Large-eddy simulation of wind flows over complex terrains for wind energy applications

Wind energy has obtained outstanding expectations due to risks of global warming and nuclear energy production plant accidents. Nowadays, wind farms are often constructed in areas of complex terrain. A potential wind farm location must have the site thoroughly surveyed and the wind climatology analyzed before installing any hardware. Therefore, modeling of Atmospheric Boundary Layer (ABL) flows over complex terrains containing, e.g. hills, forest, and lakes is of great interest in wind energy applications, as it can help in locating and optimizing the wind farms. Numerical modeling of wind flows using Computational Fluid Dynamics (CFD) has become a popular technique during the last few decades. Due to the inherent flow variability and large-scale unsteadiness typical in ABL flows in general and especially over complex terrains, the flow can be difficult to be predicted accurately enough by using the Reynolds-Averaged Navier-Stokes equations (RANS). Large- Eddy Simulation (LES) resolves the largest and thus most important turbulent eddies and models only the small-scale motions which are more universal than the large eddies and thus easier to model. Therefore, LES is expected to be more suitable for this kind of simulations although it is computationally more expensive than the RANS approach. With the fast development of computers and open-source CFD software during the recent years, the application of LES toward atmospheric flow is becoming increasingly common nowadays. The aim of the work is to simulate atmospheric flows over realistic and complex terrains by means of LES. Evaluation of potential in-land wind park locations will be the main application for these simulations. Development of the LES methodology to simulate the atmospheric flows over realistic terrains is reported in the thesis. The work also aims at validating the LES methodology at a real scale. In the thesis, LES are carried out for flow problems ranging from basic channel flows to real atmospheric flows over one of the most recent real-life complex terrain problems, the Bolund hill. All the simulations reported in the thesis are carried out using a new OpenFOAM® -based LES solver. The solver uses the 4th order time-accurate Runge-Kutta scheme and a fractional step method. Moreover, development of the LES methodology includes special attention to two boundary conditions: the upstream (inflow) and wall boundary conditions. The upstream boundary condition is generated by using the so-called recycling technique, in which the instantaneous flow properties are sampled on aplane downstream of the inlet and mapped back to the inlet at each time step. This technique develops the upstream boundary-layer flow together with the inflow turbulence without using any precursor simulation and thus within a single computational domain. The roughness of the terrain surface is modeled by implementing a new wall function into OpenFOAM® during the thesis work. Both, the recycling method and the newly implemented wall function, are validated for the channel flows at relatively high Reynolds number before applying them to the atmospheric flow applications. After validating the LES model over simple flows, the simulations are carried out for atmospheric boundary-layer flows over two types of hills: first, two-dimensional wind-tunnel hill profiles and second, the Bolund hill located in Roskilde Fjord, Denmark. For the twodimensional wind-tunnel hills, the study focuses on the overall flow behavior as a function of the hill slope. Moreover, the simulations are repeated using another wall function suitable for smooth surfaces, which already existed in OpenFOAM® , in order to study the sensitivity of the flow to the surface roughness in ABL flows. The simulated results obtained using the two wall functions are compared against the wind-tunnel measurements. It is shown that LES using the implemented wall function produces overall satisfactory results on the turbulent flow over the two-dimensional hills. The prediction of the flow separation and reattachment-length for the steeper hill is closer to the measurements than the other numerical studies reported in the past for the same hill geometry. The field measurement campaign performed over the Bolund hill provides the most recent field-experiment dataset for the mean flow and the turbulence properties. A number of research groups have simulated the wind flows over the Bolund hill. Due to the challenging features of the hill such as the almost vertical hill slope, it is considered as an ideal experimental test case for validating micro-scale CFD models for wind energy applications. In this work, the simulated results obtained for two wind directions are compared against the field measurements. It is shown that the present LES can reproduce the complex turbulent wind flow structures over a complicated terrain such as the Bolund hill. Especially, the present LES results show the best prediction of the turbulent kinetic energy with an average error of 24.1%, which is a 43% smaller than any other model results reported in the past for the Bolund case. Finally, the validated LES methodology is demonstrated to simulate the wind flow over the existing Muukko wind farm located in South-Eastern Finland. The simulation is carried out only for one wind direction and the results on the instantaneous and time-averaged wind speeds are briefly reported. The demonstration case is followed by discussions on the practical aspects of LES for the wind resource assessment over a realistic inland wind farm.

Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

Large-eddy simulation of heat transfer downstream of a backward-facing step

Large-eddy simulation is used to predict heat transfer in the separated and reattached flow regions downstream of a backward-facing step. Simulations were carried out at a Reynolds number of 28 000 (based on the step height and the upstream centreline velocity) with a channel expansion ratio of 1.25. The Prandtl number was 0.71. Two subgrid-scale models were tested, namely the dynamic eddy-viscosity, eddy-diffusivity model and the dynamic mixed model. Both models showed good overall agreement with available experimental data. The simulations indicated that the peak in heat-transfer coefficient occurs slightly upstream of the mean reattachment location, in agreement with experimental data. The results of these simulations have been analysed to discover the mechanisms that cause this phenomenon. The peak in heat-transfer coefficient shows a direct correlation with the peak in wall shear-stress fluctuations. It is conjectured that the peak in these fluctuations is caused by an impingement mechanism, in which large eddies, originating in the shear layer, impact the wall just upstream of the mean reattachment location. These eddies cause a 'downwash', which increases the local heat-transfer coefficient by bringing cold fluid from above the shear layer towards the wall.

Large eddy simulation of shock boundary layer interaction control using micro-vortex generators

The performance of supersonic engine inlets and external aerodynamic surfaces can be critically affected by shock wave / boundary layer interactions (SBLIs), whose severe adverse pressure gradients can cause boundary layer separation. Currently such problems are avoided primarily through the use of boundary layer bleed/suction which can be a source of significant performance degradation. This study investigates a novel type of flow control device called micro-vortex generators (µVGs) which may offer similar control benefits without the bleed penalties. µVGs have the ability to alter the near-wall structure of compressible turbulent boundary layers to provide increased mixing of high speed fluid which improves the boundary layer health when subjected to flow disturbance. Due to their small size,µVGs are embedded in the boundary layer which provide reduced drag compared to the traditional vortex generators while they are cost-effective, physically robust and do not require a power source. To examine the potential of µVGs, a detailed experimental and computational study of micro-ramps in a supersonic boundary layer at Mach 3 subjected to an oblique shock was undertaken. The experiments employed a flat plate boundary layer with an impinging oblique shock with downstream total pressure measurements. The moderate Reynolds number of 3,800 based on displacement thickness allowed the computations to use Large Eddy Simulations without the subgrid stress model (LES-nSGS). The LES predictions indicated that the shock changes the structure of the turbulent eddies and the primary vortices generated from the micro-ramp. Furthermore, they generally reproduced the experimentally obtained mean velocity profiles, unlike similarly-resolved RANS computations. The experiments and the LES results indicate that the micro-ramps, whose height is h≈0.5δ, can significantly reduce boundary layer thickness and improve downstream boundary layer health as measured by the incompressible shape factor, H. Regions directly behind the ramp centerline tended to have increased boundary layer thickness indicating the significant three-dimensionality of the flow field. Compared to baseline sizes, smaller micro-ramps yielded improved total pressure recovery. Moving the smaller ramps closer to the shock interaction also reduced the displacement thickness and the separated area. This effect is attributed to decreased wave drag and the closer proximity of the vortex pairs to the wall. In the second part of the study, various types of µVGs are investigated including micro-ramps and micro-vanes. The results showed that vortices generated from µVGs can partially eliminate shock induced flow separation and can continue to entrain high momentum flux for boundary layer recovery downstream. The micro-ramps resulted in thinner downstream displacement thickness in comparison to the micro-vanes. However, the strength of the streamwise vorticity for the micro-ramps decayed faster due to dissipation especially after the shock interaction. In addition, the close spanwise distance between each vortex for the ramp geometry causes the vortex cores to move upwards from the wall due to induced upwash effects. Micro-vanes, on the other hand, yielded an increased spanwise spacing of the streamwise vortices at the point of formation. This resulted in streamwise vortices staying closer to the wall with less circulation decay, and the reduction in overall flow separation is attributed to these effects. Two hybrid concepts, named “thick-vane” and “split-ramp”, were also studied where the former is a vane with side supports and the latter has a uniform spacing along the centerline of the baseline ramp. These geometries behaved similar to the micro-vanes in terms of the streamwise vorticity and the ability to reduce flow separation, but are more physically robust than the thin vanes. Next, Mach number effect on flow past the micro-ramps (h~0.5δ) are examined in a supersonic boundary layer at M=1.4, 2.2 and 3.0, but with no shock waves present. The LES results indicate that micro-ramps have a greater impact at lower Mach number near the device but its influence decays faster than that for the higher Mach number cases. This may be due to the additional dissipation caused by the primary vortices with smaller effective diameter at the lower Mach number such that their coherency is easily lost causing the streamwise vorticity and the turbulent kinetic energy to decay quickly. The normal distance between the vortex core and the wall had similar growth indicating weak correlation with the Mach number; however, the spanwise distance between the two counter-rotating cores further increases with lower Mach number. Finally, various µVGs which include micro-ramp, split-ramp and a new hybrid concept “ramped-vane” are investigated under normal shock conditions at Mach number of 1.3. In particular, the ramped-vane was studied extensively by varying its size, interior spacing of the device and streamwise position respect to the shock. The ramped-vane provided increased vorticity compared to the micro-ramp and the split-ramp. This significantly reduced the separation length downstream of the device centerline where a larger ramped-vane with increased trailing edge gap yielded a fully attached flow at the centerline of separation region. The results from coarse-resolution LES studies show that the larger ramped-vane provided the most reductions in the turbulent kinetic energy and pressure fluctuation compared to other devices downstream of the shock. Additional benefits include negligible drag while the reductions in displacement thickness and shape factor were seen compared to other devices. Increased wall shear stress and pressure recovery were found with the larger ramped-vane in the baseline resolution LES studies which also gave decreased amplitudes of the pressure fluctuations downstream of the shock.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

CFD simulations of hydrocyclones with an air core - Comparison between large eddy simulations and a second moment closure

CFD simulations of the 75 mm, hydrocyclone of Hsieh (1988) have been conducted using Fluent TM. The simulations used 3-dimensional body fitted grids. The simulations were two phase simulations where the air core was resolved using the mixture (Manninen et al., 1996) and VOF (Hirt and Nichols, 1981) models. Velocity predictions from large eddy simulations (LES), using the Smagorinsky-Lilly sub grid scale model (Smagorinsky, 1963; Lilly, 1966) and RANS simulations using the differential Reynolds stress turbulence model (Launder et al., 1975) were compared with Hsieh's experimental velocity data. The LES simulations gave very good agreement with Hsieh's data but required very fine grids to predict the velocities correctly in the bottom of the apex. The DRSM/RANS simulations under predicted tangential velocities, and there was little difference between the velocity predictions using the linear (Launder, 1989) and quadratic (Speziale et al., 1991) pressure strain models. Velocity predictions using the DRSM turbulence model and the linear pressure strain model could be improved by adjusting the pressure strain model constants.

Subfilter-scale Stress Modelling for Large Eddy Simulations

A subfilter-scale (SFS) stress model is developed for large-eddy simulations (LES) and is tested on various benchmark problems in both wall-resolved and wall-modelled LES. The basic ingredients of the proposed model are the model length-scale, and the model parameter. The model length-scale is defined as a fraction of the integral scale of the flow, decoupled from the grid. The portion of the resolved scales (LES resolution) appears as a user-defined model parameter, an advantage that the user decides the LES resolution. The model parameter is determined based on a measure of LES resolution, the SFS activity. The user decides a value for the SFS activity (based on the affordable computational budget and expected accuracy), and the model parameter is calculated dynamically. Depending on how the SFS activity is enforced, two SFS models are proposed. In one approach the user assigns the global (volume averaged) contribution of SFS to the transport (global model), while in the second model (local model), SFS activity is decided locally (locally averaged). The models are tested on isotropic turbulence, channel flow, backward-facing step and separating boundary layer. In wall-resolved LES, both global and local models perform quite accurately. Due to their near-wall behaviour, they result in accurate prediction of the flow on coarse grids. The backward-facing step also highlights the advantage of decoupling the model length-scale from the mesh. Despite the sharply refined grid near the step, the proposed SFS models yield a smooth, while physically consistent filter-width distribution, which minimizes errors when grid discontinuity is present. Finally the model application is extended to wall-modelled LES and is tested on channel flow and separating boundary layer. Given the coarse resolution used in wall-modelled LES, near the wall most of the eddies become SFS and SFS activity is required to be locally increased. The results are in very good agreement with the data for the channel. Errors in the prediction of separation and reattachment are observed in the separated flow, that are somewhat improved with some modifications to the wall-layer model.