Pipe Bend (IL)
Bending of a pipe in an isothermal fluid network.
blockType: EngeeFluids.IsothermalLiquid.Pipes.Bend
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Description
In the block Pipe Bend (IL) The hydrodynamics of a curved pipe in an isothermal fluid network is modeled. The characteristics of the pipe can be determined in such a way as to calculate hydraulic losses due to friction and pipe curvature, as well as to simulate the flow of a compressible fluid.
Pipe curvature loss coefficient
The coefficient of local resistance (pressure loss) of the curved section of the channel includes a correction factor for the angle of rotation of the channel and the channel bending coefficient :
,
In the coefficient block calculated as follows:
,
where — the angle of rotation of the channel in degrees, the value of the Bend angle parameter.
Ratio It is calculated on the basis of experimental data – a table of the dependence of the desired coefficient on the ratio of the bending radius. to the pipe diameter for channel rotation angles of 90° according to Crane data [1]:
| 1 | 1,5 | 2 | 3 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 20 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
20 |
14 |
12 |
12 |
14 |
17 |
24 |
30 |
34 |
38 |
42 |
50 |
58 |
Coefficient of friction It is interpolated based on tabular data taken for technical steels, depending on the pipe diameter [1]. The table below shows the data for the coefficient of friction of a fluid flow with developed turbulence in pipes made of industrial steels.
| Nominal size (mm) | 5 | 10 | 15 | 20 | 25 | 32 | 40 | 50 | 72,5 | 100 | 125 | 150 | 225 | 350 | 609,5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Coefficient of friction |
.035 |
.029 |
.027 |
.025 |
.023 |
.022 |
.021 |
.019 |
.018 |
.017 |
.016 |
.015 |
.014 |
.013 |
.012 |
The correction factor of the channel rotation angle is valid for curved pipes (channels) in which the ratio of the bending radius to the pipe diameter is in the range from 1 to 24. Outside of this range, nearest neighbor extrapolation is used.
Friction losses in the laminar flow regime
The pressure loss expressions are the same for the flows in ports A and B.
In the case of a laminar flow regime in the bend of the pipe, or the Reynolds number is below the critical , the pressure loss at the bend of the pipe is determined as follows:
,
where:
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— dynamic viscosity of the liquid.
-
— the constant of the coefficient of friction (Darcy coefficient), which is 64 for the laminar flow regime.
-
— the density of the liquid inside the pipe.
-
— pipe diameter.
-
— the length of the curved section of the pipe (pipe bend), is defined as the product of the bending radius and the angle of rotation of the channel (bend): .
-
— the cross-sectional area of the pipe, .
-
— mass flow rate at the appropriate port.
Friction losses in the turbulent flow regime
For flows with developed turbulence, or if the Reynolds number exceeds the critical value , the pressure loss in the pipe bend is determined as follows:
,
where — Darcy’s coefficient of friction. It is approximated by the empirical Haaland equation and is determined by the absolute roughness of the inner surface (the value of the parameter Internal surface absolute roughness). The pressure drop is taken at half of the pipe section, between port A and the inner node, as well as between the inner node and port B.
Pressure drop for incompressible liquids
In the case of an incompressible fluid, the pressure loss at the bend of the pipe is determined as follows:
.
Pressure drop for compressible liquids
In the case of a compressible fluid, the pressure inside the curved pipe is also taken into account when calculating the pressure loss at the bend. :
Conservation of mass
In the case of an incompressible fluid, the mass flow rate through the block is maintained.:
In the case of a compressible liquid, the difference in flow rates at the inlet and outlet of the block is determined by the change in the density of the liquid inside the curved section of the pipe (pipe bend):
where — the volume of the curved section of the pipe (pipe bend), which is defined as the product of the cross-sectional area of the pipe and the length of the bend, .
Ports
A — input or output port
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the fluid into the bend of the pipe. This block has no internal orientation.
B — input or output port
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the fluid into the bend of the pipe. This block has no internal orientation.
Parameters
Pipe diameter — pipe diameter
0.01 m (default) | positive scalar
Pipe diameter.
Bend radius — bend radius of the
0.04 m (default) | positive scalar
The radius of the circle formed by the bend of the pipe.
Bend angle — bend angle of the
90° (default) | positive scalar
The angle of rotation of the channel or the bend of the pipe.
Internal surface absolute roughness — roughness of the walls of the curved pipe
15e−6M (default)
The parameter is used to determine the Darcy coefficient, which is used to determine the local resistance in a turbulent flow regime.
Fluid dynamic compressibility — accounting for the dynamic compressibility of a liquid
disabled (by default) | enabled
The parameter determines whether the dynamic compressibility of the liquid will be taken into account. In the case of dynamic compressibility of a liquid, the mass flow rate through the block in short periods of time can be variable, and is determined by a change in the density of the liquid. The volume of the curved pipe section is constant. In the library of isothermal fluid components in all blocks, the density of the fluid is considered as a function of pressure.
Initial liquid pressure — the pressure of the liquid at the initial moment of time
0.101325 MPa (default)
The pressure of the liquid in the pipe at the initial time.
Dependencies
To use this option, check the box for the Fluid dynamic compressibility option.