Preset fluid properties for the simulation of a thermal liquid network

**Library:**Simscape / Fluids / Thermal Liquid / Utilities

The Thermal Liquid Properties (TL) block applies to a thermal liquid network the properties of a fluid selected from a preset list. Preset fluids include pure water, aqueous mixtures—of saline, glycol and glycerol compounds, commonly used in heat transfer applications as coolants and antifreeze solutions—and fuels such as diesel and aviation-grade Jet A. Use this block as a simple alternative to the Thermal Liquid Settings (TL) block, to define a fluid without having to specify in detail all of its properties. Every thermal liquid network in a model must contain one instance of either of these blocks.

The preset fluid properties are defined in tabular form as functions of temperature and pressure. The table data is sourced from Coolprop—an open-source fluids database—or, in the case of seawater, from a computational model developed by (and proprietary to) MIT. The values of the properties are set during simulation by linear interpolation of the nearest tabulated breakpoints. The effect of concentration is factored into the property calculations for mixtures (with mass or volume fraction providing the necessary measure of concentration).

All the fluid properties commonly specified in the Thermal Liquid Settings (TL) block are defined in the block. These properties include density, the bulk modulus and thermal expansion coefficient, the specific internal energy and specific heat, as well as the kinematic viscosity and thermal conductivity. The properties are valid over a limited region of temperatures and pressures specific to the fluid selected and dependent, in the cases of mixtures, on the concentration specified. Simulation is allowed within this validity region only.

A data visualization utility provides a means to graph the fluid properties
defined in the block. Use it to examine the temperature and pressure dependencies of
those properties or to ascertain the bounds of their validity regions (equal in the
visualizations to the bounds of the plots). To open the visualization utility,
right-click the block and from the context-sensitive menu select **Fluids** > **Plot Fluid Properties**. The plot updates automatically upon selection of a fluid property
from the drop-down list. Use the **Refresh** button to regenerate
the plot whenever the fluid selection or any of its required parameters are
changed.

**Visualization of density data for a 10% glycerol aqueous mixture**

The validity regions are defined in the block as matrices of zeros and ones. Each row corresponds to a tabulated temperature and each column to a tabulated pressure. A zero denotes an invalid breakpoint and a one a valid breakpoint. These validity matrices are internal to the block and cannot be modified; they can only be checked (using the data visualization utility of the block).

In most cases, the validity matrices are extracted directly from the tabulated data. Glycol and glycerol mixtures are a partial exception. Their pressure bounds are not available from the Coolprop data (where they are treated as incompressible fluids) and must therefore be obtained explicitly from block parameters. The figure shows an example of a validity region, that of pure water. Shaded squares are outside of the validity region.

`Water`

The properties of water are valid at temperatures above the triple-point value
(`273.160 K`

) up to the critical-point value
(`647.096 K`

). They are valid at pressures above the
greater of the triple-point value (`611.657 Pa`

) on one hand
and the temperature-dependent saturation value on the other, up to the
critical-point value (`22,064,000 MPa`

). Pressures below the
saturation point for a given temperature row are assigned a value of
`0`

in the validity matrix.

`Seawater (MIT model)`

The properties of seawater are valid at temperatures above
`0°C`

up to `120°C`

(```
273.15
K
```

to `393.15 K`

); they are valid at pressures
above the saturation point up to a maximum value of `12 MPa`

.
Pressures below the saturation point for a given temperature row (and at the
specified concentration level) are assigned a value of `0`

in
the validity matrix. Mixture concentrations can range in value from
`0`

to `0.12`

on a mass fraction
basis.

`Ethylene glycol and water mixture`

The properties of an aqueous ethylene glycol mixture are valid over a temperature domain determined from the mixture concentration; they are valid at pressures within the minimum and maximum bounds specified in the block dialog box (extended horizontally to span the width of the temperature rows).

The lower temperature bound is always the lesser of the minimum temperature
extracted from the Coolprop data and the freezing point of the mixture (the
mixture must be in the liquid state). The upper temperature bound is always the
maximum temperature extracted from the Coolprop data. Mixture concentrations can
range in value from `0`

to `0.6`

if a
mass-fraction basis is used, or from `0`

to
`1`

if a volume fraction basis is used.

`Propylene glycol and water mixture`

The properties of an aqueous propylene glycol mixture are valid over the
temperature and pressure ranges described for the case of ```
Ethylene
glycol and water mixture
```

. Mixture concentrations can range in
value from `0`

to `0.6`

if a mass-fraction
basis is used, or from `0.1`

to `0.6`

if a
volume fraction basis is used.

`Glycerol and water mixture`

The properties of an aqueous glycerol mixture are valid over the temperature
and pressure ranges as described for the case of ```
Ethylene glycol
and water mixture
```

. Mixture concentrations can range in value
from `0`

to `0.6`

on a mass-fraction
basis.

`Diesel fuel`

The properties of diesel fuel are valid at temperatures above
`-34.95°C`

up to `417.82°C`

(`238.20 K`

to `690.97 K`

); they are valid
at pressures above the saturation point up to a maximum value of ```
2.29
MPa
```

. Pressures below the saturation point for a given temperature
row are assigned a value of `0`

in the validity matrix.

`Aviation fuel Jet-A`

The properties of Jet A fuel are valid at temperatures above
`-50.93°C`

up to `372.46°C`

(`222.22 K`

to `645.61 K`

); they are valid
at pressures above the saturation point up to a maximum value of ```
2.41
MPa
```

. Pressures below the saturation point for a given temperature
row are assigned a value of `0`

in the validity matrix.

The aqueous mixtures of glycol and glycerol compounds are treated in the Coolprop database as incompressible substances. Their bulk moduli are unavailable from the data and must instead be obtained from the block parameters (where they are specified as constants). The pressure dependencies of their thermal expansion coefficients are likewise missing and must therefore be calculated (using the bulk modulus provided). Let density be:

$$\rho (T,p)=dT{\left(\frac{\partial \rho (T,p)}{\partial T}\right)}_{p}+dp{\left(\frac{d\rho (T,p)}{dp}\right)}_{T},$$

where *ρ* is density, *T* is
temperature, and *p* is pressure.

The solution has the form:

$$\rho (T,p)=\rho (T)\text{exp}\left(\frac{p-{p}_{\text{R}}}{\beta}\right),$$

where *ß* is the isothermal bulk modulus, and
where the subscript `R`

denotes a reference value, here the
atmospheric pressure at which the bulk modulus is specified. The partial derivative
of density with respect to temperature is:

$${\left(\frac{\partial \rho (T,p)}{\partial T}\right)}_{p}={\left(\frac{\partial \rho (T)}{\partial T}\right)}_{T}\text{exp}\left(\frac{p-{p}_{\text{R}}}{\beta}\right).$$

The thermal expansion coefficient is defined as:

$$\alpha (T,p)=-\frac{1}{\rho (T,p)}{\left(\frac{\partial \rho (T,p)}{\partial T}\right)}_{p},$$

Equivalently:

$$\alpha (T,p)=-\frac{1}{\rho (T,p)}{\left(\frac{\partial \rho (T)}{\partial T}\right)}_{T}\text{exp}\left(\frac{p-{p}_{\text{R}}}{\beta}\right).$$

The block provides the thermal expansion coefficient in this form to the thermal liquid network of which it is a part.

[1] Massachusetts Institute of
Technology (MIT), *Thermophysical properties of seawater database*.
http://web.mit.edu/seawater.

[2] K.G. Nayar, M.H. Sharqawy,
L.D. Banchik, J.H. Lienhard V, Thermophysical properties of seawater: A review and new
correlations that include pressure dependence, *Desalination*, Vol.
390, pp. 1-24, 2016.

[3] M.H. Sharqawy, J.H. Lienhard
V, S.M. Zubair, Thermophysical properties of seawater: A review of existing correlations
and data, *Desalination and Water Treatment*, Vol. 16, pp.
354-380.

[4] I.H. Bell, J. Wronski, S.
Quoilin, V. Lemort, Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source
Thermophysical Property Library CoolProp, *Industrial &
Engineering Chemistry Research*, Vol. 53 (6), pp. 2498–2508,
2014.