Sharp-Edged Elbow (IL)
Turning a pipe (elbow) in isothermal liquid systems.
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Description
The Elbow (IL) block simulates the flow at a pipe bend in an isothermal liquid network. It calculates the pressure losses at the pipe bend, but does not take into account the effect of viscous friction.
Two types of elbow are available: `Smoothly-curved' and `Sharp-edged (Miter)' (sharp-angled or oblique).
Loss factors
If the Elbow type parameter is set to Smoothly curved, the block calculates the loss factor as:
.
The block calculates - the angle correction factor - according to Keller [2] as
,
where is the value of the Bend angle parameter in degrees. The block defines the coefficient of friction as the value for pure commercial steel. The block then interpolates the values from the tabulated data as a function of the inner diameter of the elbow for [1]. The table below summarises the pipe friction data for pure commodity steel when flowing in a zone of full turbulence.
| 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 values given are valid for diameters up to 600 mm. The coefficient of friction for larger diameters or for wall roughness outside this range is calculated by nearest neighbour extrapolation.
If the Elbow type parameter is set to Sharp-edged (Miter), the block calculates the loss factor for the bending angle as follows [1].
| 0° | 15° | 30° | 45° | 60° | 75° | 90° | |
|---|---|---|---|---|---|---|---|
|
2 |
4 |
8 |
15 |
25 |
40 |
60 |
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Preservation of mass
The mass conservation equation for a pipe segment has the form:
.
The mass flow rate through the elbow is calculated as:
,
where:
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- flow area.
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- average density of the liquid.
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- pressure drop on the pipe section, .
Critical pressure drop is the pressure drop associated with the critical Reynolds number (block parameter Critical Reynolds number), the point of transition of the flow regime between laminar and turbulent flow:
,
where:
-
- kinematic viscosity of the fluid.
-
- internal diameter of the elbow.
Ports
A - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the fluid inlet or outlet of the pipe segment. This block has no internal directionality.
B - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the fluid inlet or outlet of the pipe segment. This block has no internal directionality.
Parameters
Elbow type - curve geometry
Smoothly curved (By default) | Sharp-edged (Miter)
Bend geometry of the pipe section. A sharp or oblique bend introduces an abrupt change in flow direction, for example at a pipe junction, and flow losses are modelled by a separate set of empirical data obtained on pipe sections with gradual curvature.
Elbow internal diameter - pipe internal diameter
0.01 m (by default) | `positive scalar'.
Internal diameter of the pipe.
Elbow angle - pipe rotation angle
90° (by default) | positive scalar
Pipe rotation angle.
Critical Reynolds number - upper limit of Reynolds number for laminar flow
150 (By default) | Positive scalar
Reynolds number for the transition between laminar and turbulent regimes in a pipe segment.