/air mixture in the scavenging case is modeled to

be adiabatic compression and adiabatic expansion. When the scav-

enge ports are connected with the cylinder and intake port, the

pressures in each block are assumed to be the same with the scav-

enge pressure.

dps

dt ¼ c p

sV s

dV sdt ð26Þ

Fig. 5. Model of the linear alternator.

Fig. 6. Thermodynamic system of FPLA.


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For two-stroke spark ignition engines with under piston or

crankcase scavenging, the scavenging efficiency is about 0.7–0.9

[24], which is also supported by the CFD scavenging analysis of

the free-piston engine mentioned in this paper. Thus, a scavenging

efficiency of 0.8 is introduced to evaluate the effects of incomplete

scavenging effect. The moment the scavenging ports are open, the

pressure and temperature are assumed to be the same with the

scavenging conditions and the incoming gases mix entirely withthe burned gases.

3.4. Parameters of the FPLA

The dynamic and thermodynamic equations of the FPLA were

solved using a numerical simulation program in Matlab and some

of the parameters were defined according to the experimental data

measured.

Before starting the program, the geometric dimensions of the

free-piston engine, the initial conditions and the initial values of

some parameters were first entered into the program. The values

used are listed in Table 1.

3.5. Free-piston motion profile

The movement of the translator is shown in Fig. 7 and the piston

movement of the original two-stroke engine (TSE) which was cho-

sen to compose the FPLA prototype, is also presented for compari-

son. Since the stroke length of the FPLA is variable, the parameters

are adjusted to ensure the same stroke length is achieved with the

TSE. The specifications of the FPLA and TSE are presented in Table 2.

Here CA is crank angle and ECA is equivalent crank angle which

are used to note the port timings. However, it is only a time nota-

tion since the free-piston engine does not have a crankshaft to de-

fine the piston’s motion (ECA = (t t 0) f 360, where t 0 is the start

time of the piston motion profiles and f is the to-and-fro frequency

of the translator [10,17]).

Only the exhaust and scavenging processes are studied in this

research, so the calculation domain is from exhaust port openingto exhaust port closing, as is marked in Fig. 7.

The piston motion profile is described using two arrays of num-

bers one of which represents the ECA and the other represents the

displacement of the piston, with the file being directly imported

into the CFD code.

3.6. Translator motion profiles with different operating conditions

Since the free-piston engine is restricted to the two-stroke

operating principle, if efficient gas exchange cannot be realized

the engine will not operate in practice. To ensure that continuous

operation can be achieved, a wide range of design and operating

ranges for the free-piston engine such as effective stroke length,

valve overlapping distance, frequency and charging pressure were

investigated to find the appropriate design options giving high

scavenging efficiency, high trapping efficiency and low short-cir-

cuiting losses. The calculation ranges are listed in Table 3.

As the piston dynamics change with different operating condi-

tions and geometrical dimensions, the piston motion profiles must

first be defined in the numerical simulation program. Since there

was no coupling between the CFD code and numerical simulation

program, the piston dynamics were adjusted depending on the de-

sired operating frequency and the stroke of the free-piston engine

in the numerical simulation program. The piston motion profiles

for different operating conditions are shown in Figs. 8–11. The de-tailed parameters for each operating point are listed in Tables 4–7.

3.6.1. Effective stroke length

Four values of effective stroke length were used to investigate

the effects of scavenging. As can be deduce from Eq. (1), longer

Table 1

Specifications of the FPLA.

Parameters Value

Bore 34 mm

Effective stroke length 20 mm

Valve overlapping distance 6 mm

Total stroke length 34 mm

Compression ratio of scavenging case 1.18

Mass of the translator 1.74 kg

Specific heat ratio in compression stroke 1.33

Specific heat ratio in expansion stroke 1.30

Load coefficient of the linear alternator 55.3 N/(m s1)

Inductance 1.29 mH

Internal resistance 2.0X

Load resistance 2.5X

Scavenging pressure 1.0 bar

Scavenging temperature 313 K

Friction force 22 N

Combustion duration 4.5 ms

Translator ignition position 12 mm

Fig. 7. Free-piston engine and two-stroke engine piston motion profiles.

Table 2Specifications of the FPLA and TSE.

Parameters Two-stroke engine Free-piston engine

D 34 mm 34 mm

Compression ratio 8 8

Leff 20 mm 20 mm

Loverlap – 6 mm

Real stroke 28.6 mm 28.6 mm

Exhaust port opening (EPO) 94.92 CA 101.6 ECA

Exhaust port closing (EPC) 265.1 CA 253.4 ECA

Scavenging port opening 117.5 CA 126.7 ECA

Scavenging port closing 242.5 CA 229.5 ECA

f 30 Hz 30 Hz

Scavenging arrangement Loop scavenged Loop scavenged

Table 3

Calculation ranges.

Paramete rs Value

Leff 20 mm 22 mm 24 mm 26 mm –

Loverlap 2 mm 4 mm 6 mm 8 mm 10 mm

f 25 Hz 30 Hz 35 Hz 40 Hz –

p0 1.0 bar 1.2 bar 1.5 bar – –


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effective stroke length with constant valve overlapping distance

will lead to longer total stroke length. As is determined by the geo-

metric structure of the scavenge port which will be discussed later,the opening area of scavenging port is larger with longer stroke. As

Fig. 8. Piston dynamics with different effective stroke lengths and constant valve

overlapping distance.

Fig. 9. Piston dynamics with different effective stroke lengths and variable valve


Fig. 10. Piston dynamics with different valve overlapping distances.

Fig. 11. Piston dynamics with different operating frequencies.

Table 4

Operating parameters with different effective stroke lengths and constant valve


Parameters Case I Case II Case III Case IV

Leff 20 mm 22 mm 24 mm 26 mm

Loverlap 6 mm 6 mm 6 mm 6 mm

Ltot 34 mm 38 mm 42 mm 46 mm

D 34 mm 34 mm 34 mm 34 mm

EPO 102.2 ECA 100.0 ECA 98.6 ECA 97.6 ECA

EPC 254.5 ECA 255.0 ECA 256.0 ECA 256.9 ECA

f 40 Hz 40 Hz 40 Hz 40 Hz

p0 1.0 bar 1.0 bar 1.0 bar 1.0 bar

Table 5

Operating parameters with different effective stroke lengths and variable valveoverlapping distance.





D 34 mm 34 mm 34 mm 34 mm

EPO 102.2 ECA 112.2 ECA 114.5 ECA 117.5 ECA

EPC 254.5 ECA 244.7 ECA 241.6 ECA 238.9 ECA

f 40 Hz 40 Hz 40 Hz 40 Hz

p0 1.0 bar 1.0 bar 1.0 bar 1.0 bar

Table 6

Operating parameters with different valve overlapping distances.

Parameters Case I Case II Case III Case IV Case VLoverlap 2 mm 4 mm 6 mm 8 mm 10 mm

D 34 mm 34 mm 34 mm 34 mm 34 mm

Leff 20 mm 20 mm 20 mm 20 mm 20 mm

Ltot 38 mm 36 mm 34 mm 32 mm 30 mm

f 30 Hz 30 Hz 30 Hz 30 Hz 30 Hz

EPO 90.8 ECA 95.9 ECA 101.6 ECA 108.3 ECA 116.8 ECA

EPC 262.6 ECA 258.4 ECA 253.4 ECA 247.6 ECA 240.6 ECA

f 40 Hz 40 Hz 40 Hz 40 Hz 40 Hz

EPO 92.3 ECA 101.2 ECA 102.2 ECA 108.1 ECA 115.1 ECA

EPC 264.1 ECA 255.0 ECA 254.5 ECA 248.7 ECA 242.2 ECA

p0 1.0 bar 1.0 bar 1.0 bar 1.0 bar 1.0 bar


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can be seen in Table 4, longer effective stroke length leads to longer

scavenging period. The movement of the translator with different

effective stroke lengths and constant valve overlapping distance

is shown in Fig. 8.

Since the opening area of scavenging ports and scavenging per-

iod which have great effects on the scavenging performance, are

also affected by the effective stroke length with constant valve

overlapping distance. Therefore, in order to analyze just the effects

of effective stroke length to scavenging performances, the valve

overlapping distances were varied to make sure that the piston justreached the bottom edge of the exhaust port at BDC for each case.

The reason for this is to make sure that the biggest opening area of

the scavenging ports of each case is the same. As can be seen in Ta-

ble 5, longer effective stroke length has shorter scavenging period.

The movement of the translator with different effective stroke

lengths and variable valve overlapping distance is shown in Fig. 9.

3.6.2. Valve overlapping distance

Valve overlapping distance is a very important parameter since

it determines the total period of the scavenging process. Usually

the valve overlapping distance is determined based on the maxi-

mum thrust force of the linear alternator to avoid the large resis-

tance caused by the pressure difference in the two cylinders. As

can be seen in Table 6, a shorter valve overlapping distance leadsto a longer scavenging period and a larger opening area of the scav-

enging ports. The movement of the translator with different valve

overlapping distances is shown in Fig. 10.

3.6.3. Operating frequency

Four values of operating frequency were chosen to investigate

the effect on scavenging, and the scavenging periods are listed in

Table 7. As can be seen in Fig. 11, a higher frequency leads to a

higher compression ratio which means that the piston will move

further down during the scavenging process and as a result a long-

er scavenging period and a larger opening area of the scavenging

ports.

3.6.4. Charging pressureThree cases of different charging pressures were also calculated.

Since the cylinder is exposed to the environment through the ex-

haust port during the gas exchanging process and the exhaust port

closes later than the scavenging ports, the dynamics of the transla-

tor for different charging pressures were assumed to be the same

for each case. The basic parameters were: bore of 34 mm, effective

stroke length of 20 mm, valve overlapping distance of 6 mm, fre-

quency of 30 Hz and EPO–EPC of 101.6–253.4 ECA.

4. Multi-dimensional scavenging analysis of the FPLA

4.1. Scavenging description

Scavenging is the simultaneous emptying of the burned gasesand filling with a fresh air/fuel mixture. Near Top Dead Center

(TDC) the spark plug initiates combustion and the cylinder pres-

sure increases dramatically driving the piston downwards. This

power stroke decreases the volume of the scavenge case and thus

pressurizes it contents consisting of the fresh charge. As the ex-

haust port begins to be uncovered by the piston, the combustion

products begin venting from the cylinder. This process is called free

blow-down and occurs because the cylinder contents are still at a

higher pressure than that of the exhaust port. As the piston contin-ues to move towards Bottom Dead Center (BDC), the scavenging

ports open providing a flow path between the cylinder and the

ports. Due to the pressure differential between the cylinder and

the scavenging ports, a flow develops whose purpose is to replace

the combustion products with a fresh charge before the scavenging

ports close. This phase is called scavenging and is unique to two-

stroke engine. The scavenging process is over when the scavenging

ports are again shielded by the piston.

Short-circuiting is a detrimental phenomenon that constitutes a

loss of fresh fuel/air mixture through the exhaust ports during

scavenging. This represents a parasitic loss where work from the

engine, used to pressurize the crankcase, is lost through the ex-

haust. More importantly, in a carbureted engine where the scav-

enging charge contains fuel and lubricating oil, short-circuiting

results in poor fuel consumption and the emission of unburned

hydrocarbons.

4.2. CFD model configuration

The geometry of the engine was represented in the form of a

computational mesh. The numerical mesh constitutes the

decomposition of the geometrical domain into small volumes

termed cells, for which the governing equations of fluid flow

are solved simultaneously. Due to the layout symmetry of

the cylinder ports, it was only necessary to model half of the

geometry in order to minimize the computational cost. The

CFD model was constructed using four blocks representing ex-

haust port, scavenging port, cylinder and the scavenging case,as can be seen in Fig. 12.

The moving parts such as the cylinder and scavenging case were

meshed with layered hexahedrons with the layers being normal to

the movement of the piston. Since the geometry of the scavenging

port was very irregular, it was meshed with hybrid grids including

tetrahedrons, prisms and hexahedrons, and the total quantity of

structure cells was more than 80% to avoid divergence and ensure

the accuracy of the results.

The total number of all cells was 149,375 including 398 tetrahe-

dron cells, 1953 prism cells and 143,608 hexahedron cells. The to-

tal number of cells varied with different geometrical dimensions of

the engine discussed above. The dimensions of the first wall cell of

the cylinder were about 2 1 0.5 mm; the dimensions of the

first wall cell of the scavenge case were 1.3 0.5 1.3 mm; andthe dimensions of the first wall cell of the exhaust port were

0.8 0.5 0.5 mm. The scavenge port was refined several times

at the sharp edges due to its complex geometry and the upper part

dimensions of the first wall cell were 0.5 0.5 0.5 mm while the

lower part were 0.5 0.5 1 mm.

The dynamic mesh tool Fame Engine in AVL_FIRE was used to

create the moving mesh according to the numerically simulated

free-piston motion profile. The update of the volume was handled

automatically at each time step based on the new position of the

piston.

Since the grid distributions of the cylinder and scavenge case

were different from that of the exhaust and scavenge ports, a

mathematical connectivity between every two contact domains

was created and the exact contact area was calculated for everytime step.

Table 7

Operating parameters with different frequencies.


f 25 Hz 30 Hz 35 Hz 40 Hz

D 34 mm 34 mm 34 mm 34 mm




EPO 113.8 ECA 112.3 ECA 111.9 ECA 110.7 ECAEPC 241.4 ECA 243.1 ECA 243.7 ECA 243.0 ECA

p0 1.0 bar 1.0 bar 1.0 bar 1.0 bar


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4.3. Boundary conditions

The boundary conditions were chosen to reflect the physical

conditions in the validation model and the prototype engine. In

the dynamic flow simulations, a fixed pressure was applied at

the outlet boundary without the inlet, since the induction process

did not take place during the gas exchange process. The exhaust

port and the combustion chamber were initialized with a homog-enous high pressure consisting of burned gas, whereas the scav-

enge port and scavenge case were initialized with compressed

fresh charge. Constant wall temperatures were also used. The stan-

dard K e model was employed to capture turbulence.

4.4. Numerical solver settings

The time step for the calculation is set about 0.1–0.4 for all the

calculation cases depending on convergence at each time step. Dis-

cretization was achieved through the second order MINMOD re-

laxed differencing scheme for momentum and continuity while

the first order upwind differencing scheme was used for turbu-

lence, energy and scalar quantities.

During a simulation, the CFD solver needed to know when to jump to the next time step for a transient run. There were two

ways the solver could make this decision. The pressure and

momentum were solved until the reduction of residuals reached

104 or the total number of iterations exceeded 50; the solver

would then jump to the next time step.

5. Results and discussion

5.1. Scavenging results for the FPE and TSE

The scavenging results for the free-piston engine (FPE) and

two-stroke engines are listed in Table 8. It seems that the scaveng-

ing results for these two engines are very similar since the piston’s

motion profiles during the scavenging process have smalldifferences, as shown in Fig. 7. The p–V diagrams of these two

engines also have negligible differences during the scavenging pro-

cess, as can be seen in Fig. 13. But what is important is that since

the free-piston engine does not have a crank mechanism, its stroke

is variable for different operating conditions which makes the

scavenging process of the free-piston engine more complicated

than the two-stroke engine.

The CFD simulated and experimentally collected pressure of

scavenge case is shown in Fig. 14. The same variation trend of

the pressure curves can be observed. The deviation between the

CFD simulated and experimental collected pressure curves is as-

sumed to be caused by the gas leak in the hole of the scavenge case

where the connecting rod passes through.

The in-cylinder mass flow during the scavenging process and a

series of snapshots of contours of mass fractions of burned gases on

a plane cut through the center of the free-piston engine, are shownin Fig. 15. As can be seen in the figure, the upper part of the engine

is initially filled with burned gases (red1) and the lower part with

fresh charge (blue).

At about 80 before BDC, the piston uncovers the exhaust port

and free blow-down occurs such that the cylinder pressure ap-

proaches the ambient pressure. About 25 later the scavenge ports

open and the fresh charge compressed by the underside of the pis-

ton in the scavenge case is able to flow into the cylinder. The

incoming air/fuel mixture is directed towards the unported cylin-

der wall, where it is deflected upwards by the cylinder wall and

the piston and flow form a ‘‘U” shaped loop. With this loop

Fig. 12. CFD model of free-piston engine.

Table 8

Scavenging results of FPE and TSE.

Scavenging efficiency (%) Trapping efficiency (%)

Two-stroke engine 79.49 68.74

Free-piston engine 78.40 68.20

1 For interpretation of color in Fig. 15, the reader is referred to the web version of this article.


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scavenge arrangement, the incoming charge displaces and mixes

with the exhaust gas residual and some of the incoming charge

flows directly into the exhaust port. The scavenge process ends

with both the scavenge case and cylinder pressure close to the

ambient pressure once the scavenge ports are closed. Towards

the end of the scavenge process there can be a backflow of fresh

charge and exhaust gas residuals into the scavenge case. The up-

ward movement of the piston now reduces the pressure in the

Fig. 13. p–V diagram during scavenging process of FPE and TSE. Fig. 14. Pressure in the scavenge case.

Fig. 15. Contours of mass fraction of burned gas during scavenging process of FPE.


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scavenge case. At about 70 after BDC, the exhaust port closes and

the whole gas exchange process ends. Later the charge in the cyl-

inder will be compressed by the upward movement of the piston.

During this process, two undesirable features are the mixing of the

incoming charge with the exhaust residuals and the passage of the

fresh charge directly into the exhaust port.

5.2. Effects of effective stroke length

The scavenging results with different effective stroke lengths

and constant valve overlapping distance are shown in Fig. 16. As

discussed earlier, longer effective stroke length leads to longer

scavenging period and larger opening area of the scavenging ports

with the parameters of Table 4. It is hard to identify just the effects

of effective stroke length to the performance of scavenging.

The results show that as the effective stroke length grows with

the current parameters, the scavenging efficiency keeps increasing

while the trapping efficiency keeps decreasing.

With the parameters setting in Table 5, the effects of just effec-

tive stroke length to the scavenging performance can be analyzed.

A longer effective stroke length means that the fresh gas flow has

to travel a longer distance to sweep the burned gas out. Thus, alonger effective stroke length would lead to lower scavenging effi-

ciency but higher trapping efficiency, as can be seen in Fig. 17.

5.3. Effects of valve overlapping distance

The scavenging results with five valve overlapping distances

and two frequencies are shown in Fig. 18. It is clear that a shorter

overlapping distance leads to a little higher scavenging efficiency

but a much lower trapping efficiency (higher short-circuiting loss)

as a shorter valve overlapping distance results in a longer scaveng-

ing period. The trends are similar for two different operating fre-

quencies. Therefore, a longer valve overlapping distance would

be favorable for achieving a high trapping efficiency.

5.4. Effects of operating frequency

The scavenging results with different operating frequencies are

shown in Fig. 19. The curves show that as the operating frequency

increases the scavenging efficiency keeps increasing while the

trapping efficiency keeps decreasing.Fig. 16. Effects of effective stroke length with constant valve overlapping distance.

Fig. 17. Effects of effective stroke length with the same opening area of scavengingports.

Fig. 18. Effects of valve overlapping distance.

Fig. 19. Effects of operating frequency.


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5.5. Effects of charging pressure

The scavenging results with three different charging pressures

are shown in Fig. 20. It seems that the free-piston engine with

low supercharging (1.5 bar) would greatly improve its scavenging

efficiency compared to the naturally aspired engine with a compar-

atively smaller reduction in trapping efficiency.

As can be seen in Fig. 21, the in-cylinder p-ECA diagram with

different charging pressures during the gas exchanging process

has the same trend except for some fluctuation during the scaveng-

ing process. At the end of the exchanging process, the in-cylinder

pressure has almost the same value for different charging pres-

sures which validates the assumption that the piston dynamics

for different charging pressures can be assumed to be the same

since constant scavenging efficieny is present in the zero-dimen-

sional simulation program model.

6. Conclusions

Computational modeling and single step parametric variationshave been used to analyze the scavenging system for a FPLA to find

the best parameter combinations for high scavenging and trapping

efficiencies. A wide range of design and operating options was

investigated including effective stroke length, valve overlapping

distance, operating frequency and charging pressure.

The results of the analysis indicate that:

(1) The scavenging performances of the FPE and TSE have minor

differences when the two kinds of engines are workingunder the same conditions.

(2) The parameters that lead to a higher scavenging efficiency

will also lead to a lower trapping efficiency.

(3) A longer effective stroke length would lead to lower scav-

enging efficiency but higher trapping efficiency.

(4) A smaller valve overlapping distance would help improve

the scavenging efficiency, but it would also lead to more

short-circuiting losses.

(5) A higher operating frequency would help to increase the

scavenging efficiency of the free-piston engine but also

decrease the trapping efficiency.

(6) A low supercharged free-piston engine would greatly

improve the scavenging efficiency (90%) while keeping

the trapping efficiency within a reasonable range (0.6–0.8).

Therefore, an optimum arrangement of the free-piston engine’s

scavenging system would utilize a higher effective stroke length to

bore ratio, a long valve overlapping distance with a low super-

charge to achieve a good scavenging performance (scavenging effi-

ciency 0.9, trapping efficiency 0.8). However, the control of

short-circuiting is challenging with the current means of supplying

the fuel (carburetor or port injection). Subsequent research will

investigate the use of in-cylinder direct injection to reduce short-

circuiting after the exhaust port (valve) is closed.

Acknowledgement

This project is supported by the National Nature Science Foun-dation of China (51005010). We would like to thank the sponsors.

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