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package.mo
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within Modelica;
package Media "Library of media property models"
extends Modelica.Icons.Package;
import SI = Modelica.SIunits;
import Cv = Modelica.SIunits.Conversions;
package UsersGuide "User's Guide of Media Library"
extends Modelica.Icons.Information;
package MediumUsage "Medium usage"
extends Modelica.Icons.Information;
class BasicUsage "Basic usage"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<h4>Basic usage of medium model</h4>
<p>
Media models in Modelica.Media are provided by packages, inheriting from the
partial package Modelica.Media.Interfaces.PartialMedium. Every package defines:
</p>
<ul>
<li> Medium <b>constants</b> (such as the number of chemical substances,
molecular data, critical properties, etc.).</li>
<li> A BaseProperties <b>model</b>, to compute the basic thermodynamic
properties of the fluid;</li>
<li> <b>setState_XXX</b> functions to compute the thermodynamic state record from
different input arguments (such as density, temperature, and composition which
would be setState_dTX);</li>
<li> <b>Functions</b> to compute additional properties (such as saturation
properties, viscosity, thermal conductivity, etc.).</li>
</ul>
<p>
There are - as stated above - two different basic ways of using the Media library which
will be described in more details in the following section. One way is to use the model BaseProperties.
Every instance of BaseProperties for any medium model provides <b>3+nXi
equations</b> for the following <b>5+nXi variables</b> that are declared in
the medium model (nXi is the number of independent mass fractions, see
explanation below):
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Variable</b></td>
<td valign=\"top\"><b>Unit</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">T</td>
<td valign=\"top\">K</td>
<td valign=\"top\">temperature</td></tr>
<tr><td valign=\"top\">p</td>
<td valign=\"top\">Pa</td>
<td valign=\"top\">absolute pressure</td></tr>
<tr><td valign=\"top\">d</td>
<td valign=\"top\">kg/m3</td>
<td valign=\"top\">density</td></tr>
<tr><td valign=\"top\">u</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">specific internal energy</td></tr>
<tr><td valign=\"top\">h</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">specific enthalpy (h = u + p/d)</td></tr>
<tr><td valign=\"top\">Xi[nXi]</td>
<td valign=\"top\">kg/kg</td>
<td valign=\"top\">independent mass fractions m_i/m</td></tr>
<tr><td valign=\"top\">X[nX]</td>
<td valign=\"top\">kg/kg</td>
<td valign=\"top\">All mass fractions m_i/m. X is defined in BaseProperties by:<br>
X = <b>if</b> reducedX <b>then</b> vector([Xi; 1-<b>sum</b>(Xi)])
<b>else</b> Xi </td></tr>
</table>
<p>
<b>Two</b> variables out of p, d, h, or u, as well as the
<b>mass fractions</b> Xi are the <b>independent</b> variables and the
medium model basically provides equations to compute
the remaining variables, including the full mass fraction vector X
(more details to Xi and X are given further below).
</p>
<p>
In a component, the most basic usage of a medium model is as follows
</p>
<pre>
<b>model</b> Pump
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
Medium.BaseProperties medium_a \"Medium properties at location a (e.g., port_a)\";
// Use medium variables (medium_a.p, medium_a.T, medium_a.h, ...)
...
<b>end</b> Pump;
</pre>
<p>
The second way is to use the setState_XXX functions to compute the thermodynamic state
record from which all other thermodynamic state variables can be computed (see
<a href=\"modelica://Modelica.Media.UsersGuide.MediumDefinition.BasicDefinition\">
Basic definition of medium</a> for further details on ThermodynamicState). The setState_XXX functions
accept either X or Xi (see explanation below) and will decide internally which of these two compositions
is provided by the user. The four fundamental setState_XXX functions are provided in PartialMedium
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Function</b></td>
<td valign=\"top\"><b>Description</b></td>
<td valign=\"top\"><b>Short-form for<br>single component medium</b></td></tr>
<tr><td valign=\"top\">setState_dTX</td>
<td valign=\"top\">computes ThermodynamicState from density, temperature, and composition X or Xi</td>
<td valign=\"top\">setState_dT</td></tr>
<tr><td valign=\"top\">setState_phX</td>
<td valign=\"top\">computes ThermodynamicState from pressure, specific enthalpy, and composition X or Xi</td>
<td valign=\"top\">setState_ph</td></tr>
<tr><td valign=\"top\">setState_psX</td>
<td valign=\"top\">computes ThermodynamicState from pressure, specific entropy, and composition X or Xi</td>
<td valign=\"top\">setState_ps</td></tr>
<tr><td valign=\"top\">setState_pTX</td>
<td valign=\"top\">computes ThermodynamicState from pressure, temperature, and composition X or Xi</td>
<td valign=\"top\">setState_pT</td></tr>
</table>
<p>
The simple example that explained the basic usage of BaseProperties would then become
<pre>
<b>model</b> Pump
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
Medium.ThermodynamicState state_a \"Thermodynamic state record at location a (e.g., port_a)\";
// Compute medium variables from thermodynamic state record (pressure(state_a), temperature(state_a),
// specificEnthalpy(state_a), ...)
...
<b>end</b> Pump;
</pre>
<p>
All media models are directly or indirectly a subpackage of package
Modelica.Media.Interfaces.PartialMedium. Therefore,
a medium model in a component should inherit from this
partial package. Via the annotation \"choicesAllMatching = true\" it
is defined that the tool should display a selection box with
all loaded packages that inherit from PartialMedium. An example
is given in the next figure:
</p>
<IMG src=\"modelica://Modelica/Resources/Images/Media/UsersGuide/mediumMenu.png\" ALT=\"medium selection menu\">
<p>
A selected medium model leads, e.g., to the following equation:
</p>
<pre>
Pump pump(<b>redeclare package</b> Medium = Modelica.Media.Water.SimpleLiquidWater);
</pre>
<p>
Usually, a medium model is associated with the variables of a
fluid connector. Therefore, equations have to be defined in a model
that relate the variables in the connector with the variables
in the medium model:
</p>
<pre>
<b>model</b> Pump
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
Medium.BaseProperties medium_a \"Medium properties of port_a\";
// definition of the fluid port port_a
...
<b>equation</b>
medium.p = port_a.p;
medium.h = port_a.h;
medium.Xi = port_a.Xi;
...
<b>end</b> Pump;
</pre>
in the case of using BaseProperties or
<pre>
<b>model</b> Pump
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
Medium.ThermodynamicState state_a \"Thermodynamic state record of medium at port_a\";
// definition of the fluid port port_a
...
<b>equation</b>
state_a = Medium.setState_phX(port_a.p, port_a.h, port_a.Xi) // if port_a contains the variables
// p, h, and Xi
...
<b>end</b> Pump;
</pre>
<p>
in the case of using ThermodynamicState.
</p>
<p>
If a component model shall treat both single and multiple
substance fluids, equations for the mass fractions have to be
present (above: medium.Xi = port_a.Xi) in the model. According
to the Modelica semantics, the equations of the mass fractions
are ignored, if the dimension of Xi is zero, i.e., for a single-component
medium. Note, by specific techniques sketched in section
\"Medium definition\", the independent variables in the medium model
need not to be the same as the variables in the connector and still
get the same efficiency, as if the same variables would be used.
</p>
<p>
If a fluid consists of a single
substance, <b>nXi = 0</b> and the vector of mass fractions Xi is not
present. If a fluid consists of nS substances,
the medium model may define the number of independent
mass fractions <b>nXi</b> to be <b>nS</b>, <b>nS-1</b>, or zero.
In all cases, balance equations for nXi substances have to be
given in the corresponding component (see discussion below).
Note, that if nXi = nS, the constraint \"sum(Xi)=1\" between the mass
fractions is <b>not</b> present in the model; in that case, it is necessary to
provide consistent start values for Xi such that sum(Xi) = 1.
</p>
<p>
The reason for this definition of Xi is that a fluid component library
can be implemented by using only the independent mass fractions Xi and
then via the medium it is defined how Xi is interpreted:
</p>
<ul>
<li> If Xi = nS, then the constraint equation sum(X) = 1 is neglected
during simulation. By making sure that the initial conditions of X
fulfill this constraint, it can usually be guaranteed that small
errors in sum(X) = 1 remain small although this constraint equation is
not explicitly used during the simulation. This approach is usually useful
if components of the mixture can become very small. If such a small
quantity is computed via the equation 1 - sum(X[1:nX-1]), there might
be large numerical errors and it is better to compute it via
the corresponding balance equation.</li>
<li> If Xi = nS-1, then the true independent mass fractions are used
in the fluid component and the last component of X is computed via
X[nX] = 1 - sum(Xi). This is useful for, e.g., MoistAir, where the
number of states should be as small as possible without introducing
numerical problems.</li>
<li> If Xi = 0, then the reference value of composition reference_X is
assumed. This case is useful to avoid composition states in all
the cases when the composition will always be constant, e.g., with
circuits having fixed composition sources.</li>
</ul>
<p>
The full vector of mass fractions <b>X[nX]</b> is computed in
PartialMedium.BaseProperties based on Xi, reference_X, and the information whether Xi = nS or nS-1. For single-substance media, nX = 0, so there's also no X vector. For multiple-substance media, nX = nS, and X always contains the full vector of mass fractions. In order to reduce confusion for the user of a fluid component library, \"Xi\" has the annotation \"HideResult=true\", meaning, that this variable is not shown in the plot window. Only X is shown in the plot window and this vector always contains all mass fractions.
</p>
</HTML>"));
end BasicUsage;
class BalanceVolume "Balance volume"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<p>
Fluid libraries usually have balance volume components with one fluid connector
port that fulfill the mass and energy balance and on a different grid components that
fulfill the momentum balance. A balance volume component, called junction
volume below, should be primarily implemented in the following way
(see also the implementation in
<a href=\"modelica://Modelica.Media.Examples.Tests.Components.PortVolume\">
Modelica.Media.Examples.Tests.Components.PortVolume</a>):
</p>
<pre>
<b>model</b> JunctionVolume
<b>import</b> SI=Modelica.SIunits;
<b>import</b> Modelica.Media.Examples.Tests.Components.FluidPort_a;
<b>parameter</b> SI.Volume V = 1e-6 \"Fixed size of junction volume\";
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
FluidPort_a port(<b>redeclare package</b> Medium = Medium);
Medium.BaseProperties medium(preferredMediumStates = <b>true</b>);
SI.Energy U \"Internal energy of junction volume\";
SI.Mass M \"Mass of junction volume\";
SI.Mass MX[Medium.nXi] \"Independent substance masses of junction volume\";
<b>equation</b>
medium.p = port.p;
medium.h = port.h;
medium.Xi = port.Xi;
M = V*medium.d; // mass of JunctionVolume
MX = M*medium.Xi; // mass fractions in JunctionVolume
U = M*medium.u; // internal energy in JunctionVolume
<b>der</b>(M) = port.m_flow; // mass balance
<b>der</b>(MX) = port.mX_flow; // substance mass balance
<b>der</b>(U) = port.H_flow; // energy balance
<b>end</b> JunctionVolume;
</pre>
<p>
Assume the Modelica.Media.Air.SimpleAir medium model is used with
the JunctionVolume model above. This medium model uses pressure p
and temperature T as independent variables. If the flag
\"preferredMediumStates\" is set to <b>true</b> in the declaration
of \"medium\", then the independent variables of this medium model
get the attribute \"stateSelect = StateSelect.prefer\", i.e., the
Modelica translator should use these variables as states, if this
is possible. Basically, this means that
constraints between the
potential states p,T and the potential states U,M are present.
A Modelica tool will therefore <b>automatically</b>
differentiate medium equations and will use the following
equations for code generation (note the equations related to X are
removed, because SimpleAir consists of a single substance only):
</p>
<pre>
M = V*medium.d;
U = M*medium.u;
// balance equations
<b>der</b>(M) = port.m_flow;
<b>der</b>(U) = port.H_flow;
// abbreviations introduced to get simpler terms
p = medium.p;
T = medium.T;
d = medium.d;
u = medium.u;
h = medium.h;
// medium equations
d = fd(p,T);
h = fh(p,T);
u = h - p/d;
// equations derived <b>automatically</b> by a Modelica tool due to index reduction
<b>der</b>(U) = <b>der</b>(M)*u + M*<b>der</b>(u);
<b>der</b>(M) = V*<b>der</b>(d);
<b>der</b>(u) = <b>der</b>(h) - <b>der</b>(p)/d - p/<b>der</b>(d);
<b>der</b>(d) = <b>der</b>(fd,p)*<b>der</b>(p) + <b>der</b>(fd,T)*<b>der</b>(T);
<b>der</b>(h) = <b>der</b>(fh,p)*<b>der</b>(p) + <b>der</b>(fd,T)*<b>der</b>(T);
</pre>
<p>
Note, that \"der(y,x)\" is an operator that characterizes
in the example above the partial derivative of y with respect to x
(this operator will be included in one of the next Modelica language
releases).
All media models in this library are written in such a way that
at least the partial derivatives of the medium variables with
respect to the independent variables are provided, either because
the equations are directly given (= symbolic differentiation is possible)
or because the derivative of the corresponding function (such as fd above)
is provided. A Modelica tool will transform the equations above
in differential equations with p and T as states, i.e., will
generate equations to compute <b>der</b>(p) and <b>der</b>(T) as function of p and T.
</p>
<p>
Note, when preferredMediumStates = <b>false</b>, no differentiation
will take place and the Modelica translator will use the variables
appearing differentiated as states, i.e., M and U. This has the
disadvantage that for many media non-linear systems of equations are
present to compute the intrinsic properties p, d, T, u, h from
M and U.
</p>
</HTML>"));
end BalanceVolume;
class ShortPipe "Short pipe"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<p>
Fluid libraries have components with two ports that store
neither mass nor energy and fulfill the
momentum equation between their two ports, e.g., a short pipe. In most
cases this means that an equation is present relating the pressure
drop between the two ports and the mass flow rate from one to the
other port. Since no mass or energy is stored, no differential
equations for thermodynamic variables are present. A component model of this type
has therefore usually the following structure
(see also the implementation in
<a href=\"modelica://Modelica.Media.Examples.Tests.Components.ShortPipe\">
Modelica.Media.Examples.Tests.Components.ShortPipe</a>):
</p>
<pre>
<b>model</b> ShortPipe
<b>import</b> SI=Modelica.SIunits;
<b>import</b> Modelica.Media.Examples.Tests.Components;
// parameters defining the pressure drop equation
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium
\"Medium model\" <b>annotation</b> (choicesAllMatching = <b>true</b>);
Component.FluidPort_a port_a (<b>redeclare package</b> Medium = Medium);
Component.FluidPort_b port_b (<b>redeclare package</b> Medium = Medium);
SI.Pressure dp = port_a.p - port_b.p \"Pressure drop\";
Medium.BaseProperties medium_a \"Medium properties in port_a\";
Medium.BaseProperties medium_b \"Medium properties in port_b\";
<b>equation</b>
// define media models of the ports
medium_a.p = port_a.p;
medium_a.h = port_a.h;
medium_a.Xi = port_a.Xi;
medium_b.p = port_b.p;
medium_b.h = port_b.h;
medium_b.Xi = port_b.Xi;
// Handle reverse and zero flow (semiLinear is a built-in Modelica operator)
port_a.H_flow = <b>semiLinear</b>(port_a.m_flow, port_a.h, port_b.h);
port_a.mXi_flow = <b>semiLinear</b>(port_a.m_flow, port_a.Xi, port_b.Xi);
// Energy, mass and substance mass balance
port_a.H_flow + port_b.H_flow = 0;
port_a.m_flow + port_b.m_flow = 0;
port_a.mXi_flow + port_b.mXi_flow = zeros(Medium.nXi);
// Provide equation: port_a.m_flow = f(dp)
<b>end</b> ShortPipe;
</pre>
<p>
The <b>semiLinear</b>(..) operator is basically defined as:
</p>
<pre>
semiLinear(m_flow, ha, hb) = if m_flow ≥ 0 then m_flow*ha else m_flow*hb;
</pre>
<p>
that is, it computes the enthalpy flow rate either from the port_a or
from the port_b properties, depending on flow direction. The exact
details of this operator are given in
<a href=\"modelica://ModelicaReference.Operators.'semiLinear()'\">
ModelicaReference.Operators.'semiLinear()'</a>. Especially, rules
are defined in the Modelica specification that m_flow = 0 can be treated
in a \"meaningful way\". Especially, if n fluid components (such as pipes)
are connected together and the fluid connector from above is used,
a linear system of equations appear between
medium1.h, medium2.h, medium3.h, ..., port1.h, port2.h, port3.h, ...,
port1.H_flow, port2.H_flow, port3.H_flow, .... The rules for the
semiLinear(..) operator allow the following solution of this
linear system of equations:
</p>
<ul>
<li> n = 2 (two components are connected):<br>
The linear system of equations can be analytically solved
with the result
<pre>
medium1.h = medium2.h = port1.h = port2.h
0 = port1.H_flow + port2.H_flow
</pre>
Therefore, no problems with zero mass flow rate are present.</li>
<li> n > 2 (more than two components are connected together):<br>
The linear system of equations is solved numerically during simulation.
For m_flow = 0, the linear system becomes singular and has an
infinite number of solutions. The simulator could use the solution t
that is closest to the solution in the previous time step
(\"least squares solution\"). Physically, the solution is determined
by diffusion which is usually neglected. If diffusion is included,
the linear system is regular.</li>
</ul>
</HTML>"));
end ShortPipe;
class OptionalProperties "Optional properties"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<p>
In some cases additional medium properties are needed.
A component that needs these optional properties has to call
one of the functions listed in the following table. They are
defined as partial functions within package
<a href=\"modelica://Modelica.Media.Interfaces.PartialMedium\">PartialMedium</a>,
and then (optionally) implemented in actual medium packages.
If a component calls such an optional function and the
medium package does not provide a new implementation for this
function, an error message is printed at translation time,
since the function is \"partial\", i.e., incomplete.
The argument of all functions is the <b>state</b> record,
automatically defined by the BaseProperties model or specifically computed using the
setState_XXX functions, which contains the
minimum number of thermodynamic variables needed to compute all the additional
properties. In the table it is assumed that there is a declaration of the
form:
</p>
<pre>
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium;
Medium.ThermodynamicState state;
</pre>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Function call</b></td>
<td valign=\"top\"><b>Unit</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">Medium.dynamicViscosity(state)</td>
<td valign=\"top\">Pa.s</td>
<td valign=\"top\">dynamic viscosity</td></tr>
<tr><td valign=\"top\">Medium.thermalConductivity(state)</td>
<td valign=\"top\">W/(m.K)</td>
<td valign=\"top\">thermal conductivity</td></tr>
<tr><td valign=\"top\">Medium.prandtlNumber(state)</td>
<td valign=\"top\">1</td>
<td valign=\"top\">Prandtl number</td></tr>
<tr><td valign=\"top\">Medium.specificEntropy(state)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">specific entropy</td></tr>
<tr><td valign=\"top\">Medium.specificHeatCapacityCp(state)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">specific heat capacity at constant pressure</td></tr>
<tr><td valign=\"top\">Medium.specificHeatCapacityCv(state)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">specific heat capacity at constant density</td></tr>
<tr><td valign=\"top\">Medium.isentropicExponent(state)</td>
<td valign=\"top\">1</td>
<td valign=\"top\">isentropic exponent</td></tr>
<tr><td valign=\"top\">Medium.isentropicEnthatlpy(pressure, state)</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">isentropic enthalpy</td></tr>
<tr><td valign=\"top\">Medium.velocityOfSound(state)</td>
<td valign=\"top\">m/s</td>
<td valign=\"top\">velocity of sound</td></tr>
<tr><td valign=\"top\">Medium.isobaricExpansionCoefficient(state)</td>
<td valign=\"top\">1/K</td>
<td valign=\"top\">isobaric expansion coefficient</td></tr>
<tr><td valign=\"top\">Medium.isothermalCompressibility(state)</td>
<td valign=\"top\">1/Pa</td>
<td valign=\"top\">isothermal compressibility</td></tr>
<tr><td valign=\"top\">Medium.density_derp_h(state)</td>
<td valign=\"top\">kg/(m3.Pa)</td>
<td valign=\"top\">derivative of density by pressure at constant enthalpy</td></tr>
<tr><td valign=\"top\">Medium.density_derh_p(state)</td>
<td valign=\"top\">kg2/(m3.J)</td>
<td valign=\"top\">derivative of density by enthalpy at constant pressure</td></tr>
<tr><td valign=\"top\">Medium.density_derp_T(state)</td>
<td valign=\"top\">kg/(m3.Pa)</td>
<td valign=\"top\">derivative of density by pressure at constant temperature</td></tr>
<tr><td valign=\"top\">Medium.density_derT_p(state)</td>
<td valign=\"top\">kg/(m3.K)</td>
<td valign=\"top\">derivative of density by temperature at constant pressure</td></tr>
<tr><td valign=\"top\">Medium.density_derX(state)</td>
<td valign=\"top\">kg/m3</td>
<td valign=\"top\">derivative of density by mass fraction</td></tr>
<tr><td valign=\"top\">Medium.molarMass(state)</td>
<td valign=\"top\">kg/mol</td>
<td valign=\"top\">molar mass</td></tr>
</table>
<p>
There are also some short forms provided for user convenience that allow the computation of certain
thermodynamic state variables without using the ThermodynamicState record explicitly. Those short forms
are for example useful to compute consistent start values in the initial equation section. Let's
consider the function temperature_phX(p,h,X) as an example. This function computes the temperature
from pressure, specific enthalpy, and composition X (or Xi) and is a short form for writing
</p>
<pre>
temperature(setState_phX(p,h,X))
</pre>
<p>
The following functions are predefined in PartialMedium (other functions can be added in the actual
medium implementation package if they are useful)
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\">Medium.specificEnthalpy_pTX(p,T,X)</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">Specific enthalpy at p, T, X </td></tr>
<tr><td valign=\"top\">Medium.temperature_phX(p,h,X)</td>
<td valign=\"top\">K</td>
<td valign=\"top\">Temperature at p, h, X</td></tr>
<tr><td valign=\"top\">Medium.density_phX(p,h,X)</td>
<td valign=\"top\">kg/m3</td>
<td valign=\"top\">Density at p, h, X</td></tr>
<tr><td valign=\"top\">Medium.temperature_psX(p,s,X)</td>
<td valign=\"top\">K</td>
<td valign=\"top\">Temperature at p, s, X</td></tr>
<tr><td valign=\"top\">Medium.specificEnthalpy_psX(p,s,X)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">Specific entropy at p, s, X</td></tr>
</table>
<p>
Assume for example that the dynamic viscosity eta is needed in
the pressure drop equation of a short pipe. Then, the
model of a short pipe has to be changed to:
</p>
<pre>
<b>model</b> ShortPipe
...
Medium.BaseProperties medium_a \"Medium properties in port_a\";
Medium.BaseProperties medium_b \"Medium properties in port_b\";
...
Medium.DynamicViscosity eta;
...
eta = <b>if</b> port_a.m_flow > 0 <b>then</b>
Medium.dynamicViscosity(medium_a.state)
<b>else</b>
Medium.dynamicViscosity(medium_b.state);
// use eta in the pressure drop equation: port_a.m_flow = f(dp, eta)
<b>end</b> ShortPipe;
</pre>
<p>
Note, \"Medium.DynamicViscosity\" is a type defined in Modelica.Interfaces.PartialMedium
as
</p>
<pre>
<b>import</b> SI = Modelica.SIunits;
<b>type</b> DynamicViscosity = SI.DynamicViscosity (
min=0,
max=1.e8,
nominal=1.e-3,
start=1.e-3);
</pre>
<p>
Every medium model may modify the attributes, to provide, e.g.,
min, max, nominal, and start values adapted to the medium.
Also, other types, such as AbsolutePressure, Density, MassFlowRate,
etc. are defined in PartialMedium. Whenever possible, these medium
specific types should be used in a model in order that medium information,
e.g., about nominal or start values, are automatically utilized.
</p>
</HTML>"));
end OptionalProperties;
class Constants "Constants"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<p>
Every medium model provides the following <b>constants</b>. For example,
if a medium is declared as:
</p>
<pre>
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialMedium;
</pre>
<p>
then constants \"Medium.mediumName\", \"Medium.nX\", etc. are defined:
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Type</b></td>
<td valign=\"top\"><b>Name</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">String</td><td valign=\"top\">mediumName</td>
<td valign=\"top\">Unique name of the medium (is usually used to check whether
the media in different components connected together
are the same, by providing Medium.mediumName as quantity
attribute of the mass flow rate in the connector)</td></tr>
<tr><td valign=\"top\">String</td><td valign=\"top\">substanceNames[nS]</td>
<td valign=\"top\">Names of the substances that make up the medium.
If only one substance is present, substanceNames = {mediumName}.</td></tr>
<tr><td valign=\"top\">String</td><td valign=\"top\">extraPropertiesNames[nC]</td>
<td valign=\"top\">Names of the extra transported substances, outside of mass and
energy balances.</td></tr>
<tr><td valign=\"top\">Boolean</td><td valign=\"top\">singleState</td>
<td valign=\"top\">= <b>true</b>, if u and d are not a function of pressure, and thus only
a function of a single thermal variable (temperature or enthalpy) and
of Xi for a multiple substance medium. Usually, this flag is
<b>true</b> for incompressible media. It is used in a model to determine
whether 1+nXi (singleState=<b>true</b>) or 2+nXi (singleState=<b>false</b>)
initial conditions have to be provided for a volume element that
contains mass and energy balance.</td></tr>
<tr><td valign=\"top\">AbsolutePressure</td><td valign=\"top\">reference_p</td>
<td valign=\"top\">Reference pressure for the medium</td></tr>
<tr><td valign=\"top\">MassFraction</td><td valign=\"top\">reference_X[nX]</td>
<td valign=\"top\">Reference composition for the medium</td></tr>
<tr><td valign=\"top\">AbsolutePressure</td><td valign=\"top\">p_default</td>
<td valign=\"top\">Default value for pressure of medium (for initialization)</td></tr>
<tr><td valign=\"top\">Temperature</td><td valign=\"top\">T_default</td>
<td valign=\"top\">Default value for temperature of medium (for initialization)</td></tr>
<tr><td valign=\"top\">SpecificEnthalpy</td><td valign=\"top\">h_default</td>
<td valign=\"top\">Default value for specific enthalpy of medium (for initialization)</td></tr>
<tr><td valign=\"top\">MassFraction</td><td valign=\"top\">X_default[nX]</td>
<td valign=\"top\">Default value for mass fractions of medium (for initialization)</td></tr>
<tr><td valign=\"top\">Integer</td><td valign=\"top\">nS</td>
<td valign=\"top\">number of substances contained in the medium.</td></tr>
<tr><td valign=\"top\">Integer</td><td valign=\"top\">nX</td>
<td valign=\"top\">Size of the full mass fraction vector X nX=nS.</td></tr>
<tr><td valign=\"top\">Integer</td><td valign=\"top\">nXi</td>
<td valign=\"top\">Number of independent mass fractions. If there is a single substance,
then nXi = 0. </td></tr>
<tr><td valign=\"top\">Boolean</td><td valign=\"top\">reducedX</td>
<td valign=\"top\">= <b>true</b>, if the medium has a single substance, or if the medium model
has multiple substances and contains the equation sum(X) = 1.
In both cases, nXi = nS - 1 (unless fixedX = true).<br>
= <b>false</b>, if the medium has multiple substances and does not contain the
equation sum(X)=1, i.e., nXi = nX = nS (unless fixedX = true).
</td></tr>
<tr><td valign=\"top\">Boolean</td><td valign=\"top\">fixedX</td>
<td valign=\"top\">= <b>false</b>: the composition of the medium can vary, and is
determined by nXi independent mass fractions (see reducedX above).<br>
= <b>true</b>: the composition of the medium is always reference_X,
and nXi = 0.</td></tr>
<tr><td valign=\"top\">FluidConstants</td><td valign=\"top\">fluidConstants[nS]</td>
<td valign=\"top\">Critical, triple, molecular and other
standard data that are provided for
every substance of a medium.</td></tr>
</table>
<p>
The record FluidConstants that is defined in PartialMedium contains the following elements
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Type</b></td>
<td valign=\"top\"><b>Name</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">String</td>
<td valign=\"top\">iupacName</td>
<td valign=\"top\">complete IUPAC name</td></tr>
<tr><td valign=\"top\">String</td>
<td valign=\"top\">casRegistryNumber</td>
<td valign=\"top\">chemical abstracts sequencing number</td></tr>
<tr><td valign=\"top\">String</td>
<td valign=\"top\">chemicalFormula</td>
<td valign=\"top\">Chemical formula, (brutto, nomenclature according to Hill)</td></tr>
<tr><td valign=\"top\">String</td>
<td valign=\"top\">structureFormula</td>
<td valign=\"top\">Chemical structure formula</td></tr>
<tr><td valign=\"top\">MolarMass</td>
<td valign=\"top\">molarMass</td>
<td valign=\"top\">molar mass</td></tr>
</table>
<p> This record is extended in the partial packages further down the hierarchy (such as
PartialTwoPhaseMedium or PartialMixtureMedium) and may contain some or all of the following
elements</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\">Temperature</td>
<td valign=\"top\">criticalTemperature</td>
<td valign=\"top\">critical temperature</td></tr>
<tr><td valign=\"top\">AbsolutePressure</td>
<td valign=\"top\">criticalPressure</td>
<td valign=\"top\">critical pressure</td></tr>
<tr><td valign=\"top\">MolarVolume</td>
<td valign=\"top\">criticalMolarVolume</td>
<td valign=\"top\">critical molar Volume</td></tr>
<tr><td valign=\"top\">Real</td>
<td valign=\"top\">acentricFactor</td>
<td valign=\"top\">Pitzer acentric factor</td></tr>
<tr><td valign=\"top\">Temperature</td>
<td valign=\"top\">triplePointTemperature</td>
<td valign=\"top\">triple point temperature</td></tr>
<tr><td valign=\"top\">AbsolutePressure</td>
<td valign=\"top\">triplePointPressure</td>
<td valign=\"top\">triple point pressure</td></tr>
<tr><td valign=\"top\">Temperature</td>
<td valign=\"top\">meltingPoint</td>
<td valign=\"top\">melting point at 101325 Pa</td></tr>
<tr><td valign=\"top\">Temperature</td>
<td valign=\"top\">normalBoilingPoint</td>
<td valign=\"top\">normal boiling point (at 101325 Pa)</td></tr>
<tr><td valign=\"top\">DipoleMoment</td>
<td valign=\"top\">dipoleMoment</td>
<td valign=\"top\">dipole moment of molecule in Debye (1 debye = 3.33564e10-30 C.m)</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasIdealGasHeatCapacity</td>
<td valign=\"top\">true if ideal gas heat capacity is available</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasCriticalData</td>
<td valign=\"top\">true if critical data are known</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasDipoleMoment</td>
<td valign=\"top\">true if a dipole moment known</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasFundamentalEquation</td>
<td valign=\"top\">true if a fundamental equation</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasLiquidHeatCapacity</td>
<td valign=\"top\">true if liquid heat capacity is available</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasSolidHeatCapacity</td>
<td valign=\"top\">true if solid heat capacity is available</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasAccurateViscosityData</td>
<td valign=\"top\">true if accurate data for a viscosity function is available</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasAccurateConductivityData</td>
<td valign=\"top\">true if accurate data for thermal conductivity is available</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasVapourPressureCurve</td>
<td valign=\"top\">true if vapour pressure data, e.g., Antoine coefficients are known</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">hasAcentricFactor</td>
<td valign=\"top\">true if Pitzer accentric factor is known</td></tr>
<tr><td valign=\"top\">SpecificEnthalpy</td>
<td valign=\"top\">HCRIT0</td>
<td valign=\"top\">Critical specific enthalpy of the fundamental equation</td></tr>
<tr><td valign=\"top\">SpecificEntropy</td>
<td valign=\"top\">SCRIT0</td>
<td valign=\"top\">Critical specific entropy of the fundamental equation</td></tr>
<tr><td valign=\"top\">SpecificEnthalpy</td>
<td valign=\"top\">deltah</td>
<td valign=\"top\">Difference between specific enthalpy model
(h_m) and f.eq. (h_f) (h_m - h_f)</td></tr>
<tr><td valign=\"top\">SpecificEntropy</td>
<td valign=\"top\">deltas</td>
<td valign=\"top\">Difference between specific enthalpy model (s_m) and f.eq.
(s_f) (s_m - s_f)</td></tr>
</table>
</html>"));
end Constants;
class TwoPhase "Two-phase media"
extends Modelica.Icons.Information;
annotation (Documentation(info="<HTML>
<p>
Models for media which can exist in one-phase or two-phase conditions inherit
from <a href=\"modelica://Modelica.Media.Interfaces.PartialTwoPhaseMedium\">
Modelica.Media.Interfaces.PartialTwoPhaseMedium</a>
(which inherits from PartialMedium). The basic usage of these
media models is the same as described in the previous sections. However, additional
functionalities are provided, which apply only to potentially two-phase media.
</p>
<p>
The following additional medium <b>constants</b> are provided:
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Type</b></td>
<td valign=\"top\"><b>Name</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">smoothModel</td>
<td valign=\"top\">If this flag is false (default value), then events are triggered
whenever the saturation boundary is crossed; otherwise, no events
are generated.</td></tr>
<tr><td valign=\"top\">Boolean</td>
<td valign=\"top\">onePhase</td>
<td valign=\"top\">If this flag is true, then the medium model assumes it will be never
called in the two-phase region. This can be useful to speed up
the computations in a two-phase medium, when the user is sure it will
always work in the one-phase region. Default value: false.</td></tr>
</table>
<p>
The setState_ph(), setState_ps(), setState_dT() and setState_pT() functions have
one extra input, named <i>phase</i>. If the phase input is not specified, or if
it is given a value of zero, then the setState function will determine the phase,
based on the other input values. An input phase = 1 will force the setState
function to return a state vector corresponding to a one-phase state, while
phase = 2 will force the setState value to return a state vector corresponding
to a two-phase state, as shown in the following example;
</p>
<pre>
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialTwoPhaseMedium;
Medium.ThermodynamicState state, state1, state2;
<b>equation</b>
// Set the state, given the pressure and the specific enthalpy
// the phase is determined by the (p, h) values, and can be retrieved
// from the state record
state = Medium.setState_ph(p, h);
phase = state1.phase;
// Force the computation of the state with one-phase
// equations of state, irrespective of the (p, h) values
state1 = Medium.setState_ph(p, h, 1);
// Force the computation of the state with 2-phase
// equations of state, irrespective of the (p, h) values
state2 = Medium.setState_ph(p, h, 2);
</pre>
<p>
This feature can be used for the following purposes:
</p>
<ul>
<li> saving computational time, if one knows in advance the phase of the medium;
<li> unambiguously determine the phase, when the two inputs correspond to a point on the saturation boundary (the derivative functions have substantially different values on either side);
<li> get the properties of metastable states, like superheated water or subcooled vapour.
</ul>
<p>
Many additional optional functions are defined to compute properties of
saturated media, either liquid (bubble point) or vapour (dew point).
The argument to such functions is a SaturationProperties record, which can be
set starting from either the saturation pressure or the saturation temperature,
as shown in the following example.
</p>
<pre>
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialTwoPhaseMedium;
Medium.SaturationProperties sat_p;
Medium.SaturationProperties sat_T;
<b>equation</b>
// Set sat_p to saturation properties at pressure p
sat_p = Medium.setSat_p(p);
// Compute saturation properties at pressure p
saturationTemperature_p = Medium.saturationTemperature_sat(sat_p);
bubble_density_p = Medium.bubbleDensity(sat_p);
dew_enthalpy_p = Medium.dewEnthalpy(sat_p);
// Set sat_T to saturation properties at temperature T
sat_T = Medium.setSat_T(T);
// Compute saturation properties at temperature T
saturationTemperature_T = Medium.saturationPressure_sat(sat_T);
bubble_density_T = Medium.bubbleDensity(sat_T);
dew_enthalpy_T = Medium.dewEnthalpy(sat_T);
</pre>
<p>With reference to a model defining a pressure p, a temperature T, and a
SaturationProperties record sat, the following functions are provided:
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Function call</b></td>
<td valign=\"top\"><b>Unit</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">Medium.saturationPressure(T)</td>
<td valign=\"top\">Pa</td>
<td valign=\"top\">Saturation pressure at temperature T</td></tr>
<tr><td valign=\"top\">Medium.saturationTemperature(p)</td>
<td valign=\"top\">K</td>
<td valign=\"top\">Saturation temperature at pressure p</td></tr>
<tr><td valign=\"top\">Medium.saturationTemperature_derp(p)</td>
<td valign=\"top\">K/Pa</td>
<td valign=\"top\">Derivative of saturation temperature with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.saturationTemperature_sat(sat)</td>
<td valign=\"top\">K</td>
<td valign=\"top\">Saturation temperature</td></tr>
<tr><td valign=\"top\">Medium.saturationPressure_sat(sat)</td>
<td valign=\"top\">Pa</td>
<td valign=\"top\">Saturation pressure</td></tr>
<tr><td valign=\"top\">Medium.bubbleEnthalpy(sat)</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">Specific enthalpy at bubble point</td></tr>
<tr><td valign=\"top\">Medium.dewEnthalpy(sat)</td>
<td valign=\"top\">J/kg</td>
<td valign=\"top\">Specific enthalpy at dew point</td></tr>
<tr><td valign=\"top\">Medium.bubbleEntropy(sat)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">Specific entropy at bubble point</td></tr>
<tr><td valign=\"top\">Medium.dewEntropy(sat)</td>
<td valign=\"top\">J/(kg.K)</td>
<td valign=\"top\">Specific entropy at dew point</td></tr>
<tr><td valign=\"top\">Medium.bubbleDensity(sat)</td>
<td valign=\"top\">kg/m3</td>
<td valign=\"top\">Density at bubble point</td></tr>
<tr><td valign=\"top\">Medium.dewDensity(sat)</td>
<td valign=\"top\">kg/m3</td>
<td valign=\"top\">Density at dew point</td></tr>
<tr><td valign=\"top\">Medium.saturationTemperature_derp_sat(sat)</td>
<td valign=\"top\">K/Pa</td>
<td valign=\"top\">Derivative of saturation temperature with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.dBubbleDensity_dPressure(sat)</td>
<td valign=\"top\">kg/(m3.Pa)</td>
<td valign=\"top\">Derivative of density at bubble point with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.dDewDensity_dPressure(sat)</td>
<td valign=\"top\">kg/(m3.Pa)</td>
<td valign=\"top\">Derivative of density at dew point with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.dBubbleEnthalpy_dPressure(sat)</td>
<td valign=\"top\">J/(kg.Pa)</td>
<td valign=\"top\">Derivative of specific enthalpy at bubble point with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.dDewEnthalpy_dPressure(sat)</td>
<td valign=\"top\">J/(kg.Pa)</td>
<td valign=\"top\">Derivative of specific enthalpy at dew point with respect to pressure</td></tr>
<tr><td valign=\"top\">Medium.surfaceTension(sat)</td>
<td valign=\"top\">N/m</td>
<td valign=\"top\">Surface tension between liquid and vapour phase</td></tr>
</table>
<p>
Sometimes it can be necessary to compute fluid properties in the thermodynamic
plane, just inside or outside the saturation dome. In this case, it is possible
to obtain an instance of a ThermodynamicState state vector, and then use it
to call the additional functions already defined for one-phase media.
</p>
<table border=1 cellspacing=0 cellpadding=2>
<tr><td valign=\"top\"><b>Function call</b></td>
<td valign=\"top\"><b>Description</b></td></tr>
<tr><td valign=\"top\">Medium.setBubbleState(sat, phase)</td>
<td valign=\"top\">Obtain the thermodynamic state vector
corresponding to the bubble point. If phase==1 (default), the state is
on the one-phase side; if phase==2, the state is on the two-phase
side </td></tr>
<tr><td valign=\"top\">Medium.setDewState(sat, phase)</td>
<td valign=\"top\">Obtain the thermodynamic state vector
corresponding to the dew point. If phase==1 (default), the state is
on the one-phase side; if phase==2, the state is on the two-phase
side </td></tr>
</table>
<p>
Here are some examples:
</p>
<pre>
<b>replaceable package</b> Medium = Modelica.Media.Interfaces.PartialTwoPhaseMedium;
Medium.SaturationProperties sat;
Medium.ThermodynamicState dew_1; // dew point, one-phase side
Medium.ThermodynamicState bubble_2; // bubble point, two phase side
<b>equation</b>