An experimental and analytical investigation on a water-coupled microchannel gas cooler was conducted in this study. With a relatively low critical temperature (31.1°C/89.9°F) and pressure (73.7 bar/1070 psi), CO2 is a supercritical fluid on the high side of a vapor compression cycle under warmer ambient conditions. This results in a non-isothermal heat rejection through the component known as the gas cooler. The large temperature glide in the heating of tap water matches well with the supercritical temperature glide of carbon dioxide. Unlike in a condensation process, here the non isothermal heat rejection can be used to advantage in a counterflow gas cooler, in which the water outlet temperature can rise to the desired high value. This minimizes temperature pinch and keeps gas cooler size economical. The focus of this thesis was to develop and experimentally validate a heat transfer model for a water-coupled microchannel gas cooler. The heat exchanger was tested in a small capacity experimental heat pump system. The heat pump system was designed to simulate conditions for heating domestic tap water to a usable temperature. A matrix of test points varying refrigerant inlet temperature, refrigerant mass flow rate, water inlet temperature and water volumetric flow rate were used to characterize the performance of the heat exchanger and validate the model.

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Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. Both methods are designed for generalised state space systems---the former for multiple-input-multiple-output (MIMO) systems from finite element discretisations and the latter for single-input-single-output (SISO) systems---and applied to relevant test problems. The dual rational Arnoldi method is designed for generating real reduced order systems using complex shift points and stabilising a system that happens to be unstable. For the rational Krylov method, a forward error in the recursion and an estimate of the error in the approximation of the transfer function are studie. A stability analysis of a heat exchanger model is made. The model is a nonlinear partial differential-algebraic equation (PDAE). Its well-posedness and how to prescribe boundary data is investigated through analysis of a linearised PDAE and numerical experiments on a nonlinear DAE. Four methods for generating reduced order models are applied to the nonlinear DAE and compared: a Krylov based moment matching method, balanced truncation, Galerkin projection onto a proper orthogonal decomposition (POD) basis, and a lumping method. / QC 20101013

<p>Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. Both methods are designed for generalised state space systems---the former for multiple-input-multiple-output (MIMO) systems from finite element discretisations and the latter for single-input-single-output (SISO) systems---and applied to relevant test problems. The dual rational Arnoldi method is designed for generating real reduced order systems using complex shift points and stabilising a system that happens to be unstable. For the rational Krylov method, a forward error in the recursion and an estimate of the error in the approximation of the transfer function are studie.</p><p>A stability analysis of a heat exchanger model is made. The model is a nonlinear partial differential-algebraic equation (PDAE). Its well-posedness and how to prescribe boundary data is investigated through analysis of a linearised PDAE and numerical experiments on a nonlinear DAE. Four methods for generating reduced order models are applied to the nonlinear DAE and compared: a Krylov based moment matching method, balanced truncation, Galerkin projection onto a proper orthogonal decomposition (POD) basis, and a lumping method.</p>