# Check Valve (TL)

One-way directional valve with pressure-actuated control element

## Library

Thermal Liquid/Valves/Directional Control Valves

## Description

The Check Valve (TL) block represents a one-way directional valve for the thermal liquid domain. The valve allows flow from port A to port B only. A minimum pressure, known as the cracking pressure, is required at port A in order to force the valve open.

Check Valve Positions

The block accepts the cracking pressure parameter as a gauge pressure at port A or as a pressure differential between ports A and B. The cracking pressure marks only the point at which the valve begins to open. The valve opens gradually with rising pressure until it is fully open.

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function does this by removing the curve discontinuities at the cracking and maximum opening pressures. The figure shows the effect of smoothing on the valve opening area curve.

Opening-Area Curve Smoothing

### Valve Opening Area

The valve opening area calculation is based on the linear expression

`${S}_{Linear}=\left(\frac{{S}_{Max}-{S}_{Leak}}{{p}_{Max}-{p}_{Crack}}\right)\left({p}_{Control}-{p}_{Crack}\right)+{S}_{Leak},$`
where:

• SLinear is the linear valve opening area.

• SMax is the valve opening area in the fully open position.

• SLeak is the valve opening area in the fully closed position. Only leakage flow remains in this position.

• pMax is the pressure at which the valve reaches the fully open position. This parameter depends on the Pressure control specification setting in the block dialog box—`Pressure at port A` or ```Pressure differential```:

In the equation, pMax, Gauge is the gauge pressure at which the valve reaches the fully open position, pAtm is atmospheric pressure, and pMax, Diff is pressure difference between ports A and B at which the valve reaches the fully open position.

• pCrack is the pressure at which the valve begins to open. This parameter depends on the Pressure control specification setting in the block dialog box—`Pressure at port A` or ```Pressure differential```:

In the equation, pCrack, Gauge is the gauge pressure at which the valve first begins to open, pAtm is atmospheric pressure, and pCrack, Diff is the pressure difference between ports A and B at which the valve first begins to open.

• pControl is the valve control pressure. This parameter depends on the Pressure control specification setting in the block dialog box—```Pressure at port A``` or `Pressure differential`:

In the equation, pA is the pressure at port A and pB the pressure at port B.

The valve opening expressions introduce undesirable discontinuities at the fully open and fully closed positions. The block eliminates these discontinuities using polynomial expressions that smooth the transitions to and from the fully open and fully closed positions. The valve smoothing expressions are

`${\lambda }_{L}=3{\overline{p}}_{L}^{2}-2{\overline{p}}_{L}^{3}$`
and
`${\lambda }_{R}=3{\overline{p}}_{R}^{2}-2{\overline{p}}_{R}^{3}$`
where:
`${\overline{p}}_{L}=\frac{{p}_{Control}-{p}_{Crack}}{\Delta {p}_{smooth}}$`
and
`${\overline{p}}_{R}=\frac{{p}_{Control}-\left({p}_{Max}-\Delta {p}_{smooth}\right)}{\Delta {p}_{smooth}}.$`
In the equations:

• λL is the smoothing expression for the fully closed portion of the valve opening curve.

• λR is the smoothing expression applied to the fully open portion of the valve opening curve.

• Δpsmooth is the temperature smoothing region:

`$\Delta {p}_{smooth}={f}_{smooth}\frac{{p}_{Max}-{p}_{Set}}{2},$`
where fsmooth is a smoothing factor between 0 and 1.

The smoothed valve opening area is given by the piecewise conditional expression

`${S}_{R}=\left\{\begin{array}{ll}{S}_{Leak},\hfill & {p}_{control}\le {p}_{crack}\hfill \\ {S}_{Leak}\left(1-{\lambda }_{L}\right)+{S}_{Linear}{\lambda }_{L},\hfill & {p}_{control}<{p}_{crack}+\Delta {p}_{smooth}\hfill \\ {S}_{Linear},\hfill & {p}_{control}<{p}_{Max}-\Delta {p}_{smooth}\hfill \\ {S}_{Linear}\left(1-{\lambda }_{R}\right)+{S}_{Max}{\lambda }_{R},\hfill & {p}_{control}<{p}_{Max}\hfill \\ {S}_{Max},\hfill & {p}_{control}\ge {p}_{Max}\hfill \end{array},\text{\hspace{0.17em}}$`
where:

• SR is the smoothed valve opening area.

## Parameters

### Parameters Tab

Pressure control specification

Specification method for the valve set pressure data. Options include `Pressure at port A` and `Pressure differential`.

Cracking pressure (gauge)

Minimum gauge pressure at port A required to force the valve partially open. The valve opening continues to expand as the fluid pressure rises above the cracking pressure. This parameter is active only when the Pressure control specification parameter is set to `Pressure at port A`. The default value is `0.1` MPa.

Cracking pressure differential

Minimum pressure differential, measured from port A to port B, required to force the valve partially open. The valve opening continues to expand as the pressure differential rises above this value. This parameter is active only when the Pressure control specification parameter is set to ```Pressure differential```. The default value is `0.01` MPa.

Maximum opening pressure (gauge)

Gauge pressure at port A required to fully open the valve. The valve opening area stays constant above this pressure. This parameter is active only when the Pressure control specification parameter is set to `Pressure at port A`. The default value is `0.2` MPa.

Pressure differential from port A to port B required to fully open the valve. The valve opening area stays constant above this pressure differential. This parameter is active only when the Pressure control specification parameter is set to `Pressure differential`. The default value is `0.02` MPa.

Maximum opening area

Valve cross-sectional area in the fully open position. This area corresponds to the maximum control member displacement. The default value is `1e-4` m^2.

Leakage area

Area through which fluid can flow in the fully closed valve position. This area accounts for leakage between the valve inlets. The default value is `1e-10` m^2.

Smoothing factor

Portion of the opening-area curve to smooth expressed as a fraction. Smoothing eliminates discontinuities at the minimum and maximum flow valve positions. The smoothing factor must be between `0` and `1`.

Opening-Area Curve Smoothing

Enter a value of `0` for zero smoothing. Enter a value of `1` for full-curve smoothing. The default value is `0.01`.

Area normal to the direction of flow at the valve inlets. This area is assumed the same for all the inlets. The default value is `0.01` m^2.

Characteristic longitudinal length

Approximate length of the valve. This parameter provides a measure of the longitudinal scale of the valve. The default value is `0.1` m^2.

Discharge coefficient

Semi-empirical parameter commonly used as a measure of valve performance. The discharge coefficient is defined as the ratio of the actual mass flow rate through the valve to its theoretical value.

The block uses this parameter to account for the effects of valve geometry on mass flow rates. Textbooks and valve data sheets are common sources of discharge coefficient values. By definition, all values must be greater than 0 and smaller than 1. The default value is `0.7`.

Critical Reynolds number

Reynolds number corresponding to the transition between laminar and turbulent flow regimes. The flow through the valve is assumed laminar below this value and turbulent above it. The appropriate values to use depend on the specific valve geometry. The default value is `12`.

### Variables Tab

Mass flow rate into port A

Mass flow rate into the component through port A at the start of simulation. The default value is ```1 kg/s```.

## Ports

• A — Thermal liquid conserving port representing valve inlet A

• B — Thermal liquid conserving port representing valve inlet B