| dc.description.abstract | Developing proper and consistent dynamic models of processes with phase changes can be challenging. Appearance and disappearance of phases result in changes in the system equations and is not known a priori. Dynamic models of such processes have to detect and adapt to these changes. In this thesis, a nonsmooth dynamic model, formulated as a DAE of index 1, of a multi-component heat exchanger is presented. The nonsmooth formulation both detects and adapts to phase changes by including a continuous extension of the phase mole fractions into the phase regime where the corresponding phase does not exist. In addition, the model is formulated in a way which allows reversal flow inside the heat exchanger. Similar to the handling of phase changes, this is done by using the nonsmooth functions min and max. The heat exchanger is modeled as a number of flash tanks with constant volume in series.
This thesis presents the development of a multiphase multicomponent flash tank model. Further a single-sided heat exchanger with given heat transfer as well as a countercurrent heat exchanger is modeled as flash tanks in series. Results from dynamic simulations of a single flash tank, one side of a heat exchanger with given heat and a countercurrent heat exchanger are presented. During the simulations the heat exchanged, the inlet flow rates and the inlet temperatures are varied. By doing so, the phases both appears and disappears during the simulations. The results show that the proposed model is both able to detect and handle phase changes. Further, a shutdown of a heat exchanger has been performed, showing the models abilities to allow reversal flow.
For simulation purposes, the model is written and implemented in Matlab. To simulate the model, an implicit Euler integrator with fixed time step is used. At the nonsmooth points, the Jacobian is not defined. As a result, the generalized derivatives are calculated through automatic differentiation and is used as a replacement for the Jacobian. The generalized derivatives are computed by using a user-defined Matlab-object. These derivatives are supplied to the Matlab-solver fsolve which is used in the Euler integrator. | |
