Rationale for Improved Thermal Efficiency of Opposed-Piston Two-Stroke Engines
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The motivation for this work is to use a rigorous thermodynamic analysis to provide rationale for why the opposed-piston two-stroke is more efficient than a comparable four-stroke engine. The goal for this work is to quantify why this is the case and also by how much.
The approach is to construct an opposed-piston engine and compare it with a referenced four-stroke engine. The figure of merit for this work will be how much the efficiency deviates from ideal engine efficiency. The work will be broken into two parts. The first part will focus on the closed cycle where we provide constant boundary conditions at the same indicated power and with the same base geometry. The second part will extend the analysis to the entire engine where we include pumping work and EGR. The added constraint for the second part of this analysis is a constant NOx emissions.
So the agenda for this work is to first provide a background on ideal engine efficiency and then move on to the engine configurations we’ll be using, or analyzing, in this study. I’ll move on to the closed-cycle analysis first and extend the analysis to the open cycle and then provide a summary at the end.
So as a background on ideal engine efficiency, the maximum closed-cycle work that can be achieved by an engine can be approximated by using some assumptions. The first assumption is isentropic compression from State 1 to State 2 on this Log P Log V diagram. The second assumption is a constant volume adiabatic combustion from State 2 to State 3. And, the third assumption is isentropic expansion from State 3 to State 4—all of this occurring with constant specific heat capacity.
Using the assumptions detailed above, you can apply an energy balance to the entire system and derive the equation for ideal engine efficiency shown in the lower left, which is one minus one over the compression ratio raised to the gamma minus one. This identifies the two leading parameters that have an effect on engine efficiency.
Using that equation, we can now understand and look at the first order effects. So the plot on the lower left shows the ideal engine efficiency for a range of compression ratios and a range of gamma values. The plots on the left show the Log P Log V diagrams associated with each of these efficiency points. So, the effect of the compression ratio is to increase the operating volume over which expansion occurs. By doing so, you are able to extract more work and increase the efficiency of the engine. By increasing the ratio of specific heats, you increase the pressure rise for a given amount of fuel energy release which results in a larger net system work and higher efficiency.
When analyzing the engine in a realistic case, you introduce non-ideal effects that make the engine efficiency deviate from the ideal case. So there are four effects that result primarily in this deviation. So the first is finite duration combustion. The second is properties of the species that vary with temperature and with the concentration of the mixture in the combustion chamber. And the third is heat transfer. So what we want to do in this analysis is to identify each of these effects and the relative magnitude as we compare the opposed-piston two-stroke to a four-stroke engine.
What’s shown in this slide is a generic engine case, which shows how we add each assumption individually to try and isolate those effects. So what’s shown here in Case 1 is that the ideal engine with constant volume combustion, constant gamma values and no heat transfer. In Case 2, we introduce a finite duration combustion only while maintaining a constant gamma and no heat transfer. In the third Case, we introduce a variable gamma without heat transfer still. And, in the final Case, is the most practical case, where you have finite duration combustion, a variable gamma value and heat transfer included. By analyzing each of these cases individually, we’re able to quantify the relative effects of each of these non-ideal factors of the engine efficiency.
So to move on to the engine configurations that were considered in this study. We first wanted to specify a four-stroke engine to which we were going to compare the Achates Power opposed-piston two-stroke. So we selected an engine architecture that was representative of a medium-duty application. In this case, it’s six cylinders with a one liter trap per cylinder. The reason we use trap volume as opposed to displaced volume is that a portion of the cylinder contents are sacrificed to scavenging in the two-stroke engine operation. So in order to have a meaningful comparison between the four-stroke and a two-stroke, we’ve got to make sure that the trap volumes are consistent.
The stroke-to-bore ratio was set at a value of 1.1, which is consistent with currently available engines. This resulted in a bore of 102.6 mm and a stroke of 112.9. The compression ratio was set at 15:1 and the valve closing event was set to occur at bottom dead center.
The goal of our engine architectures here was to maintain a constant friction work as we go from a four-stroke to the opposed-piston two-stroke. To do that, the easiest way was to hold the stroke-per-piston and the bore constant. As an intermediate step between the four-stroke and the opposed-piston two-stroke engine, we created a hypothetical opposed-piston four-stroke engine. This engine now has three cylinders instead of six with two liters of trapped volume per cylinder. Basically, what we did was take three cylinders, put them on a hinge and put them on top of the other three cylinders and remove the cylinder head in between the two.
To keep a comparable friction, we set the bore and the stroke-per-piston to be equivalent to the baseline four-stroke engine. The stroke-to-bore as a result increased to 2.2 because we had two pistons moving instead of one. The trapped compression ratio was maintained at 15:1 and this was a valve closing event at bottom dead center.
Going from the opposed-piston two stroke to the opposed-piston four-stroke, we needed to allow for scavenging to occur. To account for this, we delayed the port closing cranking of 120 before top dead center instead of bottom dead center. As a result, we now have a smaller trap volume because we sacrificed a portion of the total displaced volume to scavenging. The bore and strokes of the piston were held constant as was the trapped compression ratio.
So moving on to the closed-cycle simulation, we’ll first address the tool that we used. In this analysis, a custom tool was created at Achates Power in order to have better control over the analysis. So, by creating a custom tool, we’re able to introduce non-ideal effects one by one to have a better understanding of what the relative magnitude of these effects are. This custom tool gave us better control over the additional complexity compared to what would be commercially available in an industry code.
The three models that were relevant to this tool are the combustion model, which we said is a Wiebe combustion model. This allowed us to set the timing of combustion and duration using two parameters only. The thermodynamic properties of the species were set using NASA fluid properties available in the literature. And, the five species that we included were oxygen, nitrogen, argon, CO2, carbon dioxide and water. The final model that we needed to include was a heat transfer model and we used a Woschni heat transfer correlation, which is commonly available in codes and was easy to introduce into our custom tool.
Moving on to the results, the first comparison here is with a four-stroke engine compared to an opposed-piston four-stroke engine. So, the four-stroke engine is shown in blue and the opposed-piston four-stroke in red. The operating conditions on the left show that we are simulating a peak power condition at 2400 rpm and 300 indicated horsepower. The boundary conditions were set at 2 bar trapped pressure and 350K with only air being considered for this preliminary closed-cycle simulation. The metal temperatures were set at 550K for the pistons and the head for the crank slider four-stroke case and the liner temperature was set at 450K. The combustion was set to have a CA10 of 0 at top dead center and the duration was adjusted to achieve a maximum pressure rise rate of 5.1 bar/degrees.
With these boundary conditions, the opposed piston four-stroke achieves 2.6% fuel increase in indicated thermal efficiency, although this was achieved at the same peak pressure and roughly the same maximum temperature bulk estimate. The trapped lambda is slightly higher for the opposed-piston four-stroke because less fuel is required to achieve the peak power conditions because it’s more efficient, so it needs to have a leaner charge.
So we can go in and looking at each of the non-ideal effects identify what makes the opposed-piston architecture more efficient than a typical crank slider. So the first thing that we see is that the opposed-piston mechanism gives you a more favorable gear-to-volume ratio. The result of that is a decrease in heat transfer, which lends itself to an increase in indicated thermal efficiency. In this case, here, the losses due to heat transfer decrease 2.1% of fuel.
Because we now have lower heat transfer, we need to reduce the amount of fuel to achieve our peak power condition that leads to a leaner charge, which allows us to maintain our gamma at a higher value as it goes through the combustion event. This leads to a decrease in the losses due to the variable gamma of .2% of fuel.
Because we’ve decreased our fueling rate requirements, we’ll be able to have a shorter combustion duration while achieving the same maximum pressure rise rate. This allows us to phase the combustion more toward top dead center, leads to higher efficiency and a reduction of the losses due to the finite duration of combustion of .3% of fuel. Adding these three effects up gives us our 2.6% of fuel benefit of the opposed-piston architecture.
The next step is to introduce the two-stroke cycle in this comparison. So in this slide here, the four-stroke and the opposed-piston four-stroke are the same as what we showed previously. Now we’ve introduced the opposed-piston two-stroke in green. The operating conditions were held the same: the same peak power condition with the same pressure rise rate constraints. And, the results show that you get a further increase in indicated efficiency by introducing the two-stroke cycle to the opposed-piston architecture. The results show that the Achates Power opposed-piston two-stroke engine has a 5.6% of fuel increase in indicated thermal efficiency compared to a standard four-stroke engine. This is achieved at a lower maximum pressure and a lower maximum cylinder temperature when compared to the four-stroke engine. The one thing that we do notice here is that the overall leanness of the charge is at 2.7, or a lambda of 2.7, compared to a lambda of 1.5. The final point to note is that the lambda value has now increased to 2.7 because of the double firing frequency of the two-stroke engine cycle.
So again we can break down the results into each of the individual components and realize where the efficiency gains come from. So, in this case, we now have a much leaner charge resulting from our double firing frequency of the two-stroke engine cycle. By doing this, we now reduce the decreasing gamma associated with combustion, which allows a more efficient work extraction. Compared to the four-stroke engine, the loss due to variable gamma has decreased to 2% of fuel. Also, due to the reduced firing frequency, the energy release per unit volume has decreased, which allows us to have a much shorter combustion duration without exceeding our maximum pressure rise rate and strength. This allows us to base the combustion more toward top dead center, which leads to a more efficient work extraction and decreases the loss due to finite duration combustion by 2.2% of fuel.
So, the trade off with that is a slightly higher loss due to heat transfer compared to the opposed-piston four-stroke, but still a decrease in the loss compared to the four stroke. There’s two effects there. One is the area-to-volume ratio is slightly less favorable for the opposed-piston two stroke because we’ve now delayed our port closing crank angle to 120 before top dead center, but this is now traded off with the shorter combustion duration. The shorter combustion duration achieves higher temperatures longer, which increases the heat transfer. So even though we’re sacrificing a little bit of heat transfer, it’s a net gain in terms of increase in indicated efficiency.
Similar simulations were performed over a speed load map shown in the lower left, which assumes a linear torque rise from the C100 to the A100 condition, when the A100 condition is at 1000 N-m of indicated torque. The other conditions consider the A25, B50 and C25 with the appropriate weightings similar to the 13-rule cycle. The boundary conditions were slightly changed for each operating condition, but they were held constant when comparing the four-stroke and opposed-piston two-stroke as were the metal temperatures and pressure rise rate constraints.
So looking at the result over this cycle, we see that the opposed-piston two-stroke has a benefit of lower indicated specific fuel consumption compared to the four stroke at each of these operating conditions. The weighted average results shows a 10% decrease in indicated-specific fuel consumption compared to the four-stroke engine.
So moving on to include components of the engine system, we used a 1-D system model to evaluate the difference in pumping work required to achieve the specified boundary conditions of the Achates Power opposed-piston two-stroke compared to a four-stroke engine. In these simulations, the engine was represented as a mean value engine that allowed us to use our closed-cycle simulation tool to define the indicated thermal efficiency and the fraction of energy that goes into the exhaust, and allowed us to continue our analysis of looking at where the losses occur—whether it be finite duration combustion, differences in gamma values or heat transfer.
The air handling layouts are shown on the right. In the opposed-piston two-stroke, we have a turbocharger and then the emission of a super charger, which is required for the two-stroke engine operation. A four-stroke assumes that we have a very low geometry turbine required to drive the EGR from the exhaust side of the engine to the intake side of the engine. The efficiencies of these turbo machineries of the opposed-piston two-stroke were set at 70%. The four-stroke compressor was set at 70% and the VGT turbine isentropic efficiency was set at 65%, which is common for the added complexity of the variable geometry mechanism. In addition, we added an additional constraint of achieving constant engine-out NOx emissions, which we approximated with constant maximum cylinder temperature of 1600K and constant trapped oxygen mass direction of .18. We also considered mechanical constraints of 160 bar and 200 bar peak cylinder pressures for these simulations.
So the results shown here, the blue is a four-stroke simulation with a 200 bar peak cylinder pressure constraint. The red is a four-stroke simulation with a 160 bar peak cylinder pressure constraint and the green is the opposed-piston two-stroke simulation. The simulated maximum pressure was underneath both other mechanical constraints that we dictated so only one simulation was needed.
So the results here show, in the left table we can see that the boundary conditions have now changed. This is required to achieve our maximum cylinder temperature of 1600K and trapped oxygen mass direction of .18. The maximum pressure rise rate was again limited to 5.1 bar/degree for the four-stroke 160 bar maximum cylinder pressure condition. This could not be achieved with realistic combustion duration. Instead, the combustion duration was limited to the value set for the opposed-piston two-stroke simulation.
The results show that the opposed-piston two-stroke has an indicated thermal efficiency benefit over the four-stroke simulation in both of the mechanical constraints of 160 bar and 200 bar maximum cylinder pressure. In addition, it has a lower amount of pumping work to achieve the boundary conditions necessary to achieve our NOx constraint. Compared to the 200 bar constraint, we have .06% of fuel benefit compared to the 160 bar constraint, we have 5% fuel benefit. All of this is still achieved with a lower peak cylinder pressure in either of the four-stroke simulations.
To summarize, the closed-cycle simulation was able to identify why the Achates Power opposed-piston two-stroke engine has an indicated thermal efficiency advantage over a standard four-stroke engine. The three main components of this efficiency advantage are the opposed-piston architecture, which gives us a favorable area-to-volume ratio, reducing overall heat transfer. The double firing frequency of the two-stroke cycle allows us for a reduction in the energy release premium volume and allows us to have a shorter combustion duration for a given maximum pressure rise rate constraint. Also the double firing frequency allows for cleaner operating conditions, which maintains a higher gamma during combustion and overall more efficient engine operation. When simulated over a representative speed load map, the weighted average ISFC was 9.9% lower for the opposed-piston two-stroke than a comparable four-stroke engine.
When extending the analysis to the engine system, we are able to identify that the lower peak in-cylinder temperatures of the opposed-piston two-stroke gives us an advantage in that we need a lower boost and EGR requirement to achieve a constant NOx. The system configuration for the Achates Power opposed-piston two-stroke provides us with efficient EGR pumping with use of a super charger as well as the ability to use a fixed geometry turbine and its associated higher indicated thermal efficiency, which gives us an added benefit on the pumping load required to achieve certain boundary conditions. In our simulations, at a constant approximate NOx rate, we were able to achieve 8% lower BSFC, simulated BSFC, than the comparable four-stroke engine.
The final point to make is that the assumption that we wanted to maintain the same stroke per piston and bore as the four-stroke engine pushed us to an engine architecture that may not be ideal. Further efficiency gains can be realized through an optimal engine sizing of the Achates Power two-stroke engine.