Sharp-Edged Elbow (IL)
Pipe rotation (elbow) in isothermal liquid systems.
blockType: EngeeFluids.IsothermalLiquid.Fittings.Elbow
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Sharp-Edged Elbow (IL) Path in the library: |
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Smoothly Curved Elbow (IL) Path in the library: |
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Description
The Elbow (IL) block simulates the flow at the turn of a pipeline in an isothermal liquid network. In this case, pressure losses are calculated when the pipe is rotated, but the effect of viscous friction is not taken into account.
Two types of knee are available: Smoothly-curved (smoothly curved) and Sharp-edged (Miter) (acute-angled or oblique).
Loss coefficients
If the Elbow type parameter has the value Smoothly curved, then the block calculates the loss factor as:
.
The block calculates — angle correction factor — according to Keller [2] as
,
where — the value of the Bend angle parameter in degrees. The block determines the coefficient of friction as a value for pure commercial steel. The block then interpolates the values from the tabular data depending on the inner diameter of the elbow for [1]. The table below shows data on friction in a pipe for pure commercial steel during flow in a zone of complete 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 |
These values are valid for diameters up to 600 mm. The coefficient of friction for large diameters or for wall roughness outside this range is calculated by extrapolating the nearest neighbors.
If the Elbow type parameter has the value Sharp-edged (Miter), then 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 |
Conservation of mass
The mass conservation equation for a pipe segment has the form:
.
The mass flow through the knee is calculated as:
,
where:
-
— the area of the stream.
-
— the average density of the liquid.
-
— pressure drop in the pipe section, .
Critical pressure drop — this is the pressure drop associated with the critical Reynolds number (parameter of the Critical Reynolds number block), the point of transition of the flow mode between laminar and turbulent flow:
,
where:
-
— kinematic viscosity of the liquid.
-
— the inner diameter of the knee.
Ports
A — inlet or outlet
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the fluid into the pipe segment. This block has no internal orientation.
B — inlet or outlet
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the fluid into the pipe segment. This block has no internal orientation.
Parameters
Elbow type — geometry of the bend
Smoothly curved (by default) | Sharp-edged (Miter)
The geometry of the bend of the pipe section. An acute-angled or oblique bend makes a sharp change in the direction of flow, for example, at the junction of pipes, and flow losses are modeled by a separate set of empirical data obtained on sections of pipes with gradual rotation.
Elbow internal diameter — inner diameter of the pipe
0.01 m (default) | positive scalar
The inner diameter of the pipe.
Elbow angle — the angle of rotation of the pipe
90° (default) | positive scalar
The angle of rotation of the pipe.
Critical Reynolds number — upper limit of the Reynolds number for laminar flow
150 (default) | positive scalar
The Reynolds number for the transition between laminar and turbulent modes in a pipe segment.