Miniature Free-Piston Homogeneous Charge Compression Ignition Engine

Chemical Engineering Science 57 (2002) 4161–4171 www.elsevier.com/locate/ces

Miniature free-piston homogeneous charge compression ignition engine-compressor concept—Part I: performance estimation and design considerations unique to small dimensions H. T. Aichlmayr, D. B. Kittelson, M. R. Zachariah ∗

Departments of Mechanical Engineering and Chemistry, The University of Minnesota, 111 Church St. SE, Minneapolis, MN 55455, USA Received 18 September 2001; received in revised form 7 February 2002; accepted 18 April 2002

Abstract

Research and development activities pertaining to the development of a 10 W, homogeneous charge compression ignition free-piston engine-compressor are presented. Emphasis is placed upon the miniature engine concept and design rationale. Also, a crankcase-scavenged, two-stroke engine performance estimation method (slider-crank piston motion) is developed and used to explore the in;uence of engine operating conditions and geometric parameters on power density and establish plausible design conditions. The minimization of small-scale e=ects such as enhanced heat transfer, is also explored. ? 2002 Published by Elsevier Science Ltd.

Keywords: Two-stroke engine; Free-piston engine; Homogeneous charge compression ignition; Microchemical; Performance estimation; Micro-power generation

1. Introduction exist: Enhance batteries or develop miniature energy conversion devices. Only modest gains may be expected from the This paper is the ÿrst in a two-part series that presents re- former, consequently the latter is being vigorously pursued sults of recent small-scale engine research and development (Peterson, 2001). In particular, miniature engine-generators e=orts conducted at the University of Minnesota. Speciÿ- (Epstein et al., 1997; Yang et al. 1999; Allen et al., 2001; cally, it introduces the miniature free-piston homogeneous Fernandez-Pello, Liepmann, & Pisano, 2001) are considered charge compression ignition (HCCI) engine-compressor especially promising. concept, explores possible operating conditions and con- At ÿrst glance, replacing batteries with miniature straints, establishes potential engine conÿgurations, and engine-generators appears to be an absurd proposition. identiÿes design considerations peculiar to miniature en- Consider however, the enormous energy densities of hydro- gines. It does not, however, address details of the HCCI carbon fuels e.g., 46 MJ=kg. In contrast, the energy density combustion process; this is left to the second paper. of premium lithium batteries is approximately 1 MJ=kg (Yang et al., 1999). Therefore, an engine-generator having a 1.1. Micro-power generation fuel conversion eHciency of only 2.5% would out-perform any battery. Of note, the fuel conversion eHciency of the Considerable e=orts have been directed toward enhancing smallest commercially available model airplane engine portable electronic devices, yet their primary power source (Cox 0.010) is approximately 4% (Yang, 2000). Hence this i.e., batteries, remain essentially unchanged. Batteries en- proposition is sensible. able one to take these devices virtually anywhere, but their intrinsically low energy densities and short lifetimes impose a fundamental limitation. To mitigate it, only two options 1.2. Micro-combustion Despite the clear advantage that a miniature engine- ∗ Corresponding author. Tel.: +1-612-626-9081; fax: +1-612-625-6069. generator has relative to a battery, signiÿcant technical ob- E-mail address: [email protected] (M. R. Zachariah). stacles exist. Some of which include: (1) micro-combustion,

0009-2509/02/$ - see front matter ? 2002 Published by Elsevier Science Ltd. PII: S 0009-2509(02)00256-7 4162 H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171

(2) thermal management, (3) gas exchange, (4) friction, 1.4. Homogeneous charge compression ignition (5) sealing, and (6) materials and fabrication limitations. combustion Thus far, work at the University of Minnesota has focused upon micro-combustion. Homogeneous charge compression ignition (HCCI) Micro-combustion could be in;uenced by substantial heat combustion is an alternative engine combustion mode ÿrst and mass transfer to the boundaries. To illustrate, consider identiÿed by Onishi, Jo, Shoda, Jo, & Kato, (1979). Brie;y, the speciÿc heat transfer rate from a stagnant gas occupying HCCI entails compressing a fuel–air mixture until an explo- ˜ a chamber having a volume V and surface area As.Ifone sion occurs. It di=ers from Diesel combustion because the further considers an average heat ;ux and density, then the fresh charge is premixed and it di=ers from SI combustion speciÿc heat transfer rate deÿned by because the charge auto-ignites. Consequently, HCCI has the following experimentally veriÿed (Iida, 1994; Lavy, Q˙ q˙ dA qO˙ A Duret, Habert, Esterlingot, & Gentili, 1996; Gentili, Frigo, As s q˙ = = = ; (1) Tognotti, Patrice, & Lavy, 1997) characteristics: (1) igni- m ˜ dV O V˜ V tion occurs simultaneously at numerous locations within the combustion chamber, (2) an absence of traditional ;ame increases with the surface-area-to-volume ratio, A =V˜. The s propagation, (3) the charge is consumed very rapidly, and surface-area-to-volume ratio meanwhile, is inversely pro- (4) ignition is not initiated by an external event. portional to the characteristic dimension of the chamber. Although HCCI is a relatively recent research topic, the Thus, the speciÿc heat transfer rate increases when the char- rudiments of HCCI are well known. That is, HCCI is a form acteristic dimension decreases. of “knock” combustion and therefore its occurrence depends The phenomenon demonstrated by Eq. (1) is advan- upon chemical kinetics and the compression process (Najt tageous in micro-chemical systems (Jensen, 1999) be- & Foster, 1983). Knock combustion is typically associated cause highly exothermic processes such as catalytic with SI engines and occurs when a pocket of unreacted partial-oxidation reactions (Srinivasan et al., 1997; Hsing, charge i.e., the end gas, auto-ignites before being consumed Srinivasan, Harold, Jensen, & Schmidt, 2000; Quiram, by an advancing ;ame front. When this happens, the end gas Hsing, Franz, Jensen, & Schmidt, 2000; Quiram et al., burns very rapidly and causes the local pressure to rise vio- 1998) and the catalytic oxidation of H (Hagendorf, 2 lently. This in turn, generates pressure waves that transit the Janicke, Schuth,Q Schubert, & Fichtner, 1998) can be con- combustion chamber and initiate phenomena that ultimately trolled. Conversely, this is a disadvantage if one wishes damage engine components. Consequently, avoiding knock to minimize heat loss e.g., from a ;ame, in a micro-sized is a basic design constraint for SI engines and despite con- chamber. siderable research e=orts (Oppenheim, 1984), it is generally satisÿed by restricting compression ratios to modest values 1.3. Micro-internal combustion engines e.g., 9:1. Unfortunately, constraining the compression ratio also limits the fuel conversion eHciency. Several miniature engine programs are underway. Epstein While knock combustion is generally avoided, it has ad- et al. (1997), for instance, are developing a Micro-Gas Tur- vantages over more traditional engine combustion modes. bine Engine at the Massachusetts Institute of Technology. Some of which include: (1) the capability to burn extremely Honeywell International (Yang et al., 1999) is pursuing lean mixtures, (2) no compression ratio limitation, (3) no a 10 W, free-piston homogeneous charge compression ig- external ignition system, (4) unrestricted air intake, and (5) nition (HCCI) engine-compressor. Similarly, Allen et al. a wide variety of fuels may be used. Burning extremely (2001) are developing a free-piston spark ignition (SI) lean mixtures ( ¡0:5) is presently the most appealing engine-generator at the Georgia Institute of Technology. feature because the resulting low combustion temperatures Alternatively, a MEMS rotary engine (Fernandez-Pello yield small NOx emissions. This beneÿt, however, disap- et al., 2001) is under development at The University of pears when the mixture strength is increased (Stanglmaier California, Berkeley. & Roberts, 1999). Additionally, low combustion tempera- Although each of the aforementioned micro-engine pro- tures yield relatively large emissions of unburned hydro- grams have unique advantages and disadvantages, they share carbons and carbon monoxide. Nonetheless, HCCI remains a common problem: ;ame quenching. Each engine proposal attractive because the combination of lean mixtures, unthrot- may then be characterized according to their solution: Waitz, tled air intake, and large compression ratios promise engines Gauba, & Tzeng, 1998 exploit the unique burning proper- with “Diesel-like” fuel economy (Thring, 1989) and small ties of hydrogen and plan to burn hydrocarbons with the as- NOx emissions. sistance of a catalyst; Disseauet al. (2000) employ several Although promising, HCCI is presently impractical. The miniature spark plugs to maximize the amount of charge chief impediment is ignition control—a requirement shared consumed before quenching occurs; and Knobloch et al. by any engine that employs a reciprocating piston. Note (2000) reduce quenching e=ects by heating the walls. Yang that in spark ignition and Diesel engines, ignition con- et al. propose a novel solution: HCCI combustion. trol is achieved by ÿring a spark plug and injecting fuel, H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171 4163 respectively. Neither technique, however, is applicable to engine sizes; this topic is further investigated in the second HCCI. Hence one must resort to indirect methods i.e., those paper. which alter the compression process or the fuel oxidation kinetics. Consequently, much work has been directed toward devising and evaluating control schemes (Najt 2. A miniature free-piston HCCI engine-compressor & Foster, 1983; Thring, 1989; Ryan & Callahan, 1996; Aoyama, Hattori, & Mizuta, 1996; Christensen, Johansson, Originally based upon the MEMS Free-Piston Knock En- & Einwall, 1997; Gray & Ryan, 1997; Christensen & Jo- gine (Yang et al., 1999; Yang, Bonne, & Johnson, 2001), the hansson, 1998; Christensen, Johansson, AmnJus, & Mauss, miniature free-piston HCCI engine-compressor concept that 1998; Iwabuchi, Kawai, Shoji, & Takeda, 1999; Chris- is the subject of this work is depicted in Fig. 1. The salient tensen & Johansson, 1999; Hultqvist et al., 1999; Richter, feature of this engine is a mechanically unconstrained pis- Franke, Alden, Hultqvist, & Johansson, 1999; Christensen, ton. Therefore, in contrast to a crankshaft-equipped engine, Hultqvist, & Johansson, 1999; Flowers et al., 2000; Chen, reciprocating motion is the result of gas pressure acting on Konno, Oguma, & Yani, 2000). Of note, ignition control is the piston. somewhat less of a problem for two-stroke engines due to To illustrate, a force balance (Fig. 1(c)) on the piston incomplete gas exchange (Gentili et al., 1997). gives In addition, crankshaft-equipped engines have a feature d2x which exacerbates the ignition control problem: a ÿxed com- F = m = A P − A P − A P − A P ; (2) x p 2 C C sc sc cp cp B B pression ratio. Hence ignition timing is usually adjusted with dt pre-conditioning techniques such as varying the charge com- which couples the piston motion to the states of the gases position or temperature. These techniques, however, have occupying the combustion and bounce chambers, the scav- the disadvantages that HCCI is very sensitive to them and enge pump, and the compressor. Thus free-piston motion that they can be diHcult to implement. In light of these is the result of a “thermodynamic–dynamic balance” (Op- diHculties, alternative engine conÿgurations such as the penheim & London, 1950). Also note that because the gas free-piston, are being explored (Van Blarigan, Paradiso, & pressures in Eq. (2) depend upon the piston position, Eq. Goldsborough, 1998; Goldsborough & Van Blarigan, 1999; (2) is akin to a di=erential equation describing a spring– Galileo Research Inc., 2001). These engines feature a me- mass system. Consequently, free-piston engines are nomi- chanically unconstrained piston and hence a variable com- nally constant-speed machines whose oscillation frequency pression ratio. The advantage of an HCCI-variable compres- is determined by the piston mass and mean gas pressures. sion ratio engine conÿguration is discussed in the second Another prominent feature of free-piston engines is that paper. they execute a two-stroke cycle i.e., each expansion stroke is a power stroke. This is a necessary requirement because the combustion chamber pressure PC , must increase during 1.5. Why HCCI in a miniature engine? the compression stroke (Fig. 1(b)) and the bounce chamber pressure PB, must increase during the expansion stroke (Fig. In the context of conventional engines, HCCI is pur- 1(a)) to maintain reciprocating motion. A consequence of sued because NOx emissions can be dramatically re- employing a two-stroke cycle is that a scavenge pump (Fig. duced. Therefore, assuming that other regulated emissions 1(a)) is required to force the fresh charge into the combus- requirements—hydrocarbons in particular—can be met and tion chamber. Lastly, the air compressor is used to extract that control problems can be resolved, HCCI is an ap- energy from the piston. pealing means to comply with stringent future emissions regulations. In the context of miniature engines, however, the most important attributes of HCCI are that the charge 3. Two-stroke engine performance estimation is burned essentially without ;ame propagation and that an external ignition system is not required. Furthermore, Thus far, features of the miniature free-piston HCCI auto-ignition implies that the charge is consumed both engine-compressor have been presented, but speciÿc engine rapidly and uniformly—much like the SI scheme employed dimensions and operating speeds required to deliver 10 W by Disseau et al. (2000). Consequently, quenching e=ects have not. To provide these details and explore the in;u- are minimized without resorting to complicated ignition ence of various geometric parameters, a two-stroke engine schemes. performance estimation method is developed. HCCI o=ers another beneÿt to miniature engines: a com- One should note that although a free-piston engine bustion rate essentially limited by kinetics rather than trans- conÿguration is the ultimate objective, we assume a port. Therefore, HCCI engine operational speeds may far crankshaft-engine conÿguration in the following analysis. exceed those of conventional engines. This is a crucial re- This simpliÿcation is imposed because an expression like sult because operating speeds scale inversely with size when Eq. (2) is necessary to determine basic operating param- other variables are ÿxed. Hence HCCI promises very small eters such as the engine speed in a free-piston engine. 4164 H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171

Fig. 1. Miniature free-piston engine concept (intake, compressed air outlet, and counter balance mechanism omitted). (a) End of the expansion stroke; (b) end of the compression stroke; (c) piston free-body diagram.

The fuel conversion eHciency is deÿned by Eq. (3) and accounts for various thermodynamic limitations and dissi- pative e=ects. Consequently, it is an aggregate quantity and it is usually considered to be the product of: (1) the indicated fuel conversion eHciency, Áfc;i, (2) the mechanical eHciency, Ám, and (3) the charging eHciency, Ách. The indicated fuel conversion eHciency is the thermal eHciency of the engine cycle, or historically, that which one would obtain from an experimental P–V diagram. Hence the indicated fuel conversion eHciency is a measure of how well chemical energy is converted to work. Similarly, the mechanical eHciency accounts for dissipation in mechanical Fig. 2. Single cylinder engine geometry assumed in the performance components. While the charging eHciency is a measure of analysis. how well the combustion chamber is replenished with fresh charge i.e., the fuel–air mixture. Consequently, it depends Unfortunately, to use an expression like Eq. (2), many an- upon the gas exchange process and it is therefore strongly cillary details e.g., the piston geometry and mass, bounce related to operating conditions, scavenge port design, and chamber pressure, and air compressor and scavenge pump scavenge pump eHciency. performance are required. Such a model would therefore Next, the mass ;ow rate of fuel is replaced with the prod- be complicated and generally inappropriate for preliminary uct of the mass ;ow rate of air and the mass-based fuel– work. air ratio. The fuel–air ratio is subsequently replaced by the product of the equivalence ratio , and the stoichiometric 3.1. Performance estimation fuel–air ratio Fs. The result is m˙ =˙m F : (4) Consider a single-cylinder, two-stroke, crankcase- f a s scavenged engine having the geometry depicted in Fig. 2. Similarly, the mass ;ow rate of air is related to the gas The power delivered P, is given by exchange process through

P =˙mfecÁfc; (3) m˙ a = NiVdÁch; (5) wherem ˙ f is the mass ;ow rate of fuel, ec is its lower heating where N is the engine speed, i is the intake air density, and value, and Áfc is the fuel conversion eHciency. Vd is the swept volume of the cylinder. Here the charging H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171 4165 eHciency is deÿned to be the ratio of the actual mass of Second, the indicated fuel conversion eHciency depends air inducted to the mass of air that the cylinder could con- upon the compression ratio, the combustion process, the tain at ambient conditions. Of note, this assumption results equivalence ratio, and heat transfer to the cylinder walls. Of in the charging and volumetric eHciencies being identical these dependencies, only the compression ratio dependence (Heywood & Sher, 1999). is considered here. This dependency is approximately cap- The engine speed, however, is not a free variable. Instead, tured by deÿning an adjusted air-standard Otto cycle eH- the engine speed and the stroke S, are related through the ciency viz., mean piston speed (Heywood, 1988): (1−") Áfc;i = !{1 − r }; (13) O U p =2SN: (6) where " is a mean speciÿc heat ratio and ! is an adjust- According to Heywood, the mean piston speed is an indi- ment factor. A reasonable value for ! is 0.6 (Taylor, 1985) cator of how well an engine handles loads such as friction, and " =1:3 is assumed. Other factors that a=ect the indi- inertia, and gas ;ow resistance. Data from a wide variety of cated fuel conversion eHciency may be appreciable. Con- engines operating at rated conditions reveals that the mean sequently, they are investigated in the second paper. piston speed is nearly invariant. Consequently, the mean pis- Next, consider the charging eHciency. This parameter de- ton speed is essentially a physical limitation and the operat- pends upon the mass of fresh charge delivered to the com- ing speed thus depends upon the stroke. But one should note bustion chamber by the scavenge pump and the fraction of that in a free-piston conÿguration, the relationship between the delivered charge that is retained in the combustion cham- engine speed, operating conditions, and design parameters ber. These dependencies are captured by the delivery ratio is much more complicated. #, and the trapping eHciency Átr; hence Ách = #Átr. Unfor- Next, Eqs. (5) and (6) are related to the cylinder geometry tunately, both parameters depend strongly upon the engine with the stroke-to-bore aspect ratio: design. Consequently, they are impossible to determine a S R = ; (7) priori. B Fortunately, physical bounds exist for the charging eH- the deÿnition of the displaced cylinder volume: ciency (Heywood & Sher, 1999). For instance, if the fresh S3 charge completely displaces the exhaust gas, then the charg- V = B2S = ; (8) ing eHciency and the delivery ratio are identical i.e., Á =#. d 4 4R2 ch On the other hand, if the fresh charge completely mixes with the deÿnition of the compression ratio: the exhaust, then the charging eHciency is Vt r = (9) Á =1− e−#: (14) Vc ch and the relationship between the total and displaced volumes These extremes represent maximum and minimum bounds given by for the charging eHciency. Consequently, the arithmetic V r − 1 mean of these extremes is a reasonable approximation. d = : (10) Vt r Lastly, the charging eHciency depends upon the delivery ratio. Taylor (1985) gives Substitution of Eqs. (7)–(10) into Eqs. (3)–(6) and replacing the fuel conversion eHciency with the product of the Ns Ds P1 Ti # = Áv;s; (15) indicated fuel conversion, mechanical, and charging eHcien- N Vt Pe T1 cies i.e., Áfc = Áfc;iÁmÁch, yields where Ns, Ds, P1, Pi, Ti, T1, and Áv;s are the scavenging O 1=3 2=3 U p (r − 1)Vt pump speed, scavenging pump displacement volume, trans- P = Á Á Á F e : (11) i 2 4 rR ch fc;i m s c fer port pressure, exhaust port pressure, intake temperature, Also, the engine speed is obtained by manipulating Eqs. (6), transfer port temperature, and the volumetric eHciency of (8) and (10) to give the scavenging pump, respectively. Typically, the delivery ratio is found experimentally for O 1=3 −1=3 U p −2=3 (r − 1) a particular engine design and operating condition. Con- N = R Vt : (12) 2 4 r sequently, scavenge pump performance data is scarce. But for a non-supercharged, crankcase-scavenged two-stroke en- 3.2. Performance estimation assumptions gine, Taylor recommends Ns=N =1, P1=Pe ≈ 1, and Áv;s=0:5. Also, the quantity Ds=Vt is approximated by Eq. (10) and The remaining task is to obtain judicious values for the Ti=T1 ≈ 1. Under these assumptions, Eq. (15) reduces to mean piston speed and the various eHciencies. First, the r − 1 mean piston speed and mechanical eHciency are assumed # = Á (16) r v;s ÿxed. Heywood reports that mean piston speeds typically range from 8 to 15 m=s; thus 10 m=s is a reasonable choice. which completes the necessary set of equations and assump- Moreover, the mechanical eHciency is assumed to be 70%. tions for performance estimation. 4166 H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171

Table 1 50 Sample cylinder bores for Pi = 1 atm, Ti = 300 K and =0:5 (propane is the fuel)

Compression ratio, r Cylinder bore, B (mm) Power output (W) 40

5 4.97 10 η 10 4.13 10 30 fci 20 3.70 10 η ch 30 3.53 10 η 5 1.57 1 Percent fc 20 η , Cox 0.010 10 1.31 1 fc 20 1.17 1 30 1.12 1 10

4. Miniature engine design 0 010203040 4.1. Engine characteristic dimension and compression r, Compression Ratio ratio Fig. 3. The dependence of the charging and fuel conversion and ef- ÿciencies upon the compression ratio and comparison to the Cox The method developed in the previous section may now 0.010 Glow-Ignition Model Airplane engine (Yang, 2000). Note that be used to obtain speciÿc estimates for the size and operating Áfc = Áfc;iÁchÁm and that Ám =0:70. speed of a 10 W engine. Before proceeding however, consider Eq. (11). This equation implies that P depends upon the generally low fuel conversion eHciency is attributable O Ti, Pi, , Vt, r, R, U p, Ách, Áfc;i, Ám, ec, and Fs when i = to poor charging eHciency—a well-known characteristic of i(Ti;Pi) is assumed. Characterizing this function in terms two-stroke engines. of all 11 parameters however, is an intractable problem. Con- sequently the independent variables are grouped into: “in- 4.2. Intake conditions and power density take conditions” (Ti;Pi; ), “fuel” (ec;Fs), and “engine de- O sign” (U p;Vt;r;R;Ách;Áfc;i;Ám). The parameter space may We now proceed to investigate the in;uence of the intake be further reduced by ÿxing the power output, operating conditions on the cylinder bore. Rather than consider each conditions, mechanical eHciency, and mean piston speed. parameter i.e., Ti, Pi, and , separately, their combined e=ect Finally, propane is assumed to be the fuel throughout this on engine performance is investigated by deÿning an “intake paper. Under these constraints, Eq. (11) reduces to parameter” viz., 8P B2Á Á = = Const:; (17) i Pi To ch fc;i O ' = = ; (18) ÁmFseci U p o Po Ti where Eqs. (7), (8), and (10) were used to eliminate the where o is the density of air at 300 K and 1 atm. Hence aspect ratio R, and displacement Vt. this parameter represents the properties of the fresh charge Next, recall that Ách and Áfc;i are assumed in Section 3.2 relative to a stoichiometric mixture at ambient conditions; to depend only upon the compression ratio. Consequently, a convenience because ' =1:0 is a maximum value for B = B(r) which implies that the cylinder bore is a charac- non-supercharged HCCI engines. Whereas ' =0:5 is typ- teristic dimension under these conditions. To illustrate this ical for HCCI engines because the fresh charge is usually dependence, Table 1 presents the results of several compu- preheated and very lean mixtures are employed. One should tations with an initial temperature and pressure of 300 K and note however, that ' has little if any, physical signiÿcance 1 atm while the engine is assumed to operate at an equiva- outside the context of performance estimation. lence ratio of 0.5. Next, the cylinder bore is plotted in Fig. 4 versus ' and In Table 1, the cylinder bore decreases with compression the compression ratio r. Immediately, one notices that the ratio. This result is a consequence of the charging and fuel cylinder bore is minimized when both the compression ratio conversion eHciencies increasing with the compression ratio and ' are maximized. The relationship between compression (Fig. 3). That is, increasing the compression ratio causes the ratio and cylinder bore was already discussed in Section 4.1. fuel conversion eHciency to increase and therefore permits On the other hand, ' captures the e=ect of charge density. a smaller engine to deliver the same power—an intuitive That is, the mass of fuel burned and hence the work obtained result. from each cycle increases with '. Therefore, increasing ' Additionally, Fig. 3 indicates that despite the many crude allows one to increase the power output of a given engine approximations employed, the overall fuel conversion ef- or substitute a smaller engine in its place. ÿciency prediction is reasonably accurate for the smallest The relationships between r, ', and the cylinder bore are commercially available engine. One should also note that important results because to be consistent with the overall H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171 4167

Fig. 5. The engine speed dependence upon the aspect ratio and intake conditions for a 10 W engine, r = 25. ' =1:0 corresponds to P = 1 atm, Fig. 4. The cylinder bore dependence upon the compression ratio and i T = 300 K, and =1:0. intake conditions for a non-supercharged 10 W engine. '=1:0 corresponds i to Pi = 1 atm, Ti = 300 K, and =1:0.

One may infer from Fig. 3 however, that the product ÁchÁfc;i objective of battery replacement, maximizing the power varies from approximately 0.12 to 0.2. Consequently, the density compression ratio dependence is weak and N ≈ N(R; ') P 4P when power output is ÿxed. Hence the engine speed is plot- P = = ; (19) ted in Fig. 5 with r =25 assumed. The engine speed depends d V SB2 t strongly upon the aspect ratio, R. Hence one may conclude is a goal. Consequently, for ÿxed power output and stroke, that the speed is essentially determined by the aspect ratio maximizing the power density is equivalent to minimizing in this analysis. the cylinder bore and thus maximizing both r and '. According to Fig. 4, the power density can be increased 4.4. Engine designs for ÿxed operating conditions without bound; obviously, there are limits. For instance, pre- heating the fresh charge i.e., Ti ¿ 300 K, and using lean After exploring the in;uence of compression ratio, in- mixtures are frequent requirements for HCCI engines; both take parameter, and aspect ratio separately, we now consider decrease '. Although, these requirements may be o=set to combinations of these parameters. To do this, we ÿx the in- some extent by supercharging i.e., Pi ¿ 1 atm. The degree take parameter and obtain families of engine designs that to which this can be done however, is constrained by peak deliver 10 W. cylinder pressures. Moreover, sealing becomes increasingly For example, consider propane-fueled engines with = diHcult when the compression ratio is increased and Fig. 3 0:5, Ti = 500 K, and Pi = 1 atm (' =0:3). Assuming that may di=er from an HCCI process; the latter possibility is the compression ratio and the aspect ratio are free variables, investigated in the second paper. Eqs. (11) and (12) are used to generate the displacement and speed “maps” depicted in Figs. 6 and 7. Speciÿc engine 4.3. Estimating the engine speed designs are then obtained by choosing a compression ratio and an aspect ratio. Thus far, the compression ratio and intake parameter have To illustrate, several engine designs are presented in Table been shown to be important parameters. We now consider 2. Note that even though the bore is independent of aspect the engine speed. According to Eq. (12), it depends upon ratio, two types of engines are apparent: “small and fast” the compression ratio, mean piston speed, total volume, and (large r, small R) and “big and slow” (small r, large R). To stroke-to-bore aspect ratio; but simpliÿcation yields maximize power density, the former variety are preferred. Performance estimation gives valuable guidance regard- UO NB = p : (20) ing the selection of key design parameters, but a funda- 2R mental question has been neglected: Can an HCCI engine Again, the cylinder bore is prominent. Further manipulation operate within an entire design map such as Fig. 6? Intu- gives itively, one would expect not. Consequently, the objective 3=2 of the second paper is to identify regions in the compres- UO Á F e ' 1 1=2 N = p m s c o · : (21) sion ratio–aspect ratio space where operating conditions and 2R 8P ÁchÁfc;i HCCI are compatible. 4168 H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171

10 Table 2 Representative engine designs depicted in Figs. 6 and 7 9 1595 3 1293 Compression Aspect Vt (mm ) N (Hz) B (mm) 8 1041 890 ratio, r ratio, R 790 7 689 10 5 662 188 5.33 589 6 10 10 1324 94 5.33 488 35 1 73 1113 4.49 5 387 35 8 587 139 4.49

, Aspect Ratio 4 R 287 3 186 Although heat and mass transfer e=ects are strictly beyond 2 136 the scope of the present analysis, one can infer favorable 1 86 design conditions using geometry. According to Eq. (1), 5 10152025303540 the surface-area-to-volume ratio is the relevant parameter. r, Compression Ratio Referring to Fig. 2,

3 L Fig. 6. Total cylinder volume, Vt (mm ) required to deliver 10 W when r = (22) operating with a mixture of propane and air, =0:5, Ti = 500 K and c Pi = 1 atm (' =0:3). and the surface-area-to-volume ratio is given by A 2 4 s = + : (23) 10 V˜ L B

9 120 The clearance distance c, and the stroke however are related 8 by S 7 c = : (24) 163 r − 1 6

5 206 Next, using Eqs. (22), (24), and (7), the total combustion

, Aspect Ratio 248 chamber volume becomes R 4 291 3 334 rS 3 V = (25) 419 t 4R2(r − 1) 2 547 717 and substitution of Eqs. (22), (24), (7) and (25) into Eq. 1058 1 (23) and simpliÿcation yields 5 10152025303540 1=3 r, Compression Ratio A 2(r − 1)+4(rR) s = : (26) ˜ 1=3 2=3 1=3 Fig. 7. Engine speed, N (Hz) required to deliver 10 W when operating V Vt 4 (rR) (r − 1) with a mixture of propane and air, =0:5, Ti = 500 K and Pi = 1 atm (' =0:3). Finally, Eqs. (7), (8), and (10) are used to further simplify Eq. (26). Rearrangement yields A 2(r − 1) (r;R)=B s = +4 ; (27) 4.5. Small-scale considerations V˜ rR In addition to neglecting design–HCCI compatibility, which is essentially a non-dimensional surface-area-to- consequences of small engine dimensions have been over- volume ratio function. looked. In the context of micro-combustion, these e=ects According to Eq. (1), the speciÿc heat transfer rate is are primarily enhanced heat and mass transfer rates. Greater minimized when is minimized. Inspection of Fig. 8 re- heat transfer rates are hypothesized to have two adverse veals that this occurs when large aspect ratios are employed. e=ects on an HCCI engine: (1) decrease the e=ectiveness Also, Fig. 8 suggests that the compression ratio dependence of compressive heating, and (2) decrease the indicated fuel is weak. In contrast, small aspect ratios maximize power conversion eHciency. The e=ect of enhanced mass transfer density (Section 4.2). Therefore, minimizing heat transfer rates however, is unclear. That is, radicals can be destroyed and maximizing power density are opposing objectives. or produced on walls depending upon surface properties; Lastly, the degree to which heat transfer can be decreased resulting in totally opposite e=ects. Further investigation of by large aspect ratios is limited. That is, Eq. (27) has a heat and mass transfer rates are left to the second paper. minimum value of 4, and is within 5% of this limit when H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171 4169

Notation

2 AB bounce chamber area, Eq. (2), m 2 AC combustion chamber area, Eq. (2), m 2 Acp compressor area, Eq. (2), m 2 As surface area, Eq. (1), m 2 Asc scavenge pump area, Eq. (2), m ˜ As=V surface area to volume ratio, Eq. (1), 1=m B cylinder bore, Eq. (7), mm c clearance distance, Eq. (22), mm 3 Ds scavenge pump displacement volume, Eq. (15), m ec lower heating value of fuel, Eq. (3), kJ=kg F fuel–air ratio (mass basis), dimensionless Fs stoichiometric fuel–air ratio (mass basis), Eq. (4), dimensionless Fx x-direction force, Eq. (2), N L combustion chamber height, Eq. (22), mm Fig. 8. Non-dimensional surface-area-to-volume ratio function, Eq. (27). m mass of material, Eq. (1), kg m˙ a mass ;ow rate of air, Eq. (4), kg=s the aspect ratio is 10. Thus, aspect ratios greater than 10 m˙ f mass ;ow rate of fuel, Eq. (3), kg=s o=er almost no beneÿt. mp piston mass, Eq. (2), kg N engine speed, Eq. (5), Hz 5. Conclusion Ns scavenge pump speed, Eq. (15), Hz P delivered or brake power, Eq. (3), W This paper has presented a concept for a 10 W miniature P1 transfer port pressure, Eq. (15), atm free-piston engine-compressor and various considerations PB bounce chamber pressure, Eq. (2), atm for its design. Speciÿc results are summarized as follows: PC combustion chamber pressure, Eq. (2), atm Pcp compressor pressure, Eq. (2), atm • Combustion mode. In small scales, traditional engine 3 Pd power density, Eq. (19), W=cm combustion schemes are generally infeasible due to Pe exhaust port pressure, Eq. (15), atm quenching e=ects; HCCI is a promising alternative. Pi intake pressure, atm • Compression ratio. The nominal compression ratio for Psc scavenge pump pressure, Eq. (2), atm this engine is a crucial parameter because it determines Po normal pressure of air, Eq. (18), 1 atm the compression history of the charge, a=ects the fuel q˙ heat transfer rate per unit mass, W=kg conversion eHciency, and establishes the engine size. On q˙ heat ;ux, Eq. (1), W=m2 the other hand, it a=ects neither the engine speed nor the qO˙ average heat ;ux, Eq. (1), W=m2 speciÿc heat transfer rate. Also, HCCI does not have a Q˙ heat transfer rate, Eq. (1), W fundamental compression ratio limitation like SI. Conse- r compression ratio (r = V =V ), Eq. (9), dimension- quently, the compression ratio may be increased virtually t c less without bound. Practically however, sealing and material R stroke to bore aspect ratio, R = S=B, Eq. (7), di- properties will impose limits. mensionless • Aspect ratio. The performance analysis revealed that for S piston stroke, Eq. (6), m a crankshaft-equipped engine, the stroke-to-bore aspect T transfer port temperature, Eq. (15), K ratio establishes the engine speed. Additionally, the aspect 1 T intake temperature, Eq. (15), K ratio essentially determines the surface-area-to-volume i T normal temperature of air, Eq. (18), 300 K ratio. More signiÿcantly however, small aspect ratios o UO mean piston speed, Eq. (6), m=s were found to maximize power density while large p V cylinder clearance volume (= B2c=4), Eq. (9), aspect ratios were found to minimize heat transfer. Con- c mm3 sequently, a compromise must be sought between maxi- V displaced volume (= B2S=4), Eq. (5), mm3 mizing power density and minimizing heat transfer rates. d V total cylinder volume (= B2L=4), Eq. (10), mm3 Also, essentially no further reduction in heat transfer t V˜ volume, Eq. (1), m3 may be achieved with aspect ratios greater than 10. x Cartesian coordinate, Eq. (2), m Finally, HCCI depends strongly upon engine operation and design. Small scales are expected to impose additional Greek letters constraints. Consequently, the next step is to investigate ! air-standard Otto cycle adjustment factor (=0:6), these aspects in detail. Eq. (13) 4170 H. T. Aichlmayr et al. / Chemical Engineering Science 57 (2002) 4161–4171

" speciÿc heat ratio used in adjusted air-standard Christensen, M., & Johansson, B. (1999). Homogeneous charge Otto cycle (=1:3), Eq. (13) compression ignition with water injection. SAE Technical Paper 1999-01-0182. ' intake parameter (=i=o ), Eq. (18), dimensionless Christensen, M., Johansson, B., AmnJus, P., & Mauss, F. (1998). Á charging eHciency (=mass of fresh charge Supercharged homogeneous charge compression ignition. SAE ch Technical Paper 980787. retained=reference mass), dimensionless Christensen, M., Johansson, B., & Einwall, P. (1997). Homogeneous Áfc engine fuel conversion eHciency, Eq. (3), di- charge compression ignition (HCCI) using isooctane, ethanol, mensionless and natural gas-a comparison with spark ignition operation. SAE Technical Paper 972874. Áfc;i fuel conversion eHciency of the engine cycle, dimensionless Disseau, M. L. D. S., et al. (2000). Investigation of combustion processes in small aspect ratio combustors. Georgia Institute Ám mechanical eHciency, dimensionless of Technology Internet Document (Last loaded August 2000). Átr trapping eHciency (=mass of fresh URL http://comblab5.ae.gatech.edu/Minipiston/ConstVol.htm charge trapped=mass of fresh charge delivered), Epstein, A. H., Senturia, S. D., Anathasuresh, G., Ayon, A., Breuer, dimensionless K., Chen, K., Ehrich, F. E., Gauba, G., Ghodssi, R., Groshenry, C., Á engine volumetric eHciency, (=m = V ), Eq. Jacobson, S., Lang, J. H., Lin, C., Mehra, A., Miranda, J. M., Nagle, v a i d S., Orr, D. J., Piekos, E., Schmidt, M. A., Shirley, G., Spearing, M. (5), dimensionless S., Tan, C. S., Tzeng, Y., Waitz, I. A. (1997). Power MEMS and Áv;s scavenge pump volumetric eHciency, Eq. (15), microengines. In Transducers ’97 Chicago: Digest of technical papers dimensionless (pp. 753–756), June 16–19, 1997. Chicago, IL: IEEE. # delivery ratio (=mass of fresh Fernandez-Pello, C., Liepmann, D., & Pisano, A., et al. (2001). charge delivered=reference mass), dimension- MEMS rotary combustion laboratories. University of California less at Berkeley Internet Document (Last loaded July 2001). URL http://www.me.berkeley.edu/mrcl/ 3 density, Eq. (1), kg=m Flowers, D., Aceves, S., Smith, R., Torres, J., Girard, J., & Dibble, R. 3 i density of air at the intake, Eq. (5), kg=m (2000). HCCI in a CFR engine: Experiments and detailed kinetic O average density, Eq. (1), kg=m3 modeling. SAE Technical Paper 2000-01-0328. Galileo Research Inc. (2001). Free-piston engine-generator technology. o density of air at 300 K and 1 atm, Eq. (18), kg=m3 Internet Document (Last loaded September 2001). URL http://www.galileoresearch.com/FPEG Technology/ fuel–air equivalence ratio (=F=Fs); ¡1, peg technology.htm fuel-lean; ¿1, fuel-rich; Eq. (4), dimension- Gentili, R., Frigo, S., Tognotti, L., Patrice, H., & Lavy, J. less (1997). Experimental study on ATAC (Active Thermo-Atmosphere non-dimensional surface-area-to-volume ratio Combustion) in a two-stroke gasoline engine. SAE Technical Paper ˜ 970363. ((r;R)=BAs=V ), Eq. (27) Goldsborough, S. S., & Van Blarigan, P. (1999). A numerical study of a free piston IC engine operating on homogeneous charge compression ignition combustion. SAE Technical Paper 990619. Acknowledgements Gray III, A., & Ryan III, T. W. (1997). Homogeneous charge compression ignition (HCCI) of diesel fuel. SAE Technical Paper 971676. This project was sponsored by Honeywell International Hagendorf, U., Janicke, M., Schuth,Q F., Schubert, K., & Fichtner, M. (1998). A Pt=Al O coated microstructured reactor=heat exchanger for under DARPA Contract no. F30602-99-C-0200. 2 3 the controlled H2=O2-reaction in the explosion regime. In Process miniturization: Second international conference on microreaction technology (pp. 81–87). New Orleans, LA: The American Institute of Chemical Engineers. 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