Controlled Volumetric Flow Rate Source (2P)

Generate time-varying volumetric flow rate

Library

Thermal Liquid/Sources

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Description

The Controlled Volumetric Flow Rate Source (2P) block generates a variable volumetric flow rate in a two-phase fluid network branch. The source has two inlets, labeled A and B, with independently specified cross-sectional areas. By default, the source does isentropic work on the fluid, though the block provides the option to ignore this work.

The source is ideal. In other words, it maintains the specified flow rate regardless of the pressure differential produced between its ports. In addition, because the source is isentropic, there is no viscous friction between the ports and no heat exchange with the environment. Use this block to model an idealized pump or compressor or to set a boundary condition in a model.

Use physical signal port V to specify the desired volumetric flow rate. Use positive values for flows directed from port A to port B and negative values for flows directed from port B to port A.

Mass Balance

The volume of fluid in the source is considered negligible and is ignored in a model. There is no fluid accumulation between the ports and the sum of all mass flow rates into the source must therefore equal zero:

$${\dot{m}}_{\text{A}}+\text{}{\dot{m}}_{\text{B}}=0,$$

where $$\dot{m}$$ denotes the mass flow rate into the source through a port. Its value at port A is calculated from the specified volumetric flow rate:

$$\stackrel{.}{m_A}=\{\begin{array}{ll}\frac{\dot{V}}{v_{\text{B}}},\hfill & \text{if }\dot{V}\ge 0\hfill \\ \frac{\dot{V}}{v_{\text{A}}},\hfill & \text{otherwise}\hfill \end{array},$$

where $$\dot{V}$$ is volumetric flow rate and v is specific volume.

Energy Balance

By default, the source maintains the specified flow rate by performing isentropic work on the incoming fluid, though the block provides the option to ignore this term. The rate at which the source does work, if considered in the model, must equal the sum of the energy flow rates through the ports:

$${\varphi }_{\text{A}}+\text{}{\varphi }_{\text{B}}+\text{}{\varphi }_{\text{Work}}=0,$$

where ϕ denotes the energy flow rate into the source through a port or by means of work. The energy flow rate due to work is equal to the power generated by the source. Its value is calculated from the specific total enthalpies at the ports:

$${\varphi }_{\text{Work}}={\dot{m}}_{\text{A}}\left(h_{\text{A}}-h_{\text{B}}\right).$$

The specific total enthalpy h is defined as:

$$h_{*}=u_{*}+p_{*}{v}_{*}+\frac{1}{2}{\left(\frac{{\dot{m}}_{*}{v}_{*}}{S}\right)}^2,$$

where the asterisk denotes a port (A or B) and:

• u is specific internal energy.

• p is pressure.

• S is flow area.

The specific internal energy in the equation is obtained from the tabulated data of the Two-Phase Fluid Properties (2P) block. Its value is uniquely determined from the constraint that the work done by the source is isentropic. The specific entropy, a function of specific internal energy, must then have the same value at ports A and B:

$$s_{\text{A}}\left(p_{\text{A}},u_{\text{A}}\right)=s_{\text{B}}\left(p_{\text{B}},u_{\text{B}}\right),$$

where s is specific entropy. If the Power added parameter is set to None, the specific total enthalpies at the ports have the same value ($$h_{\text{A}}=h_{\text{B}}$$) and the work done by the source reduces to zero ($${\varphi }_{\text{Work}}=0$$).

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Ports

Conserving

A — Fluid opening

two-phase fluid

Opening through fluid can enter and exit the source.

B — Fluid opening

two-phase fluid

Opening through fluid can enter and exit the source.

Input

V — Volumetric flow rate

physical signal

Value of the volumetric flow rate from port A to port B.

Parameters

Power added — Parameterization for the calculation of power

Isentropic power (default) | None

Parameterization for the calculation of power. Work is isentropic and its calculation is based on the assumptions of zero friction losses and zero heat exchange with the environment. Change to None to prevent the source from impacting the temperature of the fluid—for example, when using this block as a boundary condition in a model.

Cross-sectional area at port A — Inlet area normal to the direction of flow

0.01 m^2 (default) | scalar with units of volume/time

Area of the fluid opening normal to the direction of flow.

Cross-sectional area at port B — Inlet area normal to the direction of flow

0.01 m^2 (default) | scalar with units of volume/time

Area of the fluid opening normal to the direction of flow.

Extended Capabilities

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

Version History

Introduced in R2015b