Fluid Pipe Connector Elements

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.

This page discusses:

Typical Applications
Choosing an Appropriate Element
Assigning a Material Definition to a Set of Fluid Pipe Connector Elements
Fluid Pipe Connector Equations
Specifying the Fluid Pipe Connector Geometry and Connector Loss
Specifying Initial and Prescribed Conditions
Specifying Loads and Boundary Conditions

Typical Applications

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

Choosing an Appropriate Element

Several fluid pipe connector element types are available. 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 both Newtonian and non-Newtonian fluids. The non-Newtonian fluids that are supported are power law, Bingham Plastic and Herschel-Bulkley (see Viscosity).

Fluid Pipe Connector Equations

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 $D_{h} = \frac{(4 A)}{P}$ . 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

△ P = K \frac{ρ V^{2}}{2},

where

$P_{1}, P_{2}$ are the pressures at the nodes and $△ P = (P_{1} - P_{2})$ ;
$V$ is the fluid velocity in the pipe.
$ρ$ is the fluid density, and;
$K$ is a loss term.

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

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

△ P = K_{1} \frac{ρ V^{2}}{2};

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

△ P = K_{2} \frac{ρ V^{2}}{2} .

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

△ P = K \frac{ρ 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.

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

△ P = K_{1} \frac{ρ V^{2}}{2};

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

△ P = K_{2} \frac{ρ V^{2}}{2} .

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

Specifying Initial and Prescribed Conditions

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

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.