Documentation

# Ball Valve (G)

Valve with longitudinally translating ball as control element

• Library:
• Simscape / Fluids / Gas / Valves & Orifices / Flow Control Valves

## Description

The Ball Valve (G) block models an orifice with a translating ball (technically a poppet) as a flow control mechanism. The ball is sized to fully cover the orifice and arranged to shift in line with the flow. Its seat is perforated, with the opening, part of the orifice through which the flow must pass, being either sharp-edged or conical in shape. The distance of the ball to the seat determines the opening area of the valve.

Open ball valve with conical seat

The flow can be laminar or turbulent, and it can reach (up to) sonic speeds. This happens at the vena contracta, a point just past the throat of the valve where the flow is both its narrowest and fastest. The flow then chokes and its velocity saturates, with a drop in downstream pressure no longer sufficing to increase its velocity. Choking occurs when the back-pressure ratio hits a critical value characteristic of the valve. Supersonic flow is not captured by the block.

Ball valves (generally) lack the opening characteristics to precisely modulate or throttle flow rate; they more commonly serve as shutoff and isolation valves, binary on/off switches which are often either fully open or maximally closed.

### Ball Mechanics

In a real valve, the ball often connects by a stem to a push button. When the button is pressed—by the magnetic force of a solenoid coil, say, or by the cyclical action of a rotary cam—the ball shifts from its seat, progressively opening the valve up to a maximum. A spring between the ball and the body of the valve acts as a return mechanism, allowing the ball to revert to its normal position once the button is released.

The block captures the motion of the ball but not the detail of its mechanics. The motion derives from a normalized displacement specified as a physical signal at port L. The normalization is with respect to the maximum position of the ball (at which the valve is fully open). It helps to think of displacement, position, and related quantities as fractions (normally from `0` to `1`) rather than as lengths.

If the action of the push button and return spring matter in your model, you can capture these elements separately using other Simscape blocks. A Simscape Mechanical subsystem makes a good source for the ball displacement signal. In many cases, however, it suffices to know what displacement to impart to the ball. You can then usually ignore the mechanics of the valve.

### Ball Position

The displacement signal allows the block to compute the instantaneous position of the ball, from which the opening of the valve follows. The opening is easily understood as a flow area but, for ease of modeling, it is often best expressed as a flow coefficient or sonic conductance. (The ``ease of modeling'' depends on the data available from the manufacturer.)

The position and displacement variables measure different things. The (instantaneous) position gives the distance of the ball to its resting place on the seat;

the displacement gives only that distance to its normal (unactuated) position. The normal position, a fixed coordinate, need not be zero: the ball can be installed so that it is normally off the seat. (The valve is then partially open even when it is disconnected and its poppet at rest.)

The normal distance between the ball and its seat is the valve lift control offset, specified in the block parameter of the same name. Think of its as the permanent displacement given to the ball while assembling the valve. The variable displacement from port L, on the other hand, captures the motion of the ball during operation of the valve, after it has been assembled and installed. The instantaneous position of the ball is the sum of the two:

`$h\left(L\right)=L+{h}_{\text{0}},$`

where:

• h is the instantaneous position of the ball, normalized against its maximum value. This variable can range from `0` to `1`, with `0` giving a maximally closed valve and `1` a fully open valve. If the calculation should return a number outside of this range, that number is set to the nearest bound (`0` if the result is negative, `1` otherwise). In other words, the normalized position saturates at `0` and `1`.

• L is the variable displacement of the ball, normalized against the maximum position of the same. This variable is obtained from the physical signal at port L. There are no restrictions on its value. You can make it smaller than `0` or greater than `1`, for example, to compensate for an equally extreme valve offset.

• h0 is the fixed offset of the ball relative to its seat in the normal position (when the valve is disconnected and free of inputs). Its value too is normalized against the maximum position of the ball, though there is no requirement that it lie between `0` and `1`.

### Numerical Smoothing

The normalized position, h, spans three regions. At a sufficiently small displacement, it saturates at `0` and the valve is fully closed. At a sufficiently large displacement, it saturates at `1` and the valve is fully open. In between, it varies linearly between its saturation bounds, giving a valve that is partially open.

The transitions between the regions are sharp and their slopes discontinuous. These pose a challenge to variable-step solvers (the sort commonly used with Simscape models). To precisely capture discontinuities, referred to in some contexts as zero crossing events, the solver must reduce its time step, pausing briefly at the time of the crossing in order to recompute its Jacobian matrix (a representation of the dependencies between the state variables of the model and their time derivatives).

This solver strategy is efficient and robust when discontinuities are present. It makes the solver less prone to convergence errors—but it can considerably extend the time needed to finish the simulation run, perhaps excessively so for practical use in real-time simulation. An alternative approach, used here, is to remove the discontinuities altogether.

Normalized position with sharp transitions

To remove the slope discontinuities, the block smoothes them over a small portion of the opening curve. The smoothing, which adds a slight distortion at each transition, ensures that the valve eases into its limiting positions rather than snap (abruptly) into them. The smoothing is optional: you can disable it by setting its time scale to zero. The shape and scale of the smoothing, when applied, derives in part from the cubic polynomials:

`${\lambda }_{\text{L}}=3{\overline{h}}_{\text{L}}^{2}-2{\overline{h}}_{\text{L}}^{3}$`

and

`${\lambda }_{\text{R}}=3{\overline{h}}_{\text{R}}^{2}-2{\overline{h}}_{\text{R}}^{3},$`

where

`${\overline{h}}_{\text{L}}=\frac{h}{\Delta {h}^{*}}$`

and

`${\overline{h}}_{\text{R}}=\frac{h-\left(1-\Delta {h}^{*}\right)}{\Delta {h}^{*}}.$`

In the equations:

• ƛL is the smoothing expression for the transition from the maximally closed position.

• ƛR is the smoothing expression for the transition from the fully open position.

• Δp* is the (unitless) characteristic width of the smoothing region:

`$\Delta {h}^{*}=\frac{1}{2}{f}^{*},$`

where f* is a smoothing factor valued between `0` and `1` and obtained from the block parameter of the same name.

When the smoothing factor is `0`, the normalized ball position stays in its original form—no smoothing applied—and its transitions remain abrupt. When it is `1`, the smoothing spans the whole of the ball's travel range (with the normalized ball position taking the shape of an S-curve).

At intermediate values, the smoothing is limited to a fraction of that range. A value of `0.5`, for example, will smooth the transitions over a quarter of the travel range on each side (for a total smooth region of half that range).

The smoothing adds two new regions to the normalized ball position function—one for the smooth transition on the left, another for that on the right, giving a total of five regions. These are expressed in the piecewise function:

`${h}^{*}=\left\{\begin{array}{ll}0,\hfill & h\le 0\hfill \\ h{\lambda }_{\text{L}},\hfill & h<\Delta {h}^{*}\hfill \\ h,\hfill & h\le 1-\Delta {h}^{*}\hfill \\ h\left(1-{\lambda }_{\text{R}}\right)+{\lambda }_{\text{R}},\hfill & h<1\hfill \\ 1\hfill & h\ge 1\hfill \end{array},$`

where h* is the smoothed valve opening area. The figure shows the effect of smoothing on the sharpness of the transitions.

### Opening Area

The opening area at a given ball position depends in part on the geometry of its seat. That geometry, specified in the Valve seat geometry parameter, can be either `Sharp-edged` or `Conical`. In each case, the bottleneck region through which the flow must pass is in the shape of a conical frustum. The lateral surface of the frustum gives the opening area.

The frustum of a cone is any section of the same taken between two planes parallel to the base. In this block, the (imaginary) cone spans from the surface of the seat (where it has its base) to the center of the ball (its apex). The frustum is formed by cutting the cone where it intersects the ball.

The base of the cone, to be precise, is the ring of contact between the seat and the ball when the valve is in the closed position. The ring coincides with the edge of the seat only if it is sharp-edged. It lies inward from the edge if the seat is conical—somewhere along the conical surface between the orifice and the chamber of the ball.

#### General Expression

A frustum of base radius R, top radius r, and slant height l has for its lateral surface area:

`$S=\pi \left(R+r\right)l.$`

To account for leakage flow, the block adds a small constant to this expression:

`$S=\pi \left(R+r\right)l+{S}_{\text{Leak}},$`

where SLeak is the small opening area that remains in the maximally closed valve due, for example, to valve bore tolerances, surface defects, or an imperfect seal between the ball and its seat. This area is obtained from the Leakage area block parameter.

#### Sharp-Edged Seat

If the seat is sharp-edged, the radius of the base of the frustum is that of the orifice itself (or half of the orifice diameter, DO, specified in the block). The radius of the top face is a small decrement, δ, from that of the base. The decrement and the slant height, l, are functions of the normalized position of the ball (h). These lengths are shown in the figure.

In terms of the orifice diameter, radius decrement, and slant height, the frustum area (S) becomes:

`$S=\pi \left[{D}_{\text{O}}+\left({D}_{\text{O}}-2\delta \right)\right]l+{S}_{\text{Leak}}$`

Rearranged and written in terms of the orifice radius (2RO = DO):

`$S=\pi \left(4{R}_{\text{O}}-2\delta \right)l+{S}_{\text{Leak}}$`

The values of δ and l are obtained from expressions of trigonometry and proportion. These are based on the sides of the triangles shown in the figure. $\overline{CD}$ corresponds to the radius decrement (δ) and $\overline{CE}$ to the slant height (l). $\overline{OA}$ is equal in length to the orifice radius.

Other relevant lengths include $\overline{OE}$ (half the diameter of the ball, RB) and $\overline{CB}$ (the position of the same, h). The various lengths are more clearly shown in the figure below. The diameters of the orifice (RO) and of the ball (RB) are obtained from the block parameters named for them. The ball position is calculated from the signal at port L.

The slant height can now be expressed as:

`$l=OC-{R}_{\text{B}},$`

where OC is the distance from the center of the ball (point O) to a point on the edge of the orifice (C). From Pythagoras' theorem:

`$OC=\sqrt{{\left[h\rho +AB\right]}^{2}+{R}_{\text{O}}^{2}},$`

where ρ is the maximum ball position in units of length (in contrast to the normalized ball position, which is unitless). Its value is computed by solving the equality:

`$S\left(h\right)={S}_{\text{Max}},$`

where SMax is the maximum opening area:

`${S}_{\text{Max}}=\pi {R}_{\text{O}}^{2},$`

where RO is the radius of the orifice (half the value specified in the Orifice diameter block parameter.

Similarly for length AB:

`$AB=\sqrt{{R}_{\text{B}}^{2}-{R}_{\text{O}}^{2}}$`

The radius decrement, δ, can likewise be expressed as:

`$\delta =\frac{l}{OC}{R}_{\text{O}}.$`

Combining these expressions and rearranging them, gives:

`$S=2\pi {R}_{\text{O}}OC\left[1-{\left(\frac{{R}_{\text{B}}}{OC}\right)}^{2}\right]+{S}_{\text{Leak}},$`

where OC is as defined above.

#### Conical Seat

If the seat is conical, the ball comes to rest not on the rim of the orifice but on the conical surface that extends from it. The base of the frustum no longer matches the orifice in its radius and this variable is instead calculated from other lengths. The figure shows the frustum-shaped opening of the valve and the mismatch in size between its base and the orifice.

The calculations of the frustum dimensions are based on the triangles shown below. As in the sharp-edged calculations, $\overline{CD}$ is the decrement in radius from base to top (δ) and $\overline{CE}$ is the slant height of the frustum (l). The length of $\overline{OA}$ gives the base radius.

Other relevant dimensions include the cone angle (θ, taken between the sides of a cross section of the cone) and the ball radius (RB). These and other dimensions are more clearly shown in the figure below.

In terms of these dimensions, the lateral surface area of the frustum is:

`$S=\pi \left(OA-2\delta \right)l+{S}_{\text{Leak}},$`

where OA is the radius of the base:

`$OA=\left(l+{R}_{\text{B}}\right)\text{cos}\left(\frac{\theta }{2}\right),$`

where θ is the angle between the side of the conical seat and its center line, obtained from the Cone angle parameter (specific to the `Conical` parameterization). The slant height of the frustum is:

`$l=\text{sin}\left(\frac{\theta }{2}\right)h\rho ,$`

where, as in the sharp-edged calculations, ρ is the maximum position of the ball in units of length. The decrement in radius from base to top is:

`$\delta =\text{cos}\left(\frac{\theta }{2}\right)l.$`

Combining these expressions, applying basic trigonometric relationships for double angles, and arranging terms gives for the opening area:

`$S=2\pi {R}_{\text{B}}h\rho \text{sin}\left(\theta \right)+\pi {h}^{2}{\rho }^{2}\text{sin}\left(\theta \right)\text{sin}\left(\frac{\theta }{2}\right)+{S}_{\text{Leak}},$`

### Sonic Conductance

As the opening area varies during simulation, so does the mass flow rate through the valve. The relationship between the two variables, however, is indirect. The mass flow rate is defined in terms of the valve's sonic conductance and it is this quantity that the opening area truly determines.

Sonic conductance, if you are unfamiliar with it, describes the ease with which a gas will flow when it is choked—when its velocity is at its theoretical maximum (the local speed of sound). Its measurement and calculation are covered in detail in the ISO 6358 standard (on which this block is based).

Only one value is commonly reported in valve data sheets: one taken at steady state in the fully open position. This is the same specified in the block dialog box (when the Valve parameterization setting is ```Sonic conductance```). For values across the opening range of the valve, this maximum is scaled by the (normalized) valve opening area:

`$C\left(S\right)=\frac{S}{{S}_{\text{Max}}}{C}_{\text{Max}},$`

where C is sonic conductance and the subscript `Max` denotes the specified (manufacturer's) value. The sonic conductance varies linearly between CMax in the fully open position and ${S}_{\text{Leak}}÷{S}_{\text{Max}}×{C}_{\text{Max}}$ in the maximally closed position—a value close to zero and due only to internal leakage between the ports.

#### Other Parameterizations

Because sonic conductance may not be available (or the most convenient choice for your model), the block provides several equivalent parameterizations. Use the Valve parameterization drop-down list to select the best for the data at hand. The parameterizations are:

• `Compute from geometry`

• `Sonic conductance`

• `Cv coefficient (USCS)`

• `Kv coefficient (SI)`

The parameterizations differ only in the data that they require of you. Their mass flow rate calculations are still based on sonic conductance. If you select a parameterization other than `Sonic conductance`, then the block converts the alternate data—the (computed) opening area or a (specified) flow coefficient—into an equivalent sonic conductance.

#### Flow Coefficients

The flow coefficients measure what is, at bottom, the same quantity—the flow rate through the valve at some agreed-upon temperature and pressure differential. They differ only in the standard conditions used in their definition and in the physical units used in their expression:

• Cv is measured at a generally accepted temperature of `60 ℉` and pressure drop of `1 PSI`; it is expressed in imperial units of `US gpm`. This is the flow coefficient used in the model when the Valve parameterization block parameter is set to `Cv coefficient (USCS)`.

• Kv is measured at a generally accepted temperature of `15 ℃` and pressure drop of `1 bar`; it is expressed in metric units of `m3/h`. This is the flow coefficient used in the model when the Valve parameterization block parameter is set to `Kv coefficient (SI)`.

#### Sonic Conductance Conversions

If the valve parameterization is set to ```Cv Coefficient (USCS)```, the sonic conductance is computed at the maximally closed and fully open valve positions from the Cv coefficient (SI) at maximum flow and Cv coefficient (SI) at leakage flow block parameters:

`$C=\left(4×{10}^{-8}{C}_{\text{v}}\right){m}^{3}/\left(sPa\right),$`

where Cv is the flow coefficient value at maximum or leakage flow. The subsonic index, m, is set to `0.5` and the critical pressure ratio, bcr, is set to `0.3`. (These are used in the mass flow rate calculations given in the Momentum Balance section.)

If the `Kv coefficient (SI)` parameterization is used instead, the sonic conductance is computed at the same valve positions (maximally closed and fully open) from the Kv coefficient (USCS) at maximum flow and Kv coefficient (USCS) at leakage flow block parameters:

`$C=\left(4.758×{10}^{-8}{K}_{\text{v}}\right){m}^{3}/\left(sPa\right),$`

where Kv is the flow coefficient value at maximum or leakage flow. The subsonic index, m, is set to `0.5` and the critical pressure ratio, bcr, is set to `0.3`.

For the `Restriction area` parameterization, the sonic conductance is computed (at the same valve positions) from the Maximum opening area, and Leakage area block parameters:

`$C=\left(0.128×4{S}_{\text{R}}/\pi \right)L/\left(sbar\right),$`

where SR is the opening area at maximum or leakage flow. The subsonic index, m, is set to `0.5` while the critical pressure ratio, bcr is computed from the expression:

`$0.41+0.272{\left(\frac{{S}_{\text{R}}}{{S}_{P}}\right)}^{0.25},$`

where the subscript `P` refers to the inlet of the connecting pipe.

### Momentum Balance

The causes of those pressure losses incurred in the passages of the valve are ignored in the block. Whatever their natures—sudden area changes, flow passage contortions—only their cumulative effect is considered during simulation. This effect is assumed to reflect entirely in the sonic conductance of the valve (or in the data of the alternate valve parameterizations).

#### Mass Flow Rate

When the flow is choked, the mass flow rate is a function of the sonic conductance of the valve and of the thermodynamic conditions (pressure and temperature) established at the inlet. The function is linear with respect to pressure:

`${\stackrel{˙}{m}}_{\text{ch}}=C{\rho }_{\text{0}}{p}_{\text{in}}\sqrt{\frac{{T}_{\text{0}}}{{T}_{\text{in}}}},$`

where:

• C is the sonic conductance inside the valve. Its value is obtained from the block parameter of the same name or by conversion of other block parameters (the exact source depending on the Valve parameterization setting).

• ρ is the gas density, here at standard conditions (subscript `0`), obtained from the Reference density block parameter.

• p is the absolute gas pressure, here corresponding to the inlet (`in`).

• T is the gas temperature at the inlet (`in`) or at standard conditions (`0`), the latter obtained from the Reference temperature block parameter.

When the flow is subsonic, and therefore no longer choked, the mass flow rate becomes a nonlinear function of pressure—both that at the inlet as well as the reduced value at the outlet. In the turbulent flow regime (with the outlet pressure contained in the back-pressure ratio of the valve), the mass flow rate expression is:

`${\stackrel{˙}{m}}_{\text{tur}}=C{\rho }_{\text{0}}{p}_{\text{in}}\sqrt{\frac{{T}_{\text{0}}}{{T}_{\text{in}}}}{\left[1-{\left(\frac{{p}_{\text{r}}-{b}_{\text{cr}}}{1-{b}_{\text{cr}}}\right)}^{2}\right]}^{m},$`

where:

• pr is the back-pressure ratio, or that between the outlet pressure (pout) and the inlet pressure (pin):

`${P}_{\text{r}}=\frac{{p}_{\text{out}}}{{p}_{\text{in}}}$`

• bcr is the critical pressure ratio at which the flow becomes choked. Its value is obtained from the block parameter of the same name or by conversion of other block parameters (the exact source depending on the Valve parameterization setting).

• m is the subsonic index, an empirical coefficient used to more accurately characterize the behavior of subsonic flows. Its value is obtained from the block parameter of the same name or by conversion of other block parameters (the exact source depending on the Valve parameterization setting).

When the flow is laminar (and still subsonic), the mass flow rate expression changes to:

`${\stackrel{˙}{m}}_{\text{lam}}=C{\rho }_{\text{0}}{p}_{\text{in}}\left[\frac{1-{p}_{\text{r}}}{1-{b}_{\text{lam}}}\right]\sqrt{\frac{{T}_{\text{0}}}{{T}_{\text{in}}}}{\left[1-{\left(\frac{{b}_{\text{lam}}-{b}_{\text{cr}}}{1-{b}_{\text{cr}}}\right)}^{2}\right]}^{m}$`

where blam is the critical pressure ratio at which the flow transitions between laminar and turbulent regimes (obtained from the Laminar flow pressure ratio block parameter). Combining the mass flow rate expressions into a single (piecewise) function, gives:

`$\stackrel{˙}{m}=\left\{\begin{array}{ll}{\stackrel{˙}{m}}_{\text{lam}},\hfill & {b}_{\text{lam}}\le {p}_{\text{r}}<1\hfill \\ {\stackrel{˙}{m}}_{\text{tur}},\hfill & {b}_{\text{cr}}\le {p}_{\text{r}}<{p}_{\text{lam}}\hfill \\ {\stackrel{˙}{m}}_{\text{ch}},\hfill & {p}_{\text{r}}<{b}_{\text{Cr}}\hfill \end{array},$`

with the top row corresponding to subsonic and laminar flow, the middle row to subsonic and turbulent flow, and the bottom row to choked (and therefore sonic) flow.

### Mass Balance

The volume of fluid inside the valve, and therefore the mass of the same, is assumed to be very small and it is, for modeling purposes, ignored. As a result, no amount of gas can accumulate there. By the principle of conservation of mass, the mass flow rate into the valve through one port must therefore equal that out of the valve through the other port:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`

where $\stackrel{˙}{m}$ is defined as the mass flow rate into the valve through port A or B. Note that in this block the flow can reach but not exceed sonic speeds.

### Energy Balance

The valve is modeled as an adiabatic component. No heat exchange can occur between the gas and the wall that surrounds it. No work is done on or by the gas as it traverses from inlet to outlet. With these assumptions, energy can flow by advection only, through ports A and B. By the principle of conservation of energy, the sum of the port energy flows must then always equal zero:

`${\varphi }_{\text{A}}+{\varphi }_{\text{B}}=0,$`

where ϕ is defined as the energy flow rate into the valve through one of the ports (A or B).

## Ports

### Input

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Input port through which to specify the control signal for the valve ball displacement. The ball position, or valve lift, is calculated as the sum of this signal and the valve lift control offset (specified in the block parameter of the same name).

When the ball position is `0`, the valve is maximally closed and flow is limited to internal leakage between the ports. When the ball position is `1`, the valve is fully open and flow is at the maximum allowed by the pressure drop between the ports.

### Conserving

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Opening through which the working fluid can enter or exit the valve. The direction of flow depends on the pressure differential established across the valve. Both forward and backward directions are allowed.

Opening through which the working fluid can enter or exit the valve. The direction of flow depends on the pressure differential established across the valve. Both forward and backward directions are allowed.

## Parameters

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Geometry of the seat of the ball. The geometry selection determines which calculation to use for the opening area of the valve. See the block description for detail on the block calculations.

Angle formed by the slope of the conical seat against its center line.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve seat specification parameter is set to `Conical`.

Diameter of the ball control element.

Diameter of the orifice of the valve. In those with a conical seat, the diameter is that of the root of the seat (where it meets the orifice). The orifice is assumed to be constant in cross section throughout its length (from the seat to the opposite entrance).

Displacement of the ball from the root of its seat, expressed as a fraction of its maximum travel distance, when no control input is provided or when that input is zero (the normal valve position. The instantaneous ball position is calculated during simulation as the sum of this offset and the control signal specified at port L. The valve is partially open in its normal position when the offset is a fraction between `0` and `1`.

Choice of ISO method to use in the calculation of mass flow rate. All calculations are based on the Sonic conductance parameterization; if a different option is selected, the data specified in converted into equivalent sonic conductance, critical pressure ratio, and subsonic index. See the block description for more information on the conversion.

This parameter determines which measures of valve opening you must specify—and therefore which of those measures appear as parameters in the block dialog box.

Equivalent measure of the maximum flow rate allowed through the valve at some reference inlet conditions, generally those outlined in ISO 8778. The flow is at a maximum when the valve is fully open and the flow velocity is choked (it being saturated at the local speed of sound). This is the value generally reported by manufacturers in technical data sheets.

Sonic conductance is defined as the ratio of the mass flow rate through the valve to the product of the pressure and density upstream of the valve inlet. This parameter is often referred to in the literature as the C-value.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Ratio of downstream to upstream absolute pressures at which the flow becomes choked (and its velocity becomes saturated at the local speed of sound). This parameter is often referred to in the literature as the b-value. Enter a number greater than or equal to zero and smaller than the Laminar flow pressure ratio block parameter.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Empirical exponent used to more accurately calculate the mass flow rate through the valve when the flow is subsonic. This parameter is sometimes referred to as the m-index. Its value is approximately `0.5` for valves (and other components) whose flow paths are fixed.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Flow coefficient of the fully open valve, expressed in the US customary units of `ft3/min` (as described in NFPA T3.21.3). This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential. This is the value generally reported by manufacturers in technical data sheets.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Cv coefficient (USCS)`.

Flow coefficient of the fully open valve, expressed in the SI units of `L/min`. This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential. This is the value generally reported by manufacturers in technical data sheets.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Kv coefficient (SI)`.

Opening area of the valve in the maximally closed position, when only internal leakage between the ports remains. This parameter serves primarily to ensure that closure of the valve does not cause portions of the gas network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Opening area`.

Area normal to the flow path at the valve ports. The ports are assumed to be the same in size. The flow area specified here should ideally match those of the inlets of adjoining components.

Pressure ratio at which the flow transitions between laminar and turbulent flow regimes. The pressure ratio is the fraction of the absolute pressure downstream of the valve over that just upstream of it. The flow is laminar when the actual pressure ratio is above the threshold specified here and turbulent when it is below. Typical values range from `0.995` to `0.999`.

Absolute temperature used at the inlet in the measurement of sonic conductance (as defined in ISO 8778).

Gas density established at the inlet in the measurement of sonic conductance (as defined in ISO 8778).

Amount of smoothing to apply to the opening area function of the valve. This parameter determines the widths of the regions to be smoothed—one located at the fully open position, the other at the fully closed position.

The smoothing superposes on each region of the opening area function a nonlinear segment (a third-order polynomial function, from which the smoothing arises). The greater the value specified here, the greater the smoothing is, and the broader the nonlinear segments become.

At the default value of `0`, no smoothing is applied. The transitions to the maximally closed and fully open positions then introduce discontinuities (associated with zero-crossings), which tend to slow down the rate of simulation.

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