Pipe Bend (IL)
Tube bending in isothermal liquid systems.
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Description
In the Pipe Bend (IL) block the hydrodynamics of a curved pipe in an isothermal liquid network is modelled. The characteristics of the pipe can be defined so that hydraulic losses due to friction and pipe curvature can be calculated and the flow of a compressible fluid can be modelled.
Pipe curvature loss factor
The local resistance coefficient (pressure loss) of a curved channel section includes a correction factor for the channel angle of rotation and the channel bending coefficient :
,
In the block, the coefficient is calculated as follows:
,
where is the channel rotation angle in degrees, the value of the Bend angle parameter.
Coefficient is calculated on the basis of experimental data - table of dependence of the sought coefficient on the ratio of bending radius to pipe diameter for channel rotation angles of 90° according to Crane [1]:
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| 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 |
The coefficient of friction is interpolated from tabulated data taken for technical steels as a function of pipe diameter [1]. The table below summarises the data for the friction coefficient of fluid flow with developed turbulence in pipes made of technical 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 duct angle correction factor is valid for bent pipe (ducts) where the ratio of bend radius to pipe diameter is in the range of 1 to 24. Outside this range, extrapolation by the nearest neighbour method is used.
Friction losses in laminar flow regime
The pressure loss expressions are the same for A and B port flows.
In the case of laminar flow regime in the pipe bend, or the Reynolds number is below the critical Reynolds number , the pressure losses at the pipe bend are determined as follows:
,
where:
-
- dynamic viscosity of the fluid.
-
- friction coefficient constant (Darcy coefficient), which is equal to 64 for laminar flow regime.
-
- density of the liquid inside the pipe.
-
- pipe diameter.
-
- length of the bent section of the pipe (pipe bend), defined as the product of the bend radius and the angle of rotation of the channel (bend): .
-
- cross-sectional area of the pipe, .
-
- is the mass flow rate at the corresponding port.
Friction losses in turbulent flow regime
For a flow with developed turbulence, or if the Reynolds number exceeds the critical Reynolds number , the pressure losses in the pipe bend are determined as follows:
,
where is the Darcy friction coefficient. It is approximated by the empirical Haaland equation and determined by the absolute roughness of the internal surface (value of the parameter Internal surface absolute roughness). The pressure drop is taken at half of the pipe section, between port A and the internal node, and between the internal node and port B.
Pressure drop for incompressible fluids
In the case of incompressible fluid, the pressure drop at the bend of the pipe is determined as follows:
.
Pressure drop for compressible fluids
In the case of compressible liquids, the pressure inside the bent pipe is also taken into account when calculating the pressure drop at the bend of the pipe :
Preservation of mass
In the case of incompressible fluid, the mass flow rate through the unit is conserved:
In the case of a compressible fluid, the difference in flow rates at the inlet and outlet of the block is determined by the change in fluid density inside the bent section of the pipe (pipe bend):
where is the volume of the bent pipe section (pipe bend), which is defined as the product of the cross-sectional area of the pipe and the length of the bend, .
Ports
A - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the fluid inlet or outlet in the pipe bend. This block has no internal directionality.
B - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the inlet or outlet of fluid in the pipe bend. This block has no internal directionality.
Parameters
Pipe diameter - pipe diameter
0.01 m (by default) | positive scalar
Pipe diameter.
Bend radius - bend radius
0.04 m (by default) | `positive scalar `
The radius of the circle formed by the pipe bend.
Bend angle - bend angle
90° (by default) | positive scalar.
Angle of channel rotation or pipe bend.
Internal surface absolute roughness - roughness of bent pipe walls
15e-6 m (By default).
The parameter is used to determine the Darcy coefficient, through which the local resistance in turbulent flow regime is determined.
Fluid dynamic compressibility - consideration of dynamic compressibility of fluid
Off (by default) | On
Parameter defines whether dynamic compressibility of liquid will be taken into account. In case of dynamic compressibility of the fluid, the mass flow rate through the block in short time intervals can be variable and is determined by the change in density of the fluid. The volume of the curved section of pipe is constant. In the library of isothermal liquid components in all blocks, the density of the fluid is considered as a function of pressure.
Initial liquid pressure - pressure of liquid at the initial moment of time
`0.101325 MPa (by default)
Liquid pressure in the pipe at the initial moment of time.
Dependencies
To use this parameter, select the Fluid dynamic compressibility checkbox.