Isothermal Liquid Properties (IL)
Physical properties of an isothermal liquid.
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Description
The Isothermal Liquid Properties (IL) block defines the liquid properties that act as global parameters for all blocks connected to the isothermal liquid network. By default, the liquid is water.
An Isothermal Liquid Properties (IL) block can be connected to each topologically separate isothermal liquid network in the model. If no Isothermal Liquid Properties (IL) block is connected to a loop, the blocks in that loop use the properties corresponding to the default values of the Isothermal Liquid Properties (IL) block parameters.
The Isothermal Liquid Properties (IL) block provides a choice of modelling options:
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Volumetric modulus of elasticity of the mixture: constant, or linear function of pressure.
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Entrained air: zero, constant, or linear function of pressure.
The equations used to calculate the various fluid properties depend on the isothermal liquid model chosen.
Ideal fluid model
The entrained air is the relative amount of undissolved gas present in the fluid. A fluid with zero air content is an ideal fluid, that is, it is a pure liquid.
In the By default configuration, the Isothermal Liquid Properties (IL) block simulates a liquid with 0.5% air added with a constant bulk modulus of elasticity:
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The Isothermal bulk modulus model parameter is set to
Constant. -
The Entrained air model is set to `Constant'.
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The Volumetric fraction of entrained air in mixture at atmospheric pressure is set to `0.005'.
In this model, the bulk modulus of elasticity is assumed to be constant, so the density of the fluid increases exponentially with increasing fluid pressure:
,
where:
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- is the bulk modulus of elasticity of the liquid.
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- density of the liquid.
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- density of liquid at opporative pressure.
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- fluid pressure.
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- reference pressure. By default, the block takes atmospheric pressure as reference pressure, `0.101325 MPa', but you can specify a different value by changing the Atmospheric pressure parameter.
In systems where the fluid pressure can vary over a wide range and the assumption of constant bulk modulus no longer applies, you can set the Isothermal bulk modulus model parameter to `Linear function of pressure' to define the fluid bulk modulus as a linear function of pressure:
,
where:
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- is the bulk modulus of elasticity of the fluid at the reference pressure.
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- is the coefficient of proportionality between the bulk modulus of elasticity and pressure increase.
If the fluid pressure decreases below the reference pressure , the value of the bulk modulus of elasticity of the fluid in the previous equation can become negative, which is contrary to physics. To ensure that the fluid’s bulk modulus always remains positive, use the Minimum valid pressure parameter to specify the minimum valid pressure, :
.
Fluid model with entrained air
In practice, the working fluid is a mixture of liquid and a small amount of entrained air. To model this type of fluid, specify a non-zero value for 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 liquid and entrained air to the total volume of liquid and entrained air at that pressure. While the total mass of the mixture remains constant with changes in pressure, the volume of the mixture does not remain constant. The entrained air is defined by volume fraction:
,
where:
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- is the volume ratio of entrained air to liquid at reference (atmospheric) pressure.
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- volume of air at reference pressure.
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- volume of pure liquid at reference pressure.
The entrained air is assumed to obey the ideal gas law. The compression or expansion of air in a liquid is a polytropic process in which the pressure of the air and the pressure of the liquid are the same:
,
where:
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- air volume.
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- is the polytropy of air.
To model the effects of air dissolution in a liquid, select the Model air dissolution checkbox.
The process of air dissolution in a liquid is described by Henry’s law. At pressures less than or equal to the reference pressure (which is assumed to be atmospheric pressure), it is assumed that all air is drawn into the liquid. At pressures equal to or greater than (the value of 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 to dissolution, , is a linear function of pressure and is approximated by a third-order polynomial function for the smooth relationship of density and bulk modulus values between the three pressure regions:
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Ports
Non-directional
A - connection port
isothermal liquid
An isothermal liquid port that connects the block to the network. It can be connected to any point on the isothermal liquid connection line on the block diagram. When you connect an Isothermal Liquid Properties (IL) block to the connection line, the software automatically detects the isothermal liquid blocks connected to the circuit and extends the liquid properties to all blocks in the circuit.
Parameters
Liquid density at atmospheric pressure (no entrained air) - liquid density
998.21 kg/m³ (by default) | ` positive scalar`
Density of an isothermal liquid at atmospheric pressure, without entrained air.
Isothermal bulk modulus model - bulk modulus of elasticity model
Constant (by default) | Linear function of pressure
Select the bulk modulus model for an isothermal liquid:
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`Constant' - the bulk modulus of elasticity is constant.
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`Linear function of pressure' - the bulk modulus of elasticity is a linear function of pressure.
Isothermal bulk modulus vs. pressure increase gain - proportionality factor for linear dependence
6 (By default) | `positive scalar'.
Proportionality coefficient between bulk modulus of elasticity and pressure increase gain.
Dependencies
Enabled when the Isothermal bulk modulus model parameter is set to `Linear function of pressure'.
Liquid isothermal bulk modulus at atmospheric pressure (no entrained air) - isothermal bulk modulus of elasticity of liquid
2.1791e9 Pa (by default) | positive scalar
Isothermal bulk modulus of elasticity of a liquid at atmospheric pressure, without air involved.
Kinematic viscosity at atmospheric pressure - kinematic viscosity of the fluid
1.0034e-6 m²/s (by default) | positive scalar
The kinematic viscosity of an isothermal liquid at atmospheric pressure.
Atmospheric pressure - absolute ambient pressure
0.101325 MPa (by default) | `positive scalar `
Absolute ambient pressure.
Minimum valid pressure - the lowest valid pressure
1 Pa (By default) | Positive scalar
The lowest valid pressure in an isothermal liquid network.
Volumetric fraction of entrained air in mixture at atmospheric pressure - volume fraction of entrained air in liquid mixture
0.005 (by default) | scalar in the range [0,1]
Volume fraction of entrained air in a liquid mixture at atmospheric pressure.
Air polytropic index - air polytropic index
1.0 (by default) | `positive scalar'.
Air polytropic index. A value by default of 1 represents an isothermal process, which is consistent with the assumptions of an isothermal liquid model.
Air density at atmospheric condition - air density at atmospheric conditions
1.225 kg/m³ (by default) | `positive scalar'.
Density of air at atmospheric conditions.
Model air dissolution - air dissolution
off (by default) | on
Select the air dissolution model for the isothermal liquid:
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If the box is unchecked, the amount of air involved remains constant. Air dissolution is not modelled.
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If the box is checked, entrained air can dissolve in the fluid. The amount of dissolved air is pressure dependent.
Pressure at which all entrained air is dissolved - pressure at which all entrained air is dissolved
3 MPa (by default) | `positive scalar'.
The pressure at which all air in a liquid is dissolved.
Dependencies
To use this parameter, select the Model air dissolution checkbox.