Isothermal Liquid Properties (IL)
Physical properties of an isothermal liquid.
blockType: AcausalFoundation.IsothermalLiquid.Properties
|
Path in the library: |
Description
Block Isothermal Liquid Properties (IL) defines the properties of the liquid, which act as global parameters for all units connected to the isothermal fluid network. By default, the liquid is water.
A block can be connected to each topologically separate isothermal fluid network in the model Isothermal Liquid Properties (IL). If the block is not connected to the contour Isothermal Liquid Properties (IL) the blocks in this contour use the properties corresponding to the block parameter values Isothermal Liquid Properties (IL) by default.
Block Isothermal Liquid Properties (IL) provides a choice of modeling options:
-
Volumetric modulus of elasticity of the mixture: constant, or a linear function of pressure.
-
Entrained air: zero, constant or linear function of pressure.
The equations used to calculate the various properties of a liquid depend on the selected isothermal fluid model.
The ideal liquid model
Entrained air is the relative amount of undissolved gas contained in a liquid. A liquid with zero air content is ideal, that is, it is a pure liquid.
In the default configuration, the block Isothermal Liquid Properties (IL) simulates a liquid with the addition of 0.5% air with a constant volumetric modulus of elasticity:
-
For the parameter Isothermal bulk modulus model the value is set
Constant. -
For the parameter Volumetric fraction of entrained air in mixture at atmospheric pressure the value is set
0.005.
In this model, the volumetric modulus of elasticity is assumed to be constant, so the density of the liquid increases exponentially with increasing liquid pressure.:
,
where
-
— volumetric modulus of elasticity of a liquid;
-
— density of the liquid;
-
— the density of the liquid at the reference pressure;
-
— liquid pressure;
-
— reference pressure. By default, the unit takes atmospheric pressure as the reference pressure.,
0.101325MPa, but you can specify a different value by changing the parameter Atmospheric pressure.
In systems where the fluid pressure can vary over a wide range, and the assumption of constancy of the volumetric modulus of elasticity is no longer valid, you can set the parameter Isothermal bulk modulus model in the value Linear function of pressure to determine the volumetric modulus of elasticity of a liquid as a linear function of pressure:
,
where
-
— volumetric modulus of elasticity of a liquid at a reference pressure;
-
— the coefficient of proportionality between the volumetric modulus of elasticity and the increase in pressure.
If the liquid pressure drops below the reference pressure the value of the volumetric modulus of elasticity of the liquid in the previous equation may become negative, which contradicts physics. To ensure that the volumetric modulus of elasticity of the liquid always remains positive, use the parameter Minimum valid pressure to specify the minimum allowable pressure, :
.
A model of a liquid with entrained air
In practice, the working fluid is a mixture of liquid and a small amount of entrained air. To simulate this type of fluid, specify a non-zero value for the parameter Volumetric fraction of entrained air in mixture at atmospheric pressure.
The density of a mixture at a given pressure is defined as the ratio of the total mass of the liquid and entrained air to the total volume of the liquid and entrained air at a given pressure. While the total mass of the mixture is maintained when the pressure changes, the volume of the mixture does not remain constant. Entrained air is determined by the volume fraction:
,
where
-
— the volume ratio of entrained air to liquid at reference (atmospheric) pressure;
-
— volume of air at reference pressure;
-
— the volume of clean liquid at the reference pressure.
It is assumed that the entrained air obeys the ideal gas law. Compression or expansion of air in a liquid is a polytropic process in which the air pressure and the liquid pressure are the same:
,
where
-
— air volume;
-
— air polytrope indicator.
To simulate the effects of air dissolving in a liquid, check the box Air dissolution model.
The process of dissolving air in a liquid is described by Henry’s law. At a pressure less than or equal to the reference pressure (which is assumed to be equal to atmospheric pressure), it is assumed that all air is drawn into the liquid. At a pressure equal to or exceeding the pressure (parameter value Pressure at which all entrained air is dissolved), all entrained air is dissolved in the liquid. At pressures between and the volume fraction of entrained air that is not lost during dissolution, , is a linear function of pressure and is approximated by a third- order polynomial function for a smooth relationship between the values of density and the volumetric modulus of elasticity between the three pressure regions:
.
Ports
Conserving
#
A
—
connection port
Isothermal liquid
Details
Isothermal liquid port connecting the unit to the network. It can be connected to any point of the isothermal liquid connection line in the block diagram. When connecting the block Isothermal Liquid Properties (IL) To the connecting line, the program automatically detects the isothermal liquid blocks connected to this circuit and distributes the properties of the liquid to all blocks in the circuit.
| Program usage name |
|
Parameters
Liquid
#
Density at atmospheric pressure (no entrained air) —
liquid density
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3
Details
The density of an isothermal liquid at atmospheric pressure, without entrained air.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Isothermal bulk modulus model —
the model of the volumetric modulus of elasticity
Constant | Linear function of pressure
Details
Choose a model of the volumetric modulus of elasticity for an isothermal fluid:
-
Constant— the volumetric modulus of elasticity is constant. -
Linear function of pressure— The volumetric modulus of elasticity is a linear function of pressure.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
# Isothermal bulk modulus vs. pressure increase gain — the proportionality coefficient for linear dependence
Details
The coefficient of proportionality between the volumetric modulus of elasticity and the increase in pressure.
Dependencies
To use this parameter, set for the parameter Isothermal bulk modulus model meaning Linear function of pressure.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Isothermal bulk modulus at atmospheric pressure (no entrained air) —
isothermal volumetric modulus of elasticity of a liquid
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Details
Isothermal volumetric modulus of elasticity of a liquid at atmospheric pressure, without entrained air.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Kinematic viscosity at atmospheric pressure —
kinematic viscosity of a liquid
m^2/s | mm^2/s | in^2/s | ft^2/s | St | cSt | newt
Details
Kinematic viscosity of an isothermal liquid at atmospheric pressure.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Atmospheric pressure —
absolute ambient pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Details
Absolute ambient pressure.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Minimum valid pressure —
lowest allowable pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Details
The lowest allowable pressure in an isothermal liquid network. Depending on the parameter value Pressure below minimum valid value The simulation may give an error if the pressure is outside the range.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Pressure below minimum valid value —
notification when pressure values exceed the minimum allowable value
None | Error
Details
Choose what happens if the liquid pressure exceeds the minimum allowable value during the simulation.:
-
None— The unit does not return an error if the pressure exceeds the minimum allowable value. -
Error— the block returns an error and stops the simulation.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
Entrained Air
# Volumetric fraction of entrained air in mixture at atmospheric pressure — volume fraction of entrained air in a liquid mixture
Details
The volume fraction of air entrained in a mixture of liquids at atmospheric pressure.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Air polytropic index — air polytropy indicator
Details
The polytropic index of air. The default value of 1 represents an isothermal process, which corresponds to the assumptions of the isothermal fluid model.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Air density at atmospheric condition —
air density under atmospheric conditions
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3
Details
Air density under atmospheric conditions.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Air dissolution model — The dissolution of air
Details
Choose an air dissolution model for an isothermal liquid:
-
If the flag is unchecked, the amount of entrained air remains constant. The dissolution of air is not simulated.
-
If this option is selected, the entrained air may dissolve into the liquid. The amount of dissolved air depends on the pressure.
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
Pressure at which all entrained air is dissolved —
the pressure at which all entrained air is dissolved
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Details
The pressure at which all the air is dissolved in a liquid.
Dependencies
To use this option, check the box Air dissolution model.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |