Modelling multistage expansion of compressed air in a single cylinder engine

I am unsure if my current approach is the best way to model the multistage expansion of compressed air in Simscape. I used a turbine block because I need the G branch to carry information about the reduced pressure after the first expansion into the second engine. However, the turbine block requires a nominal corrected mass flow rate input, which I believe is significantly reducing the accuracy of my system.

For clarity, the "Atmosphere Reservoir" is connected to a positive displacement compressor to simulate the compression of atmospheric air. The heat transfer from the compressed air to the CO₂ gas is modeled using a pipe with the same volume as the engine’s piston cylinder, which then feeds into the "Delivery Piping" block. The compressed air is subsequently fed into the "Rotational Mechanical Converter 2" block to simulate the additional work output generated by the atmospheric air’s presence in the piston cylinder.

[Yifeng Tang]

Do you have a diagram of the system you'd like to model? The Simscape model you attached is a bit confusing. Usually high-pressure high-temperature gas enters at the A port of a turbine, but it's connected to atmospheric condition now. A picture will definitely help.

[Kyle]

I saw my mistake so hopefully I've adjusted the simulation to accurate represently what I am hoping to accomplish is a feasibility analysis of a compressed air engine.

[Yifeng Tang]

I still think it'll be beneficial to share a diagram of the system. A hand sketch will do just fine. The current model, with the rotational convert with R port all connected together, it's hard to tell what you are trying to model and hard to provide suggestions.

[Kyle]

I attached a schematic of what I am trying to mode. I really hope it helps.

I attached the R ports from the turbine and rotational mechanical converter block to the flywheel block so that might be why it looks like I just connected them to each other

[Yifeng Tang]

Thanks for the diagram! That helps!

Some follow-up questions:

• Are the crankshafts of the two single cylinder engines rigidly connected or they are independent? If connected, are they off by an angle or fully synchronized? The answer will help me find out whether we can continue use the Rotational Mechanical Converter or switch to a Translational Mechanical Converter + Slider-Crank.
• I don't see any turbine in this diagram, but your model has turbine & compressor. Is that an effort to model certain effect in this diagram or there is indeed a turbine & compressor somewhere?

[Yifeng Tang]

And what is this symbol? Pressure relief to atm?

[Kyle]

Hello! The idea is to remove the spark plug from a single cylinder engine and use that as the inlet port. Thus the compressed air from the exhaust port of single cylinder engine 1 will be vented to the spark plug port of engine two and then the exhaust is vented to the atmosphere. Therefore in this configuration the engines are independent of each other.

The idea with using the turbine block was because I needed a gas branch which contained the pressure of the gas after the first expansion leading into the second engine and using two rotational mechanical converters would not achieve that effect.

The compressor in the lower right of the model is to model the compression of atmospheric air. My thinking is that as the compressed air is entering the engine through the spark plug that air is still free to enter the inlet port and is compressed when the piston is pushed down to BDC by the compressed air. Therefore I am attempting to model this compression of the air and its contribution of that air to the power output of the engine (it contributes heat to the incoming compressed air helping with expansion and it reduces the amount of compressed air required to enter the chamber for each cycle).

Also that is just the symbol for a thermistor.

Answer 1

[Yifeng Tang]

Hi @Kyle

I feel like the model should look similar to that diagram you have.

Single-cylinder engines can be modeled using a Mechanical Converter and Slider-Crank. The solenoid valves can be modeled using Local Restrictions. Of course, the valve timing, i.e. the signal to the AR ports, needs to be set up very carefully. See below for some concepts:

Some of notes:

1. the parameterization will require sizing information of the key components: stroke, bore, valve timing, etc. The valve timing probably will require you to set up some kind of lookup table, whose input is crank angle and output is area.
2. the initial condition needs to be set very carefully. Is the crankshaft of the two engines somehow related? any phase relation like 180 deg difference?
3. tighten the solver tolerance. Translational Mechanical Converter + Slider Crank will require a smaller tolerance value. Otherwise, after a few cycles, you may notice the volume inside the convert starts to drift.
4. Start with a reservoir at the desired regulated pressure as your gas supply, instead of high-pressure tank with a pressure reducing valve. This makes things easier at the beginning.

[Kyle]

Hello @Yifeng Tang,

I made a few changes to the model:

• I wasn’t sure why you implemented the ideal velocity source, but I forgot to mention that each engine has a flywheel, so I attached it to the C port of the slide crank instead.
• In your configuration, I wasn’t able to get the pressure drop in the exhaust of "engine 1" (modeled by the first translational mechanical converter) to properly feed into "engine 2" (modeled by the second translational mechanical converter). To address this, I added a constant volume chamber—equal to the engine’s displacement—between the two mechanical converters.

However, the pressure in the compressed air tank isn't decreasing over time as it should in reality.

I've uploaded the updated simulation with my changes, but I still can't figure out how to resolve this. Any suggestions would be appreciated.

Thanks!