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Jet into Cross Flow Boundary Layer Control-
an Innovation in Gas Turbine Blade Cooling
1,2Javadi, Kh.*, 1,2 Taeibi-Rahni, M., and 1Darbandi, M.,
1- Sharif University of Technology,P. O. Box, 11365-8639, Tehran, Iran.
2- Aerospace Research Institute, (Ministry of Science, Research, and Technology), P.O. Box 15875-3885,
Tehran, Iran
New standpoint of turbulent coolant jets into crossflow, which have numerous applications
in traditional and modern technology, especially in gas turbine blades, is presented in this
work. It is more than half a century that, many researchers have been studying jet into cross
flow to understand its behavior and to predict and control it better. Previous studies indicate
that, the main attentions had been on: a- geometrical parameters such as: inclined andcompound jet angles, holes shape, jets array arrangements, jets spacing, and jets channel
depth, b- flow characteristics like: blowing ratio, density ratio, jet and cross flow Reynolds
numbers, and turbulence intensity. Here, we have looked at this problem from different
viewpoints and have introduced a new approach to control the jet and the cross flow
interactions. In this approach, two smaller coolant jets have been installed at both sides in
front of the main coolant jet. The main purposes of these two new jets are controlling the jet
and the cross flow interactions and to reduce the mixing strength between them through new
interactions between the counter rotating vortex pairs. Our numerical scheme was based on
finite volume pressure based SIMPLE- method using a non-uniform staggered grid. On the
other hand, the Reynolds stress transport model was used to close the incompressible
Reynolds averaged Navier-Stocks (RANS) equations. Our results show that, this new
approach at least has four significant improvements; 1- a significant enhancement in the film
cooling effectiveness (about 50%), 2- a considerable improvement in uniformity distributionof the coolant film over the plate, 3- reduction of mixing strength between the hot free
stream and the coolant jets, and 4- skin friction drag reduction. Note; in order for the results
of this new approach to be comparable with the ones from traditionally film cooling
methods, the total coolant air and the cross sections of the newcombined triple-jetshave been
taken to be the same as the ordinary one.
*PhD Student at Aerospace Engineering Department, Sharif University of Technology, E-mail, [email protected].
Associate Prof. at Aerospace Engineering Department, Sharif University of Technology, E-mail, [email protected]
Associate Prof. at Aerospace Engineering Department, Sharif University of Technology, E-mail, [email protected].
35th AIAA Fluid Dynamics Conference and Exhibit6 - 9 June 2005, Toronto, Ontario Canada
AIAA 2005-527
Copyright 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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Nomenclature
a = Speed of Sound iu = Fluctuative Velocity Components
1C , 2C , & C = Empirical Constants in RSM Model Vcf = Cross Flow Velocity
C2, C1 , & sC = Empirical Constants in RSM Model jiij uu = = Reynolds Stress Tensor
ijC = Convection Terms in RSM Model
cfjet
cfaw
TT
TT
=
= Film Cooling Effectiveness
D = Jet Hydraulic Diameterk
kx = Component of the Unit Normal to
= the Wall
d = Normal Distance from the Wall = Viscosity
LijD
= Molecular Diffusion Terms in RSM
Model
k , , & 2 = Empirical Constants in SST
Model
TijD = Turbulent Diffusion Terms in RSM
Model , * , & = Empirical Constants in SST
Model
1F and 2F = Switching Functions in ( )Model k = Prandtl Number
ijF = Production Terms by System Rotation = Density
ijG = Buoyancy Terms = A Dependent Variable
J = Momentum Ratio; )/()(22
cfcfjetjet VV ij = Pressure Strain Terms in RSM
Model
k = Turbulence Kinetic Energy 1,ij = Slow Pressure-Strain Terms in
RSM Model
tM = Turbulent Mach Number 2,ij = Rapid Pressure-Strain Terms in
RSM model
ijP = Production Terms in RSM Model 3,ij
= Wall-Reflection Terms in RSM
Model
cfjet VVR /= = Jet-to-Cross Flow Velocity Ratio = Turbulence Energy Dissipation
Rate
,U ,V &
W
= Mean Velocity Components ij = Rare of Dissipation Terms
iU = Mean Velocity Components = Specific Dissipation Rate
( )k*
/
iU = Instantaneous Velocity Components t = Eddy Kinematics Viscosity
( )cf = Designates Cross Flow
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5) Jet Holes Spacing [42, 51],
The spanwise jet spacing, S/D, (where S is spanwise jet spacing and D is the jet hydraulic diameter) is very
important. A common value for S/D is three. Larger values can not full protect the surface and smaller values
cause structural limitations.
6) Jet Array Arrangements- Single or Double Rows Effects[33, 38, 39, 52-59]The most important keys to protect the surfaces from the high temperature hot gas are jets coolant location and
their arrangements over the surface. For the same hole geometry, compound angle orientation, inclined angle
injection, and blowing ratio, a staggered arrangement of jet arrays have higher total film cooling effectivenesswith respect to the regular (inline) jet arrays. This is because; staggered arrangements can help the jets to recover
for each other. Thus, for the same coolant hole effectiveness, a staggered arrangement will improve total surface
effectiveness significantly.
7) Jet and Cross flow Reynolds Numbers [36, 41]Both the jet and the cross flow Reynolds numbers can strongly affect the characteristics length, velocity, and
time scales of the flow, e.g. the characteristics of the separation and the size of eddies are affected by both
Reynolds numbers. Not, jets into cross flow interactions are a multi length, velocity, and time scales
phenomenon.
8) Jet and Cross Flow Turbulence Intensity [41, 47, 62- 64]The turbulence intensity affects the mixing of the coolant jet and the main hot cross flow process. Hence higher
turbulence intensity leads to stronger mixing of the coolant jet and that of the hot cross flow. This is not suitablefrom film cooling point of view.
9) Density Ratio [30-32, 36, 44, 60, 61]For the same blowing ratio, increasing of density ratio will improve cooling effectiveness.
10) Compressibility Effects and Shock Waves Interaction.
A careful review on literature indicates that, almost all of the researchers attentions are to improve film
cooling effectiveness through geometrical parameters (injection angle, hole shape, jet array, their position, etc.) and
flow characteristics (Reynolds number, blowing ratio, turbulence intensity, density ratio, etc.). In this work we have
looked at this problem from different point of view and have succeeded to innovate a new approach to control thequality of the interactions and eventually to improve film cooling effectiveness with increasing coolant film
uniformity. The basis of this idea goes back to our previous studies on film cooling [ 65, 66], where the significant
role of mixing zones in destroying the coolant film was obviously observed. In this innovation, controlling of the jetinto cross flow interactions is our main objective. For this purpose, two smaller coolant jets are considered on both
front sides of the main coolant jet. The main goal of installing these two smaller coolant jets is to control the
interactions and to reduce the mixing strength between the coolant jets and the hot free stream. Using this newapproach has many advantages such as: 1- the improvement of film cooling, 2- the improvement of the uniformity ofthe coolant jets distribution, 3- the reduction of mixing strength between the hot free stream and the coolant jets
(which increases the stability and the steadiness of the coolant effects downstream of the injection), and 4- skin
friction drag reduction.
II. Governing Equation
The governing equations are Reynolds averaged Navier-Stoks (RANS) equation conservation of mass,
momentum, and energy for a stationary turbulent incompressible flow as follow:The conservation of mass stats that:
(1)0=
i
i
x
U
,
while the conservation of linear momentum is:
(2)
+
+
=
i
j
j
i
jij
i
jx
U
x
U
xx
p
x
UU )( ji
j
uux
+ ,
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and the conservation of energy is:
(3)
)})PrPr
{()(jt
t
l
l
j
j
j x
T
xTU
x
+
=
wherejiuu are the Reynolds stress terms, which need to be modeled. Since, our problem is multiple
characteristic scales eddy viscosity models are not very suitable to employ. Thus, Reynolds stress models (RSM)which have higher potential to simulate complex flows, have been used. Also, SST (k-/k-) turbulence model wasused for calculating the turbulent diffusivity in the Reynolds stress transport equation.
The (RSM) Equations are:
(5)
( ) ( )=
+
jik
k
ji uuUx
uut
( )[ ]+++
jikikjkji
k
uupuuux
( )
ji
kk
uuxx
+
k
i
kj
k
j
kix
Uuu
x
Uuu
+
+
i
j
j
i
x
u
x
up
k
j
k
i
x
u
x
u
2 ( )jkmmiikmmjk uuuu + 2 ,
While the SST Equations:
(6)
( )
+
+
=j
tk
jj
iij
x
k
xk
x
U
Dt
kD
* ( )jj xx
kF
+
1112 2
(7)
( )
+
+
=
j
t
jj
i
ij
t xxx
U
Dt
D
2 .
More details of the terms and constants are represented in [21, 22].
III. Computational Methodology
A FORTRAN computer program was developed to solve a three-dimensional, turbulent, incompressible, andtime averaged Navier-Stocks equations. Reynolds stress turbulent model incorporated with SST model was used to
overcome the closure problem. The numerical method used was finite volume method a employing hybrid scheme
over a non-uniform, structured, and staggered grid. The continuity and the momentum equations were linked via the
pressure based SIMPLE algorithms. Other equations such as the turbulent kinetic energy and its dissipation ratesequations were solved segregately. Finally, a line by line three diagonal matrix algorithm (TDMA) was used to solve
the discretized algebraic equations with appropriate under-relaxation factor to speed up the convergence.
IV. Physical Domain and Boundary Conditions
The physical domain and the boundary condition used are described in this section. Of course, we have different
domain depending on the ordinary or new film cooling approach used in this work. The boundary conditions on the
other hand are broken into inlet, outlet, no flux, periodic, and solid wall.
A. Ordinary Film Cooling Physical Domain
The results of our new approach were compared with a basic fundamental squared jet normally injected into a
cross flow (fig. 1),which is based on Ajersch et. als experimental (LDV) and numerical (k-) works [14]. Their jet
hydraulic diameter (jet width, D) was 12.7mm and their jet Reynolds number based on D was 4700 with a fixedvelocity speed of 5.5 m/s at the entrance of the jet channel. They tried three blowing ratios (R) of 0.5, 1, and 1.5.
However, we used R=0.5, which is more common in film cooling. our computational domain was non-dimensionalized respect to D, so that, the jet channel lengths is 5D and the cross flow region is extended from 5D
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upstream of the center of the jet to 40D downstream. In the vertical direction, the domain extends to 20D above the
flat plate.
B. New Film Cooling Approach Physical Domain
In our new approach, two smaller jets have been considered in both sides in front of the main jet. Note, from filmcooling point of view, in order for the results of this new approach to be comparable with the traditionally film
cooling approach, the same amount of total coolant air and the same total cross sectional area have been used (Fig.
2). Other parameters such as the lengths of physical domain, inlet jet and cross flow velocities (blowing ratio), etc.are the same as traditional film cooling case. However, jet Reynolds number would be different.
C. Boundary ConditionsIn this work, five types of boundary conditions namely: inlet, outlet, no-flux, solid wall, and periodic (Fig. 1)
were used as follows:
1) Inlet Boundary Condition: the inlet velocities, the turbulent kinetic energy and its dissipation rate, and the
Reynolds stress terms were prescribed as in [14, 22].
2) Outlet Boundary Condition: Zero gradients of flow quantities were used at this boundary. Also, since there is nomass conservation guarantee during SIMPLE iteration, we used the following relation for the streamwise
velocity component:
)8()/(,,1,, outinKJNIKJNI MMuu &&
= ,
where inM&
and outM&
are inlet and outlet mass flow rates, respectively.
3)No-flux Boundary Condition: At infinitely far from the plate, no-flux boundary condition were used as:
)9(0=
n
,
where, n is the direction normal to the face.
4) Periodic Boundary Condition: it was assumed that there were infinite numbers of coolant injected jets inspanwaise direction. In order to consider the effects of neighboring jets, periodic boundary condition follow was
used as:
)10(1,,1,, = NKjiji ; 2,,,, jiNKji = ,
However, since we used staggered grid, the periodic condition for z velocity component is:
)11(
1,,2,, = NKjiji ww , 3,,,, jiNKji ww = .
5) Solid Wall Boundary Condition: No slip boundary condition was used at the wall [22].
V. Results and Discussions
Three-dimensional turbulent multiple jets into cross flow were computationally simulated, using finite volume
method, SIMPLE algorithm, and Reynolds stress turbulence model. For code validation purpose, we compared our
results with previous experimental [[14] and numerical [14, 21]. Also, the related grid resolution study was
performed in our previous work [22].Figures 2-5 also, show the comparisons of our results with other experimental and numerical works. As it is
obvious from these figures and also, based on discussion in our previous works [22], the abilities of RSM model for
prediction of both the mean quantities and Reynolds stress terms at different flow locations are much higher relative
to two-equation models.Generally, when a jet is injected into a cross flow, several complex physical phenomenon occur downstream of
it, particularly the counter rotating vortex pair (CRVP) which is generated just behind the jet and moves
downstream. The CRVP strength and its influence on the cross flow characteristics are highly dependent on theblowing ratio. Stronger strength leads to more jet and cross flow interactions, more penetration into the boundary
layer, and higher mixing between the coolant jets and the hot cross flow. However, this is not suitable from film
cooling point of view. To improve cooling effectiveness all previous works were focused on the geometrical and
flow characteristics parameters of the jet the cross flow (as mentioned before).
In this work, we have introduced a new approach to control the interactions between the jet and the cross flow inorder to reduce fluid mixing and eventually to improve film cooling effectiveness. We have examined several
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technique to achieve this goal, e.g., combining of suction/blowing jets [66]. In our final selection, two small coolant
jets are considered at both sides of the main coolant jet and formcombined-blowing triple-jets units.this technique
has mainly four significant effects, including: 1- drastic mixing reduction between the coolant jets and the hot cross
flow, 2-considerable film cooling enhancement, 3- significant improvement of the coolant film distribution, which
leads to more uniform cooled surfaces, and 4- noticeable skin friction drag reduction. Here, we are going to discusshow this new system works so well. Note, this work is a fundamental study to introduce this new approach for
controlling the mixing of a jet into a cross flow, particularly to improve film cooling effectiveness and thus, more
work needs to be done to optimize it. Our research teams are presently working on the effects of different jetgeometry and flow characteristics on this new approach.
1) Mixing Reduction between the Coolant Jets and the Main Hot Free StreamAs mentioned earlier, when a jet is injected into a cross flow, a counter rotating vortex pair (CRVP) will be
created after the jet and moves downstream in a helical fashion. This phenomenon also occurs for the two small jets
of our new approach. In other word, two weaker CRVPs will be created at both side of the main coolant jet, one at
the left and one at the right. Note, the vortical field generated by the main coolant jet and the two small jets interact
with each other, while the direction of their rotation are opposite to each other. In other words, as Fig. 6shows, theright mate of the CRVP generated by the left jet, interacts with the left mate of CRVP generated by the main jet and
vice versa. Note, from Fig. 6it is clear that, in the ordinary case, the vortices of the CRVP have opposite directions.
However, they can not weaken each other since they have the same direction at their contact points. Hence they cannot destroy each other after meeting. While, if we pay more attention to this figure, we will see that, at the contact
points between vortexes of the main jet and that of tow new small jets the vortices have opposite directions and thusweaken of their strength occurs in our new approach. The interactions of the vortexes, which are on the contraryrotating directions at meeting interface is the key to our new approach.In this situation, the interacted vortices will
weaken each other after meeting. Therefore, the strength of the CRVP created by the main coolant jet will be
decreased. Figures 6-aand 6-b compare the structure and the strength of the main CRVP without and with small
jets. It is clear from this figure how the CRVPs of two small coolant jets and main jet interacts and causes the
breakdown of their strength. This leads to less interaction with hot cross flow and less mixing between the coolant
jet and the hot cross flow. The reduction of the mixing strength between the hot free stream and the coolant jetscause enhancement of the stability and the steadiness of the coolant effects downstream of the coolant jet injections.
It is necessary to emphasize here that, our new technique is quite different from double rows staggered holes, which
are widely used in film cooling applications. In the staggered row approaches, there are not very strong interactionsbetween the neighboring vortices. The main goal of the staggered rows is to improve film cooling effectiveness by
overlapping of the coolant jets to improve uniform film cooling distribution, not reduction of hot and cold mixing
interactions.2) Considerable Improvement on Film Cooling Effectiveness
The injection of the coolant jet into cross flow makes a low pressure region just behind the jet. Since, this low
pressure region can not be void of fluid; hot gases flow into this region and produce a layer of hot gases under the
coolant jet and decrease the efficiency of film cooling. Figure 7-ashows this phenomenon schematically (up) and
numerically (down). The main goal of our new approach is to avoid the arrival of these hot gases into this region.Several techniques were examined [65, 66] and finally the most efficient one, (combined triple-jets units) were
obtained. Fig. 7-b shows this schematically (up) and numerically (down). If we compare Figs. 7-a and 7-b, we note
how these new small jets divert the hot gases. In this situation, the coolant jet fills in the region behind the jet isteadof the hot gases. This is the first main reason for improvement of film cooling in our new approach. Also, note from
Fig. 7-a again that, during the rotation of the CRVP generated by the main coolant jet (ordinary film cooling) the hot
gases comedown towards the surface continuously and dos not permit the coolant film to cool down surfaces well
enough. While, in our new technique, the interactions between the vortical fields generated by the main and the
small jets like a fluid barrier prevent the penetration of the hot gases towards the surface (see Fig. 8). This is thesecond reason for improving the film cooling effectiveness in our new approach.
Fig. 9illustrates the velocity vector field at x-y center plane. This figure compares the coolant jets penetration
into the boundary layer of the hot cross flow for the combined triple-jets (this work) and ordinary film cooling
techniques. As it is clear from this figure, the influence of jet into the boundary layer for our new approach is lessthan that of the ordinary film cooling. This is the third reason for improving film cooling effectiveness by our new
approach. Figure 10 compares the film cooling effectiveness for our new approach and a common ordinary filmcooling. As this figure shows, there exists a considerable improvement of the film cooling effectiveness (about 50%)
in our new approach.
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3) Significant Improvement on Film Cooling Distribution
Having more uniform film cooling distribution is also very important, especially from thermal stress point of
view. One of the advantages of the staggered rows (compared to inline rows) is that, for the same hole,
characteristics, the total uniformity of the staggered holes is higher than that of the inline holes because of the
overlapping of the coolant film distribution. The existence of two small coolant jets at both sides in front of the mainjet, which makes a unit of combine triple-coolant jet with respect to one unit of ordinary film cooling (inline or
staggered), leads to the more uniform coolant film distribution. Also, because of less interaction between the main
stream and the coolant jets in our new approach, this uniformity continues the region way downstream of the jet.Figures 11-a and 11-b compare the cooling effectiveness distribution over the surface in our new approach and in an
ordinary film cooling. From this figure, one can note that, a significant improvement on the coolant film distribution
is obtained in our new approach. It should be emphasized again that, this technique must not to be mistaken with thestaggered rows approach. To correct comparison, the uniformity of one unit of these combined triple-jetsmust be
compared with the uniformity of one hole of any staggered or inline rows. Note, these units of combined triple-jets
can be arranged in a staggered or inline form.
4) Enhancement of Skin Friction Drag ReductionAlthough many studies have been performed on the jet into cross flow, but few researches have studied the relatedfriction drag phenomenon. In our study, we have compared the skin friction drag coefficient in our new (combined
triple-jets) and in the ordinary approaches [67]. Obviously, the skin friction drag is directly related to the shear
stresses on the wall (thus, velocity gradients at the wall). Hence, we need to look at the velocity profiles at the wallwith and without the coolant jets injections. Our results show that, generally, when a jet is injected into a cross flow,
the skin friction drag is decreased. This is because, by injecting a jet into the boundary layer of a turbulent crossflow, the velocity profile, which has high gradient near the wall will be distorted by the coolant jet and new velocity
profiles will be generated. These new profiles have less gradient close to the wall, particularly near the jet injection.As the flow moves downstream, the effects of the coolant jets decrease and the flow tends to have a regular profile.
Therefore, we expect an increase in the skin friction drag, as we go far away from the jet channel. The more the
turbulent boundary layer gets distorted and the more this distortion continues downstream region, the more decrease
in the skin friction drag will be achieved. Figure 12 shows the streamwise velocity profile at different location. As it
is clear from this figure, the velocity profile for thecombined triple-jetshas less gradient near the wall (except nearthe jet exit). For comparison, the velocity profile for a fully developed turbulent flow on a flat plate without any jet
injection is presented. From fig. 12,we can see that, at all locations the velocity gradient near the wall for turbulent
flow without jet injection is higher than the others. Since, the main part of the skin friction drag is due to streamwisevelocity component, then we focus on the gradient of this velocity component close to the wall. Also, since the
velocity at the wall is zero, the velocity at the first cell above the wall dividing to its distance give us the velocity
gradient at the wall. Also, since we used a structured grid, all such distances are equal. Therefore, the same strategycan be used all along the wall. Using this strategy, we can study the distribution of the velocity gradient downstream
of the jet injection easier. Figure 13demonstrates the velocity distribution at the first cells along the wall at three
different positions, namely: the center line, 0.5D and 1.D from the centerline (spanwise direction). This figure
indicates that, except for a small region near the coolant jet injection, the velocity gradient at the wall for our new
approach is considerably less than that of the ordinary film cooling. For better understanding of the roles of the twosmall jets at both sides in front of the main jet on reduction of skin friction drag, we have solved the problem
without small coolant jet, and geometry like the main coolant jet as combined triple-jet. Finally, Fig. 14compares
the skin friction drag coefficient distribution along the streamwise direction which has been spanwized averaged. Asit is obvious from this figure, the skin friction drag coefficient in our new approach (combined triple-jet) is about
20% less than the ordinary film cooling. More details of this topic have been presented in [67].
VI. ConclusionIn this work, a new approach to control jet into cross flow interactions was introduced, in which two small
coolant jets were installed at both sides in front of the main coolant jet. Interactions between the new CRVPs
generated by small jets, and the CRVP generated by the main coolant jet considerably reduce the mixing strength of
the coolant jets with the hot cross flow. In order for the results of this new approach to be comparable with the ones
from the traditionally film cooling methods, the total coolant air and the cross sections of the new combined triple-
jetshave been taken to be the same. Our results indicate that, our new approach has at least four significant effects
as:
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1) Mixing Reduction between the Coolant Jets and the Main Hot Free Stream: the new interactions between the
weaker CRVPs created by the small jets at both side of the main hole, and the CRVP generated by the main
coolant jet weaken their strengths. Theinteraction between the vortexes of opposite sings when touching eachother at the contact points is the key of our new combined triple-jets approach. The reduction of mixing
strength between the hot free stream and the coolant jets increases the stability and steadiness of coolant effectsdownstream of the injection jets. It is necessary to emphasize that, this technique is quite different from double
rows staggered holes which is widely used in film cooling. In the staggered cases, there are not strong
interactions between neighboring vortices. The main goal of staggered rows is to improve film coolingeffectiveness by overlapping the effecetcs and help uniform.
2) Significant Improvement of the Film Cooling Effectiveness (about 50%): Installing two small new jets at
both sides in front of the main coolant jet will divert the hot cross flow and thus, does not permit it to flow intothe low pressure region behind the main coolant jet. In this situation, this is the coolant jet which fills in this
region (not the hot cross flow). Also, in our new combined triple-jetstechnique, the interactions between the
CRVPs generated by the main and the small coolant jets like a fluid barrier prevent the displacement of the hot
gases towards the surface.
3) Significant Improvement of the Coolant Film Distribution: The existences of two small coolant jets causemore uniform coolant film distribution. Because of the mixing reduction between the main stream and the
coolant jets, this uniformity extends to downstream. In combined triple-jetssystem it seems that, not only the
interactions between the new weak CRVPs and the main strong CRVP arent undesirable, but also they areuseful for accomplishing a desirable momentum and energy transport in spanwise, leading to a more uniform
coolant film distribution in that direction as well.4) Enhancement of Skin Friction Drag Reduction: Generally, when a jet is injected into a turbulent cross flow, it
disturbs the cross flow turbulent boundary layer and thus the skin friction drag will be decreased. The more the
amount of boundary layer disturbance and the more the steadiness of this disturbance along the streawise
direction, the more the skin friction drag reduction. Our results show that, in our combined triple-jetsunits the
skin friction drag reduction is about 20% higher.
It should be noted that, this work is a fundamental study to introduce this new approach for controlling the
mixing of a jet into a cross flow, particularly to improve film cooling effectiveness. Surely, more work needs tobe done to optimize it. Our research teams are presently working on the effects of different jet geometry and
flow characteristics on this new approach.
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16Amer, A.A, Jubran, B.A., and Hamdan, M.A., (1992) Comparison of Different Two-Equation Turbulence Models forPrediction of Film Cooling From Two Rows of Holes, Numerical Heat Transfer, Part A, Vol. 21, pp. 143-162.
17Hassan I., Findlay, M., Salcudean, M., and Gartshore,I. (1998) Prediction of Film Cooling with Compountd- Angle Injection
Using Different Turbulence Models, CFD 98,pp.1-6.18Medic G. and Durbin P., (2002) Toward Improved Prediction of Heat Transfer on Turbine Blades, Journal of
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Chochua, G., Shyy, W., Thakur, S., Brankovic, A., Lieneau, J., Porter, L. and Lischinsky, D., (2000) "A Computational andExperimental Investigation of turbulent Jet and Crossflow Interaction," Numerical Heat Transfer, Vol. 38, pp. 557-572.21Keimasi, M. R. and Taeibi-Rahni, M., (2001) Numerical Simulation of Jets in a cross flow Using Different Turbulence
Models, AIAA J., Vol. 39, No. 12, pp. 2268-2277.22Javadi, A., Javadi, K., Taeibi-Rahni M., and Keimasi M., (2002) Reynolds Stress Turbulence Models for Prediction of Shear
Stress Terms in Cross Flow Film Cooling Numerical Simulation, 4th International ASME/JSME/KSME Symposium oncomputational technology CFD) for fluid/thermal/chemical/stress systems and industrial application, Hyatt Regency, Vancouver,
CANADA.23Thevenin, J., Amaral, M., Malvos, H., and Mauillon, L., (1998) Computation of a Three-Dimensional Swirling Jet into a
Crossflow Using a Reynolds Stress Turbulence Model, ECCOMAS98.24
Fu, S., Launder, B.E., and Leschziner, M.A., (1987) Modeling Strongly Swirling Recirculating Jet Flow with Reynolds-StressTransport Closures, Sixth Symposium on Turbulent Shear Flows, Toulouse, France.
25Ince, N.Z. and Leschziner, M.A., (1990) Calculation of Single and Multiple Jets in Cross Flow with and without Impingement
Using Second-Moment Closure, Eng. Turbulence modeling and Experiments, Elsevier, pp. 143.26
Tyagi, M. and Acharya, S., (1999) Large eddy simulation of Jets in Crossflow: Free stream Turbulence Effects, FEDSM 99-
7799, 3rd
ASME/JSME Joint Fluid Engineering Conference.27Ramezani-Zadeh, M. and Taeibi-Rahni, M., (2001) Large Eddy Simulation of Multiple Jets in a Cross Flow Using
Smagorinsky Model, ISME 2001, pp. 293-299, Guilan University, Rasht-Iran.28
Ramezani-Zadeh, M., Saidi, M.H., and Taeibi-Rahni, M., (2004) Large Eddy Simulation of Density Ratio Effects on Two-Dimensional Film Cooling, 2ndBSME-ASME Int. Conference n Thermal Engineering, Dhaka, Bangladesh, Vol. 2, pp. 659-665.
29Eckert, E.R.G. and Livingood, J.N.B. (1954) Comparison of Effectiveness of Convection, Transpiration, and Film-Cooling
Methods with Air as Coolant, NASA-Report-1182.
30Bladauf, S., Schulz, A., and Witting, S., (2001) High-Resolution Measurements of Local Heat Transfer Coefficients From
Discrete Hole Film Cooling, Journal of Turbomachinery, Vol. 123.31
Goldstein, R.J., Jin, P., and Olson, R.L., (1999) Film Cooling Effectiveness and Mass/Heat Transfer Coefficient Downstreamof one Row of Discrete Holes, Journal of Turbomachinery, Vol.121 p.225-232.
32Bell, C.M., Hamakawa, H., and Ligrani, P.M., (2000) Film Cooling From Shaped Holes, ASME J., Vol. 122.33
Ahn J., Jung, I.S. and Lee J.S., (2003) Film Cooling from Two Rows of Holes with Opposite Orientation Angle: InjectantBehavior and Adiabatic Film Cooling Effectiveness, Int. J. Heat and Fluid Flow Vol. 24.
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Chang, Y.R. and Chen, K.S., (1995) Prediction of Opposing turbulent Line Jets Discharged Laterally into ConfinedCrossflow, Int. J. Heat Mass Transfer, Vol. 38 No. 9.
35Bridges A. and Smith D. R., (2003) Influence of Orifice Orientation on the Synthetic Jet-boundary-layer Interaction, AIAA J.
Vol. 41, No. 12.36 McGrath, L.E. and Leylek J.H., (1999) Physics of Hot Crossflow Ingestion in Film Cooling, ASME J., Vol. 121.37Goldstein, R.J. and Stone, L.D., (1997) Row-of-Holes Film Cooling of Curved Walls at Low Injection Angle, Transactions
of ASME, Vol. 119,pp.574-57938Azzi, A., Abidat, M., Jubran, B.A., and Theodoridis, G.S., (2001) "Film Cooling Predictions of Simple and Compound Angle
Injection from One and Two Staggered Rows," Numerical Heat Transfer, Part A., Vol. 40, pp. 1-23.39Jubran, B.A. and Maiteh, B.Y., (1999)" Film Cooling and Heat Transfer from a Combination of Two Rows of Simple and/or
Compound Angle Holes in Inline and/or Staggered Configurations," Journal of Heat and Mass Transfer, Vol. 34, No 6, 495-502.40Gartshore, I. and Salcudean, M., (2001) Film Cooling Injection Hole geometry: Hole Shape Comparison for Compound
Cooling Orientation, AIAA J., Vol. 39, No. 8, pp-1493-1499.41Rowbury D.A., Oldfield M.L.G., and Lock G.D., (2001) a Method for Correlating the Influence of External Crossflow on the
Discharge Coefficient of Film Cooling Holes, ASME J., Vol. 123.
42Holdeman, J.D. and Walker, R.E. (1977) Mixing of a Row of Jets with a Confined Crossflow, AIAA J., Vol. 15, No. 2, pp.243-249.
43Teng, S. and Han, Je-C., (2001) Effect of Film-Hole Shape on Turbine-Blade Heat-Transfer Coefficient Distribution, Journal
of Thermophysics and Heat Transfer, Vol. 15, No. 3.44Goldstein, R.J., Eckert, E.R. G., and Burggraf, F., (1973) Effects of Hole Geometry and Density on Three-Dimensional Film
Cooling, Int. J. Heat Mass transfer, Vol. 17, pp. 595-607.45
Hyung, H.C., Seung, G.K., and Dong, H.R., (2001) Heat/Mass Transfer Measurement within a Film Cooling Hole of Squareand Rectangular Cross Section, ASME, Vol. 123.
46Friedrichs, S., Hodson, H.P., and Dawes, W.N., (1999) the Design of an Improved End Wall Film-Cooling Configuration,ASME, Journal of Turbomachinery, Vol. 121, pp. 772-780.
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47Burd, S.W., Kaszeta, R.W., and Simon, T.W., (1998) Measurements in Film Cooling Flows: Hole L/D and Turbulenceintensity, Journal of Turbumachinary, Vol. 120, No. 4, pp. 791-798
48Walters, D.K. and Leylek, J.H. (1997) a Systematic Computational Methodology Applied to a Three-Dimensional Film
Cooling Flow Field, ASME J. Turbomachinery, Vol. 119, pp.777-785.49Seo, H.J., Lee, J.S. and Ligrani, P.M., (1998) the Effect of Injection Hole Length on Film Cooling with Bulk Flow
Pulsations, International Journal of Heat and Mass Transfer, Vol. 41.50Azzi, A. and Jubran, B. A., (2003), Numerical Modeling of Film Cooling from Short Length Stream-Wise Injection Holes, J.
Heat and Mass Transfer, Vol. 39.51Sterland, P.R. and Hollingsworth, M.A., (1975), an Experimental Study of Multiple Jets Directed Normally to a Cross-Flow,Journal of Mechanical Engineering Science, Vol. 17, No. 3.
52Ligrani, P.M., Ciriello, S., and Bishop. D.T. (1992) Heat Transfer, Adiabatic Effectiveness, and Injectant DistributionsDownstream of a; Single Row and two Staggered Rows of Compound Angle Film Cooling Holes, ASME J. Turbomachinery, Vol.114, pp. 687-700.
53Ligrani, P.M., Wigle, J.M., Ciriello, S., and Jackson, S.W., (1994) "Film-Cooling From Holes with Compound Angle
Orientations: Part 1-Results Downstream of Two Staggered Rows of Holes with 3d Spanwise Spacing," ASME Journal of HeatTransfer, Vol. 116, pp. 341-352.
54Ligrani, P.M. and Ramsey, A.E., (1997) Film Cooling from Spaswise-Orinted Holes in Two Staggered Rows, ASME J.
Turbomachinery, Vol. 119, pp. 562-567.55Dittmar, J., Schulz, A., and Wittig, S., (2004) Adiabatic Effectiveness and Heat Transfer Coefficient of Shaped Film Cooling
Holes on a Scaled Guide Vane Pressure Side Model, International Journal of Rotating Machinery, Vol. 10, No.5, pp. 345354.56
Behbahani, A.I. and Goldstein, R.J., (1983) Local Heat Transfer to Staggered Arrays of Impinging Circular Air Jets, ASMEJ. of Engineering and Power, Vol. 105, pp. 354-360.
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Florschuetz, L.W., Metzger, D.E., and Su, C.C, (1984) Heat Transfer Characteristics for Jet Array Impingement with InitialCrossflow, ASME J. of Heat Transfer Vol. 106, pp. 34-41.
58Vijay K. Garg Heat Transfer on a Film-Cooled Rotating Blade NASA/CR1999-209301
59Ekkad, S.V., Gao, L., and Hebert, R.T., (2002) Effect of Jet-to-Jet Spacing in Impingement Arrays on Heat Transfer, ASME
Paper IMECE2002-32108, New Orleans, La.
60Walters, D.K. and Leylek, J.H., (2000) Impact of Film-Cooling Jets on Turbine Aerodynamic Losses, J. Turbomachinery,
Vol. 122, pp.537-545.61Hass, W., Rodi., W., and Schonung B., (1992) the Influence of Density Difference between Hot and Coolant Gas on Film
Cooling by a Row of Holes: Prediction and Experiments, J. Turbomachinery, Vol. 114.62Mehendale, A. and Han, J., (1992) Influence of Main Stream Turbulence on Leading Edge Film Cooling Heat Transfer J.
Turbomachinery, Vol. 114 No. 10, pp. 705-715.63Kohli, A., and Bogard, D., (1998) Effects of Very High Free-Stream Turbulence on the Jet-Mainstream Interaction in a Film
Cooling Flow, ASME J. Turbomachinery, Vol. 120, pp. 785-790.64Ou, S., Mehendale, A.B., and Han, J.C. (1990) Influence of High Mainstream Turbulence on Leading Edge Film Cooling Heat
Transfer: Effect of Film Hole Row Location, ASME90-WA/HT-5, ASME Winter Annual Meeting, Dallas.65Javadi, A., Javadi, K., and Taeibi-Rahni, M., (2002) Simulation of Film Cooling in Gas Turbine Blades, Aerospace Research
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Javadi, A., Javadi, kh., Taebi-Rahni, M., Darbandi, M., Aavani, Kh., and Mahjoob, S., (2003) New Approach in Film Coolingon Gas Turbine Blades Using Combination of Suction/Blowing flows, Annual Report, Aerospace Research Inst., Ministry ofScience, Research and Technology, ARI.-82-31-FCG-4-1-1
67Javadi. Kh., Taeibi-Rahni M, and Javadi A., (2004) New Method to Control Turbulent Jet-into-CrossFlow Interaction- Skin
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Figure 1-a.Computational domain in ordinary film cooling.
Figure 1-b. Our new film cooling scheme, showing new coolant small jets
besides the main coolant jet.
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CRVP and New weak VortexesCRVP
Z/D
Y/D
-1 0 1
0
1
2
Figure 6-a. High interactions between a
strong CRVP and hot cross flow in the
ordinary film cooling
Figure 6-b. New weaker vortices generated by
the small coolant jets breaking down the
vortex strengths and reducing the interactions
and mixing process of the hot and main
coolant jets
X/D
Z/D
0 1 2 3 4-2
-1
0
1
2
Figure 7-b. The small coolant jets diverting the
hot cross flow and not permitting it to flow
into the wake region, and improving the film
cooling effectiveness.
Figure 7-a. The flow of hot gases into the low
pressure region right after jet, decreasing the
film cooling effectiveness.
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X
Y
Z
Figure 8-b. The interactions between the small
coolant jets and main jet reducing the
interactions between coolant jets and cross flow
also prevent of the influence of hot cross flow
toward the surface (comb. Triple-jets, this work).
Figure 8-a. High interactions between the
coolant jet and the hot cross flow and the
influence of hot gases toward the surface,
decreasing film cooling effectiveness (ordinary
film cooling).
X/D
Y/D
0 2 4
-1
0
1
2
3
4
Figure. 9-a, The velocity vectors at jet center
plane, Showing high interaction and more
penetration into cross flow boundary layer
(ordinary film cooling).
X/D
Y/D
0 2 4
-1
0
1
2
3
4
Figure 9-b. The velocity vectors at jet center
plane in our new combined triple-jets
approach, less interaction between cross
flow and coolant jet and less penetration
into cross flow boundary layer.
FluidBa
rrier
Influence
ofh
otgas
toward
surface
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Figure 11-a Inappropriate cooling effectiveness and uniformity over the plate in ordinary film cooling
Figure 11-b. The combined triple-jets shows a high effectiveness and proper cooling uniformity over
the plate (with a same coolant air and total cross section of coolant hole in both systems).
Figure 10 Comparison of the film cooling effectiveness ( ) between the ordinary and our new
approach film cooling, notable enhancement (about 50%) is shown in this figure.
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Num. Falt Plate
Comb. Jets
Rect.
U/Vjet
Y/D
-0.5 0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
Square
Num. Falt Plate
Comb. Jets
Rect.
U/Vjet
Y/D
-0.5 0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
Square
Figure 12. Comparison of the streamwise velocity profiles at the main jet center plane and at
X/D=3, 8, 15.
X/D=3 X/D=8 X/D=15
Num. Falt Plate
Comb. Jets
Rect.
U/Vjet
Y/D
-0.5 0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
Square
X/D
U/Vjet
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Square
Num. Falt Plate
Comb. Jets
Rect.
X/D
U/Vjet
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Square
Num. Falt Plate
Comb. Jets
Rect.
X/D
U/Vjet
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Square
Num. Falt Plate
Comb. Jets
Rect.
Figure 13. Comparison of the streamwise velocity gradient distributions along the
streamwise direction at different positions of Z/D=0., -0.5, and 1.5.
Theory
Comb. Jets (This Work)
Num. Flat Plate
X/D0 10 20 30
0
0.001
0.002
0.003
0.004
0.005
Rect.
Square
Figure 14. Comparisons of the averaged skin friction drag for our new combined triple-jets
approach and common geometries in the ordinary film cooling. A considerable reduction of
skin friction drag is shown from this figure in our new approach. (Note, for comparison
purpose, the results of the turbulent flow over flat plate without injection have also been
resented).
fC