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EXPERIMENTAL EVIDENCE OF TEMPERATURE RATIO EFFECT ON TURBINE BLADE TIP HEAT TRANSFER
H. Jiang University of Michigan-Shanghai
Jiao Tong University Joint Institute, Shanghai Jiao Tong University
[email protected] Shanghai, China
[email protected] London, UK
Oxford, UK
Astronautics, Shanghai Jiao Tong University
[email protected] Shanghai, China
Shanghai Jiao Tong University Joint Institute,
Shanghai Jiao Tong University
Astronautics, Shanghai Jiao Tong University
[email protected] Shanghai, China
ABSTRACT Determination of a scalable Nusselt number (based on
“adiabatic heat transfer coefficient”) has been the main research objective of most existing heat transfer experimental researches for turbine blade tip. They were mostly carried out at near adiabatic condition without matching the engine realistic wall-to-gas low Temperature Ratio (TR). This practice is based on the assumption that the wall thermal boundary conditions do not affect the over-tip-leakage (OTL) flow field, the aerodynamics and heat transfer can be studied separately. Recent numerical studies raised a question on the validity of this conventional practice. Due to the relatively low thermal inertia of the leakage fluids contained within the thin clearance, the fluids transport properties vary greatly with the wall thermal boundary condition and the two-way coupling between OTL aerodynamics and heat transfer cannot be neglected. The issue could become more severe when the gas turbine manufacturers are making effort to achieve much tighter clearance. However, there has been no experimental evidence to back up these numerical findings. In this study, transient thermal measurements were conducted in a high-temperature linear cascade rig for a range of tip clearances (0.3%, 0.4%, 0.6% and 1%). Surface temperature history was captured by Infrared Thermography at a range of wall-to-gas TRs. Heat Transfer Coefficient (HTC) distributions were obtained based on a conventional data processing technique. The profound influence of tip surface thermal boundary condition on heat transfer and OTL
flow was revealed by the first-of-its-kind experimental data obtained in the present study.
INTRODUCTION Most experimental research in gas turbine heat transfer
community was carried out at near adiabatic condition without matching the engine realistic wall-to-gas Temperature Ratio (TR). The underlying assumption is that the wall thermal boundary condition does not affect the flow field, the aerodynamics and heat transfer can be studied separately. Therefore, the data obtained in the “cold experiment” could be scaled to the engine operating condition. Very recently, the coupling effect between aerodynamics and heat transfer received more attention. There have been increasingly debates on whether the conventional convection-only approach still works over the rotor blade tip, considering the complex Over-Tip-Leakage (OTL) flow and the ongoing effort from the gas turbine manufacturers to achieve much tighter clearance.
The convective heat transfer coefficient (HTC) was defined as a fluid mechanical property in the Newton’s law of cooling.
(1)
where Tw is local wall surface temperature, and Td is the local fluid driving temperature. For low speed flow, it can be assumed to be the freestream temperature, while for high
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speed flow, it should be the adiabatic wall temperature Tad (Eckert, 1955; Anderson and Moffat, 1992). The linear relation of heat flux q and wall temperature Tw is implied from the linearity of the governing energy equation (Jones, 1991). For an established flow field, the HTC becomes constant and does not change with Tw, therefore the HTC value obtained at “cold” lab condition can be scaled to “hot” engine condition. This linear assumption has been widely adopted in engineering practice. In experimental data post processing, HTC can be obtained from the linear regression from heat flux and wall temperature during a transient heat transfer test (Ekkad et al., 2004; Newton et al., 2006; Xue et al.2015), or determined by the slope from several separate tests running at different wall temperatures (Thorpe et al., 2004; Polanka et al., 2008; Lavagnoli et al., 2013). In CFD based design and analysis, HTC and Td, the two unknowns in Equation 1, can be calculated through two isothermal simulations (Shyam et al., 2012; Atkins et al., 2012).
However, it has also been recognized by early researchers that the wall thermal boundary condition will affect aerodynamics of flow field and there is a two-way interaction between the fluid and the solid (Perelman, 1961; Zinnes, 1970; Luikov et al., 1971; Luikov, 1974). Their results show that the uncoupled approach might lead to contradictory and even unphysical results in many cases when the wall thermal boundary condition is specified improperly.
Conjugate Heat Transfer (CHT) has been used to overcome those limitations. Bohn et al. (2003) used CHT to analyse the effect of holes shapes on film-cooling flows. Shih et al., (2009, 2013) highlighted the need to use local Biot number and the importance to couple internal and external heat transfer. The conventional analysis techniques on film cooling effectiveness which neglect the conjugate heat transfer (CHT) effects were questioned by Harrison and Bogard (2008a, 2008b). In the numerical study of Silieti et al., (2009) on the endwall film effectiveness, a better agreement with the experimental data was achieved by using the conjugate model in comparison with the results with an adiabatic model. Conjugate simulations of whole 3-D blade with internal cooling flow, solid blade and external passage flow were carried out by Heidmann et al. (2003), Dees et al. (2010, 2011), and Starke et al., (2008). Solutions with better accuracy from CHT have been increasingly reported recently. There have been a number of publications on the numerical method and solver validation for different turbomachinery applications (e.g. Verdicchio et al., 2001; Montenay et al., 2000; Okita, 2002). An efficient and accurate unsteady conjugate solution approach was proposed and demonstrated for a turbine cascade by He and Oldfield, (2010). There is no doubt that CHT will gain its popularity in time, even though it is still computationally expensive.
Currently, the conventional usage of HTC still has its popularity and convenience in practical engine design process. There have been many correlation methods used to take wall temperature ratio effect on the gas properties into account. Different methods have been proposed to account
for the effect of variable fluid properties by including the gas-to-wall temperature ratio term into the formulation of the HTC (Eckert, 1955; Fitt et al., 1986; Kays and Crawford, 2005, etc.). The limitations of such correction are flat plate studies based, empirical, of a global nature and regardless of the dependence of local flow characteristics on the temperature ratio. For realistic turbine components with complex geometries, aerothermal characteristics are often complex flow features, associated with separation, transition, shock waves. These highly localized features challenge the applicability of a global correction method. More specifically, a global correction approach is not expected to be able to correct the “history effect” effect caused by the upstream local heating, as the interactions between the fluid and the solid not only could affect the local fluid properties, also change the development of the downstream flow field. Maffulli and He, (2014, 2017) discussed the impacts of wall temperature on the secondary flows, trailing edge shock waves, and the passage flow capacity, underlining the connection and interactions between the wall temperature and the external aerodynamics. They proposed a “3-point nonlinear method” to model the HTC dependence on wall temperature with an improved accuracy without going to the full CHT approach. The TR effect on tip aerothermal performance has been addressed numerically by some recent CFD studies. Zhang et al. (2014) found that the wall–gas temperature ratio could greatly affect the transonic OTL flow field, and there is a strong two-way coupling between aerodynamics and heat transfer. The feedbacks of the thermal boundary condition to aerodynamics behave differently at different flow regimes over the tip, clearly indicating a highly localized dependence of the HTC upon wall temperatures. Sergio et al., (2015) also reported unreliable convective heat transfer coefficients (HTCs) and unphysical levels of adiabatic wall temperature in their tip heat transfer numerical analysis for tight clearance case.
The conventional practice of obtaining HTCs over turbine blade surface has been greatly challenged by these recent numerical studies. However, due to lack of experimental evidence to support the CFD analysis, the credibility of these recent findings has been debated within the heat transfer research community. On the other hand, as the gas turbine manufacturers are making effort to achieve much tighter clearance, there is an increasingly demand for reliable experimental data with smaller tip gaps.
Completely from experimental perspective, the present study aimed to address the wall-to-gas temperature ratio effect on turbine blade tip heat transfer. The first-of-its-kind experimental data from transient thermal measurements obtained in a low-speed high-temperature linear cascade are reported for a range of tip clearances (0.3%, 0.4%, 0.6% and 1%). Comparisons are made for HTCs obtained at different wall-to-gas temperature ratios using a conventional data processing technique. Based on the experimental evidence, the profound implication on the coupling effect between tip aerodynamics and heat transfer is discussed in this paper.
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EXPERIMENTAL SETUP A low speed blow-down wind tunnel in the Aero-
Thermal Lab, Shanghai Jiao Tong University, was employed to conduct the transient heat transfer experiment in the present study, as shown in Figure 1. It consists of a 25 kW air blower, a settling chamber to stabilize the flow (flow straightener and meshes installed inside), a heater mesh, a contraction nozzle and a test section. The heater mesh was made of 310s steel with 0.1 mm in width and 0.1 mm in diameter. It was installed before the testing section to provide a step rise in the mainstream temperature during the transient measurement. This heater mesh was powered by a 100 kW DC power supply.
Figure 1 Low speed wind tunnel employed in the present study
Figure 2 Test section and instrumentations for transient thermal measurement
The test section is illustrated in Fig. 2. It consists of 7 blades and 6 passages to achieve the optimal periodicity of the flow field. There are also two boundary layer bleeds on the two sidewalls. The blade has an axial chord (Cx) of 0.039 m and is scaled from a typical high-pressure turbine blade design condition. The middle blade tip was instrumented for thermal measurement. Its upper part was made from resin with low thermal conductivity by Stereo Lithography (SLA) technology, and the lower part was made from steel for fixing purpose. The tip gap height can be justified by adding
spacers with different thickness to the bottom of the metal blade base. Measured with feeler gauges, the tested tip clearances investigated in the present study are approximately 0.3%, 0.4%, 0.6% and 1% of blade span.
During a transient thermal measurement, the tip wall surface temperature history of the central blade was recorded by a FLIR A325 Researcher infrared (IR) camera with a spatial resolution of 320 240 at a frequency of 60 Hz, through a zinc-selenide (ZnSe) IR window. To minimize the uncertainties introduced by surface emissivity, IR window transmissivity, radiation from surroundings, etc., one thermocouple was embedded in the resin tip to be flush with the tip surface in order to perform in-situ calibration of the IR images during the experiments. The thermocouple (K- type, Omega) has a wire diameter of 0.076 mm (0.003 in) and response time of less than 80 ms. Figure 3 shows an example of the linear calibration relation between the image grayscale values and the temperature readings from a surface thermocouple. The same type of thermocouple was employed in the inlet total temperature sensor. Flow conditions for the present experimental study are summarized in Table 1. The low speed wind tunnel is capable to provide a stabilized mainstream flow and the measured fluctuation of the inlet total pressure is about 1Pa.
Table 1 Detailed blade geometries and flow conditions
Figure 3 IR camera calibration curve
Axial chord, Cx (mm) 39 Inlet total Temperature, T0,in (K) 406 Inlet total pressure, P0,in (Pa) 101,446 Tip gap, G/S 0.3%,0.4%,0.6%,1% Inlet velocity (m/s) 8.5 Inlet Reynolds number (based on Cx) 0.9 10 Exit static pressure, Ps,e (Pa) 101,325 Cascade mass flow rate (kg/s) 0.18 Inlet Turbulent Intensity ~1%
SLA blade tip with thermocouple
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Figure 4 Inlet total temperature and one sample of surface temperature history during a transient thermal measurement.
Figure 4 presents the inlet mainstream total temperature (T0,in) and one sample wall surface (Tw) history during one typical transient measurement. A near step rise of 135K in the mainstream was achieved by the heater mesh employed in the present study. The mainstream total temperature fluctuation was less than 4K after being stabilized. With a step heating, the tip surface temperature increases gradually from the initial ambient condition. Twenty seconds of the transient thermal measurement data were recorded for data processing. The changes of local TR values range from 0.7 to 0.9. The heat penetration depth was estimated to be 1.6 mm in 20 seconds.
DATA REDUCTION METHOD
Conventional data reduction method for transient thermal measurement was adopted in the present study. During the transient thermal measurement process, the inlet mainstream total temperature remains constant for all the cases investigated. Based on the assumption of “1-D semi- infinite conduction,” the 1D transient conduction equation together with initial and boundary conditions are shown below.
2 ,
, , →∞, 0 (3)
, t , 0, 0 (4)
0, , 0, 0 (5)
where is the temperature history directly measured by Infrared Thermography during the experiments. The heat flux q variations with time can be numerically solved from the equations above. Figure 5 shows more details about the numerical calculation setup and one sample heat flux result obtained. Initial temperature Ti was set to be the initial value for all grid points at the beginning of each time step. A central difference scheme was used for space discretization and first order implicit backward difference scheme was used for time discretization in equation 2. The overall temperature field is iterated at each time step. The convergence criteria
for every time step is to ensure the maximum iterative error of temperature domain is less than 1e-9 K. Heat flux was then calculated according to the Fourier’s Law (
/ ). During the numerical calculation process, the time step is set the same value as the Infrared data sampling frequency of 60 Hz. The final grid size z was determined when the calculated heat flux became grid independent (a less than 0.3% error in heat flux was obtained).
The heat flux q can also be reconstructed from the transient temperature history using the “Impulse method” by Oldfield 2008. This method has been employed in a series of previous studies (Zhang et al., 2011a; Zhang et al., 2011b, O’Dowd et al., 2010; Ma et al., 2017) and proved to be accurate, computationally efficient, and reliable for transient thermal measurement data processing. As shown in Fig. 5, it has been confirmed in the present study that the difference of heat flux values obtained from direct numerical calculation and the “Impulse method” is less than 0.5%.
Next, for every IR pixel location on the blade tip, the heat transfer coefficient HTC can be easily obtained by the linear regression between q and Tw history obtained during the transient process (providing the Newton’s law of cooling is valid during the transient process). As an example, the slope value for the linear trend in Figure 5 is the HTC for the specific tip location.
In the present study, a wide range of TRs were achieved for a single 20-second transient run. During the initial heating period (0-3s), the local TRs are relatively low (0.7- 0.75), while the TRs are high (0.8-0.9) during the later period (15-20s). Data from two different periods shown in Fig. 4 were processed separately to inspect the linear correlation between heat flux and wall temperature, so the HTC values obtained at different TRs can be compared.
Figure 5 Heat flux variations obtained from direct numerical solution and “Impulse Method” (G/S=1%).
RESULTS AND DISCUSSION In this section, the HTC results processed with the conventional transient data processing method for a typical tip gap 1% are discussed first. Detailed experimental uncertainty analysis is presented. Attention is then paid to experimental results at smaller tip gaps obtained with the same data processing methodology.
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Figure 6 Heat flux and tip surface temperature histories at three sample tip locations for G/S=1%
(a) Low TR (b) High TR
Figure 7 Heat transfer coefficient distributions obtained at low and high TR conditions for G/S=1%. TR effect on tip gap G/S=1%
Figure 6 shows the heat flux and temperature history measured for three selected points on tip surface for two temperature ratio periods (low TR period in black and high TR period in blue). The red lines plotted in Fig. 6 were fitted by all the temperature data during the complete transient run period. Clearly, all data points are scattered evenly around the red regression line, and experimental data obtained at different TRs largely share the same slope (HTC value). The coefficient of determination (R2) in statistics (Devore 2010) is 0.997. Such performance in data regression is consistent with the practices reported in most of the conventional transient thermal measurements.
Figure 7 shows the HTC distributions obtained during two time periods with low and high TRs. The weak dependence of HTC on TRs is evident for most of the tip regions. Apparently, the Newton’s law of cooling is valid during all the transient process with varying TRs. The HTCs are marginally higher for the high TR case near the pressure side surface. These results are well expected, and consistent with tip heat transfer distributions obtained by many previous studies in low speed condition. A typical tip flow structure can be can be drawn from the HTC distributions shown in Fig. 7: OTL flow enters the tip gap, separates and reattaches near the pressure side edge and then develops within the gap region.
Uncertainty analysis
(a) (b) Figure 8 Contours of (a) R2, (b) relative uncertainty in HTC for G/S=1%.
The performance of linear regression between local heat
flux and wall temperature history can be further illustrated in Figure 8a. For most of the tip area, R2 is above 0.95. Relatively speaking, R2 is slightly lower near the pressure side and suction side surfaces, which should be caused by the lateral conduction error. Such linear regression performance is highly repeatable over most of the tip surface. The relative uncertainty of HTCs for repeated transient runs is below 5%, as shown in Fig 8b. In summary, the experimental uncertainty for the 1% clearance case is highly satisfactory. The HTC results can be regarded as accurate and comparable to other transient measurement data reported in the open literature. TR effect on small tip gaps
By applying the same conventional data processing technique, HTC results were obtained for three smaller tip gaps G/S=0.3%, 0.4% and 0.6%. Figure 9 presents the HTC distributions at low and high TRs. The results are surprisingly different from the previous observations. As the tip gap becomes smaller, the HTC values obtained at two TRs becomes increasingly different.
Figure 9 Heat transfer coefficient distributions for three small tip gaps (G/S=0.3%, 0.4% and 0.6%) at low and high TRs.
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Figure 10 Distributions of HTC percentage difference (HTClow TR- HTChigh TR)/ HTClow TR×100%) at low and high TRs for different tip gaps. The percentage differences shown in Fig. 10 also indicate that there seems to not have a globally uniform trend of HTC variations with TRs. The local HTC distributions could either increase or decrease with different TRs, depending on the tip locations. Generally speaking, the HTC values are higher near the pressure side edge and lower near the suction side edge at higher TR condition.
The data processing methodology has to re-examined before any further observation on the trends in Figs. 9 and 10 and physical interpretation.
Figure 11 Heat flux and tip surface temperature histories at three sample tip locations for G/S=0.3%.
Figure 11 shows the heat flux and temperature history for three selected positions over the tip surface for the smallest tip gap case investigated (G/S=0.3%). The data for the low TR period were plotted in black, and the data for the high TR period were plotted in blue. Different from what can be observed in Fig. 6, the correlation between heat flux and wall temperature change becomes highly non-linear. Apparently, the linear assumption in the Newton’s Law of Cooling becomes invalid over the period of the transient process. It can also be argued that the HTC values determined from the “slope’ of the non-linear curves shown in Fig. 11 have to be strongly dependent on the time period selected and the range of local TRs.
Such non-linear behavior has also been recently reported in the previous CFD analysis by Zhang et al. 2014 and Maffulli and He 2014, 2017. The experimental evidence obtained in the present study confirmed their previous numerical analysis and findings. The large variations of HTCs with wall-to-gas TR indicate a dramatical change of the OTL flow structure. The leakage fluids at tight tip clearances has a relatively low thermal inertia. At lower wall- to-gas TRs, the fluid properties could be greatly varied by
local heat transfer when the OTL flow passes by the tight gap region. The strong feedback from heat transfer alters the entire flow structure and OTL flow rate. As one further experimental evidence, Figure 12 shows the flow re- attachment lines qualitatively identified by maximum HTC values along OTL flow direction for two TRs at two different tip gaps. For the case of G/S=1%, there is almost no change in the re-attachment line locations. However, for the case of G/S=0.3%, the flow re-attachment line for high TR case is moved much further downstream, indicating a much larger separation bubble and a globally affected OTL flow structure.
Figure 12 Flow re-attachment lines at low and high TRs for G/S=1% and 0.3%.
CONCLUSIONS
In this study, transient thermal measurements were conducted in a low-speed high-temperature linear cascade for a flat rotor blade tip with four different tip gaps (0.3%, 0.4%, 0.6% and 1%). The local wall-to-gas temperature ratio were varied from 0.7 to 0.9 during the transient testing process. HTC values were calculated with a conventional data reduction method based on the assumption of “1D semi- infinite conduction.”
The conventional data processing technique for transient thermal measurement was proved to be reliable and accurate for the 1% tip gap case. Good linear correlations between local heat flux and temperature variations were observed over most of the tip surface. The HTC values show weak dependence on TRs.
However, highly non-linear behaviour between heat flux and temperature history was observed for the tighter tip gap cases. The strong dependence of the local tip HTCs on the wall thermal condition are experimentally confirmed. It has been observed that the local HTC distributions could either increase or decrease with different TRs, depending on the locations. The maximum difference could be over 100%.
The first-of-its-kind experimental evidence presented in this study convincingly demonstrated the strong feedback to OTL flow aerodynamics by the wall thermal boundary
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condition, and confirmed the similar findings reported in the previous numerical studies. The two-way coupling between tip heat transfer and aerodynamics cannot be neglected in the tip aero-thermal design process, especially for tight tip clearance. Also as an advisory note to future studies, the reliability and accuracy of the convection-only approach in many other heat transfer applications should also be re- examined.
NOMENCLATURE
CFD = computational fluid dynamics CHT = conjugate heat transfer
G = tip gap height (m) HTC = heat transfer coefficient (W/(m2.K))
IR = infrared OTL = Over-Tip-Leakage
R2 = coefficient of determination S = span (m)
TR = temperature ratio = temperature (K)
t = time (s) U = uncertainty x = axial coordinate y = circumferential coordinate z = radial coordinate
Subscripts 0 = total
ad = adiabatic d = driving e = exit of linear cascade i = initial
in = inlet of linear cascade w = wall
ACKNOWLEDGMENTS The authors gratefully acknowledge the support of
Chinese National Science Foundation (51376127, 51506120) for funding this work.
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Zhang Q., He L., Wheeler A., Ligrani P., and Cheong B. (2011). Overtip Shock Wave Structure and Its Impact on Turbine Blade Tip Heat Transfer. ASME J. Turbomach. 133(4), 041001. doi: 10.1115/1.4002949
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EXPERIMENTAL EVIDENCE OF TEMPERATURE RATIO EFFECT ON TURBINE BLADE TIP HEAT TRANSFER
H. Jiang University of Michigan-Shanghai
Jiao Tong University Joint Institute, Shanghai Jiao Tong University
[email protected] Shanghai, China
[email protected] London, UK
Oxford, UK
Astronautics, Shanghai Jiao Tong University
[email protected] Shanghai, China
Shanghai Jiao Tong University Joint Institute,
Shanghai Jiao Tong University
Astronautics, Shanghai Jiao Tong University
[email protected] Shanghai, China
ABSTRACT Determination of a scalable Nusselt number (based on
“adiabatic heat transfer coefficient”) has been the main research objective of most existing heat transfer experimental researches for turbine blade tip. They were mostly carried out at near adiabatic condition without matching the engine realistic wall-to-gas low Temperature Ratio (TR). This practice is based on the assumption that the wall thermal boundary conditions do not affect the over-tip-leakage (OTL) flow field, the aerodynamics and heat transfer can be studied separately. Recent numerical studies raised a question on the validity of this conventional practice. Due to the relatively low thermal inertia of the leakage fluids contained within the thin clearance, the fluids transport properties vary greatly with the wall thermal boundary condition and the two-way coupling between OTL aerodynamics and heat transfer cannot be neglected. The issue could become more severe when the gas turbine manufacturers are making effort to achieve much tighter clearance. However, there has been no experimental evidence to back up these numerical findings. In this study, transient thermal measurements were conducted in a high-temperature linear cascade rig for a range of tip clearances (0.3%, 0.4%, 0.6% and 1%). Surface temperature history was captured by Infrared Thermography at a range of wall-to-gas TRs. Heat Transfer Coefficient (HTC) distributions were obtained based on a conventional data processing technique. The profound influence of tip surface thermal boundary condition on heat transfer and OTL
flow was revealed by the first-of-its-kind experimental data obtained in the present study.
INTRODUCTION Most experimental research in gas turbine heat transfer
community was carried out at near adiabatic condition without matching the engine realistic wall-to-gas Temperature Ratio (TR). The underlying assumption is that the wall thermal boundary condition does not affect the flow field, the aerodynamics and heat transfer can be studied separately. Therefore, the data obtained in the “cold experiment” could be scaled to the engine operating condition. Very recently, the coupling effect between aerodynamics and heat transfer received more attention. There have been increasingly debates on whether the conventional convection-only approach still works over the rotor blade tip, considering the complex Over-Tip-Leakage (OTL) flow and the ongoing effort from the gas turbine manufacturers to achieve much tighter clearance.
The convective heat transfer coefficient (HTC) was defined as a fluid mechanical property in the Newton’s law of cooling.
(1)
where Tw is local wall surface temperature, and Td is the local fluid driving temperature. For low speed flow, it can be assumed to be the freestream temperature, while for high
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speed flow, it should be the adiabatic wall temperature Tad (Eckert, 1955; Anderson and Moffat, 1992). The linear relation of heat flux q and wall temperature Tw is implied from the linearity of the governing energy equation (Jones, 1991). For an established flow field, the HTC becomes constant and does not change with Tw, therefore the HTC value obtained at “cold” lab condition can be scaled to “hot” engine condition. This linear assumption has been widely adopted in engineering practice. In experimental data post processing, HTC can be obtained from the linear regression from heat flux and wall temperature during a transient heat transfer test (Ekkad et al., 2004; Newton et al., 2006; Xue et al.2015), or determined by the slope from several separate tests running at different wall temperatures (Thorpe et al., 2004; Polanka et al., 2008; Lavagnoli et al., 2013). In CFD based design and analysis, HTC and Td, the two unknowns in Equation 1, can be calculated through two isothermal simulations (Shyam et al., 2012; Atkins et al., 2012).
However, it has also been recognized by early researchers that the wall thermal boundary condition will affect aerodynamics of flow field and there is a two-way interaction between the fluid and the solid (Perelman, 1961; Zinnes, 1970; Luikov et al., 1971; Luikov, 1974). Their results show that the uncoupled approach might lead to contradictory and even unphysical results in many cases when the wall thermal boundary condition is specified improperly.
Conjugate Heat Transfer (CHT) has been used to overcome those limitations. Bohn et al. (2003) used CHT to analyse the effect of holes shapes on film-cooling flows. Shih et al., (2009, 2013) highlighted the need to use local Biot number and the importance to couple internal and external heat transfer. The conventional analysis techniques on film cooling effectiveness which neglect the conjugate heat transfer (CHT) effects were questioned by Harrison and Bogard (2008a, 2008b). In the numerical study of Silieti et al., (2009) on the endwall film effectiveness, a better agreement with the experimental data was achieved by using the conjugate model in comparison with the results with an adiabatic model. Conjugate simulations of whole 3-D blade with internal cooling flow, solid blade and external passage flow were carried out by Heidmann et al. (2003), Dees et al. (2010, 2011), and Starke et al., (2008). Solutions with better accuracy from CHT have been increasingly reported recently. There have been a number of publications on the numerical method and solver validation for different turbomachinery applications (e.g. Verdicchio et al., 2001; Montenay et al., 2000; Okita, 2002). An efficient and accurate unsteady conjugate solution approach was proposed and demonstrated for a turbine cascade by He and Oldfield, (2010). There is no doubt that CHT will gain its popularity in time, even though it is still computationally expensive.
Currently, the conventional usage of HTC still has its popularity and convenience in practical engine design process. There have been many correlation methods used to take wall temperature ratio effect on the gas properties into account. Different methods have been proposed to account
for the effect of variable fluid properties by including the gas-to-wall temperature ratio term into the formulation of the HTC (Eckert, 1955; Fitt et al., 1986; Kays and Crawford, 2005, etc.). The limitations of such correction are flat plate studies based, empirical, of a global nature and regardless of the dependence of local flow characteristics on the temperature ratio. For realistic turbine components with complex geometries, aerothermal characteristics are often complex flow features, associated with separation, transition, shock waves. These highly localized features challenge the applicability of a global correction method. More specifically, a global correction approach is not expected to be able to correct the “history effect” effect caused by the upstream local heating, as the interactions between the fluid and the solid not only could affect the local fluid properties, also change the development of the downstream flow field. Maffulli and He, (2014, 2017) discussed the impacts of wall temperature on the secondary flows, trailing edge shock waves, and the passage flow capacity, underlining the connection and interactions between the wall temperature and the external aerodynamics. They proposed a “3-point nonlinear method” to model the HTC dependence on wall temperature with an improved accuracy without going to the full CHT approach. The TR effect on tip aerothermal performance has been addressed numerically by some recent CFD studies. Zhang et al. (2014) found that the wall–gas temperature ratio could greatly affect the transonic OTL flow field, and there is a strong two-way coupling between aerodynamics and heat transfer. The feedbacks of the thermal boundary condition to aerodynamics behave differently at different flow regimes over the tip, clearly indicating a highly localized dependence of the HTC upon wall temperatures. Sergio et al., (2015) also reported unreliable convective heat transfer coefficients (HTCs) and unphysical levels of adiabatic wall temperature in their tip heat transfer numerical analysis for tight clearance case.
The conventional practice of obtaining HTCs over turbine blade surface has been greatly challenged by these recent numerical studies. However, due to lack of experimental evidence to support the CFD analysis, the credibility of these recent findings has been debated within the heat transfer research community. On the other hand, as the gas turbine manufacturers are making effort to achieve much tighter clearance, there is an increasingly demand for reliable experimental data with smaller tip gaps.
Completely from experimental perspective, the present study aimed to address the wall-to-gas temperature ratio effect on turbine blade tip heat transfer. The first-of-its-kind experimental data from transient thermal measurements obtained in a low-speed high-temperature linear cascade are reported for a range of tip clearances (0.3%, 0.4%, 0.6% and 1%). Comparisons are made for HTCs obtained at different wall-to-gas temperature ratios using a conventional data processing technique. Based on the experimental evidence, the profound implication on the coupling effect between tip aerodynamics and heat transfer is discussed in this paper.
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EXPERIMENTAL SETUP A low speed blow-down wind tunnel in the Aero-
Thermal Lab, Shanghai Jiao Tong University, was employed to conduct the transient heat transfer experiment in the present study, as shown in Figure 1. It consists of a 25 kW air blower, a settling chamber to stabilize the flow (flow straightener and meshes installed inside), a heater mesh, a contraction nozzle and a test section. The heater mesh was made of 310s steel with 0.1 mm in width and 0.1 mm in diameter. It was installed before the testing section to provide a step rise in the mainstream temperature during the transient measurement. This heater mesh was powered by a 100 kW DC power supply.
Figure 1 Low speed wind tunnel employed in the present study
Figure 2 Test section and instrumentations for transient thermal measurement
The test section is illustrated in Fig. 2. It consists of 7 blades and 6 passages to achieve the optimal periodicity of the flow field. There are also two boundary layer bleeds on the two sidewalls. The blade has an axial chord (Cx) of 0.039 m and is scaled from a typical high-pressure turbine blade design condition. The middle blade tip was instrumented for thermal measurement. Its upper part was made from resin with low thermal conductivity by Stereo Lithography (SLA) technology, and the lower part was made from steel for fixing purpose. The tip gap height can be justified by adding
spacers with different thickness to the bottom of the metal blade base. Measured with feeler gauges, the tested tip clearances investigated in the present study are approximately 0.3%, 0.4%, 0.6% and 1% of blade span.
During a transient thermal measurement, the tip wall surface temperature history of the central blade was recorded by a FLIR A325 Researcher infrared (IR) camera with a spatial resolution of 320 240 at a frequency of 60 Hz, through a zinc-selenide (ZnSe) IR window. To minimize the uncertainties introduced by surface emissivity, IR window transmissivity, radiation from surroundings, etc., one thermocouple was embedded in the resin tip to be flush with the tip surface in order to perform in-situ calibration of the IR images during the experiments. The thermocouple (K- type, Omega) has a wire diameter of 0.076 mm (0.003 in) and response time of less than 80 ms. Figure 3 shows an example of the linear calibration relation between the image grayscale values and the temperature readings from a surface thermocouple. The same type of thermocouple was employed in the inlet total temperature sensor. Flow conditions for the present experimental study are summarized in Table 1. The low speed wind tunnel is capable to provide a stabilized mainstream flow and the measured fluctuation of the inlet total pressure is about 1Pa.
Table 1 Detailed blade geometries and flow conditions
Figure 3 IR camera calibration curve
Axial chord, Cx (mm) 39 Inlet total Temperature, T0,in (K) 406 Inlet total pressure, P0,in (Pa) 101,446 Tip gap, G/S 0.3%,0.4%,0.6%,1% Inlet velocity (m/s) 8.5 Inlet Reynolds number (based on Cx) 0.9 10 Exit static pressure, Ps,e (Pa) 101,325 Cascade mass flow rate (kg/s) 0.18 Inlet Turbulent Intensity ~1%
SLA blade tip with thermocouple
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Figure 4 Inlet total temperature and one sample of surface temperature history during a transient thermal measurement.
Figure 4 presents the inlet mainstream total temperature (T0,in) and one sample wall surface (Tw) history during one typical transient measurement. A near step rise of 135K in the mainstream was achieved by the heater mesh employed in the present study. The mainstream total temperature fluctuation was less than 4K after being stabilized. With a step heating, the tip surface temperature increases gradually from the initial ambient condition. Twenty seconds of the transient thermal measurement data were recorded for data processing. The changes of local TR values range from 0.7 to 0.9. The heat penetration depth was estimated to be 1.6 mm in 20 seconds.
DATA REDUCTION METHOD
Conventional data reduction method for transient thermal measurement was adopted in the present study. During the transient thermal measurement process, the inlet mainstream total temperature remains constant for all the cases investigated. Based on the assumption of “1-D semi- infinite conduction,” the 1D transient conduction equation together with initial and boundary conditions are shown below.
2 ,
, , →∞, 0 (3)
, t , 0, 0 (4)
0, , 0, 0 (5)
where is the temperature history directly measured by Infrared Thermography during the experiments. The heat flux q variations with time can be numerically solved from the equations above. Figure 5 shows more details about the numerical calculation setup and one sample heat flux result obtained. Initial temperature Ti was set to be the initial value for all grid points at the beginning of each time step. A central difference scheme was used for space discretization and first order implicit backward difference scheme was used for time discretization in equation 2. The overall temperature field is iterated at each time step. The convergence criteria
for every time step is to ensure the maximum iterative error of temperature domain is less than 1e-9 K. Heat flux was then calculated according to the Fourier’s Law (
/ ). During the numerical calculation process, the time step is set the same value as the Infrared data sampling frequency of 60 Hz. The final grid size z was determined when the calculated heat flux became grid independent (a less than 0.3% error in heat flux was obtained).
The heat flux q can also be reconstructed from the transient temperature history using the “Impulse method” by Oldfield 2008. This method has been employed in a series of previous studies (Zhang et al., 2011a; Zhang et al., 2011b, O’Dowd et al., 2010; Ma et al., 2017) and proved to be accurate, computationally efficient, and reliable for transient thermal measurement data processing. As shown in Fig. 5, it has been confirmed in the present study that the difference of heat flux values obtained from direct numerical calculation and the “Impulse method” is less than 0.5%.
Next, for every IR pixel location on the blade tip, the heat transfer coefficient HTC can be easily obtained by the linear regression between q and Tw history obtained during the transient process (providing the Newton’s law of cooling is valid during the transient process). As an example, the slope value for the linear trend in Figure 5 is the HTC for the specific tip location.
In the present study, a wide range of TRs were achieved for a single 20-second transient run. During the initial heating period (0-3s), the local TRs are relatively low (0.7- 0.75), while the TRs are high (0.8-0.9) during the later period (15-20s). Data from two different periods shown in Fig. 4 were processed separately to inspect the linear correlation between heat flux and wall temperature, so the HTC values obtained at different TRs can be compared.
Figure 5 Heat flux variations obtained from direct numerical solution and “Impulse Method” (G/S=1%).
RESULTS AND DISCUSSION In this section, the HTC results processed with the conventional transient data processing method for a typical tip gap 1% are discussed first. Detailed experimental uncertainty analysis is presented. Attention is then paid to experimental results at smaller tip gaps obtained with the same data processing methodology.
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Figure 6 Heat flux and tip surface temperature histories at three sample tip locations for G/S=1%
(a) Low TR (b) High TR
Figure 7 Heat transfer coefficient distributions obtained at low and high TR conditions for G/S=1%. TR effect on tip gap G/S=1%
Figure 6 shows the heat flux and temperature history measured for three selected points on tip surface for two temperature ratio periods (low TR period in black and high TR period in blue). The red lines plotted in Fig. 6 were fitted by all the temperature data during the complete transient run period. Clearly, all data points are scattered evenly around the red regression line, and experimental data obtained at different TRs largely share the same slope (HTC value). The coefficient of determination (R2) in statistics (Devore 2010) is 0.997. Such performance in data regression is consistent with the practices reported in most of the conventional transient thermal measurements.
Figure 7 shows the HTC distributions obtained during two time periods with low and high TRs. The weak dependence of HTC on TRs is evident for most of the tip regions. Apparently, the Newton’s law of cooling is valid during all the transient process with varying TRs. The HTCs are marginally higher for the high TR case near the pressure side surface. These results are well expected, and consistent with tip heat transfer distributions obtained by many previous studies in low speed condition. A typical tip flow structure can be can be drawn from the HTC distributions shown in Fig. 7: OTL flow enters the tip gap, separates and reattaches near the pressure side edge and then develops within the gap region.
Uncertainty analysis
(a) (b) Figure 8 Contours of (a) R2, (b) relative uncertainty in HTC for G/S=1%.
The performance of linear regression between local heat
flux and wall temperature history can be further illustrated in Figure 8a. For most of the tip area, R2 is above 0.95. Relatively speaking, R2 is slightly lower near the pressure side and suction side surfaces, which should be caused by the lateral conduction error. Such linear regression performance is highly repeatable over most of the tip surface. The relative uncertainty of HTCs for repeated transient runs is below 5%, as shown in Fig 8b. In summary, the experimental uncertainty for the 1% clearance case is highly satisfactory. The HTC results can be regarded as accurate and comparable to other transient measurement data reported in the open literature. TR effect on small tip gaps
By applying the same conventional data processing technique, HTC results were obtained for three smaller tip gaps G/S=0.3%, 0.4% and 0.6%. Figure 9 presents the HTC distributions at low and high TRs. The results are surprisingly different from the previous observations. As the tip gap becomes smaller, the HTC values obtained at two TRs becomes increasingly different.
Figure 9 Heat transfer coefficient distributions for three small tip gaps (G/S=0.3%, 0.4% and 0.6%) at low and high TRs.
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Figure 10 Distributions of HTC percentage difference (HTClow TR- HTChigh TR)/ HTClow TR×100%) at low and high TRs for different tip gaps. The percentage differences shown in Fig. 10 also indicate that there seems to not have a globally uniform trend of HTC variations with TRs. The local HTC distributions could either increase or decrease with different TRs, depending on the tip locations. Generally speaking, the HTC values are higher near the pressure side edge and lower near the suction side edge at higher TR condition.
The data processing methodology has to re-examined before any further observation on the trends in Figs. 9 and 10 and physical interpretation.
Figure 11 Heat flux and tip surface temperature histories at three sample tip locations for G/S=0.3%.
Figure 11 shows the heat flux and temperature history for three selected positions over the tip surface for the smallest tip gap case investigated (G/S=0.3%). The data for the low TR period were plotted in black, and the data for the high TR period were plotted in blue. Different from what can be observed in Fig. 6, the correlation between heat flux and wall temperature change becomes highly non-linear. Apparently, the linear assumption in the Newton’s Law of Cooling becomes invalid over the period of the transient process. It can also be argued that the HTC values determined from the “slope’ of the non-linear curves shown in Fig. 11 have to be strongly dependent on the time period selected and the range of local TRs.
Such non-linear behavior has also been recently reported in the previous CFD analysis by Zhang et al. 2014 and Maffulli and He 2014, 2017. The experimental evidence obtained in the present study confirmed their previous numerical analysis and findings. The large variations of HTCs with wall-to-gas TR indicate a dramatical change of the OTL flow structure. The leakage fluids at tight tip clearances has a relatively low thermal inertia. At lower wall- to-gas TRs, the fluid properties could be greatly varied by
local heat transfer when the OTL flow passes by the tight gap region. The strong feedback from heat transfer alters the entire flow structure and OTL flow rate. As one further experimental evidence, Figure 12 shows the flow re- attachment lines qualitatively identified by maximum HTC values along OTL flow direction for two TRs at two different tip gaps. For the case of G/S=1%, there is almost no change in the re-attachment line locations. However, for the case of G/S=0.3%, the flow re-attachment line for high TR case is moved much further downstream, indicating a much larger separation bubble and a globally affected OTL flow structure.
Figure 12 Flow re-attachment lines at low and high TRs for G/S=1% and 0.3%.
CONCLUSIONS
In this study, transient thermal measurements were conducted in a low-speed high-temperature linear cascade for a flat rotor blade tip with four different tip gaps (0.3%, 0.4%, 0.6% and 1%). The local wall-to-gas temperature ratio were varied from 0.7 to 0.9 during the transient testing process. HTC values were calculated with a conventional data reduction method based on the assumption of “1D semi- infinite conduction.”
The conventional data processing technique for transient thermal measurement was proved to be reliable and accurate for the 1% tip gap case. Good linear correlations between local heat flux and temperature variations were observed over most of the tip surface. The HTC values show weak dependence on TRs.
However, highly non-linear behaviour between heat flux and temperature history was observed for the tighter tip gap cases. The strong dependence of the local tip HTCs on the wall thermal condition are experimentally confirmed. It has been observed that the local HTC distributions could either increase or decrease with different TRs, depending on the locations. The maximum difference could be over 100%.
The first-of-its-kind experimental evidence presented in this study convincingly demonstrated the strong feedback to OTL flow aerodynamics by the wall thermal boundary
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condition, and confirmed the similar findings reported in the previous numerical studies. The two-way coupling between tip heat transfer and aerodynamics cannot be neglected in the tip aero-thermal design process, especially for tight tip clearance. Also as an advisory note to future studies, the reliability and accuracy of the convection-only approach in many other heat transfer applications should also be re- examined.
NOMENCLATURE
CFD = computational fluid dynamics CHT = conjugate heat transfer
G = tip gap height (m) HTC = heat transfer coefficient (W/(m2.K))
IR = infrared OTL = Over-Tip-Leakage
R2 = coefficient of determination S = span (m)
TR = temperature ratio = temperature (K)
t = time (s) U = uncertainty x = axial coordinate y = circumferential coordinate z = radial coordinate
Subscripts 0 = total
ad = adiabatic d = driving e = exit of linear cascade i = initial
in = inlet of linear cascade w = wall
ACKNOWLEDGMENTS The authors gratefully acknowledge the support of
Chinese National Science Foundation (51376127, 51506120) for funding this work.
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