Counterbalance Valve (TL)

Counterbalance valve in a thermal liquid network

Since R2024b

Libraries:
Simscape / Fluids / Thermal Liquid / Valves & Orifices / Pressure Control Valves

Description

The Counterbalance Valve (TL) block represents a counterbalance pressure control valve in an thermal liquid network. A counterbalance valve is common in applications where high-pressure events are common or when a task requires high-pressure controlled manipulation at production speeds. These applications includes tasks such as overloading hydraulics or lowering suspended loads. The valve functions under the force balance between a spring, the back pressure at port B, and the load pressure at port L and responds to changes in the pilot line pressure. When the pilot pressure exceeds the back pressure, the valve begins to open.

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

This figure shows a cutaway of a typical counterbalance valve.

Valve Opening

The block balances the forces of the counterbalance valve, such that

$p_{p i l o t} A_{p i l o t} + p_{l o a d} A_{l o a d} = p_{b a c k} A_{b a c k} + F_{s e t} + k_{s p r i n g} x_{s p o o l},$

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.
k_spring is the spring constant.
x_spool is the linear position of the relief stage spool body. This position is relative to the unpressurized installed position.

The block sets the pressure-acting areas A_pilot, A_load, and A_back according to the Pilot ratio parameter, R_pilot, such that

$R_{p i l o t} = \frac{A_{p i l o t}}{A_{l o a d}},$

and the Back pressure ratio parameter, R_back, such that

$R_{b a c k} = \frac{A_{b a c k}}{A_{l o a d}} .$

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

The preset force, F_spring, represents the combined spring preloading and spring force at port B. This force is a function of p_set, the Set pressure differential parameter, such that

$F_{s e t} = p_{s e t} A_{l o a d} .$

This figure shows the schematic from the Counterbalance Valve with Test Harness example, where the pressure ports control the valve by acting on surfaces with differential area. The arrows show the direction of force due to pressure or spring force acting on the relief stage body. The gray sections represent a single, solid body that moves to the right when the relief stage opens. The check valve travels to the left when it opens.

Counterbalance valve schematic where the load pressure and pilot pressure act to the right, and the back pressure and spring act to the left.

Opening Parameterization

You can parameterize the block with linear or tabulated data. The check valve portion of the block operates identically to the Check Valve (IL) block.

Linear Parameterization

When you set Opening parameterization to Linear - Area vs. pressure, the block calculates the valve opening area, such that

$A_{v a l v e} = \hat{p} (A_{m a x} - A_{l e a k}) + A_{l e a k} .$

The block calculates the normalized control pressure, $\hat{p}$ , as

$\hat{p} = \frac{(p_{l o a d} + p_{p i l o t} R_{p i l o t} - p_{b a c k} R_{b a c k}) - p_{s e t}}{(p_{\max} - p_{s e t})},$

where p_max is the Maximum opening pressure differential parameter.

The normalized check valve pressure is

$\hat{p} = \frac{p_{c o n t r o l} - p_{c r a c k i n g}}{p_{m a x} - p_{c r a c k i n g}},$

where:

p_cracking is the Cracking pressure differential parameter.
p_max is the Maximum opening pressure differential parameter in the Check valve section.

When the valve is in a near-open or near-closed position in the linear parameterization, you can maintain numerical robustness in the simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smoothly saturates the control pressure between p_cracking and p_max. For more information, see Numerical Smoothing.

Tabulated Area Parameterization

When you set Opening parameterization to Tabulated data - Area vs. pressure, the block uses the same equations as for the linear parameterization, but with tabulated data. The tabulated data represents area with respect to a given control pressure, where P_control = p_load + p_PilotR_Pilot - p_BackR_Back. The first element of the Pressure differential vector parameter is the set pressure, which is the control pressure when the relief stage begins to open. The last element defines the control pressure when the valve is fully open.

Tabulated Flow Rate Parameterization

When you set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, the volumetric flow rate equations refer to these quantities:

${\bar{ρ}}_{v a l v e}$ is the simulated average density of the relief stage flow.
K is the flow coefficient through the relief stage.
Δp_valve is the pressure drop across the relief stage during flow.
Δp_crit is the critical pressure drop across the relief stage during flow.
p_control is the simulated control pressure.
p_{control,TLU,Ref} is an internally derived lookup table of changing control pressures.
p_set is the set pressure differential.
Re_crit is the Critical Reynolds number parameter.
C_d is the Discharge coefficient parameter.
ν is the kinematic viscosity.
K_TLU,Ref is an internally derived lookup table of changing flow coefficients as a function of valve area.
${\dot{V}}_{T L U, R e f}$ is the reference volumetric flow rate vector.
p_pilot,Ref, p_back,Ref, p_load,Ref are the pilot pressure, back pressure, and load pressure for the user-provided Reference volumetric flow rate vector parameter, respectively.

The block calculates the mass flow rate for the relief stage such that

${\dot{m}}_{v a l v e} = {\bar{ρ}}_{v a l v e} K \frac{Δ p_{v a l v e}}{{(Δ p_{v a l v e}^{2} + Δ p_{c r i t}^{2})}^{1 / 4}},$

where:

$\begin{matrix} Δ p_{v a l v e} = p_{l o a d} - p_{b a c k} \\ Δ p_{c r i t} = \frac{π \sqrt{2 {\bar{ρ}}_{v a l v e}}}{8 C_{d}} (R e_{c r i t} υ) \\ K = t a b l e l o o k u p (p_{c o n t r o l, T L U, R e f}, K_{T L U, R e f}, p_{c o n t r o l}, interpolation = linear, extrapolation = nearest) \end{matrix}$

Liquid flows from the load port to the back port. The block extrapolates K to the nearest point after it calculates K_TLU,Ref as

$K_{T L U, R e f} = \frac{{\dot{V}}_{T L U, R e f}}{\sqrt{Δ p_{v a l v e, T L U, r e f}}},$

where Δp_{valve,TLU,ref} = p_load,Ref - p_back,Ref. The block calculates the control pressure as

$p_{c o n t r o l} = R_{p i l o t} p_{p i l o t} + p_{l o a d} - R_{b a c k} p_{b a c k}$

and the reference control vector as

$p_{c o n t r o l, T L U, R e f} = R_{p i l o t} p_{p i l o t, R e f} + p_{l o a d, R e f} - R_{b a c k} p_{b a c k, R e f} + p_{o f f s e t},$

where:

$\begin{array}{l} p_{p i l o t, R e f} = 1 atm \\ p_{b a c k, R e f} = 1 atm \\ p_{l o a d, R e f} = p_{b a c k, R e f} + Δ p_{v a l v e, T L U, R e f} \end{array}$

The block internally derives Δp_flow,Ref, which is the pressure drop for fluid flow in the specified reference curve. The block calculates p_offset internally as

$p_{o f f s e t} = p_{s e t} - R_{p i l o t} p_{p i l o t, R e f} - p_{l o a d, R e f} (1) + R_{b a c k} p_{b a c k, R e f} .$

The table shows how the block controls the opening areas for the relief and check stages depending on the Opening area parameter setting.

Opening Parameterization Setting	Relief Stage	Check Stage
`Linear - Area vs. pressure`
`Tabulated - Area vs. pressure`
`Tabulated - Volumetric flow rate vs. pressure`

Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

To load a predefined parameterization:

In the block dialog box, next to Selected part, click the "<click to select>" hyperlink next to Selected part in the block dialogue box settings.
The Block Parameterization Manager window opens. Select a part from the menu and click Apply all. You can narrow the choices using the Manufacturer drop down menu.
You can close the Block Parameterization Manager menu. The block now has the parameterization that you specified.
You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the Compare selected part with block section.

Note

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

Assumptions and Limitations

The block operates in only an internal drain–external pilot, non-vented configuration.
When you set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, the block uses values of volumetric flow rate with respect to the pressure drop across the relief stage to generate reference curves. The block assumes that the pilot port and back port are open to atmospheric pressure.

Ports

Conserving

expand all

L — Fluid load
thermal liquid

Thermal liquid conserving port associated with the load.

B — Back pressure
thermal liquid

Thermal liquid conserving port associated with the back pressure of the valve.

P — Pressure port
thermal liquid

Thermal liquid conserving port associated with the pilot pressure port.

Parameters

expand all

Model Parameterization

Opening parameterization — Opening parameterization
`Linear - Area vs. pressure` (default) | `Tabulated data - Area vs. pressure` | `Tabulated data - Volumetric flow rate vs. pressure`

Method of modeling the opening of the valve. When you select Linear - Area vs. pressure or Tabulated data - Area vs. pressure, the block relates the opening area to the control pressure. When you select Tabulated data - Volumetric flow rate vs. pressure, the block takes a reference flow rate and pressure differential curve for the relief and check stages of the counterbalance valve, where the pressure at the back port and pilot port corresponds to 1 atm in the reference curve for the relief stage.

Set pressure differential — Initial spring compression pressure
`5` `MPa` (default) | nonnegative scalar

Pressure differential to lift the relief stage. Use this parameter to adjust the set pressure supplied by the data sheet.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Volumetric flow rate vs. pressure.

Pressure differential vector — Relief stage pressure drop values
`5 : 0.2 : 6` `MPa` (default) | 1-by-n vector

Vector of pressure differential values for the relief stage. The vector elements must correspond one-to-one with the elements in the Opening area vector parameter. You must enter the elements in ascending order. This vector defines the control pressures that govern valve opening and shutting. The first element in the vector defines the set pressure, which is the control pressure when the relief stage just begins to open. The last element defines the control pressure for which the valve is fully open.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Opening area vector — Relief stage opening areas
`[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001]` `m^2` (default) | 1-by-n vector

Vector of relief stage opening areas. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter. List the elements in ascending order. All elements must be greater than 0.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Reference pressure differential vector — Pressure drop across relief stage
`5 : 0.2 : 6` `MPa` (default) | vector

Vector of pressure drops across the relief stage. The vector elements must correspond one-to-one with the elements in the Reference volumetric flow rate vector parameter.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Reference volumetric flow rate vector — Flow rate through relief stage
`[6.4e-09, .0013, .0027, .0041, .0055, .007]` `m^3/s` (default) | vector

Vector of flow rates through the relief stage. The vector elements must correspond one-to-one with the elements in the Reference pressure differential vector parameter.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Maximum opening pressure differential — Maximum relief valve pressure
`6` `MPa` (default) | positive scalar

Maximum relief valve pressure.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Maximum opening area — Relief stage maximum open area
`1e-4` `m^2` (default) | positive scalar

Maximum open area of the relief stage orifice.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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 saturates to the specified leakage area. This value contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Pilot ratio — Pilot area ratio
`3` (default) | positive scalar

Ratio of the pressure-acting area of the pilot to the pressure-acting area of the load.

Back pressure ratio — Back pressure area ratio
`4` (default) | positive scalar

Ratio of the back pressure pressure-acting area to the load pressure-acting area.

Cross-sectional area at ports A and B — Area at valve entry or exit
`0.01` `m^2` (default) | positive scalar

Cross-sectional area at the entry and exit ports A and B. The block uses this area in the pressure-flow rate equation that determines mass flow rate through the valve.

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.

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-shut positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Opening dynamics — Whether to introduce flow lag due to orifice opening
`off` (default) | `on`

Whether to account for the transient effects to the fluid system due to opening the valve. Selecting Opening dynamics approximates the opening conditions by introducing a first-order lag in the pressure response.

When you select this parameter, these dynamics apply to the relief stage and not the check stage of the counterbalance valve.

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, select Opening dynamics.

Check Valve

Cracking pressure differential — Set pressure for check valve operation
`0.01` `MPa` (default) | positive scalar

Pressure differential that lifts the check valve.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Maximum opening pressure differential — Maximum pressure in valve
`0.1` `MPa` (default) | positive scalar

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

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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 in parallel with the relief stage.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Pressure differential vector — Pressure differential for check valve operation
`[0.01 : 0.01 : 0.1]` `MPa` (default) | 1-by-n vector

Vector of pressure differentials for the check valve stage.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure or Tabulated data - Volumetric flow rate vs. pressure.

Opening area vector — Check stage opening areas
`[1e-10, 1e-05, 2e-05, 3e-05, 4e-05, 5e-05, 6e-05, 7.5e-05, 8.5e-05, .0001]` `m^2` (default) | 1-by-n vector

Vector of opening areas for the check valve stage. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Volumetric flow rate vector — Check stage volumetric flow rates
`[.000358, .045, .11, .191, .284, .39, .505, .63, .764, .905] .* 1e-3` `m^3/s` (default) | 1-by-n vector

Vector of volumetric flow rates for the check valve stage. The elements of this vector must correspond to the elements in the Pressure differential vector parameter.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b

Counterbalance Valve (TL)

Description

Valve Opening

Opening Parameterization

Predefined Parameterization

Assumptions and Limitations

Ports

Conserving

L — Fluid load thermal liquid

B — Back pressure thermal liquid

P — Pressure port thermal liquid

Parameters

Model Parameterization

Opening parameterization — Opening parameterization Linear - Area vs. pressure (default) | Tabulated data - Area vs. pressure | Tabulated data - Volumetric flow rate vs. pressure

Set pressure differential — Initial spring compression pressure 5 MPa (default) | nonnegative scalar

Dependencies

Pressure differential vector — Relief stage pressure drop values 5 : 0.2 : 6 MPa (default) | 1-by-n vector

Dependencies

Opening area vector — Relief stage opening areas [1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] m^2 (default) | 1-by-n vector

Dependencies

Reference pressure differential vector — Pressure drop across relief stage 5 : 0.2 : 6 MPa (default) | vector

Dependencies

Reference volumetric flow rate vector — Flow rate through relief stage [6.4e-09, .0013, .0027, .0041, .0055, .007] m^3/s (default) | vector

Dependencies

Maximum opening pressure differential — Maximum relief valve pressure 6 MPa (default) | positive scalar

Dependencies

Maximum opening area — Relief stage maximum open area 1e-4 m^2 (default) | positive scalar

Dependencies

Leakage area — Gap area when valve is in fully closed position 1e-10 m^2 (default) | positive scalar

Dependencies

Pilot ratio — Pilot area ratio 3 (default) | positive scalar

Back pressure ratio — Back pressure area ratio 4 (default) | positive scalar

Cross-sectional area at ports A and B — Area at valve entry or exit 0.01 m^2 (default) | positive scalar

Discharge coefficient — Discharge coefficient 0.64 (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow 150 (default) | positive scalar

Smoothing factor — Numerical smoothing factor 0.01 (default) | positive scalar

Opening dynamics — Whether to introduce flow lag due to orifice opening off (default) | on

Opening time constant — Orifice opening time constant 0.1 s (default) | positive scalar

Dependencies

Check Valve

Cracking pressure differential — Set pressure for check valve operation 0.01 MPa (default) | positive scalar

Dependencies

Maximum opening pressure differential — Maximum pressure in valve 0.1 MPa (default) | positive scalar

Dependencies

Maximum opening area — Maximum open area 1e-4 m^2 (default) | positive scalar

Dependencies

Pressure differential vector — Pressure differential for check valve operation [0.01 : 0.01 : 0.1] MPa (default) | 1-by-n vector

Dependencies

Opening area vector — Check stage opening areas [1e-10, 1e-05, 2e-05, 3e-05, 4e-05, 5e-05, 6e-05, 7.5e-05, 8.5e-05, .0001] m^2 (default) | 1-by-n vector

Dependencies

Volumetric flow rate vector — Check stage volumetric flow rates [.000358, .045, .11, .191, .284, .39, .505, .63, .764, .905] .* 1e-3 m^3/s (default) | 1-by-n vector

Dependencies

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

L — Fluid load
thermal liquid

B — Back pressure
thermal liquid

P — Pressure port
thermal liquid

Opening parameterization — Opening parameterization
`Linear - Area vs. pressure` (default) | `Tabulated data - Area vs. pressure` | `Tabulated data - Volumetric flow rate vs. pressure`

Set pressure differential — Initial spring compression pressure
`5` `MPa` (default) | nonnegative scalar

Pressure differential vector — Relief stage pressure drop values
`5 : 0.2 : 6` `MPa` (default) | 1-by-n vector

Opening area vector — Relief stage opening areas
`[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001]` `m^2` (default) | 1-by-n vector

Reference pressure differential vector — Pressure drop across relief stage
`5 : 0.2 : 6` `MPa` (default) | vector

Reference volumetric flow rate vector — Flow rate through relief stage
`[6.4e-09, .0013, .0027, .0041, .0055, .007]` `m^3/s` (default) | vector

Maximum opening pressure differential — Maximum relief valve pressure
`6` `MPa` (default) | positive scalar

Maximum opening area — Relief stage maximum open area
`1e-4` `m^2` (default) | positive scalar

Leakage area — Gap area when valve is in fully closed position
`1e-10` `m^2` (default) | positive scalar

Pilot ratio — Pilot area ratio
`3` (default) | positive scalar

Back pressure ratio — Back pressure area ratio
`4` (default) | positive scalar

Cross-sectional area at ports A and B — Area at valve entry or exit
`0.01` `m^2` (default) | positive scalar

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar

Opening dynamics — Whether to introduce flow lag due to orifice opening
`off` (default) | `on`

Opening time constant — Orifice opening time constant
`0.1` `s` (default) | positive scalar

Cracking pressure differential — Set pressure for check valve operation
`0.01` `MPa` (default) | positive scalar

Maximum opening pressure differential — Maximum pressure in valve
`0.1` `MPa` (default) | positive scalar

Maximum opening area — Maximum open area
`1e-4` `m^2` (default) | positive scalar

Pressure differential vector — Pressure differential for check valve operation
`[0.01 : 0.01 : 0.1]` `MPa` (default) | 1-by-n vector

Opening area vector — Check stage opening areas
`[1e-10, 1e-05, 2e-05, 3e-05, 4e-05, 5e-05, 6e-05, 7.5e-05, 8.5e-05, .0001]` `m^2` (default) | 1-by-n vector

Volumetric flow rate vector — Check stage volumetric flow rates
`[.000358, .045, .11, .191, .284, .39, .505, .63, .764, .905] .* 1e-3` `m^3/s` (default) | 1-by-n vector

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.