Main Content

Elbow (MA)

Pipe turn in an moist air network

Since R2023a

expand all in page
  • Elbow (MA) block

Libraries:
Simscape / Fluids / Moist Air / Pipes & Fittings

Description

The Elbow (MA) block models flow in a pipe turn in a moist air 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 90o bend that models losses due to friction, you can also use the Pipe Bend (MA) block.

Loss Coefficients

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

K=30fTCangle.

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

Cangle=0.0148θ−3.9716⋅10−5θ2,

where θ is the value of the Bend angle parameter in degrees. The block defines the friction factor, fT, as the value for clean commercial steel. The block then interpolates the values from tabular data based on the internal elbow diameter for fT 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/d11.523468101214162024
K20 fT14 fT12 fT12 fT14 fT17 fT24 fT30 fT34 fT38 fT42 fT50 fT58 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].

α0°15°30°45°60°75°90°
K2 fT4 fT8 fT15 fT25 fT40 fT60 fT

Diagram displaying Mitre bends and a table for K values and corresponding bend angles.

Mass Flow Rate

The block conserves mass through the pipe segment

m˙A+m˙B=0m˙wA+m˙wB=0m˙gA+m˙gB=0m˙dA+m˙dB=0

where the subscript w denotes water vapor, the subscript g denotes trace gas, and the subscript d denotes water droplets.

The mass flow rate through the elbow is

m˙=A2ρ¯KΔp[Δp2+Δpcrit2]1/4,

where:

  • A is the flow area.

  • ρ¯ is the average fluid density.

  • Δp is the pipe segment pressure difference, pA – pB.

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

Δpthreshold=pA+pb2(1−Blam),

where:

  • pA is the pressure at port A.

  • pB is the pressure at port B.

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

Energy Balance

The block balances energy such that

ΦA+ΦB=0,

where:

  • ϕA is the energy flow rate at port A.

  • ϕB is the energy flow rate at port B.

Ports

Conserving

expand all

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

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

Parameters

expand all

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.

Internal diameter of the pipe elbow segment.

Angle of the swept pipe curve.

Pressure ratio at which the moist air 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

expand all