SCIENCE CHINA
Technological Sciences
• Article •
July 2015 Vol.58 No.7: 1218–1233
doi: 10.1007/s11431-015-5846-8
High mixing effectiveness lobed nozzles and mixing mechanisms
SHENG ZhiQiang, CHEN ShiChun, WU Zhe & HUANG PeiLin*
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Received December 23, 2014; accepted May 14, 2015; published online June 11, 2015
For a circular lobed nozzle with the exit plane displaced from the center body, adding a central plug at exit or replacing the
nozzle with an alternating-lobe nozzle can improve the mixing effectiveness. In this study, numerical investigations of jet
mixing in the lobed nozzles with a central plug and alternating-lobe nozzles in pumping operation were conducted. The effects
of the central plugs with the wake ranging from attached to separated flow on the mixing were analyzed, along with the mechanism of improving the mixing performance in a “sword” alternating-lobe nozzle. The simulation results reveal that the
large-scale mixing rate, which is dominated by streamwise vortices, is related to the intensity of the attainable heat and mass
transfer in the streamwise vortices. The effects of the streamwise vortices on the normal vortex ring are virtually a manifestation of the heat and mass transfer/mixing process of the streamwise vortices. The simulation results also show that the central
plug with the attached rear-flow performs better in improving the mixing effectiveness and pumping performance; on the contrary, if the rear-flow is separated, more pressure loss will be induced. In particular, a completely separated flow over the rear
of the central plug will severely degrade the attainable heat and mass transfer in the streamwise vortices. For the sword alternating-lobe nozzle, wider sword deep troughs help to increase the flux of the secondary stream around the core region and delay the confluence of the primary stream in the region between the deep and shallow troughs. Thus, the mixing is improved in
the middle and posterior segments. Compared to the lobed nozzle with a central plug, the improved sword alternating-lobe
nozzle can achieve a higher mixing effectiveness with much less pressure loss, which is preferred in situations when the power
loss of the engine is restricted.
jet mixing, lobed nozzle, mixing effectiveness, streamwise vortices, heat and mass transfer
Citation:
Sheng Z Q, Chen S C, Wu Z, et al. High mixing effectiveness lobed nozzles and mixing mechanisms. Sci China Tech Sci, 2015, 58: 12181233, doi:
10.1007/s11431-015-5846-8
1 Introduction
The unusual configuration of the lobed nozzle can increase
the interfacial area between the primary and secondary
streams [1], and simultaneously induce cross flows of the
primary and secondary streams. These cross flows are flows
of opposite directions and convolute to form inviscid
streamwise vortices in the wake [2]. Moreover, the normal
vortex ring formed at the interface of the streams with a
large gradient of the axial velocity will interact with the
streamwise vortices [3]. At the velocity ratio for the primary
stream to the secondary stream close to 1.0, the dominating
factors for the mixing are the interfacial area and the
streamwise vortices, and the importance of the streamwise
vortices and their interaction with the normal vortex ring
rises as the velocity ratio increases [1,4–6].
Compared to other types of nozzles, the lobed nozzle can
mix the primary and secondary streams with a higher effectiveness while inducing a lower pressure loss [7]. Consequently, it has been widely applied in the fluid engineering
field for heat and mass transfer. For instance, the lobed nozzle has been employed in turbofan engines to mix the core
*Corresponding author (email: peilin_huang@sina.com)
© Science China Press and Springer-Verlag Berlin Heidelberg 2015
tech.scichina.com link.springer.com
Sheng Z Q, et al.
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and bypass flows to augment thrust and reduce jet noise [8,
9] and in infrared suppressors to pump cool air and mix it
with the engine exhaust gas to suppress infrared radiation
[10–13]. In addition, it has been used for enhancing the
mixing between the fuel and air in combustion chambers to
improve the efficiency of combustion and reduce formation
of pollutants [14,15], and as air diffusion grilles in order to
insure more uniform flows and to reduce thermal discomfort
and draught sensation [16].
In contrast with the two-dimensional lobed nozzle and
the circular lobed nozzle with the exit plugged by a center
body, in the jet mixing of the circular lobed nozzle with the
exit plane displaced from the center body, the secondary
stream cannot penetrate into the core of the primary stream
[17,18], and there is still a large core region with high temperature. Conventional restructuring methods, such as scalloping [9,19–22] and scarfing [23], which are used to enhance the mixing performance of a lobed nozzle, cannot
help to improve the mixing in the core region; contrarily,
they worsen it, because the faster mixing around the periphery reduces the fraction of the secondary stream that can be
mixed in the core region. Currently, two efficient methods
are utilized to fix this problem: Adding a central plug at the
exit of the normal lobed nozzle [11,17,18] or replacing the
nozzle with an alternating-lobe nozzle [24–27].
The author of the present paper designed a “sword” alternating-lobe nozzle according to the mixing mechanisms
of a lobed nozzle and the geometrical characteristics of the
existing alternating-lobe nozzles. The effects of scalloping
and scarfing on the jet mixing of the sword alternating-lobe
nozzle have been investigated in [28]. The performances of
the existing alternating-lobe nozzles along with the sword
alternating-lobe nozzle, as well as their mixing mechanisms,
have been compared and analyzed in [29].
In this study, the effects of the central plugs with the
wake ranging from attached to separated flow on the jet
mixing of a lobed nozzle were investigated, and the sword
alternating-lobe nozzle was remodeled to improve its mixing performance. In pumping operation, the jet mixing of
the lobed nozzles with central plug and the alternating-lobe
nozzles are compared and the correlative mechanisms are
analyzed.
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12.1°, respectively. The diameters of the circles at the lobe
peaks and troughs are, respectively, 550 and 240 mm. The
distance from the exit to the entrance is 600 mm, and, when
taken the central plug, the exit has an equivalent diameter d
of 400 mm. The diameter of the largest section of the central plug is 200 mm, and it is located at the exit of NLN-1.
The central plug extends from the largest section forwards
and backwards, forming an ellipsoidal windward and a conical leeward segments, which are 200 and 250 mm in length,
respectively. The mixing duct is 1150 mm long, and its entrance is 100 mm ahead of the exit of the nozzle. The diameter D of the duct is 700 mm, which gives a length-todiameter ratio of the mixing segment, L/D, of 1.5. The lobed
nozzles with the central plugs No. 2 and No. 3 (PLN-2 and
PLN-3) are shown in Figure 2. For the three central plugs,
Figure 1
(Color online) PLN-1 in the mixer.
(a)
2 Geometrical configurations
(b)
Figure 1 shows the jet mixing model, wherein the nozzle is
a lobed nozzle with the central plug No. 1 (PLN-1). The
lobed nozzle without the central plug is referred to as the
normal lobed nozzle No. 1 (NLN-1) in this paper. The annular entrance of the nozzle is formed by two circles with
diameters 210 and 400 mm. The annular section is smoothly
transformed into a circular one through a cone of length
262.5 mm. The outward lobes are 44 mm wide, and the inward and outward lobe penetration angles are 12.9° and
Figure 2
(Color online) PLN-2 and PLN-3. (a) PLN-2; (b) PLN-3.
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the diameters of the largest sections and their locations are
the same, but the transitions from the windward segment to
the leeward segment are different from each other.
Figures 3(a)–(c) show a coplanar alternating-lobe nozzle
(CALN) and the sword alternating-lobe nozzles No. 1 and
No. 2 (SwALN-1 and SwALN-2), respectively. To generate
a SwALN, a part of the lobe troughs and side walls of the
normal lobed nozzles No. 2 and No. 3 (NLN-2 and NLN-3,
see Figures 3(d) and (e)) is removed first, as shown in Figures 3(f) and (g), with a scarfing angle of 40°, and then,
SwALN-1 is produced by smoothly extending a sword
spoiler from every other new trough of NLN-2, while
SwALN-2 is obtained by smoothly extending a sword
spoiler from each new wide trough of NLN-3. For the alternating-lobe nozzles in the present study, the locations and
penetration angles of the lobe peaks are the same as those of
the normal lobed nozzles, the diameters of the circles at the
deep and shallow troughs are 150 and 293.7 mm, respectively, and the equivalent diameters at the exit are close to
July (2015) Vol.58 No.7
those of NLN-1 and NLN-2. The basic dimensions of the
different lobed nozzles are given in Table 1, and the more
detailed dimensions are marked in Figures 1–3.
3 Numerical simulation method
The simulation domain is shown in Figure 4(a). Figure 4(b)
shows the surface mesh of SwALN-2. Owing to the complex geometry, tetrahedral cells were adopted to discretize
the simulation domain. Three-layer prism cells were used as
the boundary cells with the first layer height of 0.05 mm. As
indicated by the arrow in Figure 4(a), a refinement domain
was employed where drastic changes in the velocity and
temperature occur. For accurate simulation of the streamwise vortices, the maximum size of the cells in this domain
was about 15 mm. The number of cells in the refinement
domain was more than 20 million, and the number of those
outside of the domain was about 2.2 million.
(a) CALN
(b) SwALN-1
(d) NLN-2
(c) SwALN-2;
(e) NLN-3
(f) SwALN-1
(g) SwALN-2
Figure 3
(Color online) Alternating-lobe nozzles.
Sheng Z Q, et al.
Table 1
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Basic dimensions of the lobed nozzles
Annular entrance
Cone
dinner (mm) douter (mm) lcone (mm)
NLN-1
210
400
262.5
NLN-2
210
400
262.5
NLN-3
210
400
262.5
PLN-1
210
400
262.5
PLN-2
210
400
262.5
PLN-3
210
400
262.5
CALN
210
400
262.5
SwALN-1
210
400
262.5
SwALN-2
210
400
262.5
Lobe penetration angles
αoutward (°)
αinward (°)
12.9
12.9
12.9
12.9
12.9
12.9



Lobe peak circle
dpeak (mm)
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
(a)
(b)
Figure 4 (Color online) Numerical simulation model. (a) Simulation
domain; (b) surface mesh of SwALN-2.
The simulation was performed using the Fluent software
and the SST k- turbulence model. The SIMPLEC algorithm was used to solve the pressure-velocity coupling. All
convection terms were discretized by a second-order
scheme. The pressure inlet and pressure outlet conditions
were set to far field, where the operating pressure was
101325 Pa, the temperature was 300 K, and the turbulent
intensity was 5%. A velocity of 125 m/s, temperature of 850
K, and turbulent intensity of 5% were assigned to the jet
inlet.
Hu et al. [30–33] conducted a series of particle image
velocimetry experiments to investigate the jet mixing flow
of a nozzle with six lobes. Figure 5 compares the velocity
vector and axial velocity distributions of the simulation of
the six-lobe nozzle using the numerical simulation method
of the present study with Hu’s experimental results. Figure
6 presents the mixing decay of the maximum value of the
streamwise vorticity in the simulation and Hu’s experiment.
In addition, using the same method, we have simulated the
mixing in a scarfing alternating-lobe mixer [27], and the
550
550
550
550
550
550
550
550
550
Lobe trough circle diameters
ddeep trough (mm) dshallow trough (mm)
240
240
240
240
240
240
150
293.7
150
293.7
150
293.7
Equivalent diameter
D (mm)
400
400

400
400
400
400
400
400
simulated and experimental velocity vector and axial velocity distributions are compared in Figure 7.
It can be seen that the velocity vector and axial velocity
distributions obtained by the numerical simulations are in
good agreement with those determined by experiments. In
addition, the simulated maximum value of the streamwise
vorticity has a good accuracy before the vortices break
down, although some difference is displayed after the
breakdown. The major part of the enhanced mixing caused
by the special geometry of the lobed nozzle is concentrated
within the first two diameters of the lobed nozzle [30,32,
33], thus the error in the maximum value of the streamwise
vorticity after the vortices break down will only slightly
influence the accuracy of the simulated jet mixing. Therefore, all of these observations validate the numerical method
and the results of the simulation of the lobed nozzles in this
study.
To determine the adequate mesh density, the simulation
domain of PLN-1 was discretized with three different densities. The maximum sizes of the cells in the refinement domain were set to 20, 15, and 12 mm, respectively. The
number of cells in and outside the refinement domain is
given in Table 2. Figure 8 shows 700 K temperature isosurfaces simulated with these meshes. It can be seen that as the
maximum size is decreased, the number of cells in the simulation domain increases sharply, and a more refined temperature isosurface is obtained. When the maximum size is
set to 20 mm, the temperature isosurface is rough. On the
contrary, when the size is 12 mm, the number of cells becomes prohibitive. Advisably, when the size is 15 mm, the
number of cells is moderate, and the obtained temperature
isosurface can trace out the mixing process well. Thus, in
the present investigations, the maximum size of the cells in
the refinement domain of 15 mm was adopted.
4
4.1
Results and discussion
Primary stream distribution
Figure 9 shows the 700 and 650 K temperature isosurfaces
and the temperature distribution at 1.5d for each lobed noz-
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(a) DP-SPIV [33]
20 mm
60 mm
(b) SST k-ω
20 mm
60 mm
Figure 5
July (2015) Vol.58 No.7
120 mm
120 mm
(Color online) Experimental (a) and simulated (b) velocity vector and axial velocity distributions of the lobed nozzle with six lobes.
Figure 6 (Color online) Simulated and experimental maximum value of
the streamwise vorticity of the lobed nozzle with six lobes.
zle. As seen in Figure 9(a), the mixing in the region off the
lobe peaks of NLN-1 is slightly slower than that off its side
walls, and the large area of the primary stream in the core
region requires a long distance for complete mixing (the
core region immediately emanates outside of the refinement
domain). In Figure 9(b), the area of the section of the primary stream in the core region of PLN-1 is significantly
reduced, as well as its complete-mixing distance. In addition,
the mixing in the region off the side walls is slightly faster
than that of NLN-1. Compared to PLN-1, the primary
stream in the core region of PLN-2 presents an irregular
shape, the section is larger, but the complete-mixing distance is somewhat shorter, and the mixing in the region off
the side walls is slightly faster. In Figure 9(d), there is no
Figure 7 Simulated and experimental velocity vector and axial velocity
distributions of the scarfed alternating-lobe mixer.
Table 2 Number of cells with three different densities of discretizing the
simulation domain of PLN-1
The maximum size (mm)
20
15
Number in the refinement domain (million)
11.81 20.09
Number outside of the refinement domain (million) 1.61 2.22
12
34.92
2.99
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Figure 8
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July (2015) Vol.58 No.7
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(Color online) Simulated 700 K temperature isosurfaces of PLN-1 with meshes of different density. (a) 20 mm; (b) 15 mm; (c) 12 mm.
(a) NLN-1
(b) PLN-1
(c) PLN-2
(d) PLN-3
Figure 9
(Color online) 700 and 650 K temperature isosurfaces and temperature distribution at 1.5d for each lobed nozzle.
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July (2015) Vol.58 No.7
Continued
(e) CALN
(f) SwALN-1
(g) SwALN-2
Figure 9
unmixed primary stream in the core region of PLN-3, but
the mixing in the regions off the side walls and lobe peaks is
slow, with the result that the complete-mixing distances in
these regions need to be increased considerably compared
with PLN-1.
However, in the case of CALN, a smaller core region and
the region between the deep and shallow troughs replace the
large core region of NLN-1, although the complete-mixing
distances of the regions off the side walls and lobe peaks are
longer than those of NLN-1. In the core region of CALN,
although the section of the primary stream is larger than that
of PLN-1, the complete-mixing distance is somewhat shorter. In addition, the complete-mixing distance of the region
between the deep and shallow troughs is shorter than that
off the lobe peaks. Compared to CALN, the mixing of
SwALN-1 and SwALN-2 in the regions off the side walls
and lobe peaks and between the deep and shallow troughs is
faster, especially in the region off the side walls, which is
even faster than that of PLN-2. However, in the core region,
(Continued)
the section of the primary stream is larger than that of
CALN and the complete-mixing distance is longer than that
of PLN-1. In addition, the mixing in the core region and the
region between the deep and shallow troughs of SwALN-2
is faster than that of SwALN-1, whereas in the regions off
the side walls and lobe peaks the mixing is slightly slower.
4.2
Jet mixing performances
The pumping coefficient  is used to assess the pumping
performance of a lobed nozzle, and is defined as:
  ms mp ,
(1)
where mp is the mass flux of the primary stream, and ms is
the mass flux of the secondary stream. For an ejector-mixer,
a larger pumping coefficient means more mass flux of the
secondary stream can be pumped with a fixed mass flux of
the primary stream, namely, more secondary stream can be
supplied to mixing.
Sheng Z Q, et al.
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The pumping coefficient of each lobed nozzle is given in
Table 3, where Δ is the relative difference of . It can be
seen that an addition of a central plug at the exit of NLN
provides an enhancement of about one-third for PLN-1.
Relative to PLN-1, about 4 percent of the increment is cut
down in the case of PLN-2, and that of PLN-3 is decreased
to a quarter. Compared to NLN, the pumping performance
of CALN is slightly enhanced, and about 5% improvement
is achieved in that of SwALN-1 and SwALN-2.
The thermal mixing efficiency tr [34,35] can be used to
evaluate the mixing effectiveness of the lobed nozzle. Considering the components of the primary and secondary
streams are the same in the present investigation, the expression for tr is:
 tr  1 
 Tm  TM 
2
dmm
TP2 mP  Ts2 ms  TM2 mm
,
TP mP  Ts ms
,
mm
(3)
a higher thermal mixing efficiency implies a more uniform
mixing of the primary and secondary streams, which indicates a higher utilization ratio of the secondary stream.
In Figure 10, the thermal mixing efficiency is plotted
against x/d for each lobed nozzle, where x is the axial distance measured from the trailing edge of NLN-1. As shown
in Figure 10, the thermal mixing efficiency of each lobed
nozzle increases rapidly up to x = 1.0d and slowly beyond
1.5d. In terms of the thermal mixing efficiency at a fixed
section, NLN-1 is the lowest in the whole range, and for
CALN in the range of 1.0d2.0d, it increases faster than for
other nozzles. Referring to the thermal mixing efficiencies
of the lobed nozzles with a central plug, from 0.25d to 2.0d,
PLN-1 is slightly higher than PLN-2, and in the whole mixing process both of them are higher than PLN-3. In terms of
the thermal mixing efficiencies of the alternating-lobe nozzles, CALN is lower than PLN-1 and PLN-2 in the range of
0.25d2.0d, SwALN-1 is higher than CALN from 0.25d to
1.5d, but lower than CALN between 1.75d and 2.5d; however, in the range of 0.75d2.5d SwALN-2 is higher than
Table 3
nozzle
Pumping coefficient and its relative difference for each lobed
NLN-1 PLN-1 PLN-2 PLN-3 CALN SwALN-1 SwALN-2
1.0020
1.0024
4.82
4.86
 0.9559 1.2628 1.2229 1.1962 0.9652
 (%) 0.00 32.11 27.93 25.14 0.97
Figure 10 (Color online) Increase of the thermal mixing efficiency for
each lobed nozzle.
(2)
where mm is the mass flux of the local mixing stream, Tp is
the initial temperature of the primary stream, Ts is the initial
temperature of the secondary stream, Tm is the temperature
of the local mixing stream, and TM is the temperature after
the complete mixing of the primary and secondary streams,
i.e.,
TM 
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other nozzles.
The total pressure recovery coefficient σ is an indication
of how much pressure loss is induced by the jet mixing, and
is defined as:
 Pm dmm
,

*
*
 Pp dmp   Ps dms
*
(4)
where P*p is the initial total pressure of the primary stream,
P*s is the initial total pressure of the secondary stream, and
P*m is the total pressure of the local mixing stream. A superior total pressure recovery coefficient signifies less energy
being consumed in the mixing, and the initial total pressure
of the primary stream being increased by a smaller value,
which will cause a smaller power loss of the engine.
Figure 11 shows the decrease of the total pressure recovery coefficient for each lobed nozzle. Contrary to the thermal mixing efficiency, these coefficients decrease rapidly
up to 1.0d and slowly beyond 1.5d. In terms of the total
pressure recovery coefficient at a fixed section, NLN-1 is
always the highest, followed by CALN; SwALN-1 and
SwALN-2 are lower but still much higher than the lobed
nozzles with a central plug. In the anterior segment of the
mixing, the total pressure recovery coefficient of SwALN-2
is almost equal to that of SwALN-1, but thereafter, the former one is somewhat lower. Among the lobed nozzles with
the central plug, the total pressure recovery coefficient of
PLN-1 is slightly higher than that of PLN-2 for the whole
mixing process, and in contrast to other nozzles, the total
pressure recovery coefficient of PLN-3 decreases faster,
which means the largest pressure loss.
4.3
Jet mixing mechanisms
Figure 12 shows the velocity vector and temperature distributions at 0.25d for each lobed nozzle, where the color of
the velocity vectors represents the temperature of the local
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Figure 11 (Color online) Decrease of the total pressure recovery coefficient for each lobed nozzle.
flow, and all scaling factors of the velocity vectors are kept
the same. As shown in Figure 12(a), the slim streamwise
vortices are shed from the side walls of NLN-1, with the
radial scale comparable to the lobe height. The secondary
stream flowing through the lobe troughs penetrates only
superficially forward and sideward into the primary stream,
thus a large area with a high-temperature primary stream
exists in the core region.
For PLN-1, owing to the core region blocked by the central plug, only a little of the primary stream flows over the
central plug and converges in the core region (Figure 9(b)).
In addition, some secondary stream flows into the core re-
July (2015) Vol.58 No.7
gion along with this primary stream, and the radial scale of
the streamwise vortices off the side walls is decreased near
the lobe troughs. Ignoring the difference in sizes of the sections of the central plugs, the main difference between the
velocity vector distributions of PLN-2 and PLN-1 is the
irregular streamwise vortices off the central plug of PLN-2.
These irregular streamwise vortices are formed only by the
primary stream, which indicates that partially separated
flow has formed. Unlike PLN-1 and PLN-2, in the velocity
vector field of PLN-3, there are no obvious primary or secondary streams flowing into the core region. On the contrary, there is a large-scale stream with temperature of about
550 K flowing radially out of the core region. This reveals
that completely separated flow has formed (Figure 9(d)).
Compared to NLN-1, the streamwise vortices off the side
walls of the deep troughs of CALN are thinner and those off
the side walls of the shallow troughs are thicker. The secondary stream flowing through the deep troughs penetrates
more deeply forward and sideward into the primary stream,
thus more secondary stream flows into the core region,
which is beneficial to the whole mixing process in the core
region and the region between the deep and shallow troughs.
Differently from CALN, for SwALN-1 and SwALN-2, the
primary stream flowing over each sword deep trough convolutes with the inwards-penetrating secondary stream to
form the thick streamwise vortices off the sword deep
troughs, and then the primary stream between the deep and
shallow troughs is deflected towards both sides. The
streamwise vortices off the side walls of the shallow troughs
Figure 12 (Color online) Velocity vector and temperature distributions at 0.25d for each lobed nozzle. (a) NLN-1; (b) PLN-1; (c) PLN-2; (d) PLN-3; (e)
CALN; (f) SwALN-1; (g) SwALN-2.
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are thicker because of the earlier mixing and the deflection
of the primary stream.
Figure 13 shows the velocity magnitude and streamline
distributions in the symmetry plane containing a lobe peak
for PLN-2 and PLN-3. It can be seen that the flow is partially separated, and unstable separation bubbles are formed
in the leeward section of the central plug of PLN-2. The
primary stream, which flows over the plug, can still converge, but being disturbed by the unstable separation bubbles, the converged primary stream will waggle slightly.
This slight waggle benefits the converged primary stream
mixing with the surrounding secondary stream in a limited
area (Figure 9(c)). The unstable separation bubbles and the
slight waggle of the converged primary have little effect on
the formation and evolvement of the streamwise vortices off
the side walls (Figure 12(c)).
However, the flow is completely separated and a large
back-flow region is formed in the leeward section of the
central plug of PLN-3. The primary stream, which flows
over the plug, cannot converge anymore (Figure 9(d)). As a
result, the stream in the region next to the back-flow region
flows with a low speed. Furthermore, the unstable interface
of the back-flow region causes a large-scale waggle in the
low speed region. Here, the leeward section of the central
plug cannot extend the penetration depth of the lobe troughs.
Consequently, the large back-flow region and the largescale waggle in the low speed region have severe effect on
the formation and evolvement of the streamwise vortices off
the side walls (Figure 12(d)).
The non-dimensional streamwise vorticity ωx and normal
vorticity ωn are defined as:
x 
n 
D  w  v 
 ,

u p   y z 
2
(5)
2
D   u w   v  u 
 
    ,
u p  z  x   x  y 
(6)
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where D is the diameter of the mixing duct, up is the initial
velocity of the primary stream, and u, v, and w are the velocities in the x, y, and z directions of the mixing stream,
respectively.
Figure 14 shows the non-dimensional streamwise vorticity distribution at 0.25d for each lobed nozzle. The peak
values for the streamwise vortices off the side walls of
NLN-1, PLN-1, and PLN-2 lie near the lobe peaks where
the vortex cores are located, whereas those of PLN-3 lie
near the lobe troughs. In terms of the streamwise vorticity
near the lobe peaks, PLN-1 is the highest, PLN-3 is higher
than PLN-2, and NLN-1 has the lowest value. However,
near the lobe troughs, the vorticity of PLN-3 takes the
highest value, that of PLN-1 is the next highest one, and the
value of PLN-2 is slightly higher than that of NLN-1. The
streamwise vorticity is related with the intensity of the cross
flows, which form the vortex. At 0.25d, the central plug of
PLN-1 blocks more area than that of PLN-2, therefore,
compared to NLN-1, the cross flow of the primary stream of
PLN-1 is intensified more than that of PLN-2, and the
streamwise vorticity is augmented accordingly. Although
the leeward section of the central plug of PLN-3 is the same
as that of PLN-2, the flow over the central plug of PLN-3 is
completely separated in the leeward section. As a result, the
cross flow of the secondary stream is weakened while the
outward penetration depth of the primary stream is increased, and the outward cross flow of the primary stream is
intensified intensely, especially near the lobe troughs (Figure 12(d)). Therefore, near the lobe peaks, the streamwise
vorticity of PLN-3 is higher than that of PLN-2, and near
the lobe troughs of PLN-3 the value is enhanced even more.
In the case of CALN, the peak value of the streamwise
vortices off the side walls of the shallow troughs is distributed uniformly, and for the streamwise vortices off the side
walls of the deep troughs, the second peak value region exists near the deep troughs. However, for CALN, SwALN-1,
and SwALN-2, the streamwise vortices off the side walls of
the deep troughs, and for SwALN-1 and SwALN-2, the
Figure 13 (Color online) Velocity magnitude and streamline distributions in the symmetry plane containing a lobe peak for PLN-2 and PLN-3. (a) PLN-2;
(b) PLN-3.
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(a)
Sci China Tech Sci
(d)
(c)
(b)
(e)
July (2015) Vol.58 No.7
(f)
(g)
Figure 14 (Color online) Non-dimensional streamwise vorticity distribution at 0.25d for each lobed nozzle. (a) NLN-1; (b) PLN-1; (c) PLN-2; (d) PLN-3;
(e) CALN; (f) SwALN-1; (g) SwALN-2.
streamwise vortices off the side walls of the shallow troughs
and off the sword deep troughs, their peak values still lie
near the locations of the vortex cores. For SwALN-1, the
peak value of the streamwise vortices off the sword deep
troughs is slightly higher than that of SwALN-2, and it is
reverse for the vortices off the side walls. The peak value of
the streamwise vortices off the side walls of CALN is close
to that of SwALN-1.
In combination with the mixing rates of each region
shown in Figure 9 and the streamwise vorticity distributions
discussed above, it could be concluded that the mixing rate
has no certain relationship with the initial streamwise vorticity in the core region and the regions off the side walls, and
between the deep and shallow troughs. Figure 15 shows the
magnified images of Figures 12(a)–(d). It can be seen that
in the regions off the side walls of NLN-1, PLN-1, and
PLN-2, from the vortex core to the lobe trough, the secondary stream displays turning and flowing towards the primary
stream. These flows of PLN-1 and PLN-2 are slightly
stronger than that of NLN-1, thus the mixing in the regions
off the side walls of PLN-1 and PLN-2 is slightly faster than
that of NLN-1. However, in the region off the side walls of
PLN-3, the secondary stream displays turning and flowing
towards the primary stream only near the lobe troughs. Be-
cause this flow of PLN-3 is stronger, the mixing near the
lobe troughs of PLN-3 is faster than that of the previous
three lobed nozzles, but the mixing in the region outside the
troughs is slow. Therefore, the completely separated flow
over the rear of the central plug of PLN-3 severely impedes
the available heat and mass transfer in the streamwise vortices off the side walls. As a result, the mixing in the region
off the side walls of PLN-3 is inhibited.
In Figures 12(e)–(g), the secondary stream penetrates
more deeply forward into the primary stream in the region
near the deep troughs of CALN, which makes the cross section of the primary stream in the core region smaller, compared to SwALN-1 and SwALN-2. On the contrary, near
the shallow and deep troughs, the thick streamwise vortices
off the side walls and sword deep troughs of SwALN-1 and
SwALN-2 can entrain more secondary stream to flow towards the primary stream than in the case of CALN, consequently, promoting the mixing in the regions off the side
walls and lobe peaks, as well as the mixing in the region
between the deep and shallow troughs. Therefore, it is propounded that the mixing rate of the large-scale mixing
dominated by the streamwise vortices is related to the intensity of the attainable heat and mass transfer of the streamwise vortices.
Sheng Z Q, et al.
Sci China Tech Sci
July (2015) Vol.58 No.7
1229
Figure 15 (Color online) Velocity vector and temperature distributions at 0.25d for lobed nozzles with and without a central plug. (a) NLN-1; (b) PLN-1;
(c) PLN-2; (d) PLN-3.
At the transition layer with axial velocity gradient, the
normal vortices are formed by the viscous shear force. Figure 16 shows the non-dimensional normal vorticity distribution at 0.25d for each lobed nozzle. It can be seen that the
normal vortex ring is formed at the interface between the
primary and secondary streams. In addition, the normal
vortex segments and ring are formed at the interfaces of the
separated bubbles of PLN-2 and the back-flow region of
PLN-3, respectively. The initial shape of the vortex ring at
the interface between the primary and secondary streams is
determined by the geometry of the nozzle trailing edge, and
its initial vorticity is related to the axial velocity gradient
between the primary and secondary streams at the nozzle
exit. As the mixing goes on, the interface and axial velocity
gradient evolve. Therefore, the values of vorticity of the
vortex ring at the interface between the primary and secondary streams compare as follows: those of PLN-1 and
PLN-3 are close to each other, that of PLN-2 is slightly
smaller, and those of NLN-1 and CALN are at a lower level.
For SwALN-1 and SwALN-2, the normal vorticity in the
lobe peak segments is close to that of CALN; however, it is
smaller in the side wall and shallow trough segments, because of the earlier mixing, whereas in the deep trough
segments it is higher because of the relatively delayed mixing. Observably, for SwALN-1 and SwALN-2, the vortex
ring is stretched towards the primary stream at both sides of
the deep and shallow troughs. Moreover, the normal vorticity in the side wall segments is distinctly smaller than that
in the lobe peak segments. It can be envisaged that the heat
and mass transfer/mixing process of the streamwise vortices
impels the interface towards the primary stream, and dissipates the axial velocity gradient in the mixed region.
Figure 17 shows the velocity vector and temperature dis-
Figure 16 (Color online) Non-dimensional normal vorticity distribution at 0.25d for each lobed nozzle. (a) NLN-1; (b) PLN-1; (c) PLN-2; (d) PLN-3; (e)
CALN; (f) SwALN-1; (g) SwALN-2.
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Figure 17
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(Color online) Velocity vector and temperature distributions at 1.0d for each alternating-lobe nozzle. (a) CALN; (b) SwALN-1; (c) SwALN-2.
tributions at 1.0d for each alternating-lobe nozzle. Consulting the temperature distribution at 1.5d for each alternating-lobe nozzle in Figures 9(e)–(g), it can be seen in the
case of CALN that there is an adequate low-temperature
flow around the unmixed primary stream in the core region
and the region between the deep and shallow troughs,
therefore the mixing in these regions progresses at a preferable rate. Unlike CALN, the primary stream of SwALN-1 is
deflected between the deep and shallow troughs by the
streamwise vortices off the sword deep troughs and then
converges in the region off the sword deep troughs. The
mixing in the core region and the region between the deep
and shallow troughs becomes slow as the ambient
low-temperature stream is reduced. However, the sword
deep troughs of SwALN-2 are wider than those of
SwALN-1. This not only weakens the primary stream converging in the region off the sword deep troughs, but also
increases the secondary stream flowing into the core region
through the sword deep troughs. Therefore, the mixing in
the core region and the region between the deep and shallow
troughs is faster than that in SwALN-1.
4.4
July (2015) Vol.58 No.7
Discussion
The streamwise vorticity only reflects the intensity of the
cross flows that form the vortex. In the core region and regions off the side walls and between the deep and shallow
troughs, there is no certain relationship between the mixing
rate and the initial streamwise vorticity. Practically, the
mixing rate of the large-scale mixing dominated by the
streamwise vortices is related to the intensity of the heat and
mass transfer attainable in the streamwise vortices. The
normal vortex ring between the primary and secondary
streams, being stretched by the streamwise vortices, is essentially the heat and mass transfer/mixing process of the
streamwise vortices impelling the interface. Moreover, reduction of the normal vorticity with subsequent disappearance of the ring is really the dissipation of the axial velocity
gradient by mixing and homogenization the axial velocity.
For NLN-1, the streamwise vortices off the side walls
have an important effect on the mixing only in the region
off the side walls, and the secondary stream penetrates to
the zone near the end of the lobe troughs only superficially.
In the core region, there still exists a large area of unmixed
primary stream, which leads to the lowest thermal mixing
efficiency of NLN-1. On the other hand, only a fraction of
the primary stream flows over the central plug of PLN-1
and converges in the core region. The secondary stream can
follow the converged primary stream flow through the lobe
troughs into the core region. The flux of the primary stream
in the core region is thus decreased while the flux of the
secondary stream is increased. Therefore, the section area
and complete-mixing distance of the primary stream in the
core region are significantly reduced. As a result, the thermal mixing efficiency of PLN-1 is enhanced significantly.
The flow over the central plug of PLN-2 is partially separated and unstable separation bubbles are formed in the
leeward section. The area of the converged primary stream
in the core region is also larger than that of PLN-1. The
converged primary stream will waggle slightly because of
the disturbance by the unstable separation bubbles. This
benefits the mixing of the converged primary stream with
the surrounding secondary stream in a limited area, and this
waggle has little effect on the mixing in the other regions.
Overall, the thermal mixing efficiency of PLN-2 is lower
than that of PLN-1 in the main mixing segment.
The flow in PLN-3 is completely separated, and a large
back-flow region is formed in the leeward section of the
central plug. As a result, the primary stream flowing over
the plug cannot converge. However, the unstable interface
of the back-flow region causes a large-scale waggle in the
low speed region next to it. Furthermore, the leeward section of the central plug cannot extend the penetration depth
of the lobe troughs. Consequently, the formation and
evolvement of the streamwise vortices off the side walls is
disturbed, with the adverse effect of a severe reduction of
the heat and mass transfer attainable in the streamwise vortices, which causes the complete-mixing distance in the
Sheng Z Q, et al.
Sci China Tech Sci
regions off the side walls and lobe peaks to increase significantly. Therefore, in the complete mixing process, the
thermal mixing efficiency of PLN-3 is lower than that of
PLN-1 and PLN-2.
For alternating-lobe nozzles, the deep and shallow
troughs are arranged in an alternating pattern. This also
contributes to the decrease of the flux of the primary stream
and increase of the flux of the secondary stream in the core
region, but the increment and decrement are less than those
of the lobed nozzles with a central plug. The secondary
stream penetrates deeply at the end of the deep troughs in
CALN, thus more secondary stream penetrates into the core
region, which is beneficial to the overall mixing process in
the core region and the region between the deep and shallow
troughs. Thus, in the range of 1.0d – 2.0d, the thermal mixing efficiency of CALN increases faster than that of the
other nozzles.
For SwALN-1, the primary stream flows over each
sword deep trough and then forms the thick streamwise vortices off the sword deep troughs. These streamwise vortices
will deflect the primary stream both sides between the deep
and shallow troughs. Then, the streamwise vortices off the
side walls of the shallow troughs are thickened because of
the earlier mixing and the deflection of the primary stream.
As the thick streamwise vortices can entrain more secondary stream flow towards the primary stream, the mixing in
the regions off the side walls and lobe peaks, and between
the deep and shallow troughs is enhanced.
However, as the mixing in the region between the deep
and shallow troughs is very fast, the primary stream is further deflected by the streamwise vortices off the sword deep
troughs and then it converges. In the middle and posterior
segments of the jet mixing, the stream around the unmixed
primary stream in the core region and the region between
the deep and shallow troughs has a relatively high temperature. Therefore, the thermal mixing efficiency of SwALN-1
is close to that of PLN-1 in the anterior segment, but is even
lower than that of CALN in the posterior segment. The
sword deep troughs of SwALN-2 are wider than those of
SwALN-1, therefore the former has an increased secondary
stream and decreased primary stream in the core region.
Moreover, the primary stream converging in the region off
the sword deep troughs is weakened. Consequently, the
thermal mixing efficiency in the middle and posterior segments is improved.
To quantify the pumping performance, it should be noted
that the velocity of the primary stream is increased by adding a central plug at the exit of NLN, because the passage
area is reduced. When the flow over the central plug is attached in the leeward section, the pressure driving the secondary stream is large, and the passage area for the secondary stream in the region off the central plug is increased.
Therefore, the pumping performance of PLN-1 improves
considerably. The partially separated flow in the leeward
section of the central plug and its slight influence on the
July (2015) Vol.58 No.7
1231
mixing will decrease the advantages in the driving pressure
and passage area for the secondary stream. As a result, the
pumping performance of PLN-2 is inferior to that of PLN-1.
For PLN-3, the completely separated flow in the leeward
section of the central plug and the large-scale disturbance of
the mixing aggravate the loss of advantage and result in a
further diminishing pumping performance. Compared to
NLN, the pumping performance of CALN is slightly enhanced. Owing to a slightly smaller exit area, some additional improvement is achieved in the case of SwALN-1
and SwALN-2.
With regard to the pressure loss, the central plug introduces regions of accelerated and decelerated axial flow for
the primary stream. A higher exit velocity of the primary
stream results in a greater pumped secondary stream, which
increases the cross flows of the primary and secondary
streams. And the central plug has the effect of the decrease
of the primary stream along with the increase of the secondary stream in the core region. Furthermore, higher speed
of the streams and an additional surface of the plug will
cause a larger friction loss. All of these factors increase the
pressure loss of PLN-1.
The partially separated flow in the leeward section of the
central plug and its slight disturbance of the mixing increases the pressure loss, thus in the overall mixing process
the pressure loss of PLN-2 is slightly larger than that of
PLN-1. The completely separated flow in the leeward section of the central plug and its large-scale disturbance of the
mixing will induce a large pressure loss. In addition, more
unmixed primary stream being displaced and impinging on
the duct earlier contributes to additional pressure loss. Thus,
the pressure loss of PLN-3 for the overall mixing process is
larger than that of PLN-1 and PLN-2, and the dispersion
increases as the mixing progresses.
The thermal mixing efficiency of CALN is higher than
that of NLN, mainly because the interfacial area between
the primary and secondary streams is increased, thus the
increase of pressure loss is less pronounced. Additionally,
this increment partially contributes to more unmixed primary stream being displaced and impinging on the duct.
The newly formed streamwise vortices off the sword deep
troughs induce stronger cross flows of the primary and secondary streams, causing pressure losses in SwALN-1 and
SwALN-2 before 1.0d that are larger than that in CALN. In
addition, the lobe peaks of SwALN-2 are wider than those
of SwALN-1, therefore, more unmixed primary stream being displaced and impinging on the duct between 1.0d and
1.5d results in a larger pressure loss.
5
Conclusion
Improving the mixing effectiveness of a circular lobed nozzle with the exit plane displaced from the center body can
be achieved by adding a central plug at the exit and replac-
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Sheng Z Q, et al.
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ing the nozzle with an alternating-lobe nozzle. In the present
study, jet mixing of the lobed nozzles with a central plug
and the alternating-lobe nozzles were compared in pumping
operation, and the mechanisms of the correlation were analyzed. The results are summarized as follows.
(1) The mixing rate of the large-scale mixing dominated
by the streamwise vortices is related to the intensity of the
heat and mass transfer attainable in the streamwise vortices,
but has no certain relationship with the initial streamwise
vorticity distribution. The streamwise vortices stretching
and cutting the normal vortex ring is virtually the heat and
mass transfer/mixing process of the streamwise vortices.
(2) By adding a central plug at the exit of NLN when the
flow over the central plug is attached in the leeward section,
the flux of the primary stream is decreased and the penetration depth of the lobe troughs is extended, which considerably improves the thermal mixing efficiency. When the flow
over the central plug is partially separated and unstable separation bubbles are formed in the leeward section, the converged primary stream mixing with the surrounding secondary stream is induced, but the mixing in the other regions is left almost uninfluenced. In the main mixing segment, the thermal mixing efficiency of partially separated
flow is slightly lower than that of the attached flow. When
the flow over the central plug is completely separated and a
large back-flow region is formed in the leeward section, the
formation and evolvement of the streamwise vortices off the
side walls is disturbed with the most adverse effect of severe reduction of the heat and mass transfer attainable in the
streamwise vortices. In the overall mixing process, the
thermal mixing efficiency in this case is lower than that of
the attached or partially separated flow.
(3) For an alternating-lobe nozzle, the flux of the primary
stream is decreased and the flux of the secondary stream is
increased in the core region. In the case of CALN, the secondary stream penetrates deeply at the end of the deep
troughs, which is beneficial to the whole mixing process in
the core region and the region between the deep and shallow
troughs. In the case of the sword alternating-lobe nozzle, the
thick streamwise vortices can entrain more secondary
stream flow towards the primary stream, therefore, the thick
streamwise vortices off the sword deep troughs accelerate
the mixing in the region between the deep and shallow
troughs, while those off the side walls of the shallow
troughs improve the mixing in the regions off the side walls
and lobe peaks. Moreover, the wider sword deep troughs
help to increase the secondary stream flow into the core
region and decrease the primary stream convergence in the
region off the sword deep troughs. Consequently, the thermal mixing efficiency in the middle and posterior segments
is improved.
(4) By adding a central plug at the exit of NLN, the velocity of the primary stream can be augmented. When the
flow over the central plug is attached in the leeward section,
the pressure driving the secondary stream and the passage
July (2015) Vol.58 No.7
area of the secondary stream in the region off the central
plug are relatively large, which significantly contributes to
the pumping performance. As the flow separation in the
leeward section of the central plug and its disturbance of the
mixing become more severe, the loss of the advantage increases, as a result, the increment of the pumping performance decreases. The central plug changes the axial velocity of the primary stream and contributes to the cross flows
of the primary and secondary streams, as well as to the friction loss, all of these increase the pressure loss. The partially separated flow and its slight disturbance increase the
pressure loss by a small amount. However, the completely
separated flow and its large-scale disturbance induce a large
pressure loss, with a further contribution from the more severe displacement and impinging of the unmixed primary
stream on the duct.
(5) The streamwise vortices off the sword deep troughs
induce more cross flow of the primary and secondary
streams, resulting in a larger pressure loss, which, however,
is still much lower than that of the lobed nozzles with a
central plug. Furthermore, the improved sword alternating-lobe nozzle has a higher thermal mixing efficiency in
almost the whole mixing process. Therefore, the improved
sword alternating-lobe nozzle is preferred in situations with
restrictions on the power loss of the engine.
This work was supported by the Assembly Research Foundation of China.
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