Isothermal Liquid Properties (IL)

Physical properties of isothermal liquid

Since R2020a

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Libraries:
Simscape / Foundation Library / Isothermal Liquid / Utilities

Description

The Isothermal Liquid Properties (IL) block defines the liquid properties that act as global parameters for all the blocks connected to a circuit. The default liquid is water.

Each topologically distinct isothermal liquid circuit in a diagram can have a Isothermal Liquid Properties (IL) block connected to it. If no Isothermal Liquid Properties (IL) block is attached to a circuit, the blocks in this circuit use the properties corresponding to the default Isothermal Liquid Properties (IL) block parameter values.

The Isothermal Liquid Properties (IL) block provides a choice of modeling options:

• Mixture bulk modulus: either constant or a linear function of pressure

• Entrained air: zero, constant, or a linear function of pressure

Equations used to compute various liquid properties depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.

Ideal Fluid Models

Entrained air is the relative amount of nondissolved gas trapped in the fluid. Fluid with zero entrained air is ideal, that is, it represents pure liquid.

In its default configuration, the Isothermal Liquid Properties (IL) block models an ideal fluid with a constant bulk modulus:

• Isothermal bulk modulus model is Constant

• Entrained air model is Constant

• Entrained air-to-liquid volumetric ratio at atmospheric pressure is 0

In this model, the liquid bulk modulus is assumed to be constant and therefore the liquid density increases exponentially with the liquid pressure:

$${\rho }_L={\rho }_{L0}\cdot e^{\frac{p-p_0}{{\beta }_L}},$$

where:

• β_L is liquid bulk modulus.

• ρ_L is liquid density.

• ρ_L0 is liquid density at reference pressure.

• p is liquid pressure.

• p₀ is reference pressure. By default, the block assumes reference pressure to be the atmospheric pressure, 0.101325 MPa, but you can specify a different value.

In systems where the liquid pressure can change over a wide range, and the assumption of constant bulk modulus is not valid anymore, you can use the Isothermal bulk modulus model parameter to define the liquid bulk modulus as a linear function of pressure:

$${\beta }_L={\beta }_{L0}+K_{\beta p}\left(p-p_0\right),$$

where:

• β_L0 is liquid bulk modulus at reference pressure.

• K_βp is the coefficient of proportionality between the bulk modulus and pressure increase.

If liquid pressure decreases below the reference pressure p₀, the liquid bulk modulus value in the previous equation can become negative, which is nonphysical. To ensure that the liquid bulk modulus always stays positive, use the Minimum valid pressure parameter to specify the minimum valid pressure, p_min:

$$p_{\min }>p_0-\frac{{\beta }_{L0}}{K_{\beta p}}.$$

If liquid pressure drops below the Minimum valid pressure parameter value, simulation issues an error.

Fluid Models with Entrained Air

In practice, working fluid is a mixture of liquid and a small amount of entrained air. To model this type of fluid, specify a nonzero value for the Entrained air-to-liquid volumetric ratio at atmospheric pressure parameter, but keep the Entrained air model as Constant.

The mixture density at a given pressure is defined as the total mass of liquid and entrained air over the total volume of the liquid and the entrained air at that pressure. While the total mass of the mixture is conserved as the pressure changes, the mixture volume does not stay constant. The entrained air is given by a volumetric fraction:

$${\alpha }_0=\frac{V_{g0}}{V_{g0}+V_{L0}},$$

where:

• α₀ is entrained air-to-liquid volumetric ratio at reference (atmospheric) pressure.

• V_g0 is air volume at reference pressure.

• V_L0 is pure liquid volume at reference pressure.

The entrained air is assumed to follow the ideal gas law. The compression or expansion of air in the liquid is a polytropic process, in which the air pressure and liquid pressure are identical:

$$V_g=V_{g0}{\left(\frac{p_0}{p}\right)}^{1/n},$$

where:

• V_g is air volume.

• n is air polytropic index.

To model the air dissolution effects into the fluid, select the Model air dissolution check box.

The process of dissolving air into the fluid is described by Henry’s law. At pressures less than or equal to the reference pressure, p₀ (which is assumed to be equal to atmospheric pressure), all the air is assumed to be entrained. At pressures equal or higher than pressure p_c, all the entrained air has been dissolved into the liquid. At pressures between p₀ and p_c, the volumetric fraction of entrained air that is not lost to dissolution, θ(p), is a linear function of the pressure, and is approximated by a third-order polynomial function to smoothly connect the density and bulk modulus values between the three pressure regions:

$$\theta (p)=\{\begin{array}{ll}1,\hfill & p\le p_0\hfill \\ 0,\hfill & p\ge p_c\hfill \\ 1-\left(3{\left(\frac{p_c-p}{p_c-p_0}\right)}^2-2{\left(\frac{p_c-p}{p_c-p_0}\right)}^3\right),\hfill & p_0<p<p_c\hfill \end{array}.$$

Data Visualization

The block provides the option to plot the specified fluid properties (density and isothermal bulk modulus) as a function of pressure. Plotting the properties lets you visualize the data before simulating the model.

To plot the data, right-click the Isothermal Liquid Properties (IL) block in your model and, from the context menu, select Foundation Library > Plot Fluid Properties. Use the drop-down list located at the top of the plot to select the fluid property to visualize. Click the Reload button to regenerate a plot following a block parameter update.

Isothermal Liquid Properties Plot

Examples

Hydraulic Actuator with Analog Position Controller

How the Foundation library can be used to model systems that span electrical, mechanical and isothermal liquid domains. In the model, a hydraulic system implemented in the isothermal liquid domain controls the mechanical load position in response to a voltage reference demand. If the reference demand is zero, then the hydraulic actuator (and load) displacement is zero, and if the reference is +5 volts, then the displacement is 100 mm.

• Open Model

Entrained Air Effects

The effects of entrained air in a custom double acting cylinder. During the repeating cycle of oscillating pressure, the absolute pressure does not get below absolute zero as the bulk modulus of the homogeneous liquid-gas mixture decreases accordingly at low pressures.

• Open Model

Ports

Conserving

A — Connection port

isothermal liquid

Isothermal liquid conserving port that connects the block to the network. You can connect it to any point on an isothermal liquid connection line in a block diagram. When you connect the Isothermal Liquid Properties (IL) block to a connection line, the software automatically identifies the isothermal liquid blocks connected to the particular circuit and propagates the liquid properties to all the blocks in the circuit.

Settings

Liquid

Liquid density at atmospheric pressure (no entrained air) — Liquid density

998.21 kg/m^3 (default) | positive scalar

Density of the isothermal liquid at atmospheric pressure, with no entrained air.

Isothermal bulk modulus model — Select the bulk modulus model

Constant (default) | Linear function of pressure

Select the bulk modulus model for the isothermal liquid:

• Constant — The bulk modulus is constant.

• Linear function of pressure — The bulk modulus is a linear function of pressure.

Isothermal bulk modulus vs. pressure increase gain — Coefficient of proportionality for linear dependency

6 (default) | positive scalar

Coefficient of proportionality between the bulk modulus and pressure increase.

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) — Liquid isothermal bulk modulus

2.1791e9 Pa (default) | positive scalar

Isothermal bulk modulus of the liquid at atmospheric pressure, with no entrained air.

Kinematic viscosity at atmospheric pressure — Liquid kinematic viscosity

1.0034e-6 m^2/s (default) | positive scalar

Kinematic viscosity of the isothermal liquid at atmospheric pressure.

Atmospheric pressure — Absolute pressure of the environment

0.101325 MPa (default) | positive scalar

Absolute pressure of the environment.

Minimum valid pressure — Lowest pressure allowed

1 Pa (default) | positive scalar

Lowest pressure allowed in the isothermal liquid network. Depending on the Pressure below minimum valid value parameter value, the simulation can issue an error or warning when pressure is out of range.

Pressure below minimum valid value — Whether to notify when pressure is below minimum valid value

Error (default) | Warning | None

Select what happens if the fluid pressure goes below Minimum valid pressure during simulation:

• None ― The block does not return an error if the properties go out of range.

• Warning ― The block issues a warning, but continues the simulation.

• Error ― The block returns an error and stops the simulation.

Entrained Air

Volumetric fraction of entrained air in mixture at atmospheric pressure — Volumetric fraction of entrained air in the fluid mixture

0.005 (default) | scalar in the range [0,1]

Volumetric fraction of air that is entrained in the fluid mixture at atmospheric pressure.

Air polytropic index — Air polytropic index

1.0 (default) | positive scalar

Air polytropic index. The default value of 1 represents an isothermal process, which is consistent with the assumptions of the isothermal liquid domain.

Air density at atmospheric condition — Air density at atmospheric condition

1.225 kg/m^3 (default) | positive scalar

Air density at atmospheric condition.

Model air dissolution — Select whether to model air dissolution

Off (default) | On

Select the air dissolution model for the isothermal liquid:

• If the check box is cleared, the amount of entrained air is constant. Air dissolution is not modeled.

• If the check box is cleared, the entrained air can dissolve into liquid. The amount of dissolved air is a function of pressure.

Pressure at which all entrained air is dissolved — Pressure at which all entrained air is dissolved

3 MPa (default) | positive scalar

Pressure at which all entrained air in the liquid is dissolved.

Dependencies

To enable this parameter, select the Model air dissolution check box.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

R2024a: Parameter renamed for clarity

The Pressure outside valid range parameter has been renamed to Pressure below minimum valid value, for clarity.

When the parameter was first introduced, it had the same name across multiple fluid domains. However, the isothermal liquid domain has no parameter specifying the maximum allowed pressure, only the Minimum valid pressure parameter. This is purely a name change, the block functionality has not changed.

R2023a: Control block behavior when fluid properties go out of range during simulation

Previously, if fluid properties went beyond the valid range during simulation, the block would return an error. You can now use the new Pressure outside valid range parameter to control the block behavior if fluid properties go out of range during simulation.

The default value of the Minimum valid pressure parameter has been changed from 0.1 Pa to 1 Pa.