Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade
Based on the state-of-the art methods of gas turbine cascade heat transfer assessment, a theoretical model of the two-dimensional air turbine cascade is proposed, wherein gas flows past the turbine blade profile. The velocity, temperature, and pressure fields, as well as the heat transfer distributi...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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irk-123456789-1882972023-02-23T01:27:14Z Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade He, Z. Lin, J.H. Sun, X.Y. Gu, X. Научно-технический раздел Based on the state-of-the art methods of gas turbine cascade heat transfer assessment, a theoretical model of the two-dimensional air turbine cascade is proposed, wherein gas flows past the turbine blade profile. The velocity, temperature, and pressure fields, as well as the heat transfer distribution along the pressure and suction surfaces, the leading and trailing edges of the turbine blade were computed via FLUENT software at different pressure ratios. This permitted of studying the heat transfer evolution at different pressure ratios in the same position and at the same pressure ratio in different positions. На основе разработанных методов оценки теплопередачи газовой ступени турбины предложенатеоретическая модель двухмерной ступени аэротурбины, в которой газ течет мимо контура лопасти турбины. Поля скоростей, температур и давлений, а также распределениекоэффициента теплопередачи вдоль поверхностей давления и разрежения, передней и задней кромок лопасти турбины рассчитывались с помощью программы FLUENT при разном отношении давлений. Это позволило исследовать эволюцию коэффициента теплопередачи при различном отношении давлений в одинаковом положении и при одинаковом отношении давлений в различных положениях. На основі розроблених методів оцінки теплопередачі газової ступені турбіни запропонована теоретична модель двомірної ступені аеротурбіни, в якій газ тече повз контуру лопаті турбіни. Поля швидкостей, температур і тисків, а також розподіл коефіцієнта теплопередачі вздовж поверхонь тиску і розрідження, передній і задній крайок лопаті турбіни розраховувалися за допомогою програми FLUENT при різному співвідношення тисків. Це дало змогу дослідити еволюцію коефіцієнта теплопередачі при різному ставленні тисків в однаковому становищі і при однаковому ставленні тисків в різних положеннях. 2019 Article Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade / Z. He, J.H. Lin, X.Y. Sun, X. Gu // Проблеми міцності. — 2019. — № 1. — С. 5-15. — Бібліогр.: 10 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/188297 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел He, Z. Lin, J.H. Sun, X.Y. Gu, X. Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade Проблемы прочности |
| description |
Based on the state-of-the art methods of gas turbine cascade heat transfer assessment, a theoretical model of the two-dimensional air turbine cascade is proposed, wherein gas flows past the turbine blade profile. The velocity, temperature, and pressure fields, as well as the heat transfer distribution along the pressure and suction surfaces, the leading and trailing edges of the turbine blade were computed via FLUENT software at different pressure ratios. This permitted of studying the heat transfer evolution at different pressure ratios in the same position and at the same pressure ratio in different positions. |
| format |
Article |
| author |
He, Z. Lin, J.H. Sun, X.Y. Gu, X. |
| author_facet |
He, Z. Lin, J.H. Sun, X.Y. Gu, X. |
| author_sort |
He, Z. |
| title |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade |
| title_short |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade |
| title_full |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade |
| title_fullStr |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade |
| title_full_unstemmed |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade |
| title_sort |
numerical simulation of the inlet/outlet pressure ratio effect on the heat transfer coefficient in an air turbine cascade |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2019 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188297 |
| citation_txt |
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat Transfer Coefficient in an Air Turbine Cascade / Z. He, J.H. Lin, X.Y. Sun, X. Gu // Проблеми міцності. — 2019. — № 1. — С. 5-15. — Бібліогр.: 10 назв. — англ. |
| series |
Проблемы прочности |
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2025-07-16T10:17:51Z |
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2025-07-16T10:17:51Z |
| _version_ |
1837798336280657920 |
| fulltext |
SCIENTIFIC AND TECHNICAL
SECTION
UDC 539.4
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect on the Heat
Transfer Coefficient in an Air Turbine Cascade
Z. He, J. H. Lin, X. Y. Sun,
1
and X. Gu
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China
1 sunxiaoyu520634@163.com
Based on the state-of-the art methods of gas turbine cascade heat transfer assessment, a theoretical
model of the two-dimensional air turbine cascade is proposed, wherein gas flows past the turbine
blade profile. The velocity, temperature, and pressure fields, as well as the heat transfer distribution
along the pressure and suction surfaces, the leading and trailing edges of the turbine blade were
computed via FLUENT software at different pressure ratios. This permitted of studying the heat
transfer evolution at different pressure ratios in the same position and at the same pressure ratio in
different positions.
Keywords: pressure ratio, heat transfer, turbine cascade.
Introduction. Heat transfer cooling analysis is crucial for design of aero-engine
turbine blades and very topical in aerodynamic research of aircraft [1]. Since heat transfer
in a turbine cascade channel with gas flow is quite complex, its cooling design necessitates
a convenient and accurate assessment of the heat transfer characteristics of the turbine
working surface, e.g., using an effective numerical simulation method, which would
provide a quick and accurate calculation of the heat transfer coefficient. In this paper, the
pressure ratio effect on the heat transfer coefficient in the turbine cascade is explored via
such simulation.
Since 1970s, the film cooling technology became a hotspot research subject of
domestic and foreign scholars [2]. On the one hand, numerous studies were focused on the
mechanism of flat film cooling, which involved flow parameters (Reynolds number,
blowing ratio, momentum ratio, pressure gradient, turbulence, density ratio, etc.) and
geometrical parameters (film hole shape, diameter, hole spacing, etc.) affecting the heat
transfer coefficient and cooling efficiency [3, 4]. On the other hand, some studies
investigated the application of the turbine blade film holes under the test conditions, to
assess the surface heat transfer coefficient and the film cooling efficiency for blades with
film holes under the working conditions, for the further prediction of the blade surface
temperature, blade strength and durability [5].
Thus, Nealy et al. [6] revealed the basic factors controlling the surface heat transfer of
the blade, which included boundary layer transition characteristics, free flow turbulence,
pressure gradient, cooling working material injection position, blade surface curvature,
blade surface roughness, airflow separation and reattachment, and shock wave/boundary
layer interaction. An attempt to account for the effect of these factors on the heat transfer
was made by these researchers with the emphasis on the Mach and Reynolds numbers.
© Z. HE, J. H. LIN, X. Y. SUN, X. GU, 2019
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 5
Alternatively, a group of researchers from the Institute of Engineering Thermophysics
of the Chinese Academy of Sciences (Beijing, China) [7] have studied the distribution of
cooling efficiency across the single-row circular orifice of 30�, single row of diagonal holes
and downstream of the single-row square holes by the heat and mass transfer mass method.
They have inducted the cooling efficiency empirical formula in the middle line position of a
certain area downstream of the nozzle by the least squares method. The results show that
the cooling efficiency is very high.
Liu et al. [8] proposed the thermal conductance of graphene–matrix interfaces plays a
key role in controlling the thermal properties of graphene-based nanocomposites. It
represents if heat enters graphene from its basal plane one side and then leaves it the other
side at once, the corresponding interfacial thermal conductance is large; if heat enters
graphene from both sides of its basal plane and leaves it at a position on its basal plane at a
moment, the corresponding interfacial thermal conductance is small.
Cao et al. [9] proposed an article of probing nanoscale thermal transport in surfactant
solutions in 2015. They examined the thermal transport and structure in solution of AOT in
n-octane liquids using small-angle neutron scattering, thermal conductivity measurements,
the result shows that: the thermal conductivity of the surfactant solution decreases as AOT
is added until the onset of micellization but increases as more AOT is added.
1. Theoretical Solutions and Their Software Implementation. The flow process
related to heat transfer problem addressed in this paper can be reduced to the Navier–
Stokes equations in the following form:
�
�
�
x
u
i
i( ) ,� 0 (1)
�
�
�
�
�
�
�
�
�
�
�
�x
u u
p
x x
u
x
u
xj
i j
i j
i
j
j
i
( )�� � �
�
�
�
�
�
�
�
�
�
�
�
�
�
� � � �
�
�
�
x
u u
j
i j( ), (2)
�
�
�
�
�
� �
�
�
�
�
�
x
u c T
x
T
x
u
xi
i p
i
T eff
i
i
j
( )�
��
�
��
�
�
�
�
�
�� eff
i
j
j
i
eff
k
k
u
x
u
x
u
x
�
�
�
�
�
�
�
�
�
�
�
�
��
�
�
�
�
�
�
�
�
2
3
. (3)
From the fluid mechanics, the set of Navier–Stokes equations (which contain a mass
conservation equation and three momentum conservation equations) allows one to derive
four physical parameters. The system of Navier–Stokes equations has a closed form and,
thus, can yield accurate theoretical solutions. However, since their derivation requires
significant computational resources of direct numerical simulation (DNS), such solutions
are not widely used by the engineers. For engineering applications, alternative
two-equation eddy-viscosity turbulence models were proposed by Menter in 1994 [10].
These included k-epsilon(�) equation turbulence model for the near-wall region and
k-omega(�) equation turbulence model for the far field, where k is turbulent kinetic
energy, � is specific dissipation, which determines the turbulence scale, and � is turbulent
dissipation.
Based on this model, FLUENT software package was developed for simulating and
analyzing complex flow field areas. It is mainly applied to fluid flow and heat transfer in
the flow field. It supports a variety grid of different formats applicable to ICEM, GAMBIT,
and mechanical CAD software products relevant to a wide range of applications in the
automotive, aviation, aerospace, turbine, oil and gas industries. Moreover, FLUENT can
accurately simulate the non-viscous flow, laminar flow, and turbulence. Therefore, in this
study, the FLUENT software package was used for the implementation of shear stress
Z. He, J. H. Lin, X. Y. Sun, and, X. Gu
6 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
transport (SST) k� � turbulence model, which combines the advantages of the k� �
equation turbulence model and the k� � turbulence model. The former model is
automatically substituted by the latter one, depending on the distance from the wall. The
convergence condition is less than 10 6� for the parameter residual, while k and �
equations are shown as follows:
�
�
�
�
�
�
�
�
�
�
��
�x
u k
x
k
x
G G
i
i
i
t
i
k b( ) ,� �
��
�
��
�
�
�
�
�
�� � � (4)
�
�
�
�
�
� �
�
�
�
�
�
x
u c T
x
T
x
u
xi
i p
i
T eff
i
i
j
( )�
��
�
��
�
�
�
�
�
�� eff
i
j
j
i
eff
k
k
u
x
u
x
u
x
�
�
�
�
�
�
�
�
�
�
�
�
��
�
�
�
�
�
�
�
�
2
3
. (5)
In Eqs. (1)–(5), subscripts i j k, , , ,� 1 2 3 correspond to coordinates x, y, z;
C1� � 1.44, C2 � 1.9, � k � 1.0, � � � 1.2, while � t , C � , Gk , Gb and other parameters
used in the calculation can be found elsewhere [1]. Heat transfer coefficient and the
Reynolds number are derived via Eqs. (6) and (7), respectively:
h
q
t tw f
�
�
, (6)
Re .�
ul
v
(7)
Here q is heat flux density, tw and t f are the wall and fluid temperatures, respectively,
u is fluid velocity, l is chord length, and v is viscosity coefficient.
2. Study on Heat Transfer Coefficient.
2.1. Heat Transfer Coefficient and Turbine Blade Cooling Relationship. In the gas
turbine, the heat transfer coefficient of the blade is very high, while the material thermal
conductivity is quite low. This combination implies a specific distribution of the heat transfer
coefficient along the entire blade, which is controlled by a low thermal conductivity.
A typical heat transfer coefficient distribution along the blade profile is depicted in
Fig. 1. The heat transfer coefficient of the stagnation point (where the flow velocity is zero)
is the largest and affected by the inlet turbulence, while the boundary layers at suction and
pressure surfaces of the blade are turbulent or nearly turbulent. At the pressure surface of
the blade, the laminar boundary layer is developed in the leading edge, but due to the
influence of the incoming turbulence, the heat transfer coefficient gets higher than that in
the front laminar flow. After that, the boundary layer changes successively and forms
turbulent flows. The reason for the transformation is that the pressure gradient forces the
boundary layer to keep the laminar flow state, while the blade curvature characteristics are
more favorable for a turbulent flow.
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 7
Fig. 1. A typical heat transfer coefficient distribution along the blade profile.
The distribution of heat transfer coefficient along the blade profile was calculated, in
this study, by using the two-dimensional boundary layer theory. Firstly, the pressure
distribution in the cascade was assessed by the numerical simulation of non-stick
compressible two-dimensional flow. Then, the boundary layer was simulated using the
boundary layer theory. The heat transfer coefficient distributions for different pressure
values were found to be close to that depicted in Fig. 1. Although the calculated heat
transfer coefficient distribution exhibited some singularities in the vicinity of the stagnation
point and the suction layer laminar flow area, it proved to be quite accurate and robust. The
heat transfer coefficient in the transition area (upper left part of Fig. 1) increased by 1.2~1.8
times due to the turbulence flow influence.
2.2. Preprocessing. The turbine cascade model is depicted in Fig. 2, and its
dimensions are listed in Table 1. As seen in Fig. 2, the high-temperature gas enters from the
left (inlet) channel and flows out from the right (outlet) channel, the entrance angle of the
cascade is 63.4�, the outlet angle is 28.4�, and the chord length is 43.942 mm.
The turbine cascade model meshing was implemented using the GAMBIT software
for the pressure and suction walls (Fig. 3a and 3b) and inlet/outlet channels (Fig. 4a and
4b), respectively.
8 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
Z. He, J. H. Lin, X. Y. Sun, and, X. Gu
T a b l e 1
Turbine Cascade Model Dimensions
Chord length
(mm)
Inlet channel
inclination angle (deg)
Outlet channel
inclination angle (deg)
Pitch
(mm)
43.942 63.4 28.4 37.3
Fig. 2. Turbine cascade geometric model.
Fig. 3. Pressure (a) and suction (b) surface wall grids.
a b
The boundary conditions are listed in Table 2, where three inlet/outlet pressure ratios
(PR), namely 1.6, 1.8, and 2.0, are used, while the inlet/outlet temperature ratio is equal to
0.8.
2.3. Post-Processing.
2.3.1. Analysis of Heat Transfer Coefficient Distribution at Different Pressure Ratios.
For the pressure ratios of 1.6, 1.8, and 2.0 tabulated in Table 2, the heat transfer coefficient
(HTC) values calculated at the same blade contour points exhibited an increase with the
pressure ratio, which trend is illustrated by Fig. 5. The overall heat transfer coefficient
distribution range is 200 to 1400 W/( ).m K2 � The convective heat transfer coefficient of the
blade leading edge is the largest (1400 W/( ),m K2 � while that of the trailing edge exhibits a
sharp increase (up to 1050 W/( ),m K2 � as is seen in Fig. 6.
2.3.2. Analysis of the HTC Distribution along the Blade Profile. The preliminary
analysis shows that higher pressure ratios (and, thus, higher gas flow velocities) correspond
to thinner boundary layers near the blade (and, thus, smaller heat transfer heat resistance).
This complies with the well-known dependence h AR� 1 ( ), where h is heat transfer
coefficient, R is heat transfer resistance, and A is heat transfer area. If, under certain
conditions, heat transfer resistance decreases in the constant heat transfer area, the heat
transfer coefficient becomes larger.
2.3.3. Analysis of the HTC Distribution at the Blade Leading Edge. Firstly, a
boundary (interface) layer is produced by the contact between the cooling fluid and the
blade wall. This boundary layer is conventionally subdivided into the velocity boundary
layer and thermal (temperature) one. The former one is defined as a thin layer, where the
fluid velocity changes drastically near the solid surface. Its thickness corresponds to that
where the velocity is 99% of the main velocity. The latter, i.e., thermal boundary layer, is
defined as thin layer of fluid, with temperature changing drastically near the solid surface.
There is a temperature difference between the mainstream and the wall under the condition
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 9
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect ...
T a b l e 2
Boundary Conditions
PR Inlet pressure
(MPa)
Outlet pressure
(MPa)
Inlet/outlet
temperature
(K)
Blade wall
temperature
(K)
Temperature
ratio
1.6
1.8
2.0
162.120
182.385
202.650
101.325
101.325
101.325
310
310
310
248
248
248
0.8
0.8
0.8
a b
Fig. 4. Inlet (a) and outlet (b) channel grids.
of convective heat transfer. When the residual temperature at some distance from the wall
equals to 99% of the mainstream excess temperature, the respective distance is referred to
as the temperature boundary layer thickness. The heat transfer coefficient is related to the
velocity and temperature boundary layer by the following relationship: h
t
t
y y
�� �
� �
��
1.
When the temperature gradient in the temperature boundary layer is large, the convective
heat transfer coefficient in the wall vicinity is also increased. Meanwhile, the velocity
boundary layer also controls the convective heat transfer coefficient: when the cooling fluid
velocity is relatively high, the impact of the fluid on the boundary layer is quite strong, so
that the velocity boundary layer will be thinner, and the heat transfer resistance related to
the latter will be quite small.
It can be seen from Fig. 6 that the heat transfer coefficient is the largest at the leading
edge when the pressure ratio is 1.8, while Fig. 7 vividly illustrate that the temperature
gradient of the leading edge is very large, but the velocity is very low (20~60 m/s).
10 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
Z. He, J. H. Lin, X. Y. Sun, and, X. Gu
a b
Fig. 5. The calculated temperature (a) and velocity (b) distributions in the blade leading edge surface
layer for pressure ratio PR � 1.8.
Fig. 6. Heat transfer coefficient curves for three PR values (1.6, 1.8, and 2.0).
Therefore, according to the above findings, a high temperature gradient increases the heat
transfer coefficient. While the leading edge flow velocity is low, the boundary layer
thickness is high, and the convective heat transfer resistance is very large. So when the heat
flux is constant, the convective heat transfer effect is relatively small: its values calculated
at the blade leading edge for three different pressure ratios are shown in Table 3. When the
PR changes from 1.6 to 1.8, the convective heat transfer coefficient increases by 5.157%,
and when PR � 2.0, HTC increases by 7.478%, as compared to that at PR � 1.8.
Therefore, the heat transfer efficiency of the turbine cascade is the lowest at PR � 1.6, and
the highest at PR � 2.0. In other words, the heat transfer effect of the turbine cascade
increases with the pressure ratio, while the convective heat transfer coefficient of the blade
leading edge is the largest.
2.3.4. Analysis of the HTC Distribution at the Pressure Edge. The graph in Fig. 8
corresponds to three points of the pressure surface from the leading edge to the trailing one,
which are the leading point, midpoint, and trailing point of the blade pressure surface. It
can be seen from Fig. 9a that the temperature of the leading edge varies from 250 to 305 K,
while the temperature boundary layer thickness is roughly equal to 0.000032 m. Consider
the temperature gradient definition:
dt
dx
T Tw�
��
�
, (8)
where T� and Tw are the temperatures of the mainstream fluid and the blade wall,
respectively, while � is the thermal boundary layer thickness. So the temperature gradient
is �t �� 1718,750 K/m. From Fig. 9b, we can see that the temperature of the middle point
is distributed (from 250 to 300 K), and the temperature boundary layer is approximately
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 11
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect ...
a b
Fig. 7. The calculated temperature (a) and velocity (b) distributions in the turbine cascade for
pressure ratio PR � 1.8.
T a b l e 3
The Heat Transfer Coefficient of the Leading Edge
PR HTC of the leading edge [W/(m K2 � )] Increase rate (%)
1.6 1128.040 0
1.8 1186.216 5.157
2.0 1274.921 7.478
12 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
Z. He, J. H. Lin, X. Y. Sun, and, X. Gu
Fig. 8. Heat transfer coefficient distribution along the blade pressure surface.
a b
c
Fig. 9. Temperature distribution in the leading edge (a), midsection (b), and trailing edge (c)
boundary layers of the turbine blade.
0.00024 m, so �t �� 208,333.33 K/m. As it follows from Fig. 9c, at the temperature
boundary layer thickness is approximately equal to 0.00011 m, while and the trailing edge
temperature varies by 25 K (from 250 to 275 K), so that �t �� 227,272.72 K/m. It can be
seen that the temperature gradient varies from the leading edge to the trailing one on the
pressure surface as follows: 1718,750, 208,333.33, and 227,272.72 K/m. This explains why
the convective heat transfer coefficient is almost the same, except for a sharp drop from the
leading edge to the trailing one.
2.3.5. Analysis of the HTC Variation along the Suction Edge. The heat transfer
coefficient gradually decreases from the leading edge, and then increases quite abruptly
when it reaches point A, as is shown in Fig. 10.
It can be seen from Fig. 11a that the temperature at the leading edge of the suction
surface varies by 55 K (from 250 to 305 K), while the temperature boundary layer
thickness � is approx. 0.00005 m, so that �t �� 1100,000 K/m. Figure 11b indicates that
the temperature boundary layer is approximately 0.00002 m-thick, while the temperature of
the trailing edge varies by 10 K (from 250 to 260 K), so that �t �� 500,000 K/m. As seen
from Fig. 12a, the temperature of the leading edge of the suction surface is about 250 K,
and � is approx. 0.00015 m, so �t �� 0 K/m. From Fig. 12b, it follows that � is approx.
0.00003 m, and the trailing edge temperature varies by 30 K (from 250 to 280 K), so that
�t �� 1000,000 K/m.
It is known that the temperature gradient evolution along the suction surface varies
from 1100,000 to 500,000 K/m at the leading edge to 0–1000,000 K/m at the trailing one.
This explains why the convective heat transfer coefficient from the leading edge to the
trailing edge is reduced at first, and drops to zero and finally exhibits a sharp increase.
From Fig. 13, it can be seen that the gradient of the temperature boundary layer
gradually drops from the leading point to point A, which results in a gradual drop of the
heat transfer coefficient. The boundary layer separation occurs when point A is reached, so
that the disturbance near the boundary layer becomes stronger, and the nearby laminar flow
changes to a turbulent one. Meanwhile, the Reynolds number also increases, while the
convective heat transfer resistance is small, making the convection thermal coefficient
larger and, thus, strongly enhancing the heat transfer.
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 13
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect ...
Fig. 10. Heat transfer coefficient distribution along the blade suction surface at PR � 1.8.
14 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
Z. He, J. H. Lin, X. Y. Sun, and, X. Gu
a b
Fig. 11. Temperature distribution in the leading edge (a) and midsection (b) blade suction surface at
PR � 1.8.
a b
Fig. 12. Temperature distribution in point A (a) and the trailing edge (b) of the blade suction surface
at PR � 1.8.
Fig. 13. Temperature (a) and velocity (b) distributions calculated in point A of the blade profile.
a b
Conclusions. In this paper, the effect of inlet/outlet pressure ratio on the heat transfer
of the turbine cascade was explored, which made it possible to draw the conclusions:
1. For the examined pressure ratios of 1.6, 1.8, and 2.0, the heat transfer coefficient
was found to increase with the pressure ratio at the same point of the blade profile. At the
blade front, a change in the pressure ratio from 1.6 to 1.8 resulted in the convective heat
transfer coefficient increase by 5.16%, and when the pressure ratio was raised to 2.0, the
heat transfer coefficient increased by 7.48%, as compared to that at pressure ratio of 1.8.
Therefore, the heat transfer efficiency of the turbine cascade is the lowest when the
pressure ratio is 1.6 and the highest when the pressure ratio is 2.0. The overall heat transfer
coefficient variation range was from 200 to 1400 W/( ).m K2 �
2. The heat transfer coefficient attained its maximum value at the blade leading edge
and deceased along the pressure surface decreases from the leading edge to the trailing one.
The heat transfer coefficient of the suction surface decreased from the leading edge to the
trailing edge and exhibited a sharp rise at the tail point.
3. It was found that the three pressure ratios under study corresponded to different
thickness values of the temperature boundary layer: larger pressure ratios invoked higher
fluid velocities, thinner temperature boundary layers, and higher convective heat transfer
coefficients.
Acknowledgments. This work was supported by the National Natural Science
Foundation of China (No. 11602066) and the National Science Foundation of Heilongjiang
Province of China (QC2015058 and 42400621-1-15047).
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5. G. Li, C. Wu, W. Zhang, et al., “Effect of cross-flow direction of coolant on film
cooling effectiveness with one inlet and double outlet hole injection,” Propuls. Power
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6. D. A. Nealy, M. S. Mihelc, L. D. Hylton, and H. J. Gladden, “Measurements of heat
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Eng. Gas Turbines Power, 106, No. 1, 149–158 (1984).
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Thermophys., 5, 182–186 (1984).
8. Y. Liu, J. Huang, B. Yang, et al., “Duality of the interfacial thermal conductance in
graphene-based nanocomposites,” Carbon, 75, 169–177 (2014).
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solutions,” Sci. Rep., 5, 16040 (2015), doi: 10.1038/srep16040.
10. F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering
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Received 05. 03. 2018
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 15
Numerical Simulation of the Inlet/Outlet Pressure Ratio Effect ...
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
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/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
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(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
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/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
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/MultimediaHandling /UseObjectSettings
/Namespace [
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(CreativeSuite)
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]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|