Guidelines for Opposed-Piston Two-Stroke Engine Sizing in Commercial Vehicle Applications
When sizing the Achates Power opposed-piston two-stroke engine, a number of key tradeoffs need to be identified and quantified and understood to converge on the best solution possible. What’s shown here is a map of total engine displacement, from small to large and stroke-to-bore values, from small to large. These two things need to be specified in order to converge on an engine size. So, some key tradeoffs that we can see first are indicated thermal efficiency tends to increase as you increase engine displacement. You have a more favorable area-to-volume ratio and you can operate at leaner operating conditions. The piston heat flux is highest at small engine displacements with large stroke-to-bore ratios, which means small pistons, and decreases as you go to larger displacements and smaller stroke-to-bore ratios.
The friction work decreases as you decrease your total engine size because you now have smaller top total ring length and smaller mean piston speeds. The durability would tend to increase as we increase the total engine displacement because we have lower peak cylinder pressures and temperatures for the constant power condition. NOx emissions would follow the same trend as durability in that lower peak cylinder temperatures would lead to lower NOx emissions as you increase your engine displacement. Of course, the engine size decreases as you decrease the engine displacement. Each individual direction of the engine size changes as you change the stroke-to-bore ratio. As you go to smaller stroke-to-bore ratios, your stroke decreases so the size in the cylinder axis direction decreases. Conversely, as you increase the stroke-to-bore ratio, you now decrease the size in directions normal to the cylinder access. And, finally, the thing that’s specific to opposed-piston two-strokes is scavenging efficiency and that tends to increase as we increase our stroke-to-bore ratio. So that’s also a consideration that needs to be taken into account.
There are a lot of engine configurations that could conceivably work. What we want to do is figure out what’s the best combination of all these factors as we size the engine for a replacement of a four-stroke engine. The total number of configurations that could be considered for our replacement opposed-piston two-stroke engine is very large, so you need to set up some guidelines to bracket the initial selection of the engine size.
So the first guideline that has been proposed is on friction and the metric is a friction index, which allows us to numerically compare the parameters that are important to friction without having to do a detailed analysis to quantify exactly what the friction is. The friction index is only meant to provide trends in the friction work and not meant to be quantitative. The friction index relates the opposed-piston two-stroke parameters to a representative four-stroke engine as a means of comparison. So the values that are used are the mean piston speed multiplied by the total ring length, and this is indicative of the friction that originates in the power cylinder. And, because it’s assumed that two-thirds of the mechanism of friction originates in the power cylinder, this product is multiplied by two-thirds. The second component is the friction that originates in the bearings, which is multiplied by one-third because it’s assumed that one-third of the friction originates in the bearings, and the value is a mechanism force multiplied by the number of bearings. The mechanism force is the mean effect of pressure evaluated with the trap volume multiplied by the area of the piston. The trap volume is used in this analysis because a portion of the cylinder content is sacrificed to scavenging for the two-stroke engine. So for a fair comparison between an opposed-piston two stroke and a four-stroke engine, we need to use the mean effect of pressure on a trap volume basis, where the trap volume is roughly 80% of the total cylinder volume. And the guideline for this friction index is to have a value less than 1.
The second guideline is piston cooling. Piston cooling is especially challenging on a two-stroke engine because now we don’t have the gas exchange cycle that allows the incoming air to cool the piston from the top side. We have to provide all the cooling from the bottom side. So state-of-the-art piston cooling capabilities can provide a guideline of roughly 1 watt per meter squared of projected energy, assuming that 8% of the brake power is transferred through each piston.
So the final guideline we want to use here is the brake mean effect of pressure. It’s a good surrogate for maximum pressures and maximum temperatures experienced in-cylinder. So engines with low BMEP have low maximum in-cylinder pressure and temperature, which are good for durability (in terms of the pressure) and good for NOx emissions (in terms of the temperature). But, the high BMEPs are associated with smaller engine size, so there’s a tradeoff that needs to occur there. A valid guideline in this case is to keep the mean effect of pressure in the trap basis equivalent to that of a four-stroke engine. So, what we assume is that the trap volume of the opposed-piston two-stroke is roughly 80% of the displaced volume, the remainder of which is sacrificed to scavenging. In the four-stroke engine, roughly 100% of the displaced volume is available during the closed cycle. So, when you do the analysis, we can see that the BMEP of the opposed-piston two-stroke, as a guideline, should be roughly 80% of the BMEP in the four-stroke.
Using these guidelines, we can evaluate where a desired operating range would be for a preliminary engine sizing. Shown here is a map for a medium-duty application, where the Achates Power opposed-piston two-stroke engine is replacing a four-stroke engine that has 6 cylinders, 107 mm bore, 124 mm stroke and operates at 325 hp at 2400 rpm. So the initial proposed opposed-piston two-stroke has 3 cylinders and operates at the same engine speed of 2400 rpm.
Shown in the graph are colors corresponding to where the guidelines have been exceeded. The yellow shows where the heat flux and BMEP guidelines have been exceeded, the green shows where the BMEP guideline has been exceeded, the orange is where the heat flux alone has been exceeded, the red is where the friction index and heat flux have been exceeded, and the purple is where the friction index alone has been exceeded. So the end result is the white range where it would be our desired operating range in an initial sizing exercise. For this medium-duty application, it would be desired to operate between roughly 4 and 6 liters total engine displacement, the stroke-to-bore value depending on the engine displacement that is selected.
We could also operate our engine with 4 cylinders, instead of 3, at the same operating speed. As this map shows, when you increase the cylinder count, friction now becomes more of a concern as the friction index guideline has pushed us to lower displacements. The guidelines don’t mean that we can’t operate our engine with those displacements that exceed that guideline, it just means that we need to be very careful about operating there and recognize the fact that friction might be a challenge to achieve our efficiency goals.
We could also select to run a 3 cylinder at a higher engine speed to achieve the same total engine power. This also restricts our guideline operating range to very small displacements and very small stroke-to-bore ratios. The speed has a large effect on the friction. So in this case, we would likely have to sacrifice a little bit on the friction side in order to operate at such a high engine speed.
The same comparison can be made for a heavy-duty application where the reference four-stroke engine, in this case, is a 6 cylinder with a bore of 131 mm, stroke of 158, for a total engine displacement of 12.8 liters. The engine peak power for this application is 475 hp at a speed of 1800 rpm. So, if we were to size a replacement opposed-piston two-stroke engine to achieve these same operating conditions, we would initially select a 3 cylinder to operate the same engine operating speed. The range of engine displacements that achieve all of our guidelines goes from roughly 8 liters up to roughly 11 liters. So, to size an engine, we would want to be in that range, at least preliminarily. The stroke-to-bore ratio will be dictated based on the initial displacement selection.
If we were then to decide to go to a 4 cylinder based on the same engine operating speed that brings friction more into play and the larger displacement sizes and pushes our desired range to lower displacements. Again, it doesn’t mean we can’t operate at larger engine displacements, it means that we would need to pay close attention to the friction of the engine to make sure that that isn’t more than what we desire.
You could also select to operate the opposed-piston two-stroke engine at 3600 rpm with a 3 cylinder count engine. In doing so, you increase the amount of friction that you’re going to experience with this engine configuration because of the higher engine speed, and it limits the desired range to one cell at a very low displacement value. So, in order to operate at a higher engine speed, you’re going to sacrifice likely on the friction side.
So, to summarize, the architecture selection for the opposed-piston two-stroke engine is a challenging exercise of detailing a lot of tradeoffs that occur in various components of the engine operation. What’s included in this presentation are only three of those factors: friction, piston cooling and BMEP, or a surrogate for NOx emissions and durability. Factors that weren’t included, but also need to be considered, are the indicated thermal efficiency, the pumping work requirements (which is in a two-stroke application very much related to the ability to scavenge the engine efficiently), other requirements over the speed load map, whether it be at a peak torque or the most efficient operating point in the speed load map—all those things need to be taken into consideration along with air handling, emissions and after-treatment, oil control and durability, package weight, package size, cost and manufacturability—all those things need to be taken into account.
So, at Achates Power, we have done detailed analysis of all these factors that allow us to quickly determine the optimum engine architecture subject to all these various constraints.