Optimal design of the heater of a Stirling engine coupled with a fluidized bed combustor
The idea of using heat generated by combustion as a source for a Stirling engine dates back to the early achievements of Stirling Engines (SE). The original idea is to place the hot head of the engine as much as possible in direct contact of the flame generated by combustion, identifying the flame with the region of highest temperature and therefore as that which favors thermal exchange between the hot combustion gases and the working fluid of the engine. The problems that concern the use of biomass in combination with a Stirling engine are concentrated on the transfer heat from the combustion gases to the work fluid of the SE. The temperature must be high, to obtain acceptable specific power and efficiency, and the heat exchanger must be designed so that the problems of fouling are minimized.
This work investigates the possibility of inserting the head of a Stirling engine, more specifically the elements of the hot side heat exchanger, in direct contact with the sand of a Fluidized Bed Combustor (FBC). This choice is suggested by the expected much larger heat exchange coefficients between the multiphase fluidized bed medium and the surface of the heat exchanger, as compared with a heat exchanger located in the stream of hot flue gases. Moreover, the mechanical action exerted by the fluidized solid particles is expected to avoid the fouling problem usually encountered for the presence of many impurities in exhaust gases of a biomass combustion process. A mathematical model, which couples a model of the fluidized bed with a model of the Stirling engine, has been developed and used to determine the optimal working conditions with a proper design sizing of the Stirling hot side heat exchanger. The Pareto multi-objective optimization approach is adopted, to conduct a search of all non-dominated compromise solutions, in the space of the decision variables. The problem is solved by using modeFRONTIER. The design of the heat exchanger of the heater should maximize both mechanical power and global efficiency upon appropriate geometric and operational constraints. The decision variables considered are the geometrical parameters of the heat exchanger of the heater (number, diameter and average length of the tubes) and operating parameters (fuel mass flow rate, engine speed). The results have shown that the heater placed inside the fluidized bed leads to better performance than with a classic gas-gas heat exchanger. Moreover, a more compact engine head is able to enhance the global efficiency since it favors a decrease of the losses in the dead space of the Stirling while the heat flux is not affected.