Elbow (IL)

Pipe turn in an isothermal liquid network

Since R2020a

• 

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

Description

The Elbow (IL) block models flow in a pipe turn in an isothermal liquid network. Pressure losses due to pipe turns are calculated, but the effect of viscous friction is omitted.

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

Examples

Lubrication System

A simplified version of a lubrication system fed with the centrifugal pump. The system consists of five major units: Pump Unit, Scavenge Unit, Heat Exchanger Manifold, Nozzle Manifold, and Control Unit. Both the pump and the scavenge unit are built around the centrifugal pump. The Scavenge Unit collects fluid discharged by nozzles and pumps it back into the reservoir of the Pump Unit. The Control Unit generates commands to bypass either the heat exchanger, represented as a local resistance, or the nozzles block. In a real system, these commands are generated by temperature sensors installed in lubrication cavities.

Open Model

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit port to the pipe segment.

B — Liquid port

isothermal liquid

Liquid entry or exit port to the pipe segment.

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 R2020a