<div>Gas-turbine engines use film cooling to actively cool turbine components and keep thermal loads on the materials at acceptable levels for structural integrity and service life. The turbulent mixing between the film-cooling jet and the crossflow decreases the coolant temperature, which reduces the cooling performance. This turbulent mixing is sensitive to parameters such as density ratio (DR), blowing ratio (BR), velocity ratio (VR), and momentum-flux ratio (MR) and understanding the effects of these parameters on the turbulent mixing is critical for improving film cooling. </div><div><br></div><div>This research seeks to improve understanding by using large-eddy simulation (LES) as a tool to analyze the turbulence of film cooling. With this knowledge it is possible evaluate more fundamental turbulence modeling assumptions utilized by Reynolds-Averaged Navier-Stokes (RANS) approaches as they apply to film cooling. This analysis can provide insight regarding how to improve turbulence models.</div><div><br></div><div>The film-cooling problem studied involves the cooling of a flat plate, where the cooling jets issued from a plenum through one row of circular holes of diameter $D$ and length 4.7$D$ that are inclined at 35$^\circ$ relative to the plate. Parameters studied include BR = 0.5 - 1.3, DR = 1.1 - 2.1, VR = 0.3 - 0.9, and MR = 0.16 - 0.9. For LES, two different boundary layers upstream of the film-cooling hole were investigated - one in which a laminar boundary layer was tripped to become turbulent from near the leading edge of the flat plate, and another in which a mean turbulent BL is prescribed directly without any superimposed turbulent fluctuations. For RANS, two different turbulence models were investigated - realizable $k$-$\epsilon$ and $k$-$\omega$ shear-stress-transport (SST). The wall-resolved LES solutions generated are extensively verified and validated using analytical, DNS, and experimental measurements to ensure high quality. </div><div><br></div><div>LES results obtained show that having an upstream boundary layer that does not have turbulent fluctuations enhances the cooling effectiveness significantly at low VRs when compared to an upstream boundary layer that resolved the turbulent fluctuations. However, these differences diminish at higher VRs. Instantaneous flow reveals a bifurcation in the jet vorticity as it exits the hole at low VRs, one branch forming the shear-layer vortex, while the other forms the counter-rotating vortex pair. At higher VRs, the shear layer vorticity is found to reverse direction, changing the nature of the turbulence and the heat transfer. Results obtained also show the strength and structure of the turbulence in the film-cooling jet to be strongly correlated to VR. </div><div><br></div><div>RANS results obtained show the turbulent and thermal structure of the jets predicted by the two RANS models to differ considerably. However, both models are consistent in underpredicting the spread of the film-cooling jet. The counter-rotating vortex pair dominates the interaction of the jet and crossflow in the near-wall region, and neither RANS model could predict the strength and structure of this interaction. The gradient-diffusion and Boussinesq hypotheses were evaluated by using the LES data. Comparing LES and RANS results shows that $k$-$\epsilon$ tends to overpredict eddy viscosity, while SST tends to underpredict the eddy viscosity. Additionally, both models predict very low values of eddy viscosity near the wall which leads to incorrect Reynolds stresses. While regions of counter-gradient diffusion and stress-strain misalignment were identified in the near-wall region, further above the wall, the jet behaved according to the hypotheses.</div><div><br></div><div>The turbulence scaling when VR is fixed at 0.46 and 0.63 was investigated. The LES results show that separation and spreading of the film-cooling jet increase as BR, DR, and MR increase while VR remains constant. For a given VR, the LES predicts an absolute difference between the minimum adiabatic effectiveness of the lowest and highest MRs to be 2 to 5 times greater than those predicted by RANS. This is because RANS with either model cannot respond appropriately to changes in MR. However, RANS can correctly predict that adiabatic effectiveness decreases as VR increases. The LES results show the turbulent kinetic energy and Reynolds stresses near the film-cooling hole to change considerably with MRs at a constant VR, while turbulent heat flux changes negligibly. This suggests that while improved turbulence models for heat flux can improve RANS’ prediction of spreading, capturing trends, however, requires improved modeling of the Reynolds stresses.</div>

This Thesis aims to assess the reliability of turbulence models in predicting the flow fields around the horizontal axis wind turbine (HAWT) rotor blades and also to improve our understanding of the aerodynamics of the flow field around the blades. The simulations are validated against data from the NREL/NASA Phase VI wind turbine experiments. The simulations encompass the use of fourteen turbulence models including low-and high-Reynolds-number, linear and non-linear eddy-viscosity models and Reynolds stress models. The numerical procedure is based on the finite-volume discretization of the 3D unsteady Reynolds-Averaged Navier-Stokes equations in an inertial reference frame with the sliding mesh technique to follow the motion of the rotor blades. Comparisons of power coefficient, normalised thrust, local surface pressure coefficients (CP) and the radial variation of the section average of normal force coefficients with published experimental data over a range of tip-speed ratios, lead to the identification of the turbulence models that can reliably reproduce the values of the key performance indicators. The main contributions of this study are in establishing which RANS models can produce quantitatively reliable simulations of wind turbine flows and in presenting the flow evolution over a range of operating conditions. At low (relative to the blade tip speed) wind speeds the flow over the blade surfaces remains attached and all RANS models return the correct values of key performance coefficients. At higher wind speeds there is circumferential flow separation over the downwind surface of the blade, which eventually spreads over the entire surface, Moreover, within the separation bubble the centrifugal force pumps the flow outwards, which at the higher wind speeds suppresses the formation of the classical tip vortices. More refined RANS models which do not rely on the linear effective viscosity approximation generally lead to more reliable predictions over this range of higher wind speeds. In particular the Gibson-Launder version of the Reynolds stress transport model and the high-Re versions of the Lien et al non-linear k-ε produce consistently reliable simulations over the entire range of wind speeds. By contrast some popular linear effective viscosity models, like the SST (k-ω) and the v^2-f, perform the poorest over this complex flow range. Finally all RANS models are also able to predict the dominant (lowest) frequency of the pressure fluctuations and the non-linear effective viscosity models, the Launder and Shima version of RSM and the SST are also able to return some of the higher frequencies measured.

Diploma thesis deals with numerical simulations of an air flow in a water cooled charge air cooler (WCAC), specifically with pressure drops in inlet/outlet chamber. The simulations have been performed in a proprietary software Star-CCM+. Physical phenomena have been solved by the Reynolds-averaged Navier-Stokes (RANS) equations and consequently a matrix of pressure drops for miscellaneous variations of chamber's geometry and the initial flow conditions has been created. Based on the CFD results, dependence between calculated pressure drops and changing parameters has been analyzed and finally a 1D solver has been developed and implemented into a software OpenModelica.

Cette thèse s'inscrit dans le cadre des énergies renouvelables au sein du programme HARVEST centré sur le développement d'un concept d'hydrolienne dérivé des turbines Darrieus et Gorlov. L'ajout d'un dispositif appelé carénage à la turbine permet à celle-ci d'extraire une portion de l'énergie cinétique du courant plus grande. Toutefois ce dernier peut favoriser la cavitation qui nuit à la turbine. Parmi les différents axes du programme, les travaux de thèse se situent dans cette problématique. En régime subcavitant et cavitant, l'analyse de l'hydrolienne a été menée suivant une approche numérique et expérimentale. Pour ce faire deux outils ont été mis en place. Du coté expérimental, le tunnel hydrodynamique du LEGI a été équipé d'une balance qui donne la mesure instantanée des forces et du couple qui s'exercent sur la turbine. Du coté numérique, les efforts ont été orientés sur l'amélioration et le développement du code de calcul universitaire, CAVKA. L'utilisation intensive de ces deux moyens, couplée à des modèles théoriques, a permis de mettre en évidence d'une part le fonctionnement de la turbine libre ou carénée et, d'autre part, les limites de fonctionnement vis-à-vis de la cavitation.

Computational fluid dynamics (CFD) has been widely applied to simulate turbulent flows in an urban environment. The two basic methodologies in CFD that have been applied here are a Reynolds-averaged Navier-Stokes (RANS) modeling and a large-eddy simulation (LES). The nature of the flow in a built-up urban area consisting of an arbitrary aggregation of buildings is dominated by unsteady large-scale turbulent structures. Recognizing that RANS is unable to correctly capture these turbulent structures while LES is associated with high computational costs, a hybrid RANS/LES methodology that combines the computational efficiency of RANS with the predictive accuracy of LES can be a promising simulation approach for the application to urban flows. In the non-zonal approach of hybrid RANS/LES methodology, a single generalized turbulence model is used in the entire computational domain. This model can function as a RANS turbulence closure model or as a LES subgrid scale model, depending on the local grid resolution or flow properties. A variant of non-zonal approaches, referred as partially resolved numerical simulation (PRNS) in this study, obtains the generalized turbulence model from the rescaling of a conventional RANS model through the incorporation of a resolution control function (F_R). The resolution control function F_R is used to characterize the degree of modeling required to represent the unresolved scales of motion. A new generalized functional form for F_R in PRNS is proposed in this thesis. The predictive performance of PRNS is compared with unsteady RANS (URANS) and LES computations, for a plane channel flow, and for fully-developed and developing flows over a matrix of cubes resembling a group of buildings. It is demonstrated that PRNS behaves similarly to LES, in terms of the predictions of the mean flow and turbulence, but outperforms URANS in general. This indicates PRNS is a promising approach for the simulation of complex turbulent flows in an urban environment.

This master’s thesis was provided by the Swedish Defence Research Agency, FOI. The task is to test several RANS (Reynolds-averaged Navier-Stokes) models on two different case geometries and compare the results with LES and experimental data. The first is two dimensional, constructed for flow separation at a sharp edge. The second is three dimensional and flow separation occurs at a smooth surface. The models tested are implemented in the open source CFD (Computational Fluid Dynamics) program, OpenFOAM. OpenFOAM uses the finite volume method and the SIMPLE algorithm as solution procedure. The main flow features evaluated is the shape, position and size of the flow separation. Most of the models tested have problems describing the complex dynamics of flow separation in these particular cases. In addition to the simulations, the RANS k-epsilon turbulence model is presented and the RANS equations and the equation for the turbulent kinetic energy are derived from the Navier-Stokes equations. The theory behind wall functions is described and these equations together with the equations in the k-epsilon model are compared with the equations implemented in OpenFOAM.

This thesis has been a part of Forsmarks Kraftgrupp AB's evaluation of a turbulence model used in simulation of turbulent flow called PRNS (Partially Resolved Numerical Simulation). This model has promising properties and may be of use in saving computational resources. The purpose of this thesis was to analyze this model and compare it with industrially applied models such as k-omega SST and LES (Large Eddy Simulations). PRNS works as a hybrid of the k-omega SST and DNS (Direct Numerical Simulation) where a constant, RCP (Resolution Control Parameter) with a value between 0 and 1 are selected. This constant is then used in the calculations and determines the behavior of the simulation. When RCP is set to zero the equation are the same as for a DNS simulation and when RCP is set to one the equations for k-omega SST is solved. In this report four different PRNS models have been used, three where RCP was given a constant value (0.1, 0.4 and 0.6). In the fourth model RCP is calculated from the flow field variables The models have been compared to an experiment from 2008 and simulations have been made to resemble the experiment. In the experiment a Particle Image Velocimeter (PIV) was used as method of measurement. From the experimental report data such as velocity (U), turbulent kinetic energy (k) and standard deviation (URMS) have been obtained and have formed the basis for comparison. The models have been simulated in two different software programs: OpenFOAM and Fluent. The data have thereafter been post processed in the software programs MatLab and ParaView, to be compared with experimental data. The results of the simulations have shown that PRNS models generally show a good accordance with experimental data. In particular, PRNS models with constant RCP have shown good results, however, there are some discrepancies. The PRNS model with varying RCP has in most cases showed the largest deviation from experimental data but also a deviation from the other models, including the reference models. Due to the design of the mesh (coarse) further evaluation of the PRNS models will be needed. First, simulate with a finer mesh, but also more complex geometries should be simulated in order to sort out PRNS strengths and weaknesses and thus determine if the model can be used in the daily work at Forsmarks Kraftgrupp AB.

Computational fluid dynamics (CFD) has been widely applied to simulate turbulent flows in an urban environment. The two basic methodologies in CFD that have been applied here are a Reynolds-averaged Navier-Stokes (RANS) modeling and a large-eddy simulation (LES). The nature of the flow in a built-up urban area consisting of an arbitrary aggregation of buildings is dominated by unsteady large-scale turbulent structures. Recognizing that RANS is unable to correctly capture these turbulent structures while LES is associated with high computational costs, a hybrid RANS/LES methodology that combines the computational efficiency of RANS with the predictive accuracy of LES can be a promising simulation approach for the application to urban flows. In the non-zonal approach of hybrid RANS/LES methodology, a single generalized turbulence model is used in the entire computational domain. This model can function as a RANS turbulence closure model or as a LES subgrid scale model, depending on the local grid resolution or flow properties. A variant of non-zonal approaches, referred as partially resolved numerical simulation (PRNS) in this study, obtains the generalized turbulence model from the rescaling of a conventional RANS model through the incorporation of a resolution control function (F_R). The resolution control function F_R is used to characterize the degree of modeling required to represent the unresolved scales of motion. A new generalized functional form for F_R in PRNS is proposed in this thesis. The predictive performance of PRNS is compared with unsteady RANS (URANS) and LES computations, for a plane channel flow, and for fully-developed and developing flows over a matrix of cubes resembling a group of buildings. It is demonstrated that PRNS behaves similarly to LES, in terms of the predictions of the mean flow and turbulence, but outperforms URANS in general. This indicates PRNS is a promising approach for the simulation of complex turbulent flows in an urban environment.

The work presented in this dissertation concerns continued development, validation and verification of the partially averaged Navier-Stokes (PANS) method - a variable resolution closure model for turbulence. Linear eddy viscosity models (LEVM), which are popular because of their simplicity and affordability in terms of computational cost have fundamental deficiencies and cannot be trusted to accurately represent turbulence in realistic complex flows. The more high fidelity approaches such as large eddy simulations (LES) and direct numerical simulations (DNS) are out of realm of engineering applicability because of their high requirements in computing power. PANS, a variable resolution approach considered in this study, lies between LEVM and LES in terms of computational cost and is designed to prudently utilize the available computing power to improve accuracy. This dissertation presents the various studies performed to characterize the PANS fluctuations and extend the model for use in various wall bounded flows. The road map towards our goal includes: (i) Comparing a-priori and a-posteriori eddy viscosity values to establish whether PANS is capable of producing the pre-specified level of reduction. (ii) Investigating the scaling of PANS fluctuations for different levels of prescribed resolution and establishing if the fluctuations abide by known turbulence scaling laws. (iii) Extending PANS to k-w formulation which is better suited for wall-bounded shear flows, and (iv) Modifying the present LEVM to yield reasonable behavior in the rapid distortion limit where the turbulence is elastic in nature which ultimately affects PANS performance. Results reported in this dissertation illustrate that the PANS closure yields reliable and predictable reduction in the modeled viscosity. The accuracy of the simulations improve as the effective damping is reduced by lowering the specified viscosity providing credibility to the PANS method as a bridging model that performs as intended.

A numerical panel method based on the potential flow theory has been refined and applied to the simulations of steady and unsteady cavitating flows inside water-jet pumps. The potential flow inside the water-jet is solved simultaneously in order to take the interaction of all geometries (blades, hub and casing) into account. The integral equation and boundary conditions for the water-jet problem are formulated and solved by distributing constant dipoles and sources on blades, hub and shroud surfaces, and constant dipoles in the trailing wake sheets behind the rotor (or stator) blades. The interaction between the rotor and stator is carried out based on an iterative procedure by considering the circumferentially averaged velocities induced on each one by the other. The present numerical scheme is coupled with a 2-D axisymmetric version of the Reynolds Averaged Navier-Stokes (RANS) solver to evaluate the pressure rise on the shroud and simulate viscous flow fields inside the pump. A tip gap model based on a 2-D orifice equation derived from Bernoulli’s obstruction theory is implemented in the present method to analyze the clearance effect between the blade tip and the shroud inner wall in a global sense. The reduction of the flow from losses in the orifice can be defined in terms of an empirically determined discharge coefficient (CQ) representing the relationship between the flow rate and the pressure difference across the gap because of the viscous effect in the tip gap region. The simulations of the rotor/stator interaction, the prediction of partial and super cavitation on the rotor blade and their effects on the hydrodynamic performance including the thrust/torque breakdown of a water-jet pump are presented. The predicted results, including the power coefficient (P*), head coefficient (H*), pump efficiency (η), thrust and torque coefficients (KT and KQ), as well as the cavity patterns are compared and validated against the experimental data from a series of on the ONR AxWJ-2 pump at NSWCCD. / text