Towards improved RANS/k - epsilon modelling of turbulent incompressible flows for wind energy applications

The advancement of wind energy as a viable and competitive alternative to traditional sources is dependent on the development of advanced modelling techniques to decrease both the cost of energy and the cost uncertainty. Of special importance in this effort is the improvement of wind energy assessment tools. While so-called linearized models have dominated this field in the past, models based on the Reynolds-Averaged Navier-Stokes (RANS) equations are becoming more popular, especially for difficult sites involving complex terrain and multiple wakes. Although RANS modelling is implicitly more appropriate for complex flows than its lower-order derivatives, refinements are required to better adapt it to the needs of the sector and improve accuracy. With that in mind, this dissertation strives to make fundamental improvements in the use of RANS-based models for the simulation of atmospheric and wake flows.;Despite common use of the RANS equations with k - epsilon closure for simulations involving the atmospheric boundary layer, challenges remain in its implementation---even for the simplest case involving horizontally homogeneous conditions. Most notably, the distributions of turbulent kinetic energy and its dissipation rate have proved difficult to maintain near solid boundaries, particularly in wind energy and wind engineering applications where the near-wall grid is relatively coarse. In the first study of this dissertation, the origin of these errors is investigated and it is shown that by applying appropriate discretization schemes in conjunction with the Richards and Hoxey boundary conditions, truly invariant profiles of all flow properties can be obtained on such grids. Furthermore, based on this finding, a wall treatment for practical grids is proposed that could be implemented for non-homogeneous conditions.;The second study focuses on the physical modelling of atmospheric flows. The limited-lengthscale k - epsilon model proposed by Apsley and Castro for the atmospheric boundary layer is revisited with special attention given to its predictions in the constant-stress surface layer. The original model proposes a modification to the length-scale-governing epsilon equation that ensures consistency with surface-layer scaling in the limit of small ℓm/ℓmax (where m is the mixing length and max its maximum) and yet imposes a limit on ℓm as ℓm/ℓ max approaches one. However, within the equilibrium surface layer and for moderate values of z/ℓmax , the predicted profiles of velocity, mixing length, and dissipation rate using the Apsley and Castro model do not coincide with analytical solutions. In view of this, a general epsilon transport equation is derived herein in terms of an arbitrary desired mixing-length expression that ensures exact agreement with corresponding analytical solutions for both neutral and stable stability. From this result, a new expression for the closure coefficient Cepsilon3 can be inferred that shows it tends to a constant only for limiting values of z/L (where z is the height above ground and L is the Monin-Obukhov length); and, furthermore, that the values of Cepsilon3 for z/L → 0 and z /L → infinity differ by a factor of exactly two.;Wake modelling also plays an important role in wind energy assessment. These models must be reasonably accurate---to minimize financial risk---and yet economical so that many layouts can be tested within reasonable time. While numerous such models have been proposed, an especially attractive approach is based on the solution of the RANS equations with two-equation turbulence closure and an actuator disk representation of the rotor. The validity of this approach and its inherent limitations however remain to be fully understood. In the final study, detailed wind tunnel measurements in the wake of a porous disk (with similar aerodynamic properties as a turbine rotor) immersed in a uniform flow are compared with the predictions of several turbulence closures, including a newly proposed one. Agreement with measurements is found to be excellent for all models. This unexpected outcome appears to derive from a fundamental difference in the turbulent nature of the homogeneous wind tunnel flow and that of the atmospheric boundary layer. This result suggests that the largest source of uncertainty in turbulence modelling remains the production term and leads to a discussion on similarity requirements for wind tunnel testing.