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\atstartofexercises \atstartofexercises
...@@ -45,7 +45,15 @@ Balance of energy in a considered volume with steady flow: ...@@ -45,7 +45,15 @@ Balance of energy in a considered volume with steady flow:
\wherefrom{\cczero \oc} \wherefrom{\cczero \oc}
\label{exo_pipe_expansion} \label{exo_pipe_expansion}
Water flows from left to right in a pipe. On the left the diameter is \SI{8}{\centi\metre}, the water comes in with a uniform velocity of \SI{1,5}{\metre\per\second}. The diameter increases gently until it reaches \SI{16}{\centi\metre}; the expansion is smooth, so that losses (specifically, energy losses due to wall friction and flow separation) are negligible. Water flows from left to right in a pipe, as shown in fig.~\ref{fig_simple_pipe_expansion}. On the left the diameter is \SI{8}{\centi\metre}, the water comes in with a uniform velocity of \SI{1,5}{\metre\per\second}. The diameter increases gently until it reaches \SI{16}{\centi\metre}; the expansion is smooth, so that losses (specifically, energy losses due to wall friction and flow separation) are negligible.
\begin{figure}
\begin{center}
\includegraphics[width=7.5cm]{simple_pipe_expansion}
\vspace{-0.5cm}
\end{center}
\supercaption{A simple pipe expansion, with water flowing from left to right.}{\cczero \oc}
\label{fig_simple_pipe_expansion}
\end{figure}
\begin{enumerate} \begin{enumerate}
\item What are the mass and volume flows across the pipe? \item What are the mass and volume flows across the pipe?
\item What is the average velocity of the water at the right end of the expansion? \item What is the average velocity of the water at the right end of the expansion?
...@@ -55,13 +63,13 @@ Balance of energy in a considered volume with steady flow: ...@@ -55,13 +63,13 @@ Balance of energy in a considered volume with steady flow:
The volume flow of water in the pipe is now doubled. The volume flow of water in the pipe is now doubled.
\begin{enumerate} \begin{enumerate}
\shift{3} \shift{3}
\item What is the new pressure drop? \item What is the new pressure change?
\end{enumerate} \end{enumerate}
The water is drained from the pipe, and instead, air with density \SI{1,225}{\kilogram\per\metre\squared} is flowed in the pipe, incoming with a uniform velocity of \SI{1,5}{\metre\per\second}. The water is drained from the pipe, and instead, air with density \SI{1,225}{\kilogram\per\metre\cubed} is flowed in the pipe, incoming with a uniform velocity of \SI{1,5}{\metre\per\second}.
\begin{enumerate} \begin{enumerate}
\shift{4} \shift{4}
\item What is the new pressure drop? \item What is the new pressure change?
\end{enumerate} \end{enumerate}
%%%% %%%%
...@@ -69,7 +77,15 @@ Balance of energy in a considered volume with steady flow: ...@@ -69,7 +77,15 @@ Balance of energy in a considered volume with steady flow:
\wherefrom{\cczero \oc} \wherefrom{\cczero \oc}
\label{exo_pipe_with_losses} \label{exo_pipe_with_losses}
Water flows in a long pipe which has constant diameter; a valve is installed in the middle of the pipe length. Water comes in the pipe with a uniform velocity of \SI{1,5}{\metre\per\second} and the pipe diameter is \SI{250}{\milli\metre}. Water flows in a long pipe which has constant diameter; a valve is installed in the middle of the pipe length (fig.~\ref{fig_simple_straight_pipe_valve}). Water comes in the pipe with a uniform velocity of \SI{1,5}{\metre\per\second} and the pipe diameter is \SI{250}{\milli\metre}.
\begin{figure}
\begin{center}
\includegraphics[width=0.8\textwidth]{simple_straight_pipe_valve}
\vspace{-0.5cm}
\end{center}
\supercaption{A simple, straight pipe, featuring a partially-open valve in the center}{\cczero \oc}
\label{fig_simple_straight_pipe_valve}
\end{figure}
The pipe itself and the valve, together, induce a pressure loss which can be quantified using the dimensionless \vocab{loss coefficient} $K_\text{valve}$ (we later will later encounter it as eq.~\ref{eq_def_loss_coeff} p.\pageref{eq_def_loss_coeff}). With this tool, the pressure loss is related to the average incoming speed $V_\text{incoming}$ as: The pipe itself and the valve, together, induce a pressure loss which can be quantified using the dimensionless \vocab{loss coefficient} $K_\text{valve}$ (we later will later encounter it as eq.~\ref{eq_def_loss_coeff} p.\pageref{eq_def_loss_coeff}). With this tool, the pressure loss is related to the average incoming speed $V_\text{incoming}$ as:
\begin{IEEEeqnarray}{rCcCl} \begin{IEEEeqnarray}{rCcCl}
...@@ -91,7 +107,15 @@ Balance of energy in a considered volume with steady flow: ...@@ -91,7 +107,15 @@ Balance of energy in a considered volume with steady flow:
\wherefrom{\cczero \oc} \wherefrom{\cczero \oc}
\label{exo_combustor} \label{exo_combustor}
A jet engine is equipped with several \vocab{combustors} (sometimes also called \vocab{combustion chambers}). We are interested in fluid flow through one such combustor. Air from the compressor enters the combustor, is mixed with fuel, and combustion occurs, which greatly increases the temperature and specific volume of the mix, before it is run through the turbine. A jet engine is equipped with several \vocab{combustors} (sometimes also called \vocab{combustion chambers}). We are interested in fluid flow through one such combustor, shown in fig.~\ref{fig_combustor}. Air from the compressor enters the combustor, is mixed with fuel, and combustion occurs, which greatly increases the temperature and specific volume of the mix, before it is run through the turbine.
\begin{figure}
\begin{center}
\includegraphics[width=0.8\textwidth]{Core_section_of_a_sectioned_Rolls-Royce_Turboméca_Adour_turbofan_cropped.jpg}
\vspace{-0.5cm}
\end{center}
\supercaption{A combustor in a sectioned jet engine (here, a Turboméca Adour). Air enters from the right, out of the compressor (whose blades are painted blue). It leaves the combustor on the left side, into the turbine. In the combustor, high-temperature, steady combustion takes place.}{\wcfile{Core_section_of_a_sectioned_Rolls-Royce_Turboméca_Adour_turbofan.jpg} \ccbysa \oc}
\label{fig_combustor}
\end{figure}
The conditions at inlet are as follows: The conditions at inlet are as follows:
\begin{itemize} \begin{itemize}
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...@@ -11,4 +11,4 @@ ...@@ -11,4 +11,4 @@
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...@@ -51,7 +51,7 @@ ...@@ -51,7 +51,7 @@
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\contentsline {subsubsection}{\numberline {2.3}Combustor from a jet engine}{40}{subsubsection.2.7.0.3} \contentsline {subsubsection}{\numberline {2.3}Combustor from a jet engine}{40}{subsubsection.2.7.0.3}
\contentsline {subsubsection}{\numberline {2.4}Water jet on a wall}{41}{subsubsection.2.7.0.4} \contentsline {subsubsection}{\numberline {2.4}Water jet on a wall}{41}{subsubsection.2.7.0.4}
\contentsline {subsubsection}{\numberline {2.5}High-speed gas flow}{41}{subsubsection.2.7.0.5} \contentsline {subsubsection}{\numberline {2.5}High-speed gas flow}{42}{subsubsection.2.7.0.5}
\contentsline {chapter}{\numberline {3}Analysis of existing flows with\nobreakspace {}three\nobreakspace {}dimensions}{45}{chapter.3} \contentsline {chapter}{\numberline {3}Analysis of existing flows with\nobreakspace {}three\nobreakspace {}dimensions}{45}{chapter.3}
\contentsline {section}{\numberline {3.1}Motivation}{45}{section.3.1} \contentsline {section}{\numberline {3.1}Motivation}{45}{section.3.1}
\contentsline {section}{\numberline {3.2}The Reynolds transport theorem}{45}{section.3.2} \contentsline {section}{\numberline {3.2}The Reynolds transport theorem}{45}{section.3.2}
...@@ -221,7 +221,7 @@ ...@@ -221,7 +221,7 @@
\contentsline {subsubsection}{\numberline {11.6}Flow field of a tornado}{196}{subsubsection.11.5.0.6} \contentsline {subsubsection}{\numberline {11.6}Flow field of a tornado}{196}{subsubsection.11.5.0.6}
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\contentsline {subsubsection}{\numberline {11.8}Air flow over a wing profile}{198}{subsubsection.11.5.0.8} \contentsline {subsubsection}{\numberline {11.8}Air flow over a wing profile}{198}{subsubsection.11.5.0.8}
\contentsline {chapter}{Appendix}{201}{section*.121} \contentsline {chapter}{Appendix}{201}{section*.124}
\contentsline {section}{\numberline {A1}Notation}{202}{section.Alph0.1} \contentsline {section}{\numberline {A1}Notation}{202}{section.Alph0.1}
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\contentsline {subsection}{\numberline {A2.1}Gradient}{203}{subsection.Alph0.2.1} \contentsline {subsection}{\numberline {A2.1}Gradient}{203}{subsection.Alph0.2.1}
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