INTRODUCTION
Gas turbine engines are designed to continuously and efficiently convert the
energy of fuel into useful power and are developed into very reliable, high
performance engines (high ratio of power output to weight, high efficiency and
low maintenance costs). Gas turbines are now widely used in power plants, marine
industries and aircraft propulsion.
Over the past fifty years, aircraft and power generation gas turbine designers
tried to increase the combustion chamber exit and highpressure turbine stage
inlet temperatures. With higher combustion chamber exit temperatures, improved
efficiency and reduced fuel consumption can be achieved. Similarly, in aircraft
application, the higher temperatures lead to increased thrust. Unfortunately,
these higher temperatures have a negative effect on the integrity of the highpressure
turbine components and specifically the turbine blades (Altorairi,
2003).
High turbine inlet temperatures provide a challenging environment for turbine
blades which are subject to a variety of damage mechanisms, including hightemperature
oxidation, creep, corrosion and thermomechanical fatigue. Therefore, there
is a critical need to cool the blades. In internal cooling, air is bled from
the compressor stage and then passed through internal passages incorporated
into the blade for this purpose (Fig. 1 shows typical coolant
channels in turbine airfoil). This extraction incurs a penalty on the thermal
efficiency and power output of the engine so it is important to understand and
optimize the cooling technology for a given turbine blade geometry under engine
operating conditions (Han, 2004).
The objective of the recent study is to present and discuss the temperature
distribution results in the GT blade by two cooling methods using compressed
air. The temperature distribution in the blade body is estimated in two different
cooling channel configurations. In the first type, the channel wall is nonribbed,
or so called smooth. In the second type, regular repeated ribs artificially
roughen the channel walls.
MATERIALS AND METHODS
An out of use GT blade has been selected for the recent work. Laser digitizer
has identified the blade profile and geometries. It is 21 cm high and having
rectangular compressed air passage channel in the leading edge. The air channel
has dimensions of a = 9xb = 18 mm.
The cross section is modeled and meshed around the rectangular channel as shown
in Fig. 2. Meshing has resulted in 82 nodes.

Fig. 1: 
Typical coolant channels in turbine airfoils and internal
rib arrangement (Han et al., 2001) 

Fig. 2: 
Crosssection of the modeled GT blade and correspondence meshing
around the internal air channel 
FiniteDifference method is used to find the temperature distribution at the
leading edge by solving the set of the nodal equations.
Summary of nodal finite difference equations using square grids are as following:
Interior node:
Node at an internal corner with convection:
Node at a plane surface with convection:
Node at an External corner with convection:
Node at a plane surface with uniform heat flux:
where, k, T_{∞}, Δx and h are thermal conductivity of the
blade, temperature of hot gasses attacking the blade, grid space (Δx =
3 mm) and heat transfer convection coefficient (either for hot gasses or compressed
air), respectively.
Considering a typical gas turbine, the following conditions were used (Incropera,
2007):
• 
Temperature of hot gases attacking the blade is 1700 K 
• 
Temperature of compressed air (T_{a}) entering the blade root
is 400 K 
• 
Convection heat transfer coefficient (h_{∞}) for the hot
gases is 1000 W m^{2}K 
• 
Mass flow rate of compressed air entering the channel is 0.01 kg sec^{1} 
• 
Thermal conductivity of the blade is assumed to be 25 W m^{1}K 
Due to the existence of other cooling channels in the blade at left side of
the channel in Fig. 2 where the meshing is terminated, an
adiabatic line is assumed to exist for these nodes.
Cooling by nonribbed channels: For a smooth rectangular channel, Reynolds
number can be evaluated using hydraulic diameter, D_{h}:
where, ρ, μ, μ_{m}, A_{c }and P are density,
kinetic viscosity, compressed air velocity, flow cross section area and the
wetted parameter, respectively.
Considering
(
being air mass flow rate) then:
For a turbulent flow, that is fully developed, Nu number can be calculated
using Dittus boelter equation with n = 0.4 for heating (Incropera,
2007):
Heat transfer convection coefficient and Nu number are related by the following
formula:
COOLING BY RIBBED CHANNELS
In advanced gas turbine blades, repeated rib turbulence promoters are cast
on two opposite walls of internal cooling passages to enhance heat transfer.
Thermal energy conducts from the external pressure and suction surfaces of the
turbine blades into the inner zones and the heat is extracted by internal cooling
(Altorairi, 2003). Ribs mostly disturb only the near wall
flow and consequently the pressure drop penalty by ribs is acceptable for blade
cooling design. There have been many studies to understand heat transfer and
flow separation caused by ribs, e.g. (Han, 1988; Han
et al., 2001; Webb et al., 1971).
Findings showed that pressure drop and also the heat transfer is strongly connected
to the size of the rib, e and distance between two successive ribs, the pitch,
P. In experiments on ribroughened rectangular channels, most significant parameters,
apart from the Reynolds number, Re, are rib blockage ratio e/D_{h} (D_{h}
is hydraulic diameter of the channel), channel aspect ratio W/H (where W is
the width of the ribbed side of the channel and H is the height of the smoothed
side and rib angle α.
Han (1988) developed a correlation to predict the performance
of twosided orthogonal ribbed rectangular channels. The roughness function
R is given by:
The roughness Reynolds number e^{+} is given by:
And the heat transfer roughness function G was given by:
The foursided ribbed channel friction factor f is given by:
• 
is average friction factor in a channel with two opposite ribbed walls 
• 
the friction factor for smoothsided channels 
St_{r} is ribbed sidewall centerline average Stanton number for flow
in a channel with two opposite ribbed walls and is related to Nu and h as following:
Han et al. (1989) obtained the relation between
G and e^{+} as well as R and α in narrowaspect ratio rectangular
ribbed channels a s indicated in the Fig. 4. Therefore,
and St_{r,} for a desired operating condition (given W/H, e/D and Re)
can be predicted from experimentally obtained R and G correlations.

Fig. 3: 
Schematic of flow separation and rib orientations in heat
transfer coefficient enhancement (Han and Dutta, 1995) 
Air properties at 400 K are obtained as μ = 230.1x10^{7 }Ns m^{2},
k_{air }= 33.8x10^{3}W m^{1}K and Pr ^{~}
0.7, using (7) to (11) we have Re_{D}= 32192, Nu = 79.60 and h_{air
}= 224.22 W m^{1}K (Fig. 3).
Having h_{air }for smooth channel (1) to (5) are assigned to appropriate
nodes as stated and then solved for temperature distribution around the cooling
channel at the root of the blade.
Air temperature continuously changes when flowing inside the channel this in
turn changes temperature distribution for every cross section one may choose
along the height. Therefore if the height of the blade is segmented, the same
procedure can be applied to each segment to find temperature distribution.
It should be noted that h_{a} and air properties are changing since
air temperature entering each segment will differ. This change can be found
by calculating the rate of heat transfer (q') per unit length of the channel
for each segment as follow (look at Fig. 5 for location of
nodes):

Fig. 5: 
Temperature (K) distribution in the cross section of GT blade
surrounding the cooling passage at root 

Fig. 6: 
Temperature (K) distribution in the cross section of the fourth
segment (H=15.75 to 21 cm) of GT blade surrounding the cooling passage 
Once q’ is found and then change in air temperature (ΔT_{a})
can be calculated easily using:
where, H_{segment }is height of the segment and C_{p} is specific
heat capacity of air.
If the blade is divided to four equal segments along the height, the temperature
distribution at the root segment and at the top segment will be as in Fig.
5 and 6.
Air finally leaves the channel at 659.1 K. If we neglect the changes in air
properties when passing throw the channel then air leaves at 673 K, so assuming
constant properties of air the error is less than 2%.
RESULTS AND DISCUSSION
Results for smooth channel: Figure 7 shows exit air
temperature versus air mass flow rate assuming constant properties, by increasing
air mass flow rate; the outlet temperature will decrease and tends to approach
inlet temperature.

Fig. 7: 
Air outlet temperature (K) for different mass flow rates (kg
sec^{1}) for smooth channel 

Fig. 8: 
Convection coefficient (W m^{2}K) for different air
mass flow rates (kg sec^{1}) in smooth channel 

Fig. 9: 
Local convection coefficient in smooth channel 
Figure 8 demonstrates air mass flow rate and convection coefficient
relation.
According to the results shown in Fig. 9, local convection
coefficient increases as air travels to the end of channel. Figure
10 and 11 show temperature distribution along suction
and pressure surfaces for the last segment respectively, maximum temperature
occurs at the tip.

Fig. 10: 
Temperature (K) distribution along suction surface (H = 15.75
to 21 cm) 
Table 1: 
Comparison between cooling effect by different k and h_{a} 

In the gas turbine industry there is great interest in adopting measures that
reduce blade temperatures. Among them is the use of a different alloy of larger
thermal conductivity or increasing mass flow rate of coolant through the channel,
means increasing h_{a}. Table 1 shows a parametric
variations of k and h_{a}. It can be concluded that increasing k and
h_{a} reduces temperature in blade but effect of changes in h_{a}
is far more significant than that of k.
Results for ribbed channel: Effect of introducing rib angles, α
of 90, 60, 45 and 30° and ribs blockage ratios (e/D_{h}) ranging
from 0.042 to 0.078 to pressure and suction walls of the same channel discussed
later are presented here.
Referring to Fig. 4 for this case (W/H =1/2), for orthogonal
rib (α = 90°) an approximate value of 5 can be obtained for R. Substituting
R = 5, Re = 32192.12 in (12) and assuming rib blockage ratio of e/D_{h}
= 0.063, friction factor for foursided ribbed channel is calculated as: f =
0.0265. Using (13), e^{+} = 233.32, now having value of e^{+},
G can be evaluated using Fig. 4. However an alternative solution
is to use a relation presented by (8) for Pr = 0.7 as follow:
where, n = 0.35 and C = 2.24 if α = 90°. Using (19), G = 15.10. According
to (14), St_{r} = 0.0062 substituting this in (5), heat transfer convection
coefficient in the orthogonal ribbed channel with e/D _{h} = 0.063 is
found as h_{ribbed} = 388.53 W m^{2}K.

Fig. 11: 
Temperature (K) distribution along pressure surface (H = 15.75
to 21 cm) 
Table 2: 
Friction factor and convection coefficient for ribbed channel
at = 0.01 kg sec^{1} 

Assuming f_{s }= 0.011 and using (15), friction factor for this ribbed
channel will be
= 0.0162.
This procedure can be applied for other rib blockage ratios and rib angles.
Note that One may use C = 1.80 in (19) if 30°<α<90°, the
results are shown in Table 2. Figure 12
shows temperature distribution at root of the blade for different rib angles.
Knowing that Nu_{smooth }= 79.60 and h_{smooth }= 224.2 W m^{2}
K and comparing these with values presented in Table 2, it
is found that introducing the ribs in the channel regardless of the angle will
increase heat transferred to the air, friction factor will always increase as
well. Ribs mostly disturb only the near wall flow and consequently the pressure
drop penalty by ribs is acceptable for blade cooling design, so introducing
the ribs is always recommended.
Table 2 shows that maximum convection heat transfer coefficient,
h and Nu for each α occurs when the rib blockage ratio is at maximum. It
should be noted that when e/D_{h }increases friction factor also rises,
therefore an enhancement of heat transfer is achieved with penalty of increase
in the friction factor.

Fig. 12: 
Temperature (K) distribution in the cross section of GT blade
surrounding ribbed cooling channel at root of the blade 
Table 3: 
Comparison between different rib angles 

Comparing different rib angles, according to Table 2 maximum
Nu value and h is achieved when 60° ribs are used in the channel with a
rib blockage ratio of 0.078. Comparing with smooth channel (h_{smooth }=
224.22 W m^{2}K) an enhancement of 149.45% is achieved with penalty
of increase in the friction factor by 114.5%.
Table 3, compares maximum and minimum temperature, heat transfer
per length as well as total increment in air temperature w hen leaving the channel.
CONCLUSIONS
Cooling system is very essential for Gas Turbines and has a direct effect on
Gas Turbine efficiency. There are different cooling techniques available. Internal
cooling is achieved by passing the compressed air through the internal channel
provided in the blade and is enhanced by manufacturing the ribs inside the air
passage.
• 
Among the rib angles, α of 90, 60, 45 and 30° and
ribs blockage ratios, e/D_{h} ranging from 0.042 to 0.078, 60^{o}
ribbed channel with rib blockage ratio of 0.078 is recommended to be used
for the gas turbine blade. An enhancement of 149.45% is achieved with penalty
of increase in the friction factor by 114.5% 
• 
Channels with 30° ribs are recommended to be used when pressure drop
in the channel is important 
• 
The effect of increasing heat transfer convection coefficient h in the
air channel on cooling is far more effective than increasing thermal conductivity
of the blade, i.e., the material 
• 
Channels with 90° ribs do not have any advantages in terms of heat
transfer enhancement comparing with other ribs even pressure drop in these
channel is more than 30° case 
• 
Transfer enhancement and pressure drop inside the passage. Ribs mostly
disturb only the near wall flow and consequently the pressure drop penalty
by ribs 
Hence, using 90° ribs is not recommended at all when other ribs are available.
Best ribs for heat transfer enhancement are those having angles and height to
diameter ration of 60°, 0.078; 60°, 0.063; 45°, 0.078, respectively.
ACKNOWLEDGEMENT
The authors acknowledge Universiti Teknologi PETRONAS for supporting the project,
technically and financially.