(see graph above): 180° to 270°, pseudo-isothermal expansion. The expansion space is heated externally, and the gas undergoes near-isothermal expansion. 270° to 0°, near-constant-volume (or near-isometric or isochoric) heat removal. The gas is passed through the regenerator, thus cooling the gas, and transferring heat to the regenerator for use in the next cycle. 0° to 90°, pseudo-isothermal compression. The compression space is intercooled, so the gas undergoes near-isothermal compression. 90° to 180°, near-constant-volume (near-isometric or isochoric) heat addition. The compressed air flows back through the regenerator and picks up heat on the way to the heated expansion space. With the exception of a Stirling thermoacoustic engine, none of the gas particles actually flow through the complete cycle. So this approach is not amenable to further analysis of the cycle. However, it provides an overview and indicates the cycle work. Particle/mass motion Figure 2 shows the streaklines which indicate how gas flows through a real Stirling engine. The vertical colored lines delineate the volumes of the engine. From left to right, they are: the volume swept by the expansion (power) piston, the clearance volume (which prevents the piston from contacting the hot heat exchanger), the heater, the regenerator, the cooler, the cooler clearance volume, and the compression volume swept by the compression piston. Heat-exchanger pressure drop Also referred to as "pumping losses", the pressure drops shown in Figure 3 are caused by viscous flow through the heat exchangers. The red line represents the heater, green is the regenerator, and blue is the cooler. To properly design the heat exchangers, multivariate optimization is required to obtain sufficient heat transfer with acceptable flow losses. The flow losses shown here are relatively low, and they are barely visible in the following image, which will show the overall pressure variations in the cycle. Pressure versus crank angle Figure 4 shows results from an "adiabatic simulation" with non-ideal heat exchangers. Note that the pressure drop across the regenerator is very low compared to the overall pressure variation in the cycle. Temperature versus crank angle Figure 5 illustrates the adiabatic properties of a real heat exchanger. The straight lines represent the temperatures of the solid portion of the heat exchanger, and the curves are the gas temperatures of the respective spaces. The gas temperature fluctuations are caused by the effects of compression and expansion in the engine, together with non-ideal heat exchangers which have a limited rate