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Transient simulation of pulsed purge film cooling on flow and thermal characteristics of a turbine endwall
Applied Thermal Engineering 161 (2019) 114208
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Research Paper
Transient simulation of pulsed purge film cooling on flow and thermal characteristics of a turbine endwall Youhong Liu, Yifu Luo
T
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National Key Lab. of Science and Technology on Aero-thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, China
HIGHLIGHTS
numerically investigate the cooling effect of slot pulsed purge flow on turbine endwall. • We influence of slot orientation angle is studied. • The influence of mass flow ratio of cooling gas is studied. • The • The effect of Strouhal number on endwall thermal characteristics is discussed. ARTICLE INFO
ABSTRACT
Keywords: Pulsed purge flow Film cooling Turbine endwall Numerical simulation
This paper presents influence investigation of pulsed purge film on flow and thermal characteristics of a turbine endwall. Three-dimensional transient Reynolds-averaged Navier-Stokes equations coupled with SST k − ω turbulence model are utilized in this study. Varied slot orientation angles α, mass flow ratios (MFR) and Strouhal (St) numbers are selected as research parameters. The results indicate that endwall film cooling effectiveness varies as orientation angle α increases. Optimum film cooling effectiveness is obtained at α = 45° for cosine wave injection. MFR increases the level of film cooling effectiveness throughout the cascade channel. At the same MFR, square wave injection has the worst cooling effect. In a time period, instantaneous film cooling effectiveness changes drastically. The distribution of the instantaneous film cooling effectiveness is affected by St number and cooling outflow pattern. As St increases, the laterally-averaged film cooling effectiveness changes differently for cosine and square waves in the whole cascade channel.
1. Introduction Increased efficiency of modern gas turbine machine results in increased temperature and pressure at cascade inlet. The combustion chamber outlet temperature of advanced aero-engine has exceeded 2000 K, bringing huge thermal load on blade components. The hazards caused by thermal loads are mainly excessive thermal stress, thermal fatigue and creep. In order to reduce the thermal load on the turbine components and extend their service life, many cooling structures including film cooling schemes were used [1]. Temperature profiles at the combustion chamber exit was flatter in modern engines, causing high heat fluxes on the turbine endwall [2]. The turbine endwalls refer to the walls of turbine hub and tip, which together with the turbine vane surface form a turbine cascade channel. Recently, the cooling requirements on the endwall surface become a research hotspot. Many great efforts are currently devoted to restrict thermal load in endwall regions.
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The flow structures including second flow in cascade channel and near endwall undoubtedly bring a significant difficulties for the cooling of endwall. In terms of experiment, Maclsaac [3] measured mean and turbulent flow field in a low speed linear turbine cascade. The results indicated that the losses in cascade was related to turbulent Reynolds stresses. Papa [4] utilized heat/mass transfer measurement in a linear turbine cascade. The detailed convective heat/mass transfer distribution was obtained and compared with a secondary flow model. Radomsky [5] experimentally studied the influence of high freestream turbulence superimposing with secondary flow vortices on the flow field and the endwall convective heat transfer. The results showed that high freestream turbulence enhanced endwall convective heat transfer. In order to keep the turbine endwall work safely and stably under high temperature conditions, scholars have proposed many turbine endwall cooling methods. In real gas turbine, there is slot in the joint between turbine components. One of the cooling methods was to
Corresponding author. E-mail address: [email protected] (Y. Luo).
https://doi.org/10.1016/j.applthermaleng.2019.114208 Received 29 October 2018; Received in revised form 29 April 2019; Accepted 2 August 2019 Available online 03 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 161 (2019) 114208
Y. Liu and Y. Luo
Nomenclature
Greek letter
arc C Cx f h L MFR M P PS S St t tP T Tref TKE U x,y,z y+
α η ρ σ
turbine suction/pressure side arc length, mm turbine chord, mm axial turbine chord, mm pulsed frequency, Hz convective heat transfer coefficient, (W/m2 K) characteristic length of slot mass flow ratio of purge flow to mainstream flow blowing ratio, (ρcUc/ρ∞U∞) pressure, Pa pressure side local arc length, mm Strouhal number, fL/U∞ time, s pulsation period, s temperature, K reference temperature, K non-dimensional turbulence kinetic energy velocity, m/s Cartesian coordinates, mm non-dimensional distance from the wall
slot injection orientation angle, ° film cooling effectiveness (Tw Tin, )/(Tc Tin, ) gas density, kg/m3 total pressure recovery coefficient, P *out, /P *in,
Superscript *
total
Subscripts ave c ref w in out ∞
introduce cooling gas into the upstream slot to cool the downstream endwall [6]. Blair [7] first studied a two-dimensional slot cooling structure upstream of endwall by experiment. In experiment, a suction groove was designed to eliminate influence of mainstream boundary layer. The results showed that with increase of mass flow from slot, the film cooling effect on endwall increased as well. However, under influence of channel secondary flow, the distribution of cooling jet was uneven, which affected endwall film cooling effect. Cardwell [8] and Thrift [9] et al. studied effect of upstream slots of different geometric parameters on downstream endwall cooling. Their results showed that when mass flow from slot is constant, changing the width of the slot could change the coverage area of the cooling injection. Within the range of research parameters, increasing slot width enhanced the film cooling effect of the downstream endwall. Reducing the angle between the slot and the end wall could suppress the development of horseshoe vortex in the channel, thereby enhancing the endwall cooling effect. The purge flow also has significant influence on secondary flow structure, which would alter the heat transfer characteristics on the
average coolant reference wall inlet outlet mainstream
endwall [10]. Granser and Schelenberg [11] stated that the coolant film from slot leakage could attenuate the strength of the cascade channel secondary vortex due to decreases of boundary layer thickness. Steven [12,13] experimentally investigated the influence of slot injection on the flow field and thermal characteristics of endwall. Instead of being adversely affected by secondary flow, the purge flow was able to reduce secondary flow effect. Besides, the results of thermal measurements indicated that the slot flow should be strong enough to overcome the influence of secondary flow so that good thermal protection could be achieved. Ong et al. [14] used three-dimensional unsteady calculations to investigate the effect of coolant injection on the rotor under high pressure condition. The results presented that increase of coolant swirl angle could effectively reduce the secondary flow penetration depth, resulting in improvement in the coolant distribution on the rotor hub. Pasinato et al. [15] simulated and measured the flow filed of a linear cascade of turbine vanes, with and without secondary air injection from upstream slot. They stated that secondary air injection would strongly distort the flow field in cascade channel. The fluid ejected from
(a) Computational domain
(b) Partial enlargement of the computational domain Fig. 1. Geometry model. 2
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of slot pulsed film cooling on entire turbine endwall need to further study. In this paper, unsteady simulation is conducted for an entire NASA C3X turbine. Two different pulsed cooling injection including cosine wave and square wave are used at slot inlet. The purpose of this work is to compare film cooling effectiveness in different pulsed frequency and different mass flow ratios, and to provide useful reference for pulsed purge film cooling characteristics.
Table 1 Turbine vane and slot geometric parameters. Parameters
Value
Chord length C (mm) Axial chord Cx (mm) Vane height (mm) Vane pitch (mm) Inlet angle (deg) Outlet angle (deg) Slot width (mm) Slot orientation (deg)
144.93 78.16 76.2 117.73 90 72.38 4 α
2. Geometry and mesh The calculation model studied in this paper is shown in Fig. 1, which is based on noted turbine model C3X [22]. The original C3X model does not have cascade upstream slot. In order to study the effect of injection slot on the film cooling performance of enwall, an upstream slot inlet has been installed in this model (as shown in Fig. 1b). The slot is located 10.2 mm upstream of the leading edge of the vane. Other detailed geometrical parameters are shown in Table 1. Fig. 2 shows the computational mesh in cascade and slot entrance regions. All computational spaces are dispersed using un-structured mesh. Multi-layer hexahedral mesh is used on the fluid-solid interface. The height of the first layer of hexahedral mesh makes the value of y+ around 1. The total number of meshes finally obtained is around 7 million. This paper also performs verification of grid independence. A total of three different numbers of meshes are studied including coarse grid (5 million), medium grid (6 million) and fine grid (7 million). The distribution of wall temperature varies with the number of grids is shown in Fig. 3. The position of the wall temperature is shown in the green line of Fig. 3a. Fig. 3b shows the wall temperature distribution under three different mesh quality. The differences of wall temperature distribution among the three mesh strategies are less than 5%. Therefore, the increasing grid number no longer has a significant impact on the simulation results. The fine mesh is employed in the following computation.
upstream slot developed into a relatively coherent flow structure with the horseshoe vortex systems due to upstream boundary layer. Moreover, Knost et al. [16] measured endwall adiabatic effectiveness for an extensive text combining both coolant form a slot and discrete film cooling holes throughout the passage. They indicated that the slot flow would affect the near-wall flow conditions which must be considered when predicting film-coolant trajectory based on streamlines. At high slot flows, the near-wall flows swept the jet gas closer toward the suction side. To obtain a better cooling effect, some scholars proposed new slot structures. Du et al. [17] proposed a novel trigonometric curve slot configuration. Numerical results indicated that in upstream region, this new slot geometry given better cooling effectiveness than normal slot geometry. However, in downstream region, the result was reversed. In film cooling, pulsed film cooling could reduce the cold gas consumption. On the other hand, due to the periodicity of upstream flow, in real gas turbines the film jet exhibits periodic change. In pulsed film cooling study, Coulthard [18,19] used solenoid valves in gas supply to study the jet pulsing effect. The results indicated that the effect of film frequency mainly based on the reducing overall jet liftoff. At high frequency, the pulsing cooling film benefited reducing jet liftoff, while at low frequency, the pulsing cooling film enhanced jet liftoff. In terms of numerical simulation, Song [10] studied effect of purge flow on endwall in detail. The influence of injection angles and mass flow ratios on the endwall flow field and heat transfer characteristics were further explained. Muldoon and Acharya [20] used Direct Numerical Simulation (DNS) to investigate pulsed film cooling jet on a flat. When nondimensional pulsing frequencies varied from 0.004 to 0.32 at peak blowing ratio M = 1.5, they found that the best film cooling effectiveness was obtained at 0.32. Rutledge et al. [21] experimentally investigated the effect of pulsing film cooling on a cylindrical leading edge surface. The experimental results indicated that at higher coolant flow rates, the pulsed cooling was advantageous comparing with steady film cooling. Discrete film holes and upstream slot are often used in combination in turbine endwall cooling. However, the pulsed purge film from upstream slot was rarely studied. Most of the previous researches focused on the effect of slot geometry instead of jet state. In addition, the effect
3. Numerical model and boundary condition Based on finite volume method, steady and unsteady 3-D Reynoldsaveraged Navier-Stokes equations are solved with shear stress transport (SST) k − ω turbulence model. All solid walls are set to adiabatic boundaries. Mainstream fluid and slot fluid are set to air ideal gas. Total pressure, total temperature, turbulence intensity and length are set at the inlet of the cascade. Static press condition is set at cascade outlet. Total temperature and mass flow rate are set at the slot inlet. Detailed boundary conditions are shown in Table 2. In steady simulation, the advection scheme is selected in high resolution. The convergence criteria of normalized root mean square (RMS) of residuals are less than 10E−5 and conservation target is set to 0.01. In unsteady simulation, the advection and transient schemes are high resolution and second order backward Euler, respectively. And the steady simulation results
(a) Global grid diagram
(b) Mesh enlargement at slot inlet
Fig. 2. Computational mesh and partial enlargement mesh. 3
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(a) Wall temperature position
(b) Grid independence
Fig. 3. Parameter position and grid independence verification.
are in good agreement. So it is believed that the SST k − ω could provide trusted calculation results for the next study.
Table 2 Detailed boundary conditions. Parameters
Value
Mainstream inlet total pressure, Pa Mainstream inlet total temperature, K Turbulence intensity, % Eddy length scale, mm Slot inlet total temperature, K Mainstream outlet static pressure, Pa
408,105 415 6.5 0.4 298 248,299
5. Results and discussions 5.1. Effect of α on the film cooling effectiveness Fig. 7 shows the time-averaged film cooling effectiveness contours (Fig. 7a) and the laterally-averaged film cooling effectiveness distributions (Fig. 7b) on turbine endwall at St = 0.1158 and MFR = 1.0 with different angle α. Under the action of the lateral pressure gradient of the cascade channel, the cooling gas flowing out of the gap could not uniformly cover the entire cascade endwall. In most areas of the endwall near the pressure side, the film cooling effectiveness is very poor. At the leading edge of the endwall closing to the suction side, the film cooling effectiveness is the highest for the three different waves. Highest film cooling effectiveness region (shown red in Fig. 7a) extend, when α increases from 25° to 45° for both steady and cosine waves. But that region shrink, when α increases from 45° to 65° for both steady and cosine waves. Comparing the angle α = 25°, α = 45° slot structure has smaller cooling gas outlet area, which increase penetration force of cooling gas into the mainstream flow. Comparing the angle α = 65°, cooling gas from α = 45° slot structure is easier to stick to the endwall. For square wave, the film cooling effectiveness is the worse for each angle comparing with steady and cosine waves. The highest film cooling effective region shrinks, when α increases from 25° to 65° for square wave. The effect of different orientation angles on the endwall film cooling effectiveness is more apparent in Fig. 7b. It is worth noting that the laterally-averaged film cooling effectiveness follows a similar variation law under different angles: as the x/Cx increases, the laterally-averaged film cooling effectiveness decreases first and then rises. This distribution law will be explained in conjunction with Fig. 7a and previous reference [23]. From Fig. 7a, it is noted that as the gas flows downstream of the cascade channel, the coverage area of the cooling gas decreases first and then increases. At the merging point, the coverage area of the cooling gas is the smallest. In the cascade endwall region from leading edge to merging point, cooling gas develops downstream under the influence of channel vortex systems, including pressure/ suction side horseshoe vortex systems and pressure/suction side leading edge corner vortex systems. This multi-vortex move toward the suction side due to a strong transverse pressure gradient and is gradually squeezed into a single vortex as it approaches the merging point, which results in a reduction in the coverage of the cooling film. In the cascade endwall region from merging point to the trailing edge, the flow in the cascade channel receives the combined effect of the passage vortex and the wall vortex induced by the passage vortex. These vortex systems
Fig. 4. Mass flow ratio signals at the purge flow inlet.
are utilized as the initial value for the transient simulation. Coefficient loops is set in range from 3 to 5. And the convergence criteria and conservation target are the same with those in steady simulation. As shown in Fig. 4, four different nominal MFRs (0.5, 1.0, 1.5 and 2.0) are studied. Cosine wave, square wave and steady wave are considered at slot inlet. The effect of different MFRs on endwall film cooling and the comparison between steady and unsteady film cooling for endwall are investigated. 4. Turbulence model validation To further verify the accuracy of the calculation method, we conducted a comparative study with C3X experiment data [22]. C3X turbine vane is cooled by 10 internal cooling holes. Fig. 5 shows its calculation domain and grid division. A structural grid is used in the cooling channel. The mesh interface between the fluid and solid domains requires the general grid interface (GGI) method. The simulation results with SST k − ω turbulence model are shown in Fig. 6. Both the pressure data and the thermal data at middle plane of C3X turbine vane 4
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(a) Computational domain of C3X vane
(b) Mesh generation of C3X vane
Fig. 5. Geometry of C3X turbine vane and mesh generation.
(a) Surface pressure distribution
(b) Surface temperature distribution
Surface heat transfer coefficient distribution
Fig. 6. Comparison between experiment data and computational simulation results at middle plane of C3X vane.
enhance the mixing of the cooling gas and the mainstream flow, expanding the flow range of the cooling gas. From x/Cx = 0 to x/ Cx = 0.57, the laterally-averaged of time-averaged film cooling effectiveness increases first and then decreases as the angle α increases for steady and cosine waves. At the same angle α, the laterally-averaged film cooling effectiveness of the two waveforms is not much different. From x/Cx = 0.57 to x/Cx = 1.02, the angle has little effect on the laterally-averaged film cooling effectiveness. For square wave, the laterally-averaged film cooling effectiveness decreases as angle α increases from x/Cx = 0 to x/Cx = 0.51. An interesting phenomenon is that from x/Cx = 0.64 to x/Cx = 0.96, the laterally-averaged film cooling effectiveness increases slightly as angle α increases. In general, for three waveforms the effect of the angle α on the film cooling effectiveness is mainly in the area between the leading edge and the merging point (x/ Cx = 0.3), and the effect of angle α in the area from merging point to the trailing edge is less obvious. Fig. 8 presents the distributions of non-dimensional temperature and streamlines on three different sections. The A-A section is close to the suction surface of the cascade, the B-B section is facing the stagnation point of the vane, and the C-C section is close to the cascade pressure surface. As angle α is 25° for steady wave, significant difference can be found among the flow conditions of the three sections. At section A-A, the cooling gas can flow smoothly and form a gas film on the endwall. At section B-B, due to the existence of vane, the cooling gas cannot flow out of the slot, forming a vortex structure in the slot channel. Downstream of the B-B section exit, an obvious horseshoe vortex structure is formed resulting in higher pressure near the stagnation point. At section C-C, cooling gas cannot flow out of the slot.
This is because the lateral pressure gradient of the cascade channel causes the pressure on the pressure side of the cascade to be higher than the pressure on the suction side of the cascade. As angle α increases, the cooling gas of A-A section can smoothly flow out of the slot. However, the cooling gas flow conditions of B-B and C-C section do not become better. 5.2. Effect of MFR on the film cooling effectiveness Fig. 9 shows time-averaged film cooling effectiveness distributions on endwall (Fig. 9a) and the laterally-averaged of time-averaged film cooling effectiveness along x/Cx (Fig. 9b) at St = 0.1158 and α = 45° with four different MFRs. The highest film cooling effectiveness region (shown red in Fig. 9a) extends as MFR increases from 0.5 to 2 for all three waveforms. Comparing with steady and cosine waves, the region covered by coolant gas shrinks evidently for square wave. The regions covered by coolant gas for steady and cosine waves have almost no difference. It is noted that although the increase in MFR enlarges the area of the cooling region, some areas of the endwall are not cooled effectively. Taking the state (steady wave and MFR = 2) as an example, in the root region of the leading edge, the endwall film cooling effectiveness is very low. It is because the coolant injection from the slot sweep directly to the suction and pressure sides due to the horseshoe vortex and leading edge corner vortex, which resulting in less film cooling effectiveness in root region of leading edge. Under the effect of the lateral pressure gradient and the secondary flow in the cascade channel, the flow of coolant gas is biased toward the suction side of the vane. Therefore, the film cooling effectiveness on the endwall near 5
Applied Thermal Engineering 161 (2019) 114208
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α = 45°
α = 65°
increases above 1, film cooling effectiveness first decreases and then increases. For steady and cosine wave, at point MFR = 2, in the entire cascade endwall, the film cooling effectiveness of steady wave is slightly higher than that of the cosine wave. Fig. 10 shows non-dimensional turbulence kinetic energy (TKE) contours on endwall at different MFRs. The TKE distributions of cosine wave and steady wave have little difference. For the sake of brevity, Fig. 10 only shows TKE contours for cosine wave (Fig. 10a) and square wave (Fig. 10b). For cosine wave, the level of TKE in the cascade channel increases significantly as MFR increases. However, for square wave, the increase in MFR (increase from MFR = 0.5 to MFR = 2.0) has little effect on the TKE distribution. Combined with Fig. 9, where the level of TKE is high, it is the interface between the cooling gas and mainstream. With the increase of MFR, the blending between the cooling gas and the mainstream will inevitably occur, and the TKE at the interface will increase. Fig. 11 shows the total pressure recovery coefficient σ on various MFR conditions and three waveforms. As MFR increases, the total pressure recovery coefficient σ in the cascade channel decreases for all three waveforms. This is because the increase in MFR makes the blending of the cooling gas and the mainstream more intense, result in increasing the total pressure loss. When 0.5 < MFR < 1.0, the σ of steady wave is little higher than that of cosine wave. However, when 1.0 < MFR < 2.0, the σ of steady wave is little lower than that of cosine wave. Comparing with steady and
Square wave
Cosine wave
Steady wave
α = 25°
α=25°, steady
(a)
B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
α=65°, steady
α=45°, steady
A-A
(b)
α=25°, cosine wave
Fig. 7. Effect of α on the film cooling effectiveness at St = 0.1158 and MFR = 1.0 (a) time-averaged film cooling effectiveness distributions on endwall, (b) laterally-averaged of time-averaged film cooling effectiveness along x/ Cx.
pressure side is deteriorated. In addition, due to the influence of the tail recirculation, the film cooling effectiveness at the tail of the vane is also poor. These film cooling effectiveness of these areas has not improved with the increase of MFR. In Fig. 9b, the laterally-averaged of time-averaged film cooling effectiveness along x/Cx have much difference for different MFRs. At MFR = 0.5 for square wave, the time-averaged film cooling effectiveness increases as x/Cx increases (0 < x/Cx < 0.9). However, as MFR
Fig. 8. Non-dimensional temperature and streamline distributions on three different sections. 6
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Y. Liu and Y. Luo
B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
MFR=1.5
MFR=2.0
α=45°, square wave
Square wave
α=25°, square wave
Cosine wave
α=65°, cosine wave
A-A
MFR=1.0
Steady wave
α=45°, cosine wave
MFR=0.5
(a)
B-B
C-C
A-A
B-B
C-C
α=65°, square wave
A-A
Fig. 8. (continued)
cosine waveforms, the σ of square wave is higher at different MFR conditions. And the decrease rate of total pressure recovery coefficient for square wave is smaller than that of steady and cosine wave. From Fig. 10, the TKE level in cascade channel of square wave is the lowest among three waveforms, therefore, the total pressure loss is also the smallest among the three waveforms.
(b) Fig. 9. Effect of MFR on film cooling effectiveness at St = 0.1158 and α = 45° (a) time-averaged film cooling effectiveness distributions on endwall, (b) laterally-averaged of time-averaged film cooling effectiveness along x/Cx.
5.3. Effect of Strouhal number on the film cooling effectiveness
varies greatly at different times. As the time step advances, the area where the film cooling effectiveness at the inlet is high first shrinks and then extends. At time t/tP = 0.6, the film cooling effectiveness at the inlet of the cascade channel is the worst. However, at this moment, the cooling film distribution is more uniform in central and rear of the cascade channel. At time t/tP = 0.8, the film cooling effectiveness at the inlet of the cascade becomes better. As St increases, the distribution of film cooling effectiveness at different time also has obvious changes. As can be seen from Fig. 4, at time t/tP = 0.5, the mass flow rate of the cooling gas is 0 kg/s. For cosine wave, from t/tP = 0.5 to t/tP = 1, the mass flow of cooling gas is gradually increasing. At time t/tP = 0.6, the area of high film cooling effectiveness at the inlet of the cascade
To clearly see the effect of Strouhal number on the endwall film cooling effectiveness in a time period, Fig. 12a shows the instantaneous film cooling effectiveness on endwall for three different waveform at MFR = 1.0. Three different pulsation frequencies of 10 Hz, 100 Hz and 1000 Hz are studied, corresponding to three Strouhal numbers of 0.001158, 0.01158 and 0.1158 respectively, in which the condition of St = 0.1158 is used as baseline condition. To discuss the influences of the pulsation frequency on film cooling effectiveness in one time period, four moments are intercepted for research in each time cycle for different St numbers. From the first line of St = 0.001158 for cosine wave, the film cooling effectiveness at the inlet of the cascade channel
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Applied Thermal Engineering 161 (2019) 114208
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Fig. 10. Non-dimensional TKE distribution on enwall with St = 0.1158 at different MFRs (a) Cosine wave and (b) Square wave.
the inlet of the cascade increases as St increases. It is because the heat transfer between the cooling gas and the mainstream gas is smaller as the time interval decreases. Fig. 12b and c shows laterally-averaged of instantaneous film cooling effectiveness along x/Cx at time t/tP = 0.4 and t/tP = 0.6 respectively. At time t/tP = 0.4, laterally-averaged film cooling effectiveness distribution line for St = 0.001158 of cosine wave is a little different from the rest of the distribution lines. It increases as x/Cx increases between x/Cx = 0 and x/Cx = 0.9. As St increases, laterallyaveraged film cooling effectiveness increases between x/Cx = 0 and x/ Cx = 0.58 for cosine wave at time t/tP = 0.4. However, for square wave, as St increases, laterally-averaged film cooling effectiveness decreases. At time t/tP = 0.6, as St increases, laterally-averaged film cooling effectiveness increase between x/Cx = 0 and x/Cx = 0.51 for cosine wave. And as St increases, laterally-averaged film cooling effectiveness decreases between x/Cx = 0.58 and x/Cx = 1.02 for cosine wave. For square wave, laterally-averaged film cooling effectiveness of St = 0.01158 is slight higher than those of St = 0.001158 and St = 0.1158 between x/Cx = 0 and x/Cx = 0.7. Fig. 13a shows the instantaneous temperature distribution at leading edge with different St numbers. In a time period, two different time (t/tP = 0.4 and t/tP = 0.6) are chosen to study the effect of St on the temperature distribution at leading edge. Due to the effect of cooling gas and cascade inlet pressure gradient, the temperature distribution on the leading edge is not uniform. Near the pressure side, the temperature of the gas is higher. Near the D-D section (y/Cx = 1.98), the temperature of the gas is lower. At the outflow of the cooling gas, the gas temperature is lowest. As St increases, the working area of the cooling gas expands for cosine wave on leading edge at time t/tP = 0.4 and t/tP = 0.6. For square wave, as St increases, the working area of the cooling gas expands at time t/tP = 0.4. At time t/tP = 0.6, the working
Fig. 11. Total pressure recovery coefficient σ for different MFRs and waveforms
gradually shrinks as St increases for cosine wave. However, at time t/ tP = 0.8, the area of high film cooling effectiveness at the inlet of the cascade first shrinks and then extends as St increases for cosine wave. For square wave, the cooling gas only maintains a constant outlet during the first half (0 < t/tP < 0.5) of the time period and no outflow during the second half (0.5 < t/tP < 1) of the time period. At time t/ tP = 0.2 and t/tP = 0.4, the area of high film cooling effectiveness at the inlet of the cascade gradually shrinks as St increases for square wave. It is because as time interval becomes shorter, the total amount of cooling gas flowing out of the slot is also reduced. In the second half of the time period, although no cooling gas flowing out, there is still residual cooling gas in the cascade channel, so the film cooling effect of the endwall is not zero. At time t/tP = 0.8, the film cooling effectiveness at
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area of the cooling gas expands first and then shrinks. Fig. 13b and c shows the instantaneous z-axis direction temperature distribution on plane D-D for cosine and square waveforms at different times. The ordinate z/h = 0 represents the endwall surface. As St increases, the temperature of the gas near the endwall decreases and the temperature gradient increases for cosine wave at both t/tP = 0.4 and
t/tP=0.4
t/tP=0.6
t/tP=0.8
Cosine wave
t/tP=0.2
t/tP = 0.6. With the increase of St, the difference in temperature distribution near the wall at two times is getting smaller. At the points of St = 0.01158 and St = 0.1158, the temperature distributions have little different with two different times for square wave. At the points of St = 0.001158, the temperature near the endwall at time t/tP = 0.6 is higher than that at time t/tP = 0.4.
Cosine wave
St=0.001158
Cosine wave
St=0.01158
Square wave
St=0.1158
St=0.001158 Fig. 12. Effect of St on film cooling effectiveness at MFR = 1.0 and α = 45° (a) instantaneous film cooling effectiveness on endwall with different St numbers, (b) laterally-averaged of instantaneous film cooling effectiveness along x/Cx at time t/tP = 0.4, (c) laterally-averaged of instantaneous film cooling effectiveness along x/ Cx at time t/tP = 0.6.
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Square wave
Y. Liu and Y. Luo
Square wave
St=0.01158
St=0.1158
(a)
(b)
(c) Fig. 12. (continued)
6. Conclusions
stagnation point and the pressure side, resulting in high film cooling effectiveness near the suction side. Changing the slot orientation angle can significantly change the film cooling effectiveness distribution of the endwall. For cosine wave, when the orientation angle is 45°, the laterally-averaged film cooling effectiveness in the entire cascade channel is the highest. Comparing with cosine wave and steady wave, the cooling effect of the square wave is the worst at MFR = 1.0 with different orientation angles. (2) Increase MFR can effectively improve the cooling effect of the turbine endwall, expanding the region of high film cooling effectiveness near leading edge and improving the whole level of cooling effect in the cascade channel. The laterally-averaged of time-averaged film cooling effectiveness of cosine wave and steady wave are higher than that of square wave at each MFR point. As MFR increases, the rate of decline in the time-averaged film cooling effectiveness for cosine and steady wave at the front (0 < x/ Cx < 0.38) of the cascade channel gradually increases. Near the trailing edge of the cascade channel, the effect of MFR on the film cooling effectiveness is reduced for all three waves. (3) MFR increases can raise the level of TKE in the cascade channel, intensifying gas blending, resulting in higher gas flow loss. When
Transient simulation of pulsed film cooling effect on turbine endwall are studied in an engine-sized NASA C3X vane. A cooling slot geometry is installed upstream of the cascade channel. The film cooling, thermal and aerodynamic characteristics of the turbine endwall are investigated numerically by using unsteady three-dimensional Reynolds-averaged Navier-Stokes equations coupling with the SST k-ω turbulence model. The effect of different structural and aerodynamic parameters, including slot orientation angle, cooling gas mass flow ratio and Strouhal number, are investigated respectively. The results indicate that the cases of cosine wave are superior to the cases of square wave in the film cooling effectiveness. In addition, the case of cosine wave at orientation angle α = 45° presents better film cooling performance among other orientation angles. Within the parameters of the study, important conclusions can be summarized as follows: (1) Due to the lateral pressure gradient at cascade inlet, the cooling gas cannot inject from the slot uniformly. The cooling gas more likely flow out from the cooling slot near the suction side. However, the gas does not easily flow out from the cooling slot near the 10
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MFR increases from 0.5 to 2.0, the total pressure recovery coefficient is reduced by up to 0.07% for three different waves. In addition, the manner in which the cooling gas injects also has effect on the flow loss of cascade channel. The total pressure recovery coefficient for square wave injection is higher than cosine wave and steady wave injection at points of different MFRs. (4) Three different Strouhal numbers are investigated at MFR = 1.0 and α = 45°. At time t/tP = 0.4, as St increases, laterally-averaged of instantaneous film cooling effectiveness increases ranging from x/
Cx = 0 to x/Cx = 0.58 and decreases ranging from x/Cx = 0.58 to trailing edge for cosine wave. For square wave, as St increases, the laterally-averaged of instantaneous film cooling effectiveness decreases in the whole cascade channel. (5) Due to the influence of cooling gas, the instantaneous of temperature distribution on the inlet section of cascade is not uniform. The temperature of the gas near the pressure side is higher than the temperature of the gas near the suction side. The near-wall temperature gradient on the D-D section increases as St increases.
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.001158
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.01158
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.1158
Fig. 13. Effect of St on instantaneous temperature distributions at MFR = 1.0 and α = 45°(a) instantaneous temperature distribution on leading edge with different St numbers, (b) instantaneous z-axis direction temperature distribution on plane D-D for cosine waveform at different times, (c) instantaneous z-axis direction temperature distribution on plane D-D for square waveform at different times.
11
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t/tP=0.4
t/tP=0.6 Square wave, St=0.001158
t/tP=0.4
t/tP=0.6 Square wave, St=0.01158
t/tP=0.4
t/tP=0.6 Square wave, St=0.1158
(a)
(b)
(c) Fig. 13. (continued)
Appendix A. Supplementary material
slot, in: ASME Turbo Expo 2002: Power for land, Sea and Air. Amsterdam, Netherlands: ASME Paper, GT2002-30178, 2002. [2] M. Papa, V. Srinivasan, R.J. Goldstein, Film cooling effect of rotor-stator purge flow on endwall heat/mass transfer, ASME J. Turbomach. 134 (2012) 041014. [3] G.D. Maclsaac, S.A. Sjolander, T.J. Praisner, Measurements of losses and Reynolds stresses in the secondary flow downstream of a low-speed linear turbine cascade, ASME J. Turbomach. 134 (2012) 061015. [4] M. Papa, R.J. Goldstein, F. Gori, Numerical heat transfer predictions and mass/heat transfer measurements in as linear turbine cascade, Appl. Therm. Eng. 27 (2007) 771–778.
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114208. References [1] R.S. Bunker, Film cooling effectiveness due to discrete holes within a transverse surface
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Y. Liu and Y. Luo [5] R.W. Radomsky, K.A. Thole, High free-stream turbulence effects on endwall heat transfer for a gas turbine stator vane, ASME J. Turbomach. 122 (2000) 699–708. [6] S.P. Lynch, K.A. Thole, The effect of the combustor-turbine slot and midpassage gap on vane endwall heat transfer, ASME J. Turbomach. 133 (2011) 041002. [7] M.F. Blair, An experimental study of heat transfer and film cooling on large-scale turbine endwalls, J. Heat Transfer 96 (4) (1974) 524. [8] N.D. Cardwell, N. Sundaram, K.A. Thole, The effects of varying the combustor-turbine gap, ASME J. Turbomach. 129 (4) (2006) 91–102. [9] A.A. Thrift, K.A. Thole, S. Hada, Effects of orientation and position of the combustorturbine interface on the cooling of a vane endwall, in: ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, 2011, pp. 291–301. [10] L. Song, P. Zhu, J. Li, et al., Effect of purge flow on endwall flow and heat transfer characteristics of a gas turbine blade, Appl. Therm. Eng. 110 (2017) 504–520. [11] D. Granser, T. Schulenberg, Prediction and measurement of film cooling effectiveness for a first-stage turbine vane shroud, ASME Paper No. 90-GT-95, 1990. [12] S.W. Burd, C.J. Satterness, T.W. Simon, Effects of slot bleed injection over a contoured ednwall on nozzle guide vane cooling performance: part I—flow field measurements, ASME paper No. GT2000-199. [13] S.W. Burd, C.J. Satterness, T.W. Simon, Effect of slot bleed injection over a contoured endwall on nozzle guide vane performance: part II—thermal measurements, ASME paper No. GT2000-200.
[14] J. Ong, R.J. Miller, S. Uchida, The effect of coolant injection on the endwall flow of a high pressure turbine, ASME J. Turbomach. 134 (2012) 051003. [15] H. Pasinato, K. Satterness, T.W. Simon, Effects of slot bleed injection over contoured endwall on nozzle guide vane cooling performance: part I-thermal measurements, ASME Paper No. 2000-GT-200. [16] D.G. Knost, K.A. Thole, Adiabatic effectiveness measurements of endwall film cooling for a first stage vane, ASME J. Turbomach. 127 (2005) 297–305. [17] K. Du, Z.G. Li, J. Li, et al., Influence of the upstream slot geometry on the endwall cooling and plantom cooling of vane suction side surface, Appl. Therm. Eng. 121 (2017) 688–700. [18] S.M. Coulthard, R.J. Volino, K.A. Flack, Effect of jet pulsing on film cooling part I: effectiveness and flow-field temperature results, ASME J. Turbomah. 129 (2007) 232–246. [19] S.M. Coulthard, R.J. Volino, K.A. Flack, Effect of jet pulsing on film cooling—part II: heat transfer results, ASME J. Turbomach. 129 (2007) 247–257. [20] F. Muldoon, S. Acharya, DNS study of pulsed film cooling for enhanced cooling effectiveness, Int. J. Heat Mass Transf. 52 (2009) 3118–3127. [21] J.L. Rutledge, P.I. King, R.B. Rivir, Influence of film cooling unsteadiness on turbine blade leading edge heat flux, J. Eng. Gas Turb. Power 134 (2012) Paper No. 071901. [22] L.D. Hylton, M.S. Milhec, E.R. Turner, Analytical and experimental evaluation of the heat transfer distribution over the surface of turbine vane, NASA report No. CR-168015, 1983. [23] H.P. Wang, S.J. Olson, R.J. Goldstein, E.R.G. Eckert, Flow visualization in a linear turbine cascade of high performance turbine blades. ASEM J., 95-GT-7.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Transient simulation of pulsed purge film cooling on flow and thermal characteristics of a turbine endwall Youhong Liu, Yifu Luo
T
⁎
National Key Lab. of Science and Technology on Aero-thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, China
HIGHLIGHTS
numerically investigate the cooling effect of slot pulsed purge flow on turbine endwall. • We influence of slot orientation angle is studied. • The influence of mass flow ratio of cooling gas is studied. • The • The effect of Strouhal number on endwall thermal characteristics is discussed. ARTICLE INFO
ABSTRACT
Keywords: Pulsed purge flow Film cooling Turbine endwall Numerical simulation
This paper presents influence investigation of pulsed purge film on flow and thermal characteristics of a turbine endwall. Three-dimensional transient Reynolds-averaged Navier-Stokes equations coupled with SST k − ω turbulence model are utilized in this study. Varied slot orientation angles α, mass flow ratios (MFR) and Strouhal (St) numbers are selected as research parameters. The results indicate that endwall film cooling effectiveness varies as orientation angle α increases. Optimum film cooling effectiveness is obtained at α = 45° for cosine wave injection. MFR increases the level of film cooling effectiveness throughout the cascade channel. At the same MFR, square wave injection has the worst cooling effect. In a time period, instantaneous film cooling effectiveness changes drastically. The distribution of the instantaneous film cooling effectiveness is affected by St number and cooling outflow pattern. As St increases, the laterally-averaged film cooling effectiveness changes differently for cosine and square waves in the whole cascade channel.
1. Introduction Increased efficiency of modern gas turbine machine results in increased temperature and pressure at cascade inlet. The combustion chamber outlet temperature of advanced aero-engine has exceeded 2000 K, bringing huge thermal load on blade components. The hazards caused by thermal loads are mainly excessive thermal stress, thermal fatigue and creep. In order to reduce the thermal load on the turbine components and extend their service life, many cooling structures including film cooling schemes were used [1]. Temperature profiles at the combustion chamber exit was flatter in modern engines, causing high heat fluxes on the turbine endwall [2]. The turbine endwalls refer to the walls of turbine hub and tip, which together with the turbine vane surface form a turbine cascade channel. Recently, the cooling requirements on the endwall surface become a research hotspot. Many great efforts are currently devoted to restrict thermal load in endwall regions.
⁎
The flow structures including second flow in cascade channel and near endwall undoubtedly bring a significant difficulties for the cooling of endwall. In terms of experiment, Maclsaac [3] measured mean and turbulent flow field in a low speed linear turbine cascade. The results indicated that the losses in cascade was related to turbulent Reynolds stresses. Papa [4] utilized heat/mass transfer measurement in a linear turbine cascade. The detailed convective heat/mass transfer distribution was obtained and compared with a secondary flow model. Radomsky [5] experimentally studied the influence of high freestream turbulence superimposing with secondary flow vortices on the flow field and the endwall convective heat transfer. The results showed that high freestream turbulence enhanced endwall convective heat transfer. In order to keep the turbine endwall work safely and stably under high temperature conditions, scholars have proposed many turbine endwall cooling methods. In real gas turbine, there is slot in the joint between turbine components. One of the cooling methods was to
Corresponding author. E-mail address: [email protected] (Y. Luo).
https://doi.org/10.1016/j.applthermaleng.2019.114208 Received 29 October 2018; Received in revised form 29 April 2019; Accepted 2 August 2019 Available online 03 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
Greek letter
arc C Cx f h L MFR M P PS S St t tP T Tref TKE U x,y,z y+
α η ρ σ
turbine suction/pressure side arc length, mm turbine chord, mm axial turbine chord, mm pulsed frequency, Hz convective heat transfer coefficient, (W/m2 K) characteristic length of slot mass flow ratio of purge flow to mainstream flow blowing ratio, (ρcUc/ρ∞U∞) pressure, Pa pressure side local arc length, mm Strouhal number, fL/U∞ time, s pulsation period, s temperature, K reference temperature, K non-dimensional turbulence kinetic energy velocity, m/s Cartesian coordinates, mm non-dimensional distance from the wall
slot injection orientation angle, ° film cooling effectiveness (Tw Tin, )/(Tc Tin, ) gas density, kg/m3 total pressure recovery coefficient, P *out, /P *in,
Superscript *
total
Subscripts ave c ref w in out ∞
introduce cooling gas into the upstream slot to cool the downstream endwall [6]. Blair [7] first studied a two-dimensional slot cooling structure upstream of endwall by experiment. In experiment, a suction groove was designed to eliminate influence of mainstream boundary layer. The results showed that with increase of mass flow from slot, the film cooling effect on endwall increased as well. However, under influence of channel secondary flow, the distribution of cooling jet was uneven, which affected endwall film cooling effect. Cardwell [8] and Thrift [9] et al. studied effect of upstream slots of different geometric parameters on downstream endwall cooling. Their results showed that when mass flow from slot is constant, changing the width of the slot could change the coverage area of the cooling injection. Within the range of research parameters, increasing slot width enhanced the film cooling effect of the downstream endwall. Reducing the angle between the slot and the end wall could suppress the development of horseshoe vortex in the channel, thereby enhancing the endwall cooling effect. The purge flow also has significant influence on secondary flow structure, which would alter the heat transfer characteristics on the
average coolant reference wall inlet outlet mainstream
endwall [10]. Granser and Schelenberg [11] stated that the coolant film from slot leakage could attenuate the strength of the cascade channel secondary vortex due to decreases of boundary layer thickness. Steven [12,13] experimentally investigated the influence of slot injection on the flow field and thermal characteristics of endwall. Instead of being adversely affected by secondary flow, the purge flow was able to reduce secondary flow effect. Besides, the results of thermal measurements indicated that the slot flow should be strong enough to overcome the influence of secondary flow so that good thermal protection could be achieved. Ong et al. [14] used three-dimensional unsteady calculations to investigate the effect of coolant injection on the rotor under high pressure condition. The results presented that increase of coolant swirl angle could effectively reduce the secondary flow penetration depth, resulting in improvement in the coolant distribution on the rotor hub. Pasinato et al. [15] simulated and measured the flow filed of a linear cascade of turbine vanes, with and without secondary air injection from upstream slot. They stated that secondary air injection would strongly distort the flow field in cascade channel. The fluid ejected from
(a) Computational domain
(b) Partial enlargement of the computational domain Fig. 1. Geometry model. 2
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of slot pulsed film cooling on entire turbine endwall need to further study. In this paper, unsteady simulation is conducted for an entire NASA C3X turbine. Two different pulsed cooling injection including cosine wave and square wave are used at slot inlet. The purpose of this work is to compare film cooling effectiveness in different pulsed frequency and different mass flow ratios, and to provide useful reference for pulsed purge film cooling characteristics.
Table 1 Turbine vane and slot geometric parameters. Parameters
Value
Chord length C (mm) Axial chord Cx (mm) Vane height (mm) Vane pitch (mm) Inlet angle (deg) Outlet angle (deg) Slot width (mm) Slot orientation (deg)
144.93 78.16 76.2 117.73 90 72.38 4 α
2. Geometry and mesh The calculation model studied in this paper is shown in Fig. 1, which is based on noted turbine model C3X [22]. The original C3X model does not have cascade upstream slot. In order to study the effect of injection slot on the film cooling performance of enwall, an upstream slot inlet has been installed in this model (as shown in Fig. 1b). The slot is located 10.2 mm upstream of the leading edge of the vane. Other detailed geometrical parameters are shown in Table 1. Fig. 2 shows the computational mesh in cascade and slot entrance regions. All computational spaces are dispersed using un-structured mesh. Multi-layer hexahedral mesh is used on the fluid-solid interface. The height of the first layer of hexahedral mesh makes the value of y+ around 1. The total number of meshes finally obtained is around 7 million. This paper also performs verification of grid independence. A total of three different numbers of meshes are studied including coarse grid (5 million), medium grid (6 million) and fine grid (7 million). The distribution of wall temperature varies with the number of grids is shown in Fig. 3. The position of the wall temperature is shown in the green line of Fig. 3a. Fig. 3b shows the wall temperature distribution under three different mesh quality. The differences of wall temperature distribution among the three mesh strategies are less than 5%. Therefore, the increasing grid number no longer has a significant impact on the simulation results. The fine mesh is employed in the following computation.
upstream slot developed into a relatively coherent flow structure with the horseshoe vortex systems due to upstream boundary layer. Moreover, Knost et al. [16] measured endwall adiabatic effectiveness for an extensive text combining both coolant form a slot and discrete film cooling holes throughout the passage. They indicated that the slot flow would affect the near-wall flow conditions which must be considered when predicting film-coolant trajectory based on streamlines. At high slot flows, the near-wall flows swept the jet gas closer toward the suction side. To obtain a better cooling effect, some scholars proposed new slot structures. Du et al. [17] proposed a novel trigonometric curve slot configuration. Numerical results indicated that in upstream region, this new slot geometry given better cooling effectiveness than normal slot geometry. However, in downstream region, the result was reversed. In film cooling, pulsed film cooling could reduce the cold gas consumption. On the other hand, due to the periodicity of upstream flow, in real gas turbines the film jet exhibits periodic change. In pulsed film cooling study, Coulthard [18,19] used solenoid valves in gas supply to study the jet pulsing effect. The results indicated that the effect of film frequency mainly based on the reducing overall jet liftoff. At high frequency, the pulsing cooling film benefited reducing jet liftoff, while at low frequency, the pulsing cooling film enhanced jet liftoff. In terms of numerical simulation, Song [10] studied effect of purge flow on endwall in detail. The influence of injection angles and mass flow ratios on the endwall flow field and heat transfer characteristics were further explained. Muldoon and Acharya [20] used Direct Numerical Simulation (DNS) to investigate pulsed film cooling jet on a flat. When nondimensional pulsing frequencies varied from 0.004 to 0.32 at peak blowing ratio M = 1.5, they found that the best film cooling effectiveness was obtained at 0.32. Rutledge et al. [21] experimentally investigated the effect of pulsing film cooling on a cylindrical leading edge surface. The experimental results indicated that at higher coolant flow rates, the pulsed cooling was advantageous comparing with steady film cooling. Discrete film holes and upstream slot are often used in combination in turbine endwall cooling. However, the pulsed purge film from upstream slot was rarely studied. Most of the previous researches focused on the effect of slot geometry instead of jet state. In addition, the effect
3. Numerical model and boundary condition Based on finite volume method, steady and unsteady 3-D Reynoldsaveraged Navier-Stokes equations are solved with shear stress transport (SST) k − ω turbulence model. All solid walls are set to adiabatic boundaries. Mainstream fluid and slot fluid are set to air ideal gas. Total pressure, total temperature, turbulence intensity and length are set at the inlet of the cascade. Static press condition is set at cascade outlet. Total temperature and mass flow rate are set at the slot inlet. Detailed boundary conditions are shown in Table 2. In steady simulation, the advection scheme is selected in high resolution. The convergence criteria of normalized root mean square (RMS) of residuals are less than 10E−5 and conservation target is set to 0.01. In unsteady simulation, the advection and transient schemes are high resolution and second order backward Euler, respectively. And the steady simulation results
(a) Global grid diagram
(b) Mesh enlargement at slot inlet
Fig. 2. Computational mesh and partial enlargement mesh. 3
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(a) Wall temperature position
(b) Grid independence
Fig. 3. Parameter position and grid independence verification.
are in good agreement. So it is believed that the SST k − ω could provide trusted calculation results for the next study.
Table 2 Detailed boundary conditions. Parameters
Value
Mainstream inlet total pressure, Pa Mainstream inlet total temperature, K Turbulence intensity, % Eddy length scale, mm Slot inlet total temperature, K Mainstream outlet static pressure, Pa
408,105 415 6.5 0.4 298 248,299
5. Results and discussions 5.1. Effect of α on the film cooling effectiveness Fig. 7 shows the time-averaged film cooling effectiveness contours (Fig. 7a) and the laterally-averaged film cooling effectiveness distributions (Fig. 7b) on turbine endwall at St = 0.1158 and MFR = 1.0 with different angle α. Under the action of the lateral pressure gradient of the cascade channel, the cooling gas flowing out of the gap could not uniformly cover the entire cascade endwall. In most areas of the endwall near the pressure side, the film cooling effectiveness is very poor. At the leading edge of the endwall closing to the suction side, the film cooling effectiveness is the highest for the three different waves. Highest film cooling effectiveness region (shown red in Fig. 7a) extend, when α increases from 25° to 45° for both steady and cosine waves. But that region shrink, when α increases from 45° to 65° for both steady and cosine waves. Comparing the angle α = 25°, α = 45° slot structure has smaller cooling gas outlet area, which increase penetration force of cooling gas into the mainstream flow. Comparing the angle α = 65°, cooling gas from α = 45° slot structure is easier to stick to the endwall. For square wave, the film cooling effectiveness is the worse for each angle comparing with steady and cosine waves. The highest film cooling effective region shrinks, when α increases from 25° to 65° for square wave. The effect of different orientation angles on the endwall film cooling effectiveness is more apparent in Fig. 7b. It is worth noting that the laterally-averaged film cooling effectiveness follows a similar variation law under different angles: as the x/Cx increases, the laterally-averaged film cooling effectiveness decreases first and then rises. This distribution law will be explained in conjunction with Fig. 7a and previous reference [23]. From Fig. 7a, it is noted that as the gas flows downstream of the cascade channel, the coverage area of the cooling gas decreases first and then increases. At the merging point, the coverage area of the cooling gas is the smallest. In the cascade endwall region from leading edge to merging point, cooling gas develops downstream under the influence of channel vortex systems, including pressure/ suction side horseshoe vortex systems and pressure/suction side leading edge corner vortex systems. This multi-vortex move toward the suction side due to a strong transverse pressure gradient and is gradually squeezed into a single vortex as it approaches the merging point, which results in a reduction in the coverage of the cooling film. In the cascade endwall region from merging point to the trailing edge, the flow in the cascade channel receives the combined effect of the passage vortex and the wall vortex induced by the passage vortex. These vortex systems
Fig. 4. Mass flow ratio signals at the purge flow inlet.
are utilized as the initial value for the transient simulation. Coefficient loops is set in range from 3 to 5. And the convergence criteria and conservation target are the same with those in steady simulation. As shown in Fig. 4, four different nominal MFRs (0.5, 1.0, 1.5 and 2.0) are studied. Cosine wave, square wave and steady wave are considered at slot inlet. The effect of different MFRs on endwall film cooling and the comparison between steady and unsteady film cooling for endwall are investigated. 4. Turbulence model validation To further verify the accuracy of the calculation method, we conducted a comparative study with C3X experiment data [22]. C3X turbine vane is cooled by 10 internal cooling holes. Fig. 5 shows its calculation domain and grid division. A structural grid is used in the cooling channel. The mesh interface between the fluid and solid domains requires the general grid interface (GGI) method. The simulation results with SST k − ω turbulence model are shown in Fig. 6. Both the pressure data and the thermal data at middle plane of C3X turbine vane 4
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(a) Computational domain of C3X vane
(b) Mesh generation of C3X vane
Fig. 5. Geometry of C3X turbine vane and mesh generation.
(a) Surface pressure distribution
(b) Surface temperature distribution
Surface heat transfer coefficient distribution
Fig. 6. Comparison between experiment data and computational simulation results at middle plane of C3X vane.
enhance the mixing of the cooling gas and the mainstream flow, expanding the flow range of the cooling gas. From x/Cx = 0 to x/ Cx = 0.57, the laterally-averaged of time-averaged film cooling effectiveness increases first and then decreases as the angle α increases for steady and cosine waves. At the same angle α, the laterally-averaged film cooling effectiveness of the two waveforms is not much different. From x/Cx = 0.57 to x/Cx = 1.02, the angle has little effect on the laterally-averaged film cooling effectiveness. For square wave, the laterally-averaged film cooling effectiveness decreases as angle α increases from x/Cx = 0 to x/Cx = 0.51. An interesting phenomenon is that from x/Cx = 0.64 to x/Cx = 0.96, the laterally-averaged film cooling effectiveness increases slightly as angle α increases. In general, for three waveforms the effect of the angle α on the film cooling effectiveness is mainly in the area between the leading edge and the merging point (x/ Cx = 0.3), and the effect of angle α in the area from merging point to the trailing edge is less obvious. Fig. 8 presents the distributions of non-dimensional temperature and streamlines on three different sections. The A-A section is close to the suction surface of the cascade, the B-B section is facing the stagnation point of the vane, and the C-C section is close to the cascade pressure surface. As angle α is 25° for steady wave, significant difference can be found among the flow conditions of the three sections. At section A-A, the cooling gas can flow smoothly and form a gas film on the endwall. At section B-B, due to the existence of vane, the cooling gas cannot flow out of the slot, forming a vortex structure in the slot channel. Downstream of the B-B section exit, an obvious horseshoe vortex structure is formed resulting in higher pressure near the stagnation point. At section C-C, cooling gas cannot flow out of the slot.
This is because the lateral pressure gradient of the cascade channel causes the pressure on the pressure side of the cascade to be higher than the pressure on the suction side of the cascade. As angle α increases, the cooling gas of A-A section can smoothly flow out of the slot. However, the cooling gas flow conditions of B-B and C-C section do not become better. 5.2. Effect of MFR on the film cooling effectiveness Fig. 9 shows time-averaged film cooling effectiveness distributions on endwall (Fig. 9a) and the laterally-averaged of time-averaged film cooling effectiveness along x/Cx (Fig. 9b) at St = 0.1158 and α = 45° with four different MFRs. The highest film cooling effectiveness region (shown red in Fig. 9a) extends as MFR increases from 0.5 to 2 for all three waveforms. Comparing with steady and cosine waves, the region covered by coolant gas shrinks evidently for square wave. The regions covered by coolant gas for steady and cosine waves have almost no difference. It is noted that although the increase in MFR enlarges the area of the cooling region, some areas of the endwall are not cooled effectively. Taking the state (steady wave and MFR = 2) as an example, in the root region of the leading edge, the endwall film cooling effectiveness is very low. It is because the coolant injection from the slot sweep directly to the suction and pressure sides due to the horseshoe vortex and leading edge corner vortex, which resulting in less film cooling effectiveness in root region of leading edge. Under the effect of the lateral pressure gradient and the secondary flow in the cascade channel, the flow of coolant gas is biased toward the suction side of the vane. Therefore, the film cooling effectiveness on the endwall near 5
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α = 45°
α = 65°
increases above 1, film cooling effectiveness first decreases and then increases. For steady and cosine wave, at point MFR = 2, in the entire cascade endwall, the film cooling effectiveness of steady wave is slightly higher than that of the cosine wave. Fig. 10 shows non-dimensional turbulence kinetic energy (TKE) contours on endwall at different MFRs. The TKE distributions of cosine wave and steady wave have little difference. For the sake of brevity, Fig. 10 only shows TKE contours for cosine wave (Fig. 10a) and square wave (Fig. 10b). For cosine wave, the level of TKE in the cascade channel increases significantly as MFR increases. However, for square wave, the increase in MFR (increase from MFR = 0.5 to MFR = 2.0) has little effect on the TKE distribution. Combined with Fig. 9, where the level of TKE is high, it is the interface between the cooling gas and mainstream. With the increase of MFR, the blending between the cooling gas and the mainstream will inevitably occur, and the TKE at the interface will increase. Fig. 11 shows the total pressure recovery coefficient σ on various MFR conditions and three waveforms. As MFR increases, the total pressure recovery coefficient σ in the cascade channel decreases for all three waveforms. This is because the increase in MFR makes the blending of the cooling gas and the mainstream more intense, result in increasing the total pressure loss. When 0.5 < MFR < 1.0, the σ of steady wave is little higher than that of cosine wave. However, when 1.0 < MFR < 2.0, the σ of steady wave is little lower than that of cosine wave. Comparing with steady and
Square wave
Cosine wave
Steady wave
α = 25°
α=25°, steady
(a)
B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
α=65°, steady
α=45°, steady
A-A
(b)
α=25°, cosine wave
Fig. 7. Effect of α on the film cooling effectiveness at St = 0.1158 and MFR = 1.0 (a) time-averaged film cooling effectiveness distributions on endwall, (b) laterally-averaged of time-averaged film cooling effectiveness along x/ Cx.
pressure side is deteriorated. In addition, due to the influence of the tail recirculation, the film cooling effectiveness at the tail of the vane is also poor. These film cooling effectiveness of these areas has not improved with the increase of MFR. In Fig. 9b, the laterally-averaged of time-averaged film cooling effectiveness along x/Cx have much difference for different MFRs. At MFR = 0.5 for square wave, the time-averaged film cooling effectiveness increases as x/Cx increases (0 < x/Cx < 0.9). However, as MFR
Fig. 8. Non-dimensional temperature and streamline distributions on three different sections. 6
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B-B
C-C
A-A
B-B
C-C
A-A
B-B
C-C
MFR=1.5
MFR=2.0
α=45°, square wave
Square wave
α=25°, square wave
Cosine wave
α=65°, cosine wave
A-A
MFR=1.0
Steady wave
α=45°, cosine wave
MFR=0.5
(a)
B-B
C-C
A-A
B-B
C-C
α=65°, square wave
A-A
Fig. 8. (continued)
cosine waveforms, the σ of square wave is higher at different MFR conditions. And the decrease rate of total pressure recovery coefficient for square wave is smaller than that of steady and cosine wave. From Fig. 10, the TKE level in cascade channel of square wave is the lowest among three waveforms, therefore, the total pressure loss is also the smallest among the three waveforms.
(b) Fig. 9. Effect of MFR on film cooling effectiveness at St = 0.1158 and α = 45° (a) time-averaged film cooling effectiveness distributions on endwall, (b) laterally-averaged of time-averaged film cooling effectiveness along x/Cx.
5.3. Effect of Strouhal number on the film cooling effectiveness
varies greatly at different times. As the time step advances, the area where the film cooling effectiveness at the inlet is high first shrinks and then extends. At time t/tP = 0.6, the film cooling effectiveness at the inlet of the cascade channel is the worst. However, at this moment, the cooling film distribution is more uniform in central and rear of the cascade channel. At time t/tP = 0.8, the film cooling effectiveness at the inlet of the cascade becomes better. As St increases, the distribution of film cooling effectiveness at different time also has obvious changes. As can be seen from Fig. 4, at time t/tP = 0.5, the mass flow rate of the cooling gas is 0 kg/s. For cosine wave, from t/tP = 0.5 to t/tP = 1, the mass flow of cooling gas is gradually increasing. At time t/tP = 0.6, the area of high film cooling effectiveness at the inlet of the cascade
To clearly see the effect of Strouhal number on the endwall film cooling effectiveness in a time period, Fig. 12a shows the instantaneous film cooling effectiveness on endwall for three different waveform at MFR = 1.0. Three different pulsation frequencies of 10 Hz, 100 Hz and 1000 Hz are studied, corresponding to three Strouhal numbers of 0.001158, 0.01158 and 0.1158 respectively, in which the condition of St = 0.1158 is used as baseline condition. To discuss the influences of the pulsation frequency on film cooling effectiveness in one time period, four moments are intercepted for research in each time cycle for different St numbers. From the first line of St = 0.001158 for cosine wave, the film cooling effectiveness at the inlet of the cascade channel
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Y. Liu and Y. Luo
Fig. 10. Non-dimensional TKE distribution on enwall with St = 0.1158 at different MFRs (a) Cosine wave and (b) Square wave.
the inlet of the cascade increases as St increases. It is because the heat transfer between the cooling gas and the mainstream gas is smaller as the time interval decreases. Fig. 12b and c shows laterally-averaged of instantaneous film cooling effectiveness along x/Cx at time t/tP = 0.4 and t/tP = 0.6 respectively. At time t/tP = 0.4, laterally-averaged film cooling effectiveness distribution line for St = 0.001158 of cosine wave is a little different from the rest of the distribution lines. It increases as x/Cx increases between x/Cx = 0 and x/Cx = 0.9. As St increases, laterallyaveraged film cooling effectiveness increases between x/Cx = 0 and x/ Cx = 0.58 for cosine wave at time t/tP = 0.4. However, for square wave, as St increases, laterally-averaged film cooling effectiveness decreases. At time t/tP = 0.6, as St increases, laterally-averaged film cooling effectiveness increase between x/Cx = 0 and x/Cx = 0.51 for cosine wave. And as St increases, laterally-averaged film cooling effectiveness decreases between x/Cx = 0.58 and x/Cx = 1.02 for cosine wave. For square wave, laterally-averaged film cooling effectiveness of St = 0.01158 is slight higher than those of St = 0.001158 and St = 0.1158 between x/Cx = 0 and x/Cx = 0.7. Fig. 13a shows the instantaneous temperature distribution at leading edge with different St numbers. In a time period, two different time (t/tP = 0.4 and t/tP = 0.6) are chosen to study the effect of St on the temperature distribution at leading edge. Due to the effect of cooling gas and cascade inlet pressure gradient, the temperature distribution on the leading edge is not uniform. Near the pressure side, the temperature of the gas is higher. Near the D-D section (y/Cx = 1.98), the temperature of the gas is lower. At the outflow of the cooling gas, the gas temperature is lowest. As St increases, the working area of the cooling gas expands for cosine wave on leading edge at time t/tP = 0.4 and t/tP = 0.6. For square wave, as St increases, the working area of the cooling gas expands at time t/tP = 0.4. At time t/tP = 0.6, the working
Fig. 11. Total pressure recovery coefficient σ for different MFRs and waveforms
gradually shrinks as St increases for cosine wave. However, at time t/ tP = 0.8, the area of high film cooling effectiveness at the inlet of the cascade first shrinks and then extends as St increases for cosine wave. For square wave, the cooling gas only maintains a constant outlet during the first half (0 < t/tP < 0.5) of the time period and no outflow during the second half (0.5 < t/tP < 1) of the time period. At time t/ tP = 0.2 and t/tP = 0.4, the area of high film cooling effectiveness at the inlet of the cascade gradually shrinks as St increases for square wave. It is because as time interval becomes shorter, the total amount of cooling gas flowing out of the slot is also reduced. In the second half of the time period, although no cooling gas flowing out, there is still residual cooling gas in the cascade channel, so the film cooling effect of the endwall is not zero. At time t/tP = 0.8, the film cooling effectiveness at
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area of the cooling gas expands first and then shrinks. Fig. 13b and c shows the instantaneous z-axis direction temperature distribution on plane D-D for cosine and square waveforms at different times. The ordinate z/h = 0 represents the endwall surface. As St increases, the temperature of the gas near the endwall decreases and the temperature gradient increases for cosine wave at both t/tP = 0.4 and
t/tP=0.4
t/tP=0.6
t/tP=0.8
Cosine wave
t/tP=0.2
t/tP = 0.6. With the increase of St, the difference in temperature distribution near the wall at two times is getting smaller. At the points of St = 0.01158 and St = 0.1158, the temperature distributions have little different with two different times for square wave. At the points of St = 0.001158, the temperature near the endwall at time t/tP = 0.6 is higher than that at time t/tP = 0.4.
Cosine wave
St=0.001158
Cosine wave
St=0.01158
Square wave
St=0.1158
St=0.001158 Fig. 12. Effect of St on film cooling effectiveness at MFR = 1.0 and α = 45° (a) instantaneous film cooling effectiveness on endwall with different St numbers, (b) laterally-averaged of instantaneous film cooling effectiveness along x/Cx at time t/tP = 0.4, (c) laterally-averaged of instantaneous film cooling effectiveness along x/ Cx at time t/tP = 0.6.
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Square wave
Y. Liu and Y. Luo
Square wave
St=0.01158
St=0.1158
(a)
(b)
(c) Fig. 12. (continued)
6. Conclusions
stagnation point and the pressure side, resulting in high film cooling effectiveness near the suction side. Changing the slot orientation angle can significantly change the film cooling effectiveness distribution of the endwall. For cosine wave, when the orientation angle is 45°, the laterally-averaged film cooling effectiveness in the entire cascade channel is the highest. Comparing with cosine wave and steady wave, the cooling effect of the square wave is the worst at MFR = 1.0 with different orientation angles. (2) Increase MFR can effectively improve the cooling effect of the turbine endwall, expanding the region of high film cooling effectiveness near leading edge and improving the whole level of cooling effect in the cascade channel. The laterally-averaged of time-averaged film cooling effectiveness of cosine wave and steady wave are higher than that of square wave at each MFR point. As MFR increases, the rate of decline in the time-averaged film cooling effectiveness for cosine and steady wave at the front (0 < x/ Cx < 0.38) of the cascade channel gradually increases. Near the trailing edge of the cascade channel, the effect of MFR on the film cooling effectiveness is reduced for all three waves. (3) MFR increases can raise the level of TKE in the cascade channel, intensifying gas blending, resulting in higher gas flow loss. When
Transient simulation of pulsed film cooling effect on turbine endwall are studied in an engine-sized NASA C3X vane. A cooling slot geometry is installed upstream of the cascade channel. The film cooling, thermal and aerodynamic characteristics of the turbine endwall are investigated numerically by using unsteady three-dimensional Reynolds-averaged Navier-Stokes equations coupling with the SST k-ω turbulence model. The effect of different structural and aerodynamic parameters, including slot orientation angle, cooling gas mass flow ratio and Strouhal number, are investigated respectively. The results indicate that the cases of cosine wave are superior to the cases of square wave in the film cooling effectiveness. In addition, the case of cosine wave at orientation angle α = 45° presents better film cooling performance among other orientation angles. Within the parameters of the study, important conclusions can be summarized as follows: (1) Due to the lateral pressure gradient at cascade inlet, the cooling gas cannot inject from the slot uniformly. The cooling gas more likely flow out from the cooling slot near the suction side. However, the gas does not easily flow out from the cooling slot near the 10
Applied Thermal Engineering 161 (2019) 114208
Y. Liu and Y. Luo
MFR increases from 0.5 to 2.0, the total pressure recovery coefficient is reduced by up to 0.07% for three different waves. In addition, the manner in which the cooling gas injects also has effect on the flow loss of cascade channel. The total pressure recovery coefficient for square wave injection is higher than cosine wave and steady wave injection at points of different MFRs. (4) Three different Strouhal numbers are investigated at MFR = 1.0 and α = 45°. At time t/tP = 0.4, as St increases, laterally-averaged of instantaneous film cooling effectiveness increases ranging from x/
Cx = 0 to x/Cx = 0.58 and decreases ranging from x/Cx = 0.58 to trailing edge for cosine wave. For square wave, as St increases, the laterally-averaged of instantaneous film cooling effectiveness decreases in the whole cascade channel. (5) Due to the influence of cooling gas, the instantaneous of temperature distribution on the inlet section of cascade is not uniform. The temperature of the gas near the pressure side is higher than the temperature of the gas near the suction side. The near-wall temperature gradient on the D-D section increases as St increases.
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.001158
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.01158
t/tP=0.4
t/tP=0.6 Cosine wave, St=0.1158
Fig. 13. Effect of St on instantaneous temperature distributions at MFR = 1.0 and α = 45°(a) instantaneous temperature distribution on leading edge with different St numbers, (b) instantaneous z-axis direction temperature distribution on plane D-D for cosine waveform at different times, (c) instantaneous z-axis direction temperature distribution on plane D-D for square waveform at different times.
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Y. Liu and Y. Luo
t/tP=0.4
t/tP=0.6 Square wave, St=0.001158
t/tP=0.4
t/tP=0.6 Square wave, St=0.01158
t/tP=0.4
t/tP=0.6 Square wave, St=0.1158
(a)
(b)
(c) Fig. 13. (continued)
Appendix A. Supplementary material
slot, in: ASME Turbo Expo 2002: Power for land, Sea and Air. Amsterdam, Netherlands: ASME Paper, GT2002-30178, 2002. [2] M. Papa, V. Srinivasan, R.J. Goldstein, Film cooling effect of rotor-stator purge flow on endwall heat/mass transfer, ASME J. Turbomach. 134 (2012) 041014. [3] G.D. Maclsaac, S.A. Sjolander, T.J. Praisner, Measurements of losses and Reynolds stresses in the secondary flow downstream of a low-speed linear turbine cascade, ASME J. Turbomach. 134 (2012) 061015. [4] M. Papa, R.J. Goldstein, F. Gori, Numerical heat transfer predictions and mass/heat transfer measurements in as linear turbine cascade, Appl. Therm. Eng. 27 (2007) 771–778.
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114208. References [1] R.S. Bunker, Film cooling effectiveness due to discrete holes within a transverse surface
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Y. Liu and Y. Luo [5] R.W. Radomsky, K.A. Thole, High free-stream turbulence effects on endwall heat transfer for a gas turbine stator vane, ASME J. Turbomach. 122 (2000) 699–708. [6] S.P. Lynch, K.A. Thole, The effect of the combustor-turbine slot and midpassage gap on vane endwall heat transfer, ASME J. Turbomach. 133 (2011) 041002. [7] M.F. Blair, An experimental study of heat transfer and film cooling on large-scale turbine endwalls, J. Heat Transfer 96 (4) (1974) 524. [8] N.D. Cardwell, N. Sundaram, K.A. Thole, The effects of varying the combustor-turbine gap, ASME J. Turbomach. 129 (4) (2006) 91–102. [9] A.A. Thrift, K.A. Thole, S. Hada, Effects of orientation and position of the combustorturbine interface on the cooling of a vane endwall, in: ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, 2011, pp. 291–301. [10] L. Song, P. Zhu, J. Li, et al., Effect of purge flow on endwall flow and heat transfer characteristics of a gas turbine blade, Appl. Therm. Eng. 110 (2017) 504–520. [11] D. Granser, T. Schulenberg, Prediction and measurement of film cooling effectiveness for a first-stage turbine vane shroud, ASME Paper No. 90-GT-95, 1990. [12] S.W. Burd, C.J. Satterness, T.W. Simon, Effects of slot bleed injection over a contoured ednwall on nozzle guide vane cooling performance: part I—flow field measurements, ASME paper No. GT2000-199. [13] S.W. Burd, C.J. Satterness, T.W. Simon, Effect of slot bleed injection over a contoured endwall on nozzle guide vane performance: part II—thermal measurements, ASME paper No. GT2000-200.
[14] J. Ong, R.J. Miller, S. Uchida, The effect of coolant injection on the endwall flow of a high pressure turbine, ASME J. Turbomach. 134 (2012) 051003. [15] H. Pasinato, K. Satterness, T.W. Simon, Effects of slot bleed injection over contoured endwall on nozzle guide vane cooling performance: part I-thermal measurements, ASME Paper No. 2000-GT-200. [16] D.G. Knost, K.A. Thole, Adiabatic effectiveness measurements of endwall film cooling for a first stage vane, ASME J. Turbomach. 127 (2005) 297–305. [17] K. Du, Z.G. Li, J. Li, et al., Influence of the upstream slot geometry on the endwall cooling and plantom cooling of vane suction side surface, Appl. Therm. Eng. 121 (2017) 688–700. [18] S.M. Coulthard, R.J. Volino, K.A. Flack, Effect of jet pulsing on film cooling part I: effectiveness and flow-field temperature results, ASME J. Turbomah. 129 (2007) 232–246. [19] S.M. Coulthard, R.J. Volino, K.A. Flack, Effect of jet pulsing on film cooling—part II: heat transfer results, ASME J. Turbomach. 129 (2007) 247–257. [20] F. Muldoon, S. Acharya, DNS study of pulsed film cooling for enhanced cooling effectiveness, Int. J. Heat Mass Transf. 52 (2009) 3118–3127. [21] J.L. Rutledge, P.I. King, R.B. Rivir, Influence of film cooling unsteadiness on turbine blade leading edge heat flux, J. Eng. Gas Turb. Power 134 (2012) Paper No. 071901. [22] L.D. Hylton, M.S. Milhec, E.R. Turner, Analytical and experimental evaluation of the heat transfer distribution over the surface of turbine vane, NASA report No. CR-168015, 1983. [23] H.P. Wang, S.J. Olson, R.J. Goldstein, E.R.G. Eckert, Flow visualization in a linear turbine cascade of high performance turbine blades. ASEM J., 95-GT-7.
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