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Fixed-area pneumatic orifice complying with ISO 6358 standard
The Constant Area Pneumatic Orifice (ISO 6358) block models the flow rate of an ideal gas through a fixed-area sharp-edged orifice. The model conforms to the ISO 6358 standard and is based on the following flow equations, originally proposed by Sanville [1]:
$$G=\{\begin{array}{ll}{k}_{1}\xb7{p}_{i}\left(1-\frac{{p}_{o}}{{p}_{i}}\right)\sqrt{\frac{{T}_{ref}}{{T}_{i}}}\xb7sign\left({p}_{i}-{p}_{o}\right)\hfill & \text{if}\frac{{p}_{o}}{{p}_{i}}{\beta}_{lam}\text{(laminar)}\hfill \\ {p}_{i}\xb7C\xb7{\rho}_{ref}\sqrt{\frac{{T}_{ref}}{{T}_{i}}}\xb7\sqrt{1-{\left(\frac{\frac{{p}_{o}}{{p}_{i}}-b}{1-b}\right)}^{2}}\hfill & \text{if}{\beta}_{lam}\frac{{p}_{o}}{{p}_{i}}b\text{(subsonic)}\hfill \\ {p}_{i}\xb7C\xb7{\rho}_{ref}\sqrt{\frac{{T}_{ref}}{{T}_{i}}}\hfill & \text{if}\frac{{p}_{o}}{{p}_{i}}=b\text{(choked)}\hfill \end{array}$$
$${k}_{1}=\frac{1}{1-{\beta}_{lam}}\xb7C\xb7{\rho}_{ref}\sqrt{1-{\left(\frac{{\beta}_{lam}-b}{1-b}\right)}^{2}}$$
where
G | Mass flow rate |
β_{lam} | Pressure ratio at laminar flow, a value between 0.999 and 0.995 |
b | Critical pressure ratio, that is, the ratio between the outlet pressure p_{o} and inlet pressure p_{i} at which the gas velocity achieves sonic speed |
C | Sonic conductance of the component, that is, the ratio between the mass flow rate and the product of inlet pressure p_{1} and the mass density at standard conditions when the flow is choked |
ρ_{ref} | Gas density at which the sonic conductance was measured (1.185 kg/m^3 for air) |
p_{i}, p_{o} | Absolute pressures at the orifice inlet and outlet, respectively. The inlet and outlet change depending on flow direction. For positive flow (G > 0), p_{i} = p_{A}, otherwise p_{i} = p_{B}. |
T_{i}, T_{o} | Absolute gas temperatures at the orifice inlet and outlet, respectively |
T_{ref} | Gas temperature at which the sonic conductance was measured (T_{ref} = 293.15 K) |
The equation itself, parameters b and C, and the heuristic on how to measure these parameters experimentally form the basis for the standard ISO 6358 (1989). The values of the critical pressure ratio b and the sonic conductance C depend on a particular design of a component. Typically, they are determined experimentally and are sometimes given on a manufacturer data sheet.
The block can also be parameterized in terms of orifice effective area or flow coefficient, instead of sonic conductance. When doing so, block parameters are converted into an equivalent value for sonic conductance. When specifying effective area, the following formula proposed by Gidlund and detailed in [2] is used:
C = 0.128 d ^{2}
where
C | Sonic conductance in dm^3/(s*bar) |
d | Inner diameter of restriction in mm |
The effective area (whether specified directly, or calculated when the orifice is parameterized in terms of C_{v} or K_{v}, as described below) is used to determine the inner diameter d in the Gidlund formula, assuming a circular cross section.
Gidlund also gives an approximate formula for the critical pressure ratio in terms of the pneumatic line diameter D,
b = 0.41 + 0.272 d / D
This equation is not used by the block and you must specify the critical pressure ratio directly.
If the orifice is parameterized in terms of the C_{v} [2] coefficient, then the C_{v} coefficient is turned into an equivalent effective orifice area for use in the Gidlund formula:
A = 1.6986e – 5 C_{v}
By definition, an opening or restriction has a C_{v} coefficient of 1 if it passes 1 gpm (gallon per minute) of water at pressure drop of 1 psi.
If the orifice is parameterized in terms of the K_{v} [2] coefficient, then the K_{v} coefficient is turned into an equivalent effective orifice area for use in the Gidlund formula:
A = 1.1785e – 6 C_{v}
K_{v} is the SI counterpart of C_{v}. An opening or restriction has a K_{v} coefficient of 1 if it passes 1 lpm (liter per minute) of water at pressure drop of 1 bar.
The heat flow out of the orifice is assumed equal to the heat flow into the orifice, based on the following considerations:
The orifice is square-edged or sharp-edged, and as such is characterized by an abrupt change of the downstream area. This means that practically all the dynamic pressure is lost in the expansion.
The lost energy appears in the form of internal energy that rises the output temperature and makes it very close to the inlet temperature.
Therefore, q_{i} = q_{o}, where q_{i} and q_{o} are the input and output heat flows, respectively.
The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B.
The gas is ideal.
Specific heats at constant pressure and constant volume, c_{p} and c_{v}, are constant.
The process is adiabatic, that is, there is no heat transfer with the environment.
Gravitational effects can be neglected.
The orifice adds no net heat to the flow.
Select one of the following model parameterization methods:
Sonic conductance — Provide value for the sonic conductance of the orifice. The values of the sonic conductance and the critical pressure ratio form the basis for the ISO 6358 compliant flow equations for the orifice. This is the default method.
Effective area — Provide value for the orifice effective area. This value is internally converted by the block into an equivalent value for sonic conductance.
Cv coefficient (USCU) — Provide value for the flow coefficient specified in US units. This value is internally converted by the block into an equivalent value for the orifice effective area.
Kv coefficient (SI) — Provide value for the flow coefficient specified in SI units. This value is internally converted by the block into an equivalent value for the orifice effective area.
Specify the sonic conductance of the orifice, that is, the ratio between the mass flow rate and the product of upstream pressure and the mass density at standard conditions when the flow is choked. This value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 1.6 l/s/bar. This parameter appears in the dialog box if Orifice is specified with parameter is set to Sonic conductance.
Specify the orifice cross-sectional area. The default value is 1e-5 m^2. This parameter appears in the dialog box if Orifice is specified with parameter is set to Effective area.
Specify the value for the flow coefficient in US units. The default value is 0.6. This parameter appears in the dialog box if Orifice is specified with parameter is set to Cv coefficient (USCU).
Specify the value for the flow coefficient in SI units. The default value is 8.5. This parameter appears in the dialog box if Orifice is specified with parameter is set to Kv coefficient (SI).
Specify the critical pressure ratio, that is, the ratio between the downstream pressure and the upstream pressure at which the gas velocity achieves sonic speed. The default value is 0.528.
Specify the ratio between the downstream pressure and the upstream pressure at laminar flow. This value can be in the range between 0.995 and 0.999. The default value is 0.999.
Specify the gas temperature at which the sonic conductance was measured. The default value is 293.15 K.
Specify the gas density at which the sonic conductance was measured. The default value is 1.185 kg/m^3.
Use the Variables tab to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.
[1] Sanville, F. E. "A New Method of Specifying the Flow Capacity of Pneumatic Fluid Power Valves." Paper D3, p.37-47. BHRA. Second International Fluid Power Symposium, Guildford, England, 1971.
[2] Beater, P. Pneumatic Drives. System Design, Modeling, and Control. New York: Springer, 2007.