Pressure gradients in Stirling engines

Abstract

Because of pressure gradients due to the flow across the machine, pressures are not equal in the expansion and the compression cylinder, and the indicator diagrams are not the same as if pressure were uniform. Pressure gradients result from the viscous stresses and from the inertia of the fluid. The effect of inertia can be divided into acoustics, which is unsteady, and acceleration of the flow, which is present even at time scales at which acoustics is insignificant. The only irreversibility directly associated with pressure gradients is the loss due to true viscous friction, while inertia effects are reversible. We analyze the magnitude of the various components to the pressure gradient; we discuss their effects and we idenm the different situations that may arise. We show that the energy equation can be written in a form consistent with the concept of a uniform stagnation enthalpy flux leaking through the regenerator. The viscous losses in the regenerator have little effect on the enthalpy flux, but they increase the entropy flux from expansion to compression space. As a result, while in each cylinder the heat flux balances the work flux and the regenerator enthalpy, the ratio of the expansion and compression work is no longer equal to the Carnot ratio. In contrast, while inertia of the fluid does sect the indicator diagrams, it has no effect on efficiency.