The balance effects of momentum deficit and thrust in cumulative wake models

Abstract

Due to the intricacies of wind wake transition, it is necessary to estimate both the atmospheric boundary layer (ABL) contributions as well as the momentum deficit and thrust balancing. Wake superposition models such as Linear and Katic produce inconsistent wake predictions that are empirically derived. Designing an explicit cumulative model based on the momentum deficit and thrust budget analysis is not feasible. We use the analytical and machine learning approach to predict and correct inconsistencies between momentum deficits and thrust. The Mass Flow Conservation Superposition (MFCS) model is derived using the Linear Momentum equation, and the Mass Flow and Thrust Conservation Superposition (MFTCS) model is derived by fitting the Gaussian Process Regression (GPR) model to Large Eddy Simulation (LES) data. Noticeably from our results, the MFCS underestimates the thrust magnitude and the wake recovery rates. The MFTCS model based on the GPR model fit correctly estimates the momentum deficit and thrust balance. The GPR model assesses the smoothness and differentiability of the LES data to predict wake recovery. The MFTCS outperforms Katic and MFCS results but is more accurate than the LES data based on the goodness of fit criteria.