Gradual Area Change (IL)

Narrowing or widening of a pipeline in an isothermal fluid network.

blockType: EngeeFluids.IsothermalLiquid.Fittings.AreaChange

Gradual Area Change (IL)

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pipes & Fittings/Gradual Area Change (IL)

Sudden Area Change (IL)

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pipes & Fittings/Sudden Area Change (IL)

Description

In blocks Gradual Area Change (IL) and Sudden Area Change (IL) A gradual or sudden change in the cross-sectional area is modeled for pipeline systems with constant cross-section and variable flow direction. The channel narrows in the direction from port A to port B. To simulate the expansion of the channel, the unit should be installed so that the liquid moves in the direction from port B to port A. The areas at the entrance and exit can be the same.

Semi-empirical and tabular methods for determining the dependence of losses on flow characteristics are available for calculating pressure losses.

The semi-empirical method

In the analytical semi-empirical method, the dependence of pressure losses on flow rates is determined by the coefficient of hydraulic losses , which in turn is determined through user-defined parameters, Contraction correction factor and Expansion correction factor , for more information, see [1]. The coefficient of hydraulic losses is calculated based on the coefficients of expansion and contraction losses and the mass flow of fluid through the block.

In the case of gradual narrowing with a cone angle ranging from 0° before 45° The coefficient of loss in narrowing is determined as follows:

where

— channel narrowing coefficient ;
— cone angle, parameter value Cone angle.

And in the case of a gradual narrowing with a cone angle in the range between 45° and 180° the loss factor will be defined as:

In the case of a sudden narrowing of the channel, the cone angle is 180°. Then the loss coefficient is calculated as:

In the case of a gradual expansion of the channel with a cone angle in the range of 0° before 45° The loss factor will be determined as follows:

In the case of gradual expansion with a cone angle between 45° and 180°:

Based on the data obtained, the coefficient of hydraulic losses for a pipeline segment with a narrowing or widening of the channel will be determined:

where

— mass flow through port A. The mass is stored in the block:
— the value of the mass flow rate at which the separation recirculation zone occurs is determined by the value of the parameter Critical Reynolds number, :

where
- — the smallest cross-sectional area of the channel (or the values of the parameters Cross-sectional area at port A or Cross-sectional area at port B);
- — kinematic viscosity of the liquid;
- — the average density of the liquid;
- — hydraulic diameter in cross section :

Tabular parameterization method

The hydraulic loss coefficient can also be determined using user-provided interpolated data obtained in the minimum cross-section for different Reynolds numbers, i.e. data that is a function of the critical Reynolds number (parameter value Critical Reynolds number):

Intermediate values between neighboring points are determined by linear interpolation, and the nearest neighbor method is used outside the boundaries of the table.

Pressure drop

The pressure drop in the constriction/expansion is determined as follows:

where the last term is the pressure loss, determined by the expression:

Ports

Conserving

# A — Input port
Isothermal liquid

Details

The isothermal liquid port corresponds to the liquid inlet.

Program usage name

port_a

# B — Output port
Isothermal liquid

Details

The isothermal liquid port corresponds to the liquid outlet.

Program usage name

port_b

Parameters

# Local loss parameterization — hydraulic loss model
Semi-empirical correlation - sudden area change | Semi-empirical correlation - gradual area change | Tabulated data - loss coefficient vs. Reynolds number

Details

A model of hydraulic losses for narrowing/widening the channel. You can choose one of the methods for determining hydraulic pressure losses: one of two analytical semi-empirical methods (sudden or conical contraction/expansion), or substitute your own data by selecting Tabulated data - loss coefficient vs. Reynolds number.

Values	`Semi-empirical correlation - sudden area change` \| `Semi-empirical correlation - gradual area change` \| `Tabulated data - loss coefficient vs. Reynolds number`
Default value	`—`
Program usage name	`loss_type`
Evaluatable	No

# Cone angle — the angle of the cone forming the inner walls of the flow constriction/expansion channel
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The angle (solution) of the cone forming the inner walls of the narrowing channel and located at the base of the port A.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Semi-empirical correlation - gradual area change.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`30.0 deg`
Program usage name	`cone_angle`
Evaluatable	Yes

# Cross-sectional area at port A — port cross-sectional area A
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area at the entrance.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.02 m^2`
Program usage name	`port_a_area`
Evaluatable	Yes

# Cross-sectional area at port B — port cross-sectional area B
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area at the outlet.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`port_b_area`
Evaluatable	Yes

# Contraction correction factor — correction factor in the equation of pressure loss during constriction

Details

The coefficient used in the semi-empirical method for calculating the loss coefficient in case of narrowing of the flow.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Semi-empirical correlation - sudden area change or Semi-empirical correlation - gradual area change.

Default value	`1.0`
Program usage name	`k_contraction`
Evaluatable	Yes

# Expansion correction factor — correction factor in the equation of pressure loss during expansion

Details

The coefficient used in the semi-empirical method for calculating the loss coefficient in case of flow expansion.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Semi-empirical correlation - sudden area change or Semi-empirical correlation - gradual area change.

Default value	`1.0`
Program usage name	`k_expansion`
Evaluatable	Yes

# Reynolds number vector — a vector of values of Reynolds numbers for the tabular parameterization method

Details

A vector of values of Reynolds numbers for the tabular parametrization method of narrowing/widening the channel. The elements of the vector must match the elements of the vectors Expansion loss coefficient vector and Contraction loss coefficient vector. The values of the vector elements should be listed in ascending order.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Tabulated data - loss coefficient vs. Reynolds number.

Default value	`[10.0, 20.0, 30.0, 40.0, 50.0, 100.0, 200.0, 500.0, 1000.0, 2000.0]`
Program usage name	`Re_vector`
Evaluatable	Yes

# Contraction loss coefficient vector — vector of loss coefficients during narrowing

Details

Vector of loss coefficients in case of narrowing of the flow corresponding to the parameter Reynolds number vector. The items should be listed in descending order and should be larger 0.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Tabulated data - loss coefficient vs. Reynolds number.

Default value	`[5.0, 2.7, 1.8, 1.46, 1.3, 0.9, 0.65, 0.42, 0.3, 0.2]`
Program usage name	`C_contraction_loss_vector`
Evaluatable	Yes

# Expansion loss coefficient vector — vector of expansion loss coefficients

Details

Vector of loss coefficients in case of flow expansion corresponding to the parameter Reynolds number vector. The items should be listed in descending order and should be larger 0.

Dependencies

To use this parameter, set for the parameter Local loss parameterization meaning Tabulated data - loss coefficient vs. Reynolds number.

Default value	`[3.1, 2.3, 1.65, 1.35, 1.15, 0.9, 0.75, 0.65, 0.9, 0.65]`
Program usage name	`C_expansion_loss_vector`
Evaluatable	Yes

# Critical Reynolds number — the upper bound of the Reynolds numbers for laminar flow in a channel

Details

The upper bound for the Reynolds number, which characterizes the laminar flow regime of a liquid in a minimal section.

Default value	`150.0`
Program usage name	`Re_critical`
Evaluatable	Yes

Literature

Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe TP-410. Crane Co., 1981.
Idelchik I. E. Handbook of hydraulic resistance / Edited by M. O. Steinberg. — 3rd ed., reprint. and add. — M.: Mechanical Engineering, 1997. — 672 p.: ill. — ISBN 5-217-00393-6.