Modern Control Engineering
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In the study of vapor compression cycle, momentum balance equation is often ignored in the heat exchanger model. In this paper, we investigate the effect of the momentum balance through a systematic study of the open loop stability of a heat exchanger. We consider 1-D fluid flow in a pipe in four cases of increasing complexity the most general case corresponds to the heat exchanger model: 1. incompressible flow without heat transfer; 2. incompressible flow with heat transfer; 3. compressible flow without heat transfer; 4. compressible flow with heat transfer. Among the three balance equations, mass, momentum, and energy, case 1 involves only the momentum, case 2 involves both momentum and energy, case 3 involves mass and momentum, and case 4 requires all three equations. It is shown that in cases 1, which corresponding to the incompressible flow without heat input, the system is lumped and always stable, and in cases 2, 3 and 4, the system is stable if and only if the equilibrium flow velocity is sufficiently high. Finite difference approximation and linearization of the dynamic models are used for local stability evaluation in case 3 and 4. The overall cycle analysis as well as a simulation example is also included. The result of this study now forms the foundation to investigate the open loop stability and closed loop control design for vapor compression cycles used in HVAC and electronic cooling systems.