diff --git a/tex/header/preamble.tex b/tex/header/preamble.tex index ad791b89ab41cc728fc89d567f9f61d579b5d5b6..805c8a03bc6ae5cb0b391e60b41b7e1e81f34a4c 100644 --- a/tex/header/preamble.tex +++ b/tex/header/preamble.tex @@ -28,9 +28,9 @@ \addbibresource{.maindir/tex/bibliography.bib} \hypersetup{ - pdftitle={Title missing}, + pdftitle={Project 4: unsteady turbulent flow around a cylinder}, pdfauthor={Felix Hilsky}, - pdfsubject={Subject missing}, + pdfsubject={Computational fluid dynamics}, pdfcreator={LuaLaTeX}, pdfproducer={LuaLaTeX via latexmk}, pdfkeywords={}, diff --git a/tex/main.tex b/tex/main.tex index 3c0a44371ed9a26de8531275bb14c4f4583d0a1b..cd41c1cfc7ae4b5eada9c0bf63099431776e5a00 100644 --- a/tex/main.tex +++ b/tex/main.tex @@ -1,11 +1,13 @@ %! TEX program = lualatex \input{.maindir/tex/header/preamble-section} \docStart -\title{Dokumententitel} +\title{Project 4: unsteady turbulent flow around a cylinder} \author{Felix Hilsky} \maketitle % use \textinput as described in /header and _TEMPLATE \textinput{setup} +\textinput{reynold.tex} +\textinput{results} \begin{appendices} % \textinput{some-appendix-section} \end{appendices} diff --git a/tex/results.tex b/tex/results.tex index da1a9b77ac735fefb32490710a28b795fc10313c..913775c9c2710c1cd5c63a9fd360a4c402db1bc9 100644 --- a/tex/results.tex +++ b/tex/results.tex @@ -4,16 +4,24 @@ % inputs the preamble only if necessary \docStart \section{Measurements} +The drag coefficiant was calculated with the OpenFOAM intrinsic function +|forceCoeffsIncompressible| with the reference area |Aref| of +$2 · r · l = \SI{2}{\square\metre}$ where $l$ is the thickness of the domain and $r$ the radius of the cylinder. + +The average temperature gradient of the cylinder was calculated with the OpenFOAM instrinsic post processing functions |grad(T)|, |mag(grad(T))| and |patchAverage(name=cylinder,mag(grad(T)))|. +We need $\abs{n·∇T}$ instead of $\abs{∇T}$ but in this case those two values are equal since $∇T$ can be split into the tangential and normal parts and the tangential part must be zero since the temperature of the cylinder is equal everywhere. + +The results are summerized in table \ref{tab:values}. \begin{table}[htpb] \centering \caption{Scalar results of the numerical experiments} \label{tab:values} - \begin{tabular}{cccc} - $\Rey$ & $u_{in}$ & $C_D$ & $\arrow n · ∇T|_{\text{cyl}} & \Nus \\ - \num{e2} & \num{0.2} \\ - \num{e3} & \num{2} \\ - \num{e4} & \num{20} \\ - \num{e5} & \num{200} + \begin{tabular}{cccccc} + $\Rey$ & $u_{in}$ & \# cells & $C_D$ & $\vec n · ∇T\vert_{\text{cyl}}$ & $\Nus$ \\ + \num{e2} & \num{0.05} & \\ + \num{e3} & \num{0.5} & \\ + \num{e4} & \num{5} & \\ + \num{e5} & \num{50} & \end{tabular} \end{table} % do not use \input nor \begin{document nor \end{document} diff --git a/tex/reynold.tex b/tex/reynold.tex index 07a9eb3527b36df4193f61805c20d65ac249eeeb..4d09f588bd46b4451a66725ba4a36267e89daaa0 100644 --- a/tex/reynold.tex +++ b/tex/reynold.tex @@ -6,7 +6,7 @@ \section{Reynolds number} The Reynolds number is defined as \begin{align*} - \Rey = \frac{u d}{ν} ⇒ u = \frac{\Rey ν}{d} = \frac{\Rey}{500}. + \Rey = \frac{u d}{ν} ⇒ u = \frac{\Rey ν}{d} = \frac{\Rey}{2000} = \num{5e-4} \Rey. \end{align*} In the default case $d = \SI{2}{\metre}$, $ν=\SI{e-3}{\square\metre\per\second}$. The inflow velocity is chose in a way that the desired Reynold numbers are reached, diff --git a/tex/timestep.tex b/tex/timestep.tex new file mode 100644 index 0000000000000000000000000000000000000000..8e4562247ea30128a260b356479d427e2d8836e8 --- /dev/null +++ b/tex/timestep.tex @@ -0,0 +1,28 @@ +%! TEX program = lualatex + +\input{.maindir/tex/header/preamble-section} +% inputs the preamble only if necessary +\docStart +\section{Time stepping} +The timesteps were adjusted automatically because for moderate to higher velocities the Courant numbers were very high (over 40) at time steps of one second but stable. +This resulted in time steps listed in table \ref{fig:timesteps}. +As it is visible there, the combination of high Reynolds number ($\num{e5}$) with higher cell number $N > 2$) is not viable to run. + +Since for low Reynold numbers, the time step became too big, a maximal time step of \num{0.1} was introduced. + +\begin{table}[htpb] + \centering + \caption{Time steps due to automatic adjustment with max courant number of \num{1}.} + \label{tab:timesteps} + \begin{tabular}{ccc} + Nr. of cells & Reynold number & time step \\ + % 1016 = "N = 1"; 4064 = "N = 2" + 4064 & \num{e2} & 1.3 \\ % todo: run again with smaller timestep + 4064 & \num{e3} & 0.0795 \\ + 4064 & \num{e4} & 0.0065 \\ + 1016 & \num{e5} & 0.0017 \\ + 4065 & \num{e5} & 0.00051 + \end{tabular} +\end{table} + +\docEnd