Turbulence Modeling using OpenFOAM (Ontario Tech University)
Author
Arup Jyoti Chutia
License
Creative Commons CC BY 4.0
Abstract
The slides were prepared from personal experiences and without following any professional guidelines.
The slides were prepared from personal experiences and without following any professional guidelines.
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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}