Combustion Testing and Analysis of an Extreme States Approach to Low-Irreversibility Engines

Final Report Investigators Chris F. Edwards, Professor, Mechanical Engineering; Matthew N. Svrcek, Greg Roberts, Sankaran Ramakrishnan, Graduate Researchers, Stanford University Abstract This work explores the use of high-energy-density (extreme) states to improve the efficiency of internal combustion engines for both stationary power and transportation. The basic premise—that a fraction of the work lost due to combustion may be recovered by reaction at extreme states—was developed under a previous GCEP program. In this program that principle has been used to demonstrate how high efficiency can be achieved in piston engines, and its implications for optimal design of stationary power engines. Introduction In the prior years of the program, a free-piston, extreme-compression engine capable of combustion at compression ratios up to 100:1 was developed. This was used to successfully demonstrate that indicated efficiencies in excess of 60% (LHV) could be achieved. Follow-on work involved development of the methods needed to make direct measurements of combustion efficiency, emissions, and soot under these conditions. In the final year of the project, a new combustion approach based on use of an autoigniting, homogeneous mixture was developed. The details of that development are given below. Also in prior years, a methodology for developing the optimal design of an energy system was investigated. It was this work that first lead to definition of the extreme states principle by The (2007), and realization of the importance of separating reactive engines by classification—restrained or unrestrained—by Miller (2009). Follow on work extended the approach originally developed by Teh to steady flow engines (from batch), and showed that the key element in the analysis was manipulation of the equilibrium attractor state of the system. In the final year of the project, that methodology has been completed and a robust method now exists for determining the optimal architecture of steady flow engines with work, heat, and matter regeneration. Example calculations show that engines with exergy efficiencies approaching 70% are possible using optimal, regenerative cycles. Experimental Effort The previous Diesel-style emission results showed that a primary obstacle to using a Diesel-style combustion approach at extreme compression ratio is NOx emissions.

Combustion efficiency and the other pollutant species were all within current emissions regulations, even at 100:1 CR and reasonable load. Handling the NOx is complicated, however, by the overall lean equivalence ratio, and hence excess oxygen in the exhaust stream. Aftertreatment systems for NOx exist for this scenario, primarily selective catalytic reduction (SCR). However, these systems are currently expensive—in some cases comparable to the cost of the engine itself—and require maintenance such as refill of a urea tank. Currently, the least expensive and most well-developed method of reducing NOx is the three-way catalyst commonly employed with automotive spark-ignited engines. A defining characteristic of the three-way catalyst is that the engine must be operated in the vicinity of stoichiometric equivalence ratio. This provides incentive for achieving stoichiometric operation of the extreme compression engine. Rather than approaching stoichiometric equivalence ratio from the Diesel-style branch, the work described here investigates the feasibility of premixed combustion at extreme compression ratios. Premixed combustion has the advantage of intimate contact between fuel and oxidizer, resulting in low soot emissions at stoichiometric equivalence ratio. The difficulty in this case lies in achieving proper combustion phasing, with ignition occurring near the minimum volume in the cycle. Given that the compression ratios of interest here are, in all cases, much higher than conventional premixed-charge engines, the problem becomes one of delaying autoignition until the minimum volume is reached. Delaying autoignition is accomplished by keeping the reaction rate low until the desired time, by controlling the temperature of the gas. In this section three methods for controlling gas temperature are explored from a theoretical basis. The efficacy of each technique is discussed, as well as the implications of these methods for the overall engine efficiency. Results from an experimental investigation of two of these methods of temperature-controlled autoignition are reported and discussed. These experiments consist of compression, combustion, and expansion of a premixed, methane-air charge in the extreme compression device, using the temperature-control techniques to achieve ignition phasing at the minimum volume. Methane was chosen as a fuel due to its inherent autoignition resistance. To explore the theoretical basis for temperature-control of autoignition timing, modeling of the compression, combustion, and expansion process was performed. This model assumes a chemically and thermally homogeneous ideal gas mixture, but includes the effects of variable specific heats as well as chemical reaction kinetics from the GRI 3.0 mechanism for methane. Compression and expansion profiles as a function of time are taken from experiments in the extreme compression device. Note that the GRI 3.0 mechanism is not expected to provide a high degree of accuracy at the pressures obtained here, but it serves effectively to illustrate the basic principles of this combustion process. A simple way to adjust the gas temperature, and hence the onset of autoignition, is to start the compression at a lower temperature. The model results of this are shown in Fig. 1. The compression metric of interest in this case is the ratio of gas density during

compression to the density at ambient conditions. This corresponds to the effective compression ratio, whereas the volume ratio corresponds to the geometric compression ratio. In the earlier Diesel-style combustion studies, the effective and geometric compression ratios were identical. In this case, because the charge starts at a lower temperature and hence higher density, they are not the same and the effective compression ratio should be used as the compression metric. An interesting result from this model is that a drop in starting temperature of only 50 K is sufficient to achieve ignition at 100:1 effective compression ratio. This is partly due to the nature of isentropic compression—the 50 K decrease in starting temperature results in a decrease of nearly 200 K by the time the density ratio reaches 50:1. This, combined with the fact that temperature has such a direct effect on the ignition process, gives the starting temperature significant leverage on the autoignition process.

Figure 1. Temperature as a function of gas density, for compression of stoichiometric methane-air starting at atmospheric pressure and two different temperatures. Heat-Exchange Cooling One way to start compression at a lower temperature is to perform direct heat exchange with the reactant charge. To help understand this method, the left plot of Fig. 2 shows the same compression models from Fig. 1, but magnified near atmospheric conditions. One process for direct heat exchange is to cool the reactant stream prior to induction into the engine. This is shown by moving from State 1 to State 2 at constant pressure, assuming a homogeneous, stoichiometric mixture of methane and air. After reaching State 2, the process follows the normal compression in the engine. Practically speaking this could be

accomplished by a refrigeration cycle, an example of which is shown in the right part of Fig. 2. In this example a refrigerant fluid is compressed, cooled to environmental temperature, and expanded across a Joule-Thompson valve, reaching the temperature of its boiling point. Heat exchange is then performed between the refrigerant and the incoming reactant charge. Given that the charge only needs to be cooled to ~ 250 K, this can be accomplished with existing technology and refrigerants. For example, ammonia, a common refrigerant, has an atmospheric pressure boiling point of 239 K.

Figure 2. Left - Temperature as a function of density, with refrigeration cooling process indicated. Right - Example refrigeration schematic. Corresponding thermodynamic states are labeled on the plot and diagram.

Figure 3. Left - Temperature as a function of density, with intercooling process indicated. Right - Example intercooling schematic. Corresponding thermodynamic states are labeled on the plot and diagram. A second heat exchange cooling method is available. It is important to understand that as far as the autoignition process is concerned, it only matters that the gas compression follows the correct isentrope. Once the final compression isentrope is reached, the

remaining cycle is identical, regardless of where the cycle is initiated on the isentrope. The cooling process shown in Fig. 3 takes advantage of this to avoid sub-atmospheric temperatures. From the starting State 1, the charge is compressed on the room-temperature isentrope to State 2, then cooled via constant-pressure heat-exchange with the environment to State 3. State 3 lies on the same isentrope as the post-refrigeration state discussed above. This process is simply compression with intercooling, as shown on the right of the figure. In the context of engines, this is commonly done when using a turbocharger. In that instance, exhaust enthalpy drives a turbine which shares a common shaft with the compressor. The output of the compressor is then cooled to near atmospheric temperature in the intercooler via heat exchange with the environment. The points shown in Fig. 3 assume a post-intercooler temperature of 310 K, resulting in a post-compressor pressure of 2.2 bar. This is well within the range of existing, off-the-shelf turbochargers. The efficiency implications of using these methods of autoignition control are discussed below, after the evaporative cooling method is introduced. Evaporative Cooling A third method for lowering the gas temperature and delaying autoignition is to evaporate a liquid in the gas. As the liquid evaporates, sensible energy is extracted from the gas phase to supply the latent heat of vaporization, thus lowering the gas temperature. Water is a good choice because it has a high latent heat of vaporization and a boiling point in the desired temperature range. It is also a product of combustion, and thus does not complicate the existing combustion and emissions measurement systems. As was seen for the direct heat exchange methods, the nature of isentropic compression makes it desirable to lower the gas temperature as early as possible in the compression process in order to exert maximum leverage on the final temperature. Ideally, evaporating water in the gas immediately prior to the start of compression would lower the gas temperature as early as possible, while preventing time for significant heat transfer from the walls. However, the evaporation rate can be limited by saturation of the gas. Vaporization may have to occur some time during the compression stroke after the gas temperature has begun to rise. In that case, a straightforward method for introducing water into the gas during compression is to use existing fuel injection technology. The injection timing should be set as early as possible, while avoiding gas saturation. Chemical kinetic modeling of a homogeneous methane-air charge was again performed, following the same experimental volume-time profile used previously. In this case, vaporization of water was included in the model. Vaporization is assumed to occur homogeneously at a constant rate. The modeled vaporization rate is equal to the experimental rate of water injection in the water vaporization experiments reported later. The vaporization process is modeled as adiabatic mixing of the in-cylinder gas and liquid water. Water in the gas phase mixture is modeled as an ideal gas. The start of injection was chosen to ensure that the gas remains unsaturated. In this example, water evaporation begins when the gas temperature first reaches 400 K.

Figure 4. Pressure as a function of volume for homogeneous, stoichiometric methane-air, with and without water vaporization. The model results are shown in Fig. 4, compared with the earlier model results for methane-air with no water evaporation. Two features are apparent: first, the water injection successfully delays autoignition until 100:1 compression ratio is achieved. Second, the evaporative cooling can be seen in the plot as the compression line drops below the normal isentrope. Once the vaporization is completed, the compression again follows an isentrope. An important result of this exercise is that the total mass fraction of water injected is only 3% of the total charge. This is a relatively small amount—less than one-fifth the water produced from combustion—and easily achieved with existing injection technology and reasonable injection times. This model result indicates that water injection is promising as a control for autoignition. Efficiency Implications A critical factor in evaluating the above strategies for controlling autoignition is their effect on the cycle efficiency. A dramatic decrease in efficiency as a result of these methods would defeat the purpose of achieving high compression ratios. As discussed in our previous work, exergy destruction during reaction is minimized by performing the chemical reaction at the highest possible internal energy state. The cooling methods for autoignition control run counter to this, in that they function by reducing the gas temperature, and hence internal energy. However, the increased exergy destruction during reaction is offset by decreased exergy remaining in the exhaust. For simple-cycle engines, this exhaust exergy is also destroyed. The reduction in exhaust

exergy is of similar magnitude to the increased destruction during reaction, and thus the net exergy destruction is not significantly affected by these cooling strategies. Efficiency losses due to driving the cooling process itself must also be considered. The refrigeration and intercooling approaches require work to drive a compressor. The water vaporization method uses sensible energy from the gas to drive evaporation. Because the water does not recondense during the expansion, this sensible energy is not returned to the gas and the net work output is reduced. For the refrigeration and intercooling methods, exhaust enthalpy can be used to provide the required compressor work. Turbocharged, intercooled systems, in which a turbine in the exhaust flow provides the compressor work, are commonplace in conventional engines. Exhaust enthalpy could also be used in this way to drive the refrigeration method, although the practical implementation would be more complex. To provide more concrete examples, the efficiency was calculated for two of the model methane-air cases shown earlier—the intercooling approach (Fig. 3), and the water injection approach (Fig. 4). The computed efficiencies are shown in Table 1. They are compared to a model cycle with no cooling strategy, in which ignition is artificially delayed until the minimum volume by setting the reaction rate to zero in the model. The efficiencies are calculated using the same chemical kinetics, compression-expansion model described earlier, including the model of evaporation for the last two cases. For the second intercooling case, work is supplied from an external source to a compressor with 0.8 polytropic efficiency. Table 1. Calculated first-law efficiencies with different cooling strategies. In all cases, the effective compression ratio is 100:1, the charge is homogeneous, stoichiometric methane-air, and ignition occurs at the minimum volume.

Without use of exhaust enthalpy to drive the cooling process, and with a non-ideal compressor, the intercooling strategy decreases the overall efficiency by ~3%. If exhaust enthalpy is used to drive the compressor, the overall efficiency slightly increases. This is possible because the exergy reduction in the exhaust is greater than the increase in exergy destruction during reaction. The water injection strategy with the earlier injection timing also slightly improves the efficiency, for the same reason. As the water injection is moved later the efficiency is reduced, for two reasons. First, cooling the gas later in the

compression requires more total water injection to achieve the same drop in final gas temperature. Second, the gas pressure decreases below the isentropic value due to the evaporative cooling. If this happens late in the compression stroke, then additional compression work is required. The above results show that these cooling strategies do not significantly affect the efficiency, at least in the theoretical model cases. This, combined with the indications of efficacy of control discussed in the previous sections, provides motivation for experimental exploration of these techniques. Experimental Setup for Premixed Autoignition Two significant additions to the extreme compression apparatus were made to enable experimentation with a premixed charge. First, a system was constructed for filling the cylinder with a homogeneous mixture of fuel and air of known stoichiometry. Second, modifications were necessary to handle the greatly increased thermal loads from stoichiometric premixed combustion—most importantly a thermal shield for the piezoelectric pressure transducer. These new systems are described below. Premixed Gas Delivery System For the experiments described below, a homogeneous mixture of gaseous methane and air was used. In order to ensure a completely homogeneous charge, the methane and air were mixed prior to entering the cylinder. Figure 5 illustrates the system used to accomplish this.

Figure 5. Schematic of the premixed methane-air delivery system. Methane is supplied from a gas cylinder, regulated to 150 psi. Compressed air is supplied at 120 psi through a filter and dryer. Each gas then passes through a pressure regulator and a precision orifice. The orifice diameters are fixed at 75 micron for the methane and 400 micron for the air. Flow control is achieved by adjusting the pressure upstream of each orifice, via the pressure regulators and high-precision pressure gauges. Downstream of the orifices, the methane and air are mixed. For all flow conditions, the

pressure difference across each orifice is sufficient to maintain choked flow. In this way the flow rates are unaffected by fluctuations in the downstream pressure during the cylinder fill process. The system was calibrated using two independent methods. First, a wet-test meter was used to calibrate the flow rate of each gas. Second, an evacuated tank, weighed on a scale before and after filling, was used to calibrate each gas on a mass basis. These calibrations were performed for a range of upstream pressures, and agreed with each other to within ± 1%. Repeatability between tests was also within ± 1% for each method. The resulting calibration was used to set the stoichiometry of the mixture in the combustion experiments. To fill the cylinder, the piston is moved to a position near the combustor end-wall as shown in Fig. 5. The gas flow is activated with both cylinder valves open. The mixture thus flows across the combustion chamber, scavenging any gas previously existing in the chamber. The two pressure regulators are adjusted with the flow in steady-state to ensure accurate upstream pressures. The vent valve is then closed, and the methane-air mixture pushes the piston to the top. The cylinder-fill valve is closed, and the vent valve is then opened as necessary to achieve the desired final cylinder pressure. Pressure Transducer Thermal Shield A piezoelectric pressure transducer is used for the main combustor pressure measurement. This type of transducer can be affected by thermal shock on the transducer face. Radiative and convective heat transfer causes thermal expansion of the diaphragm and housing. This can relax the pre-load on the piezoelectric element and cause a negative shift in the output. With the bare, unmodified sensor, the time for heat transfer to affect the signal is such that the negative bias occurs in the latter portion of the expansion stroke. This effect is noticeable in the experimental pressure-volume traces. Without a sufficient thermal barrier, the pressure-volume trace decreases significantly below the expected isentrope towards the end of expansion. An artificial decrease in the indicated work and efficiency occurs as a result. For the earlier Diesel-style combustion experiments, a simple vinyl protective layer on the transducer face, as recommended by the manufacturer, was sufficient. This delayed the thermal shock from reaching the diaphragm until after the experiment was completed. Due to the stratified nature of that combustion strategy, the high-temperature combustion regions were away from the transducer. In contrast, with premixed combustion the reaction and high temperatures occur throughout the entire chamber, including near the wall. This situation is further exacerbated by the extremely high pressure obtained here, which compresses the thermal boundary layer. The original vinyl protection was experimentally found to be insufficient for the premixed experiments. The vinyl itself combusted, and was largely consumed, allowing the thermal shock to reach the diaphragm. Silicone RTV survived slightly better, but was still unable to sufficiently delay the thermal shock. In engine applications a metal barrier with a number of small holes is sometimes used, although this has an impact on the

frequency response of the transducer. In the current application the very high pressures correspond to a very small quench distance and hence require very small hole diameters in the thermal barrier. This results in an unacceptable curtailing of the high frequency response of the sensor.

Figure 6. Schematic of the pressure transducer thermal shield. An outer Teflon (PTFE) layer was found to successfully survive the premixed combustion, due to the very high resistance of this material to oxidation. The required thickness of Teflon to sufficiently delay the thermal shock was 0.5 mm. Teflon of this thickness is overly stiff, and can affect the frequency response of the sensor. A vinyl inner layer immediately on the diaphragm face, with a thin outer layer of Teflon, was found to have the required combination of flexibility, resistance to thermal shock, and resistance to oxidation. A final difficulty arose with attempts to use adhesives to attach these thermal protection layers—the adhesive itself was oxidized and failed. Instead, a thin, stainless steel clamp ring was used to fix the thermal barrier to the transducer face. The resulting thermal protection setup is shown in Fig. 6. As will be seen in the experimental results presented below, the log(P)-log(V) plots follow the expected isentrope at the end of the expansion stroke, indicating that the thermal shock is successfully delayed until after expansion. Also, comparison of pressure versus time for experiments repeated with and without the thermal barrier demonstrated that the frequency response of the transducer is not impacted. Experimental Investigation of Intercooling-Controlled Premixed Autoignition A method was developed for investigating premixed combustion with the intercooling strategy in the extreme-compression apparatus. In the theoretical example for intercooling, the charge was compressed isentropically, then cooled at constant pressure, and then inducted into the engine where it is further compressed isentropically. The actual experimental process differs slightly from this. A comparison between the two is

made in Fig. 7. The theoretical intercooling process followed a path through States 1, 2, and 3, as shown earlier. The experimental process instead follows a path through States 1, 2a, and 3a, ending on the same isentrope as the theoretical process.

Figure 7. Comparison of experimental and theoretical intercooling processes. Both are for stoichiometric methane-air. The cylinder is first filled with premixed methane-air as described in the previous section. At the end of the fill process, the piston is located at the top of the cylinder and the gas has come to thermal equilibrium with the walls (355 K). The gas pressure is chosen such that the charge density matches the density at atmospheric pressure and the starting temperature of the target isentrope—250 K in this example. This matching of charge density is necessary to achieve the correct effective compression ratio. At the end of this fill process, the gas state is at State 2a in Fig. 7. With the cylinder fill valve closed, the piston is then moved part way down the cylinder by driver air, thus raising the pressure in the cylinder. During this process, heat transfer occurs such that the gas remains at the wall temperature. The final pressure, and hence piston position, is chosen such that the gas ends at State 3a on the target isentrope. The normal extreme compression experiment is triggered at this point. There are two key differences between the experimental process described above and the theoretical intercooler process. First, the post-intercooler temperature is 45 K higher in the experimental process because the gas temperature is constrained to reach the average cylinder wall temperature. Second, the experimental pre-intercooler compression process is not isentropic. These differences only matter in interpreting the overall cycle efficiency, as discussed in the next section. Experiments conducted using this method are as follows: A set of intercooling experiments was performed with effective compression ratio near 35:1, while varying

equivalence ratio from 0.96 to 1.04. A second set of experiments was performed near 60:1 effective compression ratio, again varying equivalence ratio from 0.96 to 1.04. Experiments were also conducted with 1.0 equivalence ratio at 78:1 and 89:1 effective compression ratio. For the majority of these experiments, the intercooling pressure was chosen to result in ignition phasing at or slightly after the minimum volume. For all of the intercooling experiments, the following data were collected or calculated: pressure, volume, indicated work, efficiency, gas cooling requirement (via starting temperature and pressure), ignition timing, and emissions of NOx, CO, HC, and soot. The cycle performance metrics such as efficiency and cooling requirement are discussed in the next section. Emissions results are discussed in the following section. Efficiency and Autoignition Performance Results Figure 8 shows an example intercooling autoignition result for 78:1 effective compression ratio (62:1 geometric). In the left plot, compression begins at a smaller volume than the full cylinder volume and higher pressure than atmospheric. Rapid reaction at the minimum volume appears as a vertical line on the plot, followed by expansion. The expansion stops prior to reaching the full cylinder volume, in order to avoid the piston colliding with the driver section. The black dashed line shows the expansion isentrope extrapolated to the full cylinder volume. Note that V0 in the x-axis scale refers to the cylinder volume, not the volume at atmospheric conditions. Thus the x-axis scale in this plot is inversely related to the geometric compression ratio, not the effective compression ratio.

Figure 8. Pressure as a function of volume (left plot) and time (right plot), for methane-air with equivalence ratio = 1.0, and 78:1 effective compression ratio (62:1 geometric). Ignition timing is defined as the point where the pressure rises to half way between the compression and expansion isentropes, as indicated by the circle in Fig. 8. This definition is arbitrary, but is consistent across all experiments. A physical interpretation of this definition is similar to the CA50 metric often used in conventional engines [1]—it essentially corresponds to 50% completion of the exothermic stage of reaction.

The ignition timing was repeatable from one experiment to the next to within ±0.03 ms, measured relative to the time at which the minimum volume was reached. The actual timing achieved on a given experiment could be determined to within ±0.005 ms. For the 78:1 effective compression ratio experiment shown in Fig. 8, ignition occurred 0.01 ms after the minimum volume was reached. For the experiments near 35:1 effective compression ratio, the timing varied from 0.11 to 0.14 ms after the minimum volume. For most experiments near 60:1 effective compression ratio, the timing varied from 0.02 to 0.06 ms after the minimum volume. To put these values in context with the overall cycle, the time for the piston to travel from the midway point of the compression stroke to the minimum volume, and then return to the midway point on the expansion stroke, was ~5.3 ms for 35:1 effective compression ratio. For 60:1 effective compression ratio, this time was ~2.8 ms. Another feature apparent in Fig. 8 is a large degree of pressure ringing. The ringing is better visualized in the plot of pressure as a function of time on the right. The peak ringing amplitude is ±200 bar. The maximum rate of pressure rise is also extremely high—56.6 bar/μs for this case, which would translate to ~5000 bar/CAD for an engine at 1800 RPM. For comparison, maximum rate-of-rise for HCCI engines is targeted to be less than 10 bar/CAD. The rate-of-rise is higher in this case partly because no dilution was used, and partly because of the high temperature and pressure. The large pressure ringing is linked to the high rate-of-rise, as the rapid pressure rise does not occur uniformly throughout the cylinder. Pressure waves emanate from the regions of earlier ignition, in a manner very similar to knock in SI engines. Pressure ringing of this amplitude would present practical difficulties in developing an engine, for example with respect to noise, vibration, and harshness (NVH), structural integrity, and heat transfer. One potential solution is to introduce a significant amount of dilution to slow the reaction rate. Another possible solution is to inject water, as discussed in a later section. Experimental results for gross indicated efficiency are shown in Fig. 9. The results are compared to the thermodynamic limit for a stoichiometric, methane-air Otto cycle starting from ambient and with the same effective compression ratio. The indicated net work from the extreme compression experiment is determined as before, by integrating the experimental pressure over volume. The extrapolation of the expansion stroke to the full cylinder volume (shown by the dashed line in Fig. 8), is included in the integration. However, with the intercooling strategy the experiment begins at a point above atmospheric (point 3a in Fig. 7). An assumption must be made about the work required to get to this starting point—in other words, the work required for the compressor upstream of the intercooler. Two plausible assumptions are shown in Fig. 9. The higher efficiency is calculated assuming that all of the compressor work comes from a turbine in the exhaust. This case is analogous to a turbocharger with intercooling. The lower efficiency is calculated assuming that the compressor work must be supplied from another source, with a polytropic compressor efficiency of 0.8.

Figure 9. Efficiency as a function of effective compression ratio. The Otto cycle limit is calculated for premixed, stoichiometric, methane-air starting at ambient conditions, and reaching the same effective compression ratio. Variable properties and equilibration of products during expansion are included. The experimental gross indicated efficiency is shown with two different assumptions about compressor work prior to intercooling. The indicated efficiency reaches a maximum of 57%. For comparison, the lean, Diesel-style combustion from our previous work reached a maximum indicated efficiency of 60%. The theoretical limit is lower for stoichiometric, premixed methane-air—70% at 90:1 compression ratio, as compared to 77% for the lean-Diesel cases at the same compression ratio. Thus the indicated efficiency for these stoichiometric-charge experiments is higher relative to the theoretical limit than for the lean-Diesel case. This is noteworthy, because the mass and heat transfer losses are likely worse for the stoichiometric, premixed combustion, due to the higher pressure and higher bulk temperatures achieved. Heat transfer is particularly exacerbated in the premixed case, due to reaction occurring near the walls. A potential explanation is that the efficiency benefit from the rapid, premixed reaction offsets the increased heat and mass transfer losses. Especially in the free-piston device, Diesel-style combustion occurs significantly before and after the minimum volume. The premixed strategy avoids this loss mechanism. As pertains to autoignition control specifically, the performance of the refrigeration and intercooling methods is determined by the amount of gas cooling required to achieve autoignition at the desired time. This performance is set by the post-refrigeration temperature required in the refrigeration method, or by the intercooler pressure required in the intercooling method. For example, the earlier kinetics modeling predicted that a refrigeration temperature of 250 K, or an intercooler pressure of 2.2 bar, would be

required to hold off ignition of methane until the minimum volume for 100:1 effective compression ratio. This second metric corresponds, for example, to the outlet pressure of the compressor in a turbocharged, intercooled engine setup. The actual, experimental performance of the intercooling method can be calculated in this same way. The gas pressure and temperature are known at the start of each experiment. Therefore, the isentrope that the experimental compression process followed is also known. From this isentrope, the two cooling requirement metrics can be calculated. The experimental cooling requirements are shown in Fig. 10. As it was for the theoretical discussion, the post-intercooler temperature is assumed to be 310 K. Only experiments for which the ignition timing was similar—slightly after the minimum volume—are included in the calculation and figures.

Figure 10. Experimental cooling requirement to achieve ignition at the minimum volume. Cooling is expressed in terms of the atmospheric starting temperature of a compression isentrope in the left plot, and in terms of the absolute intercooler pressure for a post-intercooler temperature of 310 K in the right plot. Model results are shown for comparison. Model is the same as discussed in earlier section, with volume-time profiles from this set of experiments. The gas cooling requirement increases with effective compression ratio, as indicated by a decreasing refrigeration temperature or an increasing intercooler pressure. For 78:1 effective compression ratio, achieving ignition at the minimum volume required the equivalent of a 240 K refrigeration temperature, or a 2.5 bar intercooler pressure. From these results, it appears that a larger cooling requirement was required experimentally than was predicted in the theoretical discussion. To further this comparison, the same chemical kinetics model used in the theoretical discussion of autoignition control was used here. In this case, the volume-time profile for the model is taken from this data set for the corresponding compression ratio. The charge is again stoichiometric methane-air, with the GRI 3.0 chemical kinetics mechanism. The model cooling requirement is adjusted by changing the starting temperature of the charge, while holding the starting pressure and volume the same as in the experiment. This requires

slightly adjusting the volume profile to give the same effective compression ratio as in the experiment. The cooling requirement thus predicted by the chemical kinetic model is also shown in Fig. 10. The experimental cooling requirements are higher than those predicted by the model for all compression ratios. One likely explanation is that the kinetics mechanism may not accurately predict ignition behavior due to the very high pressures and the rapid compression-expansion profile. Further research is required to understand the accuracy of ignition prediction by the chemical kinetics mechanism under these conditions. Another possibility is that temperature inhomogeneities in the experiments hasten ignition, thus requiring greater cooling. However, inhomogeneities result primarily due to heat transfer to the cylinder walls, and therefore should be at a lower temperature than the isentropic temperature assumed in the model. Note that at 35:1 compression ratio, the intercooler pressure predicted by the model is sub-atmospheric (0.9 bar in Fig. 10). In effect, this means the model predicts that the reactant charge must be heated rather than cooled to achieve the desired ignition phasing at 35:1 compression ratio. Emissions Results Emissions of NOx, CO, CO2, O2, and hydrocarbons were measured for this set of experiments. The emissions measurements described here were performed in the same manner and using the same system described in the previous years’ report for the Diesel-style combustion study. A carbon balance was performed, comparing the amount of carbon in CO2, CO, and hydrocarbons in the exhaust to the amount of carbon in the fuel. Contribution of soot was not included in the carbon balance. The carbon balance results are shown in Fig. 11, for all of the intercooling experiments, plotted as a function of equivalence ratio. The level of variability in the balance is ±0.7%. There is, however, a persistent, average offset of -2%. The offset could be of some concern if it comes from the actual methane-air stoichiometry, resulting from the calibration of the premixed gas delivery system. The methane used in these experiments contained up to 0.6% N2, which could contribute to some, but not all, of the observed offset. An equivalence ratio shift of 2% could be important in interpreting species emissions profiles that change greatly in the vicinity of stoichiometric, such as CO and NOx. However, as discussed above, the fill system was calibrated by two independent methods in close agreement, and no source of error was determined. As such, the results are reported assuming the charge stoichiometry is correct.

Figure 11. Exhaust carbon fraction as a function of equivalence ratio for all intercooling experiments. Measured CO, HC, and NOx emissions are shown below in terms of indicated-specific emissions and mole fraction. Conversion of emissions to a mass basis assumes NOx emissions are entirely NO, and HC emissions have the same H/C ratio as the fuel. Specific emissions are computed using the indicated net work from the experiment.

Figure 12. Hydrocarbon emissions as a function of equivalence ratio, for different compression ratios, on an indicated-specific and mole fraction basis. Compression ratios listed in the legend are effective compression ratios. Hydrocarbon emissions are shown in Fig. 12. There appears to be a slight increase in hydrocarbons with increasing equivalence ratio, although the magnitude of the trend is

similar to the repeatability seen in the multiple points at 1.0 equivalence ratio. The hydrocarbons are also significantly lower for the lowest compression ratio. Both of these trends are consistent with an interpretation that the majority of the hydrocarbon emissions come from unburned hydrocarbons stored in crevice volume, as is common in premixed-charge engines.

Figure 13. Oxides of nitrogen emissions as a function of equivalence ratio, for different compression ratios, on an indicated-specific and mole fraction basis. Compression ratios listed in the legend are effective compression ratios. Oxides of nitrogen emissions are shown in Fig. 13. Only experiments with similar ignition timing (slightly after the minimum volume) are shown in the these NOx emissions figures. Compression ratio has little effect on the NOx level. At first this appears counterintuitive. However, due to the autoignition control strategy, the peak temperature is maintained relatively constant. Peak temperature is a strong predictor of NOx emissions, consistent with the observed trend. Furthermore, this result indicates that pressure does not have a strong effect on the exhaust NOx level, as the peak pressure changes from 400 bar to 800 bar over this range of effective compression ratio. In general, the rate of NO formation for the thermal NOx mechanism (relevant here) is expected to increase with pressure. However, chemical kinetics modeling (discussed below) suggests that for these experiments the NOx reaches its equilibrium value shortly after ignition, in which case the amount of NOx is no longer limited by the rate of formation. The equilibrium concentration of NOx is weakly dependent on pressure, slightly decreasing with increasing pressure, which is consistent with the experimental observation.

Figure 14. Comparison of experimental NOx mole fraction as a function of equivalence ratio to model prediction. Model and experimental results are for 60:1 effective compression ratio. The model assumptions are the same as those used to predict the cooling requirement for Fig. 10. As expected, the NOx emissions decrease with increasing equivalence ratio, due to the scarcity of oxygen. Of particular note is the steepness of this decline, with NOx levels changing by a factor of 5 over an equivalence ratio change of only 8%. For comparison, predicted NOx levels were computed using the compression-expansion model with GRI 3.0 kinetics, which includes a NOx mechanism. The model setup was the same as that used to produce the model results in Fig. 10, with the volume-time profile taken from the experiments, and the starting temperature adjusted to achieve ignition phasing at the minimum volume. The model and experimental results for 60:1 effective compression ratio are shown in Fig. 14. The steep experimental NOx trend is predicted by the model, although the amount of NOx is consistently higher in the experiments than in the model. This result suggests that the observed trend is not an experimental artifact, but rather is a property of this combustion process in the extreme compression apparatus. Furthermore, in a study of a conventional spark-ignited natural gas engine, Einewall et. al. report a linear decrease in NOx emissions of ~30% when varying equivalence ratio from 1.00 to 1.02 [1]. This trend agrees well with the results from the present study. The appearance of the same NOx trend in the conventional engine suggests that it is a general feature of methane-air engine combustion, rather than a result of the free-piston profile, high compression ratio, or HCCI combustion strategy.

Figure 15. Carbon monoxide emissions as a function of equivalence ratio, for different compression ratios, on an indicated-specific and mole fraction basis. Compression ratios listed in the legend are effective compression ratios. Mole fractions of CO predicted by the chemical kinetic model are shown for comparison. Model assumptions are the same as those used in the NOx discussion above. Carbon monoxide emissions are shown in Fig. 15. The CO emissions are low for lean and stoichiometric equivalence ratio, and then increase significantly for slightly rich equivalence ratios. Increasing compression ratio appears to reduce the CO emissions, particularly for slightly rich equivalence ratios. The chemical kinetic model predictions of CO mole fraction are also shown in the plot on the right. The model is the same as was used for the NOx emissions discussed above. The CO mole fraction values predicted by the model are similar to the experimental results. However, the experimental CO increases non-linearly for rich equivalence ratios, while the model predicts a linear increase with increasing equivalence ratio. The model also predicts higher CO for lower compression ratio, although the effect is less than that seen in the experimental results.

Figure 16. Combustion efficiency as a function of equivalence ratio, for different compression ratios. Combustion efficiency was calculated from the measured emissions of CO and unburned hydrocarbons, as well as a computed level of H2 emissions assuming an equilibrium constant for the water-gas shift reaction of 3.5 (as is common practice [1]). The results are shown in Fig. 16 as a function of equivalence ratio. At the leanest equivalence ratio, hydrocarbons are the primary contributor to fuel energy remaining in the exhaust. For this reason the combustion efficiency is higher for the lower compression ratio. At stoichiometric, CO contributes on an equal level with hydrocarbons, while for rich equivalence ratios the CO dominates. Thus the combustion efficiency follows the inverse CO emissions trend for equivalence ratios above stoichiometric. A primary goal of exploring stoichiometric combustion was to enable the use of a three-way catalyst. Recently, a significant amount of research has focused on operating conventional spark-ignited (SI) natural gas engines with stoichiometric charge and a three-way catalyst. For example, Chiu et. al. [2] and Saanum et. al. [3] both report pre- and post-catalyst emissions for modern, heavy-duty, stoichiometric, natural gas engines. To help put the emissions results into context, specific emissions from this study at 60:1 effective compression ratio are compared to those from the SI natural gas engines in Table 2. Because catalyst performance is dictated by species concentration rather than specific emissions, the results are also compared on a mole fraction basis. Approximate exhaust mole fractions for the Chiu and Saanum papers were calculated using their reported specific emissions, brake efficiency, brake power, and EGR fraction.

Table 2. Comparison of emissions levels from this study to those of spark-ignited, stoichiometric, heavy-duty natural gas engines from the literature. Three-way catalyst conversion efficiencies from the literature are used to calculate hypothetical post-catalyst emissions from this study.

Chiu and Saanum both chose an equivalence ratio that minimized post-catalyst emissions of CO and NOx. In both studies, the optimal equivalence ratio was reported to be slightly rich of stoichiometric (although an exact value was not given). The CO/NOx ratio from this study most closely matches their results at an equivalence ratio of 1.028—likewise slightly rich. The emissions results from this study are interpolated to 1.028 equivalence ratio in Table 2 for comparison. Specific emissions of both CO and NOx were lower for this study than for the SI engines. Partly this is due to the use of indicated work for the present study as opposed to brake work. Hydrocarbon emissions from the current results were dramatically lower. This is potentially due to the unusually long stroke and large clearance volume of the extreme compression apparatus. This geometry creates a relatively small ratio of crevice volume to clearance volume in comparison to conventional engines. On a mole fraction basis, the CO and NOx emissions from this study are nearly identical to the SI engine exhaust, while the HC emissions remain lower. The catalyst conversion efficiencies reported from the natural gas engine studies were greater than 90% for all species, using conventional three-way catalysts. Because the exhaust gas composition from the current study is very similar to that reported for the SI engines, it is reasonable to expect similar catalyst performance. Hypothetical post-catalyst emissions from the extreme compression experiments are therefore calculated in the right column of Table 2, using the average catalyst efficiencies from the two SI engine studies. The resulting post-catalyst emissions would be significantly below the upcoming Tier 4 CARB and EPA emissions regulations. This is a promising result, as it indicates that meeting emissions regulations with this combustion strategy might be accomplished with existing catalysts.

Experimental Investigation of Vaporization-Controlled Premixed Autoignition An experimental investigation of water vaporization for autoignition control was also conducted. To accomplish this, a stock Bosch common-rail Diesel injector was used to inject water into the cylinder during compression. The injector was connected to a stainless steel accumulator volume, which in turn was supplied with 1450 bar pressurized water from an air-driven, high-pressure pump. In order to enable early injection without significant wall-wetting, the injector was mounted axially in the end-wall of the combustor. Injection was through a single orifice along the axis of the cylinder, with an orifice diameter of 360 μm. The water vaporization experiments were only performed at stoichiometric equivalence ratio, and emissions were not measured. Because emissions were not measured, heating the cylinder walls was not required. Experiments were first performed with a wall temperature of 330 K, with an effective compression ratio up to 41:1. Further experiments were performed with a wall temperature of 298 K, up to an effective compression ratio of 61:1. As will be discussed below, achieving proper ignition phasing at compression ratios significantly higher than 61:1 was not practical with the current experimental setup. For each of these experiments, the cylinder was filled with a stoichiometric, homogeneous methane-air charge at atmospheric pressure and the cylinder wall temperature, using the process described previously for the intercooling methane-air experiments. The timing of the start of water injection was varied. The optimal start-of-injection timing was found to be near an instantaneous compression ratio of 2:1 (i.e. the midway point of the compression stroke).

Figure 17. Pressure as a function of volume for stoichiometric methane-air with water-injection cooling. An intercooling experiment at 60:1 effective compression ratio is shown for comparison. The temperature and compression ratio shown in the legend are

the initial methane-air charge temperature and the effective compression ratio, respectively. Two example pressure-volume traces from the water injection experiments are shown in Fig. 17, along with an intercooling experiment for comparison. There are several features in the water injection traces that differ from the intercooling case. First, the water injection experiments begin at atmospheric pressure and the full cylinder volume, whereas the intercooling experiments begin part way along the compression. Second, for the water injection experiments the pressure-volume trace falls below the initial isentrope as water is vaporized. Note that the temperature is not apparent in this plot—the intercooling experiment and water injection experiments do not start on the same isentrope, even though the pressure-volume traces are initially the same. The water evaporation cools the gas, which in turn reduces the pressure for a given volume. Mass is also being added to the cylinder, which would increase the pressure, but the pressure change from the evaporative cooling is much larger. This results in the decrease in pressure relative to isentropic compression that appears in the figure. Once the water evaporation is completed, the compression process again follows an isentrope, but now at a lower pressure.

Figure 18. Pressure as a function of time for a 61:1 effective compression ratio water injection experiment, compared to a 60:1 effective compression ratio intercooling experiment. A third apparent feature is a dramatic reduction in pressure ringing in the water injection cases. This can be more clearly visualized in Fig. 18. The amplitude of the ringing is reduced by more than an order of magnitude, to approximately ±5 bar. The maximum rate-of-rise is reduced by a factor of 60, from 56.6 bar/μs for the intercooling case to 0.9 bar/μs. The most likely cause of this dramatic reduction in reaction rate is the introduction of thermal inhomogeneity in the gas from evaporative cooling. The

methane-air charge is prepared in the same way as in the intercooling experiments, and should thus have similar homogeneity. Dilution, in this case by the addition of water, can also reduce the reaction rate. However, the ~8% water mass fraction injected in these cases should have a relatively small effect, based on the effect of dilution on reaction rate seen in the chemical kinetic modeling discussed previously. Thermal stratification results from the fact that the water spray does not uniformly fill the cylinder. This is particularly true for the current experiments, with injection from a single-hole nozzle in the end-wall of the combustor. Thus the evaporative cooling will occur more strongly in certain regions of the cylinder. Reaction rate in HCCI has previously been shown to correlate with the extent of thermal stratification, for example by Dec et. al. [4]. The results shown in Fig. 17 demonstrate that water vaporization is capable of achieving the desired ignition phasing at minimum volume. However, the amount of water required was far more than predicted in the water vaporization models. Statistics from an experimental water injection case at 61:1 effective compression ratio are shown in Table 3. Also shown are two cases from the water vaporization model. The first model case is for ignition phasing at the minimum volume (TDC). The second model case results in the same temperature at TDC as would have been achieved in the absence of reaction in the experiment. In other words, the temperature at minimum volume in this model matches the final temperature from isentropic compression along the experimental pressure-volume trace. An intercooling experiment for 60:1 effective compression ratio is also shown for comparison. Table 3. Comparison of a water injection experiment at 61:1 effective compression ratio with two model cases and an intercooling experiment. The water mass fraction, the bulk temperature at the minimum volume (TDC) without reaction, and the efficiency are shown.

As seen in the first line of the table, the water injection experiment required an order of magnitude more water to achieve ignition phasing at the minimum volume than was predicted by the model. There are two reasons for this: a high degree of thermal stratification, and slow water vaporization. These two effects are explained by comparison with the model results as well as the intercooling experiment. First, the water injection experiment required more gas cooling than the intercooling experiment, for the same effective compression ratio. This is evidenced by the fact that the average gas temperature the system would have reached without chemical reaction is 884 K for the

water injection experiment, and 1012 K for the intercooling experiment. For both cases ignition occurred at the minimum volume, but in the water injection case the average gas temperature was significantly lower. The likely cause of this difference is the increased thermal stratification in the water injection case. Some regions of the gas are necessarily hotter than the average. These hotter locations ignite earlier, increase the pressure and temperature, and drive ignition in the remaining gas. Therefore, the average gas temperature must be even cooler to avoid autoignition, and the evaporative cooling requirement is increased. To understand the second cause of the increased water requirement, a model case was chosen that achieves the same average temperature without reaction as the experiment. This is shown in the third column in Table 3. In effect, this isolates the water injection requirement to achieve a given overall gas cooling, regardless of the ignition properties. In this case, the model prediction for water mass fraction is still significantly less than the experimental result. The reason for this difference can best be understood by comparing the experimental pressure-volume trace to this model case, as shown in Fig. 19.

Figure 19. Pressure as a function of volume for a 61:1 effective compression ratio water-injection experiment, compared to a model case that achieves the same average gas temperature (without reaction). The model follows same volume-time profile as the experiment, with water vaporization starting at the same time, and at the same rate, as the experimental water injection.

The model and experiment start on the same isentrope at atmospheric temperature and pressure, and reach the same isentrope near the end of the compression stroke (albeit with different water mass fractions). The model assumes that the water evaporation starts at the same time as the experimental start-of-injection. Furthermore, the rate of vaporization in the model is the same as the rate of injection in the experiment. From the pressure-volume traces it can be seen that the experimental vaporization rate is slower than the injection rate, as the pressure-volume trace for the model decreases below the isentrope more rapidly than the experimental trace. Also, the model reaches the final isentrope (end of vaporization) at a geometric compression ratio of 3.5:1, while the experimental trace does not reach the same isentrope until ~16:1. This is likely caused by a combination of two things: First, some of the water injected into the cylinder may be striking the wall as a liquid, and is therefore not vaporized by the gas. Second, even if the water does not strike the wall, the vaporization may be delayed until later in the compression stroke. As discussed earlier, cooling that happens later has less of an effect on the final temperature reached, and hence more water injection would be required to reach the same temperature. The vaporization rate appears to match the injection rate near the end of injection, when the gas temperature and pressure are higher, because the experimental end-of-injection occurs at the same time that the pressure-volume trace reaches the final isentrope. As shown in the table, the indicated efficiency for the water injection experiment was 10% less than the intercooling experiment at the same compression ratio. The inability to quickly vaporize water explains the decrease in efficiency. While not a one-to-one correlation due to the log-log scale, larger area inside the pressure-volume loop in Fig. 19 translates to higher indicated work output. The late cooling in the experiment eliminates a portion of the pressure-volume loop, and thus reduces the efficiency. Said differently, the late gas cooling results in a later pressure drop in the compression stroke, and therefore, higher compression work. Both of these issues—thermal stratification and slow vaporization—stem from a single aspect of the current apparatus: the physical arrangement of the water injection. The injector setup used in these experiments was constrained by the existing combustor geometry, as well as the availability of custom injector nozzles. Injection from a single hole situated at the end of a long cylinder means that only a portion of the gas volume is in contact with the water spray, especially during the earlier part of injection. This likely causes the high degree of thermal stratification. It also means that only a portion of the gas charge is available to provide the required energy for vaporization. Furthermore, the single, large orifice results in a relatively large drop size, which would slow vaporization, as well as high jet penetration, which could result in the liquid spray intersecting the cylinder wall prior to vaporization. There is significant room to improve this injection setup using existing injection understanding and technology, which may improve the overall performance of the water injection strategy.

Optimal Architectures for Regenerative Steady-Flow Combustion Engines In the past few years we have developed a first-principle irreversibility-minimization

approach to identify optimal (maximum efficiency) architectures for combustion engines. The essential idea behind this approach can be explained using Fig. 20. In the engine, the exergetic energy resource, the fuel, can be thermodynamically manipulated using energy transfers and transformations. There are only three kinds of energy transfers relevant to combustion engines are work, heat, and matter. As shown in the figure energy can be transferred between the working fluid at two different locations in the engine (internal- regenerative transfer) or between the working fluid and the environment (external transfer). The energy transformations relevant to gas turbine engines involve mechanical, thermal, diffusive, chemical equilibration processes that occur along with energy transfers.

Figure 20: Thermodynamic representation of a generic combustion engine

Energy transformations cause irreversibility to be incurred both inside (e.g., combustion irreversibility due to chemical reactions) and outside (e.g., exhaust exergy is destroyed in the environment) the engine. The main objective of this research is to provably establish the optimal sequence of these energy transfers and transformations that minimizes the total irreversibility—thereby defining the most efficient engine architecture. It must be noted that this approach is not a parametric optimization of an existing or newly conceived cycle. Instead, this approach is to establish the most efficient architecture starting with no assumptions, just the relevant physics and key engineering constraints.

Past Work Research until the previous year—described in previous reports—led to the development of optimal architectures for work-regenerative and, heat- and work-regenerative engines. The optimal architecture of work-regenerative engines was shown to be:

CB(TB)nT where C stands for compressor, B for burner, and T for turbine. This architecture shown to have higher efficiency over a turbine-inlet-temperature limited Brayton architecture CBT. The key feature of this optimal architecture is the 2n-staged burner-turbine segment that implements part of the combustion process in a near-isothermal manner.

Extending on this approach the optimal heat- and work-regenerative architecture was shown to be,

(CI)kC(Xin)mCB(TB)n(TXout)mT

that utilizes regenerative heat transfer in addition to work to provide higher efficiency than work-regenerative architectures. The additional devices: I and X stand for intercoolers and heat-exchangers respectively. The subscripts “in” and “out” indicate the directionality of heat transfer. There are three distinctive features to this architecture. First, there is adiabatic compression after intercooled compression. Contrary to conventional intercooling the purpose of intercooling here is only to reject entropy via low-exergy transfer of energy as heat. The subsequent adiabatic compressor takes the system to high-enthalpy states necessary for reduction in combustion irreversibility. Second, the m-staged, heat-capacity matched heat transfer process reduces irreversibility in heat transfer over conventional single stage heat recuperation. Third, there is post-heating compression that allows the system to be taken to extreme states that would not be possible by temperature-limited heat exchangers alone. This compression further reduces combustion irreversibility and provides an efficiency increase. This compression is also a non-conventional, but optimal result arising from the systemic optimization approach. Research Efforts in the Previous Year In the previous year matter transfer—the third kind of energy transfer—was considered for engine-architecture optimization. As with heat and work before, matter transfers can be categorized into internal, regenerative matter transfers and external matter input/output. A wide range of matter transfers can be implemented and considered for engine architectures. Therefore, a systematic progression through model problems was employed. Only the simplest kind of architectures that involve mixing of matter streams (in mixers and burners) but no separation systems (e.g., separation of water and/or CO2 from exhaust, air-separation, etc.) were considered in this study. However, the analysis of these architectures provides thermodynamic insights for efficient design of regenerative architectures with separation systems, with extensions to efficient combined-cycle architectures. The key results from matter transfer optimization and the extensions for future work are briefly discussed in this report. The only additional device introduced is a mixer/splitter device M. The device used to split/bleed-off matter from a subsystem is indicated by Mout and the location where two matter streams are merged is denoted by Min. Systematic Selection of Model Problems Heat- and work-regenerative architectures considered in prior years involved two matter streams: fuel and air. A simple matter transfer strategy with fuel and air streams existing as separate subsystems in the pre-combustion segment of the system trajectory and mixing during combustion had been chosen. The fuel was injected into the air subsystem such that the combustion products remained in the air subsystem—an approach that is

currently in practice and is motivated by practical advantages pertaining to combustor design, such as, keeping the gas temperature lower (excess air), better fuel-air mixing, flame stabilization, etc. However, even with only two input matter streams (fuel and air) other feasible process sequences can be constructed, comprising the following model problems for matter-transfer optimization:

1) Feed-forward transfer of air: Instead of compressing and regeneratively heating all the ingested air and performing combustion with fuel, a part of the air can be bypassed (feed-forward) to burners in the near-isothermal combustion segment or the post-combustion segment. Compressor-bleed, feed-forward transfer of air in smaller quantities is already performed for the purpose of blade cooling. In this problem, a general analysis of feed-forward air transfer is considered, i.e., allowing any quantity of air to be fed forward into any downstream.

2) Feed-forward of transfer water: In addition to fuel and air, an external intake of water is considered. Water as an input stream is mixed into the main streams at various locations in wet and humidified cycles. In this problem the general case of open architectures with water as one of the working streams is considered, but no condensers and separation devices are included.

3) External transfer of air: Finally optimization of the external matter input to engine architectures is discussed. The tradeoffs in irreversibility due to in variation in the amount of external air supplied for a unit of fuel fed to the engine, is described and the optimal overall fuel-air ratio determined.

Feed-forward Transfer of Air Prior to analyzing feed-forward air transfer in a more general manner, it is useful to consider a specific case. The optimal heat- and work-regenerative architecture from the previous chapter is modified by adding one stage of air transfer (Mout) in the post-heating compression process as shown below. A prescribed amount of air bled from the compressor is then mixed at the entry of the jth inter-burner turbine in the near-isothermal combustion segment:

(CI)kC(Xin)mCMoutCB(TB)j-1(MinTB) (TB)n-j(TXout)mT In order to understand the system trajectory as per the proposed process sequence, consider the air subsystem to be split into two parts: one that is further compressed beyond Mout to be supplied to the first burner, and the other that will be fed forward. The feed-forward air subsystem is tracked as a part of the system, but it remains isolated from the fuel and main air subsystems being compressed. In order to allow representation of this three-subsystem system by a single state point (fuel, air being compressed, and air flowing without compression) we want all the subsystems to have the same pressure. Therefore, the feed-forward air is considered as undergoing a hypothetical symmetric isentropic compression and expansion through the same pressure ratio as the other two subsystems. Modeled in this way, the feed-forward air returns to the same state as that at Mout after a symmetric isentropic compression and expansion process leading up to Min—that is, the same pressure that the air was bled from the compressor. At the exit of

Min and the entry to the jth turbine, the feed-forward-air subsystem is mixed with the main air/combustion-products subsystem such that the system regains its two-subsystem identity—unused fuel, and air with partial-combustion products. With this conceptualization, the system trajectory can be evaluated now from an extreme-states principle standpoint. Consider the thermodynamic state of the feed-forward air subsystem undergoing hypothetical isentropic compression. In the absence of the feed-forward strategy, this air would have mixed and chemically equilibrated in the first burner where the total system enthalpy is higher. In contrast, the mixing with partial combustion products in Min occurs at a state with lower system enthalpy (and lower pressures) because work has been extracted in the j-1 turbines prior to injection. The extreme states principle suggests that the feed-forward case will have higher mixing and chemical equilibration irreversibility. Another way to understand this is by tracking the temperature of the stream. Since the feed-forward air is relatively cold, upon mixing it in the jth turbine the system trajectory deviates from the near-isothermal path. Regardless of which turbine j is chosen, the deviation from the near-isothermal segment prior to completion of combustion (once the isothermal combustion segment has begun) is non-optimal. Therefore the only optimal place to inject this air is the first burner. In other words, to minimize pre-equilibrium entropy generation feed-forward transfer of air is non-optimal. As another example, consider the feed-forward transfer of air to the exit of the final (n+1th) burner. If done so, the turbine inlet temperature to first post-combustion turbine is lower than the limit, again a violation of optimality.

Figure 21: Variation of efficiency with increasing feed-forward transfer of air.

This conclusion is numerically validated in Fig. 21. In this figure the candidate natural-gas/air system with overall equivalence ratio 0.43 is considered undergoing the optimal heat- and work-regenerative architecture. The process sequence in this architecture is modified by splitting the total mass of air into j+1 equal parts. Each part j is fed-forward and mixed prior to the inter-burner turbine j+1. The j=0 case corresponds to the no feed-

forward transfer case where all the mass is transferred to the first burner. The j=1 case has two air subsystem parts, one that mixes in the first burner, and a second that mixes after the second burner, i.e., prior to the second turbine. Similarly, an increase in j represents more air distributed among the turbine-burner stages. As predicted, the efficiency decreases, confirming the non-optimality of feed-forward air transfer. The proposed process sequence in this example involves splitting of the total air flow in equal parts for each burner. In this hypothetical choice, beyond j=5 the excess air necessary for dilution in burners is reduced below levels required to maintain the temperature. However, compressor-bleed blade cooling that utilizes a smaller amount of the bypass air is similar to the example of feed-forward transfer of air and is non-optimal. In practical systems the pressure drop in the cooling flow contributes to a further reduction in efficiency. But the key message here is that even without pressure drop, the mixing entropy generation will increase due to an increase in attractor entropy for lower-enthalpy attractor states. However, it is also to be noted that the decrease in efficiency is relatively small despite the large amount of feed-forward transfer. In conclusion, feed-forward transfer—although necessary in the case of blade cooling—is otherwise non-optimal. Furthermore, this conclusion applies not only to feed-forward air, but to other matter streams that can be fed forward from the pre-combustion segment to the combustion or post-combustion segments. In essence, aside from blade cooling that plays a role in improving efficiency indirectly, feed-forward transfers from the pre-chemical equilibrium part of the trajectory must be avoided. Fuel Pre-heating In previous analysis, the fuel stream was not regeneratively heated. By explicitly disallowing preheating of the fuel, it was fed forward from the pre-heating compressors to the post-heating compressor, bypassing regenerative heating undergone by the air stream. This is done from a practical standpoint of avoiding fuel pyrolysis. However, purely from an efficiency standpoint this choice can be shown to be non-optimal.

Figure 22: Effect of fuel preheating on efficiency

A reduction in mixing and combustion irreversibility can be achieved if fuel is also regeneratively heated, taking both fuel and air to high-enthalpy states prior to the burner. This is shown in Fig. 22 where the effect of regenerative heating of fuel is investigated for the natural-gas/air system in the optimal heat- and work-regenerative architecture. Although only by a small amount (~ 1%), the efficiency gain shown corroborates the optimality of not feed-forwarding matter, i.e., not skipping the regenerative heating for fuel in this case.

Feed-forward Water Transfer The conclusion from the previous section can be readily extended to water transfer within the architecture. In humidified-cycle architectures water is used in three ways: 1) water is sprayed into the air stream between compressor stages to reduce compressor work, 2) water is converted to steam by regenerative heat transfer from the exhaust and injected into post-compression air, and 3) post-compression air is humidified followed by regenerative heat-exchange with the exhaust. In the first case, evaporative cooling of air allows less work regeneration for the same pressure ratio, but reduction of total entropy generation requires the reactants to be taken to high enthalpy states not just high pressure states. In the second case, air is not regeneratively heated, therefore the air subsystem is not undergoing optimal heat and work regeneration. In the third case, both air and water (although mixed) undergo both work and heat regeneration to extreme states prior to combustion allowing greater reduction in irreversibility. Essentially, during the pre-combustion segment, all streams must be taken to the most extreme state possible using optimal work and heat transfer. Water and air must be separately compressed and pre-heated using the post-combustion gases and mixed at the entry to the combustion segment. This ensures mixing and chemical equilibration is performed at the maximum enthalpy state. Mixing and combustion of fuel must be performed in the completely mixed air and water stream in a staged manner as advocated in previous chapters. Feed-forward of any stream such as bypass to post-combustion segment or bypass of regenerative heating is non-optimal. Relevance to Combined-Cycle Architectures The conventional combined-cycle architecture that involves a gas turbine engine with a bottoming Rankine cycle can be studied as a special case of feed-forward transfer of water in the following manner. First, consider a hypothetical open Rankine-cycle bottoming engine that draws enthalpy from the exhaust of a gas turbine engine but rejects water into the atmosphere after work extraction. The process sequence undergone by the water—which involves water intake, regenerative work investment (pumping) and regenerative heating—is similar to the optimal architecture considered thus far. However instead of injecting the steam into the burner, the steam is directly fed to a turbine. This is in essence, a feed-forward transfer of the steam to the post-combustion segment of the reactive engine system trajectory. As discussed above, this strategy must be less efficient than wet-cycle architectures. Furthermore, in the open cycle the steam, air, and combustion products are destined to mix either inside the engine or in the atmosphere after exhaust. By not mixing the steam with the fuel-air subsystem at extreme states, all the mixing must occur in the atmosphere. This results in a higher external irreversibility,

which indicates lower engine efficiency. Therefore a wet-cycle architecture is likely to be more efficient than a combined cycle that employs an open Rankine bottoming cycle. However, Rankine-cycle architectures are not open. These architectures benefit from greater work extraction owing to a condenser that operates below atmospheric pressure. By mixing the water in the burner, which subsequently stays with the combustion products, the ability to employ a vacuum condenser is lost. A more efficient architecture is likely to be that which combines the optimality of using the water stream in the combustion process and then separates the water from the combustion products in a manner such that a vacuum condenser can be employed. Analysis of such architectures would be the next step in development of efficient matter-, heat-, and work-regenerative engine architectures beyond that undertaken in this dissertation. External Matter Architecture optimization performed thus far considered a fixed overall equivalence ratio. Fixing the equivalence ratio essentially determined the relevant chemical equilibrium surface in the state space for the system. Thereafter, all the optimization was directed at optimally manipulating the attractor trajectory on the chemical equilibrium surface. By varying the overall equivalence we are varying the choice the chemical equilibrium surface. Thus, from an optimization point of view, the attractor trajectory no longer lies on a fixed chemical-equilibrium surface and the analysis of variation in external matter input requires study of the attractor trajectory that traverses between different chemical equilibrium surfaces. From a thermodynamic viewpoint, increase in non-exergetic, external matter intake per unit of fuel increases internal irreversibility as there is more matter in the system to mechanically, thermally, and chemically equilibrate. In doing so, however, the external irreversibility is reduced. This is because the more dilute exhaust stream is closer to the environmental dead state. This tradeoff—the reduction of external irreversibility and increase in internal irreversibility with decreasing equivalence ration—exists for all the architectures considered so far and can be utilized for further efficiency maximization. For the optimal internal heat- and work-regenerative architecture C(Xin) mCB(TB)n(TXout)mT this tradeoff is illustrated in Fig. 23 below.

Figure 23: Tradeoff between internal and external irreversibility with variation in overall equivalence ratio.

It can be noted that making the overall system leaner reduces external irreversibility but increases internal irreversibility. This effect is similar to that associated with external heat transfer in intercooling where increasing intercooling increases internal irreversibility while decreasing external irreversibility. The tradeoff between internal and external irreversibility associated with varying external energy transfers is in contrast with the absence of such a tradeoff with variation in internal energy transfers. Varying internal energy transfers simultaneously reduces internal and external irreversibility. Variation of the efficiency of all optimal architectures established so far with a change in overall equivalence ratio is re-illustrated in Fig. 24 and Fig. 25 for a natural-gas/air system. The large stage limit is chosen for intercooled compression, capacity-matched feedback heat regeneration, and near-isothermal combustion. The maximum limit on gas temperatures has been chosen as 1650 K for turbine and compressor blades and 1100 K for heat exchangers. The architectures are: Brayton (black), optimal work-regenerative (blue), optimal internal heat- and work-regenerative (green), and optimal internal and external, heat- and work-regenerative (red).

Figure 24: Optimal efficiency and air-specific work for various equivalence ratios.

Figure 25: Optimal overall pressure ratio corresponding to different equivalence ratios

References

1. J. Heywood, Internal Combustion Engine Fundamentals. McGraw-Hill, Inc., 1988.

2. P. Einewall, P. Tunestal, and B. Johansson, “Lean burn natural gas operation vs. stoichiometric operation with EGR and a three way catalyst." SAE Paper No. 2005-01-0250, 200.

3. J. Chiu, J. Wegrzyn, and K. Murphy, “Low emissions Class 8 heavy-duty on-highway natural gas and gasoline engine." SAE Paper 2004-01-2982, 2004.

4. I. Saanum, M. Bysveen, P. Tunestal, and B. Johansson, “Lean burn versus stoichiometric operation with EGR and 3-way catalyst of an engine fueled with natural gas and hydrogen enriched natural gas." SAE Paper No. 2007-01-0015, 2007.

5. J. Dec, W. Hwang, and M. Sjoberg, “An investigation of thermal stratification in HCCI engines using chemiluminescence imaging," SAE Transactions, vol. 115(3), pp. 759-776, 2006. 

6. Horlock, J. H., 2003, Advanced Gas Turbine Cycles, Elsevier Science Ltd., Oxford, UK.

Conference Proceedings

1. K.-Y. Teh, and C. F. Edwards, “An optimal control approach to minimizing

entropy generation in an adiabatic IC engine with fixed compression ratio” IMECE2006-13581, Proc. IMECE 2006.

2. Teh, K.-Y., and Edwards, C. F., 2006. “Optimizing Piston Velocity Profile for Maximum Work Output from an IC Engine”. IMECE2006-13622, Proc. IMECE 2006.

3. S. Ramakrishnan, K.-Y. Teh, and C. F. Edwards, “Identification of optimal architecture for efficient simple-cycle gas turbine engines,” ASME Conference Proceedings, vol. 2009, no. 43796, pp. 539-548, 2009.

4. S. Ramakrishnan and C. F. Edwards, “A methodology for determining optimal architectures for heat-and-work regenerative steady-flow combustion engines,” 42nd AIAA Thermophysics Conference Proceedings, vol. 2011, no. AIAA 2011-3773.

Journal Publications

1. Teh, K.-Y. and Edwards, C. F., “An Optimal Control Approach to Minimizing Entropy Generation in an Adiabatic Internal Combustion Engine,” Journal of Dynamic Systems, Measurement and Control , Vol. 130, No. 4, 2008, pp. 041008.

2. Teh, K.-Y., Miller, S.L., and Edwards, C. F., Thermodynamic Requirements for Maximum IC Engine Cycle Efficiency (I): Optimal Combustion Strategy. International Journal of Engine Research 9:449-466, 2008.

3. Teh, K.-Y., Miller, S.L., and Edwards, C. F., Thermodynamic Requirements for Maximum IC Engine Cycle Efficiency (II): Work Extraction and Reactant Preparation Strategies. International Journal of Engine Research 9:467-481, 2008.

4. Svrcek, M.N., Miller, S.L., and Edwards, C. F., Diesel Spray Behavior at Compression Ratios up to 100:1. Atomization and Sprays, volume 20, issue 5, pp. 453-465, 2010.

5. S.L. Miller, M.N. Svrcek, K.-Y. Teh and C.F. Edwards, Requirements for designing chemical engines with reversible reactions, Energy,Volume 36, Issue 1, 2011, pp. 99-110.

6. S. Ramakrishnan, K.-Y. Teh, S. L. Miller, and C. F. Edwards, Optimal architecture for efficient simple-cycle, steady-flow, combustion engines," Journal of Propulsion and Power, vol. 27, no. 4, pp. 873-883, 2011.

Ph.D. Dissertations

1. Teh, K.-Y., Thermodynamics of Efficient, Simple-Cycle Combustion Engines.

Ph.D. dissertation, Dept. of Mech. Eng., Stanford Univ., Stanford, CA, 2007. 2. Miller, S. L., Theory and Implementation of Low-Irreversibility Chemical

Engines, Ph.D. dissertation, Dept. of Mech. Eng., Stanford Univ., Stanford, CA, 2009.

3. Svrcek, M.N., Exploration of Combustion Strategies for High-Efficiency, Extreme-Compression Engines, Ph.D. dissertation, Dept. of Mech. Eng., Stanford Univ., Stanford, CA, 2011.

4. Ramakrishnan, S., Maximum-Efficiency Architectures for Regenerative Steady-Flow Combustion Engines. Ph.D. dissertation, Dept. of Mech. Eng., Stanford Univ., Stanford, CA, 2012 (in preparation).

Contacts

Christopher F. Edwards: cfe@stanford.edu Matthew Svrcek: msvrcek@stanford.edu Greg Roberts: gregrob@stanford.edu Sankaran Ramakrishnan: rsankar@stanford.edu