Steam Jet Ejector

This Steam Jet Ejector unit model:
  • Simulates the performance of a steam jet ejector for thermal vapor compression.

  • Uses semi-empirical correlations for entrainment ratio, pressure correction factor (PCF), and temperature correction factor (TCF), based on El-Dessouky (1997).

  • Operates in steady-state only.

  • Assumes the discharge mixture pressure equals its saturation pressure.

Degrees of Freedom

In addition to the inlet state variables (i.e., temperature, pressure, and component flowrates for motive steam and entrained vapor), the Steam Ejector model has at least 1 degree of freedom that must be fixed for the unit to be fully specified. Typically, the following variables are fixed:

  • Entrainment ratio

  • Compression ratio

Model Structure

This Steam Ejector model consists of state blocks for the properties of the motive steam inlet, entrained vapor inlet, and discharge mixture. It incorporates semi-empirical equations to model key performance parameters.

Sets

Description

Symbol

Indices

Time

\(t\)

[0]

Inlet/Outlet

\(x\)

[‘in’, ‘out’]

Phases

\(p\)

[‘Liq’, ‘Vap’]

Components

\(j\)

[‘H2O’]

Performance Metrics

Metric

Equation

Entrainment Ratio

\(Ra = \frac{\dot{m}_{motive}}{\dot{m}_{entrained}}\)

Compression Ratio

\(CR = \frac{P_s}{P_{ev}}\)

Variables

Description

Symbol

Variable Name

Units

Bounds

Entrainment Ratio

\(Ra\)

entrainment_ratio

Dimensionless

<4

Compression Ratio

\(CR\)

compression_ratio

Dimensionless

>1.89

Pressure Correction Factor

\(PCF\)

PCF

Dimensionless

N/A

Temperature Correction Factor

\(TCF\)

TCF

Dimensionless

N/A

Motive Steam Pressure

\(P_m\)

properties_motive_steam[0].pressure

kPa

[100, 3500]

Entrained Vapor Pressure

\(P_{ev}\)

properties_entrained_vapor[0].pressure

kPa

N/A

Discharge Mixture Pressure

\(P_s\)

properties_discharge_mix[0].pressure

kPa

N/A

Equations

Description

Equation

Pressure Correction Factor

\(PCF = 3 \times 10^{-7} P_m^2 - 0.0009 P_m + 1.6101\)

Temperature Correction Factor

\(TCF = 2 \times 10^{-8} T_{ev}^2 - 0.0006 T_{ev} + 1.0047\)

Entrainment Ratio Model

\(Ra \times TCF = 0.296 \frac{P_s^{1.19}}{P_{ev}^{1.04}} \left(\frac{P_m}{P_{ev}}\right)^{0.015} PCF\)

Entrainment Ratio Definition

\(Ra = \frac{\dot{m}_{motive}}{\dot{m}_{entrained}}\)

Compression Ratio

\(CR = \frac{P_s}{P_{ev}}\)

Class Documentation

References

El-Dessouky, H., Modeling and simulation of thermal vapor compression desalination plant. Symposium on Desalination of Seawater with Nuclear Energy, Taejon, Republic of Korea, 26-30 May, 1997.