Elbow (TL)

Pipe turn in a thermal liquid network

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• Simscape / Fluids / Isothermal Liquid / Pipes & Fittings

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Description

The Elbow (TL) block represents flow in a pipe turn in a thermal liquid network. Pressure losses due to pipe turns are calculated, but the block omits the effects of viscous friction.

Two Elbow type settings are available: Smoothly-curved and Sharp-edged (Miter). For a smooth pipe with a 90° bend and losses due to friction, you can also use the Pipe Bend (TL) block.

Loss Coefficients

For smoothly-curved pipe segments, the loss coefficient is calculated as:

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

C_angle, the angle correction factor, is calculated from Keller [2] as:

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

where θ is the Bend angle in degrees. The friction factor, f_T, is defined for clean commercial steel. The values are interpolated from tabular data based on the internal elbow diameter for f_T provided by Crane [1]:

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

For sharp-edged pipe segments, the loss coefficient K is calculated for the bend angle, α, according to Crane [1]:

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 calculated as:

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

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_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, the flow regime transition point between laminar and turbulent flow:

$$\Delta p_{crit}=\frac{\overline{\rho }}{2}K{\left(\frac{\nu {\mathrm{Re}}_{crit}}{D}\right)}^2,$$

where

• ν is the fluid kinematic viscosity.

• D is the elbow internal diameter.

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 — Pipe bend entrance or exit

thermal liquid

Thermal liquid conserving port associated with the liquid entrance or exit of the pipe bend.

B — Pipe bend entrance or exit

thermal liquid

Thermal liquid conserving port associated with the liquid entrance or exit of the pipe bend.

Parameters

Elbow type — Bend geometry

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

Bend specification of the pipe segment. A sharp-edged, or mitre, bend introduces a sharp change in flow direction, such as at a pipe joint, and the flow losses are modeled by 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.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the pipe segment.

References

[1] Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe TP-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 R2022a