AIAA 2004-5726

2nd International Energy Conversion Engineering Conference
16 - 19 August 2004, Providence, Rhode Island

Swirl and Buoyancy Eﬀects on Mixing Performance ofa Baﬄe-Plate-Type-Miniature-Conﬁned Multi-Jet
K. Tatsumi∗, M. Tanaka† and K. Nakabe‡
Department of Energy Systems Engineering, Osaka Prefecture University, Osaka 599-8531, Japan

P. L. Woodfield§
Institute of Ocean Energy, Saga University, Saga 840-8502, Japan
Three-dimensional numerical simulation is conducted to examine the swirl motion andbuoyancy eﬀect on the mixing performance of a baﬄe-plate-type-miniature-conﬁned multijet. Swirl ﬂow is produced by inclining the jet in the circumferential direction and theresults of two diﬀerent swirl number conditions are compared with the non-swirl case.
From the authors’ previous works, it is believed that the baﬄe-plate-type conﬁned multijet enhances the mixing performance due to the reverse ﬂow generated at the central axisof the chamber and the radial ﬂow existing near the jet exit. The swirl ﬂow appeared
to interrupt this radial ﬂow and decrease the strength of the reverse ﬂow, which incurs
deterioration of the mixing performance. This tendency was more noticeable for larger
swirl number case.
For the discussion of the buoyancy eﬀect, the operating direction of the gravity force
is changed, i.e. 0, 90, 180 degrees of attack angle with the central axis. Buoyancy eﬀect
was negligible when its working direction was parallel to the central axis, however, once
the gravity force axis was tilted and possessed a certain angle with the central axis, anasymmetric pattern of ﬂow and mixture fraction was obtained. In this case, a very poor
mixing performance was achieved. For the swirl-accompanied case, a more apparent eﬀectof buoyancy force was observed even when the operating direction was parallel to thecentral axis. The swirl motion, which impairs the reverse ﬂow and radial ﬂow eﬀects, tends
to increase the sensitivity of the baﬄe-plate-type multi-jet ﬂow to the buoyancy force.

Nomenclature
A0
A2
b
Ct
d1
d2
d3
D
g
Gr
L
Lu p
m1
m2

Cross-sectional area of the chamber, m2
Total area size of the surrounding jets, m2
Baﬄe plate thickness, m
Craya-Curtet number
Center jet diameter, mSurrounding jet diameter, mCenter jet supply tube external diameter, mChamber diameter, mGravitational acceleration, m/s2
Grashof number
Distance between the baﬄe plate and domain outlet, mDistance between the baﬄe plate and domain inlet, m
Mass ﬂow rate of the center jet, kg/s
Mass ﬂow rate of the surrounding jets, kg/s

∗ Research Assistant, Department of Energy Systems Engineering, Osaka Prefecture University, Osaka, 599-8531, Japan.
† Graduate Student, Department of Energy Systems Engineering, Osaka Prefecture University, Osaka, 599-8531, Japan.
‡ Professor, Department of Energy Systems Engineering, Osaka Prefecture University, Osaka, 599-8531, Japan.
§ Postdoctoral researcher, Institute of Ocean Energy, Saga University, Saga 840-8502, Japan.

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Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

p0
Pr
r
R
Re
Rec
Res
Ri
S
Sw
Sc
T0
ui , u, v, w
U0
Wmx, y, z
β
Θ
µ
ξ
ρ
φ
ψ

Static pressure measured at outlet of the chamber, Pa
Prandtl number
Radial distance from central axis, mDistance between center jet and surrounding jets, mReynolds number of the chamber
Reynolds number of the center jet
Reynolds number of the surrounding jets
Richardson number
Step height of a backstep, m
Swirl number
Schmidt number
Surrounding jet temperature (=ambient temperature), K
Velocities in Cartesian coordinates, m/s
Inlet mean velocity of a backstep ﬂow, m/s
Cross-sectional averaged velocity, m/s
Cartesian coordinates, m
Cubical expansion coeﬃcient, 1/K
Temperature, K
Viscosity, kg/ms
Mass fraction of the center jet ﬂuid
Density, Kg/m3
Inclination angle of the surrounding jet hole, ◦Angle between the gravity force direction and central axis, ◦I.

Introduction

Fluid mixing is one of the most essential phenomena in ﬂuid mechanics and is applied in numerous
industrial applications concerning combustions, chemical reactions, thermal controls, etc. More demands
are inevitably rising for developing a mixing technique which can produce suﬃcient and eﬀective mixing
in a more compact size. For example, a high performance micro-combustor is one of the key technologies
for developing the micro gas turbine (MGT) well-known as the core part of the distributed power supply
system.1 For this combustor, a good mixing between fuel and oxidizer is required since a failure in having
a pertinent mixing will incur both deterioration of the system eﬃciency and increase of the emissions ofunburned fuel, soot, CO, and NOx from the MGT.
The decrease of ﬂow Reynolds number accompanied by the reduction of the system scale size incurs asigniﬁcant deterioration of the ﬂuid mixing performance. Therefore, it is essential to develop an eﬀective
mixing method under such low Reynolds number conditions. For such a purpose, the authors have proposed
a baﬄe-plate-type-multi-jet mixer. By introducing this multi-jet baﬄe plate, increase of local Reynolds
number and generation of recirculation in the downstream area of the plate can be obtained which remarkably
enhances the mixing between the ﬂuids provided through the jets. In the authors’ previous numerical andalso experimental works, the eﬀects of the location, size, and number of the holes of the baﬄe plate were
examined through which it has been found that the mixing characteristic is very sensitive to each condition.2, 3
The results numerically predicted for various upstream conditions also indicated that the baﬄe plate could
damp out undesirable disturbances included in the upstream ﬂow.4
In the present paper, two additional eﬀects on the multi-jet baﬄe plate are investigated by carrying out athree-dimensional numerical simulation. One is the swirl motion applied by tilting the surrounding jet holes
in the circumferential direction. The other is the buoyancy eﬀect. The former case is a typical techniqueapplied to large-scale combustors to improve the combustion performance. It is, therefore, reasonable toﬁgure out whether the interaction between the multi-jet and the swirl motion will increase or decrease themixing performance for the present case. For the latter case, since the Reynolds number considered in
the present study is very small, the inﬂuence of the buoyancy force may not be negligible. Not only thestrength of the buoyancy force but also its operating direction may aﬀect the ﬂow structure in a crucial way.
Therefore, in this study, several cases of diﬀerent angles of the buoyancy force are tested to see how the angle
aﬀects the mixing performance of the multi-jet.

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Baffle plate
Surrounding stream,

W2

Centered stream,d2

Jet holes
ChamberyzyGravity

d3 d1

z

x

W1

Flow

D
Coordinate
system origin

R
Lup

y

L

(a) Variables and coordinates

Verticalplane(b) The direction of the Gravity force

Figure 1. Computational domain.

II.
A.

Numerical Method

Computational Domain

The computational domain of the present study is illustrated in Figure 1 together with the coordinate system.
A baﬄe plate with 6 multiple jet holes are arranged axisymmetrically to surround the center-located jet.
There are a lot of combinations of which mixing ﬂuid component would be provided from each jet, though
in this paper, the condition is ﬁxed as one ﬂuid is supplied from all 6 surrounding jets and the other ﬂuid
from the center jet. When a combustor is considered as the practical use of this system, which is one of themain targets of this study, the oxide is fed through the surrounding jets and the fuel from the center. The
fuel is supplied through the fuel tube placed at the upstream side of the plate. In order to adjust the grid
system to the complicated geometry, unstructured grid system is applied in the present computation. An
example of the grid system is shown in Figure 2, in which the view point is taken from the upstream side of
the baﬄe plate.

Figure 2. A view of the computational grid near the baﬄe plate.

Three-dimensional incompressible continuity and Navier-Stokes equations are solved in steady state in
the computation.
∂ui
∂xi
Dρui
Dt

= 0

(1)



∂ui
∂
∂P
µ
+
= −
∂xi
∂xj
∂xj

(2)

To simulate the temperature ﬁeld and mixing performance of the fuel and oxidizer, energy and mass fraction
conservation equations are solved in the present study.


DρΘ
µ ∂Θ
∂
(3)
=
Dt
∂xj P r ∂xj


Dρξ
µ ∂ξ
∂
(4)
=
Dt
∂xj Sc ∂xj
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where, P r and Sc are the Prandtl number and Schmidt number which are kept constant as P r = 0.7 and
Sc = 0.7 here. ξ is the mass fraction of the primary gas (fuel) supplied from the center jet.
The present study is based on the Finite Volume Method. The pressure and velocity are both solved on
the collocated grid system. In order to avoid a checkerboard-like discontinuity in the pressure and velocity
ﬁelds, the interpolation technique for the pressure originally proposed by Rhie and Chow6 is employed in
the present study. For the discretization method applied to each governing equation, 2nd order upwind
bias scheme is applied for the convection terms while 2nd order central diﬀerencing scheme is adopted forthe diﬀusion terms. Considering the characteristic of this 2nd order upwind scheme, a so-called limiter isimplemented in the computation to prevent an unphysical over- or undershoots of the variables. The limiter
installed in the present study is based on a similar concept proposed by Gaskell and Lau.5, 7 Semi-Implicit
Method for Pressure-Linked Equations (SIMPLE) algorithm is used to couple the velocity and pressureﬁelds. More details of the numerical method is introduced in the authors’ previous papers.3, 5

1
0.8

Jiang et. al.
(1994)(Finite Element)

0.6

xGravity

Present(UFV)

Heated Le
o

y

y/H

S
Li

0.4
0.2

H
0
-1

-0.5

0

0.5

u/U

1

(a) Validation with a cavity ﬂowFlow(b) Computational domain of a (c) Comparison of streamwise velocperpendicular backstep ﬂow
ities

Figure 3. Comparison with other references for code validation.

B.

Code Validations

The present code has been validated through several tests associated with pipe ﬂow, ﬂow in an eccentric
annulus, backward facing step ﬂow and ﬂow for a compact ﬁn and tube heat exchanger element in the laminar
ﬂow regime.5 The dependency on the grid number arrangement and orientation also has been checked forpractical grid spacings5 at Reynolds numbers similar to those used in the present study. For example, thediﬀerence of the ﬂow and mixing characteristics between the presently adopted grid system and a ﬁner casewith 20% increase of grid nodes was less than 0.4%.
Two more cases of comparison with other references will be shown here for further discussion over thecode validity. The ﬁrst case is the three-dimensional lid-driven cavity ﬂow compared with Jiang et. al.8
Figure 3-(a) shows the center-line velocity distribution against the bench-mark ﬁnite-element results of Jiang
et. al .8 The grid allocation was similar to that used in the benchmark test. As can be seen, a good agreementwith their results is obtained.
The other tested case is the perpendicularly placed two-dimensional backward facing step ﬂow having
the channel bottom wall heated. The results are compared with the experiment carried out by Baek et al.9
Figure 3-(b), -(c) show the computational domain and the transverse distribution of the streamwise velocity atthree diﬀerent streamwise locations. Here S is the step height and U0 is the inlet mean velocity. The gravity
force is operating toward the upstream side, i.e. in the direction indicated by the arrow in the ﬁgure. The
conditions of the present computation have been set to be identical with those of the experiment. However,it should be noted that the exact inlet ﬂow proﬁle was not described in their paper and a uniform condition
is applied in the present study. The numerical results agree fairly well with the experiment although anover prediction is found in the area of 1.5 ≤ y/D ≤ 3. It should be noted that this tendency was also foundwhen no buoyancy eﬀect existed. Therefore, the diﬀerence might be attributed to the diﬀerence of the inlet
proﬁle. Since the near wall velocity proﬁle matches well with the experiment as is shown in Figure3-(c), it
can be concluded that the buoyancy eﬀect is well predicted by the present computation.

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C.

Computational Conditions

The fuel and oxidizer nozzle-diameters, d1 and d2 , and the distance between each nozzle, R, are ﬁxed at aconstant value. The computational domain starts from one chamber diameter, D, upstream of the baﬄeplate and the outlet is located 15D downstream of the plate so that Lup = D and L = 30D in Figure 1.
A uniform ﬂow condition is applied to the inlet condition for both surrounding and center jets. It should
be noted that the inﬂuence of the inlet ﬂow proﬁle to the mixing characteristics is negligible when the inlet
boundary is located suﬃciently far from the baﬄe plate due to the damping eﬀect of the plate and thatthe present case satisﬁes this condition.4 The Reynolds number of the system is calculated using D as thecharacteristic length and the mean velocity calculated at the outlet, and is constant as Re = 100 in all
calculated cases. For reference, the Reynolds numbers of the center jet and surrounding jets are Rec = 25
and Res = 87, respectively. The mass ﬂow rate between the fuel (center jet) and oxidizer (surrounding jets)
is ﬁxed as m1 /m2 = 0.0488. This is the ratio of methane and air operated under 16% excess air condition.
Constant ﬂuid properties were adopted in the computation. These conditions are summarized in Table 1.
Table 1. Computational conditions

d1 /D
0.182

d2 /D
0.182

d3 /D
0.282

R/D
0.341

Lup /D
1L/D
15

m1 /m20.0488Re = 100
100

Rec = 25
25

Res = 87
87

The swirl motion is generated by inclining each air-jet hole in the circumferential direction. To examine
the eﬀects of the swirl strength on the mixing performance, the inclination of the holes is changed by twolevels in the present study. As for the case considering the buoyancy eﬀect, Boussinesq approximation isadopted in the computation.10 In this case, the center jet is assumed to be preheated and to possess a higher
temperature than the surrounding jets where the temperature diﬀerence between the two ﬂuids is deﬁned
as 50◦ C. This is a much smaller value compared to that when combustion is occurring or when the fuelis actually preheated. Nevertheless, as a ﬁrst step, the aforementioned value is chosen for the purpose ofnumerical simplicity and it is believed that insights of the buoyancy eﬀects to the multi-jets can be provided,
at least in a qualitative way. When buoyancy force is considered, Eq. (2) is rewritten as follows having an
additional term at the right hand side of the equation.


Dρui
∂ui
∂
∂P
µ
+ ρβ (T − T0 ) g
+
(5)
= −
Dt
∂xi
∂xj
∂xj
Here T0 is the temperature of the surrounding jets, β the cubic expansion coeﬃcient and g the gravitational
acceleration, respectively. Since the temperature diﬀerence and Reynolds number are constants in thepresent study, the Grashof number, Gr, and Richardson number, Ri are constants. The angle of attack of
the buoyancy driving direction against the streamwise axis is varied in three levels, i.e. 0◦, 90◦, and 180◦ .

III.
A.

Results and Discussion

Basic Performance

Here is brieﬂy discussed the mixing characteristics of the baﬄe plate case without swirl and buoyancy eﬀects(hereafter referred to as Case-B) compared to a simple co-axial jet case (hereafter referred to as Case-C)
in order to demonstrate its performance. Figure 4 shows the mixture fraction of the fuel, ξ, contours andvelocity vectors on the y-z plane at x/D = 0. Poor mixing is obtained between the fuel and air jet for Case-C,
in which a moderate gradient of ξ in the streamwise direction is observed. On the contrary, a remarkable
improvement on performance is obtained for Case-B, where ξ decreases rapidly at the downstream side of
the fuel jet and a uniform distribution is obtained at z ≥ 1.0. The main reason for this is twofold. One is
the ﬂow circulation generated at the downstream of the center jet which produces a reverse ﬂow near thecenterline. The other is the radial ﬂow heading toward the chamber walls observed immediately downstreamof the baﬄe plate. A detail study of such characteristics is presented in the authors’ previous paper.3

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w/Wm = 2.0

y/D

0.0

0.0

-0.5
-0.5

w/Wm = 2.0

0.5

y/D

0.5

0.0

0.5

1.0

z/D

1.5

2.0

2.5

-0.5
-0.5

3.0

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

(b) Case-B(a) Case-Cξ

0.00 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99

Figure 4. Mixture fraction ξ contours and velocity vectors on y-z plane at x/D = 0: Comparison between the
co-axial jet case and the baﬄe plate inserted case.

B.

Eﬀect of Inlet Swirl

In this section, the eﬀect of the swirl motion on the mixing performance of the baﬄe plate type multi-jet is
discussed. Swirl motion is generated at the baﬄe plate by titling the air jet holes. The eﬀects of two kindsof jet inclination angles, φ, have been examined in the present study, i.e. φ = 20◦ and 40◦ . The baﬄe plate
thickness is b/D = 0.25 and is relatively thick compared to Case-B so that a satisfying amplitude of swirl
ﬂow is obtained. A preliminary computation was carried out to investigate the plate thickness eﬀect on the
mixing performance under the same condition of Case-B where b was varied in a range with the maximumof b/D = 0.25. The results indicated that the plate thickness eﬀect is negligible. Therefore, although theplate thickness diﬀers between Case-B and the following discussed cases, we can assume that the subject for
discussion is limited to the swirl motion eﬀect only. The swirl numbers calculated at the baﬄe plate outlet
for these two cases are, Sw = 0.20 and 0.39, respectively. Here, Sw is deﬁned as follows.
Sw =Ga
Gt D/2(6)(7)

Ga and Gt are calculated by the following equations,
 D/2
Ga

=
0

 D/2
Gt

=
0

uθ πρr2 w 2 dr

(8)



2πr ρu2θ + p0 dr(9)where uθ , r, and p0 are the streamwise ﬂow velocity component, the radial distance from the central axis
and the averaged static pressure measured at the chamber exit, respectively.
Figure 5 shows the contour maps of the mixture fraction, ξ, at the y-z plane with the velocity vector
superposed on it for cases of φ = 20◦ (hereafter referred to as Case-S20) and φ = 40◦ (hereafter referred toas Case-S40). Figure 6 depicts the streamwise distribution of ξ and streamwise velocity, w, both calculated
along the chamber central axis (z-axis) for cases Case-S20 and Case-S40. w is normalized here by thecross-sectional averaged velocity, Wm . The results of co-axial jet case, Case-C, and baﬄe plate case, CaseB, which both represent the case without swirl motion, is also shown in Figure 6 for comparison. The ξ
proﬁles for the cases Case-S20 and Case-S40 in Figure 6-(a) possess a more moderate gradient compared
to Case-B which indicates that a less eﬀective mixing is obtained by the swirl accompanied case. This canalso be seen in Figure 5 where the darker shaded area, which indicates larger ξ, increases in length in thestreamwise direction. Paying attention on the velocity vectors in Figure 5, the strength of the reverse ﬂow
located near the centerline deteriorates when the swirl motion is applied. In Figure 6-(c), indeed a weakerreverse ﬂow takes place for larger swirl number case. For Case-S40, actually no reverse ﬂow appears at thecenterline, which is the reason why a poor mixing performance is obtained in this case. Therefore, althoughswirl motions are regarded to enhance mixing performance for a fairly large number of examples in practicalapplications, this does not occur for the present multi-jet case, at least for the laminar ﬂow regime consideredin the present study, in which turbulent mixing cannot be expected.
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w/Wm = 2.0

0.0

-0.5
-0.5

w/Wm = 2.0

0.5

y/D

y/D

0.5

0.0

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

-0.5
-0.5

(a) Case-S20

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

(b) Case-S40
ξ0.00 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99

Figure 5. Mixture fraction, ξ, contours and velocity vectors on y-z plane at x/D = 0: With swirl motion.

(a) Mixture fraction, ξ(b) Magniﬁed view of (a)(c) Streamwise velocity, w

Figure 6. Mixture fraction, ξ, and streamwise velocity, w, distributions along centerline.

In Figure 7, Craya-Curtet number, Ct, of each case is compared. The deﬁnition of Ct calculated in thepresent study is shown in the following.
Ct = 
where Wm and Wd are,Wm
2
Wd2 − 0.5Wm

(10)


1
Wm =
wdA
A0 A0

 2

1
w − 0.5Wf2 dA
Wd2 =
A0 A0

1
Wf =
wdA
A2 A2

Here, A0 is the chamber cross-sectional area at the jet exit and A2 is the area of the surrounding air jet holes.
The values of Case-C and Case-B are shown for comparison. Indeed, Ct is much smaller for the baﬄe platecases compared to Case-C which indicates that the large momentum diﬀerence between the center jet andsurrounding jet is one of the reasons for the generation of the ﬂow recirculation as discussed in the previous
section. However, Ct takes nearly an identical value for the baﬄe plate cases (Case-B, Case-S20, and CaseS40). This shows that the deterioration of the mixing performance when swirl is applied is attributed toanother reason.
Figure 8 shows the ξ contours and velocity vectors of the cross-sectional plane at two streamwise locations,z/D = 0.1 and 0.5, for Case-B and Case-S40. The ﬂow at z/D = 0.1 possesses a circumferential velocity
due to the inclination of the jet nozzle and develops to a swirl motion at the downstream which can clearly
be seen at z/D = 0.5. On the contrary, the radial ﬂows found in Case-B at z/D = 0.1 and 0.5 vanishes inCase-S40. For Case-B, the ﬂuid supplied from the center jet ﬂows outwards, however, for Case-S40, the ﬂuid
remains close to the centerline forming a spiral motion as it moves downstream. It is believed that the tilted
jet interrupts the radial ﬂow motion by blocking the passage between the jets and by increasing the pressure
at the inner wall of the chamber. The lack of the radial ﬂow not only interferes the mixing near the chamber
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Figure 7. Craya-Curtet number, Ct.
u/Wm = 1.0

0.50

y/D

0.25

y/D

0.25

u/Wm = 1.0

0.50

0.00

0.00

-0.25

-0.25

-0.50
-0.50

-0.25

0.00

x/D
(a) Case-B (z/D=0.1)

0.25

0.50

u/Wm = 1.0

0.50

-0.25

0.00

x/D
(b) Case-B (z/D=0.5)

0.25

0.50

u/Wm = 1.0

0.50

y/D

0.25

y/D

0.25

-0.50
-0.50

0.00

0.00

-0.25

-0.25

-0.50
-0.50

-0.25

0.00

x/D
(c) Case-S40 (z/D=0.1)

0.25

0.50

-0.50
-0.50

-0.25

0.00

x/D
(d) Case-S40 (z/D=0.5)

0.25

0.50

Figure 8. Mixture fraction, ξ, contours and velocity vectors on x-y plane: Comparison between with andwithout swirl motion.

wall but also attenuates the development of the ﬂow circulation around the central axis. This is the reason
why the mixing performance deteriorates when swirl motion is applied to the ﬂow at the downstream sideof the baﬄe plate.
Another interesting feature found in Figure 6 is that the swirl-accompanied cases show a somewhat
poor mixing at the area adjacent to the jet exit compared to the co-axial jet case. For some practicalapplications such as combustors, ﬂow and mixing characteristics near the jet exit signiﬁcantly aﬀect theoverall characteristics. Therefore, attention will now be paid on the mixing characteristics at the area close
to the baﬄe plate. To see the order of each case in Figure 6-(a) more clearly, the magniﬁed view is shownin Figure 6-(b). Now it is apparent that ξ takes a larger value for Case-S20 and Case-S40 compared toCase-C at the area of z/D ≤ 0.32 and z/D ≤ 0.88, respectively. Figure 9 shows the transverse distributionsof ξ of x/D = 0.0 at four diﬀerent streamwise locations, z/D = 0.05, 0.25, 0.5 and 1.0. At z/D=0.05, ξsmoothly decreases along the y-axis in Case-C due the simple diﬀusion eﬀect. On the other hand, for the
baﬄe plate case, ξ also decreases as y/D increases, however, the value is larger in all locations comparedto case Case-C. It should be noted that the largest value is obtained by Case-B and not by Case-S40 at
this location. Further downstream, an abrupt descent takes place for case Case-B at z/D=0.25 and for

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(a) z/D=0.05(b) z/D=0.25(c) z/D=0.5(d) z/D=1.0

Figure 9. Cross-sectional distribution of ξ at x/D = 0.

w/Wm = 1.0

w/Wm = 1.0

0.5

0.4

0.3

0.3

0.2

0.1

0.1

0.0
0.0

0.0
0.0

0.2

(b) Case-B

0.4

z/D

0.6

0.8

1.0

y/D

0.4

0.3
0.2

w/Wm = 1.0

0.5

0.4

y/D

y/D

0.5

0.2
0.1

0.2

0.4

z/D

0.6

0.8

1.0

(c) Case-S20

0.0
0.0

0.2

0.4

z/D

0.6

0.8

1.0

(d) Case-S40

Figure 10. Mixture fraction, ξ, contours and velocity vectors on x-y plane: a magniﬁed view of Figure 5.

case Case-S20 at z/D=0.5, respectively, and ξ shows approximately a uniform distribution. As mentioned inabove, this is the point where the center jet counters with the reverse ﬂow of small ξ and changes its direction
outwards toward the chamber surface. Figure 10 shows a closer view of the ξ contours and velocity vectors
near the baﬄe plate for each case in the same manner as Figure 5. In the ﬁgure, a small ﬂow circulation isobserved near the baﬄe plate in between the center jet and surrounding jet (0.08≤y/D≤0.2). The size ofthe circulation increases in the case of larger swirl motion, i.e. the trailing end of the circulation locates atz/D0.1, z/D0.3 and z/D0.4 for cases Case-B, Case-S20 and Case-S40, respectively. The generation ofthis circulation is ascribable to the existence of the plate between the nozzles which acts as so-called ‘rim’.
The width of this rim is more than three times larger than that of the coaxial jet case and hence a muchlarger circulation is created for the baﬄe plate case. This ﬂow circulation produces ﬂow stagnation there
and interrupts the diﬀusive mixing between the two jets. The aforementioned area where ξ of the baﬄe platecases possess a larger value than the co-axial jet case in Figure 9 at z/D = 0.05 corresponds to location
where the ﬂow circulation exists.
These features of the swirl-accompanied case may not sound preferable from the viewpoint of mixing
performance. However, the relatively high concentration maintained at the center axis and the rim eﬀect
might provide a more stable (but of low eﬃciency) combustion, which can be used for system start up.

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C.

Buoyancy Eﬀect on Flow and Mixing Characteristics

Buoyancy eﬀect on the mixing performance of the baﬄe plate jet is considered in this section. As describedin the previous section, its eﬀect is evaluated by implementing the Boussinesq approximation in Eq. (2)10 in
the present computation. The Grashof number, Gr, is kept constant and the direction of the gravity force
is changed. The computational conditions are tabularized in Table 2. ψ is the angle between the gravity
force direction and the chamber streamwise axis (z axis) as indicated in Figure 1-(b). Ri is the Richardson
number.
Table 2. Computational conditions

Case-Bb0
Case-Bb90
Case-Bb180
Case-S20b0
Case-S20b90
Case-S20b180

b/D
0.05
0.05
0.05
0.25
0.25
0.25

φ [◦ ]
0
0
0
20
20
20

ψ [◦ ]
0
90
180
0
90
180

Gr
6.85 × 104
6.85 × 104
6.85 × 104
6.85 × 104
6.85 × 104
6.85 × 104

Ri
6.85
6.85
6.85
6.85
6.85
6.85

Figure 11 shows the ξ contours and velocity vectors on the y-z plane at x/D = 0. Figures 12 and 13
display the ξ and w distributions along the centerline. Comparing the results of Case-Bb0 and Case-Bb180
in all ﬁgures, ﬂow pattern and ξ distribution show no diﬀerence which indicates that the buoyancy eﬀect issmall. However, for Case-Bb90, a dramatic eﬀect of the buoyancy appears. As shown in Figure 11, the ﬂuid
from the central jet immediately changes its ﬂow direction toward the positive direction of the y axis andξ takes an asymmetric distribution. Although mixing between the fuel and air occurs along the air jet, theperformance is poor and a non-uniform distribution of ξ still exists even at z/D = 3.0. Such asymmetricproﬁle is not desirable especially for combustion chambers since it can incur a salient increase of the local
temperature and provide undesirable NOx emissions or thermal fatigue at the chamber walls. Therefore, it
should be noted that buoyancy force not large enough to directly inﬂuence the ﬂow pattern might, however,aﬀect the ﬂow in a way of producing an unfavorable asymmetric mixture fraction distribution.
For Cases-S20b0∼180, by which swirl motion is accompanied, the buoyancy eﬀect is more apparent.
Comparing Case-S20b0 and Case-S20b180 with Case-S20 in Figure 13, the size of the reverse ﬂow area decreases when the buoyancy force works in the opposite-direction of the jet and vice versa. This is reasonable,
since the buoyancy force will enhance or attenuate the strength of the reverse ﬂow depending on its working
direction and eventually aﬀect the size of the circulation. As expected, ξ converges to a constant value ina shorter length in Case-S20b180 than Case-S20b0 as is shown in Figure 12. The reason why the buoyancy
eﬀect is more noticeable for the swirl cases is related to the radial ﬂow motion near the baﬄe plate. As
mentioned in the previous section, the radial ﬂow encourages the ﬂow circulation to develop which entails
a stronger reverse ﬂow at the central axis. In this case, the inﬂuence of the buoyancy force on the reverse
ﬂow is relatively small compared to the radial ﬂow and thus the mixing performance is scarcely aﬀected.
However, since the swirl motion depresses this radial ﬂow motion, the size of the circulation depends more on
the momentum diﬀerence of the surrounding jet and the center jet. In this case, the strength of the reverse
ﬂow depends more on the buoyancy force and thus a considerable eﬀect of buoyancy force on the mixing
performance appears.
Finally, an asymmetric proﬁles of the ﬂow and ξ are obtained for the swirl accompanied case also as isshown in Case-S20b90 in Figure 11. The swirl motion did not provide the expected function of preventing
such undesirable asymmetric pattern.

IV.

Conclusions

The swirl motion and buoyancy eﬀects on the mixing performance of a baﬄe-plate-type-miniatureconﬁned multi-jet is summarized as follows:
1. By inclining the surrounding jet holes in the circumferential direction, a strong swirl motion was
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w/Wm = 2.0

0.0

-0.5
-0.5

0.0

0.0

0.5

1.0

z/D

1.5

2.0

2.5

-0.5
-0.5

3.0

(a) Case-Bb0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

w/Wm = 2.0

0.5

y/D

y/D

0.0

0.0

0.0

0.5

1.0

z/D

1.5

2.0

2.5

-0.5
-0.5

3.0

(c) Case-Bb180

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

(d) Case-S20b0
w/Wm = 2.0

w/Wm = 2.0

0.5

y/D

y/D

0.5
0.0

-0.5
-0.5

0.0

(b) Case-Bb90
w/Wm = 2.0

0.5

-0.5
-0.5

w/Wm = 2.0

0.5

y/D

y/D

0.5

0.0

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

(e) Case-S20b90

-0.5
-0.5

0.0

0.5

1.0

z/D

1.5

2.0

2.5

3.0

(f) Case-S20b180
ξ
0.00 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99

Figure 11. Mixture fraction, ξ, contours and velocity vectors on y-z plane at x/D = 0: Considering the buoyancy
eﬀect.

obtained in the chamber. However, adding the swirl motion incurred a deterioration of the mixing
performance due to the interruption of the radial ﬂow near the baﬄe plate and the pressure increased
near the chamber walls.
2. The Craya-Curtet number did not diﬀer much between the cases with and without swirl motion forthe baﬄe plate case although the strength of the reverse ﬂow at the centerline varied considerably.
3. Near the jet exit, mixing performance for the baﬄe plate case was lower compared to the co-axial jetcase. This was due to the fact that for the baﬄe plate case, the area between the jets functioned asa rim. This rim produced a ﬂow circulation at its downstream and impaired the mixing between thecenter jet and the surrounding jets. The size of the circulation increased as the swirl number increased
and the mixing performance near the baﬄe plate deteriorated compared to the co-axial jet case.
4. Buoyancy eﬀect was small for the baﬄe plate case without swirl motion when its operating direction
was inline with the central axis. However, when a certain angle existed between the gravity and central
axes, an undesirable asymmetric ﬂow and concentration patterns appeared.
5. For the swirl-accompanied case, a more apparent eﬀect of the buoyancy force was observed. The ﬂow
circulation area increased when the direction of the buoyancy force was identical with the reverse ﬂow
and decreased when opposite. The lack of the radial ﬂow in the swirl case is believed to be the reason
why a more buoyancy eﬀect was observed for this case.

Acknowledgments
This work was supported through the project “Micro Gas Turbine/Fuel Cell Hybrid-Type Distributed
Energy System” by the Japan Science and Technology Corporation (JST) as Core Research of Evolutional
Science and Technology (CREST).
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(a)Without swirl(b)With swirl

Figure 12. Mixture fraction, ξ, distribution along centerline: Considering the buoyancy eﬀect.

(a)Without swirl(b)With swirl

Figure 13. Streamwise velocity, w, distribution along centerline: Considering the buoyancy eﬀect.

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