Fluid Pipe Elements

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

The material that is defined for the fluid pipe section refers to the fluid that is flowing through the pipe. The properties that must be defined for the fluid are the pore fluid density and viscosity. For the viscosity definition fluid pipe elements support both Newtonian and non-Newtonian fluids. Non-Newtonian fluids are supported by the power law, Bingham Plastic, and Herschel-Bulkley models (see Viscosity).

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

You can use fluid pipe elements in models that use symmetry to reduce the model size. The fluid pipe elements model circular geometry. You specify a symmetry value that is greater than 0 or less than or equal to 1. This value is interpreted as scaling of the circular pipe geometry in radians. A value of 1 corresponds to $2\pi$ radians, and a value of 0.5 corresponds to $\pi$ radians. When you specify symmetry, you must scale the full model flow magnitude by the symmetry value. You do not need to apply any symmetric constraints or boundary conditions.

FLUID PIPE SECTION, SYMMETRY=value

The geometry of a pipe element is expressed in terms of hydraulic area and hydraulic diameter. The hydraulic diameter is expressed in terms of the cross-sectional area (A) of the tube or channel and the wetted perimeter (P) as $D_h=\frac{\left(4A\right)}{P}$. A pipe element is defined by two noncoincident nodes. Using a Darcy-Weisbach approach, Bernoulli's equation (including viscous loss) between two points in space can be written as

where

• $P_1,P_2$ are the pressures at the nodes and $△P=\left(P_1-P_2\right)$;

• $Z_1,Z_2$ are the elevations at the nodes and $△Z=\left(Z_1-Z_2\right)$;

• $V$ is the fluid velocity in the pipe.

• $\rho$ is the fluid density;

• $g$ is the acceleration due to gravity;

• $C_L=\frac{fL}{D_h}$ is the loss coefficient;

• $f$ is the friction factor of the pipe;

• $L$ is the length of the pipe, and;

• $K_i$ is a directional loss term.

The assumption of constant cross-sectional area in a single element results in constant fluid velocity in a pipe element. The mass flow rate $Q$ through the pipe can be related to the fluid and pipe parameters as $Q=\rho AV$.

Abaqus/Standard supports four different methods for defining the friction factor $\left(f\right)$:

• Blasius friction loss;

• Churchill friction loss;

• a tabular option, and;

• a user subroutine.

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

INITIAL CONDITIONS, TYPE=TEMPERATURE
INITIAL CONDITIONS, TYPE=FIELD

Fluid pipe elements allow for the specification of pressure boundary conditions and volumetric flow rates at the nodes. At a particular node, either a pressure or flow rate can be specified but not both. You can also specify a gravity load on the fluid pipe element to determine the hydrostatic head at the nodes.

BOUNDARY
node or node set, 8, 8, magnitude

CFLOW
node or node set, , magnitude

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