diff --git a/tex/main.tex b/tex/main.tex index 6fc1c380639a71839a2540c1120de637cf1bddb7..816ece5aed6940090cda5d58fee5185f0d77f856 100644 --- a/tex/main.tex +++ b/tex/main.tex @@ -9,7 +9,8 @@ \textinput{reynold} \section{Results} \textinput{steady-state} -\textinput{diagrams} +\textinput{unsteadystate} +% \textinput{diagrams} % \begin{appendices} % \textinput{some-appendix-section} % \end{appendices} diff --git a/tex/steady-state.tex b/tex/steady-state.tex index 4900899199faaa8cda014d3a7ce0c773df14ec8b..a77d35e2198bb032f167848b622a4732b0d75514 100644 --- a/tex/steady-state.tex +++ b/tex/steady-state.tex @@ -3,7 +3,7 @@ \input{.maindir/tex/header/preamble-section} % inputs the preamble only if necessary \docStart -\subsection{Steady state} +\subsection{Steady state} \label{sec:steady} The configuration with $\Rey = 20$ and $\bar u = \SI{0.2}{\metre\per\second}$ results in a steady state. After a very short time (\SI{0.6}{\second}) of adjusting, the flow reaches a situation that (almost) does not change anymore. Hence only the first $2$ instead of $20$ seconds were calculated. @@ -23,7 +23,7 @@ The calculations were performed with $N = 6$ ($1728$ cells), $6$ correctors, $2$ \end{figure} In figure \ref{fig:steadystate} we can see the recirculation zone with a length of approximately \SIrange{15}{20}{\centi\metre}. Here I take the area where the flow is disturbed, hence not a straight flow as the recirculation zone. -In the literature the length of the recirculation is zone is about \SI{8}{\centimetre}, +In the literature the length of the recirculation is zone is about \SI{8}{\centi\metre}, about half of my value. But the paper does not define what this zone is, hence those values are not comparable. @@ -34,7 +34,7 @@ The captions include the comparison with the literature. \tikzinput{bothpressures} \caption{Pressure in front and behind the cylinder and the difference. The pressure difference quickly steadies at \SI{0.5}{\square\metre\per\square\second}. - In the literature, the pressure difference is in most cases about \num{0.1}{\square\metre\per\second} which is a fifth of my value. + In the literature, the pressure difference is in most cases about \SI{0.1}{\square\metre\per\second} which is a fifth of my value. } \label{fig:steadyP} \end{figure} diff --git a/tex/unsteadystate.tex b/tex/unsteadystate.tex new file mode 100644 index 0000000000000000000000000000000000000000..4096c75467d4ca4012c1ef3db0aa301e590b7f20 --- /dev/null +++ b/tex/unsteadystate.tex @@ -0,0 +1,59 @@ +%! TEX program = lualatex + +\input{.maindir/tex/header/preamble-section} +% inputs the preamble only if necessary +\docStart +\subsection{Unsteady state} +The literature claims that at a Reynolds number of $\Rey = 100$ ($\bar u = \SI{1}{\metre\per\second}$) the flow becomes unsteady. + +My experiments did not support this claim. +With $u = \SI{1}{\metre\per\second}$ a steady state is reached before \SI{0.86}{\second}. +This steady state can be seen in figure \ref{fig:unsteady}. +\begin{figure}[htpb] + \centering + \newcommand{\picwidth}{0.95\linewidth} + \includegraphics[width=\picwidth]{.maindir/zeichnungen/100_u_x} + \includegraphics[width=\picwidth]{.maindir/zeichnungen/100_u_y} + \includegraphics[width=\picwidth]{.maindir/zeichnungen/100_p} + \caption{The steady state is reached at time \SI{0.6}{\second}. + Those images are from $t ="\SI{0.86}{\second}$. + From top to bottom we have the velocity in flow direction, + the velocity perpendicular to it and the pressure.% + } + \label{fig:steadystate} +\end{figure} + +The recirculation zone in this case is approximately \SIrange{25}{30}{\centi\metre} long. +The same uncertainty as in section \ref{sec:steady} applies. + +The pressure values in front and behind the cylinder and the coefficiants are plotted in the figures \ref{fig:unsteadyP}, \ref{fig:unsteadyCd} and \ref{fig:unsteadyCl}. +The captions include the comparison with the literature. +\begin{figure}[ht] + \centering + \tikzinput{unsteady_bothpressures} + \caption{Pressure in front and behind the cylinder and the difference. + The pressure difference quickly steadies at \SI{3.85}{\square\metre\per\square\second}. + In the literature, the pressure difference is in most cases about \SI{2.4}{\square\metre\per\second} which are two thirds of my value. + } + \label{fig:unsteadyP} +\end{figure} +\begin{figure}[ht] + \centering + \tikzinput{unsteady_Cd} + \caption{The drag coefficiant over time. It steadies at \num{219.5}. + In the literature $C_{D\max}$ is about \num{3.2} which is about \SI{1.5}{\percent} of my value but it is a maximum value. + } + \label{fig:unsteadyCd} +\end{figure} +\begin{figure}[ht] + \centering + \tikzinput{unsteady_Cl} + \caption{The lift coefficiant over time. It steadies at \num{2.68}. + In the literature $C_{L\max}$ is about \num{1} which is about \SI{40}{\percent} of my value. + } + \label{fig:unsteadyCl} +\end{figure} + +The comparisons to the literature indicate that there is a major flaw in the setup. +In particular I cannot see a turbulent flow and therefore a Strouhal number cannot be calculated. +\docEnd