Optimisation of an open rectangular cavity receiver and recuperator used in a small-scale solar thermal Brayton cycle with thermal losses

The successful design and operation of a small-scale solar thermal Brayton cycle depend on the successful understanding of the losses or irreversibilities in the system which are mainly due to heat transfer and fluid friction. The small-scale open solar thermal Brayton cycle uses air as working fluid which is heated in a cavity receiver which captures the solar radiation focused onto it from a parabolic concentrator. The goal of this work is to determine the optimum receiver tube diameter and counter-flow recuperator geometries of a small-scale open and direct solar thermal Brayton cycle with 4.8 m diameter parabolic dish, so that the net power output of the system is a maximum. In this work an updated receiver model is used. An open rectangular cavity receiver is used instead of a spherical receiver as was used in previous work. SolTrace is used to determine the solar heat flux rates on the receiver inner walls. The temperatures and net absorbed heat rates at different parts of the receiver tube are found by solving multiple equations using numerical methods. The model describing the heat loss rate from the recuperator to the environment is also updated in this work. Five different turbo-machines with different operating points are considered in this study. The results show the optimum geometries of the proposed system. It is shown that for the 4.8 m diameter solar dish with 0.25 x 0.25 m receiver aperture area, a receiver tube diameter of 83.3 mm will give the best results. NOMENCLATURE a Receiver aperture side length or recuperator channel width, m b Recuperator channel height, m A Area, m B Constant BSR Blade speed ratio c1 Constant used in linear equation c2 Constant used in linear equation cp0 Constant pressure specific heat, J/kgK Cr Capacity ratio D Diameter, m E Constant F View factor h Heat transfer coefficient, W/mK h Specific enthalpy, J/kg H Recuperator height, m k Thermal conductivity, W/mK k Gas constant L Length of recuperator, m m1 Slope of linear equation m2 Slope of linear equation m& System mass flow rate, kg/s M Mass of recuperator, kg MT Micro-turbine number n Receiver tube section number along the length of tube n Number of recuperator flow channels in one direction N Number of tube sections N Speed of micro-turbine shaft, rpm NTU Number of transfer units P Pressure, Pa r Pressure ratio R Gas constant, J/kgK R Thermal resistance, K/W Q& Heat transfer rate, W * Q& Rate of available solar heat at receiver cavity, W loss Q & Rate of heat loss, W net Q & Net heat transfer rate, W gen S & Entropy generation rate, W/K t Thickness, m T Temperature, K T* Apparent exergy-source sun temperature, K U Overall heat transfer coefficient, W/mK w Wind factor W& Power, W V Velocity, m/s X Dimensionless position Z Height, m