% Constitutive relation file for NozzleFlow (NozzleFlow_cr.r)
% Generated by PJG at Wed Apr 8 09:30 GMT 1998


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OPERATOR NozzleFlow;
% Ideal gas - but polytropic expansion
FOR ALL R, n, p1, p2, T1, A, Nothing
LET NozzleFlow(R,n,flow,5,
	p1,effort,1,
	p2,effort,2,
	T1,effort,3,
	A,effort,4,
	Nothing,effort,5
	) = A*p1*( (2*n/(n-1)) * (1/(R*T1)) * 
                ((p2/p1)^(2/n)) * (1 - (p2/p1)^(n-1/n) ) ^(1/2)
                );

END;

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system NozzleFlow (NozzleFlow_desc.tex)
% Generated by MTT on Thu Mar 19 13:24:59 GMT 1998.

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   The acausal bond graph of system \textbf{NozzleFlow} is
   displayed in Figure \Ref{NozzleFlow_abg} and its label
   file is listed in Section \Ref{sec:NozzleFlow_lbl}.

This 5 port component computes the mass flow in a polytropic
convergent nozzle from the formula:
\begin{equation}
  \dot m = A p_1 \sqrt{\frac{2n}{n-1}\frac{1}{RT_1} 
   \left ( \frac{p_2}{p_1} \right )^\frac{2}{n}
    \left [ 1- \left ( \frac{p_2}{p_1} \right )^\frac{n-1}{n} \right ]  }
\end{equation}

where:
\begin{itemize}
\item $n$ is the coefficient of polytropic expansion and
\item $R$ is the universal gas constant.
\end{itemize}

If the expansion is isentropic
\begin{equation}
  n=\gamma=\frac{c_p}{c_v}
\end{equation}
whre $c_p$ and $c_v$ are the spesicfic heats at constant pressure and volume.

Typical values for air are 
\begin{equation}
  \begin{align}
    R &= 287 \text{Nm}\text{kg}^{-1}{K}^{-1}\\
    \gamma &= 1.4
  \end{align}
\end{equation}

%SUMMARY NozzleFlow Subsonic ideal gas nozzle flow with polytropic expansion
%DESCRIPTION Polytropic expansion coefficient n=gamma=c_p/c_v for isentropic expansion.
 

%ALIAS $1	R	Ideal gas constant
%ALIAS $2	n	Index of polytropic expansion

%% Label file for system NozzleFlow (NozzleFlow_lbl.txt)

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%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type R
	r		NozzleFlow	R,n

% Component type SS
	[Area]		SS	external,external
	[MassFlow]	SS	external,external
	[P1]		SS	external,external
	[P2]		SS	external,external
	[T1]		SS	external,external

# Outline report file for system NozzleFlow (NozzleFlow_rep.txt)
# Generated by MTT on" Thursday September 24 09:49:01 BST 1998.

###############################################################
## Version control history
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## $Id$
## $Log$
###############################################################

mtt NozzleFlow abg tex			# The system description

# Uncomment the following lines or add others
mtt NozzleFlow ode tex	        # The system ode 
# mtt NozzleFlow sspar tex		# Steady-state parameters
# mtt NozzleFlow ss tex 		# Steady state
# mtt NozzleFlow sm tex			# State matrices (of linearised system)
# mtt NozzleFlow lmfr ps		# log modulus of frequency response (of linearised system)
# mtt NozzleFlow simpar tex		# Simulation parameters
# mtt NozzleFlow numpar tex		# Numerical simulation parameters
# mtt NozzleFlow input tex		# Simulation input
# mtt NozzleFlow odeso ps		# Simulation output