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(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

At A AA01-16748

AIAA 2001-0944Simulation of Combustion DrivenMicro-EngineM. Kirtas and S. MenonSchool of Aerospace EngineeringGeorgia Institute of TechnologyAtlanta, GA 30332

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Simulation of Combustion Driven Micro-EngineM. Kirtas*and S. Menon*

School of Aerospace EngineeringGeorgia Institute of Technology

Atlanta, GA 30332

A numerical study of a combustion driven micro-engine is presented in this paper.There are some unique issues in the design of this engine due to the dimensions of thecombustor and since Micro Electro-Mechanical Systems(MEMS) fabrication technologyhas to be used in its manufacture. Phenomena such as ignition, flame propagation, heatlosses and quenching may occur differently due to the small size of the device, especiallythe high aspect ratio of the combustor. Since these effects control the performance ofthe engine, an in-depth parametric evaluation is necessary to develop an optimal success-ful design. However, due to the MEMS fabrication limitations, parametric experimentalstudies is not only difficult but also very expensive. To complement an on-going ex-perimental effort and to reduce the design cycle costs, a large-eddy simulation (LES)methodology has been developed to carry out the aforementioned parametric studies ina more cost-effective manner and to provide guidelines for the construction of the micro-engine. The simulations results are compared with available experimental data and resultsshow reasonable agreement. The relevance and importance of various parameters of themicro-engine is then discussed and implications for design are highlighted.

IntroductionA free piston engine is a device that employs com-

bustion to establish into cyclic motion a piston thatis then used to directly produce energy. There aremany successful designs of this device and some oftheir key features were summarized on a recent sur-vey.1 In general, a free piston engine can be usedto generate hydraulic, pneumatic or electrical energyand past designs have employed either a single pistonor an opposed or dual piston setup depending on theposition of the combustion chamber(s) and piston(s).The relevance of several design parameters, such asthe fuel injection timing, energy conversion efficiency,sealing and losses have been discussed earlier1 in thecontext of past designs. Some of these issues will bere-addressed in the present study. In another recentstudy2 the application of free piston configuration withopposed combustors was discussed as a device for gen-erating electrical energy. They presented results for a"Benchtop Model" where the emphasis was on obtain-ing the experimental pressure versus volume diagramsince this type of information can give simple order ofmagnitude estimate of the efficiency of power conver-sion.

The various free-piston engines discussed in theabove noted papers were of dimensions that were smallbut not necessarily considered an extreme limit. Re-cently, with the advent of MEMS technology appli-cation to practical systems, there has been consider-able interest in investigating systems that are either

* Graduate Studentt Associate Fellow, AIAACopyright <c) 2001 by M. Kirtas and S. Menon. Published by

the American Institute of Aeronautics and Astronautics, Inc. withpermission.

very small (i.e., micron-scale) or devices that requireMEMS fabrication technology in order to build thedevice. Micro-engines that employ both these ap-proaches are being investigated. An example of aMEMS-scale engine is the micro-turbine being devel-oped at MIT,3 whereas a device that is small enoughto require MEMS fabrication technology is currentlybeing developed at Georgia Tech.4 A key feature ofall these designs is the need to demonstrate a verysmall device capable of producing appreciable energy(e.g., 10-30 Watts of electrical power) in order to beuseful for practical application. Of special interestin the present study is a device that employs fluidicpower, i.e., combustion, to drive the generator to ob-tain electric power. Compared to conventional powersources, MEMS manufactured generators will have ahigh power density and a relatively long life. As a re-sult, such a device may find many applications bothin military and civilian fields. For example, an appli-cation of key interest to the US Army is the ability toprovide portable power for the systems a soldier mustcarry. Thus, a system independent "soldier" powerpack could have many applications.

A device under development at Georgia Tech in-corporates a free piston located between two opposedcombustors. This piston is set into motion due to out-of-phase combustion in the two opposed combustors.To generate electric power from this device, the entireassembly is confined inside a magnet array. The in-teraction of the magnetic field with the piston motiongenerates the required electric energy. A schematic ofthis device is shown in Fig. 1. Note that, the actualscale of the entire device (including the magnetic ar-ray) is no larger than a pack of playing cards.

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AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 2001-0944


Although the above device is conceptually sound,the aforementioned problems regarding achievingcyclically consistent and accurate injection, mixing, ig-nition and combustion within a very small combustor(in order to generate sustained steady-state electricpower) requires significant optimization of the designof the device. Key parameters include the location ofthe inflow and outflow ports, the timing of the open-ing and closing of these ports, and control of leakageand heat transfer loss from the system. The variousproblems associated with optimizing these parametershas led the experimental effort to a more simplifiedconfiguration in which the engine consists of a sin-gle combustor with the other combustor replaced by aspring that provides a pre-defined force to mimic the"phantom" combustor. A similar device is numericallysimulated in the present paper using LES.

In the following sections we describe the method-ology used for LES, the problems addressed in thispaper and the results obtained. It is to be noted thatto the authors' knowledge this is the first attempt tosimulate a free piston combustion system using LES.Furthermore, the results of the present LES effort isbeing used to provide guidelines for the hardware con-struction. Therefore, this effort provides an uniquedemonstration of the ability and the use of LES re-sults for practical design of complex systems.

Governing Equations for LESThe governing equations of motion are the usual

Navier-Stokes equations for a general compressible, re-acting flow. Spatial Favre filtering of the governingequations using a suitable (top hat) filtering opera-tor along with the decomposition of the flow field intoa subgrid (unresolved) and supergrid (resolved) partsresults in a set of conservation equations for the re-solved properties. Unknown terms in these equationsrepresenting the contribution of the unresolved sub-grid quantities have to be modeled. The final set ofLES equations are:

+ «-• (.)

represent the subgrid stress tensor, subgrid heat flux,subgrid viscous work, species mass flux and speciesdiffusive mass flux, respectively. These terms havebeen described in detail elsewhere5"7 and therefore,only a brief description will be given here. In thepresent formulation, closure of the subgrid stress termsis achieved using a transport model for the subgrid ki-netic energy per unit mass k*98 = \ \u\ - u\ I:

for ra = 1,7V

Subgrid ClosureThere are many terms in the above equations that

appear due to the filtering process and must be closed.The unclosed terms r£", H?9, <r*f, *?£, and

- D"'

£(* (5)

where P8°8 = -r'9 and D9** =are the production and dissipation terms, respectively.

Subgrid stress tensor is closed by using an eddyviscosity hypothesis based on the subgrid turbulentkinetic energy. Thus, r?f9 = -2pvt \Sij - |5** JijJ +\~pk898&ij, where the eddy viscosity is vt =Cr

I/(fcsps)1/2A. Here, A is the filter width which is re-lated to the local grid size. There are two coefficientsCv and C£ in this model that have to be specified. Alocalized dynamic approach to determine these coeffi-cients have been developed and shown to be robust incomplex flows.7 However, for the present effort, usingresults from a recent study,8 the coefficients Cv and Ceare taken as 0.067 and 0.916, respectively. Dynamicmodeling will be carried out in the near future.

Subgrid heat flux and species subgrid mass fluxterms follow similar definitions based on gradient dif-fusion model and are given by

and

Sct

(6)

(7)

+ ̂ [(pE + p)ui + ̂ - ty ?* + /f**a -f a*/5] = 0 (3)

where the turbulent Prandtl number and Schmidtnumber are chosen as 0.9 and 0.92, respectively, his the mixture enthalpy. Subgrid diffusive mass fluxterm 0*^ is neglected since it is shown to be relativelysmall compared to the subgrid species mass flux $^.Finally, the subgrid viscous work is modeled as

Reaction Rate ClosurePremixed methane-air combustion is studied in the

present effort. For the initial study, a global, singlestep finite-rate kinetics model is employed. For LESapplications, the closure of the reaction rate is some-what problematic and has been the focus of manyrecent efforts. In general, the filtered reaction rate canbe computed (a) by assuming the joint scalar prob-ability density function (PDF),9 (b) by solving for

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the subgrid PDF10'11 or (c) by employing a simpli-fied algebraic relation such as Eddy Break-Up (EBU)or Eddy Dissipation Concept (EDC). Spalding12 pro-posed the first EBU model for computing mean re-action rate of fuel in a turbulent flow. This modelhas been used with some minor changes for both pre-mixed and non-premixed combustion. Several variantsof the model have since appeared in the literature andit has been shown also that in the limit of very fastchemistry, presumed PDF methods can be cast intoEBU type relations.13 In this study, the closure of themean reaction rate is obtained by employing a mod-ified break-up model EBU14 where the interaction ofsmall scale structures with the large eddies is mod-eled by determining the time scale at which reactionstake place. For chemistry, a global decomposition re-action of the form R —)• P for a premixed mixture ofCH\ and air is employed. The Arrhenius type reac-tion rate expression is WR = pYRAexp(-Ta/T) whereA = 5.55 x 109 I/sec and Ta = 14786 K.15 Thefiltered reaction rate is then determined as

w = [(wma88)~l (9)

where wchem is the chemical reaction rate(obtainedfrom the Arrhenius expression above) and w1710188 is themass destruction rate due to mixing which is given by

[-(v^ - v*)Mm]~1} (10)

Here, TM = (1 - 7) A™ is a characteristic mixingtime scale. In this formulation,14 the mass trans-fer per unit mass per unit time between fine struc-tures and the surrounding fluid is defined as ra =(]|r~2)1/4M1/4- Finally, the intermittency of thisprocess is modeled through the intermittency factor7 = (125^)1/4A7/5(z/3/01/4. Here, £ = 0.09 ande = fc3/2/A and v is the usual kinematic viscosity.The relevant information leading to this formulationcan be found elsewhere.14 Using the above relations,the filtered reaction rate for each species can be writ-ten as:

^-V^)w (11)

The above approach, although an approximation, iscomputationally very cost effective and is consideredsufficient for a first attempt to demonstrate a designlevel LES approach. An alternate and more accuratemethod would be to use a subgrid scalar evolutionmodel such as the subgrid linear-eddy model approachdeveloped earlier.8'11 The need for such a complexand relatively more expensive modeling approach willbe evaluated later depending upon the ability of thepresent model to provide design level results of accept-able accuracy.

The Micro-EngineDuring the course of this study, a series of engine

designs were investigated. Initially, in both the exper-iments4 and numerical efforts16'17 the dual combustorconfiguration similar to Fig. 1 were studied. Figure 2shows a schematic of the device simulated numerically.For parametric studies, different options of this devicewere also investigated. Figure 3 shows four such de-signs which differed primarily in the location(s) of theinflow and outflow ports. The rationale behind thesedesigns and some of the pertinent results (which werereported earlier16'17) are summarized in the Resultssection.

The current research effort is focused on a simplerdevice and a planform view of the engine is given inFig. 4. This design was chosen for the experimentaleffort to address some problems related to achievingcyclic combustion in the dual system and to under-stand the dynamics of the process. Typical dimensionsand parameters for this experimental device are sum-marized in Table 1 (these values were also used for theLES studies reported here). The free piston enginehas two scavenging ports one of which is also usedfor inflow of premixed reactants. In a typical cycle ofcombustion, there are three phases: an intake phase,a combustion phase and an exhaust phase. In the ex-periments, the injection is at an angle from one of theports to the wall where reactants will eventually beignited. A similar approach is employed in the LES.Ideally, the injection angle should be varied to deter-mine the ideal inclination that will give a mixture asuniform as possible after the intake phase. This is anissue to be addressed once the present model has beenvalidated using the existing experimental data.

The intake phase is a continuous one, in other words,if the pressure in the chamber is below a predeter-mined value then injection of the reactants will occurprovided that the ports are open. During the intakephase, pre-compression occurs and before the pistonreaches TDC (Top Dead Center), ignition occurs. Theignition time is of the order of 0.2 msec. After ig-nition, flame propagation, volumetric expansion andpressure rise effects causes the piston to move back toBottom Dead Center (BDC) which is the end of onecycle. Note that, there is no outside interference tocontrol the opening and closing of the ports. Rather,the opening and closing of the ports is done automati-cally by the moving piston itself. Thus, piston, duringits motion, acts as an actuating mechanism so that, de-pending on the position of the piston, the ports mightbe open or closed. This is important design considera-tion for this engine because other means of controllingthe state of the ports will require supplementary mech-anism (s). Integration of such a control mechanism ina small device will increase the complexity and driveup the cost and therefore, is to be avoided.

Since the piston motion controls the status of the

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ports (i.e., open/closed) it can effect a variety ofthings, such as the maximum pressure obtained, theconcentration of the unburned reactants just beforethe exhaust ports opens, the amount of burnt prod-ucts remaining, etc., and through these effects directlyimpact the oscillatory state of the combustion pro-cess and the frequency of oscillation. The frequencyof oscillation directly controls the power generated bythis device and therefore, achieving a fixed frequencyis critical for the success of this design. Hence, fora given fuel mixture, the ports should be at a loca-tion (relative to ignition zone) such that combustionis completed before the exhaust phase. This point isclosely linked to other phenomena such as the turbu-lence level in the combustor during combustion andquenching especially near the walls. The latter hasparticular importance in the present context since thecombustor has very small spanwise dimension and theflame will reach the lateral walls before it reaches theother walls.

Numerical IssuesThe conservation equations are solved using a

finite-volume scheme with a predictor-corrector time-stepping. This scheme is second order accurate bothin space and time. No-slip boundary conditions areapplied on all walls for the velocity field. Since un-steady heat transfer to the wall has been identifiedas an important factor in the experimental studies, atime-dependent heat flux boundary condition is em-ployed during some stage of the combustion process asdescribed later. For simplicity, mass loss from the do-main in-between the piston and the wall is neglected.The retarding force due to the magnetic coils is alsonot considered. These issues will be addressed in afuture study. Thus, the present form of the simulatedproblem is a pure combustion problem with movingboundaries. Figures 2 and 4 show the combustorsalong with the appropriate dimensions. Notice thatthe spanwise dimension is much smaller than the othertwo directions and thus, this device has a very highaspect ratio. To properly resolve this domain, a com-putational grid of 191 x 101 x 13 is used and for thisresolution the grid size is about 0.5mm in all direc-tions. Thus, a uniform grid resolution is used in thepresent effort to avoid any grid stretching errors. Ear-lier studies addressed the issue of grid resolution andit was determined that for this combustion problem,such a resolution is sufficient to resolve the flame zone.

Inflow conditions are specified using characteristicinflow conditions.18 Randomly generated turbulentfluctuations is added to the inflow velocity and subgridkinetic energy is also specified at the inflow. Typicalvalues used here are taken from Tabaczynski.19 Theexit pressure is specified at the outflow and all othervariables are extrapolated from the interior.

To move the piston, a simple force balance between

the fluidic force (obtained by multiplying the averagepressure in the chamber by the frontal area of the pis-ton) and the opposing spring force is employed. Springdetails are given in Table 1. This procedure takes intoaccount some of the inertial effects. Thus, the momen-tum of the piston is not neglected. Note that in thereal system the spring is not attached to the pistonand the spring exerts a force which is a linear func-tion of displacement. At top dead center (TDC), thespring is already displaced 5.1 mm (0.2 in). Since thetime scale of integration is on the order of 10~7sec,the corresponding piston motion is very small. Inorder to reduce the computational effort, the pistonis not moved in the computational domain at everytime step but rather, the computed displacements aresummed in time till it reaches a reasonable fraction ofthe grid size before the piston is moved. More specif-ically, a displacement based on velocity increments iscomputed by £ F x A* = M x AV where ]T F andA V are the total force acting on the piston and the ve-locity increment at each time step, respectively. Here,M is the piston mass. The total force is equal to thedifference between the average pressure in the chamberand the piston force that can be calculated by Hooke'sLaw. Then, the piston is moved when the summeddisplacements exceed the local grid size. Thus, the dis-placement, if any, is on the order of the local grid size.Furthermore, no rotational effects about the center ofgravity of the piston due to local chamber pressurevariations are considered for the present.

Results and DiscussionsResults of the present effort are summarized in this

paper. Initial studies of ignition in a constant volumecombustor was carried out to determine the impor-tance of heat transfer to the wall on the effectivepressure rise in the combustor. Subsequently, bothtwo-dimensional (2D) and three-dimensional (3D) LESstudies of the dual-combustor micro-engines (Fig. 2)were carried out and compared to determine if 2Dstudies (which are computationally very cost effective)can be used with reasonable accuracy for parametricevaluation of various designs. Finally, the experimen-tal device (Fig. 4) is simulated in 3D to investigate thenature of oscillation and to obtain data for compari-son. Discussion of the sensitivity and applicability ofthe LES results is then carried out.

Effect of Wall Heat TransferTo determine the impact of wall heat transfer, 2D

and 3D simulations were carried out using adiabaticand unsteady heat flux at the wall using a constantvolume combustor. In this case, the combustor vol-ume was 4225 (50 x 13 x 6.5)mm3 and a resolution of100 x 60 and 100 x 60 x 10 were used for 2D and 3Drespectively. This case correspons to a case that wasexperimentally investigated in the past. Details of this

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study was reported elsewhere.16'17 Fig. 5 summarizesthe results of this study. It can be seen that both 2Dand 3D calculations reproduce the pressure rise withreasonable agreement. Furthermore, the effect of wallheat transfer is dramatic and results in a significantdrop in the peak pressure. This is an important issuefor the design of this device since the pressure rise di-rectly translates into the motion of the piston whichin turn determines the power output from this device.Thus, for an optimal design, reduction in wall heattransfer should lead in a more efficient design. How-ever, practical manufacturing problems and the typesof material available for MEMS fabrication may placean upper limit on the control of the amount of heattransfer through the walls. This implies that wall heattransfer must be included in all modeling studies. Ide-ally, for proper modeling, the heat conduction problemthrough the physical walls must be solved along withthe LES flow problem in the combustor. These issueswill be considered in a follow-on study.

Although comparison with data shows reasonableagreement for the heat transfer case, there are somediscrepancies especially in the initial stages. This isrelated to the differences in the ignition process usedin the experiment and in the model. In the experi-ments, multiple spark sources were employed whereasin the simulation a small volume in the domain waspreheated. Thus, the initial flame kernel formationand its growth are quite different. Numerically, itis very difficult to mimic the spark ignition process.Furthermore, there could be other reasons that couldresult in the observed differences, for example, the useof global chemistry in the model, the effect of flamegrowth and quenching near the walls which is not mod-eled, etc. Again, these issues are being addressed andwill be reported in the near future.

Dual-Combust or Micro-Engine

As noted earlier, there were problems in the fabri-cation and operation of this engine in the early stageof this project. In fact, one of the earlier design failedto maintain the oscillation and would stop after coupleof oscillations. Since it was difficult to determine fromthe actual device what was happening inside the com-bustor, a series of numerical studies were carried outto determine the reasons. Four different configurationswere studied. Figure 3 shows these configurations andthey differ primarily in the location of the inflow andoutflow ports. Results of these studies were reportedearlier17 and therefore, only key highlights are summa-rized here. Some of these designs had a fundamentalproblem, namely that the reactant concentration inthe chamber could not be increased to a level sufficientto sustain combustion. This is shown in Fig. 6 whichshows the reactant concentration reached during theinjection phase and before the outflow is opened. Ide-ally, the concentration should reach unity as quickly

as possible. It can be seen that Designs 3 and 4 weresuccessful while Designs 1 and 2 failed to achieve highreactant concentration in the chamber before ignition.As a result, the Designs 1 and 2 does not maintain sus-tained oscillation. Note that, Design 1 is very similarto the earlier experimental device.

To determine why this design failed the flow fieldwas analyzed. It was determined that in this case,some of the burnt products gets trapped in the com-bustor and effects the inflow of the reactants. Infact, due to this trapped products, some of the re-actants escape through the outflow port before igni-tion. Representative velocity vector fields for Design-1and for Design-4 (which was successful) are shown inFig. 7. Note that, for the failed Design-1 case, burnedproducts are trapped in the top and bottom corners(marked by symbol B) and some of the reactants(marked by a symbol R) actually escape through theoutflow port before it is closed. In contrast, Design-4due to the location of the outflow port allows all theburned products to exit while the injected reactant isstill filling the chamber.

Simulations such as this are quite useful in obtain-ing quick answers to the modifications to the designsince construction of this device would have takena long time. Furthermore, the above studies werealso conducted using both 2D and 3D codes to seeif there is any similarity in the flow field. It wasdetermined from the numerical studies that 2D and3D simulations reproduce very similar process and thepredicted pressure amplitude and frequency were veryclose. This is shown in Fig. 8. This is important since2D simulations are computationally very inexpensiveand therefore, a large number of parametric simula-tions can be carried out quickly in order to obtainsome quick answers. On the other hand, for a morerealistic combustion process, the effect of small-scaleturbulence (which is 3D) needs to be included. There-fore, eventually, full 3D simulations are necessary toinvestigate the final design.

Single-Combustor Micro-Engine

The earlier study established the numerical method-ology and demonstrated its ability to capture some ofthe dynamics of the flow field. The dual-combustorstudies showed how a successful design could beachieved. However, designs such as Design-4 requiredadditional mechanism to open and close the ports(since they were located further from the piston).From an experimental point of view a more simplerdesign was preferred and this resulted in the aforemen-tioned development of the single-combustor design.

The single combustor model is designed with sim-plicity in mind and provides one with more control overthe relevant parameters. Recently some experimentalresults has been reported,4 mainly for pressure historyand position of the piston. So far, three combustors

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of different size have been experimentally studied4 butonly one with chamber thickness of 6.25mm is simu-lated here. Experimentally, this combustor achievedsustained oscillation as described below.

Experimental pressure and position history aregiven in Fig. 9. Corresponding numerical solution isalso shown in Fig. 9. General trends are captured wellin the numerical solution. The predicted frequency(43 Hz) is close to the measured value (32 Hz) and thepeak pressure is also close and differs by less than 10%.There are, however, some differences as well. The ig-nition in the numerical solution is somewhat slowerwhich in turn impact the combustion process. Asnoted earlier, the ignition process used in experiments(multiple spark plugs) is very difficult to mimic in thenumerical approach and therefore, some discrepancyin the initial period is expected. In the real configu-ration, as can be seen in Fig. 9, combustion is almostfinished at TDC, which explains the relatively higherpeak pressure obtained. On the other hand, in the nu-merical simulation (Fig. 9) combustion continues evenafter TDC. There could be various reasons for thisdifference. For example, it may be a consequence ofthe limitation of the EBU reaction rate closure modelthat is employed here which will impact the chemicalconversion rate. Additionally, the magnitude of in-flow turbulence (which in turn can effect the mixingtime scale) could impact this result. At present, thereare no measurements in the combustor to determinesome of these quantities and therefore, additional sim-ulations with different conditions may be necessary todetermine the difference.

Another observation is that the experimental pres-sure begins to decrease long before the ports are openand as a result, the P - V experimental diagram isboth qualitatively and quantitatively different thanthe computed P- V diagram. These figures are shownin Fig. lOa and lOb, respectively. This difference canbe attributed to heat and mass losses observed in theexperiments (and which are not currently included inthe model) and the model for the spring constant forthe simulation. At present, there is no quantifiedinformation available from the experiments for theseparameters and other parameters such as retardingforce due to the generator, etc., and one has to resortto guessing their values. For example, the experimen-tal value of the spring constant k = 1183.3 W/m wasnot sufficient in the simulation phenomena such as thelosses and retarding force were unaccounted. We re-sorted to including their effect by increasing the springconstant in an ad hoc manner. To determine the sen-sitivity of the simulations to the choice of the springconstant, two simulations were carried out using differ-ent values of the spring constants: k = 2081JV/m andk = 23SlN/m (as shown above). Increasing the springconstant slightly increases the peak pressure and thestroke length of the piston but the frequency is al-

most unchanged. Higher spring constant give moretime near TDC and this explains the slight pressureincrease. On the other hand, it also accelerates the re-turn to TDC from BDC, thus tending to compensatefor frequency. These result suggests that more infor-mation from the experimental device is needed to fullymodel all the features in this device.

It should be noted that although the spring con-stant was increased above the experimental value tomodel for the missing effects, it still gives a linear re-sponse in space. However, the neglected factors mayall contribute to nonlinearity to a certain degree andtherefore, without further quantified information fromthe experiments (which is likely to be nearly impos-sible), it will be very difficult to exactly match thedata. Nevertheless, the present simulations have beenable to reproduce nearly all the dynamical featuresobserved in the experiments and also provided a newcapability that can be utilized (at least in an idealizedmanner) to study such devices. Such a capability canbe very useful for optimizing the final design of themicro-engine.

Figures 11 and 12 show respectively, the subgrid ki-netic energy and temperature at ignition and injectionphase. It can be seen that in both phases there isa significant amount of subgrid kinetic energy in thedomain. Especially during injection, significant fluc-tuations are occurring in the high shear region of theinjected jet. Spanwise views show that there is also sig-nificant three-dimensionality in the domain suggestingthat for this configuration (which involves an angled,high-speed injection), full 3D simulations may be nec-essary to understand the dynamics of the mixing andcombustion process.

Finally, the experimental frequency is close to 32Hertz while either of the numerical solutions is about43 Hertz. According to Zinn et al.,4 a free piston de-vice in the frequency range 25 — 50 Hertz will produceabout 20 W electrical power. This is within the designgoal of this project.

ConclusionsA LES methodology has been developed to simu-

late combustion process in a free piston micro-engine.Simulations have been carried out for various designconfigurations in order to understand the dynamicsof the combustion process in high aspect ratio com-bustors. The simulation results have been used toidentify critical design issues and to provide guidelinefor the manufacture of this engine. These studies formthe first such reported application of LES to hard-ware design and provide confidence on the ability ofLES predictions. Comparison of the LES predictionswith available data show reasonable agreement. Inparticular, the dynamics of sustained oscillation hasbeen captured well although there are some differ-ences in the actual values. However, as noted above,

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there are many uncertainties in the experimental de-vice that cannot be quantified and hence, cannot bemodeled properly. Nevertheless, the LES model hasshown its potential for addressing these flows in a morecost-effective manner and therefore, may become animportant tool in the design of micro-engines in thenear future.

Future studies of this micro-engine will address sys-tem parameters that are critical for optimizing theperformance of the engine. Heat conduction throughthe wall will be included to model more accurately theheat transfer effect. The impact of injection strategy(orientation, location, port size, etc.) will also be ad-dressed. Finally, further effort will be directed towardsdetermining a model to include heat losses in a moreaccurate manner.

AcknowledgmentsThis work was supported by Army Research Office

and DARPA under a Multidisciplinary University Re-search Initiative.

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14Fureby, C. and Moller, S.-L, "Large Eddy Simulation ofReacting Flows Applied to Bluff Bofy Stabilized Flames," AIAAJournal, Vol. 33, No. 12, 1995, pp. 2339-2347.

15Westbrook, C. K. and Dryer, F. L., "Simplified ReactionMechanisms for the Oxidation of Hydrocarbon Fuels in Flames,"Combustion Science and Technology, Vol. 27, 1981, pp. 31-43.

16Rabindra, N. P., Kapoor, R., Kim, J. H., and Menon,S., "Simulation of Combustion-Driven Micro Power Generator,"Dec. 1999, Poster presentation, 28th Symposium(international)on Combustion.

17Rabindra, N. P., Kapoor, R., Kim, J. H., and Menon,S., "Combustion Dynamics in a Compact Power Generator,"The 8th Conference (International) on Numerical Combustion,Amelia Island, Florida, 2000.

18Poinsot, T. J. and Lele, S. K., "Boundary Condi-tions for Direct Simulations of Compressible Viscous Flows,"J.Comput.Phys., Vol. 101, 1992, pp. 104-129.

19Tabaczynski, R. J., "Turbulence and Turbulent Combus-tion in Spark-Ignition Engines," Prog. Energy Combust. Sci.,Vol. 2, 1976, pp. 143-165.

Table 1 Engine description

• single piston against an opposing spring• two stroke engine• combustion system: premixed• piston stroke: ~ 4.3cm• piston mass: 0.1 kg• flow rate: 17.75 m3/hcwr• spring constant: 1183.3 N/m• chamber dimensions (in cm):

6.00 x 5.0 x 0.625 at BDC1.70 x 5.0 x 0.625 at TDC_______

combustion chambers.

Spark

Permanent magnet-array-based generator

Fig. 1 The dual-combustor micro-engine withmagnetic array.

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(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

OOTTLOH PORTS

Fig. 2 Schematic of a dual-combust or model usedfor LES.

a a Experimental dataD ——— Adiabatic (3D)

d ———Adiabatic (2D)——— With heat transfer (3D)——— With heat transfer (2D)

0.0

,*.

ta) Design- 1

A1

*

J^

* ,1 t

* t td) Design-3

1

0««i0n-4

b) Design-2t f

e) Design-4

Fig. 3 Schematics of the different dual-combustordesigns used for LES

ignition

0.952 2.690.625

Fig. 4 Schematic of the single-combust or design.The second combustor is replaced by a spring inthis design.All dimensions are in cm.

Fig. 5 Effect of heat transfer on the peak pressurereached in a constant volume combustor.

J.OOO 0.001 0.001 0.002 0.002 0.003 0.003time

Fig. 6 Variation of reactant concentration in thecombustion chamber with injection for the variousdesigns. Clearly, Designs 1 and 2 fail to reach suf-ficient concentration level before ignition and thus,fails.

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RIGHT COMBUSTORo.oio o.oeo o.oao

time (nor)0.040

a) Design-1 a) Two-Dimensional Simulation

b) Design-4

Fig. 7 Velocity vector field for designs 1 and 4.Trapped burnt products (marked by letter B) fromthe previous cycle in Design-1 limits the magnitudeof the reactant (marked by letter R) concentrationreached at end of the injection period.

RIGHT COMBUSTOR0.04ft

b) Three-Dimensional Simulations

Fig. 8 Pressure oscillations in Design-4. Bothcombustors achieve identical oscillation amplitudeand frequency and there are many similarities be-tween the 2D and 3D results.

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I(0

1400

1200

1000

800

600

400

200

00.02 0.04 0.06

Time(sec)

a) Experiment

0.08 0.1

£3

900800700600500400300200100

6 8 10 12 14 16 18 20 22Volume(cc)

a) Experiment

0.02 0.03 0.04 0.05 0.06 0.07 0.08Time(sec)

b) Numerical

Fig. 9 Experimental and numerical results forpressure oscillation and piston stroke motion insingle-combustor device.

thethe

900800700

-3 600Q_

f 500

| 400

a! 300200

100

0

k=2081 N/mk=2381 N/m

2 4 6 8 10 12 14 16 18 20 22Volume(cc)

b) Numerical

Fig. 10 Experimental and numerical results for thepressure-volume variation in the single-combustordevice.

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a) Subgrid kinetic energy

I286.016

0.000

b) Temperature

c) Subgrid kinetic energy(spanwise)

a) Subgrid kinetic energy

1227.632

0.000

b) Temperature

c) Subgrid kinetic energy(spanwise)

2473.800

300.000

d) Temperature(spanwise)

I892.875

300.000

d) Temperature(spanwise)

Fig. 11 Subgrid kinetic energy and temperature Fig. 12 Subgrid kinetic energy and temperaturecontours at ignition. contours at injection.

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