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.

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.

Orographic precipitation in the tropics: large-eddy simulations and theory

Recent radar and rain-gauge observations from the island of Dominica, which lies in the eastern Caribbean sea at 15 N, show a strong orographic enhancement of trade-wind precipitation. The mechanisms behind this enhancement are investigated using idealized large-eddy simulations with a realistic representation of the shallow trade-wind cumuli over the open ocean upstream of the island. The dominant mechanism is found to be the rapid growth of convection by the bulk lifting of the inhomogenous impinging flow. When rapidly lifted by the terrain, existing clouds and other moist parcels gain buoyancy relative to rising dry air because of their different adiabatic lapse rates. The resulting energetic, closely-packed convection forms precipitation readily and brings frequent heavy showers to the high terrain. Despite this strong precipitation enhancement, only a small fraction (1%) of the impinging moisture flux is lost over the island. However, an extensive rain shadow forms to the lee of Dominica due to the convective stabilization, forced descent, and wave breaking. A linear model is developed to explain the convective enhancement over the steep terrain.

Evaluation of a large-eddy model simulation of a mixed-phase altocumulus cloud using microwave radiometer, lidar and Doppler radar data

Using the Met Office large-eddy model (LEM) we simulate a mixed-phase altocumulus cloud that was observed from Chilbolton in southern England by a 94 GHz Doppler radar, a 905 nm lidar, a dual-wavelength microwave radiometer and also by four radiosondes. It is important to test and evaluate such simulations with observations, since there are significant differences between results from different cloud-resolving models for ice clouds. Simulating the Doppler radar and lidar data within the LEM allows us to compare observed and modelled quantities directly, and allows us to explore the relationships between observed and unobserved variables. For general-circulation models, which currently tend to give poor representations of mixed-phase clouds, the case shows the importance of using: (i) separate prognostic ice and liquid water, (ii) a vertical resolution that captures the thin layers of liquid water, and (iii) an accurate representation the subgrid vertical velocities that allow liquid water to form. It is shown that large-scale ascents and descents are significant for this case, and so the horizontally averaged LEM profiles are relaxed towards observed profiles to account for these. The LEM simulation then gives a reasonable. cloud, with an ice-water path approximately two thirds of that observed, with liquid water at the cloud top, as observed. However, the liquid-water cells that form in the updraughts at cloud top in the LEM have liquid-water paths (LWPs) up to half those observed, and there are too few cells, giving a mean LWP five to ten times smaller than observed. In reality, ice nucleation and fallout may deplete ice-nuclei concentrations at the cloud top, allowing more liquid water to form there, but this process is not represented in the model. Decreasing the heterogeneous nucleation rate in the LEM increased the LWP, which supports this hypothesis. The LEM captures the increase in the standard deviation in Doppler velocities (and so vertical winds) with height, but values are 1.5 to 4 times smaller than observed (although values are larger in an unforced model run, this only increases the modelled LWP by a factor of approximately two). The LEM data show that, for values larger than approximately 12 cm s(-1), the standard deviation in Doppler velocities provides an almost unbiased estimate of the standard deviation in vertical winds, but provides an overestimate for smaller values. Time-smoothing the observed Doppler velocities and modelled mass-squared-weighted fallspeeds shows that observed fallspeeds are approximately two-thirds of the modelled values. Decreasing the modelled fallspeeds to those observed increases the modelled IWC, giving an IWP 1.6 times that observed.

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.

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.