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Hydraulic Pipe LP - Simulate hydraulic pipeline with resistive, fluid compressibility, and elevation properties

Library

Low-Pressure Blocks

Description

The Hydraulic Pipe LP block models hydraulic pipelines with circular and noncircular cross sections. The block accounts for friction loss along the pipe length and for fluid compressibility. The block does not account for fluid inertia and cannot be used for predicting effects like water hammer or changes in pressure caused by fluid acceleration.

The model is built of Simscape Foundation library building blocks and its schematic diagram is shown below.

The Resistive Pipe LP blocks account for friction losses, while the Constant Volume Hydraulic Chamber block accounts for fluid compressibility. By using the block parameters, you can set the model to simulate pipeline with rigid or compliant walls, including simulation of hydraulic hoses with elastic and viscoelastic properties.

The difference in elevation between ports A and B is distributed evenly between pipe segments.

The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B, and the pressure loss is determined as .

Basic Assumptions and Limitations

The model is based on the following assumptions:

Flow is assumed to be fully developed along the pipe length.
Fluid inertia is not taken into account.

Dialog Box and Parameters

The block dialog box contains three tabs:

Basic Parameters

Pipe cross section type: The parameter can have one of two values: Circular or Noncircular. For a circular pipe, you need to specify its internal diameter. For a noncircular pipe, you need to specify its hydraulic diameter and pipe cross-sectional area. The default value of the parameter is Circular.
Pipe internal diameter: Pipe internal diameter. The parameter is used if Pipe cross section type is set to Circular. The default value is 0.01 m.
Noncircular pipe cross-sectional area: Pipe cross-sectional area. The parameter is used if Pipe cross section type is set to Noncircular. The default value is 1e-4 m^2.
Noncircular pipe hydraulic diameter: Hydraulic diameter of the pipe cross section. The parameter is used if Pipe cross section type is set to Noncircular. The default value is 0.0112 m.
Geometrical shape factor: The parameter is used for computing friction factor at laminar flow and depends of the shape of the pipe cross section. For a pipe with noncircular cross section, you must set the factor to an appropriate value, for example, 56 for a square, 96 for concentric annulus, 62 for rectangle (2:1), and so on (see [1]). The default value is 64, which corresponds to a pipe with a circular cross section.
Pipe length: Pipe geometrical length. The default value is 5 m.
Aggregate equivalent length of local resistances: This parameter represents total equivalent length of all local resistances associated with the pipe. You can account for the pressure loss caused by local resistances, such as bends, fittings, armature, inlet/outlet losses, and so on, by adding to the pipe geometrical length an aggregate equivalent length of all the local resistances. This length is added to the geometrical pipe length only for hydraulic resistance computation. The fluid volume depends on pipe geometrical length only. The default value is 1 m.
Internal surface roughness height: Roughness height on the pipe internal surface. The parameter is typically provided in data sheets or manufacturer's catalogs. The default value is 1.5e-5 m, which corresponds to drawn tubing.
Laminar flow upper margin: Specifies the Reynolds number at which the laminar flow regime is assumed to start converting into turbulent. Mathematically, this is the maximum Reynolds number at fully developed laminar flow. The default value is 2000.
Turbulent flow lower margin: Specifies the Reynolds number at which the turbulent flow regime is assumed to be fully developed. Mathematically, this is the minimum Reynolds number at turbulent flow. The default value is 4000.

Wall Compliance

Pipe wall type: The parameter is available only for circular pipes and can have one of two values: Rigid or Flexible. If the parameter is set to Rigid, wall compliance is not taken into account, which can improve computational efficiency. The value Flexible is recommended for hoses and metal pipes where wall compliance can affect the system behavior. The default value is Rigid.
Static pressure-diameter coefficient: Coefficient that establishes relationship between the pressure and the internal diameter at steady-state conditions. This coefficient can be determined analytically for cylindrical metal pipes or experimentally for hoses. The parameter is used if the Pipe wall type parameter is set to Flexible. The default value is 2e-12 m/Pa.
Viscoelastic process time constant: Time constant in the transfer function that relates pipe internal diameter to pressure variations. By using this parameter, the simulated elastic or viscoelastic process is approximated with the first-order lag. The value is determined experimentally or provided by the manufacturer. The parameter is used if the Pipe wall type parameter is set to Flexible. The default value is 0.01 s.
Specific heat ratio: Gas-specific heat ratio for the Constant Volume Hydraulic Chamber block. The default value is 1.4. If Pipe cross section type is set to Noncircular, then this is the only parameter on the Wall Compliance tab.

Vertical Position

Port A elevation wrt reference plane: The parameter specifies vertical position of the pipe port A with respect to the reference plane. The default value is 0.
Port B elevation wrt reference plane: The parameter specifies vertical position of the pipe port B with respect to the reference plane. The default value is 0.

Restricted Parameters

Global Parameters

Fluid density: The parameter is determined by the type of working fluid selected for the system under design. Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.
Fluid kinematic viscosity: The parameter is determined by the type of working fluid selected for the system under design. Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

A: Hydraulic conserving port associated with the pipe inlet.
B: Hydraulic conserving port associated with the pipe outlet.

References

[1] White, F.M., Viscous Fluid Flow, McGraw-Hill, 1991