Flow Resistance (G)
Gas resistance.
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Description
The Flow Resistance (G) block models the total pressure drop in a gas line. The pressure drop is proportional to the square of the mass flow rate and inversely proportional to the gas density. The proportionality factor is based on the nominal operating condition specified in the block parameters.
This block is used when only the pressure drop as a function of mass flow rate is known about the component. This block can be combined with others to create a custom component that more accurately represents a real object - for example, a heat exchanger based on the Constant Volume Chamber block.
Mass conservation
It is assumed that the volume of gas inside the gas resistance is negligible. The mass flow rate through one port is exactly equal to the mass flow rate through the other port:
where and are the mass flow rates through ports A and B, respectively.
Energy balance
Energy can only enter and exit the gas resistance through the gas ports. There is no heat exchange between the walls and the environment. In addition, the gas does not do any work. The energy flow entering through one port is exactly equal to the energy flow leaving through the other port:
where and are the energy flux through ports A and B respectively.
Pulse balance
The external forces acting on the gas include those due to pressure at the inlets and those due to viscous friction on the walls. Gravity is not considered, as are other mechanical forces. Expressing the frictional forces in terms of the loss factor gives a semi-empirical expression:
where
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- is the mass flow rate from port A to port B;
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- is the pressure drop from port A to port B, i.e. ;
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- loss factor;
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- gas density;
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- flow area.
The pressure drop equation is realised in two modifications. The first one takes into account the change of sign when the flow direction changes, then the equation is rewritten as follows:
where the pressure drop is positive only when the mass flow rate is also positive. The second modification is designed to eliminate singularity due to changes in flow direction - which can be a problem for numerical solvers during simulations - it is linearised into a small one, with flow velocities close to zero:
where is the threshold mass flow rate below which the pressure drop linearises. The figure shows the modified pressure drop versus local mass flow rate (curve I):
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Above the pressure drop approaches the value expressed in the original equation (curve II) and varies with . This dependence is approximated from 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 with . This dependence is approximated from that observed in laminar flows.
For simplicity of modelling, the loss factor is not required as a block parameter. Instead, it is automatically calculated based on the nominal conditions specified in the block parameters:
where the asterisk ( ) denotes the value at nominal operating conditions. Underlying all these calculations is the assumption that the threshold mass flow rate is much lower than the nominal value . Substituting the fraction in the expression for the pressure drop gives:
or, equivalently:
where is 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, its nominal and actual values should always be equal. This is the case whenever the nominal value is specified in the block dialogue box as 0, a special value used to signal to the block that the gas density is constant. Then the ratio of the two values is 1 and the fraction is reduced to:
Ports
A - input or output
gas
Gas port, corresponds to the input or output of the gas resistance. This unit has no internal directionality.
B - input or output
gas
Gas port, corresponds to the input or output of the gas resistance. This unit has no internal directionality.
Parameters
Nominal pressure drop, Pa - pressure drop at known operating mode
1000.0 Pa (by default)
Pressure drop from inlet to outlet at known operating mode. The unit uses nominal parameters to calculate the proportionality factor between pressure drop and mass flow rate.
Nominal mass flow rate, kg/s - mass flow rate at known operating mode
0.1 kg/s (By default).
Mass flow rate from inlet to outlet at known operating mode. The unit uses the nominal parameters to calculate the coefficient of proportionality between pressure drop and mass flow rate.
Nominal density, kg/m³ - density at known operating mode
`0.0 kg/m³ (By default)
Mass density inside the gas resistance at known operating mode. The unit uses the nominal parameters to calculate the coefficient of proportionality between pressure drop and mass flow rate. Set this parameter to zero to ignore the dependence of pressure drop on gas density.
Cross-sectional area at ports A and B, m² - flow area at gas resistance ports
0.01 m² (by default).
Flow area at gas resistance ports. It is assumed that the ports are identical in size.
Fraction of nominal mass flow rate for laminar flow - ratio of threshold flow rate to nominal mass flow rate
1e-3 (by default).
Ratio of threshold mass flow rate to nominal mass flow rate. The unit uses this parameter to calculate the threshold mass flow rate - and ultimately to set the linearisation limits for the pressure drop.