Hydraulic pipeline with resistive, fluid compressibility, and variable elevation properties

Low-Pressure Blocks

The Hydraulic Pipe LP with Variable Elevation 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. Use this block for low-pressure system simulation in which the pipe ends change their positions with respect to the reference plane. The elevations are provided through respective physical signal inputs.

The model is a structural model and its schematic diagram is shown below.

The Resistive Pipe LP with Variable Elevation blocks account for friction losses, while the Constant Volume Hydraulic Chamber block accounts for fluid compressibility. To reduce model complexity, you can use this block to simulate not only a pipe itself, but also a combination of pipes and local resistances such as bends, fittings, inlet and outlet losses, associated with the pipe. You must convert the resistances into their equivalent lengths, and then sum up all the resistances to obtain their aggregate length. Then add this length to the pipe geometrical length. By using the block parameters, you can set the model to simulate pipeline with rigid or flexible walls, including simulation of hydraulic hoses with elastic and viscoelastic properties.

The difference in elevation between ports A and B is assumed to be distributed evenly between pipe segments. Thus, the elevation of the pipe middle point is computed as

$$el\_M=\frac{el\_A+el\_B}{2}$$

where

el_M | Elevation of the pipe middle point |

el_A, el_B | Elevations of the pipe ends A and B, respectively |

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 $$p={p}_{A}-{p}_{B}$$.

Flow is assumed to be fully developed along the pipe length.

Fluid inertia is not taken into account.

The pipe elevation is distributed evenly along the pipe length.

**Pipe cross section type**The type of pipe cross section:

`Circular`

or`Noncircular`

. For a circular pipe, you specify its internal diameter. For a noncircular pipe, you 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**Used for computing friction factor at laminar flow. The shape of the pipe cross section determines the value. For a pipe with a noncircular cross section, 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 [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`

.

**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.

Parameters determined by the type of working fluid:

**Fluid density****Fluid kinematic viscosity**

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

The block has the following ports:

`A`

Hydraulic conserving port associated with the pipe inlet.

`B`

Hydraulic conserving port associated with the pipe outlet.

`el_A`

Physical signal input port that controls pipe elevation at port A.

`el_B`

Physical signal input port that controls pipe elevation at port B.

For an example of using this block, see the Aircraft Fuel Supply System with Three Tanks example.

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

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