Impacts on Head Loss in a Pumpless Solar Thermal Heater Calculated by Hardy-Cross Methodology

This paper studies the impacts on head loss in a pumpless solar thermal heater using Hardy-Cross within a three-tube configuration for solar thermal vacuum tubes. The three-tube configuration acts as a heat exchanger component for a pumpless solar thermal heater. The design intent of the pumpless solar thermal air heater is to collect solar energy through a tube configuration in which water located in the inner tubes collects heat from solar radiation. The water then passes heat through conduction to the pipes, which pass heat through convection to the air located in the transparent outer vacuum tubes. The heat transferred to the air causes a pressure differential in the air stream that allows the solar thermal heater to operate without a pump for the air. Regardless, the water flow through the inner tubes requires a pump; this paper explores the potential head loss (and ways to minimize it) through the water tube configuration to determine the required pumping power for the water loop. To describe the setup: the inner tube configuration involved in this study includes three vertical tubes that serve as the inner component. From the inlet, water flows vertically down the center tube to a well at the bottom. From the well, the water divides between the two outer tubes and flows upwards. The water exits after the two outer tubes each pass through an elbow fitting and are joined by a tee. This configuration combines series flow (through the center tube) and parallel flow (through the outer tubes). A Python program code is developed using the Hardy-Cross method to calculate head loss across a set of varied parameters.  The parameters include roughness, length, and diameters of the outer and inner pipes, which are varied against a base case scenario to determine their impacts on total head loss from the inlet of the system to the outlet of the system. The paper will assess the pumping power required for various sets of roughness, length, and diameters of the pipes in order to explore ways to minimize total head loss. As an example, given 0.01 cubic feet per second inlet flow rate, ¼ inch outer pipes, 0.4 inch inner pipes, 2-foot long pipes, and a Hazen-Williams Coefficient of 140 for all pipes, the total head loss from the inlet to the outlet of the system is calculated to be 11.7 feet. This paper will discuss a wide range of scenario to provide general guidance for designing heat exchanger for solar thermal vacuum tube-based heaters.