The other loss accounted for by the software is Adiabatic Loss. This loss results from a high compression ratio — (maximum-engine- volume)/(minimum-engine-volume), which forces the gas temperature in the expansion and compression space (during parts of the cycle) to exceed the heater and cooler temperature, respectively. This results in heat being pumped out of the heater and cooler due to the positive temperature difference. This lowers thermal efficiency. Note that the Adiabatic Loss is inherently captured by the equations of the program, and doesn’t need to be accounted for explicitly – so it isn’t accounted for explicitly.

The other losses such as mechanical friction are not accounted for since they can only be accurately calculated with experimentation.

Here’s a section from the software manual which explains engine losses:

In a real engine there are friction losses, such as in the mechanical drive, linkages,
and between the piston/displacer seals and cylinder wall. This directly reduces
engine power. These friction losses can only be accurately calculated with
experimental measurements. They are not accounted for in the program.

• There are also thermodynamic losses such as from hysteresis effects, due to compression of the working gas in the expansion and compression space, causing it to heat up to a temperature higher than that of the cylinder wall, during parts of the cycle. As a result, heat is lost to the environment. This loss mechanism can be minimized, by insulating the outside walls of the expansion and compression space. In the program it is assumed that the expansion and compression space are adiabatic, which means that the working gas does not lose heat through the cylinder walls. This is a good assumption for large high-pressure engines.

• Other losses include: working gas leaking out of the engine, heat transfer inefficiency from heat source to heater tubes, and other thermodynamic inefficiencies due to heat loss in other parts of the engine. For instance, there are heat transfer losses that occur as a result of heat flowing along the engine wall from the hot side to the cold side. There are heating losses that occur between the gap of the displacer and the cylinder wall, due to the temperature difference between the expansion and compression space. No provision is made in the program to account for these losses. For the most part they can only be accurately calculated by experimental measurements, and then minimized by proper material selection and design.

• As mentioned, regenerator inefficiency is one of the major sources of thermal loss. But the other thermal losses mentioned above can (in combination) further reduce thermal efficiency by several percent.

• This program is meant to optimize the design based on the intrinsic engine thermodynamics, which models the main physical phenomenon occurring inside the engine. For the most part, the losses mentioned in the previous paragraph affect the thermal efficiency only (i.e. by reducing it). This means that extra heat energy input is required to compensate for these losses. In other words, the engine power itself is not affected, provided there is sufficient heat energy available to compensate for the thermal losses.

• It is very important to know that (with the exception of hysteresis losses and leakage of working gas), accounting for all the above-mentioned losses would not affect the thermodynamics and physics inside the engine. So for optimization purposes they can be excluded from the model. In other words, their exclusion will not affect the number of tubes and (proportional) regenerator volume required for maximum power.

• One way to significantly improve thermal efficiency in the design is to improve the heat transfer efficiency from heat source to heater tubes. A common loss mechanism in this regard is heat loss to the surrounding environment (e.g. warm exhaust from a burner). A way to minimize this loss is with an air Preheater. Using the exhaust stream, a Preheater heats the air before it enters the combustion chamber, and more of the heat energy of the fuel is used. This is also more economical since it reduces fuel consumption. In addition, you can also minimize heat loss by placing an insulated enclosure around the heat source.

• A well-designed heat source, such as burner with air Preheater, can have a heat transfer efficiency of 90%. This means that 10% of the heat is lost to the environment. This loss further reduces thermal efficiency by several percent. For example, an engine operating at 40% thermal efficiency with (theoretically) perfect heat transfer from the heat source, would run at 36% efficiency with 90% heat transfer efficiency (0.90×0.40).

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