Mathematical modeling of heat exchanger with liquid flow for tube with polyzone finning

Abstract

The finning of heat-transmitting surfaces is widely used in technics for heat-exchange surface increasing. The finning forms are rather various. The finning not only increases a heat-exchange surface, but also renders the big influence at stream hydrodynamics, and thus at heat-emission factor. The more favourable finning forms (so-called polyzonal and herring-bone) have been developed during experiments with various finning methods of fuel element claddings. The lacks of herring-bone surfaces are the high labour input and the cost price of manufacturing. These lacks can be removed due to the 3D-printing technology, since the advantages of 3D-printers using are the decrease of the cost price of production manufacturing, the reduction of its occurrence terms at the market, the modeling of objects of any form and complexity, the speed and high accuracy of manufacturing, the possibility of use of the various materials maintaining high temperature, intensive mechanical loadings and influence of harmful chemical substances. It is necessary to create the computer 3D-model of desirable object during preparation for 3D-printing. The analysis of classical representations has shown that their practical application is limited or demands significant efforts for construction of models of complex geometrical objects. One of the most perspective is the functional representation based at the using of implicit mathematical functions language with constructive tools of the R-functions theory developed by academician V.L. Rvachev. The developed techniques of construction of the equations of various finning surfaces at the R-functions theory basis and their subsequent 3D-realization are shown. The research of hydrodynamical and temperature fields at polyzonal finning of fuel element cladding are resulted. The consecutive construction of the longitudinal, polyzonal and herring-bone finnings  equations of the fuel element claddings allows to track the algorithm complication process due to corresponding superpositions in the initial equation which kind does not change. It is one of examples of advantage of the geometrical objects' analytical identification realized with the R-functions help. The analytical description of the designed objects enables to use symbolic geometrical parameters, complicated superposition of functions consequently allowing to change the design elements of these objects. The results of the velocity and temperature fields research for various values of twisting parameter, testifying that the warming up in the intercostal zone increases with increase in value of twisting parameter, are shown.