Development of the Gibson method—Unsteady friction

The Gibson method is commonly used for discharge measurements at hydropower plants to estimate turbine efficiency. This paper presents a detailed numerical study of this method in order to estimate the physical quantities of importance in the method. Additionally, a modification of the Gibson method is proposed that adds temporal acceleration to the calculation procedure. The modification is numerically and experimentally validated for Reynolds numbers ranging from ≈0.6×106 to 1.7×106. Using both simulations and experimental data, it is shown that the modified method, the unsteady Gibson method, can reduce the flow estimation error by as much as 0.4% compared to the standard Gibson method. Depending on the conditions, the unsteady Gibson method corrects, or partly corrects, both under- and overestimations of the flow rate that are calculated when using the standard Gibson method.

► The Gibson method is modeled numerically and validated.
► The different physical terms in the Gibson method are investigated.
► A new calculation procedure of the Gibson method is proposed.
► Flow accuracy is enhanced by up to 0.4% compared to the initial Gibson method.