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Appl. Sci. 2021, 11, 9924. https://doi.org/10.3390/app11219924 www.mdpi.com/journal/applsci
Article
Improvement of Multi-Hole Airflow Impingement on Flow
and Heat Transfer Characteristics Inside a Turbine Vane Cavity
Lixi Zhang *, Gaopan Cao, Kai Feng, Yi Jia and Zhengyang Zhang
School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China;
2020201908@mail.nwpu.edu.cn (G.C.); fengkai@mail.nwpu.edu.cn (K.F.);
17678910554@mail.nwpu.edu.cn (Y.J.); villa0913@mail.nwpu.edu.cn (Z.Z.)
* Correspondence: zhanglixi@nwpu.edu.cn
Abstract: The cooling effect of turbine vane is of great importance for ensuring thermal protection
and economic operation of gas turbines. This study aims to reveal the influence mechanism and
performance of impingement cooling and heat transfer within a turbine guide vane cavity. Then, a
turbine guide vane cavity with a complex pin fins structure is numerically investigated at a multi-
hole impingement by comparison with experiment verification. The results show that the larger the
Reynolds number is, the larger the average Nusselt number is on the upper and lower surfaces of
the cavity. The average Nusselt number increased on the upper and lower surfaces as the impinge-
ment hole diameter increased. Comparing 1 impingement hole with 16 ones, the average Nusselt
number of the lower surface of the latter is 553.9% larger than that of the former. Furthermore, the
average Nusselt number of the lower surface for pin fin height of 3 mm is only improved by 11.2%
for pin fin height of 24 mm. The heat transfer effect near the impingement holes is better than that
far away from the impingement holes. In particular, it is recommended to have 14 impingement
holes with a hole diameter of 7.2 mm, as well as circular pin fins with a height of 3 mm and spacing
of 25.8 mm. In addition, the entropy generation distribution in impingement cooling is analyzed.
This study can provide a reference to enhance the turbine vane cooling performance by optimiza-
tion design.
Keywords: turbine vane cavity; impingement cooling; pin fin; multi-hole; heat transfer
1. Introduction
In order to improve thermal efficiency, the gas inlet temperature of a gas turbine is
continuously improved. However, the super-high temperature resistance of the material
is limited, and the research on advanced cooling methods has lower cost and is less time-
consuming than the development of vane materials with ultra-high temperature re-
sistance, therefore, turbine vane cooling technology has become one of the hot spots in
the field of gas turbine research.
Jet impingement cooling is one of the most effective heat transfer enhancement tech-
nology, which is commonly used in gas turbine vane cooling, especially for the pressure
side of turbine vane [1]. There are many factors affecting the flow and heat transfer of
impingement cooling. In order to meet the different requirements, the heat transfer ca-
pacity can be further enhanced by changing the parameters of the impingement hole, in-
creasing the vortex and other methods to improve the jet intensity [2].
The methods to study the flow and heat transfer of impingement cooling include
numerical simulation, experiment and the combination of the above two. Kumar et al. [3]
Citation: Zhang, L.; Cao, G.; Feng,
K.; Jia, Y.; Zhang, Z. Improvement of
Multi-Hole Airflow Impingement on
Flow and Heat Transfer Characteris-
tics Inside a Turbine Vane Cavity.
A
ppl. Sci. 2021, 11, 9924. https://
doi.org/10.3390/app11219924
Academic Editor: Hijaz Ahmad
Received: 30 September 2021
Accepted: 21 October 2021
Published: 23 October 2021
Publisher’s Note: MDPI stays neu-
tral with regard to jurisdictional
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Copyright: © 2021 by the author. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (http://crea-
tivecommons.org/licenses/by/4.0/).
Appl. Sci. 2021, 11, 9924 2 of 21
introduced the research progress of numerical simulation for impingement cooling. At
present, Reynolds-averaged Navier–Stokes model is mostly used to analyze the flow and
heat transfer of gas turbine vane cooling, because its computational effort is little. J. Ortega
et al. [4] found that the average surface heat transfer coefficient of concave and convex
target plates is significantly larger than that of flat target plate, but in the stagnation region
of the impinging jet, the average surface heat transfer coefficient of flat target plate is bet-
ter than concave one.
Tejero et al. [5] studied the effect of the plate thermal conductivity on the heat transfer
coefficient of the impingement cooling system. There is a weak relationship between the
heat transfer coefficient and the plate thermal conductivity. During the heating process,
the heat transfer coefficient remains almost constant. Xi et al. [6] simulated the flow and
heat transfer of turbine vane leading edge by array jet impingement cooling, and found
that increasing the hole diameter ratio and reducing the hole spacing ratio can effectively
improve the comprehensive heat transfer coefficient of vane leading edge impingement
cooling. Haider et al. [7] investigated the effect of the jet diameter on the impingement
cooling flow and heat transfer at the leading edge of the turbine vane. At a fixed Reynolds
number, the wall heat transfer coefficient increases as the jet diameter increases. Zhou et
al. found that the Nusselt number Nu of the effective cooling zone first increases and then
decreases with the increase in jet hole diameter [8], and staggered arrangement of jet holes
and film holes can improve the heat transfer of the effective cooling zone [9]. Xie et al. [10]
studied the influence of the relative position of impingement holes and effusion holes on
the impingement cooling, and staggered rows of holes have larger overall cooling effi-
ciency than stacked rows of holes. Ali et al. [11] simulated the different heat transfer pat-
terns of the jet impingement on the semicircular surface. The average temperature of the
center jet surface is lower than that of the side jet, but the Nu distribution of the center jet
surface is smoother, and the maximum Nu is near the impingement point. Xiao et al. [12]
found that the Re of jet and nozzle diameter determine the thermal convection resistance,
and the plate material and thickness determine the transverse heat conduction resistance,
thus affecting the cooling effect. Lam et al. [13] simulated the flow and heat transfer of jet
impingement cooling system under different jet Re, velocity ratio and channel height. The
results show that when the Re and velocity ratio increases and the channel height de-
creases, the Nu and total entropy production increase.
Yan et al. [14] studied the heat transfer of impingement cooling at the leading edge
of turbine vane by using transient liquid crystal thermal imaging technology, and found
that the Nu and pressure drop increased with the increase in the Re; The biased impinge-
ment holes increases the average Nusselt number of the internal surface, reduces the re-
sistance coefficient and significantly improves the heat transfer uniformity. Jordan et al.
[15] investigated the effects of nozzle shape and different inlet conditions on the Nu dis-
tribution on the concave cylindrical surface of the channel in the leading edge of the tur-
bine vane, and found that after rounding the nozzle holes, there is a larger stagnation zone
in the channel and the maximum Nu decreases. Harrington et al. [16] found that the cur-
vature of the target plate has no significant effect on the flow and heat transfer. Rim et al.
[17] used Particle Image Velocimeter and Laser Doppler Velocimeter to monitor the im-
pingement cooling. The Re has little effect on the field, and the length of the jet core area
depends on the distance between the nozzle and the impingement cooling surface.
Hamed et al. [18] investigated impingement cooling by combining numerical simu-
lation with experiment. With the increase in the Re and the decrease in plate spacing-im-
pingement hole diameter ratio, the Nu of the impact zone increased. Antonio et al. [19]
found that when the hole spacing is small, the impingement cooling is more sensitive to
the relative position of film holes and impingement holes. Dushyant et al. [20] analyzed
the impingement cooling of the turbulent circular jet by combining numerical simulation
with experiment. The Nu of the target plate increases with the decrease in the ratio of
impingement hole-target plate distance to impingement hole diameter, especially in the
impacted area.
Appl. Sci. 2021, 11, 9924 3 of 21
Turbulence structure in the leading edge of gas turbine guide vanes can enhance the
flow field disturbance and improve the heat transfer. Adding pin fins can also increase
the structural strength of the vane [21]. Lu et al. [22] studied the flow and heat transfer for
array impingement cooling system with micro rectangular pin fins, and found that the
heat transfer significantly enhanced under the influence of micro pin fins. Guo et al. [23]
found that the heat transfer of turbine vane with spoiler ribs and guide vane is more uni-
form and the pressure drop of cooling channel is significantly reduced by using the
method of numerical simulation and experiment. Li et al. [24] analyzed the physical quan-
tities of the flow field in different channels with pin fins, such as the average velocity, the
Reynolds stress tensor and the Nu distribution on the model surface. The optimization
height of pin fins depends on the turbulence model. Jia et al. [25] designed a new beveled
pin fin based on airfoil profile, and this pin fin can produce lasting and stable longitudinal
vortices to strengthen the disturbance of flow field, yielding a good effect on enhancing
heat transfer of the cooling channel. Siw et al. [26] investigated the influence of the ar-
rangement of pin fins on impingement cooling. The total heat transfer of the best arrange-
ment of pin fins is about four times larger than that of the smooth channel. He et al. [27]
investigated the heat transfer characteristics of impingement cooling systems with dia-
mond, cubic, circular and elliptic pin fins. The circular pin fins can be the best choice
among the shapes studied by analyzing the Nu of the impact target surface. Ravanji et al.
[28] found that the elliptical pin fins can reduce the local temperature in the stagnation
zone and jet zone, and the average Nusselt number of the target plate is increased by about
47–54% compared with that without pin fins. Chen et al. [29] studied the flow and heat
transfer of the impingement cooling system with V-ribs, and the V-ribs enhanced the sec-
ondary flow structure in the system and increased the heat flux density on the target plate
by 1.34 times. Ligrani et al. [30] investigated the heat transfer of the target plate with the
pin fins with different heights, and with the increase in the pin fins height, the vorticity
generated by the pin fins increases, and the Nu of the target plate increases. Ravi et al. [31]
studied the effect of circular pin fins on the flow and heat transfer characteristics of the
system through numerical simulation and experiment. The result shows that the diameter
of circular pin fins is the most important factor for its flow and heat transfer. Rao et al. [32]
found through experimental research that pitting the surface of the pin fins can increase
the airflow disturbance and improve the impingement cooling. The deeper the pit depth,
the better the impingement cooling.
The impinging flow together with finned surfaces has also been employed when cou-
pled with new classes of materials like metal foam, which can increase heat transfer area
and promote flow mixing. Li et al. [33] proposed a concept of a metal foam heat sink with
pin fins to improve the cooling performance of high-powered electronics. The metal foam
heat sink with pin fins also promotes the improvement of the bottom wall temperature
uniformity. Bianco et al. [34] carried out multi-objective optimization of finned metal foam
heat sinks by considering heat transfer and pressure drop. At equal pumping power, the
finned metal foam heat sink can enhance dissipated heat rates of about 3.3~3.5 times the
metal foam heat sink.
In order to strengthen the impingement cooling heat transfer in the end wall cavity
of the gas turbine guide vane, its structure and parameters have constantly been im-
proved. In this study, the lower surface of the cavity with pin fins, and the upper surface
of it is smooth with one step is designed, under the condition of multi-hole impingement
and multiple air outlet holes, the heat transfer would be improved and uniform, and flow
field in the cavity would be complex. The effects of the impingement hole diameter, the
number of impingement holes, and the height, spacing and shape of pin fin on flow and
heat transfer are studied. Finally, this study can provide a reference to enhance the turbine
vane cooling performance by optimization design.
Appl. Sci. 2021, 11, 9924 4 of 21
2. Simulation Model and Method
2.1. Simulation Model
Taking 1/26 of the turbine guide vane (i.e., 360°/26 = 13.8° sector) as the research ob-
ject. The impingement cavity is inclined, and the upper and lower surfaces of the impinge-
ment cavity have an angle of 32° with respect to the horizontal plane. The schematic of
the impingement cavity model is shown in Figure 1. It includes the impingement cavity,
the pin fins and the air inlet and outlet. The lower surface in the impingement cavity has
pin fins, and the smooth surface with a step above the cavity is called the upper surface,
and the flow and heat transfer affect each other.
(a)
(b)
Figure 1. Schematic of impingement cavity model. (unit: mm). (a) Impingement cavity model. (b)
Size of impingement cavity.
The cold air passes through the impingement holes to the impingement cavity and
carries out heat transfer on the lower surface. At the same time, the air flow is reflected
and diffused to the upper surface for heat transfer, finally, the air flows out of the air
outlet. The impingement holes and outlet holes are on the different side surfaces. There is
an angle between them, ensuring that the air flow covers the impingement cavity better
and improves heat transfer.
The numerical simulation model has 14 impingement holes with a hole diameter of
7.2 mm, and a hole spacing of 17.48 mm. There are 6 outlet holes with a diameter of 6.6
mm. The thickness of the impingement hole plate is 30 mm. The diameter of pin fin is 10.8
mm, the height of pin fin is 12 mm, and the number of pin fin is 12 × 7. The pin fins spacing
in the horizontal and vertical is 23.4 mm. Figure 1b is the size of the impingement cavity.
Appl. Sci. 2021, 11, 9924 5 of 21
The research results [35] show that the impingement cooling of the row arrangement
of the pin fins is more significant than that of the staggered arrangement, and the compre-
hensive heat transfer efficiency is greatly improved. The investigation chooses the row
arrangement of the pin fins.
2.2. Governing Equation
The following assumptions are made in the simulation calculation: (1) the flow is
steady-state; (2) the fluid is continuous; (3) the fluid is incompressible; (4) there is no
source term in the energy equation. Therefore, the governing equations of incompressible
flow in the numerical simulation can be simplified:
Mass conservation equation:
∇×= 0V (1)
where ∇ is gradient operators and V is the velocity vector.
Momentum conservation equation:
()
∇∇∇⋅
d
ρ+ρ=-p+ τ+S
dt
VVV M
×
(2)
where ρ is air density, t is time, p is static pressure, τ is viscous stress and SM is dynamic
source term.
Energy conservation equation:
() ()
⋅∇⋅ ∇⋅ ∇
du
ρ+p = λΤ+Φ+ρq'
dt
V (3)
where u is internal energy, λ is fluid thermal conductivity, T is fluid temperature, Φ is
viscous dissipation function and q΄ is heat flux.
2.3. Boundary Condition
Unstructured meshes are used in numerical simulation, which can make the bound-
ary layer meshes denser. Figure 2 is the comparison of the average heat flux of the lower
surface under three different mesh numbers. When the number of iterations reaches 1000,
the heat flux on the lower surface begins to converge. When the number of meshes in-
creases from 4.73 million to 6.96 million, the heat flux changes by 3%. When the number
of them increases from 6.96 million to 8.52 million, the heat flux only changes by 0.28%.
Finally, the number of simulation grids of the model is 6.96 million, as shown in Figure 3.
Figure 2. Comparison of the average heat flux of the lower surface under three different mesh num-
bers.
0 1000 2000 3000 4000
1500
2000
2500
3000
3500
4000
4500
Heat Flux (W/m
2
)
Iteration number
4.73*10
6
6.96*10
6
8.52*10
6
Mesh Number
Appl. Sci. 2021, 11, 9924 6 of 21
Figure 3. Schematic mesh of numerical simulation model.
Since the Reynolds number range studied is mainly in the turbulent region, the nu-
merical simulation adopts a realizable k-ε model, which has a high calculation accuracy
in the turbulent region. Moreover, the realizable k-ε model can be extended to the calcu-
lation of transition zone. The discrete format used in this calculation is the second-order
upwind discrete format, and the algorithm is simple algorithm, because they converge
fast. The growth rate of the boundary layer in the simulation is 1.2. The residual standard
of pressure, temperature, heat flux convergence is 1 × 10−5.
The air inlet is the mass flow inlet, and the temperature of inlet air flow T0 is 300 K.
The air is an incompressible ideal gas. The air outlet is the pressure outlet. The upper and
lower surface and the surface of pin fins are heated by constant temperature Tk is 340 K.
Other walls are adiabatic and have no-slip boundary conditions.
2.4. Parameter Definition
The expressions of the parameters used in this paper are as follows.
Reynolds number:
ρvD
Re μ
= (4)
where v is air velocity, D is impingement hole diameter and μ is hydrodynamic viscosity.
Heat transfer coefficient:
()
−
q
hTT
w0
= (5)
where q is local heat flow density, Tw is local wall temperature and T0 is local air flow
temperature.
Nusselt number:
=hD
Nu λ (6)
Flow resistance:
h
2
2Δ
=pD
fρuL (7)
Appl. Sci. 2021, 11, 9924 7 of 21
where Δp is static pressure difference, D
h
is hydraulic diameter of jet channel and L is
length of jet channel.
Hydraulic diameter of impact channel:
()
-
VV
DA
tp
h
f
4
=
(8)
where V
t
is volume of jet channel without pin fins, V
p
is volume of pin fins and A
f
is effec-
tive heat transfer area of jet channel.
3. Results and Discussion
Under the condition that the cavity size, the diameter and number of outlet holes
remain fixed, this research focuses on the effects of the number of impingement holes, the
diameter of impingement hole, the pin fin height, the pin fin spacing and the pin fin shape
on the heat transfer characteristics.
3.1. Verification of Numerical Simulation Method
The schematic of the experimental system is shown in Figure 4, which is composed
of the blower, air tank, pressure regulator, flow regulator, discharge valve, electric heater,
experimental unit and measuring instrument. The inlet air is compressed by the blower.
Measure the pressure through inclined pipe differential pressure gauge and pressure dig-
ital display gauge. K-thermocouple and multi-channel temperature measuring instru-
ments are used to measure the temperature for the pipeline and the experimental unit.
The range of temperature measurement is −200~260 °C, and the accuracy of that is 0.4%.
The flow is measured by an integrated ultrasonic mass flowmeter with a measuring range
of 10~100 m³/h and an accuracy of 1%.
Figure 4. Schematic of the experimental system.
Experimental measurement parameters such as temperature, temperature, pressure
and rate of flow are related to the experimental results. In the experiments, the measure-
ment errors of temperature, pressure and rate of flow are about 0.45%, 7.39%, and 7.39%,
respectively. According to the error transfer principle, the experimental error is
222
0.45% + 7.39% + 1% = 7.47%（）（ ）（ ）
.
Appl. Sci. 2021, 11, 9924 8 of 21
Take the impingement hole diameter of 6, 7.2 and 8.4 mm, respectively, for the ex-
periment. Due to the limitation of the experimental devices working range, the Re range
in the experiment is 8 × 103~2 × 104. Compare numerical simulation results of the average
Nusselt number with experimental ones for the lower surface, and the results are shown
in Figure 5. Under the same conditions, the numerical simulation results are consistent
with the experimental ones. The heat transfer performance improves with the increase in
the impingement hole diameter. The average error of the simulation results and the ex-
perimental results is about 15.83%. This includes the error between simulation results and
real results, and the error between test results and real results. This is caused by the errors
of experiments and simulation. The simulation method can be considered to be correct.
Figure 5. Comparison of numerical simulation results of the average Nusselt number with experi-
mental ones for the lower surface. ( Nu is the average Nusselt number of surface).
3.2. Flow Field Distribution
The jet flow in the impingement cavity is closely related to the heat transfer. Figure 6
is the streamlines and Nu distribution with and without pin fins on the lower surface at
Re = 2 × 103, 14 impingement holes with a hole diameter of 7.2 mm.
Figure 6. Streamlines and Nu distribution with and without pin fins on the lower surface at Re = 2 ×
103.
0 102030405060
0
5
10
15
20
25
30
35
40
Re×103
NUM.6.0 mm
NUM.7.2 mm
NUM.8.4 mm
EXP.6.0 mm
EXP.7.2 mm
EXP.8.4 mm
Nu
Impingement Hole Diameter
Appl. Sci. 2021, 11, 9924 9 of 21
Impinging jet flow directly affects the heat transfer in the cavity, and the Nu distri-
bution on the lower surface corresponds to the streamline. The heat transfer near the out-
let holes is good, while the heat transfer in the vortex area is poor. The impingement cavity
is inclined, and the upper and lower surfaces of the impingement cavity have an angle of
32° with respect to the horizontal plane. So, there is less symmetric with respect to the
flow direction, and the heat transfer at the below outlet is stronger than that at the above
outlet. Comparing Figure 6a,b, the pin fins can make the heat transfer more uniform.
3.3. Effect of Impingement Hole
3.3.1. Effect of Impingement Hole Diameter
5 kinds of impingement hole diameters including 4.8 mm, 6.0 mm, 7.2 mm, 8.4 mm
and 9.6 mm are investigated in this part. Figure 7 shows the average Nusselt number of
the upper and lower surfaces with various impingement hole diameters at Re = 2 × 103~6
× 104. When the impingement hole diameter is constant, the average Nusselt number of
the upper and lower surfaces increases with the increase in the Re. The increase in the Re
indicates that the air jet velocity at the inlet of the impingement holes increases, the impact
is more intense, and the Nu of the surfaces increases accordingly.
(a) (b)
Figure 7. Comparison of the average Nusselt number of (a) the upper surface and (b) the lower
surface under various impingement hole diameters.
In the range of 4.8 mm~9.6 mm, the larger the impingement hole diameter, the larger
the average Nusselt number of the upper and lower surfaces. Among the five kinds of
hole diameters studied, the impingement cooling effect with 9.6 mm is the best. When the
impingement hole diameters are 6.0 mm, 7.2 mm, 8.4 mm and 9.6 mm, the average Nusselt
number of the upper surface is increased by 22.3%, 24.2%, 86.6% and 123.6% compared
with 4.8 mm. The average Nusselt number of the lower surface is increased by 19.3%,
46.2%, 79.6% and 104.3%, respectively.
The increase in the impingement hole diameter leads to the reduction in the jet ve-
locity, which makes the Nu decrease. However, when the impingement hole diameter
increases, the coverage area of the impingement flow increases and the turbulence inten-
sity in the impingement superposition region increases, which will improve the impinge-
ment cooling of the cavity. From the results, the influence of increasing the coverage area
is greater than that of reducing the jet velocity.
In addition, it is found that when Re and the impingement hole diameter are constant,
the average Nusselt number of the lower surface is higher than that of the upper surface
by comparing Figure 7a,b. Because the pin fins on the lower surface can directly improve
the impingement cooling, while the upper surface is mainly cooled by air reflux.
0 102030405060
0
10
20
30
40
Nu
Re×103
4.8 mm
6.0 mm
7.2 mm
8.4 mm
9.6 mm
Impingement Hole Diameter
0 102030405060
0
10
20
30
40
50
Nu
R
e×103
4.8 mm
6.0 mm
7.2 mm
8.4 mm
9.6 mm
Impingement Hole Diameter
Appl. Sci. 2021, 11, 9924 10 of 21
Figure 8a,b are Nu distribution of the upper and lower surfaces at Re = 2 × 104 under
different impingement hole diameters. At the same Re, the larger the impingement hole
diameter, the larger the high Nu area, that is, the impingement cooling improves obvi-
ously. With the increase in the hole diameter, the maximum Nu on the lower surface in-
creases, but the minimum decreases. When the hole diameter is 9.6 mm, the maximum Nu
is 84.403 and the minimum Nu is 0.095. That is, there is almost no cooling and heat transfer
in the local area, which may occur ablation.
(a)
(b)
Figure 8. Nu distribution of (a) the upper surface and (b) the lower surface under different impinge-
ment hole diameters at Re = 2 × 104.
With the increase in the impingement hole diameter, Nu on the upper surface near
the impingement holes increases significantly, while it is evenly distributed on the lower
surface. Pin fins on the lower surface make the heat transfer more uniform, and the upper
surface is smooth and unobstructed. The Nu of the cavity boundary area is small and the
temperature is relatively high, where may produce local ablation.
Figure 9a,b show the Nu distribution curves of the upper and lower surfaces along
the proposed geometry at Re = 2 × 103 under the impingement hole diameter of 7.2 mm. In
Appl. Sci. 2021, 11, 9924 11 of 21
Figure 9a, on the upper surface, the air flow is reflected and diffused, the upstream region
is directly impacted by the cooling air flow, the Nu in this region is high. Near the step
and outlet, the turbulence intensity of air flow increases and the heat transfer is strength-
ened. In Figure 9b, on the lower surface, the heat transfer is more uniform on the lower
surface than that on the upper surface because of the pin fins.
(a) (b)
Figure 9. Nu distribution curves of (a) the upper surface and (b) the lower surface under impinge-
ment hole diameter of 7.2 mm at Re = 2 × 103.
Enhanced heat transfer is accompanied by a corresponding pressure drop, so the
pressure drop should also be considered when realizing a better heat transfer effect. Fig-
ure 10 is a comparison of frictional resistance under various impingement hole diameters.
The larger the impingement hole diameter, the greater the flow resistance. The Re has little
effect on the flow resistance when the impingement hole diameter is small. The pressure
drop of the impingement cavity with the impingement hole diameter of 4.8 mm is the
smallest. Compared with it, the flow resistance with the hole diameter of 6.0 mm, 7.2 mm,
8.4 mm and 9.6 mm is increased by 39.7%, 123.5%, 251.7% and 459.3%, respectively.
Figure 10. Comparison of frictional resistance under various impingement hole diameters.
The average Nusselt number of the lower surface with the impingement holes diam-
eter of 7.2 mm increases by 46.2% compared with the hole diameter of 4.8 mm. That of 7.2
mm decreases by 28.1% compared with that of 9.6 mm. The flow resistance of the impact
cavity with a hole diameter of 7.2 mm is 123.5% higher than that of 4.8 mm. That of 7.2
mm is 59.1% lower than that of 9.6 mm. Considering the heat transfer and pressure loss,
the impingement holes diameter can be selected as 7.2 mm.
0 102030405060
0
1
2
3
4
5
6
f
Re×10
3
4.8 mm
6.0 mm
7.2 mm
8.4 mm
9.6 mm
Impingement Hole Diameter
Appl. Sci. 2021, 11, 9924 12 of 21
3.3.2. Effect of Impingement Hole Number
9 kinds of impingement hole numbers including 1, 2, 4, 6, 8, 10, 12, 14 and16 are in-
vestigated in this part. The average Nusselt number of the lower surface under various
impingement hole numbers at Re = 2 × 103~6 × 104 is shown in Figure 11. In the range of
1~16, the more the impingement hole number, the larger the average Nusselt number of
the lower surface. Since the distribution area of the impingement hole is fixed, the range
of hole number arranged is limited. The impingement cooling effect with 16 is the best
among nine kinds of hole numbers. When the impingement hole number are 2, 4, 6, 8, 10,
12, 14 and16, the average Nusselt number of the lower surface are increased by 53.1%,
143.7%, 230.8%, 309.8%, 362.7%, 397.4%, 436.5% and 553.9% compared with one impinge-
ment hole.
Figure 11. Comparison of the average Nusselt number of the lower surface under various impinge-
ment hole numbers.
Because the impingement holes are distributed in the fixed area, the increase in the
number of impingement holes increases the coverage area of the cooling jet and makes
the heat transfer more uniform, which improves the overall heat transfer effect.
Figure 12 is Nu distribution of the lower surface at Re = 2 × 104 under different im-
pingement hole numbers.
0 102030405060
0
10
20
30
40
Re×103
1
2
4
6
8
10
12
14
16
Nu
Impingement Hole Number
Appl. Sci. 2021, 11, 9924 13 of 21
Figure 12. Nu distribution of the lower surface under different impingement hole numbers at Re = 2
× 104.
At the same Re, the more the impingement hole number, the more uniform the Nu
distribution and the larger the high Nu area, that is, the impingement cooling improves
obviously. The maximum Nu on the lower surface increases with the increase in the hole
number. When the hole number is 16, the maximum Nu is 68.362. The minimum Nu is
0.002 when there is one impingement hole, that is, there is basically no cooling and heat
transfer in some parts where may produce local ablation. When the number of impinge-
ment holes is little, the local temperature is easy to be too high, resulting in local ablation.
Figure 13 is a comparison of frictional resistance under various impingement hole
numbers. The more the impingement hole number, the greater the flow resistance. The Re
has little effect on the flow resistance when the impingement hole number is little. The
pressure drop of the impingement cavity with one impingement hole is the smallest. Com-
pared with it, the flow resistance with the hole number of 2, 4, 6, 8, 10, 12, 14 and 16 are
increased by 3.95%, 22.9%, 52.4%, 92.7%, 141.5%, 200.8%, 258.9% and 444.2%, respectively.
Figure 13. Comparison of the frictional factor under various impingement hole numbers.
0 102030405060
0.5
1.0
1.5
2.0
2.5
3.0
3.5
f
R
e×10
3
1
2
4
6
8
10
12
14
16
Impingement Hole Number
Appl. Sci. 2021, 11, 9924 14 of 21
The average Nusselt number of the lower surface with 14 impingement holes in-
creases by 436.5% compared with one impingement hole. That with 14 impingement holes
decreases by 17.9% compared with 16 impingement holes. The flow resistance of the im-
pingement cavity with 14 impingement holes is 258.9% higher than that with one impinge-
ment hole. That with 14 impingement holes is 31.9% lower than that with 16 impingement
holes. Considering the heat transfer and pressure drop, the number of the impingement
hole can be selected as14.
3.4. Effect of Pin Fin
3.4.1. Effect of Pin Fin Height
6 kinds of pin fin heights including 0 mm, 3 mm, 6 mm, 12 mm, 18 mm and 24 mm
are investigated in this part. The average Nusselt number of the lower surface under var-
ious pin fin heights at Re = 2 × 103~6 × 104 is shown in Figure 14. Due to the limitation of
impingement cavity thickness, the pin fin height only includes 0 mm~24 mm. The higher
the pin fin height, the smaller the average Nusselt number of the lower surface generally.
Among the five kinds of pin fin heights investigated, the impingement cooling effect of 3
mm is the best. Compared with the pin fin height of 24 mm, the average Nusselt number
of the lower surface with that of 3 mm is increased by 11.2%.
Figure 14. Comparison of the average Nusselt number of the lower surface under various pin fin
heights.
As the pin fin height increases, the air flow space decreases, and the probability of
mutual collision and loss increases. Moreover, the increase in the pin fin height will cause
the air flow to roll over and climb, which will reduce the cooling effect on the surfaces of
the impingement cavity.
Figure 15 is Nu distribution of the lower surface at Re = 2 × 104 under different pin fin
heights. It can be found that when the pin fin height is 3 mm, the area of high Nu area is
the largest, and the distribution is more uniform than that without pin fins. The pin fins
can improve the heat transfer area where the Nu is too small, which is beneficial to avoid
ablation. At this time, the maximum Nu on the lower surface reaches 62.74, which is
greater than that of other pin fin heights.
0 102030405060
0
5
10
15
20
25
30
35
R
e×10
3
0 mm
3 mm
6 mm
12 mm
18 mm
24 mm
Nu
Pin Fin Height
Appl. Sci. 2021, 11, 9924 15 of 21
Figure 15. Nu distribution of the lower surface under different pin fin heights at Re = 2 × 104.
It is found that there is little difference between the average Nusselt number of the
lower surface without pin fins and that with pin fin height of 3 mm by the above research.
The pressure drop also needs to be considered when selecting the appropriate pin fin
height.
Figure 16 is a comparison of frictional resistance under various pin fin heights. The
pin fin height gets lower, the flow resistance increases and the pressure drop increases.
The pin fins can buffer the reduction in the velocity of impingement air flow, so the pres-
sure drop for the impingement cavity with pin fins is smaller than that without pin fins.
Figure 16. Comparison of the frictional factor under various pin fin heights.
The flow resistance of the impingement cavity with the pin fin height of 3 mm is
40.1% higher than that with the pin fin height of 24 mm. That of 3 mm is 6.6% lower than
that without pin fins. Considering the heat transfer and pressure drop, the pin fin height
can be selected as 3 mm.
3.4.2. Effect of Pin Fin Spacing
It studied the effect of the pin fin spacing on the heat transfer at the pin fin height of
3 mm. Five kinds of pin fin spacings including 18.6 mm, 21.0 mm, 23.4 mm, 25.8 mm and
28.2 mm are investigated in this part. The average Nusselt number of the lower surface
under various pin fin spacings at Re = 2 × 103~6 × 104 is shown in Figure 17. Figure 18 is
Nu distribution of the lower surface at Re = 2 × 104 under different pin fin spacings.
0 102030405060
0.5
1.0
1.5
2.0
2.5
3.0
f
R
e×10
3
0 mm
3 mm
6 mm
12 mm
18 mm
24 mm
Pin Fin Height
Appl. Sci. 2021, 11, 9924 16 of 21
Figure 17. Comparison of the average Nusselt number of the lower surface under various pin fin
spacings.
Figure 18. Nu distribution of the lower surface under different pin fin spacings at Re = 2 × 104.
When the pin fin spacing is 25.8 mm, the maximum Nu on the lower surface is 56.948,
which is the largest among the five spacings. Combined with Figures 17 and 18, there is
little difference in the heat transfer in the range of 18.6 mm~28.2 mm. Small spacing can
hinder airflow and increase viscous dissipation, which is more obvious at high Re than
that at low Re. At high Re, the impingement cooling effect of large pin fin spacing is better
than that of small pin fin spacing.
Figure 19 is a comparison of frictional resistance under various pin fin spacings. The
larger the pin fin spacing, the greater the flow resistance and the pressure drop. The aver-
age Nusselt number of the lower surface with the pin fin spacing of 25.8 mm increases by
7.5% compared with that of 18.6 mm. That of 25.8 mm decreases by 1.1% compared with
that of 18.6 mm. The flow resistance of the impingement cavity with the pin fin spacing of
25.8 mm is 3.5% higher than that of 18.6 mm. That of 25.8 mm is 1.5% lower than that of
28.2 mm. Considering the heat transfer and pressure drop, the pin fin spacing can be se-
lected as 25.8 mm.
0 102030 405060
0
5
10
15
20
25
30
35
40
Nu
Re×103
18.6 mm
21.0 mm
23.4 mm
25.8 mm
28.2 mm
Pin Fin Spacing
Appl. Sci. 2021, 11, 9924 17 of 21
Figure 19. Comparison of the frictional factor under various pin fin spacings.
3.4.3. Effect of Pin Fin Shape
The reference model has the circular pin fin, and this research chooses two kinds of
elliptical pin fins for comparison. Two kinds of pin fins are shown in Figure 20. The major
axis of the elliptical I pin fin is parallel to the air flow direction, and that of elliptical II is
vertical to the air flow direction. The major diameter of the two kinds of elliptical pin fins
is 10.8 mm, which is the same as the diameter of the circle pin fin. The minor diameter is
5.4 mm, which is the same as the radius of the circle pin fin.
Figure 20. Schematic of two kinds of elliptic pin fins.
The average Nusselt number of the lower surface under various pin fin shapes at Re
= 2 × 103~6 × 104 is shown in Figure 21. At the low Re, there is little difference in the average
Nusselt number on the lower surface under three-pin fin shapes. When Re increases to 3
× 104, the average Nusselt number of the lower surface with circle and elliptical I pin fins
exceeds that of elliptical II pin fins. Because the windward side of the elliptical II pin fin
is large, which hinders the air flow, and increases the turbulence intensity.
0 102030405060
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
f
R
e×103
18.6 mm
21.0 mm
23.4 mm
25.8 mm
28.2 mm
Pin Fin Spacing
Appl. Sci. 2021, 11, 9924 18 of 21
Figure 21. Comparison of the average Nusselt number of the lower surface under various pin fin
shapes.
Shown in Figure 22 is Nu distribution of the lower surface at Re = 2 × 104 under dif-
ferent pin fin shapes. The maximum Nu on the lower surface with elliptical I pin fins is
56.171. It is the largest among the three shapes, followed by the circle.
Figure 22. Nu distribution of the lower surface under different pin fin shapes at Re = 2 × 104.
Figure 23 is a comparison of frictional resistance under three kinds of pin fin shapes.
The flow resistance of the impingement cavity with elliptical pin fins are 3.9% higher than
that with circle pin fins. Considering the heat transfer and pressure drop, a circle pin fin
can be selected.
Figure 23. Comparison of the frictional factor under various pin fin shapes.
3.5. Entropy Generation in Impingement Cooling
In the process of impingement cooling heat transfer, the entropy generation of air
flow will be produced. In this study, the air is considered as the ideal gas and the heat loss
0 102030405060
0
5
10
15
20
25
30
35
R
e×10
3
Circular
EllipticⅠ
EllipticⅡ
Nu
0 102030405060
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
f
Re
×103
Circular
EllipticⅠ
EllipticⅡ
Appl. Sci. 2021, 11, 9924 19 of 21
is neglected. The entropy generation in the adiabatic process for the ideal gas can be de-
fined as:
ref
Δ
γ
CPT
SγPT
1-
γ
p
ref
=ln[ ]
(9)
where, Cp is the isobaric specific heat capacity; γ is the specific heat ratio, taken as 1.3; Pref
and Tref are the reference pressure and temperature, taking Pref and Tref as the total pressure
and temperature at the inlet of impingement cavity, respectively; P and T are the pressure
and temperature at any point in the flow field.
Figure 24 is one case of the entropy generation distribution with pin fins on the lower
surface when Re is 2 × 104, impingement hole number is 14 and the hole diameter is 7.2
mm. It can be seen from the figure that after the air flow passes through the impingement
holes, the air flow area and the air mixing degree increase, so the entropy generation near
the inlet is large; near the outlet holes, the air flow shrinks and the air flow area decreases
suddenly, so the entropy generation near the outlet holes is large; in the region of the pin
fins, for the pin fins are arranged orderly, the entropy generation is relatively uniform.
Figure 24. Entropy generation distribution with pin fins on the lower surface at Re = 2 × 104.
4. Conclusions
In order to strengthen the impingement cooling heat transfer in the end wall cavity
of the gas turbine guide vane, its structure and parameters have constantly been im-
proved. This study investigates the effects of the impingement hole diameter, the im-
pingement hole number, and the height, spacing and shape of pin fins on the impinge-
ment cooling. The key findings of this research are as follows.
1. The larger the Re, the larger the average Nusselt number of the upper and lower sur-
faces, and the average Nusselt number of the lower surface is larger than that of the
upper surface.
2. With the increase in the impingement hole diameter, the average Nusselt numbers of
the upper and lower surfaces are both increased, and the minimum Nu of the lower
surface is reduced, where may produce local ablation. The higher the number of im-
pingement holes, the larger the average Nusselt number of the lower surface, the
more uniform the Nu distribution. It is recommended to use 14 impingement holes
with a hole diameter of 7.2 mm.
3. The geometric parameters of the pin fin have less effect on heat transfer and pressure
drop. Compared with the pin fin height is 24 mm, the average Nusselt number of the
lower surface only improved by 11.2% when the pin fin height is 3 mm. The average
Nusselt number of the lower surface with the circular pin fin is larger than that of the
Appl. Sci. 2021, 11, 9924 20 of 21
elliptical pin fin, and its flow resistance is smaller. It is recommended to use the cir-
cular pin fin with a height of 3 mm and spacing of 25.8 mm.
4. The jet flow in cavity is closely related to the heat transfer. The heat transfer near the
impingement holes is better, while the heat transfer in the vortex area is poor. Due to
the turbulence effect of the pin fins, the air flow turbulence intensity increases rap-
idly, and heat transfer is enhanced.
Author Contributions: Conceptualization, L.Z.; methodology, L.Z. and G.C.; software, G.C. and
K.F.; validation, L.Z., G.C. and K.F.; formal analysis, G.C. and K.F.; investigation, G.C., K.F. and Y.J.;
data curation, Y.J. and Z.Z.; writing—original draft preparation, G.C. and L.Z.; writing—review and
editing, L.Z. and G.C.; visualization, Z.Z.; supervision, L.Z. All authors have read and agreed to the
published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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