Engee documentation

Pipe (Advanced) (TL)

Rigid pipework for fluid flow in thermal liquid systems.

blockType: EngeeFluids.ThermalLiquid.Pipes.Straight

pipe advanced tl

Path in the library:

/Physical Modeling/Fluids/Thermal Liquid/Pipes & Fittings/Pipe (Advanced) (TL)

Description

The block Pipe (Advanced) (TL) simulates the dynamics of thermal liquid flow in a pipe. The block determines the temperature in the pipe based on its difference between ports, pipe height and additional heat transfer at port H.

The pipe can have a constant or variable height difference between ports A and B. For a constant height difference, use the parameters Elevation gain from port A to port B.

You can include the effects of dynamic compressibility, fluid inertia, and wall flexibility. When the block includes these phenomena, it calculates flow properties for each number of pipe segments you specify.

pipe advanced tl 1

Pipe geometry

Use the parameters Cross-sectional geometry, to specify the shape of the pipe.

Round (Circular)

The nominal hydraulic diameter, , and the pipe diameter, , are equal to the value of the parameter Pipe diameter. The cross-sectional area of the pipe bore is

Circular (Annular)

The nominal hydraulic diameter is equal to the difference between the values of the parameters Pipe outer diameter and Pipe inner diameter = . The cross-sectional area of the pipe bore is .

Rectangular (Rectangular)

The nominal hydraulic diameter is ,

where

  • - cross-sectional width of the pipe Pipe height.

  • - height of the pipe cross section Pipe width.

The cross-sectional area of the pipe bore is

Elliptical (Elliptical)

The nominal hydraulic diameter is

where

  • - major axis of the elliptical cross section Pipe major axis.

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

The cross-sectional area of the pipe bore is

Equosceles triangle (Isosceles triangular)

The nominal hydraulic diameter is

where

  • - is the length of the side of the triangle Pipe side length.

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

The cross-sectional area of the pipe bore is

Custom (Custom)

You can specify the cross-sectional area of the pipe bore using the parameters Cross-sectional area. The nominal hydraulic diameter is the value of the parameter Hydraulic diameter.

Wall flexibility

Flexible walls can be modelled for all geometric cross-sectional shapes.

When modelling flexible walls, you can use the parameters Volumetric expansion specification, to specify the volumetric expansion of the cross-sectional area of the pipe bore.

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

where

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

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

  • - the current cross-sectional area of the pipe.

  • - internal pressure in the pipe.

  • - atmospheric pressure.

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

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

    where is the pipe wall thickness and is the Young’s modulus.

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

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

where

  • - vector of overpressures Static gauge pressure vector;

  • - vector of cross-sectional areas of pipe openings Cross sectional area gain vector.

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

where

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

  • - current hydraulic diameter of the pipe.

  • - pipe deformation coefficient depending on the 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 the formula:

If the parameter Volumetric expansion specification 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 parameter Material behavior.

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

When the parameter Material behavior is set to Linear elastic,

where

  • - Young’s modulus Young’s modulus.

  • - Poisson’s ratio Poisson’s ratio.

  • , where is the wall thickness of the pipe Pipe wall thickness.

If the parameter Material behavior is set to Multilinear elastic, 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;

  • , 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 strain-stress curve;

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

If you are modelling non-flexible walls, = and = .

Thermal expansion of the pipe wall

If you have selected the parameters Pipe thermal expansion, the block models the thermal expansion of the pipe wall using the following assumptions:

  • The pipe material is isotropic.

  • The Bio number for the pipe is , and the pipe can be modelled using a concentrated thermal capacity.

  • The temperature variation and deformation of the pipe are small enough that the first order approximation for the expansion region is accurate.

If the parameter Material behavior is set to a value of Cross-sectional area vs. pressure, Cross-sectional area vs. pressure - Tabulated or Hydraulic diameter vs. pressure and the parameter Pipe thermal expansion is selected, the block adds a thermal expansion term when calculating area or diameter.

If the Material behavior parameters are set to Cross-sectional area vs. pressure,

where

  • - is the coefficient of thermal expansion of the pipe Coefficient of thermal expansion;

  • ;

  • - is the liquid temperature at the internal node of the unit;

  • - reference temperature for the thermal expansion of the pipe Thermal expansion reference temperature.

If the parameters Material behavior are set to Cross-sectional area vs. pressure - Tabulated,

If the parameter Material behavior is set to . Hydraulic diameter vs. pressure,

If the parameter Material behavior is set to Multilinear elastic and the parameter Pipe thermal expansion is selected , the block calculates as:

where

Heat transfer of the pipe wall

You can enable heat transfer to the pipe walls using the parameters Heat transfer parameterization.

There are two analytical models:

  • Gnielinski correlation, which models the Nusselt number as a function of Reynolds and Prandtl numbers with predetermined coefficients

  • Dittus-Boelter correlation - Nusselt = a*Re^b * Pr^c, which models the Nusselt number as a function of Reynolds and Prandtl numbers with user-specified coefficients.

Models Nominal temperature differential vs. nominal mass flow rate, Tabulated data - Colburn factor vs. Reynolds number' and `Tabulated data - Nusselt number vs. Reynolds number & Prandtl number are interpolation table parameterizations based on user-supplied data.

Heat exchange between the fluid and the pipe wall occurs by convection, , and conduction, , where the total heat flux, , is .

Heat transfer by conduction is defined as follows:

where

  • - nominal hydraulic diameter, , if the pipe walls are rigid, and steady-state pipe diameter, , if the pipe walls are flexible;

  • - is the thermal conductivity of the thermal liquid, determined internally for each pipe segment;

  • - surface area of the pipe wall

  • - pipe wall temperature;

  • - the temperature of the fluid in the internal node of the unit.

Heat transfer due to convection is defined as follows:

Where:

  • - is the average specific heat capacity of the fluid, which the unit calculates using an interpolation table.

  • - is the average mass flow rate through the pipe.

  • - liquid temperature at the inlet of the pipe.

  • - heat transfer coefficient of the pipe.

The heat transfer coefficient is calculated as:

except when parameterised through the model Nominal temperature differential vs. nominal mass flow rate, where is the average thermal liquid thermal conductivity throughout the pipe and is the average Nusselt number in the pipe.

Analytical parameterizations

If the parameter Heat transfer parameterization is set to Gnielinski correlation and the flow is turbulent, the mean Nusselt number is calculated as:

where

  • - is the average Darcy friction coefficient, according to the Haaland relation:

    where is absolute roughness of pipe walls Internal surface absolute roughness;

  • - Reynolds number;

  • - Prandtl number.

When the flow is laminar, the data from [1] determine how the Nusselt number depends on the parameters Cross-sectional geometry:

  • If the parameter Cross-sectional geometry is set to a value of Circular, the Nusselt number is 3.66.

  • If the parameter Cross-sectional geometry is set to. Annular, the block calculates the Nusselt number from the tabulated data using an interpolation table with linear interpolation and nearest extrapolation.

Nusselt number

1/20

17.46

1/10

11.56

1/4

7.37

1/2

5.74

1

4.86

The block corrects the calculated Nusselt number with a correction factor

  • If the parameter Cross-sectional geometry is set to the value of Rectangular, the block calculates the Nusselt number from tabulated data using an interpolation table with linear interpolation and nearest extrapolation.

Nusselt number

0

7.54

1/8

5.60

1/6

5.14

1/4

4.44

1/3

3.96

1/2

3.39

1

2.98

  • If the parameter Cross-sectional geometry is set to the value of Elliptical, the block calculates the Nusselt number from tabulated data using an interpolation table with linear interpolation and nearest extrapolation.

Nusselt number

1/16

3.65

1/8

3.72

1/4

3.79

1/2

3.74

1

3.66

  • If the parameter Cross-sectional geometry is set to the value of Isosceles triangular, the block calculates the Nusselt number from tabulated data using an interpolation table with linear interpolation and nearest extrapolation.

θ

Nusselt number

10π/180

1.61

30π/180

2.26

60π/180

2.47

90π/180

2,34

120π/180

2,00

  • If the parameter Cross-sectional geometry is set to Custom, the Nusselt number is the value of the parameter Nusselt number for laminar flow heat transfer.

If Heat transfer parameterization is set to `Dittus-Boelter correlation' and the flow is turbulent, the mean Nusselt number is calculated as:

where

  • - empirical constant Coefficient a.

  • - empirical constant Exponent b.

  • - empirical constant Exponent c.

The Dittus-Bolter relationship is used in the block by default:

When the flow is laminar, the Nusselt number depends on the parameters Cross-sectional geometry.

Parametrization from tabular data

If the parameter Heat transfer parameterization is set to the value of Tabulated data - Colburn factor vs. Reynolds number, the average Nusselt number is calculated as:

where is the Colburn-Chilton coefficient.

If the parameter Heat transfer parameterization is set to a value of Tabulated data - Nusselt number vs. Reynolds number & Prandtl number, the Nusselt number is interpolated from the three-dimensional array of the mean Nusselt number as a function of the mean Reynolds number and the mean Prandtl number:

If the parameters Heat transfer parameterization is set to Nominal temperature difference vs. nominal mass flow rate and the flow is turbulent, the heat transfer coefficient is calculated as:

where

  • - is the mass flow rate in the pipe Nominal mass flow rate.

  • - is the average mass flow rate:

  • - nominal heat transfer coefficient, which is calculated as:

where

  • - is the nominal wall surface area.

  • - pipe wall temperature Nominal wall temperature.

  • - pipe inlet temperature Nominal inflow temperature.

  • - pipe outlet temperature Nominal outflow temperature.

This relationship is based on the assumption that the Nusselt number is proportional to the Reynolds number:

If the pipe walls are rigid, the expression for the heat transfer coefficient becomes:

Trumpet effects

This block allows you to include the effects of dynamic compressibility and fluid inertia. Including each of these effects can improve model accuracy at the cost of more complex equations and potentially increased modelling time:

  • When the option to account for the dynamic compressibility of the fluid is turned off, it is assumed that the fluid passes through the pipe in a short period of time, so there is no mass accumulation in the pipe and the inflow of mass is equal to its outflow. This is the simplest option. It is suitable when the mass of liquid in the pipe is a negligible fraction of the total mass of liquid in the system.

  • When the option to account for the dynamic compressibility of the fluid is enabled, an imbalance of mass inflow and outflow can result in an increase or decrease in the amount of fluid in the pipe. As a result, the pressure in the pipe can rise and fall, which will provide a certain amount of pliability to the system and result in rapid pressure changes. This option is enabled by default.

  • If the option to account for the dynamic compressibility of the fluid is enabled, the option to account for fluid inertia can also be enabled. This effect results in additional hydraulic resistance on top of the resistance due to friction. This additional resistance is proportional to the rate of change in mass flow rate. Accounting for fluid inertia slows down rapid changes in flow rate, but can also cause surges and fluctuations in flow rate. This option is suitable for very long pipe. Enable the fluid inertia option and connect several pipe segments in series to simulate the propagation of pressure waves along the pipe, such as in a water hammer phenomenon.

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 the loss factor to account for pipe inhomogeneities.

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

where

  • - kinematic viscosity of the fluid;

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

  • - hydraulic diameter of the pipe.

  • - pipe length for calculation of equivalent losses, parameter value 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 values Internal surface absolute roughness using the Custom setting.

  • - internal fluid density.

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




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

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

Dependence of the nominal differential pressure on the nominal mass flow rate

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

where

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

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

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

Conservation of momentum

The pressure drop in the pipe is due to pressure at the pipe ports, friction at the pipe walls, and hydrostatic changes associated with changes in elevation:

where

  • - port pressure A.

  • - port pressure B.

  • - pressure drop due to viscous friction, .

  • - acceleration due to gravity at the mean height of the pipe, Gravitational acceleration, or the signal at port G.

  • - height difference between port A and port B, or .

  • - the internal density of the fluid, which is measured at each section of the pipe. If the dynamic compressibility of the fluid is not modelled, it is:

When fluid inertia is not modelled, conservation of momentum between port A and internal node I:

When fluid inertia is not modelled, conservation of momentum between port B and internal node I:

In fluid inertia modelling, the conservation of momentum between the port A and the internal node I is:

where

  • - inertia of liquid in the port A.

  • - is the pipe length Pipe length.

  • - nominal cross-sectional area Nominal cross-sectional area.

In fluid inertia modelling, the conservation of momentum between port B and internal node I is:

where

- is the inertia of the liquid in the port B.

Discretisation of the pipe

You can divide a pipe into more than one segment. 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 tl 2

In some applications, you may need to connect blocks in series Pipe (Advanced) (TL). For example, you may need multiple pipe segments to define a thermal boundary condition along the length of the pipe. In this case, model the pipe segments using the Pipe (Advanced) (TL) block for each segment and use the thermal ports to set the thermal boundary condition.

Mass Balance

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

where

  • - is the mass flow rate at port A.

  • - is the mass flow rate at port B.

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:

where

  • - is the density of thermal liquid in the internal node I. Each pipe segment has an internal node.

  • - is the strain rate of the pipe volume.

For a flexible pipe with compressible fluid, the mass inside the pipe can vary with pressure and temperature. The volume modulus of elasticity and coefficient of thermal liquid thermal expansion take into account this dependence, and the equation of conservation of pipe mass is of the form:

where

  • - is the pressure of thermal liquid at the internal node I.

  • - is the rate of temperature change of thermal liquid at the internal node I.

  • - is the bulk modulus of elasticity of thermal liquid.

  • - coefficient of thermal expansion of the fluid.

Energy conservation

The rate of energy storage in the pipe at the internal node I is defined as follows:

where

  • - is the energy flow at port A.

  • - is the energy flux in port B.

  • - heat transfer through the pipe wall.

If the fluid is incompressible, the expression for the rate of energy accumulation has the form:

where

  • - is the specific heat of the liquid at the internal node of the unit.

  • - is the volume of the pipe;

  • - is the constant liquid density. This value is calculated from the parameters Nominal liquid temperature and Nominal liquid pressure.

If the liquid is compressible, the expression for the energy storage rate is

where



and are the specific enthalpy at the internal unit node.

If the fluid is compressible and the pipe walls are flexible, the expression for the rate of energy accumulation has the following form

Ports

Conserving

# A — Fluid inlet or outlet port
thermal liquid

Details

Thermal liquid port, corresponds to the inlet or outlet of the pipe.

Program usage name

port_a

# B — fluid inlet or outlet port
thermal liquid

Details

Thermal liquid port, corresponds to the inlet or outlet of the pipe.

Program usage name

port_b

# H — pipe wall temperature
`heat

Details

A heat port related to the temperature of the pipe wall. This temperature may be different from the fluid temperature.

Program usage name

thermal_port

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, tick the checkbox of the parameter Controlled elevation gain.

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 checkbox for the parameters Controlled graviational acceleration.

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.

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 checkbox for the parameters Fluid dynamic compressibility.

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 total 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 parameter Cross-sectional geometry 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 parameter Cross-sectional geometry 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 parameter Cross-sectional geometry 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 parameter Cross-sectional geometry to the value of 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 parameter Cross-sectional geometry to the value of 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 parameter Cross-sectional geometry to the value of 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 parameter Cross-sectional geometry to the value of 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 parameter Cross-sectional geometry to 180 degrees. 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 parameter Cross-sectional geometry 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 parameter Cross-sectional geometry 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 lift height from port A to B is constant and is set in the parameters Elevation gain from port A to port B.

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

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 Controlled elevation gain.

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 parameters Gravitational acceleration.

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 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 parameter Nominal pressure drop. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the parameter 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 parameters Nominal mass flow rate. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the parameter 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 parameter Viscous friction parameterization to 0. 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 parameter Viscous friction parameterization 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 and the parameter to . Haaland correlation`and set the Local resistances specification parameters 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 parameters to Haaland correlation`and set the Local resistances specification parameters 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 Surface roughness specification to Custom.

Dependencies

To use this parameter, set the parameters Viscous friction parameterization to Custom. 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 parameters to `Custom' and the parameters to `Custom'. `Haaland correlation`and set the Surface roughness specification parameters 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 factor — vector of Reynolds numbers for tabular parameterization

Details

Vector of Reynolds numbers for tabular parameterization of the Darcy friction coefficient. The elements of the vector Reynolds number vector for turbulent Darcy friction factor correspond to the elements of the vector 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 the value of 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

Vector of Darcy friction coefficients for tabular parameterization of Darcy friction coefficient. The elements of the vector Darcy friction factor vector correspond to the elements of the vector 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

The 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 Turbulent flow lower Reynolds number limit.

Dependencies

To use this parameter, set 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 of the Reynolds number in the turbulent flow regime. Below this number, the flow regime is transient, approaches laminar and becomes fully laminar Laminar flow upper Reynolds number limit.

Dependencies

To use this parameter, set 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 parameters to one of the following values:

  • Haaland correlation

  • Tabulated data - Darcy friction factor vs. Reynolds number

And set the parameters Cross-sectional geometry 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, if Volumetric expansion specification is set to Cross-sectional area vs. pressure. The coefficient is multiplied by the pressure drop between the pressure in the segment and the 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 coincide with the dimensionality of the vector Cross sectional area gain vector.

Dependencies

To use this parameter, check Fluid dynamic compressibility and check Flexible pipe wall, and for the parameter Volumetric expansion specification set the value 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 vector Static gauge pressure vector.

Dependencies

To use this parameter, check the checkbox Fluid dynamic compressibility and the checkbox Flexible pipe wall, and for the parameter Volumetric expansion specification set the value 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, if Volumetric expansion specification is set to Hydraulic diameter vs. pressure. The coefficient is multiplied by the pressure drop between the pressure in the segment and the 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 , for the Volumetric expansion specification parameters set the value to Based on material properties, and for the parameter Material behavior set the value 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 , for the Volumetric expansion specification parameters set the value to Based on material properties`and for the parameter Material behavior set the value 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 , for the Volumetric expansion specification parameters set the value to Based on material properties, and for the parameter Material behavior set the value 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 parameter Maximum allowable stress.

Dependencies

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

Units

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

0.01 s
Program usage name

volumetric_expansion_time_constant
Evaluatable

Yes

# Pipe thermal expansion — thermal expansion of the pipe

Details

Whether the expansion in the pipe due to temperature change needs to be taken into account.

Dependencies

To use this parameter, select the check box Fluid dynamic compressibility, and set the Pipe wall specification parameters to Flexible.

Default value

false (switched off)
Program usage name

thermal_expansion
Evaluatable

No

# Coefficient of thermal expansion — coefficient of thermal expansion of the pipe
1/K | 1/degR | 1/deltaK | 1/deltadegC | 1/deltadegF | 1/deltadegR | um/(deltaK*m)

Details

The coefficient of linear thermal expansion of a pipe. This value represents the relative change in size per degree of temperature change at constant pressure.

Dependencies

To use this parameter, select the check box Fluid dynamic compressibility, set the Pipe wall specification parameters to Flexible, and then select the check box Pipe thermal expansion.

Units

1/K | 1/degR | 1/deltaK | 1/deltadegC | 1/deltadegF | 1/deltadegR | um/(deltaK*m)
Default value

24.0 um/(deltaK*m)
Program usage name

alpha_wall
Evaluatable

Yes

# Thermal expansion reference temperature — reference temperature for the thermal expansion of the pipe
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The reference temperature that the unit uses when calculating the thermal expansion of the pipe.

Dependencies

To use this parameter, select the check box Fluid dynamic compressibility, set the Pipe wall specification parameters to Flexible, and then select the check box Pipe thermal expansion.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

T_alpha
Evaluatable

Yes

Heat Transfer

# Heat transfer parameterization — method of convective heat exchange with the pipe wall
Nominal temperature differential vs. nominal mass flow rate | Gnielinski correlation | Dittus-Boelter correlation - Nusselt = a * Re^b * Pr^c | Tabulated data - Colburn factor vs. Reynolds number | Tabulated data - Nusselt number vs. Reynolds number & Prandtl number

Details

Parameterization of the calculation of the heat transfer coefficient between the fluid and the pipe wall. Both analytical and tabular formulations are available.

Values

Nominal temperature differential vs. nominal mass flow rate | Gnielinski correlation | Dittus-Boelter correlation - Nusselt = a * Re^b * Pr^c | Tabulated data - Colburn factor vs. Reynolds number | Tabulated data - Nusselt number vs. Reynolds number & Prandtl number
Default value

Gnielinski correlation
Program usage name

heat_transfer_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 heat transfer is specified as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the parameter Nominal inflow temperature. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the parameter Viscous friction parameterization to `Nominal temperature differential 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_heat_vector
Evaluatable

Yes

# Nominal inflow temperature — pipe inlet temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The nominal inlet fluid temperature used to calculate the heat transfer coefficient is given as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the parameters Nominal mass flow rate. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Heat transfer parameterization parameter to . Nominal temperature differential vs. nominal mass flow rate.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

[293.15, 293.15] K
Program usage name

T_inflow_nominal_vector
Evaluatable

Yes

# Nominal outflow temperature — outlet temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The nominal fluid outlet temperature used to calculate the heat transfer coefficient is given as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the parameters Nominal mass flow rate. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Heat transfer parameterization parameter to . Nominal temperature differential vs. nominal mass flow rate.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

[300.0, 300.0] K
Program usage name

T_outflow_nominal_vector
Evaluatable

Yes

# Nominal inflow pressure — pipe inlet pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Nominal fluid inlet pressure used to calculate the heat transfer coefficient, given as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the parameters Nominal mass flow rate. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Heat transfer parameterization parameter to . Nominal temperature differential vs. nominal mass flow rate.

Units

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

[0.101325, 0.101325] MPa
Program usage name

p_inflow_nominal_vector
Evaluatable

Yes

# Nominal wall temperature — pipe wall temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The pipe wall temperature used to calculate the heat transfer coefficient is specified as a scalar or vector. All nominal values must be greater than 0 and have the same number of elements as the parameters Nominal mass flow rate. If this parameter is given as a vector, the scalar value is determined by least squares approximation.

Dependencies

To use this parameter, set the Heat transfer parameterization parameter to . Nominal temperature differential vs. nominal mass flow rate.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

[303.15, 303.15] K
Program usage name

T_wall_nominal_vector
Evaluatable

Yes

# Coefficient a — empirical constant in the Dittus-Bolter correlation

Details

Empirical constant for usage in the Dittus-Bolter correlation. This correlation relates the Nusselt number in turbulent flows to the heat transfer coefficient.

Dependencies

To use this parameter, set the parameter Heat transfer parameterization to `Dittus-Boelter correlation'.

Default value

0.023
Program usage name

a_dittus_boelter_const
Evaluatable

Yes

# Exponent b — empirical constant in the Dittus-Bolter correlation

Details

Empirical constant for usage in the Dittus-Bolter correlation. This correlation relates the Nusselt number in turbulent flows to the heat transfer coefficient.

Dependencies

To use this parameter, set the parameter Heat transfer parameterization to `Dittus-Boelter correlation'.

Default value

0.8
Program usage name

b_dittus_boelter_const
Evaluatable

Yes

# Exponent c — empirical constant in the Dittus-Bolter correlation

Details

Empirical constant for usage in the Dittus-Bolter correlation. This correlation relates the Nusselt number in turbulent flows to the heat transfer coefficient. The by default value reflects heat transfer in the fluid.

Dependencies

To use this parameter, set the parameter Heat transfer parameterization to `Dittus-Boelter correlation'.

Default value

0.4
Program usage name

c_dittus_boelter_const
Evaluatable

Yes

# Nusselt number for laminar flow heat transfer — Nusselt number used in heat transfer calculations for laminar flows

Details

The ratio of convective to conductive heat transfer in the laminar flow regime. The Nusselt number of a fluid affects the rate of heat transfer.

Dependencies

To use this parameter, set the Cross-sectional geometry parameters to `Custom' and the Heat transfer parameterization parameters to one of the following values:

  • Gnielinski correlation

  • Nominal temperature differential vs. nominal mass flow rate

  • `Dittus-Boelter correlation.

Default value

3.66
Program usage name

Nu_laminar
Evaluatable

Yes

# Reynolds number vector for Colburn factor — Reynolds numbers at which it is necessary to calculate the Colburn factor

Details

Vector of Reynolds numbers for the tabular parameterization of the Colburn factor. The elements of the vector form an independent axis with the parameters Colburn factor vector. The elements of the vector must be listed in ascending order and must be greater than 0. This parameter must have the same number of elements as Colburn factor vector. For reverse flows, or flows from B to A , the same data applies in the reverse direction.

Dependencies

To use this parameter, set the Heat transfer parameterization parameters to Tabulated data - Colburn factor vs. Reynolds number.

Default value

[100.0, 150.0, 1000.0]
Program usage name

Re_vector_colburn
Evaluatable

Yes

# Colburn factor vector — Colburn coefficients, where tabulated Reynolds numbers are used

Details

Vector of Colbrun coefficients for tabular parameterization of the Colburn coefficient. The elements of the vector form an independent axis with the parameter Reynolds number vector for Colburn factor. This parameter must have the same number of elements as the parameter Reynolds number vector for Colburn factor.

Dependencies

To use this parameter, set the Heat transfer parameterization parameters to . Tabulated data - Colburn factor vs. Reynolds number.

Default value

[0.019, 0.013, 0.002]
Program usage name

colburn_factor_vector
Evaluatable

Yes

# Reynolds number vector for Nusselt number — Reynolds number for tabular parameterization of the Nusselt number

Details

Vector of Reynolds numbers for the tabular parameterization of the Nusselt number. This vector forms an independent axis with the parameter Prandtl number vector for Nusselt number for the two-dimensional dependence Nusselt number table. The elements of the vector must be listed in ascending order and must be greater than 0.

Dependencies

To use this parameter, set the Heat transfer parameterization parameters to the value of Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

Default value

[100.0, 150.0, 1000.0]
Program usage name

Re_vector_Nu
Evaluatable

Yes

# Prandtl number vector for Nusselt number — Prandtl numbers for tabular parameterization of the Nusselt number

Details

The vector of Prandtl numbers for the tabular parameterization of the Nusselt number. This vector forms an independent axis with the parameter Reynolds number vector for Nusselt number for the two-dimensional dependence Nusselt number table. The elements of the vector must be listed in ascending order.

Dependencies

To use this parameter, set the Heat transfer parameterization parameters to Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

Default value

[1.0, 10.0]
Program usage name

Pr_vector_Nu
Evaluatable

Yes

# Nusselt number table, Nu(Re,Pr) — Nusselt numbers at tabulated Reynolds and Prandtl numbers

Details

Matrix of Nusselt numbers at at the tabulated Reynolds and Prandtl numbers. Linear interpolation is used between the table elements. and are the sizes of the corresponding vectors:

  • - number of vector elements in the parameters Reynolds number vector for Nusselt number.

  • - number of vector elements in the parameters Prandtl number vector for Nusselt number.

Dependencies

To use this parameter, set the Heat transfer parameterization parameters to Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

Default value

[3.72 4.21; 3.75 4.44; 4.21 7.15]
Program usage name

Nu_matrix
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, tick the checkbox Fluid dynamic compressibility.

Units

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

0.101325 MPa
Program usage name

p_start
Evaluatable

Yes

# Initial liquid temperature — initial temperature in the pipe or pipe segment
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

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

Dependencies

To use this parameters, tick the checkbox Fluid dynamic compressibility.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

T_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

0.1 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. Cengel, Y. A. "Heat and Mass Transfer: A Practical Approach (3rd edition)." New York, McGraw-Hill, 2007

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

  4. Hencky H (1924) "Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenenen Nachspannungen." Z Angew Math Mech 4:323-335

  5. 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. Pipe (Advanced) (IL)