Counterbalance Valve (IL)

High-pressure regulation valve in an isothermal liquid system

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Description

The Counterbalance Valve (IL) block models a normally closed pressure control valve in an isothermal liquid network. A counterbalance valve is commonly used when high-pressure events are expected or when controlled manipulation at high pressures is required, such as hydraulic overloading or lowering suspended loads. The valve functions under a force balance between a spring and the backing pressure at port B and the load pressure at port L. When the monitored pressure line, the pilot pressure at port P, exceeds the pressure at port B, the valve begins to open.

There is no flow between ports B and P or between ports L and P.

Valve Opening

The counterbalance valve operates under the force balance:

$$p_{pilot}{A}_{pilot}+p_{load}{A}_{load}=p_{back}{A}_{back}+F_{set},$$

where:

• p_pilot is the pressure at port P.

• p_load is the pressure at port L.

• p_back is the pressure at port B.

• F_set is the accumulated force due to the spring and preloading at port B.

The port areas A_pilot, A_load, and A_back are set by the Pilot ratio:

$$R_{pilot}=\frac{A_{pilot}}{A_{load}},$$

and the Back pressure ratio:

$$R_{back}=\frac{A_{back}}{A_{load}}.$$

A ratio of 4:1 or 3:1 is typical for counterbalance valves.

The preset force, F_set, represents the spring preloading and spring force at port B, which are characterized as a Set pressure differential, p_set:

$$F_{set}=p_{set}{A}_{load}.$$

Opening Parameterization

The linear parameterization of the valve area, for normally open valves, is:

$$A_{valve}=\widehat{p}\left(A_{leak}-A_{\max }\right)+A_{\max },$$

and for normally closed valves is:

$$A_{valve}=\widehat{p}\left(A_{\max }-A_{leak}\right)+A_{leak}.$$

The control compensator normalized pressure, $$\widehat{p}$$, is:

$$\widehat{p}=\frac{\left(p_{load}+p_{pilot}{R}_{pilot}-p_{back}{R}_{back}\right)-p_{set}}{\left(p_{\max }-p_{set}\right)},$$

where:

• p_set is the Set pressure differential.

• p_max is the Maximum opening pressure differential.

The normalized check valve pressure is:

$$\widehat{p}=\frac{p_{control}-p_{cracking}}{p_{\max }-p_{cracking}}.$$

where:

• p_cracking is the Cracking pressure differential.

• p_max is the check valve Maximum opening pressure differential.

At the extremes of the control and check valve pressure ranges, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. With a nonzero smoothing factor, a smoothing function is applied to every calculated pressure, but primarily influences the simulation at the extremes of these ranges.

When the Smoothing factor, s, is nonzero, a smoothed, normalized pressure is instead applied to the valve area:

$${\widehat{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{p}}_{}^2+{\left(\frac{s}{4}\right)}^2}-\frac{1}{2}\sqrt{{\left(\widehat{p}-1\right)}^2+{\left(\frac{s}{4}\right)}^2},$$

In the Tabulated data parameterization, the smoothed, normalized pressure is also used when the smoothing factor is nonzero with linear interpolation and nearest extrapolation.

Ports

Conserving

L — Liquid port

isothermal liquid

Load port and liquid exit port from the valve.

B — Liquid port

isothermal liquid

Back pressure port and liquid entry port to the valve.

P — Pressure port

isothermal liquid

Control, or pilot, pressure port. When the combined pressure at P and B exceeds the backing and spring pressures, the check valve between ports B and L opens.

Parameters

Model Parameterization

Opening parameterization — Opening parameterization

Linear (default) | Tabulated data

Method of modeling the opening of the valve. The opening is either parametrized linearly, which correlates the opening area to the control member opening stroke, by user-supplied data that correlate the valve opening area to the pressure differential over the valve.

Set pressure differential — Initial spring compression pressure

5 MPa (default) | positive scalar

Pressure contribution of the compressed spring before valve operation.

Maximum opening pressure differential — Maximum compensator valve pressure

6 MPa (default) | positive scalar

The maximum compensator valve pressure.

Maximum opening area — Load orifice maximum open area

8e-5 m^2 (default) | positive scalar

Maximum open area of the orifice in the load line. Internally, this orifice is connected in parallel with the load line check valve. The orifice and check valve can have different cross-sectional areas.

Dependencies

To enable this parameter, set Valve parameterization to Linear.

Leakage area — Gap area when valve is in fully closed position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Opening area vector — Vector of opening areas

[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] m^2 (default) | 1-by-n vector

Vector of valve opening areas for the tabular parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Valve parameterization to Tabulated data - Area vs. control member travel.

Pressure differential vector — Vector of pressure drop values

5 : 0.2 : 6 MPa (default) | 1-by-n vector

Vector of pressure differential values for the tabular parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Opening area parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Valve parameterization to Tabulated data.

Pilot ratio — Pilot area ratio

3 (default) | positive scalar

Ratio of the pilot port area to the load port area.

Back pressure ratio — Back pressure area ratio

4 (default) | positive scalar

Ratio of the back pressure port area to the load port area.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Opening dynamics — Whether to introduce flow lag due to orifice opening

Off (default) | On

Whether to account for transient effects to the fluid system due to opening the valve. Setting Opening dynamics to On approximates the opening conditions by introducing a first-order lag in the pressure response. The Opening time constant also impacts the modeled opening dynamics.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Opening time constant — Orifice opening time constant

0.1 s (default) | positive scalar

Constant that captures the time required for the fluid to reach steady-state conditions when opening or closing the valve from one position to another. This parameter impacts the modeled opening dynamics.

Dependencies

To enable this parameter, set Opening dynamics to On.

Check Valve

Cracking pressure differential — Set pressure for check valve operation

0.01 MPa (default) | positive scalar

Pressure differential value that triggers the valve to open.

Maximum opening pressure differential — Maximum pressure in valve

0.1 MPa (default) | positive scalar

Maximum valve pressure. This value bounds the pressures at the valve exit to maintain physical values during simulation.

Maximum opening area — Maximum open area

1e-4 m^2 (default) | positive scalar

Maximum open area of the check valve in the load line. Internally, this check valve is connected in parallel with a load line orifice. The orifice and check valve can have different areas.

Model Examples

Hydraulic Actuator with Dual Counterbalance Valves

An actuator controlled by a 4-way directional valve and loaded with an overriding load, requiring the use of counterbalance valves to prevent the load from creeping when the directional valve is in the neutral position. In the neutral position, the directional valve connects ports A and B to the reservoir while blocking the pressure port P. The counterbalance valves block flow from returning to the reservoir, thus holding the actuator in place.

Open Model

Version History

Introduced in R2020a