Kim Sørensen

Solving differential-algebraic equation systems by means of index reduction methodology

Abstract With the overall goal of optimizing the design and operation of steam boilers, a model for optimizing the dynamic performance has been developed. The model has been developed as three sub-models that are integrated into an overall model for the complete boiler. Each of the sub-models consist of a number of differential equations and algebraic equations—a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers . For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper, it is shown how the equation system, by means of an index reduction methodology , can be reduced to a system of ordinary differential equations—ODEs.

Parametric CFD Analysis to Study the Influence of Fin Geometry on the Performance of a Fin and Tube Heat Exchanger

Heat transfer and pressure loss characteristics of a fin and tube heat exchanger are numerically investigated based on parametric fin geometry. The cross-flow type heat exchanger with circular tubes and rectangular fin profile is selected as a reference design. The fin geometry is varied using a design aspect ratio as a variable parameter in a range of 0.1-1.0 to predict the impact on overall performance of the heat exchanger. In this paper, geometric profiles with a constant thickness of fin base are studied. Threedimensional, steady state CFD model is developed using commercially available Multiphysics software COMSOL v5.2. The numerical results are obtained for Reynolds number in a range from 5000 to 13000 and verified with the experimentally developed correlations. Dimensionless performance parameters such as Nusselt number, Euler number, efficiency index, and area-goodness factor are determined. The best performed geometric fin profile based on the higher heat transfer and lower pressure loss is predicted. The study provides insights into the impact of fin geometry on the heat transfer performance which help escalate the understanding of heat exchanger designing and manufacturing at a minimum cost.