Computational Analysis of

Conjugate Heat Transfer and

Particulate Deposition on a High
Pressure Turbine Vane
Weiguo Ai1 Numerical computations were conducted to simulate flash deposition experiments on gas
e-mail: aiweiguo@byu.net
turbine disk samples with internal impingement and film cooling using a computational
fluid dynamics (CFD) code (FLUENT). The standard k-␻ turbulence model and Reynolds-
Thomas H. Fletcher averaged Navier–Stokes were employed to compute the flow field and heat transfer. The
boundary conditions were specified to be in agreement with the conditions measured in
Department of Chemical Engineering,
experiments performed in the BYU turbine accelerated deposition facility (TADF). A
Brigham Young University,
Lagrangian particle method was utilized to predict the ash particulate deposition. User-
Provo, UT 84602
defined subroutines were linked with FLUENT to build the deposition model. The model
includes particle sticking/rebounding and particle detachment, which are applied to the
interaction of particles with the impinged wall surface to describe the particle behavior.
Conjugate heat transfer calculations were performed to determine the temperature dis-
tribution and heat transfer coefficient in the region close to the film cooling hole and in
the regions further downstream of a row of film cooling holes. Computational and ex-
perimental results were compared to understand the effect of film hole spacing, hole size,
and TBC on surface heat transfer. Calculated capture efficiencies compare well with
experimental results.
关DOI: 10.1115/1.4003716兴

1 Introduction peared for the smallest pitch to diameter ratio. Drost et al. 关3兴
carried out an experimental work on film cooling effectiveness
The continuous demand on performance improvement in gas
and heat transfer investigation on a flat plate. They reported that
turbine engines requires the engine components to be designed for
mainstream turbulence reduced flat plate effectiveness at low and
higher combustor exit temperatures. Current advanced gas turbine
moderate blowing ratios but increased the effectiveness at high
engines operate at turbine rotor inlet temperatures 1200– 1450° C
blowing ratios due to a better dispersion of the detaching jets in
共or 2200– 2600° F兲, which is hot enough to melt or severely
the boundary layer. For the effect of rows of cylindrical rows,
weaken critical areas of the engine downstream of the combustor.
Saumweber and Schulz 关4兴 reported that the second row hole
With the introduction of syngas derived from “dirty fuels” for
shape and blowing ratio dominated film cooling performance
replacing natural gas in a gas turbine system, small particles con-
downstream of two rows of holes. The upstream row holes in-
tained in the combustion product can accumulate on the compo-
nent surface, resulting in severe adverse effects to gas turbine creased film cooling effectiveness downstream of the second ejec-
components. Component surface temperature is one of the signifi- tion locations.
cant factors determining whether or not a particular dust is depos- A systematic computational methodology was developed by
ited. Kim et al. 关1兴 reported that the surface temperature onto Walters and Leylek 关5兴 to calculate the adiabatic effectiveness of
which the particles impact must be above a certain threshold tem- film cooling. Four critical issues to the success of a computational
perature if deposition is to occur. Increasing the vane metal tem- prediction were proposed: 共i兲 computational model, 共ii兲 geometry
perature increases the amount of deposits significantly. representation and grid generation, 共iii兲 discretization scheme, and
Film cooling is a common technique used in the gas turbine 共iv兲 turbulence modeling. Their computational results tended to
industry to prevent hot-section components from failing at el- show that the use of unstructured grids overpredicted the center-
evated temperatures. The efficiency of this technique depends on line effectiveness values and underpredicted the lateral average
several parameters such as the injection blowing ratio, the main- values but showed more consistent agreement with experimental
stream characteristics, the surface roughness, the spacing of the data than with a structured grid simulation. Hoda and Acharya 关6兴
holes, and their arrangement and injection angle. To design effi- investigated the performance of several existing turbulence mod-
cient cooling systems and mitigate particulate deposition, it is els on the prediction of film coolant jets in crossflow. Computa-
important to know the influence of a variety of parameters on the tional results were compared with measurements reported by Ajer-
cooling performance and their correlation with particulate deposi- sch et al. 关7兴 to examine whether the models accurately predicted
tion to predict deposition development. the dominant features of flow field. The use of the k-␻ model
Brown and Saluja 关2兴 studied coolant injection through a single yielded an improved prediction of near-wall structures. Jia et al.
hole and rows of holes with three ratios of pitch to diameter. The 关8兴 performed a systematic evaluation of the current computa-
greatest average effectiveness in the region close to the holes ap- tional model to study the film cooling fluid injection from slots or
holes into a crossflow. They concluded that the shear stress trans-
port k-␻ model provided a more faithful prediction of the mean
and root-mean-square 共RMS兲 velocity distribution. The 30 deg jet
1
Corresponding author.
Contributed by the International Gas Turbine Institute 共IGTI兲 of ASME for pub- provided the highest film cooling effectiveness. Harrison and Bog-
lication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 21, 2010;
final manuscript received December 3, 2010; published online July 25, 2011. Editor: ard 关9兴 found that the standard k-␻ 共SKW兲 model best predicted
David Wisler. laterally averaged adiabatic effectiveness, and that the realizable

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 C ap

Coola nt
Entra nc e

Ra diation
Shie ld

25 m m diam e te r
TBC-coated
target coupon

De pos it-lade n
com bus tor ex haust
ga s @1 20 0C

Fig. 1 Schematic of the BYU turbine accelerated deposition facility

k-␧ 共RKE兲 model was best along the centerline. The Reynolds motion for particles with normalized relaxation times ranging
stress model yielded the best predicted heat transfer coefficients. from 0.3 to 1000. Their results showed very good agreement with
In turbomachinery applications, the heat conduction inside the the experimental data of Liu and Agarwal 关16兴 over a wide range
solid cannot be neglected. It is therefore necessary to consider the of particle sizes. Greenfield and Quarini 关18兴 considered the drag
flow field together with temperature distributions within the metal. force as the principal force acting on particles. They represented
Bohn et al. 关10兴 studied the calculations of a film-cooled duct wall the effect of turbulence on the particles by using the eddy lifetime
with the boundary condition of an adiabatic heat transfer condi- model.
tion and a conjugate heat transfer condition for various configu- The previous numerical simulations applied different methods
rations of film holes. The conjugate heat transfer was found to in FLUENT package to study the secondary flow in the film cooling
influence the velocity field within the cooling film. The magnitude technology and compare the experimental results. Although the
of the peak secondary flow velocities was much higher for the agreement is not made completely, the conclusions from them are
adiabatic case than with the conjugate heat transfer, which de- still helpful to the numerical model built-up here. This paper in-
graded the performance of the cooling. Silieti et al. 关11兴 predicted vestigates film cooling effectiveness and heat transfer coefficients
film cooling effectiveness using three different turbulence models: with both conjugate heat transfer and adiabatic conditions in the
the RKE model, the shear stress transport 共SST兲 k-␻ model, and region close to film cooling holes and in the region further down-
the v2-f model. They predicted that film effectiveness obtained stream of a row of film cooling holes, based on the unstructured
from the conjugate model is in better agreement with the experi- grids and standard k-␻ turbulence model. Comparisons are made
mental data compared with the adiabatic model. Andreini et al. between computational and experimental results to understand the
关12兴 carried out several calculations to infer the trends of adiabatic effect of film hole spacing, hole size, and TBC on surface heat
and conjugate heat transfer performances in terms of heat transfer transfer. After heat transfer calculation, particle capture efficien-
coefficient and overall and adiabatic effectiveness. They con- cies are calculated and compared with measured values to evalu-
cluded that the reduction of metal temperature upstream of each ate the performance of the ash particulate deposition model. The
cooling hole increased as the blowing rate grew. Na et al. 关13兴 prediction combining those factors occurred in gas turbine is a
performed computations to study the conjugate heat transfer of a meaningful try for film cooling art.
flat plate with and without TBC. They found that the surface tem-
perature increased slightly when the thermal conductivity was re-
duced to a certain value.
Models of particle transport and deposition can be developed 2 Experimental Test Case
either by the Eulerian approach or the Langrangian approach. The The three-dimensional computational model is a simulation of
first major deposition models using a Eulerian approach were de- the experiments performed in the turbine accelerated deposition
veloped by Friedlander and Johnstone 关14兴 and Davies 关15兴. Liu facility 共TADF兲. A complete description of the experimental facil-
and Agarwal 关16兴 proposed a new expression for particle diffusiv- ity, including the test section, and instrumentation used in obtain-
ity, containing an additional term to account for enhanced depo- ing the temperature data was given by Ai et al. 关19兴. Only a brief
sition by inertia. The model yielded reasonable agreement with summary is provided here. A 1 in. diameter coupon sample was
deposition rate measurements for intermediate particle relaxation exposed to a jet from a natural gas burning combustor at turbine
times but poor agreement at high relaxation times. relevant temperatures and the correct flow Mach number 共Fig. 1兲.
In the Lagrangian approach, a number of particle trajectories The combustor was seeded with particulate to study deposition in
are simulated by solving the equations of continuity, momentum, an accelerated time. The bare metal sample was manufactured
and energy for individual representative particles. Multiple forces with three cylindrical holes spaced 4.5 mm apart at a 30 deg
on the particle are considered in the particle equation of motion. inclined angle relative to the freestream. The diameter 共d兲 of each
This approach provides detailed information on particle collisions hole was 1.5 mm. The middle hole exit was located in the center
at the surface that are required for sticking studies. Kallio and of the circular coupon, and the other two hole exits were located
Reeks 关17兴 presented a Lagrangian approach to model particles along a line of symmetry. The coupons were composed of Inconel
transported in turbulent duct flows. They solved the equation of alloy.

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 Table 1 Coupon configuration category dup 18␮ CD Rep
= 共u − up兲 + Fx 共1兲
d dt ␳pd2p 24
Plate Material 共mm兲 ␣ s/d The first term on the right-hand side of this equation represents
0 the drag force per unit particle mass and Fx stands for the Saffman
M1 Inconel 1 30 3.375
M2 Inconel 1 300 4.5
lift force 关22兴. Phase changes of the particle are not taken into
M3 Inconel 1.5 300 3 account. The equation of particle temperature is defined as
TBC Nickel alloy with TBC 1 300 4.5 dTp
m pC p = hcAp共T⬁ − Tp兲 共2兲
dt
The assumption is made that the particles have no effect on the
fluid flow due to the low particle loading.
The coolant chamber simulates film cooling that is typically The El-Batsh deposition model 关23兴 was employed in this simu-
used in modern vanes and rotors. The coolant was heated to the lation to study the particle-wall interaction. This model determines
appropriate temperature and entered the coolant chamber, im- the fraction of incident particles that remain on the surface, and
pinged on the back side of the coupon, and exited through the consists of two interaction processes. One interaction is a pure
holes in the coupon. The design allows for coolant temperature mechanical interaction in the absence of the fluid force. It mainly
measurement near the hole entrance using a thermocouple determines the condition at which no rebound occurs and is called
mounted 4 mm behind the coupon and in the center of the coolant the sticking process. The other interaction is the detachment pro-
air flow. The gas and particulate impinged on the coupon surface cess, which is a fluid dynamic interaction between the fluid and
at a 45 deg angle. The rear and front surface temperatures of the the adhered particles. Detachment is related to the stability of the
coupon were measured using an Red/Green/Blue 共RGB兲 camera particles at the surface. van der Waals force, electrostatic forces,
with a two-color technique. and liquid bridges play a significant role during the process of
The coupons employed in the experiments are described in particle sticking. In the case of particle deposition on gas turbine
Table 1. The thickness of the TBC layer was 0.25 mm. The cool- surfaces, the van der Waals force is the major contributor to the
ant was injected from the film cooling holes and its density ratio particle sticking force. The sticking force Fpo is calculated as
共␳c / ␳⬁兲 is controlled by the heater. To study the effect of hole
geometry, hole spacing, and TBC, a series of tests were performed Fpo = ksWAdp 共3兲
to measure surface temperature, capture efficiency, deposit pattern where WA共J / m 兲 is a constant that depends on the properties of
2

features, and deposit thickness. Blowing ratios 共M兲 of 0.5–4.0 the particle and of the surface 共WA is also used in Eq. 共5兲兲. ks is a
were used with the density ratio maintained from 1.5 to 2.2. constant equal to 3␲ / 4. The capture velocity in the present study
is given by

3 Details of Numerical Simulation vcr = 冋 册

2E
dp
10/7
共4兲

3.1 Approach where E is the Young modulus. The particle normal impact veloc-
ity is compared with the particle capture velocity. If the particle
3.1.1 Gas Phase Simulation. Simulations were performed us-
normal impact velocity is smaller than the capture velocity, the
ing FLUENT 6.3.26 with Reynolds-averaged Navier–Stokes 共RANS兲
particle sticks. Otherwise, the particle rebounds and continues the
transport equations and standard k-␻ turbulent model 关20,21兴. The
trajectory until it leaves the domain or impacts the surface at
continuity, momentum, and energy equations in the fluid and solid
another place.
regions were solved to predict velocity, temperature fields, and
The critical momentum theory is applied to describe the mecha-
film cooling effectiveness for conjugate heat film cooling from the
nism of particle detachment from a surface. The critical wall shear
holes. The interface between fluid and solid was specified as a
velocity u␶c is
coupled boundary, which avoided the use of the film cooling heat
transfer boundary condition and allows a direct calculation of the
heat transfer and wall temperature. The physical domain was
separated into fluid and solid blocks by the wall. The three-
u2␶c = 冉 冊
C uW A W A
␳ d p d pK c
1/3
共5兲

dimensional Navier–Stokes equations and turbulence equations The particle will be removed from the surface if the turbulent
were solved in the fluid blocks. The Fourier equation was applied flow has a wall friction velocity 共=冑␶␻ / ␳, where ␶␻ is the wall
in the solid body blocks. Coupling of fluid blocks and solid blocks shear stress兲 that is larger than u␶c. The relevant parameters and
was achieved by equating the local heat fluxes passing through the more details regarding the interaction between the particles and
common cell faces. the wall were stated in Ref. 关23兴.
The semi-implicit method for pressure-linked equations Since the particle phase is sufficiently dilute, particle-particle
共SIMPLE兲 algorithm was used to couple the pressure and velocity. interactions and effects of particle volume fraction on the gas
Coefficients are determined by the quadratic upstream interpola- phase are negligible.
tion for convective kinematics 共QUICK兲 scheme for the momen-
tum equations. The discretization of the energy governing equa- 3.1.3 Geometry. A schematic of the computational domain to
tion was performed using the first upwind scheme and the k-␻ simulate the experiment is shown in Fig. 2. The computational
equation used the second upwind scheme. Convergence was de- domain includes the coolant supply channel, the cylindrical cool-
termined by the orders of magnitude reduction of parameter re- ing holes, and the mainstream duct. The crossflow section is 39
siduals: four for continuity, six for velocity, seven for energy, and mm in width, 36 mm in height, and 81 mm in length. The row of
five for turbulence quantities. three inclined film cooling holes with a 30 deg angle against the
plate is located 36 mm downstream of the flat plate leading edge
3.1.2 Particle Phase Simulation. The Lagrangian approach and 45 mm upstream of the fluid outlet. The hole diameter is 1.5
was used for the particle phase. The two forces considered in the mm and hole spacing is 3 times that of the hole diameter for case
particle transport model are the drag force at steady state and the M3 共refer to Refs. 关19,24兴兲. The thickness of the plate is 3.5 mm
Saffman lift force. The trajectory of the particle is predicted by the and the length-to-diameter ratio 共L/d兲 of coolant passage is 4. A
integration of its equation of particle motion 共shown here for the high temperature circular gas jet with a diameter of 25.4 mm
x-direction兲 impinges on the flat plate with a 45 deg angle, and blends with the

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 Fig. 2 Schematic of the overall computational domain

film cooling air, and then flows out at the exit located in the cooling of the flat plate with conjugate heat transfer, with
schematic to the right side of duct. The coolant fluid was injected 475,034–1,551,455 cells. The centerline effectiveness down-
from a tube with a diameter of 13.5 mm to a plenum located stream of the middle film hole is shown in Fig. 4 for the grid-
beneath the plate. The coolant plenum is 40.5 mm in height, 39 independence calculations. The finer mesh resulted in little change
mm in width, and 81 mm in length. The mainstream gas tempera- downstream in the region close to film holes 共Y / d ⬍ 10兲. There-
ture was specified at 1453 K, and the measured density ratio was fore, due to computational time restrictions, the mesh with the
matched by varying the temperature of the inlet coolant. Addi- lowest number of grids was adapted for subsequent computational
tional cases were performed with the same geometry, except for cases.
different hole sizes and hole spacing.
3.2 Boundary Conditions. Seven simulation cases were cho-
3.1.4 Grid Generation and Independence. Geometry and sen to match the experimental test cases, as shown in Table 2. The
mesh grid were generated using GAMBIT with unstructured tetra- boundaries were defined from experimental conditions. The main-
hedral topology grids, which consist of tetrahedral cells, as shown stream inlet air velocity was set to 173 m/s and 1453 K for all
in Fig. 3. The total number of computational cells was 475,034 for cases. The k and ␻ profiles were specified using a uniform distri-
case M3 and 421,949 for cases M1 and M2. The accuracy of the bution corresponding to a turbulence intensity of 4.7% for most
computational model is strongly dependent on the quantity and cases. The temperatures on the top and side walls of the main-
location of grids that resolve the relevant flow physics. To study stream duct were set to 900 K, except for the wall close to the
grid-independence, three test grids were used to compute film inlet, which was 300 K. The fluid viscosity was held constant at
1.79⫻ 10−5 kg/ 共m s兲. The top and bottom walls of the solid plate
are specified as a coupled wall in the FLUENT solver, which avoids
specifying the heat flux or other boundary conditions. The sur-

0 .7
4 7 5 ,0 3 4 C e lls
0 .6 6 5 8 ,4 5 5 C e lls
1 ,5 5 1 ,6 5 5 C e lls
Cooling Effectivenss

0 .5

0 .4

0 .3

0 .2

0 .1

0 .0
0 2 4 6 8 1 0 1 2

Y/d
Fig. 4 Grid sensitivity study-centerline normalized tempera-
Fig. 3 Details of the grid used in the simulations ture for the three grids

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 Table 2 Summary of cases simulated „kt is the thermal conductivity and SA means superalloy,
versus TBC…

kt of SA/TBC Blowing ratio

Case Plate hot side Plate s/d TBC 共W / m K兲 共M兲

1 Conjugate M1 3.4 N/A 9/n.a. 0.5,1.0,2.0

2 Conjugate M2 4.5 N/A 9/n.a. 0.5,1.0,2.1
3 Conjugate M3 3.0 N/A 9/n.a. 0.5,1.0,1.5,2.0
4 Adiabatic M2 4.5 N/A 0/n.a. 1.0
5 Adiabatic M3 3.0 N/A 0/n.a. 1.0
6 Conjugate TBC 4.5 Yes 9/1.78 1.0
7 Conjugate TBC 4.5 Yes 9/0.3 1.0

rounding walls of the solid plate were set to be adiabatic, requir- schematic of the model is presented in Fig. 5. The model geom-
ing the heat flux to be in only one direction inside the solid plate. etry included 30,100 cells. The inlet velocity was 173 m/s and the
At the outflow boundary, the gradients of all flow variables with wall of the inlet tube was adiabatic. All other walls were assumed
respect to the streamwise direction were set to zero, and the no- as a pressure outlet with a temperature of 300 K, simulating at-
slip condition with wall function was applied at the walls. The mospheric conditions.
temperature at the inlet of the coolant plenum was varied to obtain When the particles arrive at the target surface, the sticking
the measured density ratio in each experiment. The walls of the model was applied to determine whether the particle sticks to the
coolant plenum were set to be adiabatic. The gas was modeled surface or escapes. To investigate the correlation of Young modu-
with gas density as only a function of the fluid temperature. lus with temperature, the model was tuned to fit the capture effi-
In the deposition simulation, 5000 ash particles were released at ciency obtained in the experiments. The assumption was made, in
the center of the mainstream inlet surface and impinged the target which the particle sticking properties represent the target surface
plate. The temperatures and velocities of the particles were ini- properties as well. The composite Young modulus was computed
tially set to the same values as the mainstream gas. The properties by setting the Poisson ratio to a constant value of 0.27 for both the
of the ash particles are listed in Table 3. The average size of particle and the surface 关26兴.
particles in the simulation was 13.4 ␮m and the particle size bins The continuous-phase flow field was solved and the discrete-
complied with a Rosin–Rammler logarithm distribution. Particle phase injection was tracked. As the particle impacted on the target
trajectories and temperatures were modeled on a particle-by- surface, the particle temperatures and velocity were calculated as
particle basis in the stochastic random-walk model, which is based well. The capture velocities were calculated on the basis of the
on the force balance on the particle and on the convective heat assumed value of the Young modulus. The particles with normal
from the particle. The Runge–Kutta method was used to integrate velocities less than the capture velocity stuck to the surface. The
the particle equations, and the Cunningham correction to Stokes’ capture efficiency is the ratio of the mass of the adhered particles
drag law was also used. Each particle in the deposition simulation to the total mass of particles injected into the domain. The average
was tracked as it was carried through the computational domain between the particle temperature and the surface temperature was
by a combination of mean velocities and turbulent velocities cal- used to determine the properties for the deposition model. This
culated from k and ␻. process was iterated with different values of Ep until the capture
efficiency in the model was in agreement with the result obtained
4 Results and Discussion
4.1 Young Modulus Determination. The sticking model
used here calculates the capture velocity of the particle at the
surface based on the van der Waals force. The capture velocity
was determined by the size of the particle, the temperature, and
the material properties of the particle and target surface. An im-
portant model parameter in the model is the Young modulus 共E兲,
which is not available in literature. Soltani and Ahmadi 关25兴 docu-
mented that the value of E of a steel target surface is 2.15
⫻ 1014 while E of particles ranges from 1 ⫻ 105 Pa to 1
⫻ 1010 Pa. The E was obtained in this model by fitting experi-
mental data. Experiments were performed in the TADF with gas
temperatures varying from 1294 K to 1453 K. The coupon was
made of Inconel and the back side was insulated by ceramic ma-
terial, resulting in adiabatic conditions. The ash-laden gas im-
pinged on the disk with a 45 deg angle. The capture efficiency was
calculated as the deposit mass divided by the particle mass fed
into the system.
Two-dimensional numerical computations were performed to
solve the flow field and particle trajectories for this set of tests. A

Table 3 Particle properties

d ␳ Cp K
共␮m兲 共kg/ m3兲 共J / kg K兲 共W / m K兲

13.4 990 984 0.5

Fig. 5 Schematic of the 2D model

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 1 0 1 0 0

Capture Efficiency (%)

8 M o d e l
E x p e r im e n t 8 0 1 4 5 3 K
1 4 2 5 K

Im p a c t E ffic ie n c y ( % )
6 1 4 0 8 K
6 0 1 3 7 4 K
4
1 3 5 2 K
1 2 9 3 K

2
4 0

0 2 0
1 2 5 0 1 3 0 0 1 3 5 0 1 4 0 0 1 4 5 0 1 5 0 0

Tg (K) 0
0 2 4 6 8 1 0 1 2
Fig. 6 Calculated capture efficiencies obtained from 2D CFD
modeling versus measured values (a) P a r tic le D ia m e te r ( m m )

1 0 0
in the experiments for each gas temperature. The dependence of 1 4 5 3 K
Young modulus on the temperature was then fit to an exponential 1 4 2 5 K
function, as shown in Eq. 共6兲. Figure 6 shows the calculated cap- 8 0
1 4 0 8 K
ture efficiency from the CFD model using Eq. 共6兲. Good agree-

S tic k in g E ffic ie n c y ( % )
1 3 7 4 K
ment is shown with the experiments performed as a function of 1 3 5 2 K
6 0 1 2 9 3 K
gas temperature.
Ep = 3 ⫻ 1020 exp共− 0.02365Tg兲 共6兲
4 0
Although particles can be delivered by the inertial force to the
targeted surface, the deposition that occurs depends on whether
particles stick upon arrival at the surface. To specify the effect of 2 0
delivery and attachment on surface deposition, the capture effi-
ciency is divided into two terms: impact efficiency and sticking
efficiency. Impact efficiency is defined as the ratio of mass of 0
particles impacting the surface to the total particle mass flowing 0 2 4 6 8 1 0 1 2
into the system. Sticking efficiency is the ratio of the mass of
particles sticking on the surface to the mass of impacted particles. (b) P a r tic le D ia m e te r ( m m )
Figure 7 shows calculated impact efficiency, sticking efficiency,
and overall capture efficiency for different size-classes of par- 6 0
ticles. As can be seen, the impact efficiency increases with particle 1 4 5 3 K
size. For 8 – 10 ␮m diameter particles, the impaction efficiency in 5 0 1 4 2 5 K
this experiment is close to 100%. This is due to the large Stokes 1 4 0 8 K
number, which enables particles to maintain their trajectories and 1 3 7 4 K
C a p tu r e E ffic ie n c y ( % )

4 0 1 3 5 2 K
impact the target surface. The temperature has only a slight effect 1 2 9 3 K
on impingement efficiency.
Equation 共4兲 shows that critical capture velocity of particles is 3 0
inversely proportional to particle size, which indicates that small
particles have a greater tendency to stick on the surface than large
particles. Figure 7共b兲 shows that sticking efficiency decreases with 2 0
increasing particle size. For particles larger than 10 ␮m, the effi-
ciency is close to zero while for particles less than 2 ␮m, the 1 0
efficiency is 100%. For a given particle size, the sticking effi-
ciency increases with increasing temperature.
The capture efficiency for different particle sizes was obtained 0
0 2 4 6 8 1 0 1 2
by multiplying the impact efficiency by the sticking efficiency, as
shown in Fig. 7共c兲. At the lowest temperature of 1293 K, the peak (c) P a r tic le D ia m e te r ( m m )
capture efficiency appeared in the size range of 2 – 4 ␮m. At 1453
K, the peak is located in the range of 8 ␮m. The influence of Fig. 7 2D CFD calculations of „a… impact efficiency, „b… stick-
temperature on deposition for various particle sizes is treated in ing efficiency, and „c… capture efficiency versus particle size for
the Young modulus correlation 共Eq. 共6兲兲. The capture efficiency various gas temperatures
peak shifts to the larger sized particles with increased temperature.
This result is consistent with the conclusion made by Wenglarz
and Wright 关27兴 who reviewed test results for a number of alter-
nate fuels. Above the transition temperature, particles larger than cases with hole spacing of s / d = 3.4 共case 1兲 and 4.5 共case 2兲 for
1 ␮m are molten. Due to the high delivery rate of large particles, blowing ratios 共M兲 from 0.5 to 2.0. Comparisons were made of
a much greater mass of large particles stick on the surface, result- predicted and measured average front and rear plate temperatures
ing in a significant increase in the mass of deposit. 共Fig. 8兲 and deposition capture efficiencies 共Fig. 9兲. The plate
surface impinged by freestream is the front side while the plate
4.2 Hole Spacing (s Õ d = 3.375 and 4.5). To study the effect of surface on the coolant side is the back side. As can be seen in Fig.
hole spacing on film cooling, computations were made for two 8, the predicted temperatures at M = 2.0 for case 1 agrees with

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 1 4 0 0 0 .4 5

S p a n w is e A v e r a g e d C o o lin g E ffe c tiv e n s s

s /d = 3 .3 7 5 4 .5
M = 2 .0 M = 1 .0 M = 0 .5
C F D F ro n t 0 .4 0 s /d = 3 .3 7 5
E x p F ro n t s /d = 4 .5
1 3 0 0 C F D B a c k
E x p B a c k 0 .3 5
T e m p e ra tu re (K )

0 .3 0
1 2 0 0
0 .2 5

0 .2 0
1 1 0 0
0 .1 5

1 0 0 0 0 .1 0
0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 0 2 4 6 8 1 0 1 2

Y /d
B lo w in g R a tio ( M )
Fig. 10 Laterally averaged film cooling effectiveness at the
Fig. 8 Comparison of averaged front side and back side plate variation of M from 0.5 to 2.0 with s / d = 3.4 „case 1… and 4.5
temperature for cases s / d = 3.4 and 4.5 from experiment and 3D „case 2…
modeling

from Y / d = 1 to Y / d = 12, where Y = 0 at the hole axis. The diam-

experiments better than at M = 1.0. The predicted temperatures for eter of coupons used in experiment is 25.4 mm. Therefore, only
both front and back sides at M = 0.5 are higher than the measured the local points within a radius of less than 12.7 mm are averaged.
values. For case 2, the predicted temperatures at M = 0.5 and 2.0 Figure 10 shows the results of the laterally averaged effective-
are close to the experimental results while there is a slight dis- ness for a variation of the blowing ratio from 0.5 to 2.0 with the
agreement at M = 1.0. In general, the predictions for case 2 agreed two differing hole spacing. The curves reflect the effects of three
with the data better than for case 1. cooling air jets interacting with each other and mixing with hot
Figure 9 shows the deposition capture efficiency as the function gas crossflow. The figure shows that cooling effectiveness rises
of blowing ratio for varying hole spacing cases. This figure sug- with the increase of blowing ratio. The development of lateral
gests that the deposition model predicts capture efficiency fairly effectiveness with downstream distance continuously decays due
accurately over this range of blowing ratios. The areas of dis- to the interaction with the hot mainstream after ejection from the
agreement shown in this figure reflect the areas of disagreement cooling holes. The different hole spacing causes a slight variation
shown earlier for the respective plate surface temperature. Capture in the downstream decay characteristic, which develops more rap-
efficiency is overpredicted slightly for case 1 with M = 0.5 and 1.0 idly for a plate with a wider hole spacing. The cooling effective-
due to a higher simulated surface temperature. The predicted cap- ness for the plate with wide hole spacing is larger than the case
ture efficiency for case 2 with M = 1.0 is lower in the simulation with close hole spacing at all blowing ratios in the location near
than that obtained from experiments. This figure also shows that cooling holes. Due to less support of neighboring coolant jets with
the capture efficiency for close hole spacing is slightly lower than large hole spacing, the coolant flow is diluted by the hot gas flow
for wide hole spacing. at the region far away from the cooling holes, resulting in a lower
The use of an overall effectiveness factor is a method of nor- cooling effectiveness than the close spacing at the Y/d greater than
malizing the temperature, and is defined as value of 5. This is most apparently observed at the low blowing
T − Tm ratio of 0.5.
␩= 共7兲 The centerline cooling effectiveness for a variation of the blow-
Tc − Tm ing ratio from 0.5 to 2.0 with two differing hole spacing is shown
where T is the wall surface temperature downstream of film holes, in Fig. 11. The centerline is defined as the region downstream of
Tc is the coolant temperature at the entry of the passage of the the middle hole. As can be seen, the centerline cooling effective-
holes, and Tm is the mainstream temperature. The laterally aver- ness monotonically decreased along the downstream distance. The
aged effectiveness is obtained by spanwise averaging of the local value of the cooling effectiveness along the centerline is slightly
values. This evaluation is performed for the downstream range higher than the laterally averaged spanwise cooling effectiveness.

6 0 .5
M o d e l E x p M = 2 .0 M = 1 .0 M = 0 .5
5 s /d = 3 .3 7 5 s /d = 3 .3 7 5
C e n te r lin e C o o lin g E ffe c tiv e n s s

s /d = 4 .5 s /d = 4 .5
0 .4
C a p tu r e E ffic ie n c y ( % )

3 0 .3

2
0 .2
1

0 0 .1
0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 0 2 4 6 8 1 0 1 2

B lo w in g R a tio ( M ) Y /d

Fig. 9 Capture efficiency at M = 0.5– 2.0 for cases s / d = 3.4 and Fig. 11 Centerline film cooling effectiveness at the variation of
4.5 from experiment and 3D modeling M from 0.5 to 2.0 with s / d = 3.4 „case 1… and 4.5 „case 2…

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 1 .4
0 .5 d = 1 .0 d = 1 .5
M = 2 .0
1 .2 M = 1 .0
0 .4 M = 0 .5

C o o lin g E ffe c tiv e n s s

C a p tu r e E ffic ie n c y ( % )
1 .0 M o d e l
E x p e r im e n t 0 .3
0 .8
0 .2
0 .6

0 .1
0 .4

0 .2 0 .0
0 2 4 6 8 1 0 1 2

0 .0
0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 Y /d

Fig. 14 Centerline film cooling effectiveness with the variation

B lo w in g R a tio ( M )
of M from 0.5 to 2.0 for case 2 „d = 1 mm… and case 3 „d
= 1.5 mm…
Fig. 12 Predicted and measured capture efficiencies at M
= 0.5– 2.0 for a hole size of d = 1.5 mm „case 3…

is readily entrained by the mainstream and results in a relative

small peak. The plot can also be seen, in which the effectiveness
The centerline effectiveness curves are similar to the spanwise- provided by a large hole is larger than small holes, which is due to
averaged curves. For all of the blowing ratios, the wide hole spac- the increase of flow rate.
ing yielded better cooling effectiveness than close hole spacing in Centerline film cooling effectiveness is shown in Fig. 14. The
the region close to the exit of coolant. effectiveness value reduces with the decrease of the blowing ratio,
4.3 Hole Size „d = 1.5 mm, s Õ d = 4.5…. The hole diameters and case 3 has larger cooling effectiveness than case 2. However,
were changed from 1 mm to 1.5 mm for case 3, with M ranging the peaks do not appear in the region close to the holes as did the
from 0.5 to 2.0. Figure 12 shows the predicted and measured spanwise-averaged effectiveness shown in Fig. 13. The increase of
capture efficiencies. It is clearly seen that the prediction at M coolant flow rate for case 3 slows down the effectiveness decay
= 1.0 and 2.0 presents a good match with the experimental result. downstream of the cooling holes.
At M = 0.5, the prediction capture efficiency was higher than the The flow field results for M = 0.5– 2.0 for cases 2 and 3 are
measured value. The capture efficiencies for this case are much shown in Fig. 15. The computed velocity magnitude contours are
lower than in cases 1 and 2 共compare Fig. 9兲, in which trend is obtained along the centerline plane 共y = 0兲 and their scales are
accurately modeled. The reason for the disagreement at low blow- different. Velocity gradients in the cooling hole passage are appar-
ing ratio in Fig. 12 is not yet known but is within a factor of 2. ent in each case. The exit velocity from the large holes is less than
A comparison of laterally averaged cooling effectiveness be- that from the small holes, due to a slight difference in predicted
tween case 2 and case 3 is shown in Fig. 13. For case 3, the gas temperature at the hole exit. The large hole case has a higher
effectiveness increases at the location close to the ejection of the coolant mass flow rate to maintain the same blowing ratio. Jet
cooling holes until a maximum value appears at Y / d = 2, where penetration into the region just above the hole exit and slightly
the best surface coverage is obtained. Downstream of this loca- downstream is greater for the larger diameter hole case. The for-
tion, effectiveness begins to decay due to the entrainment of hot mation of a boundary layer is more apparent for the M = 1.0 and
gas, which seemingly overweighs the beneficial effect yielded by 0.5 cases. Vertical slices of the gas temperature distribution near
the increased film cooling coverage. At M = 0.5, the peak is not the center cooling hole at a downstream location of X / d = 2 are
obvious, compared with the other two blowing ratios. It is likely shown in Fig. 16 for cases 2 and 3. The jet lift-off can be observed
that coolant jet was spread on the surface immediately after exit- to occur at M = 2.0 for case 3 共Fig. 16共b兲兲 since the low tempera-
ing the holes. Due to the decrease of coolant flow rate, the coolant ture core of the jet is lifted slightly above the coupon surface. The
temperature map just downstream of the small hole simulation
共Fig. 16共a兲兲 shows that the coolant jet core is closer to the wall
0 .5 and avoided lift-off.
d = 1 .0 d = 1 .5 4.4 Effect of Conjugate Heat Transfer. This section dis-
M = 2 .0
0 .4 M = 1 .0 cusses the predicted effect of conjugate heat transfer. The thermal
M = 0 .5
conductivity of the plate was set to a value close to zero for the
C o o lin g E ffe c tiv e n e s s

adiabatic conditions. Cases 4 and 5 are the adiabatic simulations

0 .3
corresponding to cases 2 and 3 with M = 1.0. Comparison of the
adiabatic cases with the conjugate heat transfer cases shows the
0 .2 influence of heat transfer through the coupon on the film cooling
effectiveness.
0 .1
Figure 17 compares the temperature contours of the entire hot
surface for the adiabatic and conjugate conditions 共cases 2 and 4兲.
For the adiabatic case, the surface temperature approaches the hot
0 .0 gas temperature, except in the flow paths of the coolant jets. Low
0 2 4 6 8 1 0 1 2
surface temperatures are observed near the hole exits. When con-
Y /d jugate heat transfer is taken into account, the average surface tem-
perature is significantly lower than the adiabatic wall case, espe-
Fig. 13 Laterally averaged film cooling effectiveness with M cially in the regions uncovered by the coolant. The decrease in
= 0.5– 2.0 for case 2 „d = 1 mm… and case 3 „d = 1.5 mm… surface temperature is caused by both film cooling and internal

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 M=2.0 M=2.0

M=1.0 M=1.0

M=0.5 M=0.5

(a) d=1 mm, s/d=4.5 (b) d=1.5 mm, s/d=3

Fig. 15 Velocity magnitude contours „m/s… with blowing ratio from 0.5 to 2.0 along center-
line plane for cases 2 and 3

cooling from back side impingement on the coupon. effectiveness is shown downstream of the holes as the mainstream
Figure 18 shows the laterally averaged film cooling effective- hot gas entrains with the coolant in the film. In the conjugate
ness versus the distance downstream of the cooling holes for cases condition, the coolant is heated as it impinges on the cooler side
4 and 5. It is apparent that the conjugate case has a higher value, of the coupon. Additional heat transfer occurs during passage
representing better cooling performance than the adiabatic case through the holes, which leads to an additional temperature in-
for both hole diameter sizes. An effectiveness peak appears at the crease compared with the adiabatic condition. As a result, the film
location of Y / d = 1.0 for cooling holes with large sizes. Effective- cooling effectiveness at the exit of the jet is 0.4–0.5, much lower
ness for the adiabatic case decays more rapidly than for the con- than the adiabatic condition. Due to a slower decay, the conjugate
jugate case. This is because of temperature increase of the hot condition outperforms the adiabatic cases at a distance Y / d ⬎ 8.
surface in the region far downstream of the holes. For the conju- In the conjugate heat transfer condition, the convective heat
gate case, this increase is suppressed by the internal cooling. load to the hot coupon surface is given by
Figure 19 shows centerline film cooling effectiveness at M
q⬙ = h共Taw − Tw兲 共8兲
= 1.0 for both the adiabatic case and the conjugate heat transfer
case. In the adiabatic condition, the coolant jet is not heated up by where Taw is the surface temperature at each location from the
the plate wall before exiting the hole and hence maintains the adiabatic prediction. Figure 20 illustrates the change in the heat
coolant inlet temperature. Therefore, the cooling effectiveness ap- transfer coefficient along the distance downstream of the film
proaches 1.0 at the exit of the holes. However, a rapid decay of the cooling hole for different hole sizes. Generally, a cooling jet in-

Fig. 16 Gas temperature distribution in X / d = 2 for cases 2 and 3. Temperatures are in Kelvin.

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 2 5 0
d = 1 .5
d = 1 .0
2 0 0

1 5 0

K )
2
Adiabatic

h (W /m
1 0 0

5 0

0
0 2 4 6 8 1 0
Conjugate
Y /d
Fig. 17 Surface temperature profiles of the coupon surface for
M = 1.0 from the adiabatic and conjugate predictions. Hole di- Fig. 20 Centerline conjugate heat transfer coefficient for
ameters were 1.0 mm. Temperatures are in Kelvin. cases 2 and 3 with M = 1.0

jected into a mainstream flow generates high levels of turbulence, is then transferred from the gas to the wall. The positive heat
which increases the local convective heat transfer coefficient. This transfer coefficient shown in Fig. 20 indicates that heat flows from
trend dwindles with the further mixing of mainstream. Therefore, the wall to the coolant stream. At Y / d ⬍ 7, heat transfer coeffi-
the heat transfer coefficient at the location close to the jets is at a cient value for holes with small and large sizes are similar while at
maximum value of 240 W / 共m2 K兲. On account of the lower tem- the further distances, the value of h has more rapid decay than for
perature of coolant directly downstream of the hole exit, the cool- the smaller hole case.
ant has a lower temperature than the surface temperature, so heat 4.5 TBC Effect „d = 1.0 mm, s Õ d = 4.5…. A TBC layer with a
is transferred from the surface to the coolant. Further downstream, thickness of 0.25 mm was added to the coupon surface, and the
coolant mixes with the hot gas, and the gas mixture near the thermal conductivity 共k兲 of the TBC layer was set to 1.78 W / m K
surface is heated up to a higher temperature than the surface. Heat for case 6 and 0.3 W / m K for case 7. Predictions were performed
to examine the effect of a TBC layer on the metal surface tem-
perature. A comparison of predictions obtained for cases 2, 4, 6,
0 .4 5 and 7 is shown in Figs. 21 and 22. Note that with the addition of
0 .4 0 d = 1 .5 d = 1 .0 an insulating TBC layer 共case 6兲, the centerline and laterally av-
c o n ju g a te eraged surface temperature along the centerline was reduced 50 K,
0 .3 5 a d ia b a tic
compared with the case without TBC. However, with the thermal
C o o lin g E ffe c tiv e n e s s

0 .3 0 conductivity decreasing from 1.78 to 0.3, metal surface tempera-

0 .2 5 ture does not continue to reduce but, instead, had an increase of 40
K, still less than the surface temperature from the case without
0 .2 0
TBC. This simulation result of first decreasing then increasing
0 .1 5 surface temperature with decreasing thermal conductivity coin-
0 .1 0 cides with Na’s study 关13兴. When k = 0, the temperature curve in
Fig. 22 crosses the curves from the other cases and elevates to a
0 .0 5
higher temperature than the other cases at location Y / d ⬎ 5. Ex-
0 .0 0 periments to study the effect of TBC 关24兴 show that the measured
0 2 4 6 8 1 0 1 2
surface temperature for the TBC coupon was higher than the bare
Y /d metal coupon. The temperature map was measured after a few
minutes in the deposition test, so that the TBC surface had already
Fig. 18 Laterally averaged film cooling effectiveness at M captured some fine particles. Since the thermal conductivity of ash
= 1.0 for adiabatic and conjugate cases

1 .0 1 4 0 0
C e n te r lin e S u r fa c e T e m p e r a tu r e ( K )

d = 1 .5 d = 1 .0
A d ia b a tic 1 2 0 0
0 .8
C o n ju g a te
C o o lin g E ffe c tiv e n e s s

1 0 0 0
0 .6 C o n ju g a te
8 0 0 T B C ,k = 0 .3
T B C ,k = 1 .7 8
0 .4 A d ia b a tic
6 0 0

0 .2
4 0 0

0 .0 2 0 0
0 2 4 6 8 1 0 1 2 0 2 4 6 8 1 0 1 2

Y (m m ) D is ta n c e ( in c h e s )

Fig. 19 Centerline effectiveness at M = 1.0 for adiabatic and Fig. 21 Centerline surface temperature for M = 1.0 with a TBC
conjugate cases layer and different values of thermal conductivity

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 1 4 0 0 ing performed better than wide hole spacing at downstream
locations due to the interaction of neighboring jets.
1 3 5 0 4. Predictions of the TADF experiments with different hole
sizes indicated that the larger hole 共1.5 mm兲 provides better
1 3 0 0 cooling than a small hole 共1 mm兲 based on centerline and
averaged spanwise film cooling effectiveness. A small peak
(K )

1 2 5 0 in the cooling effectiveness curve appears just downstream

s

C o n ju g a te of the large holes, indicting jet lift-off, especially at high

T

1 2 0 0 T B C , k = 0 .3 blowing ratios.
T B C , k = 1 .7 8 5. Conjugate heat transfer calculations indicated that back side
A d ia b a tic
1 1 5 0 impingement cooling in the TADF experiments improved
the overall cooling effectiveness, especially in the region far
1 1 0 0 downstream of the cooling holes. The centerline heat trans-
0 2 4 6 8 1 0 1 2 fer coefficient was predicted to decrease with distance
downstream of the holes.
Y /d
6. The addition of a TBC layer will effectively reduce the outer
Fig. 22 Laterally averaged surface temperature for M = 1.0 with surface temperature initially. As a thin ash deposition layer
a TBC layer with different values of thermal conductivity forms with low thermal conductivity, the thermal resistance
layer ultimately increases the outer surface temperature. The
increase in surface temperature speeds up the deposit forma-
is as low as 0.1– 0.2 W / 共m K兲 关28兴, the coupon thermal resis- tion and further decreases conductive heat transfer.
tance is close to adiabatic condition, possibly resulting in a sur-
face temperature that is higher than the same experiment with a Acknowledgment
bare metal surface. The increase of surface temperature speeds up This work was partially sponsored by the U.S. Department of
the deposit formation and further decreases conductive heat trans- Energy—National Energy Technology Laboratory through a coop-
fer. erative agreement with the South Carolina Institute for Energy
Studies at Clemson University.
5 Summary and Conclusions
3D numerical simulations of film cooling fluid injection Nomenclature
through a row of different-sized cylindrical holes distributed at A ⫽ surface area 共m2兲
varying hole spacing were performed using FLUENT at blowing C ⫽ particle specific heat 共kJ/ 共kg K兲兲
ratios from 0.5 to 2.0. Simulations used the RANS and the k-␻ d ⫽ hole diameter
turbulence model to compute the flow field and heat transfer to a dp ⫽ particle diameter
metal coupon for three cases: 共a兲 adiabatic, 共b兲 conjugate heat D ⫽ coupon diameter
transfer, and 共c兲 TBC layer. The boundary conditions were set to E ⫽ Young modulus 共Pa兲
be those measured in an experimental facility 共the TADF兲. Com- F ⫽ force 共N兲
parisons of film cooling effectiveness and heat transfer coeffi- Fpo ⫽ sticking force 共N兲
cients were presented to illustrate the effects of hole size, hole h ⫽ convective heat transfer coefficient 共W / m2 K兲
spacing, conjugate heat transfer, and TBC layer on film cooling k ⫽ kinetic energy per unit mass 共J/kg兲
heat transfer. A series of particle-laden flow calculations were per- Kc ⫽ composite Young modulus
formed using a 2D Lagrangian model. Model predictions were ks ⫽ constant used in Eq. 共3兲
compared with deposition capture efficiency from new kt ⫽ thermal conductivity 共W / m K兲
temperature-dependent experiments to determine a correlation for m ⫽ mass 共kg兲
the particle Young Modulus 共Ep兲 for this system. This correlation M ⫽ blowing ratio= ␳cUc / ␳⬁U⬁
was then used in 3D computations of ash particulate deposition M1 ⫽ s / d = 3.375, d = 1 mm, metal coupon
for experiments with film cooling at different blowing ratios. M2 ⫽ s / d = 4.5, d = 1 mm, metal coupon
User-defined subroutines were developed to describe particle M3 ⫽ s / d = 3, d = 1.5 mm, metal coupon
sticking/rebounding and particle detachment on the impinged wall q⬙ ⫽ heat flux 共W / m2兲
surface. Conclusions are as follows. S ⫽ hole spacing 共mm兲
1. Results from the 2D deposition model indicated that the T ⫽ temperature
small particles have a greater tendency to stick to the surface TADF ⫽ turbine accelerated deposition facility
in the TADF experiments. After the initial deposition, and as TBC ⫽ thermal barrier coating
the surface of the deposit rises above the transition tempera- Tu ⫽ turbulence intensity
ture, large particles dominate the excessive deposition due to U ⫽ velocity 共m/s兲
the high delivery rate, which is in agreement with the ex- u Tc ⫽ critical wall shear velocity 共m/s兲
perimental results. vc ⫽ capture velocity 共m/s兲
2. Predictions with the 3D deposition model, using the corre- WA ⫽ constant used in the sticking force 共J / m2兲
lation developed for the particle Young modulus, generally x ⫽ spanwise coordinate from left edge of coupon
agree well with measured capture efficiencies for different y ⫽ streamwise coordinate from film hole center
blowing ratios and different hole sizes. Capture efficiency ␧ ⫽ turbulent dissipation rate 共m2 / s3兲
decreases with increased blowing ratio and increased hole ␻ ⫽ specific dissipation rate 共s−1兲
size 共when blowing ratio is held constant兲. ␣ ⫽ inclined angle of cooing holes 共deg兲
3. Predictions of the TADF experiments with different hole ␳ ⫽ density 共kg/ m3兲
spacing 共s / d = 3.4 and 4.5兲 indicated that the averaged span- ␩ ⫽ overall film cooling effectiveness
wise and centerline cooling effectiveness rises with the in-
crease of blowing ratio. The effectiveness at locations close Subscripts
to the exit of jets for wide hole spacing is slightly higher aw ⫽ adiabatic wall
than for small hole spacing. Meanwhile, the small hole spac- b ⫽ blackbody

Journal of Turbomachinery JULY 2012, Vol. 134 / 041020-11

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 c ⫽ property value of coolant for film cooling and Conjugate Heat Transfer Models,” ASME Paper No. GT2005-68431.
关12兴 Andreini, A., Carcasci, C., Gori, S., and Surace, M., 2005, “Film Cooling
m ⫽ property value of mainstream System Numerical Design: Adiabatic and Conjugate Analysis,” ASME Sum-
p ⫽ property value of particle mer Heat Transfer Conference, San Francisco, CA, 3.
s ⫽ target surface 关13兴 Na, S., Williams, B., Dennis, R. A., Bryden, K. M., and Shih, T. I. P., 2007,
w ⫽ wall “Internal and Film Cooling of a Flat Plate With Conjugate Heat Transfer,”
⬁ ⫽ freestream property ASME Paper No. GT2007-27599.
关14兴 Friedlander, S. K., and Johnstone, H. F., 1957, “Deposition of Suspended
Particles From Turbulent Gas Streams,” Ind. Eng. Chem., 49, pp. 1151–1156.
References 关15兴 Davies, C. N., 1966, “Deposition From Moving Aerosols,” Aerosol Science,
Academic Press, New York, pp. 393–446.
关1兴 Kim, J., Dunn, M. G., Baran, A. J., Wade, D. P., and Tremba, E. L., 1993,
关16兴 Liu, B. Y. H., and Agarwal, J. K., 1974, “Experimental Observation of Aerosol
“Deposition of Volcanic Materials in the Hot Sections of Two Gas Turbine
Deposition in Turbulent Flow,” J. Aerosol Sci., 5, pp. 145–148.
Engines,” ASME J. Eng. Gas Turbines Power, 115共3兲, pp. 641–651.
关17兴 Kallio, G. A., and Reeks, M. W., 1989, “A Numerical-Simulation of Particle
关2兴 Brown, A., and Saluja, C. L., 1979, “Film Cooling From a Single Hole and a
Deposition in Turbulent Boundary-Layers,” Int. J. Multiphase Flow, 15共3兲, pp.
Row of Holes of Variable Pitch to Diameter Ratio,” Int. J. Heat Mass Transfer,
22共4兲, pp. 525–534. 433–446.
关3兴 Drost, U., Bolcs, A., and Hoffs, A., 1997, “Utilization of the Transient Liquid 关18兴 Greenfield, C., and Quarini, G., 1997, “Particle Deposition in a Turbulent
Crystal Technique for Film Cooling Effectiveness,” ASME Paper No. 97-GT- Boundary Layer, Including the Effect of Thermophoresis,” ASME Fluids En-
26. gineering Division Summer Meeting, Vancouver, Canada, 17.
关4兴 Saumweber, C., and Schulz, A., 2003, “Interaction of Film Cooling Rows: 关19兴 Ai, W. G., Harding, S., Murray, N., Fletcher, T. H., Lewis, S., and Bons, J. P.,
Effects of Hole Geometry and Row Spacing on the Cooling Performance 2008, “Deposition Near Film Cooling Holes on a High Pressure Turbine
Downstream of the Second Row of Holes,” ASME Paper No. GT2003-38195. Vane,” ASME Paper No. GT2008-50901.
关5兴 Walters, D. K., and Leylek, J. H., 1996, “Systematic Computational Method- 关20兴 Fluent Inc., 2005, Fluent 6.2 User Guide.
ology Applied to a Three-Dimensional Film-Cooling Flowfield,” International 关21兴 Wilcox, D. C., 1998, Turbulence Modeling for CFD, DCW Industries, Inc., La
Gas Turbine and Aeroengine Congress and Exhibition, Birmingham, UK. Canada, California.
关6兴 Hoda, A., and Acharya, S., 2000, “Predictions of a Film Coolant Jet in Cross- 关22兴 2005, Fluent 6.2 User Guide, pp. 23-5–23-10.
flow With Different Turbulence Models,” ASME J. Turbomach., 122共3兲, pp. 关23兴 El-Batsh, H., and Haselbacher, H., 2002, “Numerical Investigation of the Ef-
558–569. fect of Ash Particle Deposition on the Flow Field Through Turbine Cascades,”
关7兴 Ajersch, P., Zhou, J.-M., Ketler, S., Salcudean, M., and Gartshore, I. S., 1995, ASME Paper No. GT-2002-30600.
“Multiple Jets in a Crossflow: Detailed Measurements and Numerical Simula- 关24兴 Ai, W. G., Harding, S., Murray, N., Fletcher, T. H., and Bons, J. P., 2009,
tions,” International Gas Turbine and Aeroengine Congress and Exposition, “Effect of Hole Spacing on Deposition of Fine Coal Flyash Near Film Cooling
Houston, TX. Holes,” ASME Paper No. GT2009-59569.
关8兴 Jia, R., Sunden, B., Miron, P., and Leger, B., 2005, “A Numerical and Experi- 关25兴 Soltani, M., and Ahmadi, G., 1994, “On Particle Adhesion and Removal
mental Investigation of the Slot Film-Cooling Jet With Various Angles,” Mechanisms in Turbulent Flows,” J. Adhes. Sci. Technol., 8共7兲, pp. 763–785.
ASME J. Turbomach., 127共3兲, pp. 635–645. 关26兴 Ai, W., 2009, “Deposition of Particulate From Coal-Derived Syngas on Tur-
关9兴 Harrison, K. L., and Bogard, D. G., 2008, “Comparison of RANS Turbulence bine Blades With Film Cooling,” Ph.D. thesis, Chemical Engineering, Brigham
Models for Prediction of Film Cooling Performance,” ASME Paper No. Young University, Provo, UT.
GT2008-51423. 关27兴 Wenglarz, R. A., and Wright, I. G., 2003, “Alternate Fuels for Land-Based
关10兴 Bohn, D., Ren, J., and Kusterer, K., 2003, “Conjugate Heat Transfer Analysis Turbines, Materials and Practices to Improve Resistance to Fuel Derived En-
for Film Cooling Configurations With Different Hole Geometries,” ASME vironmental Damage in Land- and Sea-Based Turbines,” pp. 4-45–4-64.
Paper No. GT2003-38369. 关28兴 Robinson, A. L., Buckley, S. G., and Baxter, L. L., 2001, “Experimental Mea-
关11兴 Silieti, M., Kassab, A. J., and Divo, E., 2005, “Film Cooling Effectiveness surements of the Thermal Conductivity of Ash Deposits: Part 1. Measurement
From a Single Scaled-Up Fan-Shaped Hole a CFD Simulation of Adiabatic Technique,” Energy Fuels, 15共1兲, pp. 66–74.

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