Simscape™

Variable Area Orifice

Simulate hydraulic variable orifice created by cylindrical spool and sleeve

Library

Hydraulic Elements

Description

The Variable Area Orifice block models a variable orifice created by a cylindrical sharp-edged spool and a variable-area slot in a sleeve. The area of the orifice is expected to be computed outside the block and imported via the AR physical signal connection. The minimum orifice area value is 1e-12 m^2. If the input signal falls below this level (for example, turns negative), the area is saturated to this value. The flow rate through the orifice is proportional to the orifice area and the pressure differential across the orifice.

The flow rate is determined according to the following equations:

where

`q`	Flow rate
`p`	Pressure differential
`p_A,p_B`	Gauge pressures at the block terminals
`C_D`	Flow discharge coefficient
`A`	Orifice passage area, provided through the signal port
`D_H`	Orifice hydraulic diameter
ρ	Fluid density
ν	Fluid kinematic viscosity

The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B and the pressure differential is determined as .

Basic Assumptions and Limitations

The model is based on the following assumptions:

Fluid inertia is not taken into account.
The transition between laminar and turbulent regimes is assumed to be sharp and taking place exactly at Re=Re_cr.

Dialog Box and Parameters

Flow discharge coefficient: Semi-empirical parameter for orifice capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.7.
Critical Reynolds number: The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is supposed to take place when the Reynolds number reaches this value. The value of the parameter depends on orifice geometrical profile, and the recommendations on the parameter value can be found in hydraulic textbooks. The default value is 12, which corresponds to a round orifice in thin material with sharp edges.

Global Parameters

Fluid density: The parameter is determined by the type of working fluid selected for the system under design. Use the Custom Hydraulic Fluid block, or the Hydraulic Fluid block available with SimHydraulics^® block libraries, to specify the fluid properties.
Fluid kinematic viscosity: The parameter is determined by the type of working fluid selected for the system under design. Use the Custom Hydraulic Fluid block, or the Hydraulic Fluid block available with SimHydraulics block libraries, to specify the fluid properties.

Ports

The block has the following ports:

A: Hydraulic conserving port associated with the orifice inlet.
B: Hydraulic conserving port associated with the orifice outlet.
AR: Physical signal port that provides the value of the orifice area.