Flow Resistance (G)
Gas resistance.
blockType: AcausalFoundation.Gas.Elements.FlowResistance
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Description
Block Flow Resistance (G) simulates the total pressure drop in a gas line. The pressure drop is proportional to the square of the mass flow and inversely proportional to the density of the gas. The proportionality coefficient is determined based on the nominal operating mode specified in the unit parameters.
This block is used when only the pressure drop depending on the mass flow rate is known about the component. This block can be combined with others to create a custom component that more accurately reflects a real object, such as a block—based heat exchanger. Constant Volume Chamber (G).
Conservation of mass
It is assumed that the volume of gas inside the gas resistance is negligible. The mass flow through one port is exactly equal to the mass flow through the other port:
where and — mass expenses through ports A and B, respectively.
Energy conservation
Energy can enter and exit the gas resistance only through the gas ports. There is no heat exchange between the walls and the environment. Besides, the gas doesn’t do any work. The energy flow entering through one port is exactly equal to the energy flow exiting through the other port:
where and — energy flow through ports A and B respectively.
Conservation of momentum
External forces acting on the gas include forces due to inlet pressure and forces due to viscous friction on the walls. Gravity is ignored, as are other mechanical forces. Expression of friction forces in terms of the loss coefficient gives a semi-empirical expression:
where
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— mass flow rate from port A to port B;
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— pressure drop from port A to port B, that is ;
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— loss ratio;
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— gas density;
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— the area of the stream.
The differential pressure equation is implemented in two modifications. The first one takes into account the change in sign when the flow direction changes, then the equation is rewritten as follows:
where the pressure drop is positive only if the mass flow rate is also positive. The second modification is designed to eliminate the singularity due to a change in the flow direction, which may pose a problem for numerical solvers during simulation. The pressure drop is linearized in a small neighborhood at flow rates close to zero:
where — the threshold mass flow rate below which the pressure drop is linearized. The figure shows the changed pressure drop relative to the local mass flow (curve I):
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Higher the pressure drop approaches the value expressed in the original equation (curve II) and varies depending on . This dependence is approximated to that observed in turbulent flows.
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Below the pressure drop approaches a straight line with a slope partially dependent on (curve III), and varies depending on . This dependence is approximated to that observed in laminar flows.
For ease of modeling, the loss factor is it is not required as a block parameter. Instead, it is automatically calculated based on the nominal conditions specified in the block parameters.:
where is the asterisk ( ) indicates the value at the nominal operating mode. All these calculations are based on the assumption that the threshold mass flow rate much less than the nominal value . Replacing fractions in the expression for the pressure drop, it gives:
or, equivalently:
where — the coefficient of proportionality between the pressure drop across the gas resistance and the local mass flow rate, which is defined as:
If the gas density is assumed to be constant, then its nominal and actual values should always be equal. This is the case whenever the nominal value is specified in the block dialog box as 0 — a special value used to signal to the unit that the gas density is constant. Then the ratio of these two values is 1, and the share decreases to:
Ports
Conserving
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A
—
entrance or exit
gas
Details
The gas port corresponds to the inlet or outlet of the gas resistance. This block has no internal orientation.
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B
—
entrance or exit
gas
Details
The gas port corresponds to the inlet or outlet of the gas resistance. This block has no internal orientation.
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Parameters
Parameters
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Nominal pressure drop —
pressure drop under known operating conditions
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Details
Pressure drop from inlet to outlet at a known operating mode. The unit uses nominal parameters to calculate the proportionality coefficient between pressure drop and mass flow.
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Yes |
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Nominal mass flow rate —
mass flow rate at a known operating mode
kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s
Details
The mass flow rate from the input to the output at a known operating mode. The unit uses nominal parameters to calculate the proportionality coefficient between pressure drop and mass flow.
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Yes |
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Nominal density —
density at a known operating mode
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3
Details
The mass density inside the gas resistance at a known operating mode. The unit uses nominal parameters to calculate the proportionality coefficient between pressure drop and mass flow. Set this parameter to zero to ignore the dependence of the pressure drop on the gas density.
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Yes |
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Cross-sectional area at ports A and B —
flow area at gas resistance ports
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Details
The flow area at the gas resistance ports. The ports are assumed to be identical in size.
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Yes |
# Fraction of nominal mass flow rate for laminar transition — the ratio of threshold flow to nominal mass flow
Details
The ratio of the threshold mass flow to the nominal mass flow. The unit uses this parameter to calculate the threshold mass flow rate — and, ultimately, to set linearization limits for the pressure drop.
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| Evaluatable |
Yes |