Computation of vertically averaged velocities in irregular sections of straight channels

Two new methods for vertically averaged velocity computation are presented, validated and compared with other available formulas. The first method derives from the well-known Huthoff algorithm, which is first shown to be dependent on the way the river cross section is discretized into several subsections. The second method assumes the vertically averaged longitudinal velocity to be a function only of the friction factor and of the so-called "local hydraulic radius", computed as the ratio between the integral of the elementary areas around a given vertical and the integral of the elementary solid boundaries around the same vertical. Both integrals are weighted with a linear shape function equal to zero at a distance from the integration variable which is proportional to the water depth according to an empirical coefficient β. Both formulas are validated against (1) laboratory experimental data, (2) discharge hydrographs measured in a real site, where the friction factor is estimated from an unsteady-state analysis of water levels recorded in two different river cross sections, and (3) the 3-D solution obtained using the commercial ANSYS CFX code, computing the steady-state uniform flow in a cross section of the Alzette River.

Uniform flow formulas for irregular sections

Two new methods for uniform flow discharge computation are presented, validated and compared with other available formulas. The first method derives from the well-known Huthoff algorithm, which is first shown to be dependent on the way the river cross-section is discretized into several sub-sections. The second method assumes the vertically averaged longitudinal velocity to be a function only of the friction factor and of the so-called "local hydraulic radius", computed as the ratio between the integral of the elementary areas around a given vertical and the integral of the elementary solid boundaries around the same vertical. Both integrals are weighted with a linear shape function, equal to zero at a distance from the integration variable which is proportional to the water depth according to an empirical coefficient β. Both formulas are validated against (1) laboratory experimental data, (2) discharge hydrographs measured in a real site, where the friction factor is estimated from an unsteady-state analysis of water levels recorded in two different river cross sections, (3) the 3-D solution obtained using the commercial ANSYS CFX code, computing the steady state uniform flow in a short reach of a prismatic channel, with known water level in the downstream section.

Flow Control and Unsteady-State Analysis on Thermal Performance of Solar Air Collectors

Promotion of the use of renewable energy, such as solar heat, for space heating and drying crops and wood is desired to prevent global warming. High-temperature collection of heat by air collectors producing as much as 50°C in winter for space heating and about 80°C in summer for exchanging heat to circulating water for hot water supply would be appropriate applications. In this study, first, a flow control system for constant outlet temperature was installed in a hot air supply system to examine the feasibility of the control system. After experiments, it was found that the control system could function satisfactory. Second, an unsteady-state analysis was made to predict the thermal performance of a flat-plate collector under a given condition of variable flow rate. The analytical model became simple by the assumptions that the heat capacity of the air in the collector and heat conduction in the flow direction through the air and the materials of the collector could be neglected. The maximum differences in outlet temperature and collector efficiency for constant flow rate between the analysis and the experiment were 1.8°C and 6% of the collector efficiency, respectively, except in the beginning of experiments. The biggest difference in the collector efficiency was 30% at 3:00 P.M., which occurred at the end of one of the experiments. The analytical results generally agreed well with the experimental results even when the flow rate and solar radiation changed greatly as time went on. Transient effects are important to predict outlet temperature for variable solar radiation intensity, wind speed, and flow rate.