Simulation of Free Piston Linear Engine Motion with Different Intake ...

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Simulation of Free Piston Linear Engine Motion with Different Intake and Exhaust Port Positions

Ahmad Kamal Ariffin, Nik Abdullah Nik Mohamed and Syarizal Fonna

Department of Mechanical and Materials Engineering Faculty of Engineering Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor D.E. email: [email protected] Received Date: 12th March 2005

Accepted Date: 15th May 2006

ABSTRACT This paper presents the simulation of two-stroke free piston linear engine motion consisting of combustion and air-kickback chambers. Dynamic and gas-dynamic models for slider-piston motion are presented. The influence of the intake and exhaust port position on the engine performance is explored. Using chosen variables, the motion of two-stroke free piston linear engine is successfully simulated. It shows that the velocity profile of slider-piston motion is far from sinusoidal. The comparison between both simulations with different location of intake and exhaust port reveals that the slider-piston velocities are not similar. Slider-piston velocity of model 2 with intake and exhaust port at the top of the cylinder block is 19 % higher than model 1 (intake and exhaust port at the cylindrical-side of cylinder block). Although that was the case, model 1 has an advantage in a way that it does not need valves and openclose valves system. Keywords: Free piston engine, two-stroke engine, intake, exhaust, dynamic ABSTRAK Kertas kerja ini membentangkan simulasi gerakan enjin linear omboh bebas dua lejang yang mempunyai satu kebuk pembakaran dan satu kebuk udara-tendang balik. Model dinamik dan model dinamik-gas untuk gerakan gelangsar-omboh dibentangkan. Kajian ini menyelidiki kesan kedudukan pancarongga masukan dan ekszos terhadap pergerakan enjin. Hasil simulasi menunjukkan bahawa profil halaju gelangsar-omboh tidak menyerupai bentuk sinus. Perbandingan hasil simulasi antara kedua model yang berbeza kedudukan pancarongga mendapati bahawa halaju kedua-dua model adalah tidak serupa. Halaju gelangsar-omboh model 2 dengan pancarongga terletak di hujung atas silinder adalah 19 % lebih tinggi daripada model 1 yang pancarongga di sisi silinder. Walaupun demikian, model 1 memiliki satu kelebihan iaitu tidak memerlukan injap dan sistem injap buka-tutup. Kata kunci: Enjin linear omboh bebas, enjin dua lejang, masukan, ekzos, dinamik

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Ahmad Kamal Ariffin, et al./ Jurnal Kejuruteraan 18 (2006): 97-106

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INTRODUCTION

MODELED ENGINE

A free piston linear engine is a machine with linear motion as the primary motion. The crankshaft that is present on the conventional engine has been elimi-nated. This linear engine has benefits in terms of efficiency, weight reduction, robustness, variable compression operation and multi-fuel possibilities (Arshad et al. 2002). Free piston linear engines offer the potential to provide power without the conversion of linear to rotary motion (Nandkumar 1998). The most common model that has been developed for free piston linear engine systems is dual opposed combustion chamber model (Atkinson et al. 1999; Goldsborough & Blarigan 1999;Houdyschell 2000; Nandkumar 1998). Meanwhile, the other model of free piston linear engine that have been developed is the model that replace one combustion chamber with other device. For example, a free piston linear engine that uses a spring as the opposite to combustion chamber has been developed (Annen et al. 2002). Air cushion chamber has been developed by Aichlmayr et al. (2002) in order to replace a combustion chamber in common free piston linear engine. This paper focuses on free piston linear engine that one combustion chamber is replaced with air kickback chamber. The influences of different location of intake and exhaust ports in modeled engine are investigated for the system. The previous work, Fonna et al. (2004), clearly shows that the motion profile of linear engine is far from sinusoidal.

Free piston linear engine could be divided into two categories. The first category is free piston linear engine with intake and exhaust port at the cylindrical-side of the cylinder block. This engine is shown in Figure 1. The second category is engine with intake and exhaust port at the top of the cylinder block that is shown in Figure 2. These engines are called model 1 and model 2, respectively, for easy identification. The models are two-stroke spark ignition engine. The free piston linear engines consist of five main parts, i.e. combustion chamber, scavenging chamber, kickback chamber, generator housing, and sliderpiston. The term slider-piston is used to describe the unity of combustion piston, kickback piston, connecting rod, and permanent magnet. The rod connects the two oppositely placed pistons and also acts as a prime mover for linear engine. The permanent magnet is placed at certain position of the rod. The two opposing pistons have different diameter. Kickback piston diameter is larger than combustion piston diameter to ensure the generated force in the kickback chamber is adequate to push back slider-piston. Free piston linear engine when coupled with linear alternator becomes a linear generator. When the slider-piston moves linearly, it will cause a disturbance of the field that was produced by the permanent magnet.Thus, an electromagnetic force will be in-duced in the coil of the linear alternator. This is the working principle of free piston linear generator that is producing electricity directly from the linear motion of the

Scavenging chamber Intake port

Kickback chamber

Transfer duct

Exhaust port magnet Combustion chamber

Generator housing

rod

Exhaust & intake port

Figure 1. Free piston linear engine with intake and exhaust port at cylindrical-side of the cylinder block (model 1)

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Scavenging chamber

Combustion chamber Intake port

99

Kickback chamber

Transfer duct

Exhaust Port magnet Generator Housing

rod

Exhaust & make port

Figure 2. Free piston linear engine with intake and exhaust port at the top of the cylinder block (model 2

pistons. The salient feature of free piston linear engine is a mechanically unconstrained piston (Aichlmayr et al. 2002). Thus, the system obeys Newton’s second law,

d 2x � F � m dt 2

(1)

scavenging chamber pressure,Ac is the combustion piston area, Ak is the air-kickback piston area, As is the combustion piston back area, Ff is the friction force, and Fe is the electromagnetic force. Assuming the engine is running within no load condition, i.e. no power delivered, the electromagnetic force may be neglected in this simulation. According to Atkinson et al. (1999), the friction force is not significant for linear engine.Thus, it can be neglected since the force is relatively very small due to no crankshaft system. Figure 3 is given to illustrate a force balance on free piston for simplified no load condition.

where the left handn side of equation (1), i.e. ∑F, � constof the forces that act represents the sPV ummation in the plane of motion, the right hand side of equation (1), i.e. d2x/dt2, is the acceleration of sliderPV � mRTthe displacement of piston with x representing sliderpiston and m is the slider-piston mass. In order to analyze the slider dynamics, the THE GAS-DYNAMIC MODEL forces acting on the slider-piston are determined. � � � L1 � a � Q ( n � 1 ) � � These forces are due to the combustion cylinder n n in n � � �a� a � � L1scavenging � the � � aira � MODEL 1� L2 � c � � pressure, pressure, the P � A � P � � � � � � � atm � c atm ( L1 �piston a ) Ac ring-wall and expansion of each � a pressure, � � c � kickback� cylinder the � � a � x � The compression �� cylinder are modeled adiabatically and internally friction,��and electromagnetic force. The forces reversible. The process in combustion chamber balance on free piston is given by equation (2) is represented by Otto cycle, while in kickback at combustion condition and equation (3) at air chamber and scavenging chamber by the ideal kickback condition. n n 2 � (b3 ) 2 L5 � gas � � (b1 )adiabatic 2 L � pro-cess (Figure 4). The dimensions c �� Ak � Patm � � As 1, i.e. intake and exhaust port 2 ) 2 (engine 2 L � x)model � L2 � L4 � c � x � � (b2 3 ) L5 � (b1of � dd 2 xx at cylindrical-surface of cylinder block, are also P Pcc A Acc � �P Pkk A Akk � �P Pss A Ass � �F F ff � �F Fee � �m m dt 22 (2) described in Figure 4. The effects of intake and dt exhaust port length to the generated pressure in 2 each chamber are considered in the analysis. d x dd 22 xx � F f � Fe � m 2 For the initial condition, the slider is considered P (3) Pkk A Akk � �P Pcc A Acc � �P Pss A Ass � �F Fdtff � �F Fee � �m m dt 22 to move from the left (combustion chamber top dt dead center) to the right in positive x direction i.e. n n n n expansion combustion chamber where Pc is the instantaneous � c � L2 � c � � � L1 � a � process. � a �Then, combustion. chamber �� Ak � Patm � �� AcAt these conditions, the is �chosen �as�reference. pressure, PPk atm is �the instantaneous air-kickback a� x� � c � � L2 � L4 � c � x � � a in � �combustion pressure chamber is Pc3 as the chamber pressure, P s is the instantaneous

� Patm As � F f � Fe � m

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� �

n

d 2x dt 2

� �L�a� Qin � � (n � 1)�

n

n

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100

Ac

m Ps

Pc

Pk A5

x

Ak

Figure 3. Slider free-body diagram

L5

L4 b3

b2

b1 L1

a

L3

L

L4

L

L

x TDC

x

BDC

3

Pc

c

L2

Pk

Ps

2 2 2 4 1

1

1

Vk

Vs

Vc

Figure 4. The dimension of engine and pressure volume diagrams for each chambers modeled for the simulation of model 1 (TDC: top dead center, BDC: bottom dead center) A m Ps

Pc

P x

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A

A

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result of instantaneous heat addition in the combustion process. Meanwhile the pressure in the kickback chamber and scavenging chamber are free-air pressure Pk1 and Ps1, respectively. When the slider is moving to the right, the combustion pressure will follow 3-4 path of the PcVc diagram and at point 4 the exhaust port s tarts to open, and the pressure suddenly drops to Pc1 due to instantaneous heat rejection. The scavenging pressure will in-crease along 1-2 path in the PsVs diagram and the pressure drops to Ps1 from point 2 when the intake port starts to open.The kickback pressure mean-while remains at Pk1 along L4 because the port is still open and starting from point 1, the pressure will increase following 1-2 path in the PkVk diagram. Considering the condition when the slider moves from r ight to left after the expansion stroke i.e. compression stroke, the combustion pressure is Pc1 along L3 and the pressure increase following 1 -2 path in PcVc diagram starting from point 1. The kickback pressure will take the same path as the expansion stroke; while the scavenging pressure remains at Ps1 along compression stroke.

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MODEL 2 The dimensions of engine model 2, i.e. intake and exhaust port at the top of cylinder block, are described in Figure 5. Similar to model 1, the slider is considered to move from left to right in positive x direction i.e. expansion process. At these conditions, the pressure in combustion chamber is P’c3 as a result of instantaneous heat addition in combustion process, while the pressure in kickback chamber and scavenging chamber are free-air pressure P’k1 and P’s1, respectively. When the slider is moving to the right, the combustion pressure will follow 3-4 path in the P’cV’c diagram and at point 4 the pressure suddenly drop to P’c1 because of instantaneous heat rejection. The scavenging pressure will increase along 1-2 path in the P’sV’s diagram; while the kickback pressure will increase following 1-2 path in the P’kV’k diagram. Considering the slider moves from the right to the left after the expansion stroke i.e. compression stroke, the compression increases following 1-2 path in the P’cV’c diagram starting at point 1. The kickback pressure will take the same path as expansion stroke; meanwhile the scavenging pressure remains at P’s1 along compression stroke.

L5

b3 b2

b1 a

L

L

L

c

x TDC

P’ c

x

BDC

3

P’ k

P’ s

2 2

2 4 1

1

1

V’ c

V’ s

V’ k

Figure 5. The dimension of engine and pressure volume diagrams for each chambers modeled for the simulation of model 2 (TDC: top dead center, BDC: bottom dead center)

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d 2x d 2x � mAriffin, Ahmad et al./ Jurnal Kejuruteraan 18 (2006): 97-106 F � m � FKamal � dt 2 dt 2

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In order to develop the pressure equations of RESULTS AND DISCUSSION n each chamber, the processes are assumed to obey PV � const PV n � const 2 MODEL 1 2 d x a Fpolytropic process. The relationship between d x �m 2 � mvolume The equations that described the pressures the pressure for polytropic dt andF the dt 2 2 d x of each chambers are derived from equation process is described by (Heywood 1988): PV � mRT 2 F �m 22 PV � mRT (6) and (7) (4) and/or d x d xequation (5). Equations dtd x 2 n PV n � const FFPV � m dequations x F � m � m � const (4) represent for 2 the force balance 22 F � m dt dtdt 2 expansion process and for compression process, dt d 2x PV n � F const � L �in �a �engine� model 1, where respectively, L � a �Patm is � The interdependence between the� three � m Qin � 1 � � (n � 1)� n Qnin �� 1 2 n n n � (n � 1)� n � n dt PV � mRTPV PV PV const atmospheric pressure, Q is the heat PV � const L � a a ��const thermodynamic properties pressure (P), volume a n � 1 � � L2 � c�� a � n � � � a addition � �� a�in� � const � mRT � L2 � � � L1PV � P � A � P � � � � 2 � � � �during ccombustion atm atm � � Ac � Patm � �aP)atm �� to combustion chamber d(V), x and temperature (T) is given by the�� state a ( L � A a � x c � ( L1 � a )�Ac � � a� � � 1 c� � �� a � x � F � m equation. ngases, the state equation is heat ratio. process, and n�is the specific PVideal � For � � PVmRT � const dt 2 � � � � � d 2 �x given by (Heywood mRT PV � mRT � � LPV �a��mRT �PV �1988): 1 � � � F m L � a � � PV � mRT Qin � � (n � 1Q)2� � 1 n n MODEL 2 n� ( n � 1) � n � � L2 � cn� � n � L1 � a � �� La � a� � n dt �in� aa � � L2 � c � � �� a � � � �A�c � Patm PV � � � Patm�� const�� P � 1 PV �� mRT � L1 �� aa �� x � Ac � Patm �n (8) and � (9) represent the force � ��(5) c � Equations atm( L � a ) A � a �� 1 a c � Q � � ( L�1 (�na�)1A)�c an� x � c� cn �� (b ) 2 L � (�bn ) 2 2 L ��n (b ) 2 L � (b ) 2 2 L � n � in � � � � � � n c�3 5 1 balance process and 3 a � � const c��L � a� � �for expansion 5 1 � L ��equations �� L1 � PV � � ��L��a1L1��a�a� �� (n ��1��)� a�� axatm � � P�atmc�n� x2 Q � (n(b� 1))2�L � (b ��)n2�(AL �) �� As �2 n � in A��k n1��nPatm � n�n QQ k1 � P � � (n � 1�)�� L� A 2 ��P�atm �� in in n�nc L for 2 L � compression process respectively, in engine L � L � c � x ( b ) L � ( b ) � �(�n�L�2 13�)�c � 5 �2��c��c� �a� � � �2 3 4� �5 n a Q1�in � �Lthe a1L1��gas (�L�1 �aVais ) A�the a��a�xa� �2 � L1 4� a �� LcL � P�is �volume, a�a� � pressure, 1n ( 2 L � x ) � � � � c� where gas 2 �� P � PV � mRT Patm� � P�atm��2.These � L1 �show �L � �Ac �a Patm� � � � �� a � Patm � � � Patm� �AA � � �� equations c�� a�� that � �atm �� mass, � Ac � Patm � ac � �� and L1��aLconstant, ) A�c a � x � compression c � �� a a��Tx xis � c amodel m is��the � c c ( L� 1� � Paatm a a � �R is the( L(gas )a1 A)�A � � � � � � � gas � 1 c � Qin � � (n � 1)� a �than model ( L1 � 1a )since Ac n � n ratio for model� 2 nis �higher � �� a � x � the absolute �� n temperature. �� 2 �� asan � L1 � � a �mRT This a also � PV � L2n ��c � �) 2 is �(bknown n � � � � � ( b L � ) 2 L � Pideal atm � � c2.� � � � gases. theclaw of (Abc1 )�12 and 2Pdatm L2 x�L>L c � � �3 L �5 a ) A 1� (�b��3 )a2��L5xA��s L>L 2 �� ax�� Ak ��a Patm� � (b )��2 L(A 1 � P 2c� d x A �L � � 1c�� k� (b atm s L � L � 2 m � n 2 Qin 4� 1) L4 � c�n� 3xn � 5 1 ) (2 � F f � Fe � m 2 (bL � ) 2nxF L)f�� (F be ) � (2 L �n x2 ) � � ��(nL� 2 �� L(2b�3�)c23 L � L1 � a � �� 5 �5 (b1 ) 21 2 L �dt � � dt � �a � � c � � a� � �� Paatm � � P�atm n Lc 1� � Patm � � � �� n�Ank�A� nAns n �� 2 � 2� 2 2 2 2) 2 2 L � � � � ( b ) L � ( b � c a ( L � a ) A a � x c � � Q ( n � 1 ) (b3 ) L5 � (n b1 ) 2 2 L � � �c ��n x � � in � ��b3 )(bL3�5)3 ��L(5b5� c�Lx) �� n 1 ��L 2 � cL 4 c n12)1L 2 � 1 ) (b � � � � A � P A � � � � A � P A(sb3 ) 2 L5 � (b1 ) 2 2 L c � � A�k k�aPatmatm a� � 2 2 �� L1 � �a � atm � �� (b 2)�2 �L � �) �LA � 2� s�s ck � 2 2A � P n � � n � � �� n L � L � c � x ( b ) ( 2 L � x Patm �c � � (�b3 ) L5 n� (b�1 ) L(k2�La�atm x)� n n n � �AL xc)�� x � ��P�Latm2 22�� L4 4�� c� � x � � cL 4�� (b3 )3 �L�5 a5��(bL 1�2)1L( 2 � 1 c � ��(b�a3 ) 2 L� 5 � (b1 )�2 L L � L � c � x � (21 L��a x�) L � c n � 2Ln � a ) A 2 � c �2 �� d x a ( x c � 2 4 � � � 2 � � 2 1 c � (bPatm ��L � � A � P A d �x � � � � � � � � � P A � P � � � � ) L � ( b ) 2 � F f � Fe � �m � �F atm k c c � atm atm � � x �k �� dt��2 f � Fe � m ��2 Ak � Patm � �� 23 � 5 c 21 � � L2 �� LA 4 s� c � �x � c � � L2� � La4 � �c �� ax � � a � � dt 2 L � L � c � x ( b ) L � ( b ) ( 2 L � x ) � 2 4d x � � 3 5 1 �

�

�

� ��

�

�

�

�

�

� F f � F�e � m 2 2 2 2 � � (b3 )dt c d 2x dLd5 x�x (nb1 ) 2 L �� A d 2x �� Ak��F nP n n d 2x F � F � m d 2x � F � F � m atm s n � F � m 2 2 n n n f e f e 2 � � � P A � F � F � m L � c L � a c a f e 2e � � � � � � (6) 2 � P A � F � F � m L � L � c � x 2 1 ( b ) L � ( b ) ( 2 L � x ) atm s f � F � F � m 2 n n f � 2 4 P � a dt� f atm e s � ��1� Ak � cPatm�� 2 � � � L � adt� 2 e � �� P � �� 3Lc2 �5cdtdt atm � dt 2 (a b�3 ) ALk 5��aP(� b1x)�2�21LAc �� 2 A dt � � atm atm c c L � L � c � x � a � Asa � x � � �� 2 � 4 cn � ��d�LAxk��LPatm � �c�n� x � � � �c4 F��e �c��mx �� 22c 4 ��(b3 ) 2� L5 � (b�1L)12 (��2 La ��n x�) ��a � � n � ��LL2F2�f �L � nAn � Patm � Patm � � � n dt � n� n n � An n n n L �c�c� n��2L�2 � L4 c�cc � x �� k L �ac�a� ��a��axa� � n�c c � � � L � n c a � � L1 � a � � a L � � � 2 1 � � 2 2 1 2 � � 2 d x P A � P A � � � � L � c � � � � c P A � P � � � � � � � � � � � � A �L �a� A k� atm � � A atm atm c c � PdatmxAs �PFatmfatm�� F�e cP �c m��A��2��LF Patm � x�2�� k � �� atmL� � aa � � a��Axk �� Pcatm � 1 � L2 2��LFL4 4��cm c��dx x��x�� k a � �� L a2�� xa x�4� � c L c � � a a L � F f � Fe � m � � �2 � L4 �� c � x � atm dt s e 2 L a n nf n n �1) c � � � Q ( n � � � � n n n Q ( n � 1 ) dt 2 dt in � � � � L � a � L1 � a � �a� a � � n a in � L2 � c �d 2�x d 2 xc c�� a � n � � A � �P�� a � � L �� L A � a � � � P � � atmA � � atm c�� Ac � Patm � Fe�2�L m� L2 2� c ��xP�atm � k ��FPatm � �� A � Patm � �Patm s e F f � �F c fm��dt ) Ax�cd�2 xa ��a � x � ( L � a ) Ac�2 c ��a � x � c � 2 dtdd4 x x � � � a � � a (�L ��aa� � �m 22 n d (7) x � � Patm As � F f � Fe � m 2 ��PPatmAAns��FFf f��FF n e e� m � a �n � � P A � F � F � m �dta � � � c atm s� � � � L2 � c � � � L1 dt dt � atm s f e � Patm � � � �� dt 2 � � L ��a A � k � Patm�� L �a a ��d 2�xa ��x � Ac n 1)�� c � � L2 �n L�4 Q�inc��xP� �A(n�n �FQ � n n n n � �c sn� � f in�� Fe ac� m�� (n2��1)� � L � �cn L�1 � a � � a � n � �L�a� � ��LLa� 2 atm a a L � c a � � � � � � � � � dt P A � P A � � � P � A � P � � � � � � � � � atm � atm �k � atm �� Aca� P�atm��a � x �� c �x�c� 1�)�xc �� atm A�c �� LL2��a(aLL�� c � a �� Patm 2��(�L �an ca )��Q n 4� n ( n n � 2 a ) Ac� �� a � n x nc in � � � Ld� a b�1n) 2 2 L �� (b3 ) 2 L5 � (b1 ) 2 2 L � � �a� � c � � � L ��c�L� � �(ab��3 ) L c � �La�L��a�a� � 5 �( �m x � � � � � � P��atm As � F f ��F � A � Patm� �� n�n2� (n � 1) �2 Ak � Patm � A 2 � n� � �L �Asa � n QQ � nAnc ��Patm n k � Qin � � � � �(n(n��1�)1��)� �� dt in in �P�eatm� (b1x)� � inx��)n �� (b3 )�2 (Ln5��L1(b)��1 )c2 (�2n L � xn ) �� s ��aLxa� �a�� xa�� LcL��c�(c��ab�3�) L�L�5 �c � aL��a�a� � (�L� �aa) A ��cL ��(n 2 LaQ L � � � � c� d 2 x �� L � a�� AAc�� PP�atm� � �� A a� P�atm � �� a � �� A�� F � F � m atm ��PP ��aP�atm atm � �c �� a�� x � c � Ac � Patm ( L�e��aLa)�A )A �x �x� � ac � atm � � c(cL��P ac �2 � f (L a ) A � � atm a � � c�� aaPatm � �� s � � c � � dt� (n�� 1)� Qin � a � ( L � a ) Ac a � x� � � n n n � � � � �� L�a� 2 � L �c� � a � �n� �n � �� a � � 2 � � � c �� Patm � �c (�b3n)� L5 � (b1 �) 2 2 L(b )��2 L ��(b ) 2 2 L� A�c n � P � � d atmx� � d 2x � � A � P A a ( L � a ) A a � x c 3 5 1 � � � � �2� A � P 2 � � � � c� L� ��ka �� atm s�� F f � �Fe � m � F � F � m � (8) A 2 f e � 2 k s atm Q�in �x � � �� (Ln��c1(n)�b�3x) �L5 � (bn1 ) (2(Lb�) 2xL) �� (b� )n2 (2 L �n x) dt �L n �c dt � � �L�a� �� a �� (�b3 ) 23L5��5L(b�1 )c�21�2 L � � � �a � �c � � � �� LAc� �a P � �Patm � � atm � � � n � �nA�nk a��Patm � nAn n ( L��L�a�)cAc� n � a � (3b�5)3(2�)nL2(�5L�b51�1)�)2c(�b((21b)1L�2)22�2LxL)c�n�� s � � n(b3 ) 2 L5 � (nb1 ) 2 2 L � ��n Qxin��(b�3 )(2bL cc x � �� As(b3 ) 2 L5 � (b1 ) 2 2 L � �Patm Patm L � a� �AA a � ��AA Latm��c �� 2 c a A � P � � � � � � � � � � � � � � � k s k 2 � 2 2 k s 2 2)� ( 2 L ��nx )A � P � �� A �n �� L5 � 2 (b 2) L � (b� � nA � Pxn ) ��n � �P L��d�c c�x�x x�� cx�2x�c)��cx �cn atm �� c ��(b�L�3 )L ��cLn��(bxa1�)� c(2�k L �a�atm �� (b3 ) 2 L5��L(b�1 )a2 �(2n �L �ax) �� n s � F f � Fe ��Latm m � �2 F a �� F n� m d(�L�(xb�3 )3a )LA5 c5� P(b21 )1��(L2a�L � c � � � � A � k A�c Patm � e� k �� Patm �� Ac (b3 )atmL�5 � c(b1 )� 2�LL ��c � x � PA 2 � �dt cf atm � � � �d A2 kx �dtPatm � � c �� aL �� c��ax�� x � � a � �a� x� � �� 2 � � � As � 2 � (b3 ) L5 � (b1 ) (2 L � x) � � F�f L��Fce �� xm� 2 2 n d x n d 2x dtd2 x � � ��(FbF3f )f�2 � � m c LF5F � ( b ) 2 L d 2x � F � F � m � � � m 1 f e e e 2 22 n n n Ak �n Patm � A � F � F � m � � dt � dt s f e dt n 2 2 L�� L x�)�2a�n �� a2 �� LA� a2� n � a n � n d 2 x dtd22 x � L �Pc ��xL� � c �� (cb�3 )L L��5 c�A�(b�� 1 )nP( 2c atm atm k c � � d x c ( b ) L � ( b ) 2 L � P A � F � F � m P A � P A � � � k 3 atm5� atm 1 s � � f � P A � Ff � Fe � m 2 e� c � c � � L �atmc�� xnc�� F��f ��L FA dt 2 atm s xa��2 � � 2a � x �� an2 � � a n�� xA�s n�Patm e�k�c�m dt dt L � c � x ( b ) L � ( b ) ( 2 L � x ) L � c c L � a a � � � � � �� P3 �� 5 1� � Patm2 � A n n � n� n � nAnk � � � � n n c n n n n atm n n � �nL � a � � an � ��a�a� �L�a��caxa� �� Ac dP�x� ��LcL��c�c� ��L�� cc�c x �� A � P�� LaLP L � c c � a �12:39:04 a � A � P Ac � L3/13/08 � � � � � � � � � � � � � � � � Journal.indb 102 PM P A � P A � � � � � � � F f � Fe � m atmatm atm k c atm atm k atm k c �� a � � a �� xA�k � Patm � � � � Ac dt 2 � � c c �d��2 �xLL��c c��x x� � 2 � � aa � �� c�aa��x x� �L � c � x �Patm � n

n

� � Ak � Patm � � As 2 2 �L�c� x� � (b3 ) L5 � (b1 ) (2 L � x) �

d 2x � F f � Fe � m 2 d 2 x dt � F f � Fe � m 2 dt Ahmad Kamal Ariffin, et al./ Jurnal Kejuruteraan 18 (2006): 97-106 n

n

n

103

n

c �L�c� � � �L�a� � a � Patm � n � � � Ak � Patm � n � � n � Ac n � L � c� � c� � c� L � �c � x � � L � �a � a� �a � a� � x � Patm � � � � Ak � Patm � � � � Ac � c � �L�c�x� � a � �a� x�

d 2x � Patm As � Ff � Fe � m 2 d 2 x dt � Patm As � Ff � Fe � m 2 dt

(9)

Table 1. Simulated engine specifications Parameter

Model 1

Model 2

Effective combustion stroke

0.04 m (L1)

0.07 m (L)

Effective kickback stroke

0.055 m (L2)

0.07 m (L)

Exhaust length (L3)

0.03 m

0.03 m

Intake length (L4)

0.015 m

0.015 m

Back-scavenging length (L5)

0.05 m

0.05 m

Specific heat ratio (n)

1.4

1.4

4.6 kg

4.6 kg

Free air pressure (P1)

100 kPa

100 kPa

Combustion crevice length (a)

0.004 m

0.004 m

Kickback crevice length (c)

0.006 m

0.006 m

Combustion bore diameter (b1)

0.076 m

0.076 m

Kickback bore diameter (b2)

0.11 m

0.11 m

Back-scavenging diameter (b3)

0.114 m

0.114 m

300 J

300 J

Mass of slider (m)

Heat addition (Qin)

In order to generate free piston simulation, some engine specifications have been chosen. These specifications are given in Table 1 including the geometry of the modeled engines. By using the force balance equations, the simulations of the slider-piston motion are derived. The slider-piston velocity profiles of both models are shown in Figure 6. The velocity is taken as parameter because it gives a clear description about motion profile than acceleration. These velocity profiles are far from sinusoidal as for conventional engine. Comparing the velocity profile between simulation of model 1 and model 2 in Figure 6, model 2 gives higher velocity and also less time needed to complete one stroke than model 1. As shown in Figure 5, engine model 2 has different configuration than model 1 in term of the position of intake and exhaust port. This arrangement gives the higher effective volume for engine model 2. Thus, the work is higher for engine model 2 as represented by wider area under PV curve. Therefore, the

Journal.indb 103

velocity of slider-piston is also higher for engine model 2. From Figure 6, it can be concluded that the average velocity of slider-piston of model 2 is 19 % higher than model 1. Figure 7 shows the slider-piston position versus stroke time for both modeled engine. It reveals that, both modeled engine give approximately the same stroke length, ~70mm, although they have different slider-piston velocities. The modeled engines have the same geometry. However, the effective combustion and kickback strokes are different. Therefore, each engines has different compression ratio, i.e. engine model 2 compression ratio is higher than engine model 1 since the effective stroke length of model 2 is longer than model 1. This is due to the fact that, the generated pressures/forces in each chamber, i.e. combustion chamber and kickback chamber, is higher for engine model 2. The increased pressure in kickback chamber in engine model 2 compensates the increased pressure in combustion chamber, thus the slider-

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104

piston stroke remains the same as engine model 1. Figure 7 also shows that the stroke time is shorter for engine model 2 since the increased pressure would increase the sliderpiston acceleration. The relationship between the slider-piston velocity and the slider-piston position for both modeled engines is illustrated in Figure 8. It gives a clear description that model 2 slider-piston velocity is higher than for model 1 and the stroke length for both modeled engine is approximately the same. This fact revealed that model 2 would produce

more power since the producing power is linear to engine speed. Although such was the case, model 2 has a disadvantage in a way that it needs valves and open-close valve system comparing to model 1.These would increase engine component number and mechanical losses. The results show good compromise with the previous work by Nandkumar (1998) although by a different engine model was used. Nandkumar (1998) also indicated that the increasing of compression ratio will increase engine speed/velocity.

12000 model 2

velocity (mm/s)

10000 8000 6000

model 1

4000 2000 0 0

0.002

0.004

0.006

0.008

0.01

0.012

time (s)

Figure 6. Piston velocity versus stroke time

80 70 model 2

60

model 1

position (mm)

50 40 30 20 10

0

0.002

0.004

0.006

0.008

0.01

0.012

time (s)

Figure 7. Piston position versus stroke time

Journal.indb 104

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105

12000 10000

model 2

velocity (mm/s)

8000 model 1

6000 4000 2000 0 0

20

40

60

80

position (mm)

Figure 8. Piston velocity versus piston position

CONCLUSIONS Dynamic and gas-dynamic model of free piston linear engine have been presented in this paper. The velocity and displacement profiles of slider-piston motion with respect to time are investigated for different modeled engines. The slider-piston motion of two-stroke free piston linear engine was successfully simulated. By comparing the results between engine model 1 and model 2, it revealed that the sliderpiston velocity for the engines are not similar

in completing one stroke, even for the samemodeled engine geometry. Slider-piston velocity of model 2 is 19 % higher than model 1. However, model 1 does not need valves and open-close valves system as for model 2. ACKNOWLEDGMENTS The project was financed by Malaysian Ministry of Science, Technology, and Innovation under IRPA project 03-02-02-0056 PR0025/04-03.

TERMINOLOGY Symbol A b

F

m n

P

Journal.indb 105

Description Area Diameter Force mass Specific heat ratio Pressure

Units

Symbol

Description

Units

m2

Qin

Heat addition

J

m N

kg Pa

R T t

V x

Gas constant Temperature Time Volume Displacement

kJ/(kmol.K) K s

m3 m

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106


REFERENCES Aichlmayr, H.T., Kittelson, D.B. & Zachariah, M.R. 2002. Miniature Free-Piston Homogeneous Charge Compression Ignition Engine-Compressor Concept Part I: Performance Estimation and Design Considerations Unique to Small Dimensions. Chemical Engineering Science 57 :4161-4171. Annen, K.D., Stickler D.B. & Woodroffe J. 2002. Miniature Internal Combustion Engine (MICE) for Portable Electric Power, Aerodyne Research. Inc. Proceeding of 23rd Army Science Conference. Florida. Arshad W.M., Bäckström T., Thelin P., and Sadarangani C. 2002. Integrated Free-Piston Generator: an Overview. Proceeding of NORPIE/2002. Stockholm. Sweden. Atkinson, C.M., Petreanu, S., Clark, N.N., Atkinson, R.J., McDaniel, T.I., Nandkumar, S. &Famouri, P. 1999. Numerical Simulation of Two-Stroke Linear Engine-Alternator Combination. SAE Paper 199901-0921.

Journal.indb 106

Fonna, S., Mohamed, N.A.N. & Ariffin, A.K. 2004. Simulation Including Intake and Exhaust Port Effects of Two-stroke Free Piston Linear Generator Engine Motion. Proceedings Seminar Computational Mechanics & Numerical Analysis. pp. 57-62. June 5th. Banda Aceh. Goldsborough, S.S. &Van Blarigan, P. 1999. A Numerical Study of a Free Piston IC Operating on Homogeneous Charge Compression Ignition Combustion. SAE Paper 1999-01-0619. Heywood, J.B. 1988. Internal Combustion Engine Fundamentals. Singapore: McGraw-Hill Book Company. Houdyschell, D. 2000. A Diesel Two-stroke Linear Engine. Master of Science Thesis. West Virginia University: Morgantown. West Virginia. Nandkumar, S. 1998. Two-Stroke Linear Engine. Master of Science Thesis. West Virginia University: Morgantown. West Virginia.

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