Part 1 GT2013-94544 1-10-2013 final submittedeccc.uno.edu/pdf/Xu-Wang GT2013-94544 Part1...

1 Copyright © 2013 by ASME

Proceedings of ASME Turbo Expo GT2013

July 3-7, 2013, San Antonio, Texas, USA

GT2013-94544

Numerical Investigations of Wake and Shock Wave Effects on Film Cooling Performance in a Transonic Turbine Stage, Part 1 – Methodology Development and Qualification over Stationary Stators and Rotors

Huazhao Xu and Jianhua Wang University of Science and Technology of China

Hefei, 230027, China

Ting Wang Energy Conversion and Conservation Center

University of New Orleans New Orleans, LA 70418, USA

ABSTRACT To understand the unsteady shock wave and wake effects

on the film cooling performance over a transonic 3-D rotating stage, a series of numerical investigations have been conducted and are presented in this two-part paper. Part 1 is focused on the development of the computational model and methodology of the system setup and model qualification; Part 2 is to investigate the unsteady effects of shock waves and wakes on film cooling performance in a transonic rotating stage.

In Part 1, the film cooling experimental conditions (non-rotating) and test sections of Kopper et. al. and Hunter are selected for model qualification. The numerical computation is carried out by the commercial software Ansys/Fluent using the pressure based compressible flow governing equations. The effects of four turbulence models are carefully compared with the experimental data. The Realizable k-ε turbulence model is found to match the experimental data better than the other models and is thus used for the rest of the study, including Part 2. The results show that 1) the weak shock emanating from the neighboring stator’s trailing edge results in a temperature rise and a reduction of film cooling effectiveness on the suction side near the trailing edge, 2) cooling ejection from the trailing edge reduces the shock strength in the stator passage, 3) an increase in Mach number from 0.84 to 1.50 can reduce the total pressure losses of fluid flow near the end-walls, 4) the film cooling effectiveness increases with increasing blowing ratio and becomes more even on the stator with a higher blowing ratio, and 5) an increase in Mach number from 0.84 to 1.50 gives rise to a higher cooling effectiveness in the region from the cooling holes to 80% of the chord length of the stator on the pressure side, but becomes lower after this up to the trailing edge. However, on the stator's suction side, higher Mach number results in a lower cooling effectiveness region around the film holes from 30% to 55% of the chord length, but cooling effectiveness increases downstream.

NOMENCLATURE Br Blowing ratio (ρVc/ρVg) Bx Axial Chord length, m Cp Heat capacity, J/(kg·K)

CP Cooling penalty Mc Cooling air mass flow rate, kg/s Mg Mainstream mass flow rate, kg/s K Thermal conductivity, W/(m·s)

,t inletP Area-averaged total pressure at the stator inlet, Pa

,t exitP Area-averaged total pressure at the stator exit, Pa Tg Mainstream temperature, K Tc Cooling air temperature, K. Taw Adiabatic wall Temperature with film cooling, K Taw,o Adiabatic wall Temperature without film cooling, K To Stagnation or total temperature, K a Sonic velocity, m/s ∇P Pressure gradient, Pa/m

Uur

Local velocity, m Xt Location of a nozzle throat, m

Greek η Adiabatic film cooling effectiveness ρ Density μ Dynamic viscosity, N·s/m2

Subscripts c cooling air g mainstream gas o total value INTRODUCTION

To achieve higher efficiency in a gas turbine, the inlet temperature is often raised, but, in most cases, this temperature far exceeds the melting point of most current blade materials. According to Auxier’s [1] analysis regarding the flame temperature of stoichiometric combustion, there is still a large potential to continuously increase the inlet turbine temperature to augment gas turbine efficiency. Therefore, more effective cooling techniques, such as internal impingement cooling, external film cooling, and combined internal and external cooling, are required to be continuously


improved to protect turbine airfoils from the ever increasing turbine inlet temperature. Experimental investigations on the blade film cooling have been conducted for quite a long time. Goldstein [2] summarized the early studies of film cooling at subsonic conditions. Han et al. [3] reviewed the recent studies of the influences of turbulence, rotating, channel shape and orientation, and hole-shapes on the film cooling effectiveness and heat transfer coefficient. Arts [4] classified the influence factors of film cooling performance into five kinds: 1) free stream Reynolds number and turbulence intensity; 2) blowing ratio or mass ratio; 3) airfoil geometry–curvature of the cooling air emission location; 4) film hole shape and location; and 5) transitional location, boundary layer state, and shock/boundary layer interaction. Due to the complexity of these influence factors, Bogard et al. [5] thought that, in order to understand the fundamental physics, it is necessary to separately investigate these factors at laboratory environments even at low turbulence intensity and density ratio. Therefore, this approach of studying each factor separately has been used in many experimental investigations.

It is quite a challenge to experimentally study the film cooling behaviors of a transonic gas turbine stage, due to the shock-boundary layer interaction. Kopper et al. [6] constructed an experimental system to measure the aerodynamic loss across the shock waves and trailing wake. Newman et al. [7] used the transient thin film technique to gauge the film cooling effectiveness and heat transfer coefficient of a nozzle guide vane at the Mach numbers 0.6, 0.8, and 1.0. Ochs et al. [8] discussed what effects the shock wave located at the trailing edge of a transonic stator blade had on the film cooling at the suction surface of the neighboring blade.

In a laboratory, it is difficult and expensive to create an experimental environment of film cooling that truly represents the actual gas turbine operating conditions. Therefore, numerical simulation schemes become a valuable and affordable research tool for gas turbine heat transfer research. Rehder et al. [9] numerically analyzed the total cascade losses contributed individually from boundary layers, shocks, trailing edge wakes, and mixing of coolant with the mainstream. Their analysis indicated that the losses caused by the shocks and boundary layers are a major contribution to the total losses. When coolant ejection was applied, the flow mixing induced further large pressure losses but it did not affect the existing losses caused by interactions between shock/wake and boundary layers. Hylton et al. [10] conducted parametric studies of the effects of Mach number, Reynolds number, turbulence intensity, and wall-to-gas temperature ratio on film cooling characteristics over a stator. They used a zero-equation mixing length hypothesis turbulence model and a more effective viscosity formulation for film cooling simulation. Laskowski et al. [11] used the standard k-ω turbulence model to simulate the cooling air ejected from trailing edge slot, and their simulation indicated that the cooling air ejection can reduce the passage shock wave strength, and thereby decrease the stator load. Lee et al. [12] used the Shear Stress Transportation (SST) k-ω turbulence model to discuss the geometrical effect of film holes including laidback angle, lateral expansion angle and ratio of length-to-diameter of the hole on the spatially-averaged film cooling effectiveness. Gabry et al. [13] applied the Reynolds-Averaged Navier-Stokes (RANS) turbulence model to simulate the

cooling air injection from circular film holes into a cross flow at blowing ratios ranging from 0.5 to 2.0. Their investigation could accurately predict the extent and trajectory of cooling air film, but could not reach a good agreement with experimental data provided by Dhungel et al. [14] of the heat transfer coefficient in the near wall region downstream of the film holes. Larsson et al. [15] used two-equation turbulence models as well as the low Re k-ε and Wilcox’s k-ω models to simulate the heat transfer performances of subsonic and transonic blades. They concluded that both models are unable to correctly predict the transition phenomenon at the suction side, and the turbulence intensity obtained in the stagnation region is much higher than the real value. Calzada et al. [16] applied an in-house code with standard k-ω model to solve the film cooling phenomenon with flow separation.

As mentioned above, it has been difficult to obtain relatively comprehensive data regarding film cooling behaviors under transonic and supersonic conditions through experiments due to the harsh environment of running gas turbine engines. To help understand the unsteady shock wave and wake effects on the film cooling performance over a transonic 2-D rotating stage, a series of numerical investigations are conducted in this study in a sequence of three-part papers. Part 1 is focused on development of the computational model and methodology of system setup and model qualification, while Part 2 is focused on investigating the unsteady effects of shock waves and wakes on film cooling performance in a transonic rotating stage.

Even though the gas turbine operating conditions can be relatively easier to set up in a numerical simulation than in an experiment, which computational scheme or turbulence models are best suited to capture the film cooling behavior are still subject to discussion. The Part 1 paper focuses on validating the computational model against the experimental data reported by Kopper et al. [6] and Hunter [17], including investigating the effect of turbulence models on the computed results. Using the validated computational scheme and the selected turbulence model, the 2-D total pressure losses over the stator and rotor passage and 3-D film cooling effectiveness over the stator are studied. The aim is to provide the investigators and designers with relatively comprehensive thermal-flow fields and fundamental physics regarding the effect of complex interactions of wakes and shock waves with the boundary layer on film cooling performance.

GEOMETRIES OF STATOR AND ROTOR

In this Part 1 study, the computational domain is based on a stationary, linear cascade. The flow fields of the stator and rotor are not connected, i.e. they are studied separately. A connected stator-rotor rotating stage will be studied in Part 2 with modified geometry. The geometries of the stator and rotor adopted here were reported by the experimental investigation of Kopper et al. [6]. In the stator, there are three rows of 36 film holes with a diameter of 0.025 inches on the suction side, two rows of 25 holes with a diameter of 0.032 inches on the pressure side, and one row of 40 holes with a diameter of 0.021 inches at the trailing edge. In the rotor, there is only one row of film slots with a width of 0.024in in the trailing edge. A detailed description of the parameters of the stator and rotor is listed in Table 1. Figure 1 illustrates the


structures of the stator and rotor, as well as the mass flow ratio of the film coolant and the main gas flow.

2.49%

1.27%

0.08128cm (0.032 in)

0.96%

0.0635cm (0.025 in)

0.05334cm (0.021in) 0.06096cm

(0.024in) 1%

(a)Stator (b) Rotor Fig. 1 2D geometries and percentages of mass flow rate for film cooling.

Table 1 Geometries of the stator and rotor Stator Rotor Reaction level 43 43 Axial chord, in 1.364 0.92 Pitch, in 3.333 1.359 Throat, in 0.597 0.37 Leading edge radius, in 0.206 0.061 Trailing edge radius, in 0.021 0.021 Inlet metal angle, (deg) 89.33 40.15 Inlet wedge angle, (deg) 90.00 30.00 Exit metal angle, (deg) 11.10 17.07 Exit wedge angle, (deg) 4.00 2.00 Uncovered turning, (deg) 11.73 6.00 NUMERICAL STRATEGY

The computational domains of the separated stator and rotor stages are shown in Fig. 2. Only a single pitch is selected for computational efficiency with periodic boundary conditions. Both 2-D and 3-D geometries are studied. The 2-D results are used for validation with the experimental data. The validated CFD model will be further employed to study 3-D film cooling interaction with wake passing and shock waves.

(a) Stator (b) Rotor

Pressure inlet

Pressure outlet

Wall Periodic

Wall

1.359 in

Mass inlet

Pressure outlet

Periodic

3.333 in 40.150

900

Fig 2. Computational domains for the stator and rotor.

(a) 2D stator (b) 3D stator

Stator

Film holes

Hub wall

Film holes

Fig 3. 2D and 3D meshes of the stator. Structured grids with quadrilateral and hexahedral cells

are employed because, in comparison with unstructured grids, they offer more precise prediction in the region with severe gradients using the same cell numbers; in addition, they take fewer iteration steps to get convergent results. The 2-D and 3-D meshes for the stator are given in Fig. 3. Mesh and Boundary Conditions

The ideal gas laws are used for air properties, including viscosity, thermal conductivity, and heat capability. They are curve-fitted by a polynomial expression at the temperature range from 300 to 2100K, using the data provided by Incopera et al. [18]. The fitting results are listed in Table 2. Table 2 Polynomial expressions of air properties

The total pressure is given as 1.6 atm and the exit pressure

is 1atm to match the test rig in the laboratory. The total pressure at the cooling air inlets is given as 1.8 atm, which results in the mass ratio of the cooling air over the mainstream being 2.47% at the leading edge, 1.27% in the mid-chord, and 0.96% at the trailing edge, as labeled in Fig. 1. The total temperature of the mainstream at the inlet is 347K while the cooling air's total temperature is given as 340K. At the circumferential sides of the passage, periodic boundary conditions are applied. When the flow field is investigated without film cooling, the film holes are blocked by assigning their inlets as adiabatic and non-slip solid walls.

Grid independence is verified using the realizable k-ε turbulence model through three grids with progressively increasing meshes, including 34,648; 77,061; and 151,078 cells for the 2-D stator and 44,741; 81,125; and 158,261 cells for the rotor. The static pressure distributions on the stator resulting from these three grids are shown in Fig. 4a. Note that the differences are not discernible. The grid independence validation for the rotor reaches a similar result. Therefore, the grid with 77,061 meshes is chosen for the 2-D rotor and stator simulations. In the 3-D computation, the grid independence is validated from three grids including 1,635,254, 2,424,360, and 3,243,152 cells. The results of static pressure at the mid-span of the stator, as shown in Fig.

P=a0+a1x+a1x2+a2x3

a0 a1 a2 a3 Cp(J/kg⋅k) 1.0187e3 -6.9921e-2 -3.3333e-5 4.4444e-7 K( W/m⋅k) -0.001865 0.0001102 -5.6729e-08 1.6727e-11 μ(N⋅s/m2) 2.02509e-6 6.3510e-8 -3.0959e-11 7.8708e-15


4b, are almost identical. To save computational time, the cell number 2,424,360 is chosen.

(a) 2-D

(b) 3-D

Fig. 4 Grid independent study for both 2-D and 3-D cases for static pressure ratio on the stator.

A pressure-based solver is applied to solve the coupled

conservation equations of continuity, momentum, energy, and turbulence transport using the commercial code, Ansys/Fluent. The second-order upwind scheme is used in the discretization of the convective terms. To speed up the convergence, an interpolation method is applied through mapping the results from a coarse mesh to a fine mesh. The residual tolerance for the conservation equations of mass, momentum, and turbulence is set as 1.0×10-4, but, for the energy equation, the residual tolerance is 1.0×10-7.

CFD MODEL VALIDATION Selection of Turbulence Models

When the mainstream flow with a high Reynolds number (around 1.0 x 106) enters into a transonic gas turbine stage, the force of inertia, turbulence fluctuation, and compressible effects dominate, and the inviscid turbulence model seems to be reasonable. Four different turbulence models are considered. The standard k-ε model suggested by Launder et al. [19] offers robustness, economy, and reasonable accuracy for high Reynolds-number, fully-developed turbulent flows. The SST k-ω model developed by Menter et al. [20] can provide an accurate and reliable result for complex flow including adverse pressure gradient flow and transonic shock waves. The realizable k-ε model derived by Shih et al. [21] has been validated to be suitable for the fluid flow including rotating

homogeneous shear flow, channel and boundary layer flow, as well as separated flow. The higher order Reynolds Stress Model (RSM) model, modified by Launder and Gibson [22, 23, 24] solves transport equations for the Reynolds stress tensor together with an equation for the dissipation rate.

The static pressure results over the mid-span section of the stator calculated from the inviscid flow and viscous flow with the four aforementioned turbulence models are compared with the experimental data of Kopper et al. [6] in Figs. 5 and 6 under transonic conditions at Ma = 0.84 with and without film cooling. In the supersonic condition, the CFD results are compared with the experimental data of Hunter [17] at Ma = 1.91 in Fig. 7. Figure 5 clearly shows that, when the cooling air is not ejected, the result of using the standard k-ε model shows the largest deviation from the experimental data at the suction side of the stator. This phenomenon can be explained by the fact that, in the downstream of the leading edge, the flow state at the suction side is mainly undergoing laminar-turbulent transition to low-Reynolds number turbulent flow, which deviates from the high-Reynolds number fully turbulent state assumed by the k-ε model. The result of inviscid flow seems to match the experimental data fairly well.

Fig. 5 Comparison of computational and experimental data Kopper et al. [6] for static pressure distribution over the stator's surface using different turbulence models without film cooling air in a transonic condition at Ma=0.84.

Fig. 6 Comparison of computational and experimental data [6] for static pressure distribution over the stator's surface using different turbulence models with film cooling at Ma=0.84.


Fig. 7 Comparison of computational and experimental data [17] for pressure ratio along the centerline of a C-D nozzle at P0/Pexit = 2.4 Hunter [17] using different turbulence models. A shock wave occurs at X/Xt=1.65X.

When the cooling air is ejected, Figure 6 shows that the results obtained by the inviscid model deviate the most from the experimental data near the film holes. This phenomenon is reasonable because, when the cooling air is injected, the flow downstream from the cooling holes are triggered to become turbulent flow, and the inviscid flow model can't capture the appropriate turbulent boundary layer flow structure. However, all of the turbulent models predict similar pressure distributions, and it is difficult to tell which model is better.

The above CFD model validation is conducted under transonic flow conditions. However, to calibrate the CFD model for supersonic conditions, another set of experimental data obtained in a convergent-divergent (C-D) nozzle with an exit Mach number of 1.91, reported by Hunter [17], is used, especially for verifying the CFD model’s capability of accurately capturing the shock waves. Figure 7 shows that both the realizable k-ε and the RSM turbulence models reliably predict the pressure ratio distribution and accurately capture the shock wave at X/Xt = 1.6 better than other turbulence models in comparison with the experimental data.

Through the comparisons with the experimental data mentioned above, it can be concluded that both the RSM model and the realizable k-ε model equally well predict the static pressure distribution under transonic flow conditions, and both can actually capture the shock wave under supersonic conditions. However, since the computational time is approximately an order of magnitude lower than the RSM model, the realizable k-ε model will be used in the rest of the study, including Part 2.

RESULTS AND ANALYSIS (A) 2-D Studies Aerodynamic Behaviors and Validation of Numerical Method The above section describes the process of selecting an appropriate turbulence model for the current study. In that selection process, the computational results have also been validated through comparing the pressure ratio distributions

with the experimental data under both subsonic and transonic flow conditions with and without film cooling air, including the code's capability of accurately capturing shock waves. Further validations are undertaken by comparing the total pressure losses over the stator and pressure ratio distribution over the rotor. Aerodynamic Characteristics of Stator

Numerical simulations are carried out with the same stator geometry with two different exit isentropic Mach numbers of 0.83 and 0.9 and several different cooling-air-to-primary-stream mass flow ratios (Mc/Mg) ranging from 0.95 to 3.3(Br from 0.75 to 1.75). The mass-averaged total pressure losses due to cooling air injection into the primary stream from the film holes at both the suction and pressure sides are computed and compared with the experimental data of Kopper et al. [6] in Fig. 8. The following results are observed: 1) the total pressure losses of the experimental data increase with the mass flow ratio on both the suction and pressure sides, but with more losses on the pressure side, 2) the numerical results for the suction side injection are overestimated 15-20% with both Mach numbers, and 3) the numerical result at the pressure side is independent of the mass flow ratio, but within 15% of the experimental data.

Mc/Mg

Fig. 8 Comparison of computational results with the experimental data [6] for total pressure losses due to cooling air injection over the stator with different cooling air mass flow ratios and exit Mach numbers. Aerodynamic Characteristic of Rotor

In the rotor, there is no film cooling from the surfaces, rather the film cooling air is ejected at the trailing edge. Figure 9 shows the static pressure distribution along the rotor wall with three mass flow ratios (cooling air/primary flow) of 1%, 2%, and 3%. The rotor exit isentropic Mach number is 1.0. It is expected that the cooling air injection from the rotor’s trailing edge will not significantly change the static pressure distribution over the rotor. The trailing edge-cooled CFD data is close to the experimental data, which did not employ trailing edge cooling.


Fig. 9 Comparison of computational results with the un-cooled experimental data [6] for pressure ratio distribution on the rotor with three trailing edge coolant ejection ratios at exit Ma = 1.0.

Mc/Mg=1

Fig. 10 Static pressure on the 2-D rotor wall under un-cooled and cooled conditions at different exit Mach numbers with coolant ratio 1.0.

From transonic cases with trailing edge cooling air injection, static pressure variations along the rotor wall are computed for exit Mach numbers 0.8, 1.0, and 1.2. The coolant mass flow ratio for each of these cases is 1%. As illustrated in Fig. 10, the CFD results are generally consistent with the experimental data. The cooling air ejected from the trailing edge slots does not noticeably change the static pressure distribution along the rotor under transonic conditions in most places, except for the fact that a slight increase in the static pressure appears near X/Bx = 0.72 at the suction side for Ma = 1.2.

This phenomenon can be explained by the fact that the shock strength emanating from the trailing edge seems to be significantly diminished by the trailing edge coolant injection as in Fig. 11. The shock strength is evaluated as:

U Pa P

∇•

ur

(1)

where Uur

is the local fluid velocity and a is the speed of sound. ∇P and |P| are the local pressure gradient and the magnitude of local pressure, respectively. The evidence of the shock can also be seen in the Mach number distribution shown in Fig. 12.

(a)Uncooled rotor (b) Cooled rotor

Shock Trailing ejection

Diminished shock

Fig. 11 Interaction of shock and rotor trailing edge coolant injection shown in shock strength in rotor passage (Ma =1.2).

The shock occurs near the throat area of the rotor passage, which happens to be formed between the trailing edge and the adjacent rotor suction surface. The Mach number is increased from 0.7 to 1.35 and then 1.50 in the convergent-divergent throat area. The effect of the oblique shock on the static pressure and temperature are shown in Figs. 13 and 14. It seems a bit strange that the trailing coolant's static temperature at 340K is hotter than the temperature of the surrounding air. This is the result of the experiment which provided a total stator inlet temperature at 347K. After acceleration, the static temperature decreases.

(a)Uncooled (b)Cooled

Fig. 12 Comparison of Ma distributions in rotor passage for uncooled and cooled cases at Ma=1.2.

(a)Uncooled (b)Cooled

Fig. 13 Comparison of static temperature distributions in the rotor passage for uncooled and cooled cases at Ma=1.2.


(a)Uncooled (b)Cooled Fig. 14 Contours of static pressure in the rotor passage for un-cooled and cooled cases at Ma=1.2. Penalty of Film Cooling in a Stator Cascade

To further validate the current computational model, a comparison is made between the current computational results and the experimental data from Kopper et al. [6] for additional total pressure losses due to film cooling air flow injection. In addition, the CFD results are also compared with the analytical results derived from the experimental data by employing the 2-D boundary layer theory reported by Kopper et al. [6]. Four 2-D cases are considered, and their conditions are described in Table 5. The additional total pressure losses due to the cooling air injection into the mainstream are represented as the film cooling penalty (CP), defined as:

( ) ( ), , , ,

,

t inlet t exit t inlet t exitcooled uncooled

t inlet

P P P PCP

P

− − −= (2)

Table 3 Comparison of film cooling penalties in total pressure losses between CFD results, experimental data, and 2-D boundary layer theory with Ma =0.82 and Toc/Tog = 0.984

Table 3 shows that the current computational model

predicts the film cooling penalty within 5 - 10% of the experimental data for all four cases, which is even more accurate than the 2-D boundary layer theory prediction conducted by Kopper et al. themselves with their own data.

Through the above validations with the experimental data, it can be concluded that the current CFD model and numerical approach are acceptable to conduct film cooling flow analysis in more complicated cases. (B) 3-D Studies Aerodynamics and 3-D Film Cooling Characteristics at Real Turbine Conditions

Numerical simulations are carried out to predict the influences of exit Mach number and cooling air mass flow ratio on the flow field and film cooling effect in real turbine blade

working environments. To simulate this, the following values are incorporated into the model: the total inlet temperature is 2161 K, the inlet temperature of cooling air is 850 K, the cooling air mass flow ratios are 4.72% and 9.44%, which is equivalent to Br = 1.0 and 2.0, the isentropic exit Mach numbers are 0.84 and 1.5, and the inlet total pressures are 1.8 atm and 4.0 atm, respectively. The walls are assumed to be adiabatic.

Aerodynamic Characteristics

To reveal the development process of the flow structure in the stator passage, five cross-sectional planes from the 3-D cases at X = 0, 0.75 in, 1.0 in, 1.25 in, and 1.5 in are adopted as shown in Fig. 15. The contour plots of total pressure in these five planes are demonstrated in Fig. 15 with exit Mach numbers of 0.84 and 1.5, respectively. In Fig.15(a), it can be seen that regions of large total pressure losses occur near the hub and tip areas due to secondary flows in these two regions. As the exit Mach number increases to 1.5, the sizes of pressure loss regions are reduced by comparing Fig. 15 (a) and (b).

Mainstream

X=1.5in

X=1.25in X=1.0in X=0.75in X=0

(a) Ma =0.84

Mainstream

X=1.5in

X=1.25in X=1.0in X=0.75in X=0

(b) Ma=1.5

Fig. 15 Total pressure distribution in five cross planes for two Mach number cases in stator passage. Figure 16 shows the shock strength in the stator stage at Ma = 1.5. There are two shock impinging locations, marked

Cases Coolant injection

Cooling Penalty (CP %) Mc/Mg(%) Exp. B.L Theory CFD

1 all holes 4.72 0.9 1.78 0.85 2 at PS 1.27 0.14 0.09 0.126 3 at SS 2.49 0.75 1.81 0.68 4 at trail. edge 0.96 0.19 0.10 0.18


as “S1” and “S2,” at the rotor suction side wall. The shock reflections form a diamond pattern, which can also be shown in Fig.17. This phenomenon is a product of the isolated stator stage in the laboratory condition. In other words, the exit of the stator stage is exposed to the atmosphere, which provides a free boundary for reflecting the compression waves. A rise of static temperature on the stator suction side wall induced by the shocks is shown in Fig.18 as S1 and S2.

Shock regions

S2

S1

Fig. 16 Contour shock strength on the mid-span plane in the 3D stator passage at Ma=1.50.

Fig. 17 Contour of static pressure.

Shock affected region

KS2

S1

Fig. 18 Contour of static temperature on the stator.

Film Cooling Characteristics The static temperature distributions on the stator wall

with Ma = 0.84 and Br = 1.0 are shown in Fig. 19. On the suction side, the high temperature region near the end-wall expands toward the middle. This is reasonable because, when the mainstream with high velocity passes through the cascade, the cooling air mixes quickly with the growing wall-vortices in the mainstream. Downstream of the first row of film holes, the hot streaks are very distinct. But, after the second row of film holes, these hot streaks disappear gradually due to the superposition of the film cooling effects from the downstream second and third rows of film cooling holes. On the pressure side, a high temperature region appears between the two rows of film holes, where the cooling air coverage is poor. This phenomenon can be explained by a locally enlarged A-A profile, in which the cooling air near the “B” region lifts off from the wall. The hot streaks on the pressure side persist downstream of the second row of film cooling holes. The averaged film cooling effect in the “C” region near the edges has more uniform cooling coverage than that in the middle.

B

C

C

C

C

SS PS

Fig. 19 Static temperature on the stator wall at Ma=0.84, Br=1.0.

As shown in Fig.16, the flow enters the stator passage going through a very complicated process, including expansion, separation, compression, and especially the interatction with the shock wave on the suciton side. To evaluate the film cooling performance, the adiabatic wall film cooling effectiveness is defined as:

,g aw c

g c

T TT T

η−

=−

(2)

Howerver, note that, in compressible flow, viscous dissipation will add additional heating load to the wall, so the film cooling has to perform better to achieve the same η-value as in incompressible flow.

Figures 20 and 21 exhibit the net film cooling effectiveness of the stator at exit isentropic Ma = 0.84 with Br = 1.0 and 2.0, respectively. When the effect of blowing ratio on film cooling effectiveness is compared, it can be seen that at the pressure side, the area coverage in the case of η ≈ 0.5 with Br = 2.0 in Fig. 21 is larger than that with Br = 1.0 in Fig. 20 and the cooling coverage is also more uniform with a higher coolant mass ratio. At the suction side, the area covered by η = 0.4-0.5 is clearly larger for the higher blowing ratio in Fig. 21 than that of the lower blowing ratio shown in Fig. 20. These differences can be simply explained as being caused by the increased cooling air mass flow.


(a) Pressure side

(b) Suction side

Fig. 20 Film cooling effectiveness on the stator with exit Ma=0.84 and Br=1.0.

(a) Pressure side

(b) Suction side

Fig. 21 Film cooling effectiveness on the stator with exit Ma = 0.84 and Br=2.0.

(a) Pressure side

S2

(b) Suction side

Fig. 22 Film cooling effectiveness on the stator with exit Ma=1.5 and Br=1.0.

When the blowing ratio is kept at Br = 1.0, and the exit Mach number is raised to 1.5, the cooling effectiveness distribution on the stator changes as shown in Fig. 22. In comparison with Fig. 20, it can be found that, at the pressure side, with an increase in mainstream velocity, the cooling effectiveness after the 2nd row of film holes is more uniform and greater in magnitude. This is reasonable, because a higher mainstream momentum can suppress the penetration of the cooling air into the main flow and allows more effective protection of the surface. At the suction side, the difference between these two cases is not significant in most regions: only in the region marked “S2” in Fig. 21 is the difference more obvious. The "S" region, corresponding to the "S2" region in Fig. 18, is affected by the impingement of a weak shock emanating from the trailing edge of a neighboring stator. The film cooling in the region corresponding to the "S1" region in Fig. 18 doesn't show any apparent effects from the weak shock. This could be explained that the intensive film cooling overshadows the minor shock interference on the wall boundary layer.

The film cooling effectiveness along the centerline of the stator and the span-wise averaged film cooling effectiveness are given in Figs. 23 and 24. Two high cooling effectiveness regions on the pressure side are located at the exits of film cooling holes. As stated before, an increase in blowing ratio increases the film cooling effectiveness, and an increase of Mach number results in higher cooling effectiveness on the rotor pressure side in the region between the cooling holes and up to 80% of the chord of the stator. The cooling effectiveness decreases after this film-covered region up to


the trailing edge. On the suction side, a higher Mach number causes a smaller cooling effectiveness extending from film holes up to 30% to 55% of the chord of the stator. However, the cooling effectiveness becomes higher downstream of this region.

Fig. 23 Film cooling effectiveness along the mid-span of the stator wall.

Fig. 24 Spanwise averaged film cooling effectiveness.

CONCLUSION

In this Part 1 of a series of investigations, the computational model and strategy have been validated against experimental data. The pressure-based compressible flow code, Ansys/Fluent is used. The effect of turbulence models on the computational results has been analyzed, and the appropriate turbulence model is selected. Then, the 2-D characteristics of aerodynamic losses in a stationary transonic stator and rotor passage and the 3-D performances of the film cooling at the stator surface are simulated by the validated CFD model and strategy. The following conclusions can be drawn: 1 Four turbulence models are used. Through comparison with

the experimental data, the RSM turbulence and realizable k-ε model offer more accurate predictions than other turbulence models, and both can accurately capture the shock wave in under supersonic conditions. The realizable k-ε model is selected for the remaining study because it is an order magnitude faster than the more elaborate RSM model.

2 The total pressure loss ratios predicted by the validated numerical model are within 15-20% of those in the

experimental data with cooling film injection. In terms of film cooling penalty, the current CFD results are within 5-10% of those in the experimental data.

3 Cooling air ejection at the rotor trailing edge has no apparent influence on the rotor static pressure distribution under transonic conditions, but it reduces shock strength and raises the static pressure under supersonic conditions.

4 Increase in Mach number reduces the end-wall secondary flow losses. Under supersonic conditions, the shocks raise the static temperature on the suction side wall.

5 Film cooling effectiveness increases with increasing blowing ratio and Mach number on the stator's suction side. However, on the pressure side, increasing Mach number only increases cooling effectiveness up to 80% of the chord of the stator: the cooling effectiveness decreases afterwards.

ACKNOWLEDGEMENT The first author is grateful to the Chinese Scholarship

Committee for proving the opportunity to conduct two-years of research at the University of New Orleans. In addition, the project is supported by the Natural Science Foundation of China (Contract No. 91016016). The resources in the University of New Orleans are supported by the Louisiana Governor's Energy Initiative via the Clean Power and Energy Research Consortium (CPERC) under the authority of the Louisiana Board of Regents.

REFERENCE [1] Auxier, T. A., 2001, “Importance of Film Cooling

Techno-logy in Propulsion and Power System”, RTO-MP-069(I).

[2] Goldstein, R. J., Irvine, T. F., Jr. and Hartnett, J. P.,1971, “Film Cooling”, Advances in Heat Transfer, 7, pp.321-380.

[3] Han, J. C., 2004, “Recently Study in Turbine Blade Cooli-ng”, International Journal of Rotating Machinery, 10(6) pp. 443-457.

[4] Arts, T., 2001, “Film Cooling: What Did We Learn from Our Measurement?”, Heat Transfer in Gas Turbine System, Annals of the New York Academy of Science. 934, pp. 126-134.

[5] Barigozzi G., Perdichizzi A., Ravelli S., 2012, “Pressure Side and Cutback Trailing Edge Film Cooling in a Linear Nozzle Vane Cascade at Different Mach Numbers”, J. of Turbo-machinery, vol. 134, 051037, pp.1-10.

[6] Kopper, F. C., Milano, R., Davis, R. D., Dririg, R. P., Stoeffler, R. C., 1981, “Energy Efficient Engine High Pressure Turbine Component and Integration Program: High Pressure Turbine Supersonic Cascade Technology Report”, NASA CR-165567.

[7] Newman, A., Xue, S., Ng, W., Moon, H.K., and Zhang, L. 2011, “Performance of a Showerhead and Shaped Hole Film Cooled Stator at High Freestream Turbulence and Transonic Condition,” ASME paper GT2011-45142.

[8] Ochs, M., Schulz, A., Bauer, H. J., 2007, “Investigation of the Influence of Trailing Edge Shock


Waves on Film Cooling Performance of Gas Turbine Airfoils”, ASME paper GT2007-27482.

[9] Rehder H. J., 2012, “Investigation of Trailing Edge Cooling Concepts in a High Pressure Turbine Cascade – Aerodynamic Experiments and Loss Analysis”, ASME J. Turbomachinery, 134, 051029( 1-11)

[10] Nirmalan, N. V., Hylton, L. D., 1990, “An experimental Study of Turbine Stator Heat Transfer with Leading Edge and Downstream Film Cooling”, ASME Journal of Turbomachinery, 112,pp.477-487.

[11] Laskowski, G. M., Felten F. N., 2010, “Steady and Unsteady CFD Simulation of Transonic Turbine Stator Wakes with Trailing Edge Cooling”, ECCOMAS CFD.

[12] Lee, K. D., Kim, K.Y., 2010, “Shape Optimization of a Fan-shaped hole to Enhance Film-cooling Effectiveness”, International Journal of Heat and Mass Transfer, 53, 2996-3005.

[13] El-Gabry, L., Heidmann, J., Ameri, A., 2009, “Numercial Analysis of Film Cooling at High Blowing Ratio”, NASA TM2009-215517.

[14] Dhungel, S., Philips, A., Ekkad, S. K., Heidmann, J. D., “Experimental Investigation of a Novel Anti-Vortex Film Cooling Hole Design”, ASME Paper, GT-2007-27419.

[15] Larsson, J., 1997, “Turbine Blade Heat Transfer Calculation Using Two-Equation Turbulence Models”, Journal of Power and Energy, 211(3) pp. 253-262

[16] Calzada P. de la., Alonso A., 2003, “Numerical Investigation of Heat Transfer in Turbine Cascades with Separated Flows”, ASME J. Turbomachinery, 125, pp. 260-266.

[17] Hunter C.A., 1998, “Experimental, Theoretical and Computational Investigation of S;leparated Nozzle Flows”, AIAA Paper No.AIAA 98-3107.

[18] Incopera, F. D., Dewitt, D. P., Berg00man, T. D., Lavine, A. S., 2007, “ Fundamental of Heat and Mass Transfer”, 6th John Wiley & Sons.

[19] Launder, B. E., Spalding, D. B., 1972, “Lectures in Mathematical Models of Turbulence”, Academic Press, London, England.

[20] Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal, 32(8), 1598–1605, August 1994.

[21] Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., Zhu, J., 1995, “A New-Eddy-Viscosity Model for High Reynolds Number Turbulent Flows-Model Development and Validation”, Computers Fluids, 24(3), 227–238.

[22] Launder, B. E., Reece, G. J., Rodi, W., 1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure”, J. Fluid Mech., 68(3), 537–566.

[23] Gibson, M. M., Launder, B. E., 1978, “Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer”, J. Fluid Mech., 86, 491–511.

[24] Launder, B. E., 1989, "Second-Moment Closure: Present and Future?" Inter. J. Heat Fluid Flow, 10(4), 282–300.

[25] Ansys Help Document Version 12.0, 2009.

Part 1 GT2013-94544 1-10-2013 final submittedeccc.uno.edu/pdf/Xu-Wang GT2013-94544 Part1...

Documents

Transcript of Part 1 GT2013-94544 1-10-2013 final submittedeccc.uno.edu/pdf/Xu-Wang GT2013-94544 Part1...