Elbow (G)

Pipe turn in a gas network

Since R2023a

• 

Libraries:
Simscape / Fluids / Gas / Pipes & Fittings

Description

The Elbow (G) block models flow in a pipe turn in a gas network. The block calculates pressure losses due to pipe turns, but omits the effect of viscous friction.

You can model a smoothly curved or sharp-edged pipe elbow by setting the Elbow type parameter to Smoothly curved or Sharp-edged (Miter), respectively. To model a smooth pipe with a 90^o bend that models losses due to friction, you can also use the Pipe Bend (G) block.

Loss Coefficients

When the Elbow type parameter is Smoothly curved, the block calculates the loss coefficient as:

$$K=30f_T{C}_{angle}.$$

The block calculates C_angle, the angle correction factor, from Keller [2] as

$$C_{angle}=0.0148\theta -3.9716\cdot {10}^{-5}{\theta }^2,$$

where θ is the value of the Bend angle parameter in degrees. The block defines the friction factor, f_T, as the value for clean commercial steel. The block then interpolates the values from tabular data based on the internal elbow diameter for f_T based on Crane [1]. This table contains the pipe friction data for clean commercial steel pipe with flow in the zone of complete turbulence.

r/d	1	1.5	2	3	4	6	8	10	12	14	16	20	24
K	20 fT	14 fT	12 fT	12 fT	14 fT	17 fT	24 fT	30 fT	34 fT	38 fT	42 fT	50 fT	58 fT

The values provided by Crane are valid for diameters up to 600 millimeters. The friction factor for larger diameters or for wall roughness beyond this range is calculated by nearest-neighbor extrapolation.

When the Elbow type parameter is Sharp-edged (Miter), the block calculates the loss coefficient K for the bend angle, α, according to Crane [1].

α	0°	15°	30°	45°	60°	75°	90°
K	2 fT	4 fT	8 fT	15 fT	25 fT	40 fT	60 fT

Mass Flow Rate

Mass is conserved through the pipe segment

$${\dot{m}}_A+{\dot{m}}_B=0.$$

The mass flow rate through the elbow is

$$\dot{m}=A\sqrt{\frac{2\overline{\rho }}{K}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where:

• A is the flow area.

• $$\overline{\rho }$$ is the average fluid density.

• Δp is the pipe segment pressure difference, p_A – p_B.

The critical pressure difference, Δp_threshold, is the threshold for transition between laminar and turbulent flow

$$\Delta p_{threshold}=\frac{p_A+p_b}{2}\left(1-B_{lam}\right),$$

where:

• p_A is the pressure at port A.

• p_B is the pressure at port B.

• B_lam is the value of the Laminar flow pressure ratio parameter.

Energy Balance

The block balances energy such that

$${\Phi }_A+{\Phi }_B=0,$$

where:

• ϕ_A is the energy flow rate at port A.

• ϕ_B is the energy flow rate at port B.

Ports

Conserving

A — Inlet or outlet

gas

Gas conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

B — Inlet or outlet

gas

Gas conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

Parameters

Elbow type — Bend geometry

Smoothly curved (default) | Sharp-edged (Miter)

Bend specification of the pipe segment. When you set this parameter to Sharp-edged (Miter), the block introduces a sharp change in flow direction, such as at a pipe joint, and models the flow losses using a separate set of empirical data from gradually turning pipe segments.

Elbow internal diameter — Pipe internal diameter

0.01 m (default) | positive scalar

Internal diameter of the pipe elbow segment.

Elbow angle — Pipe curve angle

90 deg (default) | positive scalar

Angle of the swept pipe curve.

Laminar flow pressure ratio — Pressure ratio at which flow transitions between laminar and turbulent regimes

0.999 (default) | positive scalar

Pressure ratio at which the gas flow transitions between the laminar and turbulent regimes.

References

[1] Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe: Technical Paper No. 410. Crane Co., 1981.

[2] Keller, G. R. Hydraulic System Analysis. Penton, 1985.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023a