A Model of a Marine Two-Stroke Diesel Engine with EGR for Low Load Simulation

Transcription

1 A Moel of a Marine Two-Stroke Diesel Engine with EGR for Low Loa Simulation Xavier Llamas Vehicular Systems Dept. of Electrical Engineering Linköping University, Sween xavier.llamas.comellas@liu.se Lars Eriksson Vehicular Systems Dept. of Electrical Engineering Linköping University, Sween lars.eriksson@liu.se Abstract A mean value engine moel of a two-stroke marine iesel engine with EGR that is capable of simulating uring low loa operation is evelope. In orer to be able to perform low loa simulations, a compressor moel capable of low spee extrapolation is also investigate an parameterize for two ifferent compressors. Moreover, a parameterization proceure to get goo parameters for both stationary an ynamic simulations is escribe an applie. The moel is valiate for two engine layouts of the same test engine but with ifferent turbocharger units. The simulation results show a goo agreement with the ifferent measure signals, incluing the oxygen content in the scavenging manifol. I. INTRODUCTION The marine shipping inustry is facing increase emans in the reuction of harmful exhaust gas emissions. Stricter emission limits of Sulphur Oxies (SOx) an Nitrogen Oxies (NOx) are impose in certain Emission Control Areas (ECAs). The emission values to fulfill in these ECAs are set by the IMO Tier III limits [] that came into play in January 6. One of the available technical solutions to achieve the targete reuction in NOx emissions is Exhaust Gas Recirculation (EGR). An EGR system recirculates a fraction of the exhaust gas into the scavenging manifol, proviing burne gases in the combustion chamber that irectly ecreases the prouction of NOx uring the combustion. EGR technologies for two-stroke engines are still at the initial phases of its evelopment. In aition, there are not many available vessels with an EGR system installe an thus performing tests is often ifficult. Furthermore, testing any new system in marine two-stroke engines is also very costly mainly ue to the fuel cost associate with the sizes of such engines. Hence, in orer to improve the performance of the EGR control systems, a fast an accurate simulation moel is a very valuable tool. Mean Value Engine Moels (MVEMs), are a very common approach for control oriente moeling of internal combustion engines. In particular, EGR systems have been also moele using this approach. Many interesting research articles about EGR moeling in automotive applications can be foun in the literature, some examples are, [] an []. On the other han, marine two-stroke engines have not been wiely stuie. Nevertheless, some research papers focuse on MVEMs for two-stroke engines are [4], [5] an [6]. In aition, in [7] the moeling of the low loa operation of a two-stroke engine without EGR is stuie. The work presente here is an extension of the moel propose in [8], which enables the moel to simulate low engine loas. The low loa operation is very relevant for the EGR control since the Tier III emission limits have to be fulfille near certain coasts, e.g. harbors, where the vessel is normally operating at low loas. The main new component that nees to be introuce for this low loa simulation is the auxiliary electrical blower. Its mission is to ensure that there is enough scavenging pressure at low loas when the turbocharger is not capable to provie it. Moreover, the turbocharger moel will be require to simulate at low spees an pressure ratios. This area is normally not measure in the provie performance maps, so a moel that can extrapolate to this area is also require. The evelope moel is, as in [8], base on the 4T5ME- X test engine from MAN Diesel & Turbo. The 4T5ME-X is a two-stroke uniflow iesel engine, turbocharge, with variable valve timing an irect injection. Its maximum rate power is 78 kw at rpm. Also, it is equippe with an EGR system an a Cyliner Bypass Valve (CBV). II. EXPERIMENTAL DATA The targete test engine is constantly being rebuilt to test new components an new control strategies. This implies that it is ifficult to fin measurement ata from the same engine configuration. Most of the measurement ata available is from the same layout as the ata use in [8]. For layout number the oxygen sensors were not properly calibrate an thus cannot be use for valiating the oxygen levels at the manifols. For the moel parameterization ifferent stationary points are extracte from the measurement ata. another 4 stationary points are save for the valiation. Some more ata is available from another layout of the engine an will be use for valiation of the oxygen level in the scavenging manifol. However, in this layout, number, the turbocharger was change an some sensors where remove. Moreover, there is much less ata available, an only 8 stationary points coul be extracte for the parameterization an the valiation of the moel.

2 W leak, blow, Tscav W leak, blow, W cyl Exhaust Manifol p exh Cyliners X exh inj t inj EVO eng Turbine W t tc u cbv p t,out W t,out ifferent submoels interconnecte. The submoels are mainly control volumes, e.g. scavenging manifol, an flow elements e.g. cyliner bypass valve, compressor, turbine, etc. Since the moel is an extension of the one escribe in [8], only the new or moifie submoels are presente here. u cov, u cov, W egr p scav W el X scav Scavenging Manifol u aux Tscav W cool p c,out W cbv W c Compressor Fig.. Engine moel iagram with states (blue) an control inputs (re). III. MODELING The complete MVEM moel consists of thirteen states an nine control inputs. Figure epicts a moel iagram. The states are compressor outlet pressure, p c,out, scavenging manifol pressure, p scav, exhaust manifol pressure, p exh, turbine outlet pressure, p t,out an turbocharger spee, ω tc. The chemical species mass fractions are states in the scavenging an the exhaust manifols, X scav an X exh. The species inclue in the moel are oxygen, carbon ioxie, water an sulfur ioxie, X = [X O, X CO, X HO, X SO ]. The ynamic equations are the same for each species so (6) an (7) correspon to eight single ODEs. The ynamic behavior of the moele states is governe by the following ifferential equations t ω tc = P t P c J t ω tc () t p c,out = R a T c,out (W c W cool W cbv ) V c,out () t p scav = R at scav (W cool + W egr W el ) V scav () t p exh = R e T exh (W cyl W egr W t + W cbv ) V exh (4) t p t,out = R e T t,out (W t W t,out ) V t,out (5) t X scav = R at scav (X exh X scav ) W egr p scav V scav t X exh pc,in Tc,in + R at scav p scav V scav (X amb X scav ) W cool (6) = R et exh p exh V exh (X cyl X exh ) W cyl (7) The control inputs are EGR blower spees, ω blow, ω blow,, blower cut-out valves (COV) position, u cov, u cov,, fuel injection angle α inj, fuel injection time, t inj, exhaust valve closing angle, α EV C, CBV position, u cbv, an auxiliary blower operation u aux. Engine spee, ω eng, an compressor inlet pressure an temperature, p c,in T c,in, are consiere known inputs to the moel. It is simple to reuce the moel to seven states if we are only intereste in tracking the oxygen level in the manifols. Then in (6) an (7), the mass fraction only refers to oxygen, e.g. X = X O. The moel is built using A. Compressor In orer to properly simulate low loas, a compressor moel capable of preicting mass flow an efficiency at low spees is require. The chosen compressor mass flow moel is the one evelope in [9], which is capable of this extrapolation. In aition, the propose moel is capable of preicting mass flows own to pressure ratios below one an to zero compressor spee. The area where the compressor normally operates uring low loa is below the slowest measure spee line, which is epicte in Figures an. In the moel, each compressor spee line is escribe by a super ellipse, which mathematically is written as ( Wc W ) CUR ( ) CUR ZS Πc Π Ch W Ch W + = (8) ZS Π ZS Π Ch where W ZS, WCh, Π ZS, Π Ch an CUR are functions of compressor spee. More etails about these functions an the moel in general can be foun in [9]. Since (8) is invertible, it can be use to preict either pressure ratio given compressor spee an mass flow or mass flow given compressor spee an pressure ratio. The latter case is use in the propose engine moel. The compressor efficiency is moele using the ieas from [] for the isentropic efficiency efinition. The key for the moel is to use the Euler s equation [] applie to the compressor velocity triangles. Using the simplifications from [], the conclusion is that the actual enthalpy rise for a fixe compressor spee can be moele as a linear function of the mass flow. This simplifies the number of parameters require an since it is base in the physical equations, makes the extrapolation to the low loa area more reliable. The propose compressor moel requires 5 parameters for the mass flow submoel an 4 parameters for the efficiency submoel. The mass flow moel together with the efficiency moel fitte to the two compressors use in this stuy is epicte in Figures an. The absolute value of the relative errors for both compressors are shown in Table I. B. Turbine The Turbine mass flow moel is very similar to the one use in [8]. However, a moification in the moel is require to escribe the turbine spee epenence observe for Turbine. The mass flow is escribe by the following function from [] W t = C t (Π t + Π ) kt (9) where k t, Π an C t are constant parameters to be estimate for Turbine. For Turbine, k t an C t are also constants but Π is moele using a quaratic polynomial

3 Low loa operation Wt ηt Πc Π t BSR W c Fig.. Compressor moel, in black, plotte together with the measure map points, in blue ots. The first spee line in the lower left corner represents the stan still characteristics of the compressor. The thinner level lines represent the moele efficiency extrapolation own to unity pressure ratio. Fig. 4. Left: turbine mass flow moel, in re, plotte together with the measure map points, in blue ots. Right: turbine efficiency moel, in re, plotte with the measure efficiency points, in blue ots. Low loa operation Πc Wt ηt Π t BSR Fig. 5. Left: turbine mass flow moel, in re, plotte together with the measure map points, in blue ots. Right: turbine efficiency moel, in re, plotte with the measure efficiency points, in blue ots. W c Fig.. Compressor moel, in black, plotte together with the measure map points, in blue ots. The first spee line in the lower left corner represents the stan still characteristics of the compressor. The thinner level lines represent the moele efficiency extrapolation own to unity pressure ratio. TABLE I ABSOLUTE VALUE OF THE RELATIVE ERRORS (%) FOR BOTH COMPRESSORS AND TURBINES. MEAN INDICATES THE MEAN VALUE OF ALL ERRORS WHILE MAX. IS THE MAXIMUM ERROR COMPUTED. Compressor Compressor Mean Max. Mean Max. W c η c Turbine Turbine Mean Max. Mean Max. W t η t of correcte turbine spee to capture the ifferent spee lines observe in Figure 5. The quaratic polynomial is efine as Π = c Π, N t + c Π, N t + c Π, () where c Π,, c Π, an c Π, are moel parameters. The two moels fitte to the two turbines are shown on the left sie of Figures 4 an 5. The turbine efficiency is moele using the Blae Spee Ratio (BSR), as in [] an [8]. The relation between turbine efficiency an BSR is efine as Π = c BSR + c BSR + c () where c, c an c are also quaratic functions of turbine correcte spee, an each polynomial is efine as follows c X = c X, N t + c X, Nt + c X, () In total the turbine efficiency consists of nine parameters. The moele an the measure efficiencies for both turbines are epicte in Figures 4 an 5. Furthermore, for both turbines, the absolute value of the relative errors are presente in Table I.

4 C. EGR Blowers The EGR blowers are moele exactly as in [8]. The only ifference here is that there are two equal blowers in parallel. The EGR flow is controlle with the blower spee control inputs, ω blow, an ω blow,, an the cut-out valves are use to open or close the EGR flow. Depening on the engine running moe, there can be only one blower operating or both of them if more EGR flow is require. D. Auxiliary Blower The pressure increase of an electric blower is often moele as a quaratic function of the volumetric flow [7]. Since the blower s pressure increase is available from the system states, the quaratic function is inverte to obtain the volumetric flow. Using the pressure an temperature at the inlet the mass flow provie by the blower is obtaine W Aux = pc,out(caux, + caux, caux, (p scav p c,out)) R at c,out () where c Aux,, c Aux, an c Aux, are tuning parameters estimate with the blower technical specifications. For the stuie test engine, the auxiliary blower is installe in parallel with the air cooler after the compressor. This means that when operating it will pull air mass flow from the compressor outlet control volume to the scavenging manifol. When active, the pressure ifference between these two control volumes will reverse. When the auxiliary blower is operate (since there is no restriction valve for reverse flow in the cooler), there is flow recirculation in the air cooler. This issue nees to be moele in orer to capture the measure system behavior. Thus, the flow from the compressor outlet to the scavenging manifol is then moele using () an two incompressible flow restrictions from [] W Aux A cool,r W cool = A cool p scav(p scav p c,out) T scav if u aux = p c,out(p c,out p scav) T c,out if u aux = (4) where A cool represents the flow restriction when the blower is inactive an A cool,r moels the magnitue of the recirculation when the blower is running. Both are parameters to be estimate. E. Exhaust Back Pressure An incompressible flow restriction together with a control volume is use to moel the back pressure for the turbine, p t,out. The pressure ynamics are escribe by (5). An the exhaust flow W t,out is moele using the stanar incompressible flow restriction from [] where the restriction area is a tuning parameter. F. Fuel Mass Flow In [8] the fuel mass flow is consiere an input. Here a fuel mass flow moel is use instea, using injection time, engine spee an hyraulic fuel pressure as inputs. The hyraulic fuel pressure is regulate by the control system epening on the engine loa an running moe. For the simulation results presente in Section V, it is consiere a known signal. The moel is inspire by the ones escribe in [], an it is efine as follows W f = c f ω eng phy (t inj t f, ) (5) where c f an t f, are tuning parameters. G. Combustion Species an Thermoynamic Parameters The species mass fraction out of the cyliners, X cyl, are calculate using the stoichiometric combustion equation an the air an fuel flows entering the cyliners. Without incluing the nitrogen explicitly, the combustion equation can be written CH ys z + ( + y/4 + z)o = CO + (y/)h O + zso (6) where y is the hyrogen to carbon ratio an z the amount of sulfur in the fuel, which are known parameters. In the case of the reuce moel with only oxygen mass fraction, X cyl can be compute as in [8] an []. Furthermore, the species vector is use to compute the thermoynamic parameters, R, c p an γ of the working gas. This is one for each ifferent gas composition an compute together with the gas temperature using the Nasa polynomials that can be foun in []. IV. PARAMETERIZATION PROCEDURE The parameterization is one in similar steps as it is escribe in [8]. First the following submoels are parameterize alone: compressor, turbine, ERG blowers, Aux blower an fuel mass flow. These submoel parameters are kept fixe in the following parameterization steps. A. Complete stationary parameterization The path to follow woul be to estimate the ifferent flow restrictions of the moel inepenently an then o a complete parameterization of the whole moel together. However, this is not possible since there is no mass flow measurement available. Hence, the next step in the parameterization is to use the complete moel to get the best set of parameters that preict the measure states. The metho followe here iffers from the one use previously in [8] where the erivatives of the states are use in the parameterization. Here instea the whole moel is simulate at each stationary point an the simulate stationary states are use to compute the relative errors, e rel. In the en, a least-squares problem is formulate with objective function efine as V stat (θ) = NS S i= n= N (e i rel[n]) (7) where S is the number of ifferent measure signals use to compute the relative errors, in the general case those signals are: [p scav, p exh, p c,out, p t,out, ω tc, T exh, P eng, W egr ]. N is the number of stationary points use. The vector θ represents the parameters to be estimate, which in this case are

5 TABLE II ABSOLUTE VALUE OF THE MODEL RELATIVE ERRORS (%) FOR BOTH ENGINE LAYOUTS. LOW LOAD IS WITH AUX. BLOWER ACTIVE, MID LOAD IS BELOW 7 % AND HIGH LOAD IS ABOVE 7 % pscav [Pa] x 5 4 Meas Mo pexh [Pa] 4 x 5 Engine Layout p scav p exh p c,out p t,out ω tc T exh P eng,i W egr Low Loa Mi Loa High Loa Engine Layout p scav p exh p c,out p t,out ω tc T exh X O - Low Loa Mi Loa High Loa all the static parameters, except of the fixe parameters of the submoels state in the beginning of Section IV. The stationary simulations are one using a Matlab/Simulink implementation of the moel. To reuce the computational time require, the Matlab parallel computing toolbox is use to run simultaneous simulations. Furthermore, a check on the state erivatives is one in orer to stop the simulation once the stationary levels are reache. Different estimation steps are one to ensure that the solver oes not get lost with too many parameters. The parameterization is starte without EGR, CBV or low loa stationary points which are progressively inclue in the successive steps. Also, the results from each parameterization step are use as initial guess for the following one. Finally, a complete parameterization with all stationary points available is one. B. Dynamic estimation Fixing the estimate parameters at the previous steps, the ynamic parameters, J t, V scav, V exh, V c,out, V t,out an τ cov, are tune using the same proceure as in [8]. In this case, 7 ifferent step responses are use, incluing tree loa steps with the auxiliary blowers active. V. MODEL VALIDATION Table II presents the absolute value of the relative errors separate for ifferent loa ranges. For Layout, the 4 valiation stationary points are use. For Layout, since there is few ata available, the errors are compute with the same stationary points use in the estimation. For both Layouts, the higher pressure errors are mostly in the high loa case, where also the exhaust temperature an inicate engine power errors are higher. This inicates that the moel an in particular the Seiliger cycle coul be improve in this area. One reason for this coul be that at high loa is where the engine protection controls limit the maximum pressure in the cyliners, an this might not be totally capture in the moel. On the other han, for the mi an low loa ranges the errors are in general of similar magnitue. Note that for the Layout, the engine power an the EGR mass flow measurements are not available. ωtc [ra/s] Peng,i [kw] Texh [K] ωblow [ra/s] ω blow, ω blow, pc,out [Pa] ωeng [ra/s] Valves [-] Wegr [kg/s] x 5 COV CBV AUX Fig. 6. Moel simulation vs measurements for Engine Layout. Figure 6 shows the simulation results of Layout compare to the measurements of a ataset not use in the estimation. This simulation has a low loa phase where the auxiliary blower is enable, where it can be seen that the system behavior is capture by the moel. In particular the measure pressure an turbocharger spee values are matche by the moel. More iscrepancy is observe in the moele exhaust temperature uring the transients. For Layout, the simulation results are presente in Figure 7. There is also a low loa operation that the moel is capable to capture. In this case the turbocharger spee preiction is worse than for the Layout which in turn affects the stationary levels of the pressures. Nevertheless, it is important to mention that it has been parameterize with few ata. Oxygen mass fraction valiation coul not be one ue to unreliable measurements for Layout an in the previous investigations from [8]. Therefore, the most relevant result from Layout is that the scavenging oxygen level is capture as it can be seen in Table II an in Figure 7. VI. CONCLUSIONS An MVEM for a marine two-stroke iesel engine capable of simulating low loas is propose an valiate. A parameterization metho to overcome the lack of mass flow measurements is also propose. The main characteristic is that it uses a Simulink moel to integrate the moele states with stationary inputs an is use to compute the resiuals. Two ifferent layouts of the same engine but with ifferent turbochargers are investigate, the results show a goo agreement between simulation results an measurements with some room for improvement at high loas. The oxygen preiction capabilities are also valiate for the secon engine layout since the oxygen measurements are reliable.

6 Peng,i [kw] ωtc [ra/s] Texh [K] ωblow [ra/s] pscav [Pa] x 5 Meas Mo pexh [Pa] pc,out [Pa] XO,scav [%] ωeng [ra/s] Valves [-] 4 x 5 4 x COV CBV AUX TABLE IV LIST OF SYMBOLS A Area [m ] c p Specific heat at constant pressure [J/(kgK)] J Inertia [kg m ] W Mass flow [kg/s] W Correcte mass flow [kg/s] p Pressure [P a] P Power [kw ] R Gas constant [J/(kgK)] T Temperature [K] V Volume [m ] X Mass fraction [ ] α angle [ra] γ Specific heat capacity ratio [ ] η Efficiency [ ] Π Pressure ratio [ ] N Correcte rotational spee [rpm] ω Rotational spee [ra/s] Fig. 7. Moel simulation vs measurements of for Engine Layout. ACKNOWLEDGMENT This project has receive funing from the European Union s Horizon research an innovation programme uner grant agreement No 645. MAN Diesel & Turbo an in particular Guillem Alegret are also acknowlege for their support an suggestions about the moele test engine. APPENDIX TABLE III SUBSCRIPTS cov cut-out valve inj injection blow blower meas measure c compressor mo moele scav scavenging manifol cool cooler cyl cyliner t turbine el elivere eng engine e exhaust gas a air tc turbocharger x, in inlet of x aux auxiliary blower x, out outlet of x exh exhaust manifol egr EGR gas [4] M. Blanke an J. A. Anerson, On moelling large two stroke iesel engines: new results from ientification, IFAC Proceeings Series, pp. 5, 985. [5] G. Theotokatos, On the cycle mean value moelling of a large two-stroke marine iesel engine, Proceeings of the Institution of Mechanical Engineers, Part M: Journal of engineering for the maritime environment, vol. 4, no., pp. 9 6,. [6] J. M. Hansen, C.-G. Zaner, N. Peersen, M. Blanke, an M. Vejlgaar-Laursen, Moelling for control of exhaust gas recirculation on large iesel engines, Proceeings of the 9th IFAC conference on Control Applications in Marine Systems,. [7] C. Guan, G. Theotokatos, P. Zhou, an H. Chen, Computational investigation of a large containership propulsion engine operation at slow steaming conitions, Applie Energy, vol., pp. 7 8, 4. [8] G. Alegret, X. Llamas, M. Vejlgaar-Laursen, an L. Eriksson, Moeling of a large marine two-stroke iesel engine with cyliner bypass valve an EGR system, IFAC-PapersOnLine, vol. 48, no. 6, pp. 7 78, 5, th IFAC Conference on Manoeuvring an Control of Marine Craft MCMC. [9] O. Leufvén an L. Eriksson, Measurement, analysis an moeling of centrifugal compressor flow for low pressure ratios, Int. J. Engine Res., pp. 6, December 4. [] G. Martin, V. Talon, P. Higelin, A. Charlet, an C. Caillol, Implementing turbomachinery physics into ata map-base turbocharger moels, SAE Int. J. of Engines, vol., no., pp. 9, April 9. [] S. L. Dixon an C. A. Hall, Flui Mechanics an Thermoynamics of Turbomachinery, 7th e. Butterworth-Heinemann,. [] L. Eriksson an L. Nielsen, Moeling an Control of Engines an Drivelines. John Wiley & Sons, 4. [] D. G. Goowin, H. K. Moffat, an R. L. Speth, Cantera: An objectoriente software toolkit for chemical kinetics, thermoynamics, an transport processes, 4, version... REFERENCES [] International Maritime Organization, MARPOL: Annex VI an NTC 8 with Guielines for Implementation. IMO,. [] J. Wahlström an L. Eriksson, Moelling iesel engines with a variable-geometry turbocharger an exhaust gas recirculation by optimization of moel parameters for capturing non-linear system ynamics, Proceeings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 5, pp ,. [] M. Nieuwstat, I. Kolmanovsky, P. Moraal, A. Stefanopoulou, an M. Jankovic, EGR-VGT control schemes: experimental comparison for a high-spee iesel engine, IEEE Control Systems Mag., vol., no., pp. 6 79,.