- Email: [email protected]
Comparative study on steady and unsteady conjugate heat transfer analysis of a high pressure turbine blade
Accepted Manuscript Title: Comparative study on steady and unsteady conjugate heat transfer analysis of a high pressure turbine blade Author: Sunwoo Hwang, Changmin Son, Doyoung Seo, Dong-Ho Rhee, Bongjun Cha PII: DOI: Reference:
S1359-4311(16)00034-X http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.139 ATE 7557
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
18-9-2015 29-12-2015
Please cite this article as: Sunwoo Hwang, Changmin Son, Doyoung Seo, Dong-Ho Rhee, Bongjun Cha, Comparative study on steady and unsteady conjugate heat transfer analysis of a high pressure turbine blade, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.139. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
APPLIED THERMAL ENGINEERING
Comparative Study on Steady and Unsteady Conjugate Heat Transfer Analysis of a High Pressure Turbine Blade Sunwoo Hwang School of Mechanical Engineering, Pusan National University Busan 609-735, Korea e-mail: [email protected] Changmin Son1 School of Mechanical Engineering, Pusan National University Busan 609-735, Korea e-mail: [email protected] Doyoung Seo School of Aerospace Engineering, Pusan National University Busan 609-735, Korea Dong-Ho Rhee, Bongjun Cha Korea Aerospace Research Institute, Daejeon, 305-380, Korea e-mail: [email protected] ABSTRACT In this study, an analysis of steady-state and unsteady-state Conjugate Heat Transfer (CHT) of an aeronautic high pressure gas turbine was conducted, which can calculate fluid and solid domain at the same time. ANSYS CFX V16.0, was used to solve the problem. The main emphasis of this study was on three dimensional behavior of the temperature distribution in blade of the 1st stage high pressure turbine. The Conjugate heat transfer approach in this study is validated with 1983 NASA internally cooled C3X experimental data. Results from the unsteady state were compared to the results of steady state calculations. This paper focuses on the importance of unsteady conjugate heat transfer analysis of the rotor blade by the prediction of the thermal environment around the rotor blade and heat conductions in the rotor blade as it is necessary to carry out the rotor blade thermal load analysis and finally life assessment.
1
Corresponding author
1 Page 1 of 27
APPLIED THERMAL ENGINEERING
Keyword Conjugate heat transfer, Unsteady, High pressure turbine blade INTRODUCTION Modern gas turbine engines are designed to operate at high turbine inlet temperature (TIT), which is far beyond the allowable metal temperatures. Thus, a reliable and accurate numerical prediction of the temperature field in the metal of the hot components is becoming more and more important for the cooling designer of modern gas turbines. This involves convection heat transfer in the fluid component and conduction heat transfer in the solid component. Thus, the conjugate heat transfer analysis plays a key role in predicting the temperature field of high pressure turbine components see in Figure 1. Several researchers have investigated the coupled conjugate heat transfer analysis of turbine systems. One of the first uses of conjugate heat transfer calculations in turbomachinery was the work of Bohn et al. [1]. Using the same code, Bohn et al. [2] extended the conjugate approach to investigate leading edge film cooling. The showerhead at the leading edge is notorious for its complex thermal field that is greatly influenced by conduction in the metal, and the conjugate approach is more physically realistic than the study of heat transfer coefficients and adiabatic effectiveness separately. Bohn et al. [3] also used a conjugate solver to investigate discrete jet film cooling from two round holes at the leading edge of a steel turbine vane. In addition, much effort went into developing and applying methods to account for the coupling between the fluid and solid parts [4-8] Above works are steady-state CFD simulations to provide fluid and solid temperature distribution. However, a real high pressure turbine experiences unsteady flow conditions depending on time. In aerodynamic study, much research was conducted [9-12]. Alternatively, the unsteady conjugate heat transfer simulation was applied by Alejandro et al. [13] to investigate the temperature distribution on the thermal barrier coated gas turbine bucket. This work showed the variations of the blade surface temperature depending on time. He et al. [14] is motivated by the need to address acute mismatch of time scales between the solid conduction and the typical periodic flow unsteadiness in HP 2 Page 2 of 27
APPLIED THERMAL ENGINEERING
turbines. A frequency-domain conduction model was introduced. Ameri et al. [15] noted the effect that segregation might have on blade heat transfer. This segregation occurs because the Mach number profile in the circumferential direction stays approximately constant while the rotor wake, having a lower temperature, forces the local absolute velocity to diminish. The cooler wake flow and hotter free stream flow would be distributed at different angles. The phenomenon would be absent in the case of a steady simulation and it would be expected that a steady and an unsteady computation lead to different heat transfer patterns on the blade surface. In the following research, a steady-state conjugate heat transfer analysis of high pressure turbine blade has been carried out to understand the complex interaction between thermal conduction inside the blade metal and convection heat transfer inside the fluid domain. Also, an unsteady conjugate heat transfer analysis has been carried out to emphasize the transient effects on gas turbine heat transfer which is an important process to be considered in gas turbine design HIGH PRESSURE TURBINE 1st STAGE BLADE DESCRIPTION In this study, a high pressure turbine 1st stage blade was considered. A high pressure turbine nozzle geometry in this study, which has 56 nozzles in total, is explained in Seo et al [16]. The number and geometry of the blade is described in Table 1. A high pressure turbine 1st stage blade is fully designed with internal and external cooling scheme, shown in Figure 2. Blade cooling design needs high cooling performance and structural stability due to the rotating effect. U-shaped serpentine type internal passages are designed for effective convective cooling inside the blade. To enhance convective cooling, an angled rib turbulator scheme is designed on internal passages. For external cooling design of the blade, a film cooling scheme was applied to the leading edge (3 rows) and pressure side (2 rows). Except for the leading edge region, all of the film rows at pressure side are fan shaped film cooling holes, which have a diffusor effect. More detailed information of the blade geometry is show in Table 1.
COMPUTATIONAL METHOD -
Steady-state calculation 3 Page 3 of 27
APPLIED THERMAL ENGINEERING
Conjugate Heat Transfer (CHT) analysis is a method of calculating convection (eq. 1) in fluids and conduction (eq. 2) in solids with the heat balance between the fluid and solid domain.
(1)
(2)
Simulations were carried out using the commercial computational fluid dynamics (CFD) code ANSYS CFX V16.0 to solve the steady Reynolds-Averaged Navier-Stokes equations (RANS). High-resolution scheme was used to solve the governing equations. As to turbulence model, Shear Stress Transport (SST) turbulence model was used for the simulations and the inlet intensity was set at 5%. Convergence was considered adequate when the root mean squared (RMS) residual fell below 1E-05 and steady state conditions had been met for quantities of interest such as efficiency and mass flow rate. Coupled conjugate heat transfer was achieved solving the energy equation for the fluid-solid domains in the same matrix. In this way, the coupling between the two sides of the interfaces can be easily treated in an implicit way by discretizing the energy flux in terms of both solid and fluid adjacent cell. At the same time, it is necessary to respect at each iteration both the continuity of temperature profiles and the equality of thermal fluxes across the interface. This implicit technique allows faster convergence rates if compared to standard explicit coupling used in other codes. This is mainly due to the fact that energy balance is strictly respected at each iteration step, meaning that the temperature residuals in the solid only follow the implicit relaxation and not the update of the boundary conditions, basically not overloading non-conjugate calculations convergence rate. -
Unsteady calculation
For unsteady conjugate heat transfer analysis, the blade domain needs to be modified. The interface between the nozzle and the blade was updated each timestep as the relative position of the grids on each side of the interface changes. This method required large, in
4 Page 4 of 27
APPLIED THERMAL ENGINEERING
terms of simulation time, disk space. Furthermore, the resource requirement problem was exacerbated if there was an unequal pitch between the nozzle and blade domain. Therefore, blade fluid domain pitch should be the same as the nozzle fluid domain pitch. The number of blades was modified from 104 to 112, leaving the total number of nozzles to 56. Finally, the ratio of nozzle to blade was changed to 1:2. Unsteady conjugate heat transfer analysis was also performed by means of CFX V16.0. Transient rotor-stator model was used to count for transient interaction of the flow between a nozzle and blade passage, using sliding interface. By using this approach, the transient relative motion between the components on each side of the connection is simulated. The interface position is updated each timestep, as the relative position of the grids on each side of the interface changes. The blade passing frequency (BPF) of the high pressure turbine was 0.00315ms and the time steps per iteration was 0.00126ms. This time step corresponds to 1 step for 0.13° rotation. 1 revolution has to be chosen to be able to perform the Fast Fourier Transformation (FFT) considering the transformation into the frequency domain in the further procedure. For each time step, all residuals such as pressure, temperature were converged to 1E-05 after 20 internal loops. These convergences of the residual have to be regarded as sufficient concerning the data of interest.
Computational Grids In order to include the effects of stator on the rotor flow and heat transfer, the whole stage was simulated. The turbine stage simulation was separated into two domains such as fluid domain and solid domain in each nozzle guide vane and rotor blade. Figure 3 shows the CFD grids for conjugate heat transfer analysis. The CFD grid was generated using ANSYS MESHING. The whole calculation domain consists of 44 million elements for the complete 1st stage model. Figure 3(a) shows fluid domains of the nozzle and blade. They were generated with prism and tetrahedral mesh, maintaining the mean value of y+ under 1. As shown in Table 2, the number of elements in the fluid and solid domain of each nozzle and blade were chosen. Figure 3(b) shows the solid domain for the nozzle and blade. The grid near the film hole was generated with a very fine size grid.
5 Page 5 of 27
APPLIED THERMAL ENGINEERING
Grid dependency analysis A grid dependency analysis was been carried out using an unstructured grid such as a tetrahedral and prism grid. A domain composed by a single blade fluid and solid was used for this purpose. The boundary conditions were the same as mentioned later. Ten different grids have been generated shown in Table 3. In this study, the fluid(15.8 million) and solid domain(4.6 million) of the blade were chosen to analyze see in Figure 4.
Three Dimensional Validation The validation of the shear stress transport (SST) turbulence model in conjugate heat transfer analysis was carried out comparing the experimental data of C3X by Hylton et al. [17]. For fluid domain, two types of grids were generated. One was a fine hexa grid and the other was a tetrahedral grid with a prism grid generated. On the other hand, for the solid domain, a tetrahedral grid was applied. Both experimental data and CFD results were normalized by inlet total pressure(eq.3) and temperature(eq.4) at the mid-span.
(3)
(4)
As seen in Figure 5, it should be noted that the maximum error was 6 % and 10 % on normalized pressure and temperature distribution, respectively, showing great reliability of this calculation. In addition, the calculated temperature distribution was slightly over the predicted experimental data over the whole region. Therefore, these predicted results show a reasonable agreement with the experimental data, enabling the use the SST turbulence model in the conjugate heat transfer analysis.
Boundary Conditions Total pressure and total temperature were applied as the nozzle inlet condition. Static pressure conditions were applied at the blade outlet. Also, the inlet temperature profile was applied in order to imitate the combustor outlet condition in Figure 6, which is the Radial Temperature Distortion Factor (RTDF) normalized with the nozzle inlet total 6 Page 6 of 27
APPLIED THERMAL ENGINEERING
temperature(
). Cooling air total temperature and total pressure are defined in the
engine performance cycle sheet seen in Table 4. Interface between fluids and solids is applied to conjugate heat transfer. At a solid-fluid 1:1 interface, duplicated nodes exist. The conservative value for the solid-side node is the variable values averaged over the half on the control volume that lies inside the solid. The conservative value for the fluidside node is the variable values averaged over the half on the control volume that lies in the fluid. The Periodic boundary conditions were applied to the nozzle and blade fluid domain in the circumferential direction. The mixing-plane approach was adopted to consider the rotor and stator interface between stationary and rotating components. This approach, instead of assuming a fixed relative position of the components, performs a circumferential averaging of the fluxes through bands on the interface, enabling steadystate predictions to be obtained for multistage. The designed rotational speed of the HPT was about 17,000rpm. Therefore, the blade fluid domain was rotated within the absolute frame of the reference axial axis (z-direction) so that there was a relative motion between the casing and the blade. RESULTS AND DISCUSSION 1. Flow Characteristic of HPT blade -
Steady-state flow characteristics
Surface oil flow of both the pressure side and the suction side is shown in Figure 7. There is a stagnation line on the leading edge of rotor blade. At the leading edge of rotor blade hub, a horseshoe vortex(yellow) was generated and separated into the suction side and the pressure side of the blade. Also, corner vortex(green) and passage vortex(blue) were predicted as well (Sharma et al. [18]). As clearly seen from the figure, tip leakage flow(red) starts from the tip region of the blade pressure side. Due to the pressure gradient from the pressure side to the suction side, tip leakage flow comes out from the pressure side to the suction side through blade tip. Furthermore, at the suction side hub region, secondary vortex grows toward the mid-span of trailing edge. The external flow contours of the normalized pressure distribution, , static temperature distribution, total temperature distribution and relative Mach number (
) distribution at
the mid-span are shown in Figure 8 and 9. These figures indicate that the cooling flow was at a high pressure, low Mach number, and low temperature in the internal passage. 7 Page 7 of 27
APPLIED THERMAL ENGINEERING
The normalized static pressure distributions shown in Figure 8(a) illustrates the existence of a high pressure field at the blade’s leading edge stagnation point that rapidly reduced around the leading edge suction side. Low pressure was observed in the blade exit throat corresponding to the sonic flow and formed a shock wave in the trailing edge shown in Figure 8(b). The normalized static temperature distribution shown in Figure 9(a) indicates that the suction side (SS) gas temperature is lower than the pressure side (PS) because the gas flow on the suction side was accelerated. In Figure 9(b), the normalized relative total temperature of the gas was high at the inlet and flowed downstream to the exit region along the pressure side. There was a lower temperature layer that covers the suction side from the airfoil throat to the trailing edge due to the heat conduction from the internal cooling and the secondary flow vortexes mentioned above.
-
Unsteady flow characteristics
A single time that a blade passes the nozzle passage is divided into 50 steps. All unsteady results are processed every 5 steps in 50. Then there were 10 time steps(T*) in a period. Figure 10 shows the time-variation of the unsteady streamline at the blade midspan. These show 10 of the 50 divisions for each interval which a single nozzle pitch was passed by a full blade pitch. The blade inlet flow tended to change its inlet angle in rotating. This can be easily checked out by monitoring the movement of film cooling at the leading edge stagnation point. During the 1st ~ 4th time period, film cooling at leading edge tended to be ejected toward the suction side. That means that the stagnation point at the leading edge of the blade was changed by the interaction between the nozzle and the blade position. On the other hand, for the 5th ~ 7th time period, the leading edge film cooling had the tendency to eject toward the pressure side and then go to the suction side again. This phenomenon was repeated periodically in the blade domain. However, in the steady state results, it seemed that stagnation point blade at the leading edge was at a constant position. This is because a mixing plane mode was applied between the nozzle and blade interface, which performs a circumferential averaging of the fluxes through bands on the interface.
8 Page 8 of 27
APPLIED THERMAL ENGINEERING
2. Heat Transfer Characteristics of HPT blade -
Steady-state heat transfer characteristics
The normalized temperature distribution of the blade can be captured in Figure 11 and 12. As clearly seen from Figure 12, it is clearly to observe that hot spot exists at the leading edge of the blade. Hot spot at the leading edge of the blade is captured mostly at the mid-span where the temperature of the main flow is highest due to the inlet temperature profile applied at the nozzle inlet in Figure 11(b). Also, some hot spot on pressure side is predicted at 70 % of span height in Figure 12. On the other hand, in Figure 11(a), secondary vortex at the suction side hub region and tip leakage flow from the pressure side (see in Figure 7(a)) affects the temperature distribution of the suction side blade. The thermal load on the suction side rise gradually toward the trailing edge of the blade. In addition, the thermal load on the suction side is much larger than that on the pressure side. Figure 13 shows the normalized average temperature distribution on the blade surface, cross section, and cooling passage surface along the span height. Fan shaped film cooling on the external surface has a great effect on reducing the heat load, which blades have to endure, presented as a black line in Figure 13. The maximum averaged temperature appears at span of 90 % of each region. The average temperature of each region increases along the span height. This is because the internal cooling temperature rises toward the tip from the hub, which means that the cooling capacity decreases in span-wise direction. The temperature difference between the internal cooling passage and the blade cross section was almost the same value as the temperature difference from the blade cross section and the cross section of the blade surface
-
Unsteady heat transfer characteristics
Figure 14 shows the periodic total temperature distribution of the stationary frame of blade at a span 50 %, which is normalized by total temperature at nozzle inlet. Two types of nozzles downstream were chopped with the rotor leading edge, then bowed and stretched in the stream-wise direction periodically. Downstream of the nozzle with a relatively low total temperature reached the blade’s leading edge surface at the 1st time step. Then, a low total temperature flow was bowed and stretched in the stream-wise 9 Page 9 of 27
APPLIED THERMAL ENGINEERING
direction from the 2nd to 5th time step. Downstream of the nozzle with a relatively high total temperature reached the blade’s leading edge surface at the 6th time step. Then, a high total temperature flow was bowed and stretched in the stream-wise direction from the 7nd to 10th time step. These two types of periodic phenomena were repeated to the blade while it was rotating. This means that the leading edge of the blade experienced periodical thermal stress from the downstream of nozzle. In Figure 15, periodical temperature movements at the leading edge are clearly noted, which can support the description above. There were four specific points at the leading edge of blade. In the external region, the red point monitors the fluid domain temperature at the blade surface and the green point investigates the solid domain temperature at the blade surface. On the other hand, as for the internal region, the blue and black points monitor the solid domain temperature and solid temperature, respectively. As seen in the figure, the red line shows the periodic behavior of external fluid temperature depending on the time step, showing the difference of temperature between maximum and minimum value with 450 K. In contrast, although external fluid temperatures changed periodically, external and internal solid temperature and internal cooling temperature seemed to be constant. Moreover, the internal cooling temperature showed very little fluctuation in temperature and was mostly constant. Figure 16 gives a good impression of the conjugate calculation principle. The temperature distribution along a section line as marked left corner in the figure. Section lines are normalized, designating the starting point as ‘0.0’ in red and ending point as ‘1.0’ in blue. Starting in the external hot gas region, the temperature fluctuated along the time steps until the very thin external temperature boundary layer was reached periodically. From the 1st to 5th time step, temperature gradients were extremely high, changing from approx. 1.0 to 0.7 very close to the blade surface. On the other hand, from the 6th to 10th time step, temperature gradients were relatively low; the figures decreased from slightly over 0.8 to 0.7. This is because the nozzle affects the flow of the leading edge film cooling movement downstream of the blade. In the case of the solid body region, the temperature decrease is nearly linear. The gradient of the curve in combination with the thermal conductivity of the blade material gives the local specific heat flux. The temperature difference in the solid was small, indicating a small thermal 10 Page 10 of 27
APPLIED THERMAL ENGINEERING
resistance. In the internal cooling passage, the temperature gradient was lower and temperature boundary layer was thicker than that on the external surface side, signifying a smaller heat transfer coefficient of the internal convection. In addition, the fluctuation of cooling temperature was quite small by comparison with the external flow’s temperature.
CONCLUSIONS In this study, steady state and unsteady conjugate heat transfer analysis were conducted to predict the flow and heat transfer characteristics of a high pressure turbine blade. From the results, a strong influence of unsteadiness is observed on the blade temperature distribution. Unlike steady-state results, the leading edge stagnation point and the blade inlet flow angle vary with time. Hence, cooling designers need to position film holes to cover the wide range of the surface at the leading edge. Due to nozzle exit flow, the blade surface experiences relatively cooler and hotter temperature field periodically. The key findings are as follows.
The maximum variation of the blade inlet flow angle is around 2 degree. Due to nozzle exit flow, the blade surface experiences relatively cooler and hotter temperature field periodically.
The blade surface experiences relatively cooler and hotter temperature field periodically.
Specifically, its maximum difference is almost 450 K at leading edge of blade.
Unsteady conjugate heat transfer analysis provides very useful design guidelines for considering the periodical movement of nozzle wake and temperature fluctuation, which may cause serious damage to HPT blade. Therefore, these findings confirm that the prediction of unsteady effects on the blade heat transfer is a very important area in cooling design process that should be considered for further investigation.
ACKNOWLEDGMENT
11 Page 11 of 27
APPLIED THERMAL ENGINEERING
This work was supported by the “Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (NO.20144030200570) and this work was also supported by the Korea Aerospace Research Institute (KARI) and grant funded by the Korea government Ministry of Knowledge Economy (KA000157)
12 Page 12 of 27
APPLIED THERMAL ENGINEERING
NOMENCLATURE
CHT
=
Conjugate heat transfer
HPT
=
High pressure turbine
BPF
=
Blade passing frequency
LE
=
Leading edge
TE
=
Trailing edge
PS
=
Pressure side
SS
=
Suction side
P
=
Static pressure, Pa
T
=
Static temperature, K
Mn
=
Mach number
TS
=
Time step, Sec
L
=
Length, mm
t
=
Physical time
f
=
Any fluid property
α
=
Thermal diffusivity
SUBSCRIPTS
Avg.
Average
s
Static property
t
Total property
c
Coolant
in
Inlet
out
Outlet
nz
Nozzle
13 Page 13 of 27
APPLIED THERMAL ENGINEERING
bl
Blade Free stream
14 Page 14 of 27
APPLIED THERMAL ENGINEERING
REFERENCES [1] Bohn, D., Bonhoff, B., Schonenborn, H., 1995, “Combined Aerodynamic and Thermal Analysis of a Turbine Nozzle Guide Vane”, IGTC Paper 95-108 [2] Bohn et al., 1997a, “3D Conjugate Flow and Heat Transfer Calculations of a Film Cooled Turbine Vane at Different Operation Conditions”, ASME Paper 97-GT-23 [3] Bohn et al., 1997b, “Experimental and Numerical Conjugate Flow and Heat Transfer Investigation of a Shower Head Cooled Turbine Guide Vane”, ASME Paper 97-GT-15 [4] Han et al., 2000, “Simultaneous Prediction of External Flow Field and Temperature in Internally Cooled 3D Turbine Blade Material”, ASME Paper 2000-GT-253 [5] D. L. Rigdy, J. Lepicovshy, 2001, “Conjugate Heat Transfer Analysis of Internally cooled Configurations”, ASME Paper 2001-GT-0405 [6] Heidmann, J., Girby, D. and Ameri, A., 1999, “A Three Dimensional Coupled Internal/External Simulation of a Film Cooled Turbine Vane”, ASME Paper 99-GT-186 [7] Toshihiko Takahashi, Kazunori Watanabe, Takeshi Takahashi, 2000, “Thermal Conjugate Analysis of a First Stage Blade in a Gas Turbine”, Proceedings of ASME Turbo Expo 2000-521 [8] Dong P., Huang H. Y., Feng G. T., 2008, “Conjugate Heat Transfer Analysis of a High Pressure Turbine Vane with Radial Internal Cooling Passages”, J.
Aerospace
Power 2008, Vol. 23, pp. 201-207 [9] Dirk Witteck, Derek Micallef, Ronald Mailach, 2014. “Comparison of Transient Blade Row Methods for the CFD Analysis of a High-Pressure Turbine”, Proceedings of ASME Turbo Expo 2014-26043 [10] Martin Lipfert, J. Habermann, Martin G. Rose, S. Staudacher, Yavuz Guendogdu, 2014, “Blade Row Interactions in an LP Turbine at Design and Strong Off-Design Operation”, Proceedings of ASME Turbo Expo 2014-25343 [11] R. Denos, T. Arts, G. Paniagua, V Michelassi, G. Martelli, 2001, “Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage”, ASME J. Turbomach., Vol. 123, pp. 81-89 [12] C. H. Custer, J. M. Weiss, V. Subramanian, W. S. Clark, K. C. Hall, 2012, “Unsteady Simulation of a 1.5 Stage Turbine Using an Implicitly Coupled Nonlinear Harmonic Balance Method”, Proceedings of ASME Turbo Expo 2012-69690 15 Page 15 of 27
APPLIED THERMAL ENGINEERING
[13] Alejandro H. R., Zdzislaw M. C., Eder A. Bautista P, 2008, “Unsteady 3-D Conjugated Heat Transfer Simulation of a Thermal Barrier Coated Gas Turbine Bucker”, Proceedings of ASME Turbo Expo 2008-50597 [14] L. He, M. L. G. Oldfield, 2011, “Unsteady Heat Transfer Modeling”, ASME J. Turbomach., Vol. 133, 031022 [15] Ali A. Ameri, D. L. Rigby, E. Steinthorsson, J. Heidmann, J. C. Fabian, 2008, “Unsteady Analysis of blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes”, Proceedings of ASME Turbo Expo 2008-51242 [16] Seo, J. C., Hwang, S. W., Son, C. M., 2014, “Conjugate Heat Transfer Analysis of a High Pressure Turbine Nozzle”, Proceedings of the KSME 2014 Spring Annual Conference (KSME14TE-Fr02A200), pp. 356-357 [17] L.D. Hylton, 1983, “Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surface of Turbine Vanes”, NAS 3-22761, NASA [18] O. P. Sharma, T. L. Butler, 1987, “Predictions of Endwall losses and Secondary Flows in Axial Flow Turbine Cascades”, J. Turbomachinery, Vol. 109, pp. 229-236
16 Page 16 of 27
APPLIED THERMAL ENGINEERING
Figure 1. Conjugate heat transfer modeling
Figure 2. Schematic of the blade
17 Page 17 of 27
APPLIED THERMAL ENGINEERING
Figure 3. Computational grids: (a) Fluid domain and (b) Solid domain (Nozzle, Blade)
18 Page 18 of 27
APPLIED THERMAL ENGINEERING
Figure 4. Grid dependency study: (a), (b), (c) Fluid grid, (d) Solid grid
Figure 5. Validation results: (a) pressure distribution and (b) temperature distribution
19 Page 19 of 27
APPLIED THERMAL ENGINEERING
Figure 6. Normalized turbine inlet temperature profile
Figure 7. Surface oil flow visualization: (a) Suction side and (b) Pressure side
20 Page 20 of 27
APPLIED THERMAL ENGINEERING
Figure 8. Mid-span (a) static pressure ( distribution
) and (b) Mach number
Figure 9. Mid-span (a) normalized static temperature ( (b) normalized total temperature distribution (
) and )
21 Page 21 of 27
APPLIED THERMAL ENGINEERING
Figure 10. Streamline of blade at span 50 %
Figure 11. Normalized temperature distribution of blade ( (a) Suction side and (b) Pressure side
)
22 Page 22 of 27
APPLIED THERMAL ENGINEERING
Figure 12. Normalized surface temperature distribution of blade at each span ( )
Figure 13. Normalized averaged temperature of blade (
)
23 Page 23 of 27
APPLIED THERMAL ENGINEERING
Figure 14. Normalized total temperature distribution of blade at span 50 % ( ) 24 Page 24 of 27
APPLIED THERMAL ENGINEERING
Figure 15. Periodical normalized temperature behavior at blade leading edge ( )
Figure 16. Normalized temperature gradient at leading edge of blade (
)
25 Page 25 of 27
APPLIED THERMAL ENGINEERING
Table 1. Geometry parameters HPT Blade No. of blades
104
Inlet angle ( °)
40
Outlet angle (°)
65
Chord length (mm)
22
Span height (mm)
17
Table 2. Computational grid for a high-pressure tubine stage The type of grid The number of elements Nozzle Tetrahedral with prism 16.4 million Fluid Domain Blade Tetrahedral with prism 15.3 million Nozzle Tetrahedral 7.5 million Solid Domain Blade Tetrahedral 4.7 million
Table 3. Grid Sensitivity Analysis Blade Domain
1 2 3 4 5
Fluid Grid 2.1M 4.1M 7.9M 16M 31.5M
Solid Grid 4.6M 4.6M 4.6M 4.6M 4.6M
Average y+ 0.77 0.82 0.84 0.85 0.88
6 7 8 9 10
Fluid Grid 15.8M 15.8M 15.8M 15.8M 15.8M
Solid Grid 1.0M 2.0M 4.6M 10.2M 19.5M
Average y+ 0.85 0.85 0.85 0.85 0.85
Table 4. Boundary conditions Boundary Condition Inlet total pressure [bar] Inlet total temperature [K]
Main
Coolant (nozzle/blade)
30
32/22
1600
837/837
(averaged value)
Inlet turbulence level [%]
5
Outlet static pressure [bar]
1
5
26 Page 26 of 27
APPLIED THERMAL ENGINEERING
27 Page 27 of 27
S1359-4311(16)00034-X http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.139 ATE 7557
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
18-9-2015 29-12-2015
Please cite this article as: Sunwoo Hwang, Changmin Son, Doyoung Seo, Dong-Ho Rhee, Bongjun Cha, Comparative study on steady and unsteady conjugate heat transfer analysis of a high pressure turbine blade, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.139. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
APPLIED THERMAL ENGINEERING
Comparative Study on Steady and Unsteady Conjugate Heat Transfer Analysis of a High Pressure Turbine Blade Sunwoo Hwang School of Mechanical Engineering, Pusan National University Busan 609-735, Korea e-mail: [email protected] Changmin Son1 School of Mechanical Engineering, Pusan National University Busan 609-735, Korea e-mail: [email protected] Doyoung Seo School of Aerospace Engineering, Pusan National University Busan 609-735, Korea Dong-Ho Rhee, Bongjun Cha Korea Aerospace Research Institute, Daejeon, 305-380, Korea e-mail: [email protected] ABSTRACT In this study, an analysis of steady-state and unsteady-state Conjugate Heat Transfer (CHT) of an aeronautic high pressure gas turbine was conducted, which can calculate fluid and solid domain at the same time. ANSYS CFX V16.0, was used to solve the problem. The main emphasis of this study was on three dimensional behavior of the temperature distribution in blade of the 1st stage high pressure turbine. The Conjugate heat transfer approach in this study is validated with 1983 NASA internally cooled C3X experimental data. Results from the unsteady state were compared to the results of steady state calculations. This paper focuses on the importance of unsteady conjugate heat transfer analysis of the rotor blade by the prediction of the thermal environment around the rotor blade and heat conductions in the rotor blade as it is necessary to carry out the rotor blade thermal load analysis and finally life assessment.
1
Corresponding author
1 Page 1 of 27
APPLIED THERMAL ENGINEERING
Keyword Conjugate heat transfer, Unsteady, High pressure turbine blade INTRODUCTION Modern gas turbine engines are designed to operate at high turbine inlet temperature (TIT), which is far beyond the allowable metal temperatures. Thus, a reliable and accurate numerical prediction of the temperature field in the metal of the hot components is becoming more and more important for the cooling designer of modern gas turbines. This involves convection heat transfer in the fluid component and conduction heat transfer in the solid component. Thus, the conjugate heat transfer analysis plays a key role in predicting the temperature field of high pressure turbine components see in Figure 1. Several researchers have investigated the coupled conjugate heat transfer analysis of turbine systems. One of the first uses of conjugate heat transfer calculations in turbomachinery was the work of Bohn et al. [1]. Using the same code, Bohn et al. [2] extended the conjugate approach to investigate leading edge film cooling. The showerhead at the leading edge is notorious for its complex thermal field that is greatly influenced by conduction in the metal, and the conjugate approach is more physically realistic than the study of heat transfer coefficients and adiabatic effectiveness separately. Bohn et al. [3] also used a conjugate solver to investigate discrete jet film cooling from two round holes at the leading edge of a steel turbine vane. In addition, much effort went into developing and applying methods to account for the coupling between the fluid and solid parts [4-8] Above works are steady-state CFD simulations to provide fluid and solid temperature distribution. However, a real high pressure turbine experiences unsteady flow conditions depending on time. In aerodynamic study, much research was conducted [9-12]. Alternatively, the unsteady conjugate heat transfer simulation was applied by Alejandro et al. [13] to investigate the temperature distribution on the thermal barrier coated gas turbine bucket. This work showed the variations of the blade surface temperature depending on time. He et al. [14] is motivated by the need to address acute mismatch of time scales between the solid conduction and the typical periodic flow unsteadiness in HP 2 Page 2 of 27
APPLIED THERMAL ENGINEERING
turbines. A frequency-domain conduction model was introduced. Ameri et al. [15] noted the effect that segregation might have on blade heat transfer. This segregation occurs because the Mach number profile in the circumferential direction stays approximately constant while the rotor wake, having a lower temperature, forces the local absolute velocity to diminish. The cooler wake flow and hotter free stream flow would be distributed at different angles. The phenomenon would be absent in the case of a steady simulation and it would be expected that a steady and an unsteady computation lead to different heat transfer patterns on the blade surface. In the following research, a steady-state conjugate heat transfer analysis of high pressure turbine blade has been carried out to understand the complex interaction between thermal conduction inside the blade metal and convection heat transfer inside the fluid domain. Also, an unsteady conjugate heat transfer analysis has been carried out to emphasize the transient effects on gas turbine heat transfer which is an important process to be considered in gas turbine design HIGH PRESSURE TURBINE 1st STAGE BLADE DESCRIPTION In this study, a high pressure turbine 1st stage blade was considered. A high pressure turbine nozzle geometry in this study, which has 56 nozzles in total, is explained in Seo et al [16]. The number and geometry of the blade is described in Table 1. A high pressure turbine 1st stage blade is fully designed with internal and external cooling scheme, shown in Figure 2. Blade cooling design needs high cooling performance and structural stability due to the rotating effect. U-shaped serpentine type internal passages are designed for effective convective cooling inside the blade. To enhance convective cooling, an angled rib turbulator scheme is designed on internal passages. For external cooling design of the blade, a film cooling scheme was applied to the leading edge (3 rows) and pressure side (2 rows). Except for the leading edge region, all of the film rows at pressure side are fan shaped film cooling holes, which have a diffusor effect. More detailed information of the blade geometry is show in Table 1.
COMPUTATIONAL METHOD -
Steady-state calculation 3 Page 3 of 27
APPLIED THERMAL ENGINEERING
Conjugate Heat Transfer (CHT) analysis is a method of calculating convection (eq. 1) in fluids and conduction (eq. 2) in solids with the heat balance between the fluid and solid domain.
(1)
(2)
Simulations were carried out using the commercial computational fluid dynamics (CFD) code ANSYS CFX V16.0 to solve the steady Reynolds-Averaged Navier-Stokes equations (RANS). High-resolution scheme was used to solve the governing equations. As to turbulence model, Shear Stress Transport (SST) turbulence model was used for the simulations and the inlet intensity was set at 5%. Convergence was considered adequate when the root mean squared (RMS) residual fell below 1E-05 and steady state conditions had been met for quantities of interest such as efficiency and mass flow rate. Coupled conjugate heat transfer was achieved solving the energy equation for the fluid-solid domains in the same matrix. In this way, the coupling between the two sides of the interfaces can be easily treated in an implicit way by discretizing the energy flux in terms of both solid and fluid adjacent cell. At the same time, it is necessary to respect at each iteration both the continuity of temperature profiles and the equality of thermal fluxes across the interface. This implicit technique allows faster convergence rates if compared to standard explicit coupling used in other codes. This is mainly due to the fact that energy balance is strictly respected at each iteration step, meaning that the temperature residuals in the solid only follow the implicit relaxation and not the update of the boundary conditions, basically not overloading non-conjugate calculations convergence rate. -
Unsteady calculation
For unsteady conjugate heat transfer analysis, the blade domain needs to be modified. The interface between the nozzle and the blade was updated each timestep as the relative position of the grids on each side of the interface changes. This method required large, in
4 Page 4 of 27
APPLIED THERMAL ENGINEERING
terms of simulation time, disk space. Furthermore, the resource requirement problem was exacerbated if there was an unequal pitch between the nozzle and blade domain. Therefore, blade fluid domain pitch should be the same as the nozzle fluid domain pitch. The number of blades was modified from 104 to 112, leaving the total number of nozzles to 56. Finally, the ratio of nozzle to blade was changed to 1:2. Unsteady conjugate heat transfer analysis was also performed by means of CFX V16.0. Transient rotor-stator model was used to count for transient interaction of the flow between a nozzle and blade passage, using sliding interface. By using this approach, the transient relative motion between the components on each side of the connection is simulated. The interface position is updated each timestep, as the relative position of the grids on each side of the interface changes. The blade passing frequency (BPF) of the high pressure turbine was 0.00315ms and the time steps per iteration was 0.00126ms. This time step corresponds to 1 step for 0.13° rotation. 1 revolution has to be chosen to be able to perform the Fast Fourier Transformation (FFT) considering the transformation into the frequency domain in the further procedure. For each time step, all residuals such as pressure, temperature were converged to 1E-05 after 20 internal loops. These convergences of the residual have to be regarded as sufficient concerning the data of interest.
Computational Grids In order to include the effects of stator on the rotor flow and heat transfer, the whole stage was simulated. The turbine stage simulation was separated into two domains such as fluid domain and solid domain in each nozzle guide vane and rotor blade. Figure 3 shows the CFD grids for conjugate heat transfer analysis. The CFD grid was generated using ANSYS MESHING. The whole calculation domain consists of 44 million elements for the complete 1st stage model. Figure 3(a) shows fluid domains of the nozzle and blade. They were generated with prism and tetrahedral mesh, maintaining the mean value of y+ under 1. As shown in Table 2, the number of elements in the fluid and solid domain of each nozzle and blade were chosen. Figure 3(b) shows the solid domain for the nozzle and blade. The grid near the film hole was generated with a very fine size grid.
5 Page 5 of 27
APPLIED THERMAL ENGINEERING
Grid dependency analysis A grid dependency analysis was been carried out using an unstructured grid such as a tetrahedral and prism grid. A domain composed by a single blade fluid and solid was used for this purpose. The boundary conditions were the same as mentioned later. Ten different grids have been generated shown in Table 3. In this study, the fluid(15.8 million) and solid domain(4.6 million) of the blade were chosen to analyze see in Figure 4.
Three Dimensional Validation The validation of the shear stress transport (SST) turbulence model in conjugate heat transfer analysis was carried out comparing the experimental data of C3X by Hylton et al. [17]. For fluid domain, two types of grids were generated. One was a fine hexa grid and the other was a tetrahedral grid with a prism grid generated. On the other hand, for the solid domain, a tetrahedral grid was applied. Both experimental data and CFD results were normalized by inlet total pressure(eq.3) and temperature(eq.4) at the mid-span.
(3)
(4)
As seen in Figure 5, it should be noted that the maximum error was 6 % and 10 % on normalized pressure and temperature distribution, respectively, showing great reliability of this calculation. In addition, the calculated temperature distribution was slightly over the predicted experimental data over the whole region. Therefore, these predicted results show a reasonable agreement with the experimental data, enabling the use the SST turbulence model in the conjugate heat transfer analysis.
Boundary Conditions Total pressure and total temperature were applied as the nozzle inlet condition. Static pressure conditions were applied at the blade outlet. Also, the inlet temperature profile was applied in order to imitate the combustor outlet condition in Figure 6, which is the Radial Temperature Distortion Factor (RTDF) normalized with the nozzle inlet total 6 Page 6 of 27
APPLIED THERMAL ENGINEERING
temperature(
). Cooling air total temperature and total pressure are defined in the
engine performance cycle sheet seen in Table 4. Interface between fluids and solids is applied to conjugate heat transfer. At a solid-fluid 1:1 interface, duplicated nodes exist. The conservative value for the solid-side node is the variable values averaged over the half on the control volume that lies inside the solid. The conservative value for the fluidside node is the variable values averaged over the half on the control volume that lies in the fluid. The Periodic boundary conditions were applied to the nozzle and blade fluid domain in the circumferential direction. The mixing-plane approach was adopted to consider the rotor and stator interface between stationary and rotating components. This approach, instead of assuming a fixed relative position of the components, performs a circumferential averaging of the fluxes through bands on the interface, enabling steadystate predictions to be obtained for multistage. The designed rotational speed of the HPT was about 17,000rpm. Therefore, the blade fluid domain was rotated within the absolute frame of the reference axial axis (z-direction) so that there was a relative motion between the casing and the blade. RESULTS AND DISCUSSION 1. Flow Characteristic of HPT blade -
Steady-state flow characteristics
Surface oil flow of both the pressure side and the suction side is shown in Figure 7. There is a stagnation line on the leading edge of rotor blade. At the leading edge of rotor blade hub, a horseshoe vortex(yellow) was generated and separated into the suction side and the pressure side of the blade. Also, corner vortex(green) and passage vortex(blue) were predicted as well (Sharma et al. [18]). As clearly seen from the figure, tip leakage flow(red) starts from the tip region of the blade pressure side. Due to the pressure gradient from the pressure side to the suction side, tip leakage flow comes out from the pressure side to the suction side through blade tip. Furthermore, at the suction side hub region, secondary vortex grows toward the mid-span of trailing edge. The external flow contours of the normalized pressure distribution, , static temperature distribution, total temperature distribution and relative Mach number (
) distribution at
the mid-span are shown in Figure 8 and 9. These figures indicate that the cooling flow was at a high pressure, low Mach number, and low temperature in the internal passage. 7 Page 7 of 27
APPLIED THERMAL ENGINEERING
The normalized static pressure distributions shown in Figure 8(a) illustrates the existence of a high pressure field at the blade’s leading edge stagnation point that rapidly reduced around the leading edge suction side. Low pressure was observed in the blade exit throat corresponding to the sonic flow and formed a shock wave in the trailing edge shown in Figure 8(b). The normalized static temperature distribution shown in Figure 9(a) indicates that the suction side (SS) gas temperature is lower than the pressure side (PS) because the gas flow on the suction side was accelerated. In Figure 9(b), the normalized relative total temperature of the gas was high at the inlet and flowed downstream to the exit region along the pressure side. There was a lower temperature layer that covers the suction side from the airfoil throat to the trailing edge due to the heat conduction from the internal cooling and the secondary flow vortexes mentioned above.
-
Unsteady flow characteristics
A single time that a blade passes the nozzle passage is divided into 50 steps. All unsteady results are processed every 5 steps in 50. Then there were 10 time steps(T*) in a period. Figure 10 shows the time-variation of the unsteady streamline at the blade midspan. These show 10 of the 50 divisions for each interval which a single nozzle pitch was passed by a full blade pitch. The blade inlet flow tended to change its inlet angle in rotating. This can be easily checked out by monitoring the movement of film cooling at the leading edge stagnation point. During the 1st ~ 4th time period, film cooling at leading edge tended to be ejected toward the suction side. That means that the stagnation point at the leading edge of the blade was changed by the interaction between the nozzle and the blade position. On the other hand, for the 5th ~ 7th time period, the leading edge film cooling had the tendency to eject toward the pressure side and then go to the suction side again. This phenomenon was repeated periodically in the blade domain. However, in the steady state results, it seemed that stagnation point blade at the leading edge was at a constant position. This is because a mixing plane mode was applied between the nozzle and blade interface, which performs a circumferential averaging of the fluxes through bands on the interface.
8 Page 8 of 27
APPLIED THERMAL ENGINEERING
2. Heat Transfer Characteristics of HPT blade -
Steady-state heat transfer characteristics
The normalized temperature distribution of the blade can be captured in Figure 11 and 12. As clearly seen from Figure 12, it is clearly to observe that hot spot exists at the leading edge of the blade. Hot spot at the leading edge of the blade is captured mostly at the mid-span where the temperature of the main flow is highest due to the inlet temperature profile applied at the nozzle inlet in Figure 11(b). Also, some hot spot on pressure side is predicted at 70 % of span height in Figure 12. On the other hand, in Figure 11(a), secondary vortex at the suction side hub region and tip leakage flow from the pressure side (see in Figure 7(a)) affects the temperature distribution of the suction side blade. The thermal load on the suction side rise gradually toward the trailing edge of the blade. In addition, the thermal load on the suction side is much larger than that on the pressure side. Figure 13 shows the normalized average temperature distribution on the blade surface, cross section, and cooling passage surface along the span height. Fan shaped film cooling on the external surface has a great effect on reducing the heat load, which blades have to endure, presented as a black line in Figure 13. The maximum averaged temperature appears at span of 90 % of each region. The average temperature of each region increases along the span height. This is because the internal cooling temperature rises toward the tip from the hub, which means that the cooling capacity decreases in span-wise direction. The temperature difference between the internal cooling passage and the blade cross section was almost the same value as the temperature difference from the blade cross section and the cross section of the blade surface
-
Unsteady heat transfer characteristics
Figure 14 shows the periodic total temperature distribution of the stationary frame of blade at a span 50 %, which is normalized by total temperature at nozzle inlet. Two types of nozzles downstream were chopped with the rotor leading edge, then bowed and stretched in the stream-wise direction periodically. Downstream of the nozzle with a relatively low total temperature reached the blade’s leading edge surface at the 1st time step. Then, a low total temperature flow was bowed and stretched in the stream-wise 9 Page 9 of 27
APPLIED THERMAL ENGINEERING
direction from the 2nd to 5th time step. Downstream of the nozzle with a relatively high total temperature reached the blade’s leading edge surface at the 6th time step. Then, a high total temperature flow was bowed and stretched in the stream-wise direction from the 7nd to 10th time step. These two types of periodic phenomena were repeated to the blade while it was rotating. This means that the leading edge of the blade experienced periodical thermal stress from the downstream of nozzle. In Figure 15, periodical temperature movements at the leading edge are clearly noted, which can support the description above. There were four specific points at the leading edge of blade. In the external region, the red point monitors the fluid domain temperature at the blade surface and the green point investigates the solid domain temperature at the blade surface. On the other hand, as for the internal region, the blue and black points monitor the solid domain temperature and solid temperature, respectively. As seen in the figure, the red line shows the periodic behavior of external fluid temperature depending on the time step, showing the difference of temperature between maximum and minimum value with 450 K. In contrast, although external fluid temperatures changed periodically, external and internal solid temperature and internal cooling temperature seemed to be constant. Moreover, the internal cooling temperature showed very little fluctuation in temperature and was mostly constant. Figure 16 gives a good impression of the conjugate calculation principle. The temperature distribution along a section line as marked left corner in the figure. Section lines are normalized, designating the starting point as ‘0.0’ in red and ending point as ‘1.0’ in blue. Starting in the external hot gas region, the temperature fluctuated along the time steps until the very thin external temperature boundary layer was reached periodically. From the 1st to 5th time step, temperature gradients were extremely high, changing from approx. 1.0 to 0.7 very close to the blade surface. On the other hand, from the 6th to 10th time step, temperature gradients were relatively low; the figures decreased from slightly over 0.8 to 0.7. This is because the nozzle affects the flow of the leading edge film cooling movement downstream of the blade. In the case of the solid body region, the temperature decrease is nearly linear. The gradient of the curve in combination with the thermal conductivity of the blade material gives the local specific heat flux. The temperature difference in the solid was small, indicating a small thermal 10 Page 10 of 27
APPLIED THERMAL ENGINEERING
resistance. In the internal cooling passage, the temperature gradient was lower and temperature boundary layer was thicker than that on the external surface side, signifying a smaller heat transfer coefficient of the internal convection. In addition, the fluctuation of cooling temperature was quite small by comparison with the external flow’s temperature.
CONCLUSIONS In this study, steady state and unsteady conjugate heat transfer analysis were conducted to predict the flow and heat transfer characteristics of a high pressure turbine blade. From the results, a strong influence of unsteadiness is observed on the blade temperature distribution. Unlike steady-state results, the leading edge stagnation point and the blade inlet flow angle vary with time. Hence, cooling designers need to position film holes to cover the wide range of the surface at the leading edge. Due to nozzle exit flow, the blade surface experiences relatively cooler and hotter temperature field periodically. The key findings are as follows.
The maximum variation of the blade inlet flow angle is around 2 degree. Due to nozzle exit flow, the blade surface experiences relatively cooler and hotter temperature field periodically.
The blade surface experiences relatively cooler and hotter temperature field periodically.
Specifically, its maximum difference is almost 450 K at leading edge of blade.
Unsteady conjugate heat transfer analysis provides very useful design guidelines for considering the periodical movement of nozzle wake and temperature fluctuation, which may cause serious damage to HPT blade. Therefore, these findings confirm that the prediction of unsteady effects on the blade heat transfer is a very important area in cooling design process that should be considered for further investigation.
ACKNOWLEDGMENT
11 Page 11 of 27
APPLIED THERMAL ENGINEERING
This work was supported by the “Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (NO.20144030200570) and this work was also supported by the Korea Aerospace Research Institute (KARI) and grant funded by the Korea government Ministry of Knowledge Economy (KA000157)
12 Page 12 of 27
APPLIED THERMAL ENGINEERING
NOMENCLATURE
CHT
=
Conjugate heat transfer
HPT
=
High pressure turbine
BPF
=
Blade passing frequency
LE
=
Leading edge
TE
=
Trailing edge
PS
=
Pressure side
SS
=
Suction side
P
=
Static pressure, Pa
T
=
Static temperature, K
Mn
=
Mach number
TS
=
Time step, Sec
L
=
Length, mm
t
=
Physical time
f
=
Any fluid property
α
=
Thermal diffusivity
SUBSCRIPTS
Avg.
Average
s
Static property
t
Total property
c
Coolant
in
Inlet
out
Outlet
nz
Nozzle
13 Page 13 of 27
APPLIED THERMAL ENGINEERING
bl
Blade Free stream
14 Page 14 of 27
APPLIED THERMAL ENGINEERING
REFERENCES [1] Bohn, D., Bonhoff, B., Schonenborn, H., 1995, “Combined Aerodynamic and Thermal Analysis of a Turbine Nozzle Guide Vane”, IGTC Paper 95-108 [2] Bohn et al., 1997a, “3D Conjugate Flow and Heat Transfer Calculations of a Film Cooled Turbine Vane at Different Operation Conditions”, ASME Paper 97-GT-23 [3] Bohn et al., 1997b, “Experimental and Numerical Conjugate Flow and Heat Transfer Investigation of a Shower Head Cooled Turbine Guide Vane”, ASME Paper 97-GT-15 [4] Han et al., 2000, “Simultaneous Prediction of External Flow Field and Temperature in Internally Cooled 3D Turbine Blade Material”, ASME Paper 2000-GT-253 [5] D. L. Rigdy, J. Lepicovshy, 2001, “Conjugate Heat Transfer Analysis of Internally cooled Configurations”, ASME Paper 2001-GT-0405 [6] Heidmann, J., Girby, D. and Ameri, A., 1999, “A Three Dimensional Coupled Internal/External Simulation of a Film Cooled Turbine Vane”, ASME Paper 99-GT-186 [7] Toshihiko Takahashi, Kazunori Watanabe, Takeshi Takahashi, 2000, “Thermal Conjugate Analysis of a First Stage Blade in a Gas Turbine”, Proceedings of ASME Turbo Expo 2000-521 [8] Dong P., Huang H. Y., Feng G. T., 2008, “Conjugate Heat Transfer Analysis of a High Pressure Turbine Vane with Radial Internal Cooling Passages”, J.
Aerospace
Power 2008, Vol. 23, pp. 201-207 [9] Dirk Witteck, Derek Micallef, Ronald Mailach, 2014. “Comparison of Transient Blade Row Methods for the CFD Analysis of a High-Pressure Turbine”, Proceedings of ASME Turbo Expo 2014-26043 [10] Martin Lipfert, J. Habermann, Martin G. Rose, S. Staudacher, Yavuz Guendogdu, 2014, “Blade Row Interactions in an LP Turbine at Design and Strong Off-Design Operation”, Proceedings of ASME Turbo Expo 2014-25343 [11] R. Denos, T. Arts, G. Paniagua, V Michelassi, G. Martelli, 2001, “Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage”, ASME J. Turbomach., Vol. 123, pp. 81-89 [12] C. H. Custer, J. M. Weiss, V. Subramanian, W. S. Clark, K. C. Hall, 2012, “Unsteady Simulation of a 1.5 Stage Turbine Using an Implicitly Coupled Nonlinear Harmonic Balance Method”, Proceedings of ASME Turbo Expo 2012-69690 15 Page 15 of 27
APPLIED THERMAL ENGINEERING
[13] Alejandro H. R., Zdzislaw M. C., Eder A. Bautista P, 2008, “Unsteady 3-D Conjugated Heat Transfer Simulation of a Thermal Barrier Coated Gas Turbine Bucker”, Proceedings of ASME Turbo Expo 2008-50597 [14] L. He, M. L. G. Oldfield, 2011, “Unsteady Heat Transfer Modeling”, ASME J. Turbomach., Vol. 133, 031022 [15] Ali A. Ameri, D. L. Rigby, E. Steinthorsson, J. Heidmann, J. C. Fabian, 2008, “Unsteady Analysis of blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes”, Proceedings of ASME Turbo Expo 2008-51242 [16] Seo, J. C., Hwang, S. W., Son, C. M., 2014, “Conjugate Heat Transfer Analysis of a High Pressure Turbine Nozzle”, Proceedings of the KSME 2014 Spring Annual Conference (KSME14TE-Fr02A200), pp. 356-357 [17] L.D. Hylton, 1983, “Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surface of Turbine Vanes”, NAS 3-22761, NASA [18] O. P. Sharma, T. L. Butler, 1987, “Predictions of Endwall losses and Secondary Flows in Axial Flow Turbine Cascades”, J. Turbomachinery, Vol. 109, pp. 229-236
16 Page 16 of 27
APPLIED THERMAL ENGINEERING
Figure 1. Conjugate heat transfer modeling
Figure 2. Schematic of the blade
17 Page 17 of 27
APPLIED THERMAL ENGINEERING
Figure 3. Computational grids: (a) Fluid domain and (b) Solid domain (Nozzle, Blade)
18 Page 18 of 27
APPLIED THERMAL ENGINEERING
Figure 4. Grid dependency study: (a), (b), (c) Fluid grid, (d) Solid grid
Figure 5. Validation results: (a) pressure distribution and (b) temperature distribution
19 Page 19 of 27
APPLIED THERMAL ENGINEERING
Figure 6. Normalized turbine inlet temperature profile
Figure 7. Surface oil flow visualization: (a) Suction side and (b) Pressure side
20 Page 20 of 27
APPLIED THERMAL ENGINEERING
Figure 8. Mid-span (a) static pressure ( distribution
) and (b) Mach number
Figure 9. Mid-span (a) normalized static temperature ( (b) normalized total temperature distribution (
) and )
21 Page 21 of 27
APPLIED THERMAL ENGINEERING
Figure 10. Streamline of blade at span 50 %
Figure 11. Normalized temperature distribution of blade ( (a) Suction side and (b) Pressure side
)
22 Page 22 of 27
APPLIED THERMAL ENGINEERING
Figure 12. Normalized surface temperature distribution of blade at each span ( )
Figure 13. Normalized averaged temperature of blade (
)
23 Page 23 of 27
APPLIED THERMAL ENGINEERING
Figure 14. Normalized total temperature distribution of blade at span 50 % ( ) 24 Page 24 of 27
APPLIED THERMAL ENGINEERING
Figure 15. Periodical normalized temperature behavior at blade leading edge ( )
Figure 16. Normalized temperature gradient at leading edge of blade (
)
25 Page 25 of 27
APPLIED THERMAL ENGINEERING
Table 1. Geometry parameters HPT Blade No. of blades
104
Inlet angle ( °)
40
Outlet angle (°)
65
Chord length (mm)
22
Span height (mm)
17
Table 2. Computational grid for a high-pressure tubine stage The type of grid The number of elements Nozzle Tetrahedral with prism 16.4 million Fluid Domain Blade Tetrahedral with prism 15.3 million Nozzle Tetrahedral 7.5 million Solid Domain Blade Tetrahedral 4.7 million
Table 3. Grid Sensitivity Analysis Blade Domain
1 2 3 4 5
Fluid Grid 2.1M 4.1M 7.9M 16M 31.5M
Solid Grid 4.6M 4.6M 4.6M 4.6M 4.6M
Average y+ 0.77 0.82 0.84 0.85 0.88
6 7 8 9 10
Fluid Grid 15.8M 15.8M 15.8M 15.8M 15.8M
Solid Grid 1.0M 2.0M 4.6M 10.2M 19.5M
Average y+ 0.85 0.85 0.85 0.85 0.85
Table 4. Boundary conditions Boundary Condition Inlet total pressure [bar] Inlet total temperature [K]
Main
Coolant (nozzle/blade)
30
32/22
1600
837/837
(averaged value)
Inlet turbulence level [%]
5
Outlet static pressure [bar]
1
5
26 Page 26 of 27
APPLIED THERMAL ENGINEERING
27 Page 27 of 27