HCCI free-piston engine generator with electric mechanical valves

Applied Energy 102 (2013) 336–346

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Dynamic modeling of a SI/HCCI free-piston engine generator with electric mechanical valves Chia-Jui Chiang a,⇑, Jing-Long Yang a, Shao-Ya Lan a, Tsung-Wei Shei b, Wen-Shu Chiang b, Bo-Liang Chen b a b

Department of Mechanical Engineering at National Taiwan University of Science and Technology, Taipei 10607, Taiwan, ROC Mechanical and Systems Research Laboratories at Industrial Technology Research Institute, Hsinchu 31040, Taiwan, ROC

h i g h l i g h t s " A dynamic physics-based model for FPEG is developed for control synthesis and design. " The model includes piston motion, gas filling dynamics, combustion and generator. " Successful mode transition requires proper scheduling of the system inputs. " Scavenging is key for trapped mass balance and thus compression ratio regulation. " The electric mechanical valves (EMVs) enable optimization of the scavenging process.

a r t i c l e

i n f o

Article history: Received 9 March 2012 Received in revised form 24 June 2012 Accepted 19 July 2012 Available online 29 August 2012 Keywords: Free-piston engine generator HCCI Dynamic modeling EMV

a b s t r a c t For the purpose of model-based analysis and control design, a dynamic physics-based model for free-piston engine generator (FPEG) is developed in this paper. The physics-based model contains 17 states, which include piston dynamics, alternator current, runners and cylinder gas filling dynamics and thermal dynamics. Homogeneous charge compression ignition (HCCI) combustion is employed for better efficiency and reduced emissions, whereas spark ignition (SI) combustion can be used for quick start of the FPEG and higher power demand. Equipped with electric mechanical valves (EMVs) and direct injection, the free-piston engine generator is deemed to achieve optimized and clean combustion. Key features in this dynamic model include the runners and cylinder filling dynamics and cycle-to-cycle coupling between the piston motion and combustion process. Simulation results demonstrate that during a transition from SI to HCCI mode, the scavenging process needs to be properly maintained so as to achieve trapped mass balance between the opposite cylinders and thus regulation of the compression ratio. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction The free-piston engine generator (FPEG), which consists of a free-piston engine coupled to a linear alternator, has attracted considerable research interest due to its potential application to hybrid electric vehicles [1,2]. In a free-piston engine, the piston motion is not restricted by the rotating crankshaft, but determined by the interaction between the gas and load forces acting upon it [3]. This extra degree of freedom gives the free-piston engine some distinctive characteristics such as variable compression ratio and the need for active control of piston motion [1,4,5]. Compared to the conventional crankshaft internal combustion engine combined with a rotary generator, free-piston engine generator directly ⇑ Corresponding author. Tel.: +886 2 27303283; fax: +886 2 27376460. E-mail addresses: [email protected] itri.org.tw (T.-W. Shei).

(C.-J.

Chiang),

0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.07.033

JerryShei@

utilizes the linear piston force without additional mechanical compartments and thus offers a more compact and efficient hybrid electric power system [6]. The variable compression ratio allows optimization of the combustion process in terms of efficiency and emissions [1]. In addition, since the linear package contains fewer moving parts than a rotary machine, free-piston engine generator is more reliable [7]. Compared to the hydrogen fuel cell system, which requires platinum catalysts and proton exchange membranes, free-piston engine generator is less expensive and more durable. Another advantage over hydrogen fuel cell system is the fuel flexibility allowed by the variable compression ratio in the free-piston engine [1]. The variable compression ratio in the free-piston engine, combined with modern engine technology such as direct fuel injection and variable valve timings, enables more efficient and cleaner combustion process such as homogeneous charge compression ignition (HCCI) [8]. Potential advantages of HCCI include high efficiency due

C.-J. Chiang et al. / Applied Energy 102 (2013) 336–346

to the rapid heat release process and the possibility to burn lean mixtures with reduced gas temperatures and thereby some types of emissions [1,9–12]. In HCCI mode, a premixed charge is compressed to achieve autoignition, resulting in very rapid combustion with challenges in ignition timing control [13]. The autoignition timing of HCCI combustion is determined by the cylinder charge conditions, rather than spark timing or fuel injection timing, which are used to initiate combustion in conventional gasoline and diesel engines, respectively [14,15]. Instead, controlled autoignition requires regulation of the charge properties, especially charge temperature, as demonstrated by many experimental results [16,17]. In a two-stroke free-piston engine, trapped residual provides high dilution and also increases the charge temperature inside the cylinder. The heated cylinder charge is then compressed by the piston to achieve autoignition. The variable compression ratio of free-piston engine yields a flexible autoignition control on a cycle-to-cycle basis [18]. On the other hand, the interaction between the piston motion and combustion process is critical to the success of controlled autoignition in free-piston engines [19]. HCCI operation of free-piston engine generators (FPEGs) has been attempted by a couple of research groups as an alternative to conventional engine generators [1]. In [20], performance of HCCI combustion with different fuels was evaluated by conducting experiments on a rapid compression–expansion machine, which consists of a double-ended free piston allowed to move freely along a double-ended cylinder. Above 50% indicated efficiency was accomplished by the nearly constant volume combustion at high compression ratio. Moreover, NOx emission was successfully reduced by decreasing the equivalence ratio [20]. Steady-state operation of a hydrogen fueled HCCI free-piston engine was analyzed using a zero-dimensional thermal dynamic model in [21]. Arrhenius kinetics was applied for reaction rate constants of individual reactions whereas empirical models were used for the heat transfer and scavenging process. The authors in [21] concluded that the scavenging process is key to the free-piston engine’s successful operation. More recently, Fredriksson and Denbratt [6] integrated three different software tools for iterative simulation of the piston motion, gas exchange process and detailed chemical calculations. Assuming the initial charge conditions were given, the iterative computations start a certain period after valve closing. A similar approach was adopted in [22] with the inclusion of a alternator model. Concurrently with Fredriksson and Denbratt [6], Kleemann et al. [23] developed a computational methodology based on iterations between zero-one-dimensional and simplified computational fluid dynamics (CFD) simulations to define the operating conditions and overall geometrical parameters that achieve the best engine performance. A more detailed three-dimensional CFD calculations have also been used in [23] to specify the optimal intake and exhaust port configurations and injection characteristics. More recently in [24], a zero-dimensional thermal dynamic model is combined with a Finite Element Method Magnetics (FEMM) alternator model for a two-stroke HCCI free-piston engine with an embedded linear alternator and a hydraulic pump. In [25], single and multi-zone Chemkin model with detailed chemical kinetics and subsequential CFD/Chemkin method have been used to analyze the HCCI combustion characteristics of a two-stroke freepiston engine. The authors in [25] concluded that higher scavenged temperature is needed to keep the combustion phasing. The above mentioned models [21,6,23,22,25] contains the level of detail necessary for accurately predicting the overall process of HCCI combustion, particularly emissions. For the purpose of control synthesis and design, however, a simplified model that captures the runners and cylinder filling dynamics and cycle-to-cycle coupling between the piston motion and combustion process is needed. In this paper, physics-based approach is applied to build a dynamic model for a two-stroke free-piston engine generator (FPEG) with

337

electric mechanical valves (EMVs) developed by ITRI. The EMV developed by ITRI provides the flexibility for almost instantaneous control of the intake and exhaust valve timings and thus chances to optimize the scavenging process. The dynamical behavior of this model is associated with states representing the piston dynamics, alternator current, combustion timings, and charge properties (mass, composition, pressure and temperature) in the cylinder, intake runners and exhaust runners. The most critical part of the HCCI combustion model is the timing of start of combustion (SOC) determined by the Arrhenius integral [26]. After the combustion starts, a Wiebe function [27] is applied to approximate the heat release process. System inputs of the FPEG model includes the injected fueling level, valve timings and load resistance of the linear alternator, whereas performance variables contain HCCI combustion timing, air-to-fuel ratio (AFR) and the electric power generated. The paper is organized as follows. In Section 2 we briefly introduce the configuration of the FPEG and the electric mechanical valve (EMV) developed for the free-piston engine. In Section 3 we present the dynamic model developed in this paper which includes the gas filling dynamics, alternator equivalent circuit, and the coupling between the piston motion and the combustion process. In Section 4 we investigate the dynamic behavior of the FPEG during a transition from SI mode to HCCI mode. We demonstrate that successful and unsuccessful transitions can happen if the system inputs such as the electric load, valve timings and fueling level are scheduled differently. The scavenging process needs to be properly maintained during the transition so as to achieve trapped mass balance between the opposite cylinders and thus regulation of the compression ratio.

2. System configuration Fig. 1 shows the two-stroke free-piston engine generator (FPEG) considered in this paper which consists of a double-ended free piston moving freely along a double-ended cylinder. The FPEG is equipped with the following features: 1. 2. 3. 4. 5. 6.

electric mechanical valves, intake/exhaust runners, compressed intake air, linear alternator, direct fuel injection, and spark plug.

Fig. 2 shows a set of the electric mechanical valve (EMV) developed by ITRI, which provides the flexibility for almost instantaneous control of the valve timings. The DC brushless motor and valvespring system are connected via a nonlinear mechanism in a compact manner such that it can fit an industrial cylinder head. Design of the contour of the nonlinear mechanism is critical in determining not only the valve lift but also valve motions. With appropriate design of the nonlinear mechanism and the spring, the EMV achieves soft landing and energy saving. Fig. 3 shows an example of the valve displacement measured by a Bently Nevada proximity transducer installed below the valve head. At 1500 r/min peak motor speed, the EMV completes 9.3 mm full stroke (from fully closing to fully open) within 4.5 ms with landing speed less than 3 cm/s and peak power less than 100 W. By controlling the EMV opening and closing timings, scavenging is thus provided through the intake/exhaust runners. The intake runner is fed with compressed air to facilitate the scavenging process. The linear electrical machine is assumed to be a permanent magnet machine. Appropriate power electronics is needed to allow control of the electric load. Direct fuel injection is used to solve the emission problem in two-stoke engines. Isooctane is chosen as the fuel for this study but this model can easily adopt

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piston

intake valve

permanent magnet

coil

intake runner

spark plug injector nozzle

exhaust runner exhaust valve

right cylinder

left cylinder Fig. 1. Cross section of the free-piston engine generator (FPEG).

3. Model description Fig. 4 shows the schematic diagram of the free-piston engine generator (FPEG). The dynamic FPEG model contains 17 states: two states for the displacement and velocity of the piston; one state for the current in the linear alternator; six states for the pressure in each volume; eight states for the mass and burned gas fraction in each cylinder and exhaust runner. For description of the gas filling dynamics in each relevant volume, besides conditions in the cylinder denoted by subscript c, conditions in the intake runners and in the exhaust runners are denoted by subscript 1 and subscript 2 respectively. The ambient conditions are denoted with subscript 0. For each volume, the volumes are denoted by V, pressures by p, temperatures by T, and masses by m. The rate of the flow from volume x to volume y is denoted by Wxy and is calculated using the orifice flow equation [27]. 3.1. Cylinder geometry and piston dynamics The volume of each cylinder and its time derivative can be derived from the geometry of the FPEG shown in Fig. 4.

V c;l ¼ V r þ V_ c;l ¼ Ap x_ V c;r Fig. 2. Electric mechanical valve (EMV) developed by ITRI.

V_ c;r

Displacement (mm)

 L þ x Ap 2



 L  x Ap ¼ Vr þ 2 ¼ Ap x_

ð1Þ ð2Þ ð3Þ ð4Þ

where Vc,l and Vc,r are the left cylinder volume and right cylinder volume respectively, Lr and Vr are the cylinder clearance gap and clearance volume respectively, L is the nominal piston stroke, x is the displacement of the piston (x = 0 when piston is at the center position), and Ap is the piston crown surface area. The piston dynamics is described by Newton’s second law:

11 9 7 5

Mt €x ¼ ðpc;l  pc;r ÞAp  F e

3 1 0 60



62

64

66

68

70

72

74

76

78

80

Time (ms)

ð5Þ

where Mt is the mass of the total piston assembly, pc,l and pc,r are the pressures in the left cylinder and right cylinder respectively which will be introduced in Section 3.4, and Fe is the electric magnetic force which will be introduced in Section 3.2.

Fig. 3. Valve displacement of the ITRI EMV.

different type of fuels by changing the combustion model in Section 3.5. Spark plugs are equipped for quick start of the FPEG and higher power demand. The FPEG may switch from spark ignition (SI) mode to homogeneous charge compression ignition (HCCI) mode for better efficiency and reduced emissions. Details of the engine design and parameters can be found in Appendix A.

3.2. Linear alternator The linear alternator is modeled based on its equivalent circuit shown in Fig. 5 [28,29]:

Lg

di þ ðRg þ Rload Þi ¼ eg dt

ð6Þ

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Fig. 4. Schematic diagram of the FPEG.

where i is the current state, Lg and Rg are the inductance and resistance of the generator coil respectively, the load resistance Rload can be adjusted by appropriate power electronic circuits, and the electromotive force (emf) generated eg is, in general

ð7Þ

where k/ ¼ d/ , and the flux linkage /(x) = npDBmx is a function of dx piston position x, strength of the magnetic field Bm and geometric parameters such as the diameter D and the number of the alternator coils n. Equalizing electrical and mechanical power, we obtain:

F e  x_ ¼ eg  i:

Left cylinder intake valve Left cylinder exhaust valve Right cylinder intake valve Right cylinder exhaust valve

10

8

Lift (mm)

   d/ d/ dx ¼ k/ x_ ¼ eg ¼  dt dx dt

12

6

4

ð8Þ

Combining (7) and (8), the electric magnetic force Fe is a function of current i,

2

F e ¼ k/  i:

0

ð9Þ

0

5

10

15

20

25

30

35

40

Time (ms)

3.3. Valve lift profiles Fig. 6 shows an example of the lift profiles of the intake and exhaust valves in both cylinders obtained by the electric mechanical valves (EMVs) described in Section 2. Different valve lifts are chosen for the intake and exhaust valves to facilitate the scavenging process. The opening/closing timings of intake and exhaust valves, IVO, IVC, EVO and EVC can be varied by the electric mechanical valves independent of piston motions for different operating conditions. For instance, exhaust valve opening intervals can be adjusted to change the trapped hot residuals inside the cylinder. The valve lift profiles are extracted from the EMV test data and are implemented by look-up tables in MATLAB SIMULINK. 3.4. Gas filling dynamics The gas filling dynamics model described in this section can be applied to both the left and right cylinders. Each end of the cylinder

Fig. 5. Equivalent circuit of the linear alternator.

Fig. 6. Valve lift profiles.

is described by the same set of equations for the gas dynamics in the cylinder and runners. The flow through the throttles and valves is derived using a quasi-steady model of flow through an orifice assuming one-dimensional, steady, compressible flow of an ideal gas [27].

W xy

8  2ðccþ1 > 1Þ 1 px > 2 > ffi c2 cþ1 for > C D AT pffiffiffiffiffi < RT x ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼    1c  c1 > c > py py px 2c > > for : C D AT pffiffiffiffiffiffi px c1 1  px RT x

py px

6 rcr

py px

> r cr

c

2 c1 where rcr ¼ cþ1 is the critical pressure ratio, AT is the effective open area of the valve, Tx is the upstream stagnation temperature, px is the upstream stagnation pressure, py is the downstream stagnation pressure, and CD is the discharge coefficient for the real gas flow effects. The thermodynamic constants are the difference of specific heats at constant pressure and at constant volume (R = Cp  Cv, kJ/(kg K)) and the ratio of these specific heats (c = Cp/ Cv). The dependence of these variables on the gas composition has been neglected and thus are considered constant throughout this work.

3.4.1. Intake runner dynamics Due to the compressed air upstream the intake runners, the back flow form cylinder to intake runners is negligible. Therefore, gas in the intake runners is considered isothermal and the model describing the breathing process for the intake runner contains

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only one state: the total mass m1 or pressure p1. Conservation of total mass in each intake runner provides the state equation:

p_ 1 ¼

RT 1 ðW 01  W 1c Þ V1

ð10Þ

where W01 is the mass flow rate entering the intake runner and W1c is the mass flow rate from intake runner to the cylinder. 3.4.2. Exhaust runner dynamics Each exhaust runner model contains three states: the total mass, m2, the burned gas fraction, b2, and pressure, p2.

_ 2 ¼ ðW c2  W 2c Þ  ðW 20  W 02 Þ m 1 b_ 2 ¼ ½W c2 ðbc  b2 Þ  W 02 b2  m2 p_ 2 ¼

cR V2

½W c2 T c  W 2c T 2  W 20 T 2 þ W 02 T 0  

ð11Þ ð12Þ

c1 V2

A2 h2 ðT 2  T w Þ

3.5. Combustion model The combustion phasing is determined by a two-phase combustion model which includes start of combustion (SOC) and the heat release process. 3.5.1. Ignition model for isooctane In SI mode, the ignition timing is directly actuated by the spark timing. On the other hand, in HCCI mode, autoignition occurs when the cylinder charge is highly compressed after valve closing (VC). HCCI ignition delay model for isooctane (i-C8H18) was proposed in [30], which is regressed from the pressure time history generated by a rapid-compression facility. The inverse of the ignition delay time is the integrand of the Arrhenius integral [26].

ARXHe ¼

where V2 is the volume of each exhaust runner, Tw is the temperature of exhaust runner wall, h2 is the heat transfer coefficient, and A2 is the effective heat transfer area. 3.4.3. Cylinder dynamics The cylinder is modeled as a plenum with homogeneous pressure, temperature and density distributions. Each cylinder model contains three states: the total mass, mc, burned gas fraction, bc and pressure, pc. Conservation of total mass provides the first state equation in each cylinder.

ð14Þ

where Wf is the fuel flow rate injected into the cylinder, which is controlled by the injection pulse width (IPW) following the start of injection (SOI) timing. The cylinder pressure (or temperature) dynamic equation is derived from the first law of thermodynamics:

X dðmc uc Þ _ cþ ¼ Q_ c  W m_ j hj dt

ð15Þ

where mc is the mass of species in the cylinder, uc is the in-cylinder internal energy, Q_ c is the heat transfer rate for the cylinder, which includes the combustion heat release rate and the heat loss to the cylinder wall, W_ c ¼ p V_ c is the in-cylinder work output rate, hj is c

the enthalpy of species from the intake and exhaust runners. The second state equation in each cylinder can thus be derived.

p_ c ¼

c Vc þ

ðRT 1 W 1c þ RT 2 W 2c  RT c W c2  pc V_c Þ

c1 Vc

ðW afb Q LHV  Ac hc ðT c  T cool ÞÞ

ð16Þ

where pc is the pressure of each cylinder, Vc is the volume of each cylinder, T1, T2 and Tc are the temperature of intake runners, exhaust runners and cylinder respectively, Tcool is the coolant temperature, hc is the heat transfer coefficient, Ac is the effective heat transfer area, Wafb is the apparent fuel burn rate, and QLHV is the lower heating value of isooctane, kJ/kg as defined in [27]. Finally, the conservation of burned mass gives the third state equation in each cylinder:

1 b_ c ¼ ðð1 þ AFRs Þaf W afb þ W 2c ðb2  bc Þ  W 1c bc  W f bc Þ mc

ð17Þ

where AFRs is the stoichiometric air-to-fuel ratio and af is a scaling factor matching the apparent fuel burned and the total fuel injected in quantity. The air-to-fuel ratio in the cylinder can thus be derived.

AFRc ¼

ð1  bv c Þmv c mf

tsoc

tv c

ð13Þ

_ c ¼ W 1c þ W 2c þ W f  W c2 m

Z

ð18Þ

where mvc and bvc are the total mass and burned gas fraction in the cylinder at valve closing and mf is the mass of fuel injected.

vO2 vC8 H18

!0:77 0:64 P1:05 v0:77 C8 H18 vO2 exp c s

  33700 dt RT c

ð19Þ

where tvc represents the valve closing timing, tsoc is the start of combustion timing, Tc and pc are cylinder temperature and pressure respectively, ARXHe is a scaling threshold regressed based on the experimental data in [30], vC8 H18 and vO2 are the fuel and oxygen   vO mole concentrations in percent respectively, and v 2 is the C8 H18

s

air-to-fuel ratio under stoichiometric condition. To estimate the compositions vC8 H18 and vO2 , we assume complete combustion and perfect mixing of fresh charge and trapped residual during the scavenging process for lean or stoichiometric isooctane HCCI:

C8 H18 þ 12:5kðO2 þ 3:773N2 Þ þ af8CO2 þ 9H2 O þ 12:5ðk  1ÞO2 þ 47:16kN2 g  C8 H18 þ 12:5ðak  a þ kÞO2 þ 47:16kða þ 1ÞN2 þ 8aCO2 þ 9aH2 O

ð20Þ

where k is the relative air to fuel ratio, and a  NNburned is the ratio of fresh the moles of burned gas, Nburned, to the moles of inducted fresh charge, Nfresh. Thus the mole percent of the fuel C8H18 and oxygen O2 can be estimated:

NC8 H18 1 ¼  100 60ak þ 4:5a þ 60k þ 1 Ntotal NO 2 12:5ðak  a þ kÞ ¼ ¼  100 Ntotal 60ak þ 4:5a þ 60k þ 1

vC8 H18 ¼

ð21Þ

vCO2

ð22Þ

3.5.2. Combustion heat release After start of combustion, the heat released during the combustion process is approximated by a single zone combustion model in which the fuel mass, mf, and the lower heating value, QLHV, are multiplied by the derivative of the mass fraction burned, xb. In this study, the mass fraction burned, xb, is represented by an exponential Wiebe function [27].

Q_ hr ¼ Q LHV W afb ¼ Q LHV mf x_ b "  n þ1 # t  tsoc w xb ¼ 1  exp aw Dt "  n  n þ1 # @xb aw ðnw þ 1Þ t  tsoc w t  t soc w exp aw x_ b ¼ ¼ @t Dt Dt Dt

ð23Þ ð24Þ ð25Þ

where the start of combustion tsoc is determined in (19), Dt is the combustion duration (from xb = 0 to xb = 1) which is much shorter in HCCI mode than in SI mode, and aw and nw are adjustable parameter to fit the actual mass fraction burned curve. In this simulation study, the values for parameters QLHV, aw and nw are set based on [27] whereas the value of combustion duration Dt is chosen based on the experimental study in [20].

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3.6. Heat transfer model

2

hc ¼ CBg1 ðpc Þg wg ðT c Þ0:751:62g

ð26Þ

where the bore length B is taken as the characteristic length, pc and Tc are the cylinder pressure and temperature respectively, C and g are empirical parameters, and the gas velocity w (meters per second) determined for a two-stroke engine without swirl is expressed as follows:

w ¼ C 1 Sp þ C 2

V dT c ðp  pm Þ pc V c c

ð27Þ

where Vd is the displaced volume, pc, Vc and Tc are the cylinder pressure, volume and temperature respectively, Sp is the mean piston speed, and pm is the motored cylinder pressure at the same position as pc. The empirical parameters C1 and C2 are assigned with different values for each engine event. In this simulation study, the values for parameters g, C, C1 and C2 are set based on [27].

SI mode Lean SI mode HCCI mode 1

10

0

10

1

2

10

3

10

10

Volume (cm3) 1000

Velocity (cm/s)

The heat transfer coefficient hc in (16) is obtained from Woschni’s correlation [27]:

Pressure (bar)

10

500 0 −500 −1000 −6

−4

−2

0

2

4

6

Position (cm) Fig. 7. Cylinder pressure vs. volume and velocity vs. position in SI mode, lean SI mode and HCCI mode.

4. Simulation results In this simulation study, the temperature of cylinder wall is kept at 700 K, the inlet pressure is compressed to 1.2 bar, exhaust pressure is 1 bar, and inlet temperature is constant 298 K. Table 1 summarizes some key features under three different operating conditions: stoichiometric spark ignition (SI) mode, lean SI mode and HCCI mode. In each operating mode, the electric load, valve timings and fueling level are properly selected for suitable air-tofuel ratio, burned gas fraction and compression ratio. Specifically, the electric load Rload is used to control the piston stroke and thus the compression ratio of the FPEG. The intake/exhaust valve opening/closing timings and fueling level are adjusted to prepare stoichiometric mixture in SI mode. On the other hand, to compensate for the longer piston strokes in the lean SI and HCCI mode shown in Fig. 7, the intake/exhaust valves are opened later and closed earlier so as to retain more residuals in the cylinder. Combination of more cylinder trapped mass and reduced fueling level results in higher air-to-fuel ratio in HCCI mode. As the cylinder trapped mass and compression ratio both are increasing, so is the cylinder pressure. On the other hand, as the cylinder mixture becomes leaner, the peak cylinder temperature is effectively reduced in HCCI mode and as a result, low NOx emission is achieved [1,9–12]. The SI mode generates more power than the other two modes while consuming more fuel. On the other hand, the indicated efficiency in HCCI mode is much higher than the other two modes as the areas enclosed by the p–V curves in Fig. 7 at different modes are about the same while less fuel is consumed in the HCCI mode. Due to the longer stroke, the operating frequency at HCCI mode is slightly lower than the

Table 1 Operating modes of the FPEG. Parameter

SI mode

Lean SI mode

HCCI mode

Rload (X) Fuel injection (mg) IVO, IVC (cm) EVO, EVC (cm) Peak pressure (bar) Peak temperature (K) Air-to-fuel ratio Burned gas fraction (%) Compression ratio Ave. power (kW) Indicated eff. (%) Frequency

45 20 ±3.8 ±3.6 44.4 2340 15.1 23 9.4 9.18 29 26.5

75 15 ±4.2 ±4.0 46 2000 20.5 25 11 6.1 40 26.8

75 10.4 ±4.4 ±4.2 50 1600 36.4 17 13.5 5.65 56.3 24.9

other two modes. To ensure combustion stability, the burned gas fraction in each mode is regulated close to 20%. In the following simulations, we focus on the transition from the high power SI mode to the more efficient HCCI mode, which is an important step for the success of the SI/HCCI FPEG. In Section 4.1, we demonstrate that direct transition from the SI mode to the HCCI mode may be failed if the valve timings, load resistance and the fueling level are not properly scheduled. In Section 4.2, we show that with a transitional lean SI mode, the FPEG is able to switch to the HCCI mode successfully. 4.1. Direct transition from SI mode to HCCI mode In this section, we attempt to complete a one-step transition from a high power SI mode to HCCI mode by simultaneously applying the input settings defined for each mode in Table 1. Fig. 8 shows the step changes of the spark ignition on/off, fueling level, valve timings and load resistance. The commands for the left cylinder are given when the piston is moving towards the right from the center position (x = 0 in Fig. 4). On the other hand, the commands for the right cylinder are given when the piston is moving towards the left from the center position. To facilitate the explanation, the cycle numbers are labeled on the top of each figure. As shown in Fig. 8 around 75 ms in the beginning of the 3rd cycle when the piston is moving towards the right from the center position, the intake/exhaust valves are opened later and closed earlier while less fuel is injected and spark ignition is turned off for the left cylinder. In the mean time, the load resistance is raised which in turn drops the alternator current and thus the electric magnetic force. As a result, the piston is less decelerated and moves slightly further to the right, which can be observed from the slope of the piston velocity v in Fig. 10 and the right dead center (RDC) position in Fig. 11. A deeper RDC position leads to slightly higher compression ratio (CR) and slightly higher cylinder pressure for the right cylinder, as can be seen from the CR in Fig. 11 and pressure in Fig. 9 in the 3rd cycle. Meanwhile, as the intake/exhaust valves are opened later and closed earlier, the scavenging period Dtsc of the left cylinder in the 3rd cycle is shortened as shown in Fig. 11 and thus the scavenging process in the left cylinder is incomplete, resulting in less trapped mass and about 50% burned gas fraction as shown in Fig. 9. The hot residual significantly raises the charge temperature at valve closing, Tvc, resulting in an extremely early autoignition timings for the first HCCI combustion in the left cylin-

C.-J. Chiang et al. / Applied Energy 102 (2013) 336–346

SI mode 5 0 −5 0

HCCI mode 2

1 50

4

3 100

150

5 200

Right cylinder Left cylinder

0

50

100

150

200

250

0

50

100

150

200

250

0 4.5 4 3.5 0

50

100

150

200

250

50

100

150

200

250

EVO/EVC (cm)

−3.5 −4 −4.5 0 4.5 4 3.5 0

(Ω )

−3.5 −4 −4.5

IVO/IVC (cm)

20 10

R

load

80 60 40

4.2. Transition to HCCI mode through a transitional lean SI mode In the previous section, we have shown that direct transition from high power SI mode to HCCI mode is failed due to one cycle 50

100

150

200

250

1

2

3

4

5

5 50

0

100

50

150

100

150

200

x (cm)

Fuel (mg)

Spark

1 0.5 0

250

The imbalance of the trapped mass between the left and right cylinders slows down the piston, resulting in shorter piston stroke and thus dropped compression ratio (CR) of the right cylinder in the 4th cycle, as can be observed from the piston velocity in Fig. 10 and RDC and CR in Fig. 11. The dropped compression ratio results in exceedingly low right cylinder pressure in the 4th cycle in Fig. 9, which further slows down the piston and enables longer scavenging period Dtsc for the left cylinder, as shown in Figs. 10 and 11. With lower temperature at valve closing Tvc and dropped compression ratio, as shown in Fig. 11, the charge temperature in the left cylinder after compression is too low (less than 1000 K) to make HCCI autoignition happen in the 4th cycle in Fig. 9 and thus fails the transition to the HCCI mode defined in Table 1.

250

200

Fig. 8. System inputs for direct transition from SI mode to HCCI mode.

0

50

100

150

200

250

0

50

100

150

200

250

0

50

100

150

200

250

1000

250

Time (ms)

0 −5

v (cm/s)

Poistion (cm)

342

0 −1000

4

Right cylinder Left cylinder 50

100

150

200

250

−5000

Time (ms) 0

50

100

150

200

250

Fig. 10. Displacement (x), velocity (v) and acceleration (a) of the free piston during the direct transition from SI mode to HCCI mode.

1 0

50

100

150

200

250

1

0

50

100

150

200

250

x (cm)

0

2

3

4

5

5 SOC, right cylinder Right dead center

0 0

0.5

0

50

100

150

200

250

100

150

200

250

SOC, left cylinder Left dead center

−5

40

0

50

0

50

100

150

200

250

Time (ms)

CR

der, as can be observed in Fig. 11. The incomplete scavenging process, however, induces insufficient fresh charge and thus rich mixture, resulting in higher peak cylinder temperature for the first HCCI combustion in the left cylinder, as shown in the 3rd cycle in Fig. 9. The insufficient trapped mass in the left cylinder also results in an even deeper left dead center (LDC) in the 3rd cycle as shown in Fig. 11, which enables longer scavenging period Dtsc and thus more trapped mass for the right cylinder in the following cycle, as shown in the 4th cycle in Fig. 9.

Δt

sc

Fig. 9. Charge conditions in both cylinders during the direct transition from SI mode to HCCI mode.

vc

0

(K)

20

T

Mass (mg) Burned gas fraction c

500 400 300

0

0

x (cm)

0

5

(ms)

Pressure (bar) Temp. (K)

3

50

2000 1000 0

AFR

2

a (m/s 2)

5000 1

550 500 450 400

Right cylinder Left cylinder 0

50

100

150

200

250

0

50

100

150

200

250

0

50

100

150

200

250

12 11 10 9

10 0

Time (ms) Fig. 11. Start of combustion (SOC), right/left dead center, temperature at valve closing (Tvc), scavenging period (DtSC) and compression ratio (CR) during the direct transition from SI mode to HCCI mode.

343

R

load

(Ω)

4.5 4 3.5

80 60 40

4

HCCI mode 6

5

7

8

9

10

50

100

150

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400

50

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0

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0

50

100

150

200

250

300

350

Temp. (K)

Fuel (mg) EVO/EVC (cm) IVO/IVC (cm)

20 10 0

−3.5 −4 −4.5

3

Right cylinder Left cylinder

0

4.5 4 3.5

Lean SI mode

1

0

−3.5 −4 −4.5

2

400

1

0

50

100

150

200

250

300

350

3

4

5

6

7

8

9

10

500 400 300

0

50

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0

50

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0

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0

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350

400

1 0.5 0 40 Right cylinder Left cylinder

20 0 0

0

2

50

2000 1000 0

Burned gas Mass (mg) fraction

1 0.5 0

1

AFRc

Poistion (cm) Spark

SI mode 5 0 −5

Pressure (bar)

C.-J. Chiang et al. / Applied Energy 102 (2013) 336–346

50

100

150

400

200

250

300

350

400

Time (ms) Fig. 13. Charge conditions in both cylinders during the transition from SI mode to HCCI mode through a transitional lean SI mode.

0

50

100

150

200

250

300

350

400

Time (ms) 1

x (cm)

Fig. 12. System inputs for transition from SI mode to HCCI mode through a transitional lean SI mode.

3

4

5

6

7

8

9

10

0 −5 0

50

100

150

200

250

300

350

400

0

50

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0

50

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150

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350

400

v (cm/s)

1000 0 −1000 5000 2

a (m/s )

of incomplete scavenging process and thus imbalance of the trapped mass between the opposite cylinders. In this section, we demonstrate that with a transitional lean SI mode at medium power, the FPEG is able to switch to HCCI mode successfully. Fig. 12 shows the scheduled system inputs such as the spark ignition on/off, fueling level, valve timings and load resistance. As defined in Section 4.1, the commands for the left cylinder are given when the piston is moving towards the right from the center position (x = 0), whereas the commands for the right cylinder are given when the piston is moving towards the left from the center position. As shown in Fig. 12 around 75 ms in the beginning of the 3rd cycle, an increase in load resistance reduces the electric magnetic force, resulting in deeper right dead center (RDC), higher compression ratio and higher cylinder pressure, as shown in Figs. 13 and 15. The scavenging period D tsc for the left cylinder in the 3rd cycle shown in Fig. 15 is shortened by the valve timing settings, resulting in less trapped mass and slightly higher burned gas fraction, as shown in the 3rd cycle in Fig. 13. The higher right cylinder pressure and reduced trapped mass in the left cylinder in the 3rd cycle speeds up the piston, resulting in an even deeper left dead center (LDC) and higher compression ratio (CR) for the left cylinder, as shown in Figs. 14 and 15. As the trapped charges in the opposite cylinders balance out in the subsequent (4th) cycle, the engine settles at lean SI mode with higher compression ratio, as shown in Figs. 13 and 15. In the beginning of the 5th cycle around 150 ms in Fig. 12, the fueling level and valve timings for the left cylinder are adjusted to the HCCI settings defined in Table 1. The scavenging period Dtsc of the left cylinder in the 5th cycle shown in Fig. 15 is again shortened by the valve timing settings, resulting in less trapped mass and slightly higher burned gas fraction, as shown in the 5th cycle in Fig. 13. Imbalance of the trapped mass between the opposite cylinders is still observed but it is much less severe than the situation in Section 4.1. Specifically, the temperature at valve closing

2

5

0 −5000

Time (ms) Fig. 14. Displacement (x), velocity (v) and acceleration (a) of the free piston during the transition from SI mode to HCCI mode through a transitional lean SI mode.

Tvc of the left cylinder as shown in the 5th cycle in Fig. 15 is only slightly higher (compared to the 3rd cycle in Fig. 11) and thus the autoignition timing of the first HCCI cycle is still within a tolerable range. The slightly early autoignition timing of the left cylinder and minor trapped mass imbalance between the opposite cylinders result in a lower but still adequate compression ratio (CR) for HCCI combustion with slightly lower peak pressure in the right cylinder in the 6th cycle, as shown in Figs. 13 and 15 around 200 ms. As the scavenging process of the left cylinder recovers in the 6th cycle, the cylinder charge becomes leaner and the temperature at valve closing is reduced to about 400 K, as shown in Figs. 13 and 15. As the temperature at valve closing is decreased, the autoignition timing (SOC) is retarded and the dead centers become deeper, as shown in Fig. 15. As a result, the compression ratio and cylinder pressure are gradually raised and thus complete the transition to the more efficient HCCI mode defined in Table 1.

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C.-J. Chiang et al. / Applied Energy 102 (2013) 336–346 1

x (cm)

5.5 5 4.5 4

2

3

4

5

6

7

8

x (cm)

10

SOC, right cylinder Right dead center 0

50

100

150

200

250

300

−4 −4.5 −5 −5.5

350

400

SOC, left cylinder Left dead center 0

50

100

150

200

250

300

500

Tvc (K)

9

350

400

Right cylinder Left cylinder

450

Δ tsc (ms)

400 0

50

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0

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0

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0

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400

12 11 10 9

Indicated efficiency

CR

15 10

60 40 20

Time (ms) Fig. 15. Start of combustion (SOC), right/left dead center, temperature at valve closing (Tvc), scavenging period (DtSC), compression ratio (CR) and indicated efficiency during the transition from SI mode to HCCI mode through a transitional lean SI mode.

2

p1 (bar)

1

3

4

5

6

7

8

9

10

1.3 1.25 0

50

100

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m (mg)

350

2

300 250

b

2

0.6 0.4

p2 (bar)

0.2 1.05

1

2

T (K)

600

Right cylinder Left cylinder

500 400

0

50

100

150

200

250

300

350

400

Time (ms) Fig. 16. Gas filling dynamics in the intake and exhaust runners during the transition from SI mode to HCCI mode through a transitional lean SI mode.

Fig. 16 shows the gas filling dynamics in the intake and exhaust runners during the mode transitions. Smaller spikes in the intake pressure p1 are observed during the scavenging process of the left cylinder in the 3rd and 5th cycle due to the shortened scavenging period Dtsc shown in Fig. 15. The incomplete scavenging process also results in less exhaust gas m2, higher burned gas fraction b2,

and higher exhaust temperature T2 in the exhaust runner of the left cylinder during those periods. The exhaust states temperature T2 and burned gas fraction b2 provide an estimate of the cylinder charge conditions such as temperature at valve closing Tvc shown in Fig. 15, which is an important factor for the HCCI autoignition timing [31].

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C.-J. Chiang et al. / Applied Energy 102 (2013) 336–346 Table 2 List of all parameters and their values, if constant.

Table 2 (continued) Definition

Definition

Value

Dt

Combustion duration, ms

0.4(HCCI), 0.8(SI)

Dtsc

Scavenging period, ms Mole ratio of burned gas to fresh charges Scaling factor for apparent fuel burned Oxygen mole concentration

a af

vO2 vC8 H18 c g k

U A2 Ac Ap ARXHe AT AFRc AFRs aw B b1 b2 bc bvc C C1 C2 CD eg Fe h2 hc hj i k/ L Lg Lr Mt m1 m2 mc mf mvc nw pc,l pc,r px py p1 p2 Q_ c QLHV R Rg Rload rcr Sp T0 T1 T2 Tcool Tvc Tw Tx tsoc tvc uc Vc,l Vc,r

Fuel mole concentration Ratio of specific heats Empirical parameter Relative air-to-fuel ratio Flux linkage Exhaust runner effective heat transfer area, m2 Cylinder effective heat transfer area, m2 Piston crown surface area, m2 Scaling threshold for the Arrhenius integral Effective open area of valves, m2 Air-to-fuel ratio in the cylinder Stoichiometric air-to-fuel ratio for isooctane Adjustable parameter for the Wiebe function Bore length, mm Burned gas fraction in the intake runners Burned gas fraction in the exhaust runners Burned gas fraction in the cylinder Burned gas fraction in the cylinder at valve closing Empirical parameter for Woschni’s correlation Empirical parameter assigned for each engine event Empirical parameter assigned for each engine event Discharge coefficient for gas flowing through a valve Electromotive force, V Electric magnetic force, Nt Exhaust runner heat transfer coefficient, W/m2 K Cylinder heat transfer coefficient, W/m2 K Enthalpy of species from intake and exhaust runners linear alternator current, Amp Back emf constant, V(m/s)1 nominal piston stroke, mm Inductance of the generator coil, mH Cylinder clearance gap, mm Mass of the total piston assembly, kg Total mass in the intake runners, mg Total mass in the exhaust runners, mg Total mass in the cylinder, mg Mass of the fuel injected per cycle, mg Total mass in the cylinder at valve closing, mg Adjustable parameter for the Wiebe function Pressure in the left cylinder, bar Pressure in the right cylinder, bar Upstream stagnation pressure, bar Downstream stagnation pressure, bar Intake runner pressure, bar Exhaust runner pressure, bar Heat transfer rate for the cylinder, kJ/s

1.40 0.8

Vd Vr V1 V2 w Wafb Wxy Wf x xb xsoc

Displaced volume, m3 Clearance volume, m3 Intake runner volume, m3 Exhaust runner volume, m3 gas velocity, m/s Apparent fuel burn rate, kJ/s Mass flow rate from volume x to y, kg/s Fuel flow rate, kg/s Displacement of piston, cm Mass fraction burned Start of combustion timing (position), cm

Value

0.00019237 0.0004

0.001 0.005026 0.05

15.1 6.908 80

3.26

267

76 100 2 10 8

5. Conclusion In this paper, a dynamic physics-based model for a free-piston engine generator (FPEG) with electric mechanical valves (EMVs) is proposed. The FPEG model contains piston dynamics, alternator equivalent circuit, runners and cylinder gas filling dynamics, combustion model and thermal dynamics. Simulation results show that HCCI-FPEG achieves better efficiency and much lower peak temperature (and thus much lower NOx emission [1,9–12]) than SIFPEG. Simulation results also demonstrate that misfire may happen during a direct transition from high power SI mode to HCCI mode if the electric load, valve timings and the fueling level are not properly scheduled. On the other hand, with a transitional lean SI mode at medium power level, the FPEG is able to switch to the HCCI mode successfully. The scavenging process needs to be properly maintained so as to achieve trapped mass balance between the opposite cylinders and thus regulation of the compression ratio, especially during the transient or in existence of large disturbances. The EMV provides the flexibility for almost instantaneous control of the intake and exhaust valve timings and thus chances to optimize the scavenging process. Based on this model, predictive estimators and optimal controllers can be developed so as to ensure optimal energy conversion efficiency and stable operation of the FPEG system. Acknowledgment

2.25

This work was supported by the National Science Council, Taiwan, R.O.C., under Grant NSC-98-2221-E-011-154.

Appendix A. Variables and parameters See Table 2.

Lower heating value of isooctane, kJ/kg gas constant, J/kg K Resistance of the generator coil, X Load resistance, X Critical pressure ratio Mean piston speed, m/s

44,300 290 1.5

Ambient temperature, K Intake runner temperature, K Exhaust runner temperature, K Coolant temperature, K Cylinder temperature at valve closing, K Exhaust runner wall temperature, K Upstream stagnation temperature, K Start of combustion timing, ms Valve closing timing, ms In-cylinder internal energy, kJ/kg Left cylinder volume, m3 Right cylinder volume, m3

298 298

0.5283

700 400

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