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# Efficient Numerical Methods for Reynolds Averaged Navier-Stokes Equations of Flow over Topography and Application

Efficient Numerical Methods for Reynolds Averaged Navier-Stokes Equations of Flow over Topography and Application

 Title: Efficient Numerical Methods for Reynolds Averaged Navier-Stokes Equations of Flow over Topography and Application Author: Yu, Xiao Abstract: Recently, wind energy has been used widely as a complement to the common used energy resources such as oil, coal, and natural gas. Fossil fuels can generate heavy pollution and release greenhouse gases, which are recognized as the main cause of the global warming. As a result, green and renewable energy technologies, such as wind energy and solar energy, are highly recommended nowadays. In order to build the wind farms and make the wind energy assessments, wind flow over topography has been studied intensively in wind energy industry. In my thesis, we first improve an under-relaxed iteration scheme for the steady-state RANS equations of neutrally stratified airflow over complex topography. The NLMSFD scheme failed on predicting flow over terrains with a relatively high slope and we improve this iteration scheme to a much higher maximum slope. In the second part, we develop the efficient characteristic finite volume method (CFV) to solve the time-dependent RANS equations of flow over topography with various surface roughnesses. In viscous flow, the convective term plays a more important role than the diffusive term, especially for the turbulent flow with a high Reynolds number. The CFV scheme is developed by combining the characteristic method and the finite volume method. It treats the convective term efficiently. Numerical experiments of solving the time-dependent RANS equations with k-epsilon closure show the advantages of the accuracy, efficiency and stability of the method. In the last part, the CFV method is further applied to model wind flow and turbine wakes of large wind farms. We simulate the wind turbine wakes behind a cluster of wind farms which take into account the roughness change on the topography. We propose to consider RANS models with the Coriolis effect in modelling wind flows under a large scale due to the rotation of Earth. The wind flows within and downwind of the wind farms are predicted numerically. Simulation results on the Horns Rev wind farm are compared with field measurements. Subject: Mathematics Keywords: Wind EnergyReynolds Averaged Navier-Stokes EquationsNumerical AnalysisCharacteristic Finite Volume method Type: Electronic Thesis or Dissertation Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests. URI: http://hdl.handle.net/10315/27639 Supervisor: Liang, Dong Degree: PhD - Doctor of Philosophy Program: Mathematics & Statistics Exam date: 2014-01-24 Publish on: 2014-07-09