Modeling and Calculation of Air Flow in Solar Chimney Power Plant

Abstract

Solar updraft power technology is attracting interest in many regions worldwide, being a compelling prospect for producing clean and renewable energy. Very import operational parameters of solar chimney power plant (SCPP) are mass flow rate and pressure difference inside the chimney. Based on the assumption of one-dimensional flow, a comprehensive mathematical model for buoyancy driven air flow inside the SCPP is developed. It consists of system of nonlinear differential equations which describes the flow inside collector and the chimney, and algebraic equations which describes the flow in collector to chimney transition section and turbines. Validity of the model is confirmed by numerical solution of the equations for the case of Manzaneres SCPP, where good agreement is found between obtained solution and available experimental data. Additionally, nonlinear differential equations that describes the flow in the chimney are further analyzed analytically. A perturbational approach based on Rayleigh-Janzen perturbation scheme is developed, in which effects of gravity and variability of cross section are considered in first approximation, while inertia and friction are treated in second approximation. For both approximation, the exact analytical solution is found. That fact enables very good insight into the role of each important parameter that governs the flow inside the chimney, which is also elaborated. This theory also enables evaluation of chimney shape that affects the flow in a way which can be prescribed in advance.