Ejector (G)

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The ejector in the gas network.

blockType: EngeeFluids.Gas.Turbomachinery.Ejector

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/Physical Modeling/Fluids/Gas/Turbomachinery/Ejector (G)

Description

Block Ejector (G) simulates an ejector in a gas network. The ejector directs the primary high-pressure flow through a nozzle with a reduced critical cross-section, creating a low-pressure jet that draws in the secondary flow. The expansion of the primary jet creates a critical nozzle cross-section for the secondary flow. The block assumes that two streams are mixed at the same pressure, and the combined stream exits through a diffuser to restore pressure. The primary and secondary streams must consist of the same gas.

The ejector can be used as a pump or compressor to supply secondary liquid. Unlike a pump or compressor, there is no external source of mechanical energy, and the primary high-pressure liquid serves as the energy source for supplying the secondary fluid.

Geometry of the ejector

The primary high-pressure flow enters the ejector at the point and it passes through a tapering-expanding nozzle with a critical cross-sectional area. , which is defined by the parameter Primary nozzle throat area. The ejector blocks the primary flow in the critical section of the nozzle (point ) and accelerates it to a supersonic low-pressure jet at the outlet of the primary nozzle (point ). The low pressure of the supersonic jet of the primary stream draws in the secondary stream at the point around the nozzle.

The supersonic primary flow jet continues to expand and decrease pressure outside the nozzle outlet until it reaches its largest area in the expanded primary flow jet (point ). The expansion of the supersonic primary flow jet creates a fictitious aerodynamic critical nozzle section for the secondary flow at the point , which is located in the same place as the dot . The secondary flow is also blocked in the aerodynamic critical section of the nozzle. After passing through the aerodynamic critical section of the nozzle, the primary and secondary streams mix under the same pressure (point ). If the mixed flow is still supersonic, the flow causes a compaction surge in the mixing chamber at the point , and the diffuser (dot ) slows down the mixed flow by increasing the outlet pressure.

This diagram describes the ejector, where

point — primary flow input;
point — secondary flow input;
point — critical cross-section of the primary nozzle;
point — primary nozzle outlet;
point — expanded primary flow jet;
point — the aerodynamic critical section of the secondary flow nozzle;
point — mixed flow;
point — compression surge in the mixing chamber;
point — diffuser output.

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Mass consumption

The ejector accelerates the primary gas flow through the nozzle. The mass flow rate of the primary flow is

where

— parameter value Primary nozzle throat area;
— the ratio of heat capacities, where — specific heat capacity at constant pressure and — specific heat capacity at constant volume;
— parameter value Efficiency for primary flow through nozzle;
— pressure at the primary flow inlet;
— pressure after mixing of primary and secondary streams;
— the density at the primary flow inlet.

The primary flow draws the secondary gas stream into the intake chamber and accelerates it towards the fictitious aerodynamic critical section of the nozzle created by the expanding primary jet. The mass flow rate of the secondary flow is

where

— the area of the fictitious aerodynamic critical section of the nozzle. The block calculates the value based on the expansion of the primary stream jet.
— parameter value Efficiency for secondary suction flow;
— pressure at the secondary flow inlet;
— density at the secondary flow inlet.

By , where , the primary flow is blocked, and the mass flow reaches its maximum value

By The secondary flow is blocked, and the mass flow reaches its maximum value.

Ratios of primary and secondary flows

The expansion of the cross-sectional area of the supersonic primary flow jet is determined by the ratio

where — parameter value Efficiency for primary flow expansion.

The block uses the area of the expanded supersonic primary flow jet to calculate the area of the fictitious aerodynamic critical section of the secondary flow nozzle

where

— parameter value Area ratio of mixing chamber to throat;
— parameter value Area ratio of nozzle exit to throat.

The velocity of the primary flow of the expanded jet is

The velocity of the secondary flow in the aerodynamic critical section of the nozzle is

The secondary flow rate is limited by a preset value. By The secondary flow velocity reaches its maximum value

The mixing model

After the fictitious aerodynamic critical section of the nozzle, the primary and secondary streams mix under the same pressure. The temperature of the mixed flow is

where

— the temperature of the primary flow at the inlet. The block assumes that this value is equal to the braking temperature of the primary flow, since the kinetic energy at the inlet is negligible compared to the inside of the ejector.
— the temperature of the mixed flow.
— the temperature of the secondary flow at the inlet. The block assumes that this value is equal to the deceleration temperature of the secondary flow, since the kinetic energy at the inlet is negligible compared to the inside of the ejector.
— specific gas constant.
— the flow rate after mixing the primary and secondary streams.
— the mass flow rate after mixing the primary and secondary streams, i.e. .

The momentum balance in the mixing area is

where — the cross-sectional area after mixing the primary and secondary streams.

The pressure terms are excluded due to the assumption of mixing under the same pressure, and the velocity of the mixed flow is

where — parameter value Efficiency for mixing.

The Mach number of the mixed flow is

Flow ratio in a diffuser with mixed flow

If, after mixing, the flow becomes supersonic, i.e. , a compaction surge occurs. The pressure increase after the seal jump is equal to

where — the Mach number after mixing the primary and secondary streams.

The Mach number after the seal jump is

After the seal jump, the diffuser slows down the flow, increasing the pressure. The block assumes that the kinetic energy at the outlet of the diffuser is negligible, and slows the flow down to the braking pressure. :

If , then there is no compaction jump and

The ratio between the mixing pressure and the pressure at the outlet of the diffuser it has the form

Critical operation mode

In normal operation, the primary flow is under high pressure and is blocked during operation. The unit can also operate if the secondary flow is blocked. If both the primary and secondary streams overlap, the block is operating in critical mode.

Critical mixing pressure It represents a low pressure threshold that causes both primary and secondary flows to overlap.:

The block uses the same equations as above, with the substitution on , to calculate the critical pressure at the diffuser outlet . If the actual outlet pressure is greater than the critical outlet pressure of the diffuser, then the ejector is in a subcritical state, and the unit correlates the mixing pressure with the outlet pressure of the diffuser. If the actual outlet pressure is less than the critical outlet pressure of the diffuser, then the ejector is in critical condition, and the block limits the mixing pressure to the critical mixing pressure. This means that

Assumptions and limitations

The block uses isentropic formulas of an ideal gas to derive the model equations.
The unit accounts for losses caused by friction, mixing, expansion waves, and compaction surges at the nozzle outlet using empirical loss coefficients.
After the primary stream exits the nozzle, the streams do not mix until the primary stream is fully expanded.
After expansion, the streams mix at the same pressure.
The kinetic energy at the inlet of the primary flow, at the inlet of the secondary flow and at the outlet of the diffuser is negligible compared to the kinetic energy of the flow inside the ejector.
The flow is stationary and one-dimensional.
The flow is adiabatic.
The results of backflow modeling may be inaccurate.

Ports

Conserving

# A — primary stream input
gas

Details

An undirected port connected to the primary stream input.

Program usage name

primary_inlet

# B — exit
gas

Details

A non-directional port connected to the diffuser outlet.

Program usage name

outlet

# S — secondary stream input
gas

Details

An undirected port connected to the secondary stream input.

Program usage name

secondary_inlet

Parameters

# Primary nozzle throat area — the area of the critical section of the primary nozzle
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The area of the critical section of the primary flow nozzle.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.0001 m^2`
Program usage name	`throat_area`
Evaluatable	Yes

# Area ratio of nozzle exit to throat — the ratio of the area of the outlet section of the nozzle to the area of the critical section of the nozzle

Details

The ratio of the area of the outlet section of the nozzle to the area of the critical section of the nozzle. This parameter limits the size of the secondary aerodynamic critical section.

Default value	`3.0`
Program usage name	`nozzle_area_ratio`
Evaluatable	Yes

# Area ratio of mixing chamber to throat — the ratio of the area of the mixing chamber to the area of the critical section of the nozzle

Details

The ratio of the area of the mixing chamber to the area of the critical section of the nozzle. The difference between the area of the mixing chamber and the area of the expanded primary flow jet creates a fictitious aerodynamic critical section for the secondary flow.

Default value	`8.0`
Program usage name	`mixing_area_ratio`
Evaluatable	Yes

# Minimum area ratio of secondary throat to primary throat — limitation on the ratio of the aerodynamic areas of the secondary and primary critical sections of the nozzle

Details

The minimum ratio of the aerodynamic areas of the secondary and primary critical sections of the nozzle. The block does not allow the area of the fictitious aerodynamic critical section to fall below this value. To avoid reaching this minimum, increase the value of the parameter Area ratio of mixing chamber to throat.

Default value	`0.1`
Program usage name	`min_secondary_area_ratio`
Evaluatable	Yes

# Report when secondary throat area falls below minimum — notification of a drop in the area of the secondary critical section of the nozzle below the minimum
None | Error

Details

The unit may do nothing or issue an error when the area of the secondary critical section of the nozzle falls below the minimum set by the parameter Minimum area ratio of secondary throat to primary throat.

Values	`None` \| `Error`
Default value	`None`
Program usage name	`secondary_area_assert_action`
Evaluatable	Yes

# Efficiency for primary flow through nozzle — efficiency of the primary flow through the nozzle

Details

An empirical coefficient that takes into account the reduction in the mass flow rate of the primary flow due to losses in the primary nozzle.

Default value	`0.95`
Program usage name	`primary_loss`
Evaluatable	Yes

# Efficiency for secondary suction flow — efficiency of the secondary suction flow

Details

An empirical coefficient that takes into account the reduction in the mass flow rate of the secondary stream due to losses during suction of the secondary stream.

Default value	`0.85`
Program usage name	`secondary_loss`
Evaluatable	Yes

# Efficiency for primary flow expansion — efficiency of primary flow expansion

Details

An empirical coefficient that takes into account the decrease in the expansion of the primary stream jet due to mixing losses.

Default value	`0.88`
Program usage name	`expansion_loss`
Evaluatable	Yes

# Efficiency for mixing — efficiency of the mixed flow velocity due to mixing

Details

An empirical coefficient that takes into account the decrease in the speed of the mixed flow due to losses in the mixing chamber.

Default value	`0.84`
Program usage name	`mixing_loss`
Evaluatable	Yes

# Cross-sectional area at port A — port cross-sectional area A
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the port A.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`primary_inlet_area`
Evaluatable	Yes

# Cross-sectional area at port B — port cross-sectional area B
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the port B.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`outlet_area`
Evaluatable	Yes

# Cross-sectional area at port S — port cross-sectional area S
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the port is S.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`secondary_inlet_area`
Evaluatable	Yes

Literature

Huang, B. J., et al. «A 1-D analysis of ejector performance.» International journal of refrigeration 22.5 (1999): 354–364.
Chen, WeiXiong, et al. «A 1D model to predict ejector performance at critical and sub-critical operational regimes.» International journal of refrigeration 36.6 (2013): 1750–1761.