Engee documentation

Pipe (Advanced) (IL)

A pipe segment in an isothermal liquid network.

pipe advanced il

Description

The Pipe (Advanced) (IL) unit simulates flow in a pipe with rigid or flexible walls with losses due to wall friction. Optionally, the effects of dynamic compressibility, fluid inertia and pipe lift can be modelled. You can define multiple pipe segments and set the fluid pressure for each segment. By dividing the pipe into segments and selecting the Fluid inertia checkbox, it is possible to simulate water hammer in the system.

Pipe Characteristics

The Number of segments parameter allows you to specify the number of segments into which the pipe is divided. If the pipe consists of several segments, the pressure in each segment is calculated based on the inlet pressure and the effect of fluid compressibility and wall flexibility on the mass flow rate in the segment, if considered. The volume of fluid in each segment remains unchanged. For a two-segment pipe, the pressure varies linearly with the pressure determined at ports A and B. For a pipe with three or more segments, you can specify the liquid pressure in each segment as a vector or scalar in the Initial liquid pressure parameters. If Initial liquid pressure is set as a scalar, a constant pressure value will be used for all segments.

Flexible Walls

Flexible walls can be modelled for all cross-sectional geometries.

If the Flexible pipe wall checkbox is selected, uniform expansion along all directions is assumed and the specified cross-sectional shape is retained. This setting can lead to incorrect physical results for non-circular cross-sectional geometries experiencing high pressure compared to atmospheric pressure. When modelling flexible walls, the Volumetric expansion specification parameters can be used to control the method of specifying the volumetric expansion of the pipe cross-sectional area.

If the Volumetric expansion specification parameters are set to `Cross-sectional area vs. pressure', the volume change is modelled as follows:

where

  • ;

  • - is the length of the pipe, the value of the Pipe length parameters;

  • - the nominal cross-sectional area of the pipe, defined for each shape;

  • - current cross-sectional area of the pipe;

  • - internal pressure in the pipe;

  • - atmospheric pressure;

  • - pipe deformation coefficient as a function of area, value of the parameter Static gauge pressure to cross-sectional area gain.

    To calculate under the assumption of uniform elastic deformation of a thin-walled cylindrical pipe with an open end, use:

    where is the wall thickness of the tube and is the Young’s modulus;

  • - is the pipe deformation time constant, the value of the parameter Volumetric expansion time constant.

If the Volumetric expansion specification parameters are set to Cross-sectional area vs. pressure - Tabulated, the block uses the same equation as for Cross-sectional area vs. pressure to calculate . The value is determined using the table lookup function:

where

  • - is the overpressure vector Static gauge pressure vector;

  • - cross sectional area gain vector Cross sectional area gain vector.

If the Volumetric expansion specification parameters are set to Hydraulic diameter vs. pressure, the volume change is modelled as follows:

where

  • ;

  • - is the nominal hydraulic diameter determined for each mould.

  • - is the current hydraulic diameter of the pipe.

  • - pipe deformation coefficient as a function of diameter Static gauge pressure to hydraulic diameter gain.

    To calculate assuming uniform elastic deformation of a thin-walled cylindrical pipe with an open end, use:

If the Volumetric expansion specification parameter is set to Based on material properties, the block uses the same equation for as for Hydraulic diameter vs. pressure, but calculates depending on the value of the Material behaviour parameter:

This parameterization assumes a cylindrical thin-walled pressure vessel, where .

If Linear elastic is selected for the Material behaviour parameters, then

where

  • - Young’s modulus Young’s modulus;

  • - Poisson’s ratio Poisson’s ratio;

  • where is the pipe wall thickness Pipe wall thickness;

  • .

If `Multilinear elastic' is selected for the Material behaviour parameters, the block calculates the von Mises stress , which is simplified to , to determine the equivalent strain. The circumferential strain is

where

  • block calculates Young’s modulus from the first elements of the stress vector Stress vector and strain vector Strain vector;

  • , where and are the equivalent total stress and equivalent total strain, respectively. The block calculates the equivalent total strain from the von Mises stress and the strain-stress curve;

  • , where are the elements of the Cauchy stress tensor.

If you are not modelling flexible walls, and .

Pipe with circular cross-section

The nominal hydraulic diameter and the Pipe diameter are the same.

The cross-sectional area of the pipe bore is .

Pipe with annular cross-section

The nominal hydraulic diameter is the difference between the Pipe outer diameter and the Pipe inner diameter: .

The cross-sectional area of the pipe is .

Pipe with rectangular cross-section

The nominal hydraulic diameter is:

where

  • - is the width of the pipe cross-section Pipe height;

  • - is the height of the pipe cross-section Pipe width.

The cross-sectional area of the pipe bore is .

Pipe with elliptical cross-section

The nominal hydraulic diameter is:

where

  • - is the major axis of the elliptical cross-section Pipe major axis;

  • - is the minor axis of the elliptical cross-section Pipe minor axis.

The cross-sectional area of the pipe bore is .

Pipe with isosceles triangle cross-section

The nominal hydraulic diameter is:

where

  • - is the triangle side length Pipe side length.

  • - is the angle at the vertex of the triangle Pipe vertex angle.

The cross-sectional area of the pipe bore is .

Pressure loss due to friction

Haaland’s ratio

Haaland’s analytical relation models the loss due to wall friction either by means of a cumulative equivalent length, which accounts for drag due to inhomogeneities either by adding the length of straight pipe, resulting in equivalent losses, or by means of a local loss factor, which uses a loss factor to account for pipe inhomogeneities.

If the Local resistances specification parameters are set to Aggregate equivalent length and the Reynolds number is below the Laminar flow upper Reynolds number limit, then the pressure loss across all pipe segments is:

where

  • - kinematic viscosity of the fluid;

  • - loss factor for calculation of local resistance (Darcy friction factor) in laminar flow regime Laminar friction constant for Darcy friction factor, which can be set if Cross-sectional geometry is set to Custom, otherwise it is equal to 64;

  • - hydraulic diameter of the pipe.

  • - pipe length for calculating equivalent losses, the value of the parameter Aggregate equivalent length of local resistances;

  • - mass flow rate at port A;

  • - mass flow rate at port B.

When the Reynolds number is greater than Turbulent flow lower Reynolds number limit, the pressure loss in the pipe is:

where

  • - Darcy’s coefficient of friction. This coefficient is approximated by the empirical Haaland equation and is based on the surface roughness , Surface roughness specification, and the hydraulic diameter of the pipe:

    Pipe roughness for brass, lead, copper, plastic, steel, wrought iron and galvanised steel or iron is provided as ASHRAE standard values. You can also provide your own Internal surface absolute roughness values using the `Custom' setting.

  • - internal fluid density.

If the Local resistances specification parameters are set to Local loss coefficient and the Reynolds number is less than the Laminar flow upper Reynolds number limit, the pressure loss across all pipe segments is:

When the Reynolds number is greater than the Turbulent flow lower Reynolds number limit, the pressure loss in the pipe is:

where is the loss coefficient, which can be defined in the Total local loss coefficient parameters either as a single coefficient or as the sum of all loss coefficients along the pipe.

Dependence of nominal pressure drop on nominal mass flow rate

When the Viscous friction parameterization is set to Nominal pressure drop vs. nominal mass flow rate, the losses are determined using the loss coefficient for rigid or flexible walls. When the fluid is incompressible, the pressure loss across the pipe due to wall friction is:

where

  • - pressure drop to calculate the loss factor Nominal pressure drop as a scalar or vector;

  • - mass flow rate to calculate the loss factor Nominal mass flow rate as a scalar or vector.

If parameters Nominal pressure drop and Nominal mass flow rate are given as vectors, the scalar value is determined from vector elements by least squares approximation.

Table data - Darcy friction coefficient as a function of Reynolds number

If the Viscous friction parameterization parameter is set to Tabulated data - Darcy friction factor vs. Reynolds number, the viscous friction pressure losses are determined from user provided tabulated data for the Darcy friction factor vector and Reynolds number vector for turbulent Darcy friction factor parameters. Linear interpolation is used between data points.

Pipe discretisation

You can divide a pipe into multiple segments. If the pipe consists of more than one segment, the mass flow balance and momentum conservation equations are calculated for each segment.

If you want to capture specific phenomena in your application, such as water hammer, choose as many segments as will provide sufficient transient resolution. The following formula, derived from Nyquist’s discretisation theorem, is a rule of thumb for discretising a pipe by the minimum number of segments :

where

  • - pipe length Pipe length;

  • - transient frequency;

  • - sound velocity.

pipe advanced il 1

Conservation of momentum

If the Fluid dynamic compressibility checkbox is not selected, the mass flow rate at the pipe inlet is equal to the mass flow rate at the pipe outlet:

If Fluid dynamic compressibility is checked and Flexible pipe wall is unchecked, the difference between the mass flow rates at the inlet and outlet of the pipe depends on the change in fluid density due to compressibility:

If the Fluid dynamic compressibility checkbox is checked and the Flexible pipe wall checkbox is unchecked, the difference between the mass flow rates at the inlet and outlet of the pipe depends on the change in fluid density due to compressibility and the amount of fluid accumulated in the newly deformed areas of the pipe:

The change in momentum between the inlet and outlet of the pipe includes the change in pressure due to pipe wall friction, which is modelled according to Viscous friction parameterization and pipe height.

If Fluid inertia is not checked, the momentum balance will be:

where

  • - is the pressure in the port A;

  • - is the internal pressure in the liquid volume;

  • - port pressure B;

  • - pressure loss due to wall friction, parameterised by the Viscous friction losses specification for the respective port;

  • - pipe elevation. In the case of constant height pipes this is the parameter Elevation gain from port A to port B, otherwise it is taken as a scalar at port EL.

  • - Free fall acceleration. In case of fixed gravitational constant, this is the Gravitational acceleration parameter, otherwise it is taken as a scalar in port G.

If Fluid inertia is checked, the momentum balance will be:

where

  • - is the acceleration of the fluid in the corresponding port;

  • - is the cross-sectional area of the pipe port.

Ports

Conserving

# A — Fluid inlet or outlet port
isothermal liquid

Details

The isothermal liquid port corresponds to the inlet or outlet of the pipe.

Program usage name

port_a

# B — fluid inlet or outlet port
isothermal liquid

Details

The isothermal liquid port corresponds to the inlet or outlet of the pipe.

Program usage name

port_b

Input

# EL — pipe lift
scalar

Details

Variable lift from port A to port B as a scalar. The value at this port is limited between and , where is the pipe length, the value of the Pipe length parameters.

Dependencies

To use this port, select the Controlled elevation gain checkbox.

Data types

Float64.
Complex numbers support

No

# G — free-fall acceleration
scalar

Details

The variable acceleration of free fall given as a physical signal.

Dependencies

To use this port, select the Controlled graviational acceleration checkbox.

Data types

Float64.
Complex numbers support

No

Parameters

Configuration

# Fluid dynamic compressibility — accounting for dynamic compressibility of the fluid

Details

Determines whether the dynamic compressibility of the fluid is taken into account. If Fluid dynamic compressibility is checked, changes due to the mass flow rate of the fluid in the block are calculated in addition to density changes due to pressure changes. In the isothermal liquid library, all blocks calculate density as a function of pressure.

Default value

true (switched on)
Program usage name

dynamic_compressibility
Evaluatable

No

# Fluid inertia — fluid inertia

Details

Determines whether the inertia of the fluid flow will be taken into account. Flow inertia resists changes in mass flow rate.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox.

Default value

false (switched off)
Program usage name

inertia
Evaluatable

No

# Number of segments — number of pipe divisions

Details

The number of pipe divisions. Each division is a separate segment for which the pressure is calculated, depending on the pressure at the pipe inlet, the compressibility of the fluid and the flexibility of the walls, if taken into account. The volume of fluid in each segment remains fixed.

Default value

1
Program usage name

segment_count
Evaluatable

Yes

# Pipe length — pipe length
m | cm | ft | in | km | mi | mm | um | yd

Details

Total pipe length for all segments.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

5.0 m
Program usage name

length
Evaluatable

Yes

# Cross-sectional geometry — pipe cross-section geometry
Circular | Annular | Rectangular | Elliptical | Isosceles triangular | Custom

Details

The geometry of the pipe cross-section. The nominal hydraulic diameter and nominal cross-sectional area are calculated from the cross-sectional geometry.

Values

Circular | Annular | Rectangular | Elliptical | Isosceles triangular | Custom
Default value

Circular
Program usage name

cross_section_geometry
Evaluatable

No

# Pipe diameter — pipe diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

Diameter for pipes with a round cross-section.

Dependencies

To use this parameter, set the Cross-sectional geometry parameter to Circular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

circular_diameter
Evaluatable

Yes

# Pipe inner diameter — pipe inner diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

Internal diameter for a pipe with an annular cross-section, or for flow between two concentric pipes.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Annular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.05 m
Program usage name

annular_inner_diameter
Evaluatable

Yes

# Pipe outer diameter — pipe outer diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

The outside diameter for a pipe with an annular cross-section, or a flow between two concentric pipes.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Annular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

annular_outer_diameter
Evaluatable

Yes

# Pipe width — width of the rectangular cross-section of the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

Width of the rectangular cross-section of the pipe.

Dependencies

To use this parameter, set the Cross-sectional geometry parameter to Rectangular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

rectangular_width
Evaluatable

Yes

# Pipe height — height of the rectangular cross-section of the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

Height of the rectangular cross-section of the pipe.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Rectangular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

rectangular_height
Evaluatable

Yes

# Pipe major axis — major axis of the elliptical cross-section of the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

Major axis of the elliptical cross-section of the pipe.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Elliptical.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

elliptical_major_axis_length
Evaluatable

Yes

# Pipe minor axis — minor axis of the elliptical cross-section of the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

Minor axis of the elliptical cross-section of the pipe.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Elliptical.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.05 m
Program usage name

elliptical_minor_axis_length
Evaluatable

Yes

# Pipe side length — side length of the triangular cross-section of the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of two equal sides of a pipe cross-section in the form of an isosceles triangle.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to Isosceles triangular.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

triangular_side_length
Evaluatable

Yes

# Pipe vertex angle — angle at the apex of the triangular cross section of the pipe
deg | rad | rev | mrad

Details

Angle at apex of triangle for a pipe with a cross-section in the form of an isosceles triangle. The value must be less than 180 degrees.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to `Isosceles triangular'.

Units

deg | rad | rev | mrad
Default value

30.0 deg
Program usage name

triangular_vertex_angle
Evaluatable

Yes

# Cross-sectional area — pipe cross-sectional area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the pipe bore for a custom pipe geometry.

Dependencies

To use this parameter, set the Cross-sectional geometry parameter to Custom.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Hydraulic diameter — hydraulic diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

The hydraulic diameter used in calculating the Reynolds number of a pipe. For non-round pipes, the hydraulic diameter is the diameter of an equivalent cylindrical pipe with the same cross-sectional area. For round pipes, the hydraulic diameter and the pipe diameter are the same.

Dependencies

To use this parameter, set the Cross-sectional geometry parameter to `Custom'.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1128 m
Program usage name

hydraulic_diameter
Evaluatable

Yes

# Controlled elevation gain — pipe lifting specification

Details

If this checkbox is not selected, the pipe elevation gain from port A to B is constant and is specified in the Elevation gain from port A to port B parameters.

If this checkbox is selected, the elevation gain is variable and is taken as a scalar in port EL.

Default value

false (switched off)
Program usage name

controlled_elevation
Evaluatable

No

# Elevation gain from port A to port B — constant pipe lift height
m | cm | ft | in | km | mi | mm | um | yd

Details

Constant pipe lifting height.

Dependencies

To use this parameter, uncheck the Controlled elevation gain box.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.0 m
Program usage name

const_elevation_gain
Evaluatable

Yes

# Controlled graviational acceleration — free-fall acceleration specification

Details

If this checkbox is not selected, the free fall acceleration is constant and is specified in the Gravitational acceleration parameters.

If this checkbox is selected, the free fall acceleration can vary and is taken as a scalar in the G port.

Default value

false (switched off)
Program usage name

controlled_gravity
Evaluatable

No

# Gravitational acceleration — free-fall acceleration
gee | m/(s^2) | cm/(s^2) | ft/(s^2) | in/(s^2) | km/(s^2) | mi/(s^2) | mm/(s^2)

Details

Constant acceleration of free fall.

Dependencies

To use this parameter, set the Gravitational acceleration specification parameters to Constant.

Units

gee | m/(s^2) | cm/(s^2) | ft/(s^2) | in/(s^2) | km/(s^2) | mi/(s^2) | mm/(s^2)
Default value

9.81 m/(s^2)
Program usage name

g_const
Evaluatable

Yes

Viscous Friction

# Viscous friction parameterization — method for calculating pressure loss due to wall friction
Nominal pressure drop vs. nominal mass flow rate | Haaland correlation | Tabulated data - Darcy friction factor vs. Reynolds number

Details

Parameterization of pressure loss due to wall friction. Both analytical and tabular formulations are available.

Values

Nominal pressure drop vs. nominal mass flow rate | Haaland correlation | Tabulated data - Darcy friction factor vs. Reynolds number
Default value

Haaland correlation
Program usage name

pressure_loss_type
Evaluatable

No

# Nominal mass flow rate — mass flow rate for calculating the loss factor
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The nominal mass flow rate used to calculate the pressure drop coefficient for rigid and flexible pipes is specified as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the Nominal pressure drop parameters. If this parameter is specified as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Viscous friction parameterization to `Nominal pressure drop vs. nominal mass flow rate'.

Units

kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)
Default value

[0.1, 1.0] kg/s
Program usage name

mdot_nominal_vector
Evaluatable

Yes

# Nominal pressure drop — Pressure drop for calculating the loss factor
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The nominal pressure drop used to calculate the pressure loss coefficient for rigid and flexible pipes is specified as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the Nominal mass flow rate parameters. If this parameter is specified as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Viscous friction parameterization to `Nominal pressure drop vs. nominal mass flow rate'.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

[0.001, 0.01] MPa
Program usage name

delta_p_nominal_vector
Evaluatable

Yes

# Mass flow rate threshold for flow reversal — mass flow threshold
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The mass flow threshold value for reversible flow. Between the positive and negative values of the mass flow threshold a transition region around 0 kg/s is defined. Within this transition region, numerical smoothing is applied to the flow response. The threshold value must be greater than `0.

Dependencies

To use this parameter, set the Viscous friction parameterization parameters to `Nominal pressure drop vs. nominal mass flow rate'.

Units

kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)
Default value

1e-6 kg/s
Program usage name

mdot_threshold
Evaluatable

Yes

# Local resistances specification — method for quantifying pressure losses in the Haaland ratio
Aggregate equivalent length | Local loss coefficient

Details

A method for quantifying pressure losses due to pipe inhomogeneity.

Dependencies

To use this parameter, set the Viscous friction parameterization parameter to `Haaland correlation'.

Values

Aggregate equivalent length | Local loss coefficient
Default value

Aggregate equivalent length
Program usage name

local_pressure_loss_type
Evaluatable

No

# Aggregate equivalent length of local resistances — pipe length for calculation of equivalent losses
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of pipe that will result in equivalent hydraulic losses as a pipe with bends, area changes or other non-uniform characteristics. The effective pipe length is equal to the sum of Pipe length and Aggregate equivalent length of local resistances.

Dependencies

To use this parameter, set the Viscous friction parameterization parameter to `Haaland correlation' and the Local resistance specifications parameter to `Aggregate equivalent length'.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

1.0 m
Program usage name

length_add
Evaluatable

Yes

# Total local loss coefficient — pipe loss factor

Details

The loss factor associated with each irregularity in the pipe. You can enter a single loss factor or the sum of all loss factors along the pipe.

Dependencies

To use this parameter, set the Viscous friction parameterization parameter to `Haaland correlation' and the Local resistance specifications parameter to `Local loss coefficient'.

Default value

0.1
Program usage name

C_local_loss
Evaluatable

Yes

# Surface roughness specification — pipe material for roughness determination
Commercially smooth brass, lead, copper, or plastic pipe : 1.52 um | Steel and wrought iron : 46 um | Galvanized iron or steel : 152 um | Cast iron : 259 um | Custom

Details

Absolute surface roughness depending on the pipe material. The values given are ASHRAE standard roughness values. You can also enter your own value by setting the Surface roughness specification to `Custom'.

Dependencies

To use this parameter, set the Viscous friction parameterization parameter to `Haaland correlation'.

Values

Commercially smooth brass, lead, copper, or plastic pipe : 1.52 um | Steel and wrought iron : 46 um | Galvanized iron or steel : 152 um | Cast iron : 259 um | Custom
Default value

Commercially smooth brass, lead, copper, or plastic pipe : 1.52 um
Program usage name

roughness_specification
Evaluatable

No

# Internal surface absolute roughness — pipe wall roughness
m | cm | ft | in | km | mi | mm | um | yd

Details

Absolute roughness of the pipe walls. This parameter is used to determine the Darcy friction coefficient, which contributes to the pressure loss in the pipe.

Dependencies

To use this parameter, set the Viscous friction parameterization parameter to `Haaland correlation' and the Surface roughness specification parameter to `Custom'.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

15e-6 m
Program usage name

roughness
Evaluatable

Yes

# Reynolds number vector for turbulent Darcy friction — vector of Reynolds numbers for tabular parameterization

Details

Reynolds number vector for tabular parameterization of the Darcy friction coefficient. The elements of the Reynolds number vector for turbulent Darcy friction correspond to the elements of the Darcy friction factor vector. The elements of the vector should be listed in ascending order. A positive Reynolds number corresponds to the flow from port A to port B.

Dependencies

To use this parameter, set the Viscous friction parameterization parameters to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value

[400.0, 1000.0, 1500.0, 3e3, 4e3, 6e3, 1e4, 2e4, 4e4, 6e4, 1e5, 1e8]
Program usage name

Re_friction_vector
Evaluatable

Yes

# Darcy friction factor vector — vector of friction coefficients for tabular parameterization

Details

Darcy friction factor vector for tabular parameterization of Darcy friction factor. The elements of the Darcy friction factor vector correspond to the elements of the Reynolds number vector for turbulent Darcy friction factor. The elements of the vector must be unique and greater than or equal to `0'.

Dependencies

To use this parameter, set the Viscous friction parameterization parameters to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value

[0.264, 0.112, 0.071, 0.0417, 0.0387, 0.0268, 0.0250, 0.0232, 0.0226, 0.0220, 0.0214, 0.0214]
Program usage name

friction_factor_vector
Evaluatable

Yes

# Laminar flow upper Reynolds number limit — upper limit of Reynolds number in the laminar flow regime

Details

Upper limit of the Reynolds number in the laminar flow regime. Beyond this number, the flow regime becomes transient, approaches the turbulent regime and becomes fully turbulent at the Turbulent flow lower Reynolds number limit.

Dependencies

To use this parameter, set the Viscous friction parameterization to one of the following values:

  • `Haaland correlation

  • `Tabulated data - Darcy friction factor vs. Reynolds number

Default value

2000.0
Program usage name

Re_laminar
Evaluatable

Yes

# Turbulent flow lower Reynolds number limit — lower limit of Reynolds number in turbulent flow regime

Details

The lower limit value of the Reynolds number in the turbulent flow regime. Below this number, the flow regime is transient, approaches laminar and becomes fully laminar on the Laminar flow upper Reynolds number limit page.

Dependencies

To use this parameter, set the Viscous friction parameterization to one of the following values:

  • `Haaland correlation

  • `Tabulated data - Darcy friction factor vs. Reynolds number

Default value

4000.0
Program usage name

Re_turbulent
Evaluatable

Yes

# Laminar friction constant for Darcy friction factor — loss coefficient for calculation of local resistance (Darcy coefficient) in laminar flow regime

Details

loss coefficient for calculating the Darcy coefficient in laminar flow regime. The Darcy friction coefficient takes into account the contribution of wall friction in pressure loss calculations. If Cross-sectional geometry is not set to `Custom', the value of this parameter is `64'.

Dependencies

To use this parameter, set the Viscous friction parameterization to one of the following values:

  • `Haaland correlation

  • `Tabulated data - Darcy friction factor vs. Reynolds number

And set the Cross-sectional geometry parameters to Custom.

Default value

64.0
Program usage name

shape_factor
Evaluatable

Yes

Pipe Wall

# Flexible pipe wall — wall flexibility

Details

If this box is checked, uniform expansion along all directions is assumed and the specified cross-sectional shape is retained. This may not be accurate for non-circular cross-sectional geometries under severe deformation.

Dependencies

To use this parameter, select Fluid dynamic compressibility.

Default value

false (switched off)
Program usage name

wall_flexibility
Evaluatable

No

# Volumetric expansion specification — method of specifying the volumetric expansion of the pipe cross-sectional area
Cross-sectional area vs. pressure | Cross-sectional area vs. pressure - Tabulated | Hydraulic diameter vs. pressure | Based on material properties

Details

The settings for this parameter relate the new cross-sectional area or hydraulic diameter to the pressure in the pipe.

Dependencies

To use this parameters, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox.

Values

Cross-sectional area vs. pressure | Cross-sectional area vs. pressure - Tabulated | Hydraulic diameter vs. pressure | Based on material properties
Default value

Cross-sectional area vs. pressure
Program usage name

volumetric_expansion_model
Evaluatable

No

# Static gauge pressure to cross-sectional area gain — pipe deformation coefficient as a function of area
m^2/MPa

Details

Coefficient for calculating pipe deformation when the Volumetric expansion specification is set to Cross-sectional area vs. pressure. The coefficient is multiplied by the pressure drop between segmental pressure and atmospheric pressure.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Cross-sectional area vs. pressure'.

Units

m^2/MPa
Default value

1e-6 m^2/MPa
Program usage name

area_to_static_gauge_pressure_gain_const
Evaluatable

Yes

# Static gauge pressure vector — overpressure vector
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A vector containing overpressure values. The block uses this vector in the table to calculate the cross-sectional area of the pipe bore. The elements of the vector must be strictly positive and monotonically increasing, and the dimensionality of the vector must match the dimensionality of the Cross sectional area gain vector.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Cross-sectional area vs. pressure - Tabulated'.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

[0.1, 1.0] MPa
Program usage name

static_gauge_pressure_vector
Evaluatable

Yes

# Cross sectional area gain vector — vector of cross-sectional areas of pipe bores
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

A vector containing the cross-sectional areas of pipe bores. The block uses this vector in the table to calculate the cross-sectional area of a pipe bore at other pressures. The elements of the vector must be strictly positive and monotonically increasing, and the dimensionality of the vector must coincide with the dimensionality of the Static gauge pressure vector.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Cross-sectional area vs. pressure - Tabulated'.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

[1e-5, 1.1e-5] m^2
Program usage name

area_to_static_gauge_pressure_gain_vector
Evaluatable

Yes

# Static gauge pressure to hydraulic diameter gain — pipe deformation coefficient depending on diameter
m/MPa

Details

Coefficient for calculating pipe deformation when the Volumetric expansion specification is set to Hydraulic diameter vs. pressure. The coefficient is multiplied by the pressure drop between segment pressure and atmospheric pressure.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to Hydraulic diameter vs. pressure.

Units

m/MPa
Default value

1e-6 m/MPa
Program usage name

hydraulic_diameter_to_static_gauge_pressure_gain_const
Evaluatable

Yes

# Material behavior — the method used to specify the behaviour of the material
Linear Elastic | Multilinear Elastic

Details

The method the block uses to calculate the material behaviour.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Based on material properties'.

Values

Linear Elastic | Multilinear Elastic
Default value

Linear Elastic
Program usage name

material_behavior_model
Evaluatable

No

# Pipe wall thickness — pipe wall thickness
m | cm | ft | in | km | mi | mm | um | yd

Details

The wall thickness of the pipe. The block uses this value to calculate the stress.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Based on material properties'.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.05 m
Program usage name

wall_thickness
Evaluatable

Yes

# Young's modulus — Young’s modulus of pipe wall material
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Young’s modulus of the pipe wall material.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, set the Volumetric expansion specification to `Based on material properties' and the Material behaviour parameters to `Linear Elastic'.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

69.0 GPa
Program usage name

E
Evaluatable

Yes

# Stress vector — stress vector of pipe wall material
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A vector containing the stress values for the pipe wall material.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, set the Volumetric expansion specification to `Based on material properties' and the Material behaviour parameter to `Multilinear Elastic'.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

[276.0, 310.0] MPa
Program usage name

stress_vector
Evaluatable

Yes

# Strain vector — deformation vector of pipe wall material

Details

A vector containing the strain values for the pipe wall material.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, set the Volumetric expansion specification to `Based on material properties' and the Material behaviour parameters to `Multilinear Elastic'.

Default value

[0.004, 0.02]
Program usage name

strain_vector
Evaluatable

Yes

# Check if stress exceeds allowable level — notification when the voltage exceeds the set maximum
None | Error

Details

The value of this parameter determines the behaviour of the unit when the voltage exceeds the maximum voltage specified by the Maximum allowable stress parameters.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, set the Volumetric expansion specification to `Based on material properties' and the Material behaviour parameters to `Multilinear Elastic'.

Values

None | Error
Default value

None
Program usage name

stress_assert_action
Evaluatable

No

# Maximum allowable stress — maximum allowable stress on the pipe wall
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The maximum stress that is allowed on the pipe wall. Control what the unit will do if the stress exceeds this value using the Check if stress exceeds specified allowable level parameters.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, set the Volumetric expansion specification to `Based on material properties', the Material behaviour parameter to `Multilinear Elastic', and the Check if stress exceeds specified allowable level parameter to `Error'.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

400.0 MPa
Program usage name

max_stress
Evaluatable

Yes

# Poisson's ratio — Poisson’s ratio of pipe wall material

Details

Poisson’s ratio of the pipe wall material.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox, and set the Volumetric expansion specification parameters to `Based on material properties'.

Default value

0.33
Program usage name

poisson_ratio
Evaluatable

Yes

# Volumetric expansion time constant — time constant of pipe deformation
d | s | hr | ms | ns | us | min

Details

The time required for the wall to reach a steady state after deformation of the pipe. This parameter affects the dynamic change of the pipe volume.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Flexible pipe wall checkbox.

Units

d | s | hr | ms | ns | us | min
Default value

0.01 s
Program usage name

volumetric_expansion_time_constant
Evaluatable

Yes

Initial Conditions

# Initial liquid pressure — initial pressure in the pipe or pipe segment
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The initial fluid pressure, specified as a scalar or vector. A vector of length elements defines the fluid pressure for each of the pipe segments. If the vector length is two elements, the pressure along the pipe is linearly distributed between the two element values. If the vector length is three or more elements, the initial pressure in -th segment is determined by -th element of the vector.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

0.101325 MPa
Program usage name

p_start
Evaluatable

Yes

# Initial mass flow rate from port A to port B — initial mass flow rate for inertia calculation
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Initial mass flow rate for pipes with modelled fluid inertia.

Dependencies

To use this parameter, select the Fluid dynamic compressibility checkbox and the Fluid inertia checkbox.

Units

kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)
Default value

0.0 kg/s
Program usage name

mdot_start
Evaluatable

Yes

Literature

  1. Budynas R. G. Nisbett J. K. & Shigley J. E. (2004). Shigley’s mechanical engineering design (7th ed.). McGraw-Hill.

  2. Ju Frederick D., Butler Thomas A., Review of Proposed Failure Criteria for Ductile Materials (1984) Los Alamos National Laboratory.

  3. Jahed H, A Variable Material Property Approach for Elastic-Plastic Analysis of Proportional and Non-proportional Loading, (1997) University of Waterloo

See also

  1. Pipe (IL)

  2. Pipe (TL)

  3. Sharp-Edged Elbow (IL)