Orifice ISO 6358 (G)

Flow restriction of fixed area modeled per ISO 6358

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Description

The Orifice ISO 6358 (G) block models the pressure loss incurred in a gas network due to a purely resistive element of fixed size—such as a flow restriction, an orifice, or a valve—using the methods outlined in the ISO 6358 standard. These methods are widely used in industry in the measurement and reporting of gas flow characteristics. The availability of data on the coefficients of the ISO formulas makes the ISO parameterizations useful when component geometries are unavailable or cumbersome to specify.

Orifice Parameterizations

The default orifice parameterization is based on the most recommended of the ISO 6358 methods: one based on the sonic conductance of the resistive element at steady state. The sonic conductance measures the ease with which a gas can flow when choked, a condition in which the flow velocity is at its theoretical maximum (the local speed of sound). Choking occurs when the ratio between downstream and upstream pressures reaches a critical value known as the critical pressure ratio

The remaining parameterizations are formulated in terms of alternative measures of flow capacity: the flow coefficient (in either of its forms, C_v or K_v) or the size of the flow restriction. The flow coefficient measures the ease with which a gas can flow when driven by a certain pressure differential. The definition of C_v differs from that of K_v in the standard pressure and temperature established in its measurement and in the physical units used in its expression:

• C_v is measured at a generally accepted temperature of 60°F 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 Orifice parameterization block parameter is set to Cv coefficient (USCS).

• K_v is measured at a generally accepted temperature of 15°C and pressure drop of 1 bar; it is expressed in metric units of m^3/h. This is the flow coefficient used in the model when the Orifice parameterization block parameter is set to Kv coefficient (SI).

Mass Balance

The volume of fluid inside the resistive element, 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 fluid 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:

$${\dot{m}}_A+{\dot{m}}_B=0,$$

where $$\dot{m}$$ is defined as the mass flow rate into the valve through the port indicated by the subscript (A or B).

Momentum Balance

The causes of the pressure losses incurred in the passages of the resistive element are ignored in the block. Whatever their natures—sudden area changes, flow passage contortions—only their cumulative effect is considered during simulation. It is this cumulative effect that the sonic conductance in the default orifice parameterization captures in a model. If a different parameterization is selected, the coefficients on which it is based are converted into the parameters of the default parameterization; the mass flow rate calculation is then carried out as described in Sonic Conductance Parameterization.

Sonic Conductance Parameterization

In a choked flow, the mass flow rate through the resistive element is calculated as:

$${\dot{m}}_{\text{ch}}=C{\rho }_{\text{0}}{p}_{\text{in}}\sqrt{\frac{T_{\text{0}}}{T_{\text{in}}}},$$

where:

• C is the sonic conductance inside the resistive element.

• ρ is the gas density, here at standard conditions (subscript 0, 1.185 kg/m^3).

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

• T is the gas temperature at the inlet (subscript in) or at standard conditions (subscript 0, 293.15 K).

In a subsonic and turbulent flow, the mass flow rate calculation becomes:

$${\dot{m}}_{\text{tur}}=C{\rho }_{\text{0}}{p}_{\text{in}}\sqrt{\frac{T_{\text{0}}}{T_{\text{in}}}}{\left[1-{\left(\frac{p_{\text{r}}-b_{\text{cr}}}{1-b_{\text{cr}}}\right)}^2\right]}^m,$$

where:

• p_r is the ratio between downstream pressure (p_out) and upstream pressure (p_in) (each measured against absolute zero):

  $$p_{\text{r}}=\frac{p_{\text{out}}}{p_{\text{in}}}$$

• b_cr is the critical pressure ratio at which the gas flow first begins to choke.

• m is the subsonic index, an empirical coefficient used to more accurately characterize the behavior of subsonic flows.

In a subsonic and laminar flow, the mass flow rate calculation changes to:

$${\dot{m}}_{\text{lam}}=C{\rho }_{\text{0}}\left(\frac{p_{\text{out}}-p_{\text{in}}}{1-b_{\text{lam}}}\right)\sqrt{\frac{T_{\text{0}}}{T_{\text{in}}}}{\left[1-{\left(\frac{b_{\text{lam}}-b_{\text{cr}}}{1-b_{\text{cr}}}\right)}^2\right]}^m,$$

where b_lam is the critical pressure ratio at which the flow transitions between laminar and turbulent regimes. Combining the calculations for the three flow regimes into a piecewise function gives across all pressure ratios:

$$\dot{m}=\{\begin{array}{ll}{\dot{m}}_{\text{lam}},\hfill & \text{if }{b}_{\text{lam}}\le p_{\text{r}}<1\hfill \\ {\dot{m}}_{\text{tur}},\hfill & \text{if }{b}_{\text{cr}}\le p_{\text{r}}<b_{\text{lam}}\hfill \\ {\dot{m}}_{\text{ch}},\hfill & \text{if }{p}_{\text{r}}<b_{\text{cr}}\hfill \end{array},$$

Conversions to Sonic Conductance

If the orifice parameterization is set to Cv coefficient (USCS), the parameters of the mass flow rate calculation are set as follows:

• Sonic conductance: C = 4E-8 * C_v m^3/(s*Pa)

• Critical pressure ratio: b_cr = 0.3

• Subsonic index: m = 0.5

If the Kv coefficient (SI) parameterization is used:

• Sonic conductance: C = 4.78E-8 * K_v m^3/(s*Pa)

• Critical pressure ratio: b_cr = 0.3

• Subsonic index: m = 0.5

For the Restriction area parameterization:

• Sonic conductance: C = 0.128 * 4 S_R/π L/(s*bar), where S is the flow area in the resistive element (subscript R).

• Critical pressure ratio: b_cr = 0.41 + 0.272 (S_R/S_P)^0.25

• Subsonic index: m = 0.5

Energy Balance

The resistive element is modeled as an adiabatic component. No heat exchange can occur between the fluid and the wall that surrounds it. No work is done on or by the fluid 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

Conserving

A — Flow passage

gas

Opening through which the flow can enter or exit the flow resistance. Which of the ports serves as inlet and which as outlet depends on the direction of flow.

B — Flow passage

gas

Opening through which the flow can enter or exit the flow resistance. Which of the ports serves as inlet and which as outlet depends on the direction of flow.

Parameters

Orifice parameterization — Parameterization by which to specify the flow characteristics of the orifice

Sonic conductance (default) | Cv coefficient (USCS)Kv coefficient (S)Restriction area

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 parameterization is selected, the coefficients that characterize it are converted into sonic conductance, critical pressure ratio, and subsonic index.

Sonic conductance — Measure of flow rate capacity in the choked flow regime

1.6 l/(s*bar) (default) | positive scalar in units of volume/(time*pressure)

Ratio, measured at the onset of choking, of the mass flow rate through the resistive element to the product of the upstream pressure and mass density at standard conditions (defined in ISO8778). This parameter determines the maximum flow rate allowed at a given upstream pressure.

Critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes

0.3 (default) | positive unitless scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the fraction of the absolute pressure downstream of the resistive element over the absolute pressure upstream of the same component.

Subsonic index — Exponent used to more accurately characterize mass flow in the subsonic flow regime

0.5 (default) | positive unitless scalar

Exponent used to more accurately calculate the mass flow rate in the subsonic flow regime as described in ISO 6358.

Cv coefficient (USCS) — Flow coefficient expressed in US customary units

0.4 (default) | positive unitless scalar

Flow coefficient expressed in US customary units of ft^3/min as defined in NFPA T3.21.3. This parameter measures the ease with which the gas traverses the resistive element when driven by a pressure differential. See the block description for the correspondence between these parameters.

Kv coefficient (SI) — Flow coefficient expressed in SI units

0.3 (default) | positive unitless scalar

Flow coefficient expressed in SI units of L/min. This parameter measures the ease with which the gas traverses the resistive element when driven by a pressure differential. See the block description for the correspondence between these parameters.

Restriction area — Flow area of the local restriction

1e-5 m (default) | positive scalar in units of area

Area normal to the direction of flow at the point of shortest aperture. The restriction area is converted into an equivalent sonic conductance and critical pressure ratio for use in calculations of mass flow rate. See the block description for detail on the conversion.

Cross-sectional area at ports A and B — Flow area at the gas ports

0.01 m^2 (default) | positive scalar in units of area

Area normal to the flow path at each port. The ports are assumed to be equal in size. The flow area specified here should match those of the inlets of those components to which the resistive element connects.

Laminar flow pressure ratio — Pressure ratio at which flow transitions between laminar and turbulent regimes

0.999 (default) | positive unitless scalar

Pressure ratio at which flow transitions between laminar and turbulent flow regimes. The pressure ratio is the fraction of the absolute pressure downstream of the resistive element over the absolute pressure upstream of the same component. Typical values range from 0.995 to 0.999.

Reference temperature — ISO 8778 reference temperature

293.15 K (default) | scalar in units of temperature

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

Reference density — ISO 8778 reference density

1.185 (default) | positive scalar in units of mass/volume

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

Model Examples

Antagonistic McKibben Muscle Actuator

This demo shows a muscle actuation based on two air muscle actuators (or McKibben artificial muscles) in antagonistic connection. The air muscle actuators are connected to the opposite sides of a lever. The 4-way directional valve is controlled by an electro-mechanical valve actuator. In the 4-way directional way when the high-pressure path P-A and return line B-T are open, the top air muscle actuator contracts and forces the bottom air muscle actuator on the opposite side to extend. Similarly, as the high-pressure path P-B and return line A-T open, the bottom air muscle actuator starts to contract and forces the top air muscle actuator to extend. The oscillating motions of the muscles are converted into the angular rotation of the output load connected to the mechanical linkage modeled with the slider-cranks.

References

[1] P. Beater, Pneumatic Drives, Springer-Verlag Berlin Heidelberg, 2007.

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