Tidal energy has the potential to make a valuable contribution to meeting future global energy demands. Converting the energy of tidal streams into useful electricity can be achieved with use of tidal-stream turbines, such as the Momentum-Reversal and Lift (MRL) device. This turbine utilises a blade motion where each blade rotates continuously through 180° about its own axis for every 360° of turbine rotation. The aim of the design is to harness both useful lift and drag forces when rotating at relatively slow speeds. However, no detailed analysis of the time-varying fluid dynamic behaviour of the turbine has been undertaken before this study. The primary aim of this study has been to further understanding of the performance characteristics of the MRL turbine design, focusing on a laboratory- scale device. The study has analysed both the time-averaged and time-varying torque and power output, and the associated fluid-dynamic structure of flow through the turbine. A secondary aim was to generate data that can be used by other researchers who focus on the wake generation of the MRL tidal turbine. This study has used OpenFOAM to develop a time-dependent RANS CFD model and investigate the performance of the MRL turbine. To allow validation of the CFD model, experiments were firstly undertaken in order to measure the cycle-mean torque and power output of the turbine when operating in a laboratory flume. Measurements of the flow velocity at a number of upstream and downstream locations were also taken, in order to allow comparison with the CFD simulation results, where appropriate. Also, in order to allow validation of the CFD approach against time-varying data, the motion of the turbine blades was analysed. This allowed suitable experimental test cases to be identified from the literature and CFD simulation results have been compared to these. A detailed sensitivity analysis of the MRL turbine CFD model was carried out, followed by two-dimensional simulations of the turbine involving a single-blade and three-blades. Three-dimensional simulations were also undertaken, with results compared to the gathered experimental results. Finally, the effect of varying turbine solidity was investigated with the CFD model. Overall it was found that the CFD simulations successfully reproduce the rotational speed at which maximum torque and power are developed. However, the three-dimensional simulations significantly over-predict the magnitude of results in comparison to the gathered experimental results. Regardless, the two- and three-dimensional simulations have allowed detailed analysis of the flow behaviour and structures that are responsible for the development of blade forces and turbine torque.

Artificial intelligence techniques have been widely used for prediction in various areas of sciences and engineering. In the thesis, applications of AI techniques are studied to predict the dilution of industrial outfall discharges. The discharge of industrial effluents from the outfall systems is broadly divided into two categories on the basis of density. The effluent with density higher than the water receiving will sink and called as negatively buoyant jet. The effluent with density lower than the receiving water will rise and called as positively buoyant jet. The effluent discharge in the water body creates major environmental threats. In this work, negatively buoyant jet is considered. For the study, ANFIS model is taken into consideration and incorporated with algorithms such as GA, PSO and FFA to determine the suitable model for the discharge prediction. The training and test dataset for the ANFIS-type models are obtained by simulating the jet using the realizable k-ε turbulence model over a wide range of Froude numbers i.e. from 5 to 60 and discharge angles from 20 to 72.5 degrees employing OpenFOAM platform. Froude number and angles are taken as input parameters for the ANFIS-type models. The output parameters were peak salinity (Sm), return salinity (Sr), return point in x direction (xr) and peak salinity coordinates in x and y directions (xm and ym). Multivariate regression analysis has also been done to verify the linearity of the data using the same input and output parameters. To evaluate the performance of ANFIS, ANFIS-GA, ANFIS-PSO, ANFIS-FFA and multivariate regression model, some statistical parameters such as coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE) and average absolute deviation in percentage are determined. It has been observed that ANFIS-PSO is better in predicting the discharge characteristics.

Liquid waste discharged from industrial outfalls is categorized into two major classes based on their density. One type is the effluent that has a higher density than that of the ambient water body. In this case, the discharged effluent has a tendency to sink as a negatively buoyant jet. The second type is the effluent that has a lower density than that of the ambient water body and is hence defined as a (positively) buoyant jet that causes the effluent to rise. Negatively/Positively buoyant jets are found in various civil and environmental engineering projects: discharges of desalination plants, discharges of cooling water from nuclear power plants turbines, mixing chambers, etc. This thesis investigated the mixing and dispersion characteristics of such jets numerically. In this thesis, mixing behavior of these jets is studied using a finite volume model (OpenFOAM). Various turbulence models have been applied in the numerical model to assess the accuracy of turbulence models in predicting the effluent discharges in submerged outfalls. Four Linear Eddy Viscosity Models (LEVMs) are used in the positively buoyant wall jet model for discharging of heated waste including: standard k-ε, RNG k-ε, realizable k-ε and SST k-ω turbulence models. It was found that RNG k-ε, and realizable k-ε turbulence models performed better among the four models chosen. Then, in the next step, numerical simulations of 30˚ and 45˚ inclined dense turbulent jets in stationary ambient water have been conducted. These two angles are examined in this study due to lower terminal rise height for 30˚ and 45˚, which is very important for discharges of effluent in shallow waters compared to higher angles. Five Reynolds-Averaged Navier-Stokes (RANS) turbulence models are applied to evaluate the accuracy of CFD predictions. These models include two LEVMs: RNG k-ε, and realizable k-ε; one Nonlinear Eddy Viscosity Model (NLEVM): Nonlinear k-ε; and two Reynolds Stress Models (RSMs): LRR and Launder-Gibson. It has been observed that the LRR turbulence model as well as the realizable k-ε model predict the flow more accurately among the various turbulence models studied herein.

Polímeros sintéticos ocupam uma posição de grande importância no estilo de vida moderno, servindo como matérias-primas para a construção de uma variedade de utensílios. Apesar do grande número de operações de processamento e produtos disponíveis, o planejamento de produtos e a otimização dos processos de produção raramente constituem-se de tarefas triviais. Isso deve-se ao fato da maioria das operações aplicadas na indústria de processamento de polímeros envolverem geometrias e padrões de escoamento complexos, além da dificuldade intrínseca relacionada ao comportamento reológico complexo de polímeros fundidos ou soluções poliméricas. Devido a estes fatores, o desenvolvimento de técnicas de dinâmica de fluido computacional (computational fluid dynamics – CFD) para a simulação de escoamentos de fluidos poliméricos e etapas de operações de processamento tem sido assunto de numerosos estudos durante as últimas décadas. Sob esta perspectiva, o solver viscoelasticFluidFoam, merece destaque. Ele é capaz de resolver simulações de escoamentos de fluidos viscoelásticos utilizando diferentes equações constitutivas. Contudo, apesar de resultados existentes na literatura apresentarem um bom potencial de aplicação, uma análise extensiva de seu desempenho numérico ainda não foi realizada. Neste contexto, a proposta do presente trabalho é a análise da influência de parâmetros de malha, numéricos e constitutivos no comportamento do solver. As bases para os testes compreendem uma geometria simples – escoamento laminar entre duas placas paralelas – o modelo constitutivo de Oldroyd-B e respectivas soluções analíticas para os campos de velocidade e tensão. Mesmo os testes demonstrando a inegável versatilidade do solver, eles revelam limitações em lidar com algumas configurações de malha e parâmetros constitutivos, principalmente com relação ao refinamento na direção perpendicular ao escoamento, diminuição do número de Reynolds e aumento do número de Weisenberg. Estas limitações podem ser parcialmente contornadas com escolha adequada de parâmetros de relaxação das variáveis e da razão de aspecto dos volumes de controle. Tais dificuldades não estão presentes em simulações de escoamentos de fluidos newtonianos em condições semelhantes, sugerindo que trabalhos futuros devem focar em implementações mais robustas do solver viscoelasticFluidFoam. / Synthetic polymers hold a position of great importance in modern lifestyle, serving as raw materials for the construction of a wide variety of appliances. Despite the large number of processing operations and products available, product planning and optimization of production processes rarely constitute a trivial task. This is due to the fact of operations applied in polymer processing industry involve complex geometries and flow patterns, plus the intrinsic difficulty related to the molten polymers or polymer solutions complex rheological behavior. Because of these factors, the development of techniques of computational fluid dynamics (CFD) for the simulation of flows of polymeric fluids and stages of processing operations has been the subject of numerous studies during the last decades. From this perspective, the viscoelasticFluidFoam solver deserves mention. The solver is capable of resolving simulations of viscoelastic fluid flows using different constitutive equations. However, despite the existing results in the literature present a great potential for application, an extensive analysis of their numerical performance has not been performed yet. The purpose of this paper is to examine the influence of mesh, numerical and constitutive parameters in the behavior of the solver. Bases for the tests comprise a simple geometry – laminar flow between two parallel plates – the constitutive model of Oldroyd-B and its analytical solutions for the velocity and stress fields. Although the tests show the undeniable versatility of the solver, they also reveal limitations in dealing with some mesh settings and constitutive parameters, particularly with respect to refinement in the direction perpendicular to the flow, decreasing in the Reynolds number and increasing in the Weisenberg number. This limitation can be partially circumvented with proper choice of variables relaxation parameters and aspect ratio of the control volumes. Such difficulties are not present in simulations of Newtonian fluids flows under similar conditions, suggesting that future works should focus on more robust implementations of the viscoelasticFluidFoam solver.

Polímeros sintéticos ocupam uma posição de grande importância no estilo de vida moderno, servindo como matérias-primas para a construção de uma variedade de utensílios. Apesar do grande número de operações de processamento e produtos disponíveis, o planejamento de produtos e a otimização dos processos de produção raramente constituem-se de tarefas triviais. Isso deve-se ao fato da maioria das operações aplicadas na indústria de processamento de polímeros envolverem geometrias e padrões de escoamento complexos, além da dificuldade intrínseca relacionada ao comportamento reológico complexo de polímeros fundidos ou soluções poliméricas. Devido a estes fatores, o desenvolvimento de técnicas de dinâmica de fluido computacional (computational fluid dynamics – CFD) para a simulação de escoamentos de fluidos poliméricos e etapas de operações de processamento tem sido assunto de numerosos estudos durante as últimas décadas. Sob esta perspectiva, o solver viscoelasticFluidFoam, merece destaque. Ele é capaz de resolver simulações de escoamentos de fluidos viscoelásticos utilizando diferentes equações constitutivas. Contudo, apesar de resultados existentes na literatura apresentarem um bom potencial de aplicação, uma análise extensiva de seu desempenho numérico ainda não foi realizada. Neste contexto, a proposta do presente trabalho é a análise da influência de parâmetros de malha, numéricos e constitutivos no comportamento do solver. As bases para os testes compreendem uma geometria simples – escoamento laminar entre duas placas paralelas – o modelo constitutivo de Oldroyd-B e respectivas soluções analíticas para os campos de velocidade e tensão. Mesmo os testes demonstrando a inegável versatilidade do solver, eles revelam limitações em lidar com algumas configurações de malha e parâmetros constitutivos, principalmente com relação ao refinamento na direção perpendicular ao escoamento, diminuição do número de Reynolds e aumento do número de Weisenberg. Estas limitações podem ser parcialmente contornadas com escolha adequada de parâmetros de relaxação das variáveis e da razão de aspecto dos volumes de controle. Tais dificuldades não estão presentes em simulações de escoamentos de fluidos newtonianos em condições semelhantes, sugerindo que trabalhos futuros devem focar em implementações mais robustas do solver viscoelasticFluidFoam. / Synthetic polymers hold a position of great importance in modern lifestyle, serving as raw materials for the construction of a wide variety of appliances. Despite the large number of processing operations and products available, product planning and optimization of production processes rarely constitute a trivial task. This is due to the fact of operations applied in polymer processing industry involve complex geometries and flow patterns, plus the intrinsic difficulty related to the molten polymers or polymer solutions complex rheological behavior. Because of these factors, the development of techniques of computational fluid dynamics (CFD) for the simulation of flows of polymeric fluids and stages of processing operations has been the subject of numerous studies during the last decades. From this perspective, the viscoelasticFluidFoam solver deserves mention. The solver is capable of resolving simulations of viscoelastic fluid flows using different constitutive equations. However, despite the existing results in the literature present a great potential for application, an extensive analysis of their numerical performance has not been performed yet. The purpose of this paper is to examine the influence of mesh, numerical and constitutive parameters in the behavior of the solver. Bases for the tests comprise a simple geometry – laminar flow between two parallel plates – the constitutive model of Oldroyd-B and its analytical solutions for the velocity and stress fields. Although the tests show the undeniable versatility of the solver, they also reveal limitations in dealing with some mesh settings and constitutive parameters, particularly with respect to refinement in the direction perpendicular to the flow, decreasing in the Reynolds number and increasing in the Weisenberg number. This limitation can be partially circumvented with proper choice of variables relaxation parameters and aspect ratio of the control volumes. Such difficulties are not present in simulations of Newtonian fluids flows under similar conditions, suggesting that future works should focus on more robust implementations of the viscoelasticFluidFoam solver.

Polímeros sintéticos ocupam uma posição de grande importância no estilo de vida moderno, servindo como matérias-primas para a construção de uma variedade de utensílios. Apesar do grande número de operações de processamento e produtos disponíveis, o planejamento de produtos e a otimização dos processos de produção raramente constituem-se de tarefas triviais. Isso deve-se ao fato da maioria das operações aplicadas na indústria de processamento de polímeros envolverem geometrias e padrões de escoamento complexos, além da dificuldade intrínseca relacionada ao comportamento reológico complexo de polímeros fundidos ou soluções poliméricas. Devido a estes fatores, o desenvolvimento de técnicas de dinâmica de fluido computacional (computational fluid dynamics – CFD) para a simulação de escoamentos de fluidos poliméricos e etapas de operações de processamento tem sido assunto de numerosos estudos durante as últimas décadas. Sob esta perspectiva, o solver viscoelasticFluidFoam, merece destaque. Ele é capaz de resolver simulações de escoamentos de fluidos viscoelásticos utilizando diferentes equações constitutivas. Contudo, apesar de resultados existentes na literatura apresentarem um bom potencial de aplicação, uma análise extensiva de seu desempenho numérico ainda não foi realizada. Neste contexto, a proposta do presente trabalho é a análise da influência de parâmetros de malha, numéricos e constitutivos no comportamento do solver. As bases para os testes compreendem uma geometria simples – escoamento laminar entre duas placas paralelas – o modelo constitutivo de Oldroyd-B e respectivas soluções analíticas para os campos de velocidade e tensão. Mesmo os testes demonstrando a inegável versatilidade do solver, eles revelam limitações em lidar com algumas configurações de malha e parâmetros constitutivos, principalmente com relação ao refinamento na direção perpendicular ao escoamento, diminuição do número de Reynolds e aumento do número de Weisenberg. Estas limitações podem ser parcialmente contornadas com escolha adequada de parâmetros de relaxação das variáveis e da razão de aspecto dos volumes de controle. Tais dificuldades não estão presentes em simulações de escoamentos de fluidos newtonianos em condições semelhantes, sugerindo que trabalhos futuros devem focar em implementações mais robustas do solver viscoelasticFluidFoam. / Synthetic polymers hold a position of great importance in modern lifestyle, serving as raw materials for the construction of a wide variety of appliances. Despite the large number of processing operations and products available, product planning and optimization of production processes rarely constitute a trivial task. This is due to the fact of operations applied in polymer processing industry involve complex geometries and flow patterns, plus the intrinsic difficulty related to the molten polymers or polymer solutions complex rheological behavior. Because of these factors, the development of techniques of computational fluid dynamics (CFD) for the simulation of flows of polymeric fluids and stages of processing operations has been the subject of numerous studies during the last decades. From this perspective, the viscoelasticFluidFoam solver deserves mention. The solver is capable of resolving simulations of viscoelastic fluid flows using different constitutive equations. However, despite the existing results in the literature present a great potential for application, an extensive analysis of their numerical performance has not been performed yet. The purpose of this paper is to examine the influence of mesh, numerical and constitutive parameters in the behavior of the solver. Bases for the tests comprise a simple geometry – laminar flow between two parallel plates – the constitutive model of Oldroyd-B and its analytical solutions for the velocity and stress fields. Although the tests show the undeniable versatility of the solver, they also reveal limitations in dealing with some mesh settings and constitutive parameters, particularly with respect to refinement in the direction perpendicular to the flow, decreasing in the Reynolds number and increasing in the Weisenberg number. This limitation can be partially circumvented with proper choice of variables relaxation parameters and aspect ratio of the control volumes. Such difficulties are not present in simulations of Newtonian fluids flows under similar conditions, suggesting that future works should focus on more robust implementations of the viscoelasticFluidFoam solver.

El modelado CFD se ha convertido en una herramienta aceptada y ampliamente utilizada en el ámbito del diseño de motores de combustión interna alternativos. Los modelos de combustión avanzados ayudan a comprender los fenómenos complejos químicos y físicos del proceso de combustión y aportan información detallada que no se puede obtener con experimentos. Indudablemente, el modelado del proceso de combustión turbulenta parcialmente premezclada característico de los chorros Diesel es particularmente difícil y por lo tanto es un tema de gran interés para la comunidad científica. Los retos más importantes del modelado de este tipo de llamas son la predicción del proceso del auto-encendido, caracterizado por el tiempo de retraso, y la estructura de la llama cuasi-estacionaria con su característica longitud de lift-off. Estos dos parámetros globales de los chorros Diesel son importantes por varios aspectos. Primero, es relativamente sencillo medir estos dos parámetros y por lo tanto utilizarlos para la validación de modelos y segundo, son factores determinantes en el proceso de la combustión en un motor. El auto-encendido marca el inicio de la tasa de liberación de calor y la longitud de lift-off desempeña un papel fundamental en la formación de hollín. El mecanismo de estabilización de la llama en la zona del lift-off todavía no es bien conocido aunque existen diferentes teorías en la literatura, por lo que su modelado es en la actualidad un reto no resuelto. De acuerdo con el contexto descrito previamente, en este trabajo se pretende implementar un modelo de combustión integrado en un solver RANS utilizando la plataforma CFD OpenFOAM de código abierto. El modelo propuesto está basado en el concepto de flamelets usando una química detallada combinado con funciones de probabilidad determinadas a priori (presumed-PDF) para considerar el efecto de interacción entre la química y las características del flujo turbulento, que implica hipótesis importantes. En primer lugar, con el concepto flamelet se asume que una llama Diesel turbulenta quema localmente como un conjunto de llamas laminares de difusión de flujos opuestos. En segundo lugar se asume que las fluctuaciones de las propiedades introducidas por el flujo turbulento, que son las responsables de los fenómenos de interacción entre la química y la turbulencia durante la combustión, siguen un comportamiento estadístico en el tiempo de acuerdo a una distribución de probabilidad conocida a priori. Los fenómenos complejos del auto-encendido de hidrocarburos exigen el uso de mecanismo químicos detallados para recuperar satisfactoriamente los tiempos de retraso del auto-encendido en un rango amplio de condiciones termoquímicas. Una estrategia de interés para mantener los costes computacionales dentro de límites aceptables consiste en pre-tabular los resultados del cálculo de la química en tablas. Los parámetros independientes de estas tablas son la fracción de mezcla, la variable de progreso y la tasa de disipación escalar. Además, la hipótesis de que la distribuciones de probabilidad de las fluctuaciones generadas por la turbulencia sobre las propiedades del flujo son conocidas permite generar una tabla con la información química del problema apta para su aplicación en cálculo CFD en un entorno RANS. Esta aproximación basada en la pre-tabulación de los resultados químicos presenta dos ventajas fundamentales, siendo la primera de ellas la posibilidad de considerar modelos avanzados de interacción química-turbulencia y la segunda el relevante ahorro de tiempo de cálculo. Sin embargo, estas tablas representan un gran espacio de datos cuya gestión eficiente no es trivial. El desarrollo de un almacenamiento adecuado para un acceso de datos rápido y directo así como un esquema de interpolación multidimensional también forma parte del presente trabajo. / Winklinger, JF. (2014). Implementation of a combustion model based on the flamelet concept and its application to turbulent reactive sprays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48488 / TESIS

This work deals with study of swirling flows where the spiral vortical structure appears. The main relation is to flow seen in the draft tube cone of hydraulic turbines operated out of the design point (i.e. best efficiency point). In this cases large coherent vortex structure (vortex rope) appears and consequently high pressure pulsations are propagated to the whole machine system leading to possible restriction of turbine operation. This flow features are consequence of flow instability called vortex breakdown in case of Francis turbine operated at part load (flow rate lower than optimal one). The present study is carried out using simplified device of swirl generator in order to access similar flow conditions as can be found in real hydraulic turbines. Both the dynamic and dissipation effect of spiral vortex breakdown are investigated. The first part of thesis deals with spiral form of vortex breakdown. The experimentally measured velocity profiles (LDA) and wall static pressures are correlated with numerical simulations carried out using open-source CFD package OpenFOAM 2.2.2. The high speed camera recording of cavitating vortex core is used to obtain image ensemble for further post-processing. The dissipation effect of spiral vortex structure is in detail discussed based on computed flow fields. The second part of thesis is dedicated to the application of POD decomposition to the study of spatio-temporal features of spiral vortex dynamics. Firstly the POD is applied to the both the experimentally obtained image ensemble of cavitating vortex and numerically computed static pressure fields. Secondly the comprehensive analysis of spiral vortex mitigation effect by the axial water jet is analyzed. The collaborative study employing the swirl generator apparatus designed by the researchers from Politehnica University of Timisoara in Romania is performed and changes in spatio-temporal vortex dynamic are studied. In this study the numerical data (in a form of three-dimensional pressure and velocity fields) are obtained using commercial CFD software ANSYS Fluent R14.

This is a master’s thesis performed at the Department of Shipping and Marine Technology research group in Hydrodynamics at Chalmers University of Technology and is written for the Center for Naval Architecture at the Royal Institute of Technology, KTH.In order to meet increased requirements on efficient ship propulsions with low noise level, it is important to consider the complete system with both the hull and the propeller in the simulation.OpenFOAM (Open Field Operation and Manipulation) provides different techniques to simulate a rotating propeller with different physical and computational properties. MRF (The Multiple Reference Frame Model) is, perhaps, the easiest way but is a computationally efficient technique to model a rotating frame of reference. The sliding grid techniques provide the more complex way to simulate the propeller and its surrounding region, rotating and interpolate on interface for transient effects. AMI, Arbitrary Mesh Interface, is a sliding grid implementation which is available in the recent versions of OpenFOAM, introduced in the official releases after v2.1.0.In this study, the main objective is to compare these two techniques, MRF and AMI, to perform the open water characteristics of the propeller with the Reynolds-Averaged Navier-Stokes equation computations (RANS) and study the accuracy in parallel performance and the benefits of each approach.More specifically, a self-propelled ship is simulated to study the interaction between the hull and propeller. In order to simplify and decrease the computational complexity the free surface is not considered. The ship under investigation is a 7000 DWT chemical tanker which is subject of a collaborative R&D project called STREAMLINE, strategic research for innovative marine propulsion concepts. In self-propelled condition, the transient forces on the propeller shall be evaluated. This study investigates the results of the experimental work with advanced CFD for accurate analysis and design of the propulsion. In this thesis, all simulations are conducted by using parallel computing. Therefore, a scalability analysis is studied to find out how to affect the average computational time by using different number of nodes.

Liquid waste discharged from industrial outfalls is categorized into two major classes based on their density. One type is the effluent that has a higher density than that of the ambient water body. In this case, the discharged effluent has a tendency to sink as a negatively buoyant jet. The second type is the effluent that has a lower density than that of the ambient water body and is hence defined as a (positively) buoyant jet that causes the effluent to rise. Negatively/Positively buoyant jets are found in various civil and environmental engineering projects: discharges of desalination plants, discharges of cooling water from nuclear power plants turbines, mixing chambers, etc. This thesis investigated the mixing and dispersion characteristics of such jets numerically. In this thesis, mixing behavior of these jets is studied using a finite volume model (OpenFOAM). Various turbulence models have been applied in the numerical model to assess the accuracy of turbulence models in predicting the effluent discharges in submerged outfalls. Four Linear Eddy Viscosity Models (LEVMs) are used in the positively buoyant wall jet model for discharging of heated waste including: standard k-ε, RNG k-ε, realizable k-ε and SST k-ω turbulence models. It was found that RNG k-ε, and realizable k-ε turbulence models performed better among the four models chosen. Then, in the next step, numerical simulations of 30˚ and 45˚ inclined dense turbulent jets in stationary ambient water have been conducted. These two angles are examined in this study due to lower terminal rise height for 30˚ and 45˚, which is very important for discharges of effluent in shallow waters compared to higher angles. Five Reynolds-Averaged Navier-Stokes (RANS) turbulence models are applied to evaluate the accuracy of CFD predictions. These models include two LEVMs: RNG k-ε, and realizable k-ε; one Nonlinear Eddy Viscosity Model (NLEVM): Nonlinear k-ε; and two Reynolds Stress Models (RSMs): LRR and Launder-Gibson. It has been observed that the LRR turbulence model as well as the realizable k-ε model predict the flow more accurately among the various turbulence models studied herein.