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 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
Multiple Fluid Flow
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, a T-connector, or a diffuser.

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 supported non-Newtonian fluids are power law, Bingham Plastic, and Herschel-Bulkley models (see Viscosity).

Input File Usage

Use the following options to specify the pore fluid density and viscosity:

FLUID PIPE CONNECTOR SECTION, MATERIAL=material name
MATERIAL, NAME=material name
DENSITY, PORE FLUID
VISCOSITY, DEFINITION=NEWTONIAN or POWER LAW or HERSCHEL-BULKLEY or BINGHAM PLASTIC

Multiple Fluid Flow

Abaqus allows the use of multiple fluids in an analysis, up to a maximum of four fluid types. This capability is useful in situations where the spatial distribution of the different fluid types is known (that is, precomputed) at all times during the analysis. In other words, the type of fluid at each node in the domain is known at all times during the analysis.

The definition of multiple fluids in an analysis involves associating each fluid with a unique integer and a specific predefined field variable. This integer acts as a fluid identifier. You can utilize this fluid identifier to specify the properties (for example, viscosity) of each fluid. The field variable associated with a fluid type allows you to predefine the fluid type at a node as a function of time using amplitude definitions or as functions of both time and space utilizing user subroutine UFIELD or USDFLD.

You specify a value for each field variable that is associated with a fluid identifier at each node. It is recommended that you specify a value for the field variable ( $F V$ ) such that $0.0 \leq F V \leq 1.0$ . Abaqus assigns the fluid type at an integration point to be the one for which the field variable has the maximum value at that point. If all field variables have the same numerical value at an integration point, the first fluid (fluid identifier 1) is assumed to be active.

Input File Usage

VISCOSITY, FLUID ID=Fluid Id number,DEFINITION=NEWTONIAN or POWER LAW or HERSCHEL-BULKLEY or BINGHAM PLASTIC
FLUID ID FIELD
Fluid Id number, field_id

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 plays 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} .

Input File Usage

FLUID PIPE CONNECTOR LOSS, TYPE=CONNECTION

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.

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

△ 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} .

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 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 a 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=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