Fluid properties in two-phase fluid network

Two-Phase Fluid/Utilities

The Two-Phase Fluid Properties (2P) block provides the thermophysical properties of a two-phase fluid. The properties in this block apply to the entire two-phase fluid network—the group of continuously connected two-phase fluid blocks—to which the block connects.

A two-phase fluid network can contain a maximum of one instance of this block. If a network does not contain any instances of this block, the fluid properties are set to those of water. In models with different two-phase fluid networks, each network can contain a separate instance of this block.

The block parameterizes the fluid properties in terms of pressure and normalized internal energy—a linear transformation of the specific internal energy. In a subcooled liquid, the normalized internal energy definition is

$$\begin{array}{cc}\overline{u}=\frac{u-{u}_{min}}{{u}_{sat}^{L}(p)-{u}_{min}}-1,& {u}_{min}\le u<{u}^{L}{}_{sat}\end{array}(p),$$

*$$\overline{u}$$*is the normalized internal energy of the fluid.*u*is the specific internal energy of the fluid.*u*_{min}is the lowest specific internal energy allowed in the two-phase fluid network.*u*^{L}_{sat}is the specific internal energy of the liquid phase at saturation.

In a superheated vapor, the normalized internal energy definition is

$$\begin{array}{cc}\overline{u}=\frac{u-{u}_{max}}{{u}_{max}-{u}_{sat}^{V}(p)}+2,& {u}^{V}{}_{sat}(p)<u\le {u}_{\mathrm{max}}\end{array},$$

*u*_{max}is the highest specific internal energy allowed in the two-phase fluid network.*u*^{V}_{sat}is the specific internal energy of the vapor phase at saturation.

In a two-phase mixture, the normalized internal energy definition is

$$\begin{array}{cc}\overline{u}=\frac{u-{u}_{sat}^{L}(p)}{{u}_{sat}^{V}(p)-{u}_{sat}^{L}(p)},& {u}^{L}{}_{sat}(p)\le u\le {u}^{V}{}_{sat}(p)\end{array}.$$

These expressions correspond to a normalized internal energy that is at all pressures -1 at the minimum valid specific internal energy, 0 at the liquid saturation boundary, +1 at the vapor saturation boundary, and +2 at the maximum valid specific internal energy.

In a two-phase mixture, the normalized internal energy ranges in value from 0 to 1 and is therefore equivalent to vapor quality—the mass fraction of the vapor phase in a two-phase mixture. In subcooled liquid and superheated vapor, the normalized internal energy behaves as an extension of vapor quality.

The normalized internal energy provides an advantage over the
specific internal energy. It transforms the *p*-*u* phase
diagram so that the subcooled liquid and superheated vapor phases
occupy distinct rectangular regions. This transformation, shown in
the figure, enables you to specify the fluid properties on separate
rectangular *p*-*$$\overline{u}$$* grids,
one for each phase.

A pressure vector, of length *N*, and two normalized
internal energy vectors, of lengths *M*_{L} and *M*_{V},
provide the (*p*, *$$\overline{u}$$*) coordinates
of the two grids. The pressure vector is common to both grids. The
subcooled liquid grid is *M*_{L}-by-*N* in
size and the superheated vapor grid *M*_{V}-by-*N*.

Two-way lookup tables provide the fluid property values on the (*p*, *$$\overline{u}$$*) grids.
The table rows correspond to different normalized internal energies
and the table columns to pressures. Fluid properties in the *p*-*$$\overline{u}$$* continuum
are computed using linear interpolation between the *p*-*$$\overline{u}$$* data points.

**Two-Way Property Lookup Table**

Saturated specific internal energy vectors provide the phase
boundaries in the (*p*, *$$\overline{u}$$*) phase
diagram. These separate the different regions of the phase diagram—subcooled
liquid, two-phase mixture, and superheated vapor.

Along with the minimum and maximum valid specific internal energy values, the saturated specific internal energy vectors enable the Two-Phase Fluid blocks to convert the normalized internal energies specified in this block into the specific internal energies they use for calculation purposes.

**Minimum valid specific internal energy**Lowest specific internal energy allowed in the two-phase fluid network. The default value is

`25`

kJ/kg.**Maximum valid specific internal energy**Highest specific internal energy allowed in the two-phase fluid network. The default value is

`4000`

kJ/kg.**Pressure vector**Vector of length

*N*containing the pressure values corresponding to the columns of the fluid property tables. The default vector is a logarithmically spaced 60-element vector ranging from 1e-3 to 15 MPa.**Atmospheric pressure**Absolute pressure of the two-phase fluid system surroundings. The default value,

`0.101325`

Pa, is the atmospheric pressure at mean sea level.**Dynamic pressure threshold for flow reversal**Dynamic pressure at which the flow at a port begins to reverse in direction. Simscape™. The dynamic pressure is the difference between the total pressure and the static pressure. Treat this parameter as a means to smooth the flow reversal. Larger values correspond to smoother reversals and smaller values to sharper reversals. The default value is

`0.01`

Pa.The Two-Phase Fluid domain uses an upwind scheme that derives the flow rate at a port from its value just upwind of the port. During flow reversals, the source of the flow rate value changes abruptly and the flow rate can become discontinuous. To prevent discontinuities and improve simulation robustness, flow reversals are smoothed out, with the dynamic pressure threshold marking the beginning of the smoothed transitions.

**Normalized liquid internal energy vector**Vector of length

*M*_{L}containing the normalized internal energy values corresponding to the rows of the liquid property tables. The vector must start at`-1`

and end at`0`

. The default is a uniformly spaced 25-element vector.**Liquid specific volume table***M*_{L}×*N*matrix containing the liquid specific volume values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Liquid specific entropy table***M*_{L}×*N*matrix containing the liquid specific entropy values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Liquid temperature table***M*_{L}×*N*matrix containing the liquid temperature values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Liquid kinematic viscosity table***M*_{L}×*N*matrix containing the liquid kinematic viscosity values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Liquid thermal conductivity table***M*_{L}×*N*matrix containing the liquid thermal conductivity values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Liquid Prandtl number table***M*_{L}×*N*matrix containing the liquid Prandtl number values corresponding to the normalized liquid internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Saturated liquid specific internal energy vector**Vector of length

*N*containing the saturated liquid specific internal energy values corresponding to the pressure vector. The default is a 60-element vector for water.

**Normalized vapor internal energy vector**Vector of length

*M*_{V}containing the normalized internal energy values corresponding to the rows of the vapor property tables. The vector must start at`1`

and end at`2`

. The default is a uniformly spaced 25-element vector.**Vapor specific volume table***M*_{V}×*N*matrix containing the vapor specific volume values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Vapor specific entropy table***M*_{V}×*N*matrix containing the vapor specific entropy values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Vapor temperature table***M*_{V}×*N*matrix containing the vapor temperature values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Vapor kinematic viscosity table***M*_{V}×*N*matrix containing the vapor kinematic viscosity values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Vapor thermal conductivity table***M*_{V}×*N*matrix containing the vapor thermal conductivity values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Vapor Prandtl number table***M*_{V}×*N*matrix containing the vapor Prandtl number values corresponding to the normalized vapor internal energy and pressure vectors. The default matrix is a 25 × 60 table for water.**Saturated vapor specific internal energy vector**Vector of length

*N*containing the saturated vapor specific internal energy values corresponding to the pressure vector. The default is a 60-element vector for water.

The block has a two-phase fluid conserving port. This port identifies the two-phase fluid network whose fluid properties the block provides.

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