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Flow Divider

Hydraulic two-path flow divider

Library

Flow Control Valves

Description

The Flow Divider block simulates a hydraulic two-path flow divider, which consists of a spring-centered spool installed in a case, as shown in the figure.

The flow from the source enters the valve through port P and is split into two parts flowing through the P–A and P–B paths. Each path contains a fixed orifice and a variable orifice. The fixed orifices must be precisely matched to divide flow in equal parts, or arranged in a certain proportion if unequal division is required.

The purpose of variable orifices is to maintain a constant pressure drop across the fixed orifices, regardless of pressure fluctuations at valve outlets. The load increase on any outlet causes the pressure drop across the spool (and across fixed orifices) to change, and thus shift the spool. As a result, the passage areas of variable orifices change until the pressure drop values across the fixed orifices even out.

The model of the flow divider uses the Double-Acting Servo Cylinder, Fixed Orifice, and Orifice with Variable Area Round Holes blocks. The following figure shows the schematic diagram of the model. The Double-Acting Servo Cylinder detects the pressure drop and shifts the variable orifice control member accordingly.

    Note:   You cannot use this block as a flow combiner.

Assumptions and Limitations

  • Friction between moving parts is not taken into account.

  • Inertia effects are not taken into account.

  • Fluid compressibility is not taken into account.

  • Leakage flows are assumed to be negligible.

  • The hard stops in the Double-Acting Servo Cylinder are assumed to be fully inelastic.

  • The transition between laminar and turbulent regimes is assumed to be sharp and taking place exactly at Re=Recr.

Dialog Box and Parameters

The block dialog box has three tabs:

Fixed Orifices

Fixed orifice A area

The cross-sectional passage area of the fixed orifice in the P–A path. The default value is 1e-4 m^2.

Fixed orifice B area

The cross-sectional passage area of the fixed orifice in the P–B path. The default value is 1e-4 m^2.

Fixed orifice A flow discharge coefficient

Semi-empirical parameter defining the capacity of the fixed orifice in the P–A path. The 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.

Fixed orifice B flow discharge coefficient

Semi-empirical parameter defining the capacity of the fixed orifice in the P–B path. The 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.

Fixed orifice A critical Reynolds number

The maximum Reynolds number for laminar flow for the fixed orifice in the P–A path. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.

Fixed orifice B critical Reynolds number

The maximum Reynolds number for laminar flow for the fixed orifice in the P–B path. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.

Variable Orifices

Diameter of round holes

Diameter of the round holes in the two identical Variable Orifice with Round Holes blocks. The default value is 0.005 m.

Number of round holes

Number of holes in each of the Variable Orifice with Round Holes blocks. The default value is 4.

Variable orifices flow discharge coefficient

Semi-empirical parameter defining the orifice capacity of the Variable Orifice with Round Holes blocks. The value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.65.

Variable orifice A initial opening

Initial opening of the variable orifice in the P–A path. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or 0 for zero-lap configuration. The value of initial opening does not depend on the orifice orientation. The default value is 0.0025.

Variable orifice B initial opening

Initial opening of the variable orifice in the P–B path. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or 0 for zero-lap configuration. The value of initial opening does not depend on the orifice orientation. The default value is 0.0025.

Variable orifice A critical Reynolds number

The maximum Reynolds number for laminar flow through the variable orifice in the P–A path. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.

Variable orifice B critical Reynolds number

The maximum Reynolds number for laminar flow through the variable orifice in the P–B path. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.

Variable orifice leakage area

The total area of possible leaks in each variable orifice when it is completely closed. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from becoming isolated after the orifice is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is 1e-9 m^2.

Servo Cylinder

Servo cylinder piston area

The face area of the piston in the servo cylinder. The default value is 1.6e-4 m^2.

Servo cylinder piston stroke

The full piston stroke in the servo cylinder, from one hard stop to another. The piston is located initially in the middle of the stroke and can travel half a stroke in the positive and negative direction. The default value is 0.005 m.

Servo cylinder spring rate

The spring rate of the centering springs in the servo cylinder. The default value is 1000 N/m.

Servo cylinder damping coefficient

The damping coefficient in the contact between the piston and the case of the servo cylinder. The default value is 150 N/(m/s).

Servo cylinder stop penetration coefficient

The penetration property of the piston hard stop in the servo cylinder. The hard stop is represented as absolutely inelastic, and its property is characterized by the penetration coefficient. The default value of the coefficient is 1e12 N/m/(m/s).

Global Parameters

Parameters determined by the type of working fluid:

  • Fluid density

  • Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

P

Hydraulic conserving port associated with the inlet port P.

A

Hydraulic conserving port associated with the outlet port A.

B

Hydraulic conserving port associated with the outlet port B.

Examples

The Hydraulic System with Flow Divider example shows the use of a Flow Divider block to split the flow equally between two consumers represented by Orifice with Variable Area Slot blocks.

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