# Elbow (TL)

Pipe turn in a thermal liquid network

Since R2022a

Libraries:
Simscape / Fluids / Isothermal Liquid / Pipes & Fittings

## 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

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

`$K=30{f}_{T}{C}_{angle}.$`

The block calculates Cangle, 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, 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 from 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 parameter is ```Sharp-edged (Miter)```, the block calculates the loss coefficient K for the bend angle, α, according to Crane [1].

α15°30°45°60°75°90°
K2 fT4 fT8 fT15 fT25 fT40 fT60 fT

### Mass Flow Rate

Mass is conserved through the pipe segment:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0.$`

The mass flow rate through the elbow is calculated as:

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

where:

• A is the flow area.

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

• Δp is the pipe segment pressure difference, pApB.

The critical pressure difference, Δpcrit, is the pressure differential associated with the Critical Reynolds number, Recrit, 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:

• ϕA is the energy flow rate at port A.

• ϕB is the energy flow rate at port B.

## Ports

### Conserving

expand all

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

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

## Parameters

expand all

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.

Internal diameter of the pipe elbow segment.

Angle of the swept pipe curve.

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.

## Version History

Introduced in R2022a