Chapter 14 – distributed parameter heat exchangers — modeling, dynamics and control

Cascade control of a class of distributed parameter systems

A mathematical model is developed for heat exchangers with condensing vapors on one side which includes the effects of variations in the local film heat transfer coefficients and allows for energy accumulation and conduction in the tube wall. A numerical integration scheme for the flow forced case is presented. The model is tested against experimental steady state and transient data for a steam-water exchanger. It was necessary to modify the standard correlations of heat transfer coefficients to get a match of the overall steady state heat flux actually obtained in the apparatus. With these modified heat transfer coefficients, the model proved capable of predicting flow forced transients. These results are contrasted with transients predicted by a simple lumped parameters model employing empirically fit overall heat transfer coefficients. The lumped parameters model is shown quite adequate for predicting transient behavior under the specific conditions studied. The reasons for and limitations on the success of this very simple model are explored.



On a mis au point un modele mathematique pour les echangeurs de chaleur dans lesquels les vapeurs se condensent sur un cote; il tient compte des effets des variations dans les coefficients de transmission de la chaleur de la pellicule ainsi que de l'accumulation d'energie et de la conduction dans la paroi du tube. On presente un systeme d'integration numerique daus le cas de l'ecoulement force. On a compare les donnees du modele avec les resultats experimentaux, dans le cas de regimes permanents et transitoires pour un echangeur de vapeur et d'eau. On a dǔ modifier les correlations normales des coefficients de transmission de la chaleur pour atteindre l'equivalent du flux global de chaleur en regime permanent obtenu dans l'appareil. En utilisant les coefficients modifies de transmission de la chaleur, on a pu predire avec le modele des comportements transitoires lorsque l'ecoulement est force; ces resultats font contraste avec les comportements transitoires predits par un simple modele avec parametres assembles ou l'on utilise des coefficients de transmission globale de la chaleur qui conviennent empiriquement. Le modele ou les parametres sont assembles semble tout a fait suffisant pour predire un comportement transitoire dans des conditions specifiques. On discute les facteurs responsables du succes du modele simple precite ainsi que ses limitations.

Dynamics of convection heat exchangers

Suboptimal Direct Digital Control of a Trickle-Bed Absorption Column

For the selection of the best process variables to be used in a suboptimal feedback controller the design scheme proposed by Crosby and Durbin is further investigated and the selection procedure is improved. Furthermore, the suboptimal controllers formed by the selected variables are tested on-line on a trickle bed absorption column. The controllers used include the integral mode for the controlled variable plus the proportional mode for some selected state variables including the controlled variable. Substantial reductions in the performance index and peak overshoot are obtained by using the suboptimal controllers instead of conventional feedback controllers.

L. B. Koppel

Papers

Two-Point Practical Control of a Class of Distributed Processes