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Applied Energy 130 (2014) 679–684
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
Experimental and numerical analysis of supersonic air ejector
Daotong Chong, Mengqi Hu, Weixiong Chen ⇑, Jinshi Wang, Jiping Liu, Junjie Yan
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
h i g h l i g h t s
The performance and flow field inside ejectors are studied numerically and experimentally.
The pressures before the second shock position remain constant during the critical mode.
NXP has an optimal value for entrainment ratio, but no effect on the critical discharged pressure.
a r t i c l e
i n f o
Article history:
Received 19 November 2013
Received in revised form 28 January 2014
Accepted 10 February 2014
Available online 28 February 2014
Air ejector
Entrainment ratio
Static wall pressure
a b s t r a c t
The present paper performs experimental and numerical investigations on the global performance and
internal flow of a supersonic air ejector. The effects of operation parameters and geometrical factor on
the air ejector performance have been analyzed. The results show that: the static wall pressure and
axisymmetric line static pressure remain constant in critical mode under different discharged pressures,
but they both increase in sub-critical mode with the increase of the discharged pressure. The shock
position of the mixed fluid moves upstream in critical mode. The second shock position disappears in
sub-critical mode. The experimental and numerical results indicate that there exists an optimal nozzle
exit position (NXP) corresponding to maximum entrainment ratio, but the critical value of discharged
pressure is almost independent of NXP.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Supersonic ejector is a simple mechanical device where two
gases are allowed to mix and recompress. The primary gas with
high total energy can transfer part of its mechanical energy to
the secondary gas with low energy in supersonic ejector without
any moving parts. Today, in view of pressures for protecting the
environment, ejectors are becoming popular in industrial fields
as an energy saving and emission reduction technique [1]. We
are using them in many engineering fields, such as heat pump in
the district-heating system [2], pressure booster in natural gas
industry [3,4]. The steam jet refrigeration is the most widely used
device because of its relative simplicity and low capital cost compared to an absorption refrigerator, and the most important benefit
is that the ejector refrigeration system could be powered by the
low-grade heat [5,6].
Nevertheless the low performance in present conditions is the
main problem, which primarily limits the widespread use in industry. The ejector performance is greatly affected by the mixing
process between primary flow and secondary flow. Therefore, it
⇑ Corresponding author. Tel.: +86 29 82667753; fax: +86 29 82665359.
E-mail address: [email protected] (W. Chen).
0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.
is very necessary to investigate the mixing mechanism of ejector
in order to improve the ejector performance.
Two mixing models about ejector mixing process were
proposed by Keenan et al. [7,8]. The first mixing model is called
as constant area model, assuming that the gas obeys the law of
ideal gas and the flow is isentropic. The second model named constant pressure model has been widely accepted and developed by
many researchers, and widely used due to its superior performance. The choking phenomenon was first proposed by Munday
and Bagster [9]. They proposed that the high and the low pressure
flows reached the same pressure at some place inside the mixing
chamber, which is named as an effective area. Huang et al. [10] further proposed that the effective area was located in the constant
area section, and found out that the effective area position was
affected by operation conditions. Based on this assumption, their
1D model could accurately calculate the entrainment ratio when
the discharged pressure was less than critical discharged pressure
[11]. Later, Zhu et al. [12] proposed a 2D exponential model to
predict the velocity distribution in ejector, however the pressure
is still assumed to be uniform in the radial direction. Zhang et al.
[13] explored the behavior of direct flow induction based on
pressure exchange utilizing supersonic wave structure in a
crypto-steady mode, their results indicated that very high
D. Chong et al. / Applied Energy 130 (2014) 679–684
diameter, mm
Length, mm
mass flow rate, kg/s
nozzle exit position, mm
pressure, MPa
generalized source
time, s
entrainment ratio, %
generalized diffusion coefficient
compressor–expander efficiencies are possible even in the presence of strong supersonic wave structure. Although these models
are helpful to predict the ejector performance, they cannot accurately predict the internal flow process along the ejector because
of the one-dimensional model.
To study the mixing mechanism of ejectors, researchers focused
on the local phenomenon of ejector by experimental study. Desevaux et al. [14] paid their attention to investigate the flow fields inside the ejector by experimental work. They obtained the
centerline static pressure through a slide measuring system. Then,
Desevaux [15] obtained the mixing zone roughly using Rayleigh
scattering method. Subsequently, Desevaux et al. [16] applied laser
tomography method to study the choking phenomena, and gained
the good agreement with CFD results. Recently, the numerical
methods have been an important tool for researchers to study
the mixing process inside the ejector and predict the ejectors’ performance. These methods which are quiet economical l to investigate the internal flow phenomena and mixing mechanism of
ejectors. In Hemidi et al. [17] numerical work, some local flow features were revealed and relation between overall performance and
local flow were also investigated. Bartosiewicz et al. [18,19] investigated the ejector using CFD technique. They proposed that the
RNG k-epsilon model was suitable to represent the entrainment
ratio of the ejector.
Though some researchers have carried out to investigate the
internal flow inside the ejector, the efforts are still needed to go
deep into the mixing mechanism inside the ejector. The present
paper focuses on the entrainment ratio and the static wall pressure
distributions along the mixing tube for air ejectors by experiment.
Moreover, a 2D CFD model is developed to study the local phenomena and global performance of air ejector. The operation and
geometrical factors on the ejector overall and local performance
are investigated. Then the internal flow fields are analyzed experimentally and numerically.
2. Experimental setup
An air ejector experimental system is set up to investigate the
global and local performance, as shown in Fig. 1. The pressurized
air then expands in the primary nozzle, and the secondary airflow
is induced and accelerated due to pressure difference and flows
into the mixing chamber. Then these two streams are mixed
together and exchange mass, momentum and energy in the mixing
tube. Finally, the discharged air will be exhausted into the atmosphere. The air flow rates of primary flow and secondary flow are
both controlled by ball values, and the corresponding pressure is
adjusted by pressure regulator behind the ball value, and the
discharged pressure is also controlled by the pressure regulator.
The air flow rates are both then measured by vortex shedding flowmeter with the accuracy of 1.5%. The experimental uncertainty
density, kg/m3
generalized variable
primary air flow
secondary air flow
discharged air flow
analysis was executed using the method of estimation which was
proposed by Moffat [20]. The uncertainty of the primary air flow
rate is less than 2.1%, and the secondary air flow rate less than
3.1%. The static wall pressure along the mixing tube is measured
by four static pressure sensors with accuracy of 0.5%, as shown
in Fig. 2.
The design parameters, such as primary and secondary pressures, used to create the supersonic air ejector are shown in Table 1.
The design of structural parameters has been essentially determined by the results of research [3,4]. A simplified schematic of
the air ejector installed in this experimental system is shown in
Fig. 2. The primary nozzle (A), secondary nozzle (B), mixing chamber (C), mixing tube (D) and diffuser (E) are the main parts of air
ejector, the material is stainless steel. The other parts of the ejector
are made up of carbon steel.
3. 2D model of air ejector
The commercial CFD software package, FLUENT, is adopted to
simulate the global performance and mixing processes of the
supersonic air ejector. All computational domains are taken from
the experimental air ejector. Considering the model is in a regular
pattern, mapped mesh containing only structured elements are
presented. The flow region is regular and symmetric, so the axisymmetric space is chosen to simulate the whole flow process in
the ejector. The mesh profile with 295810 quadrilateral elements
is presented in Fig. 3, which has been proven to be sufficient to represent the ejector flow field. The enhanced wall function is selected
and the pressure gradient effect is considered to ensure that the air
flow adjacent to the ejector walls is realistic, when the value of Y+
is about 1.
The air flows passing through the supersonic ejector are supposed to be compressible flow, and the controlling equations of
mass conservation, momentum conservation and energy conservation are in steady-state forms. The conservation equations are
implicitly solved. The SIMPLEC algorithm is applied to get the pressure field. The second order upwind scheme is used to discretize
the convective terms. The RNG k-epsilon turbulence viscosity model, which is proved for better simulate the ejector performance
than the other models, is chosen to simulate the turbulent flow
The conservation equations of the supersonic air ejector are in
the general form:
þ divðqV uÞ ¼ divðCgraduÞ þ S
where generalized variable u, generalized diffusion coefficient U
and generalized source S denote different parameters in different
equations, and they are related with each other [21].
The working fluid used is air. The ideal gas model is used to
approximately deal with its density. Other properties are kept
D. Chong et al. / Applied Energy 130 (2014) 679–684
Fig. 1. Schematic of the apparatus.
Fig. 2. Structure of the air ejector.
Table 1
Design parameters of air ejector.
Primary pressure
Primary air flow rate
Secondary pressure
Secondary air flow rate
Discharged pressure
Throat diameter of primary nozzle
Diameter of mixing tube
Length of mixing tube
Inclination angle of diffuser
Inclination angle of mixing chamber
Nozzle exit position
Fig. 3. Mesh generation of air ejector.
constant obtained from Fluent data. The inlet types of primary flow
and secondary flow are both pressure-inlet type, and the values are
set to be the primary inlet pressure and secondary inlet pressure,
respectively. Meanwhile, the mixed flow outlet is set as pressureoutlet type. All the wall surfaces are set to be adiabatic since the
heat loss at wall surfaces has less impact on the solution.
During the simulation, two converging criteria are adopted to
obtain the converged solution: (1) The mass flow difference
between the two inlet flows (primary flow and secondary flow)
and the outlet flow (discharged flow) of the air ejector is no more
than 108 kg/s. (2) All residual results are no larger than 106.
4. Results and discution
4.1. Effect of operating parameter
The entrainment ratio is defined as a = mS/mP. When using
entrainment ratio as index, the ejector can be operated in three different modes: the critical operation mode, sub-critical operation
mode and back flow operation mode. When the discharged pressure is smaller than the critical value, the entrainment ratio is
independent of the discharged and the chocked phenomena occur
with the primary flow and secondary flow, and operation mode is
called critical mode. With the increase of discharged pressure and
larger than the critical value, the entrainment ratio are linearly decreased with the discharged pressure because the secondary flow
is not chocked, and this is called sub-critical mode. With further increase of discharged pressure, the secondary flow may be reversed
into the secondary nozzle because of high discharged pressure,
which deduced negative value of entrainment ratio. This is called
back flow mode.
To research the influence of discharged pressure to the ejector
performance, the entrainment ratios and static wall pressures are
all measured when PP is 1.0 MPa, PS is 0.5 MPa and PD ranges from
0.4 MPa to 0.7 MPa. As it can be seen from Fig. 4, the entrainment
ratio does not immediately reduce when the discharged pressure
increases. But when the discharged pressure is larger than the critical pressure, the entrainment ratio starts to decrease with the increase of discharged pressure. The results of experiment and
D. Chong et al. / Applied Energy 130 (2014) 679–684
Fig. 4. Variation of entrainment ratio with discharged pressure.
Fig. 6. Comparison of experimental data and CFD results for different operation
conditions (a) deviation of entrainment ratios and (b) deviation of static wall
Fig. 5. Experimental data of static wall pressures with different discharged
numerical simulation agree well on the trend and the value of critical pressure. Fig. 5 gives the values of four static pressure measurements fixed along the mixing tube under different
discharged pressure. As shown in the figure, the static wall pressures remain unchanged before the discharged pressure reaches
the critical value. And the static wall pressure increases remarkably when the discharged pressure is larger than the critical value.
To investigate the accuracy of the numerical model, the error
analysis is made. As shown in Fig. 6(a), the deviations are less than
15% when the ejector operates in critical mode and less than 30% in
sub-critical mode. The deviations of entrainment ratio are in a reasonable range, so the RNG k-epsilon model can predict the global
performance with considerable accuracy. The deviations of static
wall pressure are illustrated in Fig. 6(b). The figure shows that
the deviation is less than 20%, so the enhanced wall function can
obtain good forecasting results in static wall pressure. Based on
the above, a conclusion could be drawn that the present CFD model
can be used to simulate the overall performance and local phenomena accurately for air ejectors. So the distribution of static wall
pressure, axisymmetric line static pressure and Mach contour lines
obtained from numerical simulation can be used to analyze the
internal flow field of air ejector.
Static wall pressure and axisymmetric line static pressure along
the ejector is shown in Fig. 7 based on the numerical data. The
curves markedly differ between critical mode and sub-critical
Fig. 7. Numerical data of static wall pressure and axisymmetric line static pressure
with discharged pressure.
mode. As shown in Fig. 7, when the discharged pressure is less than
the critical value (0.6 MPa), the static wall and axisymmetric line
static pressure in the mixing tube change repeatedly because of
the presence of consecutive shocks. The shock train can lead to
strong momentum transfer. After the shock train the velocity of
primary flow is still higher than the secondary flow. The nonuniformity in velocity results in intensive momentum transfer. These two
D. Chong et al. / Applied Energy 130 (2014) 679–684
fluids then intermix in the mixing tube by momentum transfer.
After the mixed air flows downstream to diffuser, at some section,
the second shock is generated, which induces that the supersonic
flow changes to subsonic flow and the pressure abruptly increases.
This section is regarded as the position of second shock, which is
affected by discharged pressure in critical mode. As shown in Figs. 7
and 8, the second shock’s position moves upstream as the discharged pressure rises from 0.4 MPa to 0.6 MPa. When the discharged pressure reaches to the critical value, the second shock
will move close to the exit of chamber tube. Moreover, the static
pressure along the mixing tube and the chock position remains unchanged when the discharged pressure is less than critical value. It
indicates that, the change of downstream condition can affect the
second shock’s position in critical mode, while the information of
downstream cannot travel back to the upstream. So the mixing
behavior of the two fluid streams will not be affected and the
entrainment ratios remain constant.
As shown in Figs. 7 and 8, when the discharged pressure is larger than 0.6 MPa (critical value), the static wall and axisymmetric
line static pressure along the mixing tube and diffuser will change
continuously without abruptly process. It can be concluded that
the second shock disappears and the first and second series of oblique shocks combine with each other. Therefore, the information
of downstream will travel back to the mixing tube. So the static
wall pressure increases as the discharged pressure increases and
the mixing process is disturbed, which results in the decrease of
the entrainment ratio.
Fig. 9. Experimental data of entrainment ratios with different NXPs.
4.2. Effect of structure parameter
The structural parameters of air ejector involve the geometric
parameters of the main parts of air ejector. These parameters have
different influences on the ejector performance. In the present
study, the influence of NXP on the ejector performance is performed. The NXP, which means of primary nozzle exit position, is
one of the most important structure parameters.
The entrainment ratios and static wall pressures are all measured when the NXP is 2.4 mm, 2.8 mm, 3.6 mm and 4.8 mm,
respectively. Fig. 9 shows the relation between the entrainment
ratio of critical mode and NXP. As shown in this figure, the entrainment ratio increases firstly and then decreases when the NXP
Fig. 10. Experimental data of static pressures with different NXPs.
Fig. 11. Experimental data of entrainment ratios with different discharged
Fig. 8. Numerical data of Mach number contour lines with different discharged
increases. Moreover, the entrainment ratio reaches the maximum
when the NXP is 2.8 mm which is the design value. The higher
the secondary pressure is, the greater the impact on entrainment
ratio can be. Experimental value of pressure measuring point 1
fixed in the exit of secondary nozzle with different NXP is
D. Chong et al. / Applied Energy 130 (2014) 679–684
(2) For different NXPs, the entrainment ratio increases firstly
and then decreases, obtained through the experimental data.
The flow fields analyzed by the experimental and numerical
methods prove that there exists an optimum NXP, which is
corresponding to the maximum entrainment ratio, but the
NXP almost has no influence on the critical discharged
These results shows that the CFD method, the RNG k-epsilon
turbulence coupled with enhanced wall function, offers an efficient
tool to study both global and local ejector performance. Also CFD
visualization represents a detained flow field and insightful study
inside the ejector flow. These results help to improve the design
and application of the supersonic air ejector.
Fig. 12. Numerical data of static wall pressure with different NXPs.
illustrated in Fig. 10. As shown in this figure, the static wall
pressure of the exit of secondary nozzle decreases firstly and then
increases when the NXP increases. It reaches the minimum value
when the NXP is 2.8 mm, which indicates that the NXP has a great
impact on the pressure difference of secondary nozzle. The lower
the pressure of measuring point 1, the higher the pressure difference of secondary nozzle. So when the NXP is 2.8 mm, the entrainment ratio reaches the maximum.
The lifting-pressure performance, which is represented by the
critical discharged pressure, is another important index of ejector
performance. The higher the critical discharged pressure is, the
better the lifting-pressure performance obtains. As shown in
Fig. 11, the critical discharged pressure remains constant with
different NXP. It can be concluded that the lifting-pressure performance is little affected by NXP. Fig. 12 gives the static wall pressure distribution along the ejector. The first series of oblique
shocks are influenced by the change of NXP. So the mixing process
is disturbed, the entrainment ratio will change by NXP. But the
position and the strength of second shock remains unchanged
when the NXP changes. It indicates that the mixing flow is choked
in the same position, so the critical discharged pressure is
5. Conclusion
In this study, the experimental and numerical methods have
been used to research the global performance and interior flow
behaviors of air ejector. The numerical results are in good agreement with the experimental data. The effects of operation parameters and geometrical parameter (NXP) on the ejector performance
are studied, and the numerical visualization is employed to analyze
the local phenomena and global performance of supersonic air
ejector. Based on the above work, the following results can be
(1) The static wall pressure along the axisymmetric line remains
unchanged when the air ejector works in critical mode, but
increases remarkably in the sub-critical mode with the
increase of discharged pressure. Meanwhile, the position of
second shock moves upstream to the exit of mixing tube
as the discharged pressure increases. In sub-critical mode,
the static wall and axisymmetric line static pressure along
the mixing tube increase and the second shock disappears
as the discharged pressure increases. The entrainment ratios
remain constant due to the mixing process is independent of
discharged pressure.
The present work is funded by the National Natural Science
Foundation of China (Nos. 51006081 and 51125027), and National
Basic Research program of China (973 Program) (No. 2009CB
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