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Use the following option to specify a gravity load on the fluid pipe connector element:

\*DLOAD

element or element set, , GRAV, gravity constant, comp1, comp2, comp3

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# 32.15.2 FLUID PIPE ELEMENT LIBRARY

Product: Abaqus/Standard

# References

• \*FLUID PIPE SECTION   
• \*FLUID PIPE FLOW LOSS

# Overview

This section provides a reference to the fluid pipe elements available in Abaqus/Standard.

# Element types

# Element for use in 2D models

FP2D2 2-node linear

Active degrees of freedom 8

Additional solution variables None.

# Element for use in 3D models

FP3D2 2-node linear

Active degrees of freedom 8

Additional solution variables None.

# Nodal coordinates required

2D: X, Y   
3D: X, Y, Z

# Element property definition

Both available fluid pipe elements (FP2D2 and FP3D2) are defined by two nodes, which cannot be coincident (a zero length pipe is not allowed). You must associate a fluid pipe section with a set of pipe elements.

Input File Usage: \*FLUID PIPE SECTION, ELSET=name

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# Element-based loading

Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID(*DLOAD)</td><td>Units</td><td>Description</td></tr><tr><td>GRAV</td><td> $LT^{-2}$ </td><td>Gravity loading in specified direction (magnitude is input as acceleration).</td></tr></table>

Element output 

<table><tr><td>FPDPRESS</td><td>Pressure drop across the element.</td></tr><tr><td>FPMFL</td><td>Mass flow rate through the element.</td></tr><tr><td>FPFLVEL</td><td>Velocity of the fluid flowing through the element.</td></tr></table>

# Node ordering on elements

2D and 3D

![](images/page-1094_6abad437eb72aa8894299ff3dd0303db346b103626314379ac9176e9b2256eb6.jpg)

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# 32.16 Fluid pipe connector elements

• “Fluid pipe connector elements,” Section 32.16.1   
• “Fluid pipe connector element library,” Section 32.16.2

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# 32.16.1 FLUID PIPE CONNECTOR ELEMENTS

Product: Abaqus/Standard

# References

• “Fluid pipe connector element library,” Section 32.16.2   
• \*FLUID PIPE CONNECTOR SECTION   
• \*FLUID PIPE CONNECTOR LOSS

# Overview

Fluid pipe connector elements:

• allow you to simulate discrete viscous pressure loss terms in a fluid pipe network; and   
• can be used to simulate control valves allowing you to reduce and/or increase the resistance to flow or alternatively to turn the flow off.

Fluid pipe connectors in Abaqus/Standard use a pure pressure formulation to model steady-state flow of a single-phase, incompressible fluid through a fully filled junction in a pipe network.

# Typical applications

Fluid pipe connector elements are typically used to simulate the junction between two or more fluid pipe elements (see “Fluid pipe elements,” Section 32.15.1) such as a valve, T-connector, diffuser, etc.

# Choosing an appropriate element

Two types of fluid pipe connector elements are provided. For two-dimensional and axisymmetric analyses use element type FPC2D2. For three-dimensional analyses use element type FPC3D2.

# Assigning a material definition to a set of fluid pipe connector elements

You must associate a material definition with each connector element section property.

The material that is defined for the fluid pipe connector section refers to the fluid that is flowing through the connector. The properties that must be defined for the fluid are the pore fluid density and viscosity. For the viscosity definition fluid pipe connector elements support only Newtonian fluids (see “Viscosity,” Section 26.1.4).

Input File Usage:

Use all of the following options:

\*FLUID PIPE CONNECTOR SECTION, MATERIAL=material name   
\*MATERIAL, NAME=material name   
\*DENSITY, PORE FLUID   
\*VISCOSITY, DEFINITION=NEWTONIAN

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The geometry of a fluid pipe connector element is expressed in terms of hydraulic area and hydraulic diameter. The hydraulic diameter is expressed in terms of the cross-sectional area (A) and the wetted perimeter (P) as $\begin{array} { r } { D _ { h } = \frac { ( 4 A ) } { P } } \end{array}$ . A fluid pipe connector element is defined by two nodes. Unlike the fluid pipe elements, the geometric length of fluid pipe connector elements play no role in the fluid equilibrium equations and, therefore, the nodes are usually modeled as being coincident. The viscous pressure loss across a fluid pipe connector in Abaqus/Standard is given as

$$
\triangle P = K \frac {\rho V ^ {2}}{2},
$$

where

• $P _ { 1 } , P _ { 2 }$ are the pressures at the nodes and $\triangle P = ( P _ { 1 } - P _ { 2 } )$ ;   
• is the fluid velocity in the pipe.   
• $\rho$ is the fluid density, and;   
• is a loss term.

The mass flow rate through the connector can be related to the fluid and pipe parameters as $Q = \rho A V$ .

# Specifying the fluid pipe connector geometry and connector loss

Abaqus/Standard supports four different types of fluid pipe connector loss terms:

• Standard connection type with bidirectional loss terms;   
• a Hooper2K connector;   
• a Darby3K connector, and;   
• a user subroutine that you can use to define bidirectional loss terms.

# Specifying standard connector loss terms

The standard fluid pipe connector uses constant bidirectional loss terms $K _ { 1 }$ and $K _ { 2 }$ that you define. If the flow is from local node 1 to node 2, the total pressure loss is

$$
\triangle P = K _ {1} \frac {\rho V ^ {2}}{2};
$$

and if the flow is from local node 2 to node 1, the dynamic pressure loss is

$$
\triangle P = K _ {2} \frac {\rho V ^ {2}}{2}.
$$

Input File Usage: \*FLUID PIPE CONNECTOR LOSS, TYPE=CONNECTION

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# Specifying the connector loss based on Reynold’s number

This method utilizes the Hooper 2K parameters or Darby 3K parameters. The K values for different types of connectors and valves can be found in the literature. The 2K parameter or 3K parameter methods are sometimes preferable to constant bidirectional loss terms because they include a Reynold’s number dependence. Irrespective of the flow direction, a flow-dependent loss value is computed during the analysis and is given by

$$
\triangle P = K \frac {\rho V ^ {2}}{2}.
$$

The Hooper 2K loss term is defined as

$$
K = \frac {K _ {1}}{R e} + K _ {\infty} (1 + \frac {1}{D _ {h}}),
$$

where $K _ { 1 }$ and $K _ { \infty }$ are constant loss terms. The Darby 3K loss term is defined as

$$
K = \frac {K _ {1}}{R e} + K _ {\infty} (1 + \frac {K _ {d}}{D _ {h} ^ {0 . 3}}),
$$

where $K _ { 1 } , K _ { \infty }$ , and $K _ { d }$ are constant loss terms.

Input File Usage: \*FLUID PIPE CONNECTOR LOSS, TYPE=HOOPER2K

\*FLUID PIPE CONNECTOR LOSS, TYPE=DARBY3K

# Specifying the connector loss with a user subroutine

You can specify bidirectional connector loss terms $( K _ { 1 }$ and $K _ { 2 } )$ for fluid pipe connector elements using user subroutine UFLUIDCONNECTORLOSS. As with the standard connector, if the flow is from local node 1 to node 2, the total pressure loss is

$$
\triangle P = K _ {1} \frac {\rho V ^ {2}}{2};
$$

and if the flow is from local node 2 to node 1, the dynamic pressure loss is

$$
\triangle P = K _ {2} \frac {\rho V ^ {2}}{2}.
$$

Input File Usage: \*FLUID PIPE CONNECTOR LOSS, TYPE=USER

# Specifying the laminar flow transition for low Reynolds number flows

You can specify the laminar flow transition parameter that is used to switch flow computations from a purely laminar, linear formulation to a nonlinear iterative formulation. The Hooper 2K and Darby 3K methods include Reynold’s number dependence. Therefore, the laminar flow transition can be used only when the connector loss is defined by either one of these types. This ensures better convergence when the flow in the connector is zero or close to zero in magnitude. The default laminar transition flow Reynold’s

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number is 1.0. User subroutine UFLUIDCONNECTORLOSS is not called when the computed Re is less than the default or specified value.

Input File Usage: \*FLUID PIPE CONNECTOR LOSS, LAMINAR FLOW TRANSITION=Reynold's number value

# Specifying the control valve behavior

You can control the flow in the connector by simulating the presence of a control valve. By default, no valve behavior is defined and the fluid is fully flowing. When activated, user subroutine UFLUIDCONNECTORVALVE is called to determine the valve opening whose value must be between 0.0 and 1.0. The valve control option is valid only with the Hooper 2K and Darby 3K connector loss methods. This is because the flow in the connector can be set to zero, and the use of laminar flow transition gives better convergence behavior under these conditions.

Input File Usage: \*FLUID PIPE CONNECTOR LOSS, VALVE CONTROL=USER

# Specifying initial and prescribed conditions

You can define an initial temperature or field distribution over the nodes of the fluid pipe connector elements.

Input File Usage: Use one or both of the following options: \*INITIAL CONDITIONS, TYPE=TEMPERATURE \*INITIAL CONDITIONS, TYPE=FIELD

# Specifying loads and boundary conditions

Fluid pipe connector elements allow for the specification of pressure boundary conditions and volumetric flow rates at the nodes. The flow rate must be a nonzero value. At a particular node, either a pressure or flow rate can be specified but not both. Since the fluid pipe connectors do not use the geometric length in the fluid equilibrium equations, gravity loads are not supported for these elements.

Input File Usage: Use the following option to specify the pressure at the inlet or outlet: \*BOUNDARY node or node set, 8, 8, magnitude Use the following option to specify the flow rate at the inlet or outlet: \*CFLOW node or node set, , magnitude
