Modelling of wind farms using computational fluid dynamics (CFD) resolving the flow field around each wind turbine's blades on a moving computational grid is still too costly and time consuming in terms of computational capacity and effort. One strategy is to use sub-models for the wind turbines, and sub-grid models for turbulence production and dissipation to model the turbulent viscosity accurately enough to handle interaction of wakes in wind farms.A wind turbine sub-model, based on the Blade Momentum Theory, see Hansen (2008), has been implemented in an in-house CFD code, see Hallanger et al. (2002). The tangential and normal reaction forces from the wind turbine blades are distributed on the control volumes (CVs) at the wind turbine rotor location as sources in the conservation equations of momentum. The classical k − ε turbulence model of Launder and Spalding (1972) is implemented with sub-grid turbulence (SGT) model, see Sha and Launder (1979) and Sand and Salvesen (1994).Steady state CFD simulations were compared with flow and turbulence measurements in the wake of a model scale wind turbine, see Krogstad and Eriksen (2011). The simulated results compared best with experiments when stalling (boundary layer separation on the wind turbine blades) did not occur. The SGT model did improve turbulence level in the wake but seems to smear the wake flow structure.It should be noted that the simulations are carried out steady state not including flow oscillations caused by vortex shedding from tower and blades as they were in the experiments. Further improvement of the simulated velocity defect and turbulence level seems to rely on better parameter estimation to the SGT model, improvements to the SGT model, and possibly transient-instead of steady state simulations.

The problem investigated is the break of a high‐pressure pipeline carrying natural single‐phase gas which may condensate (retrograde) when the pressure drops. Single‐phase non‐ideal gas is assumed using a general‐ ized equation of state. Taking advantage of the choked massflow condition, the break is split into a pipe flow problem and a dispersion flow problem, both solved using a finite difference control volume scheme. The transient flow field from the pipeline break location is expanded analytically, using an approximation of the governing equations, until ambient pressure is reached and matched to the corresponding gas dispersion flow field using as subgrid model a jet box with a time‐varying equivalent nozzle area as an internal boundary of the dispersion domain. The turbulence models used for the pipe and dispersion flow fields are an empirical model of Reichard and the k–ϵ model for buoyant flow respectively. The pipe flow simulations indicate that the flow from the pipeline might include dispersed condensate which will affect quantitatively the mass flow rate from the pipeline and qualitatively the gas dispersion if the condensate rains out. The transient dispersion simulation shows that an entrainment flow field develops and mixes supersaturated gas with ambient warmer air to an unsaturated mixture. Because of the inertia of the ambient air, it takes time to develop the entrainment flow field. As a consequence of this and the decay of the mass flow with time, the lower flammability limit of the gas–air mixture reaches its most remote downstream position relatively early in the simulation (about 15 s) and withdraws closer to the break location.

The problem investigated is the stability of a flame anchored by recirculation within a channel with a cavity, acting as a two-dimensional approximation to a gas turbine combustion chamber. This is related to experiments of Vaneveld, Hom & Oppenheim (1982). The hypothesis studied is that hydrodynamic oscillations within the cavity can lead to flashback.The method used is a semi-analytical-numerical technique where the conservation equations for enthalpy and fuel fraction are represented by the low-Mach-number combustion model of Ghoniem, Chorin & Oppenheim (1982). Burnt and unburnt gas are treated as incompressible fluids where the reaction zone acts as a source for volume expansion. The flame is modelled by a Lagrangian technique using a simple line interface calculation algorithm.The turbulent flow field is determined using conformal mapping theory and the hybrid random vortex method. The vorticity generation takes place at the walls to achieve no slip, and is influenced by boundary-layer separation. To avoid locating the separation points a priori the numerical viscous sublayer is extended continuously past the corners, and their singularities are in effect cut off by using locally a corner rounding technique within the conformal mapping.The computed unsteady boundary-layer separation and reattachment of the non-reacting flow field agrees with unsteady boundary-layer theory. On the basis of the numerical simulations of the flame stability problem it is concluded that hydrodynamic oscillations within the cavity, combined with unsteady boundary-layer separation and reattachment can cause a flashback.

The problem investigated is the stability of a flame anchored by recirculation within a channel with a cavity, acting as a two-dimensional approximation to a gas turbine combustion chamber. This is related to experiments of Vaneveld, Hom and Oppenheim (1982). The hypothesis studied is that hydrodynamic oscillations within the cavity can lead to flashback

The frictional damping of the rolling motion of a circular cylinder is nonlinear. Although negligible at full scale, it may be important in model scale. The damping force is calculated using Fourier analysis of the frictional force on the surface of a cylinder with a vertical axis executing simple harmonic oscillations about its axis. Calculations of the velocity profile in the fluid near the oscillating cylinder, needed for the calculations of the frictional force, are carried out in the laminar and turbulent case using the boundary-layer approximation. For Reynolds shear stress modeling, the mixing length concept of Prandtl and an analogy to van Driest's model are used. The resulting nonlinear partial differential equation of the parabolic type is solved numerically using the Du Fort-Frankel explicit finite-difference scheme.