Spool with Orifice Hole (IL)

A spool valve with holes.

blockType: EngeeFluids.IsothermalLiquid.DesignComponents.Spools.OrificeHole

Spool with Orifice Hole (IL)

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Valves & Orifices/Spools & Poppets/Fixed Body/Spool with Orifice Hole (IL)

Spool with Orifice Hole with Moving Body (IL)

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Valves & Orifices/Spools & Poppets/Moving Body/Spool with Orifice Hole with Moving Body (IL)

Description

Block Spool with Orifice Hole (IL) It is a one-dimensional movement of a spool in a sleeve with one or more holes. Depending on the parameter value Edges geometry The edges of the spool may be sharp or rounded. The equations for calculating the bore area and hydraulic diameter differ for different block parameters.

Circular;
Triangular;
Rectangular;
Trapezoidal;
Trapezoidal with rounded edges.

spool with hole section il 1

The resulting force acting on the spool is due to the pressure force and external forces. It is assumed that the pressure in port B acts on the active region adjacent to the hole and tends to open the hole. The pressure in port A does not act directly on the spool. These assumptions give the pressure force acting on the spool. This force can be adjusted using hydrodynamic force. For a spool with sharp edges, it is assumed that the angle of inclination of the jet is constant. If a spool with rounded edges is modeled, the angle of inclination of the jet is determined by interpolating experimental results.

The movement and speed of the rod are transmitted to the RA port. There are no restrictions on the displacement value in the block, but restrictions can be provided by an attached block using end stops (Translational Hard Stop).

If the check box is selected Moving body, then the block is implemented Spool with Orifice Hole with Moving Body (IL) and the body movement is simulated. In this case, the displacement and velocity of the case are transmitted to the CA port. There are no restrictions on the displacement value in the block, but restrictions can be provided by an attached block using end stops.

The area of the open hole is a variable related to the movement of the spool and the movement of the housing, if it is modeled.

Sometimes it is useful to limit the hole area to a minimum and/or maximum value. The minimum area can be used to simulate a leak or a special hole allowing flow through, even when the spool is in the overlap position. The maximum area can be used to simulate the flow area adjacent to the opening when the valve is wide open.

The minimum and maximum hole areas are determined by the corresponding overlap values (Underlap corresponding to maximum area, Underlap corresponding to minimum area). Default values imply that there are no restrictions on the area. The lower limit value must be greater than zero. Regardless of the upper limit , the area of the flow should not exceed the area of the holes.

The flow rate is calculated based on the movement of the spool.

The equations

If the check box Moving body removed, and the body movement is not simulated, then the overlap value is defined as:

where

— overlap corresponding to the zero offset, the value of the parameter Underlap corresponding to zero displacement;
— moving the spool in port RA.

If the check box is Moving body is installed, and the body movement is simulated, then the overlap value is defined as:

where — moving the case in port CA.

The length of the camera is defined as:

where — the length of the camera at zero offset, the value of the parameter Chamber length at zero displacement.

The volume of the camera is:

where

— diameter of the spool;
— diameter of the stem.

Flow coefficient calculated as:

where

— pressure difference between ports;
— hydraulic diameter;
— kinematic viscosity;
— the average density of the liquid.

Expense ratio calculated as:

where

— maximum flow rate, parameter value Maximum flow coefficient;
— critical flow coefficient, parameter value Critical flow number.

For meaning practically does not change. For low meaning it changes linearly with the change .

A reasonable value the default value is `1000'. However, for holes with complex (rough) geometry, it may be less than `50'. For very smooth geometry, it can be set to `50,000'.

The average fluid velocity is:

The volume flow in port A is:

where

— the area of the hole;
— the density of a liquid at atmospheric pressure.

The volumetric flow rate in port B, taking into account the contribution to the flow due to the movement of the spool, is calculated as:

where — the speed of the spool movement.

The hydrodynamic force acting on the spool is determined by estimating the change in momentum. This force tends to close the valve. For a steady-state fluid flow, the hydrodynamic force is:

where — the angle of inclination of the jet, which is considered constant for a spool with sharp edges and is set in the parameter Jet angle, and for a spool with rounded edges is determined from experimental data.

The force in the port RA is calculated taking into account the force in the port RB, the pressure force and the hydrodynamic force as:

where — the value of the hydrodynamic force depending on the overlap .

If the check box is selected Moving body, and the hull movement is modeled, then the force at port CA is calculated based on the force at port CB:

Cylindrical spool with sharp edges and a round hole in the sleeve_

If for the parameter Edges geometry value selected Sharp, and for the parameter Effective flow area model value selected Cylindrical, then the equations given in this section are used to calculate the effective area and hydraulic diameter.

When the hole is fully open, the passage channel is the intersection of two cylinders with perpendicular axes, as shown in the figure.

spool with orifice hole il 1 1

For each overlap value An iterative method is used to calculate the corresponding area by numerical integration.

The area is calculated as:

where

— overlap value;
— the length of the elementary area is wide (highlighted in red in the picture above).

Hole area calculated as:

By swapping variables, we end up with:

where

— the radius of the spool;
— the radius of the hole.

The perimeter is calculated using the iterative method in the same way.:

where

— projection onto the plane perpendicular to the axis of the hole of the angle between the plane in which the axes of the spool and the hole lie, and the radius vector drawn from the center of the hole to the point of intersection of the edge of the spool with the line of the hole;
— the length of the elementary section of the perimeter of the angular width ;
— the length of the red line (see the picture above) when .

The hydraulic diameter is:

The number of steps for the iterative method used to calculate the area and hydraulic diameter is set as an integer in the parameter Number of iterations.

Overlap value limited between and .

The flow area is also limited by the cross-sectional area of the opening:

where — the diameter of the hole.

Dependence of the hydrodynamic force from overlap It is defined as follows:

In this case, there is no reactive force in the overlap.

Cylindrical spool with rounded edges and a round hole in the sleeve_

If for the parameter Edges geometry the value is set Rounded It is assumed that the edges of the spool are rounded and there is a diameter gap between the spool and the sleeve, which is a more realistic geometric model.

spool with orifice hole il 1 2

The rounding is determined by the following values:

radius of rounding , parameter value Rounded corner radius;
diametrical gap , parameter value Clearance on diameter It should be borne in mind that for diametrical gaps of more than 60 microns, leaks should be overestimated.

Positive overlap

When the overlap value is positive if the diameter of the hole is , and the displacement of the spool from the closed position is , then the area of the open hole is:

where

and the hydraulic diameter is:

Please note that the area obtained by this formula cannot exceed the area of the hole specified by the formula:

which corresponds to .

Overlap value it is limited from above by the smaller of the values and . Maximum overlap value It is usually very high (Inf), but a much lower value can be set to simulate an additional hole.

Negative overlap

Negative overlap flow — this is the leakage flow between the spool and its body, it can be expressed based on the approximation of the Poiseuille flow.

spool with orifice hole il 3 en

The layer affected by the Poiseuille current depends on and should be considered as a function of the shape of the hole.

spool with orifice hole il 4

The simplified Poiseuille equation can be written as:

where

— the absolute average viscosity of the liquid;
;
.

The Poiseuille equation is transformed into:

what gives

where

;
— correction term that ensures continuity of the flow:

where basic consumption:

The area and flow rate are then multiplied by the number of holes.

The cosine of the jet angle is found by interpolating the experimental results shown in the figure below. Linear spline interpolation is used for this purpose.

spool with annular orifice il 3

Dependence of the hydrodynamic force from overlap It is defined as follows:

Cylindrical spool with sharp edges and holes of different geometries in the sleeve_

If for the parameter Edges geometry value selected Sharp, and for the parameter Effective flow area model value selected Planar, then you can set the geometry of the holes in the parameter Geometry of section orifice. The values of the open hole area and the hydraulic diameter are calculated depending on the selected hole geometry.

If for the parameter Geometry of section orifice the value is set Circular, then the area of the open hole and the hydraulic diameter calculated using the formulas:

where

The hydraulic diameter is:

In these formulas — hole diameter, parameter value Hole diameter.

spool with orifice hole il 5

Please note that the area obtained by this formula cannot exceed the area of the hole specified by the formula:

which corresponds to .

If for the parameter Geometry of section orifice the value is set Triangular, then the area of the open hole and the hydraulic diameter calculated using the formulas:

The hydraulic diameter is:

In these formulas — the angle of the triangular hole, the value of the parameter Aperture angle of the triangular opening.

spool with orifice hole il 6

Please note that the area obtained by this formula cannot exceed the area of the hole specified by the formula:

which corresponds to .

If for the parameter Geometry of section orifice the value is set Rectangular, then the area of the open hole and the hydraulic diameter calculated using the formulas:

The hydraulic diameter is:

In these formulas — the width of the rectangular hole, the value of the parameter Width of the rectangular opening.

spool with orifice hole il 7

Please note that the area obtained by this formula cannot exceed the area of the hole specified by the formula:

which corresponds to .

If for the parameter Geometry of section orifice the value is set Trapezoidal, then the area of the open hole and the hydraulic diameter calculated using the formulas:

The hydraulic diameter is:

In these formulas — the width of the trapezoidal hole, the value of the parameter Initial width of the trapezoidal opening, and — the angle of the trapezoidal hole, the value of the parameter Angle of the trapezoidal opening.

spool with orifice hole il 8

Please note that the area obtained by this formula cannot exceed the area of the hole specified by the formula:

which corresponds to .

If for the parameter Geometry of section orifice the value is set Trapezoidal with rounded edges, then the area of the open hole and the hydraulic diameter calculated using the formulas:

where

The hydraulic diameter is:

In these formulas — the width of the trapezoidal hole, the value of the parameter Initial width of the trapezoidal opening, and — the diameter of the rounded sides of the trapezoidal hole, the value of the parameter Diameter of the round edges .

spool with orifice hole il 9

Please note that the area obtained by this formula cannot exceed the area of the hole corresponding to .

Ports

Conserving

# A — Isothermal liquid port
Isothermal liquid

Details

The port of the isothermal liquid corresponds to the inlet or outlet of the hole.

Program usage name

port_a

# B — Isothermal liquid port
Isothermal liquid

Details

The port of the isothermal liquid corresponds to the inlet or outlet of the hole.

Program usage name

port_b

# RA — stock
Translational mechanics

Details

Mechanical translational port corresponding to the rod.

Program usage name

rod_flange_a

# RB — stock
Translational mechanics

Details

Mechanical translational port corresponding to the rod.

Program usage name

rod_flange_b

# CA — housing
Translational mechanics

Details

Mechanical translational port corresponding to the body.

Dependencies

To use this port, check the box Moving body.

Program usage name

case_flange_a

# CB — housing
Translational mechanics

Details

Mechanical translational port corresponding to the body.

Dependencies

To use this port, check the box Moving body.

Program usage name

case_flange_b

Parameters

# Opening orientation — the direction of movement of the spool corresponding to the opening of the hole
Positive relative rod displacement opens orifice | Negative relative rod displacement opens orifice

Details

The direction of movement of the element corresponding to the opening of the hole:

Positive orientation Positive relative rod displacement opens orifice this means that the positive movement of the spool opens the hole.
The negative direction Negative relative rod displacement opens orifice this means that the negative movement of the spool opens the hole.

Values	`Positive relative rod displacement opens orifice` \| `Negative relative rod displacement opens orifice`
Default value	`Positive relative rod displacement opens orifice`
Program usage name	`opening_orientation`
Evaluatable	No

# Moving body — movable body

Details

Check this box if you are modeling a movable enclosure.

If the flag is unchecked, it is assumed that the body is stationary.

Default value	`—`
Program usage name	`moving_case`
Evaluatable	No

# Edges geometry — geometry of the spool edges
Sharp | Rounded

Details

Select the geometry type of the spool edges:

Sharp — sharp edges.
Rounded — rounded edges.

Values	`Sharp` \| `Rounded`
Default value	`Sharp`
Program usage name	`edges_geometry`
Evaluatable	No

# Effective flow area model — effective flow area model
Cylindrical | Planar

Details

A model of the effective flow area. Options to choose from:

Cylindrical;
Planar.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Sharp.

Values	`Cylindrical` \| `Planar`
Default value	`Cylindrical`
Program usage name	`opening_area_model`
Evaluatable	No

# Number of orifice holes — Number of holes

Details

The number of holes.

Default value	`1`
Program usage name	`hole_count`
Evaluatable	Yes

# Number of iterations — the number of iterations to calculate the hydraulic diameter and effective flow area

Details

The flow area and hydraulic diameter are calculated based on the value of the spool position and the number of iterations. This parameter determines the number of flow area and hydraulic diameter values depending on the position of the spool. The number of iterations is used to calculate the sampling step between two offset values.

Dependencies

To use this parameter, set for the parameter Effective flow area model meaning Cylindrical.

Default value	`1000`
Program usage name	`discretization_interval_count`
Evaluatable	Yes

# Geometry of section orifice — geometry of the hole section
Circular | Triangular | Rectangular | Trapezoidal | Trapezoidal with rounded edges

Details

Hole geometry, options to choose from:

Circular;
Triangular;
Rectangular;
Trapezoidal;
Trapezoidal with rounded edges.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Sharp, and for the parameter Effective flow area model meaning Planar.

Values	`Circular` \| `Triangular` \| `Rectangular` \| `Trapezoidal` \| `Trapezoidal with rounded edges`
Default value	`Circular`
Program usage name	`hole_geometry`
Evaluatable	No

# Spool diameter — diameter of the spool
m | cm | ft | in | km | mi | mm | um | yd

Details

The diameter of the spool must be larger than the diameter of the stem.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`15.0 mm`
Program usage name	`spool_diameter`
Evaluatable	Yes

# Rod diameter — stem diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

The diameter of the stem.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`5 mm`
Program usage name	`rod_diameter`
Evaluatable	Yes

# Hole diameter — Hole diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

The diameter of the hole.

Dependencies

To use this parameter:

set for the parameter Edges geometry meaning Sharp, and for the parameter Effective flow area model meaning Cylindrical;
set for the parameter Edges geometry meaning Rounded;
set for the parameter Edges geometry meaning Sharp, for the parameter Effective flow area model meaning Planar, and for the parameter Geometry of section orifice meaning Circular.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 mm`
Program usage name	`circular_hole_diameter`
Evaluatable	Yes

# Aperture angle of the triangular opening — The angle of the triangular hole
deg | rad | rev | mrad

Details

The inner corner of the triangular hole.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Sharp, for the parameter Effective flow area model meaning Planar, and for the parameter Geometry of section orifice meaning Triangular.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`30.0 deg`
Program usage name	`triangular_hole_angle`
Evaluatable	Yes

# Width of the rectangular opening — the width of the rectangular hole
m | cm | ft | in | km | mi | mm | um | yd

Details

The width of the rectangular hole.

Dependencies

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 mm`
Program usage name	`rectangular_hole_width`
Evaluatable	Yes

# Initial width of the trapezoidal opening — the width of the trapezoidal opening
m | cm | ft | in | km | mi | mm | um | yd

Details

The width of the trapezoidal opening.

Dependencies

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 mm`
Program usage name	`trapezoidal_hole_width`
Evaluatable	Yes

# Angle of the trapezoidal opening — the angle of the trapezoidal hole
deg | rad | rev | mrad

Details

The inner corner of the trapezoidal hole.

Dependencies

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`45.0 deg`
Program usage name	`trapezoidal_hole_angle`
Evaluatable	Yes

# Diameter of the round edges — the diameter of the rounded sides of the trapezoidal hole
m | cm | ft | in | km | mi | mm | um | yd

Details

The diameter of the rounded corners of the trapezoidal hole.

Dependencies

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 mm`
Program usage name	`trapezoidal_hole_side_diameter`
Evaluatable	Yes

# Chamber length at zero displacement — camera length at zero offset
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the camera at zero offset (within the calculated volume of the camera).

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`chamber_length_offset`
Evaluatable	Yes

Underlap Definition

# Underlap corresponding to zero displacement — overlap corresponding to the zero offset
m | cm | ft | in | km | mi | mm | um | yd

Details

The overlap corresponding to the zero offset.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`offset`
Evaluatable	Yes

# Underlap corresponding to minimum area — overlap corresponding to the minimum area
m | cm | ft | in | km | mi | mm | um | yd

Details

The overlap corresponding to the minimum opening area.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Sharp.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`orifice_opening_at_min_area`
Evaluatable	Yes

# Underlap corresponding to maximum area — overlap corresponding to the maximum area
m | cm | ft | in | km | mi | mm | um | yd

Details

The overlap corresponding to the maximum opening area.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`Inf mm`
Program usage name	`orifice_opening_at_max_area`
Evaluatable	Yes

Leakages on the Spool

# Rounded corner radius — radius of rounding a corner
m | cm | ft | in | km | mi | mm | um | yd

Details

The radius of the rounded corner of the spool edges.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Rounded.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.005 mm`
Program usage name	`edge_radius`
Evaluatable	Yes

# Clearance on diameter — diametrical gap
m | cm | ft | in | km | mi | mm | um | yd

Details

The diameter gap between the spool and the sleeve, due to the fact that the edges of the spool are rounded. It should be borne in mind that for diametrical gaps of more than 60 microns, leaks should be overestimated.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Rounded.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.003 mm`
Program usage name	`clearance`
Evaluatable	Yes

Jet Force Evaluation

# Jet angle — The angle of the jet
deg | rad | rev | mrad

Details

In this simple model, the angle of the jet is assumed to be constant. For most applications, this value can be left at default. The jet angle is set relative to the valve axis.

Dependencies

To use this parameter, set for the parameter Edges geometry meaning Sharp.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`69.0 deg`
Program usage name	`jet_angle`
Evaluatable	Yes

# Jet force coefficient — coefficient of hydrodynamic force

Details

The hydrodynamic force coefficient, which disables the hydrodynamic force when set to 0 (by default), and turns it on when set to 1. If there is experimental data for this coefficient, then you can adjust the model to fit this data.

Default value	`0.0`
Program usage name	`jet_force_coefficient`
Evaluatable	Yes

Flow Coefficient Law

# Maximum flow coefficient — maximum flow rate

Details

The maximum flow rate affects the flow rate/pressure drop characteristics in the orifice. For most applications, this value can be left at the default.

Default value	`0.7`
Program usage name	`C_q_max`
Evaluatable	Yes

# Critical flow number — critical flow coefficient

Details

The critical flow coefficient affects the flow rate/pressure drop characteristics in the orifice. For most applications, this value can be left at the default.

Default value	`100.0`
Program usage name	`critical_flow_number`
Evaluatable	Yes

Initial Conditions

# Initial rod displacement — initial displacement of the rod
m | cm | ft | in | km | mi | mm | um | yd

Details

The initial displacement of the rod.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`rod_displacement_start`
Evaluatable	Yes

# Initial case displacement — initial displacement of the body
m | cm | ft | in | km | mi | mm | um | yd

Details

The initial displacement of the body.

Dependencies

To use this option, check the box Moving body.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`case_displacement_start`
Evaluatable	Yes

Literature

McCloy D., Martin H. R., Control of fluid power: analysis and design, Chichester. – 1980.
Lebrun M., A model for a four-way spool valve applied to a pressure control system, J. Fluid Control. – 1987. – Vol. 17. – No. 4. – pp. 38-54.
Blackburn J. F., Reethof G., Shearer J. L., Fluid power control, (No Title). – 1960.