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\title[Turbulence Modeling (Group Project)]{Turbulence Modeling using OpenFOAM}
\subtitle{(Introduction to Turbulence - ENGR5005G)}
\institute[]{Mechanical Engineering \\Ontario Tech University }
\titlegraphic{\includegraphics[height=2.5cm]{ontario.png}}
\author[Arup Jyoti Chutia]{
Arup Jyoti Chutia ,
Brayden York and
Marcus Ebert }
\institute[]{Mechanical Engineering \\Ontario Tech University }
\date{\today}
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\begin{document}
\begin{frame}
\titlepage
\end{frame}
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\logo{\includegraphics[scale=0.2]{ontario.png}~%
}
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\begin{frame}{Outline}
\vspace{1cm}
\begin{center}
\begin{itemize}
\item Introduction
\item Objectives
\item Governing equations
\item OpenFOAM solvers
\item Geometry and problem parameters
\item Mesh and boundary conditions
\item Results
\item Conclusions and recommendations
\item References
\end{itemize}
\end{center}
\end{frame}
\begin{frame}{Introduction }
Turbulent flow
\begin{center}
\begin{columns}[onlytextwidth]
\column{0.5\textwidth}
\begin{itemize}
\item Chaotic changes in field values :
\begin{itemize}
\item velocity
\item pressure
\end{itemize}
\item High Reynolds number flow :
\vspace{2.5mm}
\begin{itemize}
\item low momentum diffusion ($\mu$)
\item high momentum convection
\end{itemize}
%\item Mathematical models !
\end{itemize}
\column{0.5\textwidth}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{turb.jpg}
\caption{1. Flow visualisation (source: www.bronkhorst.com).}
% \label{fig:my_label}
\end{figure}
\end{columns}
\end{center}
\end{frame}
\begin{frame}{Introduction (contd...)}
\begin{center}
\begin{columns}[onlytextwidth]
\column{0.5\textwidth}
%\vspace{1 cm}
Why turbulence modeling?\\
\vspace{1cm}
\begin{itemize}
\item No general analytical theory
\item Chaotic flow
\item Closure Problem
\item Mathematical models.
\end{itemize}
\column{0.5\textwidth}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{vel.png}
\caption{2.(a)Laminar and (b) turbulent velocity (source: https://nptel.ac.in).}
% \label{fig:my_label}
\end{figure}
\end{columns}
\end{center}
\end{frame}
\begin{frame}{Objectives}
\vspace{1.5cm}
\begin{itemize}
\item Understanding turbulence models in CFD (OpenFOAM).
\item Simulations for transient and steady state conditions.
\item Selecting turbulence model.
\end{itemize}
\end{frame}
\begin{frame}{Governing equations (Mean flow)\autocite{Lecture3}}
\textit{\textbf{RANS} equations for incompressible flow}:\\
\textbf{Continuity equation}
\begin{equation}
\frac{\partial \overline{u_{i}}}{\partial x_{i}}=0
\end{equation}
\textbf{Momentum equations }
\begin{equation}
\frac{\partial \overline{u_{i}} }{\partial t} + \overline{u_{j}} \frac{\partial \overline{u_{i}} }{\partial x_{j}} = -\frac{1}{\rho}\frac{\partial \overline{P}}{\partial x_{i}}+\nu\frac{\partial ^2\overline{u_{i}}}{\partial x_{j}\partial x_{j}}-\frac{\partial \overline{u_{i}'u_{j}'}}{\partial x_{j}}+\overline{g_{i}}
\end{equation}
\textbf{Scaler equation }
\begin{equation}
\frac{\partial \overline{\phi}}{\partial t}+\overline{u_{i}}\frac{\partial \overline{\phi}}{\partial x_{i}}=\frac{\partial}{\partial x_{i}}(D\frac{\partial \overline{\phi}}{\partial x_{i}})-\frac{\partial (\overline{{u_{i}^{'}\phi^{'}}})}{\partial x_{i}}
\end{equation}
\end{frame}
\begin{frame}{Standard \textit{k-$\epsilon$} model\autocite{versteeg2007introduction}}
$\nu_{eff}=\nu+\nu_{t},\,\, \nu_{t}=?$
\begin{itemize}
\item k-turbulent kinetic energy
\begin{equation}
k= \frac{1}{2}(\overline{u'^2}+\overline{v'^2}+\overline{w'^2})
\end{equation}
\item $\epsilon$ -turbulent dissipation
\begin{itemize}
\item rate of dissipation of $k$.
\end{itemize}
\item Turbulent viscosity
\begin{itemize}
\item $\nu_{t}=0.09\frac{k^2}{\epsilon}$
\end{itemize}
\item Transport equations for $k$ and $\epsilon$
\end{itemize}
\end{frame}
\begin{frame}{OpenFOAM solvers }
OpenFOAM solvers used in this project
\vspace{1cm}
\begin{itemize}
\item \textbf{simpleFoam\autocite{chapter6}}: for steady state simulation.
\begin{itemize}
\item RAS models: \textit{kEpsilon, kOmega} and \textit{LRR}.
\end{itemize}
\item \textbf{pisoFoam\autocite{chapter7}}: transient simulation for incompressible flow.
\begin{itemize}
\item LES models : \textit{Smagorinsky,
kEqn}.
\item RAS model: \textit{kEpsilon}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}{Geometry and problem parameters }
%\textbf{Geometry and problem parameters }
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{pitz.PNG}
\caption{3.Schematic of geometry used for simulations (source: http://training.uhem.itu.edu.tr). }
%\label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{ Mesh and boundary conditions}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{mesh.png}
\caption{4.Hexahedral mesh (source:www.cfdsupport.com).}
% \label{fig:my_label}
\end{figure}
Velocity boundary conditions
\begin{itemize}
\item \textit{Inlet}: Dirichlet
condition.
\item \textit{Outlet}: Zero-gradient condition.
\item \textit{Upper Wall}: No slip .
\item \textit{Bottom Wall}: No slip.
% \item \textit{Side Walls}: No slip.
\end{itemize}
\end{frame}
\begin{frame}{Turbulence – Steady State: Results}
\begin{figure}
\centering
\includegraphics[width=0.65\textwidth]{steady_velocity.png}
\caption{5.Velocity magnitude for \textit{kEpsilon, kOmega} \,\,and \text{LRR} models.}
% \label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence – Steady State: Results(contd...)}
\begin{figure}
\centering
\includegraphics[width=0.65\textwidth]{steady_nut.png}
\caption{6.Turbulent viscosity for \textit{kEpsilon, kOmega} \,\, and \text{LRR} models.}
%\label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence - Transient : Results (Smargorinsky model)}
\begin{figure}
\centering
\includegraphics[width=0.62\textwidth]{smagorinsky_velocity.png}
\caption{7.Smargorinsky velocity magnitude at different time steps.}
% \label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence - Transient : Results (Smargorinsky model)}
\begin{figure}
\centering
\includegraphics[width=1\textwidth]{FlowField.png}
\caption{8.Streamlines at 0.2s for Smargorinsky model.}
% \label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence - Transient : Results (kEpsilon)}
\begin{figure}
\centering
\includegraphics[width=0.62\textwidth]{kEpsilon_velocity.png}
\caption{9.\textit{kEpsilon} model - Velocity magnitude at different
time steps
.}
\label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence - Transient : Results (contd...)}
\begin{figure}
\centering
\includegraphics[width=0.65\textwidth]{transient_velocity_02.png}
\caption{10.Velocity vectors for different turbulence models - at
0.2s}
% \label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Turbulence - Transient : Results (contd...)}
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{nutturb.png}
\caption{11.Turbulent viscosity for different turbulence models - at
0.2s}
% \label{fig:my_label}
\end{figure}
\end{frame}
\begin{frame}{Conclusions and Recommendations}
\textbf{Steady State Simulations}
\begin{itemize}
\item Similar results for \textit{kEpsilon, kOmega}\,\,and \textit{LRR}.
\end{itemize}
\textbf{Transient Simulations}
\begin{itemize}
\item LES -(\textit{Smagorinsky, kEqn)} detail, fluctuation based.
\item RAS -(\textit{kEpsilon}), averaging nature.
\end{itemize}
\end{frame}
\begin{frame}{References}
\printbibliography
\end{frame}
\end{document}