Jet Pump (IL)
Jet pump in an isothermal liquid network.
Description
The Jet Pump (IL) unit simulates a jet pump in an isothermal liquid network with identical moving and suction fluids. The driving fluid enters the primary nozzle through port A and draws the suction fluid through the inlet port S. After mixing in the throat, the combined flow expands in the diffuser and is discharged through port B. The total pressure change in the pump is the sum of the individual contributions of friction and area change in each pump section, and the change in momentum at the throat. The signs in the equations below correspond to positive flow in the throat.
The figure shows a schematic diagram of a jet pump.
Pressure change with change of area
The mass flow rate in the pump is maintained:
where
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- is the mass flow rate through port A;
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- is the mass flow rate through port S;
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- mass flow through port B.
Using the law of conservation of mass and Bernoulli’s law, the change in area of the pump segments can be expressed in terms of the change in pressure. The pressure change associated with the nozzle is:
or 0, whichever is greater. In this formula:
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- nozzle area at the widest cross-section, the value of the parameter Nozzle area;
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- the density of the fluid.
It is assumed that the inlet orifice of the nozzle is much larger than the outlet orifice.
Although the geometry of a typical suction duct is not similar to the shape of a nozzle, it has a similarly reduced area as it transitions to an annular gap around the nozzle outlet. It is assumed that this annular gap is much smaller than the area of the suction orifice. The pressure change caused by this reduction in area is:
or 0, whichever is greater. In this formula, is the cross-sectional area of the hole.
The pressure change with diffuser expansion is:
where is the ratio of cross-sectional areas of the diffuser inlet and outlet openings, the value of the parameter Diffuser inlet to outlet area ratio.
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Reverse flows In the case of reversible flow, the effect of nozzle area on the pressure change is not modelled, so the flow from the throat through the nozzle will not experience any pressure increase. This ensures numerical stability of the block when modelling reversible flows. |
Pressure change due to mixing
At the throat, mixing of the driving and suction flows takes place. The change in momentum is related to the change in pressure:
where is the ratio of the largest and smallest nozzle cross-sectional area, the value of the parameter Nozzle to throat area ratio.
Pressure loss due to friction
The flow experiences pressure losses due to friction in the nozzle, suction inlet, throat and diffuser. These losses are calculated based on the ratio determined for each section and the area, or ratio of areas, between the different sections of the pump. Note that friction causes pressure losses regardless of the direction of flow. The pressure losses due to friction in the nozzle are:
where is the value of the parameter Primary flow nozzle loss coefficient.
The pressure loss due to friction in the suction flow through the annular gap is:
where is the value of the parameter Secondary flow entry loss coefficient.
The pressure loss due to friction in the throat is:
where is the value of the Throat loss coefficient parameter.
The pressure loss due to friction in the diffuser is:
where is the value of the Diffuser loss coefficient parameter.
Note that the sign corresponds to negative flow from the throat in the direction of port B. The losses are determined for the areas of highest velocity in the flow. For this reason, a throat area equal to the diffuser inlet area is used in the diffuser loss equation.
Saturation pressure in the nozzle
Cavitation occurs when the pressure value falls below the vapour saturation pressure in the low pressure region. This creates vapour cavities in the liquid and prevents the flow through the pump from increasing further. A flow limit can be set by setting a value in Minimum nozzle pressure beyond which the liquid velocity will remain constant. The total change in pump pressure depends on this nozzle outlet pressure threshold. Between the nozzle and diffuser, the pressure change will be defined as
or as , whichever is smaller.
The total pressure change in the nozzle is:
The total pressure change in the annular gap is:
Assumptions and limitations
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The driving fluid and the suction fluid are the same.
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It is assumed that mixing at the throat is uniform and complete.
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The nozzle inlet orifice is much larger than the outlet orifice and the annular gap for the suction fluid is much smaller than the inlet orifice.
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Pressure changes in the nozzle are not modelled for reversible flows.
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Cavitation effects are modelled by limiting the maximum flow rate at the throat.
Ports
Conserving
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A
—
moving fluid port
isothermal liquid
Details
A port for the entry of the driving fluid.
| Program usage name |
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B
—
mixed fluid port
isothermal liquid
Details
Mixed fluid outlet port.
| Program usage name |
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#
S
—
suction port
isothermal liquid
Details
Suction fluid inlet port.
| Program usage name |
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Parameters
Parameters
#
Nozzle area —
nozzle inlet area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The cross-sectional area of the orifice at the widest point of the nozzle. The moving fluid enters the jet pump through the nozzle.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Nozzle to throat area ratio — ratio of the cross-sectional areas of the nozzle outlet and throat
Details
Characteristic ratio of cross-sectional areas of nozzle outlet and throat.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Diffuser inlet to outlet area ratio — ratio of cross-sectional areas of the inlet and outlet aperture of the diffuser
Details
Characteristic ratio of the cross-sectional areas of the inlet and outlet orifices of the diffuser.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Primary flow nozzle loss coefficient — nozzle friction loss coefficient
Details
Characterises the pressure loss in the moving flow due to friction in the nozzle.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Secondary flow entry loss coefficient — friction loss coefficient at the inlet of the suction duct
Details
Characterises the pressure loss in the suction flow due to friction at the inlet of the suction duct.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Throat loss coefficient — friction loss coefficient in the neck
Details
Characterises the pressure loss in mixed flow due to friction in the throat.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Diffuser loss coefficient — friction loss coefficient in the diffuser
Details
Characterises the pressure loss in the mixed flow due to friction in the diffuser.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Minimum allowable nozzle pressure —
minimum nozzle outlet pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
The maximum allowable pressure change in the jet pump. If the nozzle outlet pressure falls below this value, the unit simulates the cavitation effect by limiting the fluid velocity to the velocity at the minimum nozzle pressure.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |