Reply by Author to C.T. Hsu

Abstract

T comments were made by Hsu. They all dispute the power output limitation of the Tornado-Type Wind Energy System proposed by Yen. * Any wind turbine output, considering incompressible flow, is limited to the product of the volume flow rate through the turbine multiplied by the difference in total pressure of the air upstream minus that downstream of the turbine. This is also called the Extended Bernouilli Equation. The first comment made is that Loth erroneously used the free wind speed V^ to compute the turbine upstream total pressure value and used P. = ^ 'upstream POO + 1/2 p V^ instead of using the exit velocity Ve. The next comment is that Loth's derivation for the maximum value of the tower exit velocity is somewhat doubtful. Loth's maximum value of Ve is based on the assmption that the angular momentum of the flow leaving the tower can never be greater than that of the flow entering the tower through the slots in the tower wall. Therefore, the higher the peak tangential velocity inside the tower the higher the angular momentum and thus the lower is the allowable axial exhaust velocity Ve. Hsu argues that this seems unreasonable and shows disagreement with Yen's test data. I attribute this disagreement to high viscous dissipation of angular momentum in the tower. Because Ve is only caused by the exhaust plume drag, I see no reason why Ve would ever be greater than the value assumed by conservation of angular momentum.