Heavy-duty gas turbine 3D blade modelling and flow field analysis

Hydrogen-fuelled heavy-duty gas turbine is an important trend of gas turbine due to its low emission characteristics. Due to the change of components and thermodynamic properties of the fuel, the physical properties of the working fluid of the turbine will change and affect the performance of the gas turbine. In this study, through 3D scanning and inverse modelling, the parametric models of the turbine blades were obtained. CFD analysis was conducted to analyse the change of thermodynamic performance and flow field under different fuel, which is natural gas, 50% natural gas and 50% hydrogen and hydrogen. The result of the CFD indicated that the efficiency of natural gas fuelled working flux is 92.86%, and decreased by 0.19% and 0.83% with hydrogen doped in. It is analysed that though the increased magnitude of relative velocity with hydrogen doped in, the increased flow attack angle of the rotor, from -4.74°, to -3,61°, to -1.88° with hydrogen doped in, caused the split of rotor leading edge cooling air and decreased the efficiency of the turbine stage. Modification of blade metal angle could boost the efficiency of the turbine stage under hydrogen-doped fuel.


Introduction and literature review
Due to low emission and improved system stability, hydrogen-fuelled heavy-duty gas turbine is an important trend in gas turbine industry, those gas turbines are usually fuelled by syngas or hydrogen byproduct from the industry [1].However, due to high flaming speed, increased working flow amount and increased turbine inlet temperature [2], gas turbines need to be modified or optimized to match the flow from the combustion chamber.This study focus on parameterize and inverse model of the blade of the turbine so as to analyse the flow field of the turbine under different fuel and main flux.
Turbine blade profile could be parameterized by several methods.Among those non-uniform rational B-spline (NURBS) is the most common method [3] [4], which uses NURBS to fit the suction surface and the pressure surface.Lida proves that NURBS knot insertion is an effective way to reconstruct the blade contour [5].Alternate NURBS method divide either suction surface and pressure surface into two sections, divided by the point of maximum width of the blade, so as use 4 NURBS to describe the blade.Pritchard method uses 11 parameters to describe the blade profile [6].Kler used cubic splines to describe the blade and did joint optimization for power plant cycle parameter and the gas turbine [7].Agromayor improved the method of the parameterization of the blade geometry to allow gradient based shape optimization work flows and fit the tolerances of current manufacturing technologies [8].
NURBS method focus on the molded lines of the blade, while Pritchard method focus on the digitized design parameter of the blade.In this study, both methods are referenced, the final output parameters match the blade design profile in Numeca.
For hydrogen fuelled gas turbine research, current research mainly focus on the thermodynamic analysis of the turbine [9], or the mechanism of turbine blade cooling [10], or the study on gas turbine combustion chamber with hydrogen-rich fuel [11], few literature has mentioned the 3D CFD analysis of turbine under different fuel with cooling air injected so as to analyse the performance of the turbine under different working main flux and to achieve the through-flow matching of the gas turbine.
This paper introduced the method to extract blade profile and inverse model of the blade from an actual turbine blade to analyse the performance of turbine stage 1 under different working flux with cooling air injected.The aim is to observe the flow field and performance parameters of the turbine stage 1 under different fuel condition, discuss the reason of performance change under different working flux and find out whether need to modify the blade to boost efficiency of rematch the through flow design.

Blade profile extraction process
In this study, the blades are obtained from an actual 9FA gas turbine power plant in Hangzhou, China, The turbine of GE 9FA gas turbine has three stages, which is three rows of stators and three rows of rotors.
As shown in Figure 1.(a),The blades were scanned by Creaform 3D scanner, which has 15 laser crosses, of 0.025mm accuracy and of 0.064mm volumetric accuracy, with reflective markers sticking on the blade.
As shown in Figure 1.(b),The point cloud obtained from 3D scanning was pieced, smoothed, denoised, and processed by Geomagic to inverse model the blade and get the blade profile at typical blade heights (10%, 50%(mean radius), 90%).
Then the blade profile is analyzed in Matlab to perform parameter extraction for all blades, and extract the parameterized blade profile, the method is in chapter 2.2, as shown in Figure 1.(c).
At last, the blade profile is stacked and the blade is inverse modelled with the extracted blade profile parameter, as shown in Figure 1.(d).

Blade profile extraction method
The parameterized blade profile is shown in Table 1, all angles listed in the table are the angle with the flow direction, in which: 1) Piece two blade profile together and define the two blades as blade 1 and blade 2, all the parameters are extracted from blade1 except for the pitch and the radius of throat.
2) Divide the blade section into four areas: leading edge circle, trailing edge circle, suction surface and pressure surface.This study used least squares fitting method the separate the leading edge circle ( ) Le Leading edge and the trailing edge ( ) Te Trailing edge circle from the blade section.Then the rest of the blade is divided into the pressure surface ( ) Ps Pressure surface and the suction surface ( ) l Ss Suction surface .In this step, LE R and TE R could be acquired by the least squares fitting method.
3) The chord is defined by the maximum distance between the points of the leading edge and the points of the trailing edge.The blade metal angle is the angle between the chord and the X axis.The axial chord is the length of the chord's projection on the X axis.The chord, the attack angle and the axial chord could be acquired by following: The maximum radius is calculated by half of the maximum of the minimum distance between  1 shows the blade profile of all the stators and rotors at mean radius, all the angles listed in the table are the angle with the flow (axial) direction.

CFD analysis
After the inverse modelling of the blade, the first stage of 9FA gas turbine is analysed in Numeca to study the performance of the first stage of the turbine under different Hydrogen doped ratio fuel.

Meshing and the cooling holes
After the blade profile extraction is completed, the blade model for stage 1 is reconstructed to perform CFD analysis.The entire mesh has 13.184 million grids, all the grids are structured(hex) grids. in which the stator has 8.203 million girds and the rotor has 4.980 million grids.Due to the large number of cooling holes in the stator, and the meshes near the cooling holes need to be dense, the number of meshes of the stator is 64.7% larger than that of the rotor.The row of the stator has 48 blades, and the row of the rotor has 92 blades.Y+ of the mesh is less than1, and mesh has passed grid independence validation.5 rows of cooling holes are considered.The Stator has 3 rows of cooling holes, 2 rows are staggered film cooling holes at the pressure surface near the maximum width of the blade, these two roles are for the film cooling of the pressure surface, and 1 row is for the trailing edge.The rotor has 2 rows of cooling holes, 1 row is at the leading edge and is for the film cooling, and 1 row is for the trailing edge.

Boundary conditions and fluid model
The mesh of the calculation is accomplished by Numeca Autogrid5, and the calculation is accomplished by Numeca Fine/Turbo, and the post processing is accomplished by Numeca CFview.The turbulent model of the analysis is SA(Spalart Allmaras).Only 1 blade for each the stator and the rotor blades is modeled and meshed, the interface between the rotor and the stator is set as conservative coupling.The tip clearance of the rotor is considered and set to 0.2mm.
Because conventional initial solution may cause the calculation do not converge, the cooling hole inlet is set as solid wall first to run the calculation, and the result of which is used as the initial solution of the calculation with the cooling air.This will greatly improve the rate of convergence of the iteration.
The whole calculation has 3 inlet and 1 outlet.The main flux inlet is set as total pressure(1.537MPa)and total temperature(1691K) inlet, the stator and rotor cooling hole inlet is set as mass flow inlet, the mass flow set is for all the blades of the row, and the mass flow of each cooling hole will be distributed by NUMECA algorithm.the boundary condition of the stator and the rotor cooling hole inlet is set as mass flow and static temperature inlet, the boundary condition of the cooling holes is decided by the fact of modelling, meshing, and reference [9] [10] data about stator and rotor cooling.The outlet condition is set as static pressure at 0.9MPa and is of radial equilibrium at reference radius 1.338m(mean radius of the rotor).The mass ratio of the main flux and the cooling air is shown in Table 3, the mass flux is obtain by 1D thermodynamic gas turbine system calculation, in which the TIT (Turbine Inlet Temperature) is set as the same (1691K), and the compressor and the pumping ratio of the cooling air are also set as the same.The mass ratio of CO2 at the main flux inlet is decreased from 7.14%, 5.54%, to 0.00%, and the mass ratio of H2O is increased from 5.84%, 6.79% to 10.10% for 100% natural gas fuelled, 50% Natural Gas and 50% Hydrogen fuelled, and 100% Hydrogen fuelled condition.As for the cooling air, because it is pumped from the compressor, its composition is set as dry air-76.5% of Nitrogen and 23.5% of Oxygen.

Fluid field performance
Figure 3 shows the static temperature and static pressure of the stage under different fuel at the mean radius.Because of similar boundary conditions, the flow field only have slight differences.Judging from the static temperature field, the staggered film cooling holes of the stator has established a low-temperature area near the stator.In the condition of 100%NG and 50% NG+50%H2, the cooling air from leading edge trailing hole of the rotor mainly goes to the pressure side of the rotor, but in the condition of 100%H2, the cooling air split and goes to both the pressure surface and the suction surface, this will be discussed in Chapter 4.3.Both the stator and the rotor foamed a trail behind the trailing edge of the blade.
From the static pressure field, injection of cooling air caused local low-pressure surface near the blade surface, this is similar in all the fuel conditions.The streamline position of the cooling holes of the stator aligns with the position that the static pressure magnificently decreases.

Discussion
To discuss why the mass fraction change of the main flux caused the decrease in stage isentropic efficiency, the mass fraction of water vapor is inspected to research the mixing of the cooling air and the main flux, for cooling air is dry air and do not include water vapor, and all the main flux under different conditions includes water vapor.Figure 4 shows the streamline of the leading edge cooling hole of the rotor and the rotor streamline, the angle of the main flux and the relative speed of the rotor inlet has changed with the main flux mass fraction.In the condition of 100%H2 fuel, the changed flow angle caused the cooling air of the leading edge split to the suction surface and thus caused the decreased turbine stage efficiency.As shown in Table 1, the blade leading edge angle of the rotor is 48.02°, and the average flow angle at the rotor inlet is 52.76°, 51.63°, 50.90° for 100%NG fuel, 50%NG+50%H2 fuel, and 100%H2 fuel, as shown in Table 4, thus caused the increase of flow attack angle at rotor inlet from -4.74°, -3.61°, to -1.88°, and caused the split of the rotor leading edge cooling air under 100%H2 fuel condition, as shown in Figure 4.(f).
The average magnitude of relative velocity at rotor inlet is 208m/s, 212m/s, 226m/s, 50%NG+50%H2 fuel increased 1.9% compared to that of 100%NG fuel, 100%H2 fuel increased 8.7% compared to that of 100%NG fuel.And the average rothalpy(rotational stagnation enthalpy) at rotor inlet is 1.45MJ/kg for all the conditions.For the rothalpy are the same for all the conditions, and larger flow speed is advantageous for turbine performance, it is inferred that increased flow attack angle caused the decrease in efficiency of the turbine stage.Proper minus flow attack angle is proved to be good for turbine performance, and increased flow attack angle caused more cascade loss of the blades, and caused the split of leading edge cooling air and decreased power output.

Conclusion
This research accomplished the full path to acquire blade profile from actual blade from gas turbine.This simplified ten-parameter model is fit for blade reconstruction and CFD analysis.The mean camber line is also acquired in the research.The blade profile of all the 6 rows of blades are obtained.These parameters are sufficient for parameterized optimization of the turbine blades under different operating conditions and fuels.CFD analysis is conducted to analyse the change of thermodynamic performance and flow field under different working flux of different fuel, which is natural gas, 50% natural gas and 50% hydrogen, and hydrogen.
• The result of CFD analysis indicates that the efficiency of the first turbine stage under the same boundary conditions will decrease by 0.19% and 0.83% for 50%NG+50%H2 fuel and 100%H2 fuel compare to 100%NG fuel, the pressure ratio are almost the same, and the mass flow also decreased by 0.61% and 2.63% for 50%NG+50%H2 fuel and 100%H2 fuel compare to that of 100%NG fuel, which is 593.18kg/s.• The analysis of the flow, the relative velocity, and the rothalpy indicates that the rothalpy are almost the same for different main flux, and the relative velocity increased with more Hydrogen doped into the fuel.The decreased flow angle caused the flow attack angle of the rotor increased from -4.74°, -3.61°, to -1.88° for 100%NG fuel, 50%NG+50%H2 fuel, and 100%H2 fuel and caused the split of the rotor leading edge cooling air under 100%H2 fuel condition, thus caused the decrease of turbine stage efficiency.• According to the result of this study, it is concluded that changing the blade metal angle or modifying the rotor blade with hydrogen doped into the fuel could boost turbine stage efficiency.

Figure 1 .
Figure 1.Extracting the blade profile and inverse modelling of actual turbine blade (rotor for stage 1).

LER--
Radius of leading edge TE R -Radius of trailing edge max α -Angle of leading edge β -Angle of trailing edge γ -Blade metal angle throat R Radius of throat The methods of blade profile extraction are as follows:

k 5 ) 6 )
Ps and all the points of the suction surface.The maximum radius of the blade could be acquired as followingLet the leading edge and trailing edge arc center and the center of leading edge circle and trailing edge circle be , le te   ,the blade angle are the angle between , le te   and the X axis. the inlet and outlet angle of the blade are as follows: For the pitch and the radius of the throat, both two blades are considered, the points of blade 2 are named as 2 m Blade , the pitch is defined by the length of the vector's projection on the Y axis, which vector is formed by the point of the minimum X coordinate in k Ps and 2 m Blade .The radius of the throat is calculated by half of the minimum of the minimum distance between k Ps and all the points of the blade 2. Pitch and the radius of throat could be acquired by: [(min ( 2 )), (min ( ))] [0,1]

Figure 3 .
Figure 3. Static temperature and static pressure under different fuel at mean radius.

Figure 4 .
Figure 4. Main flux and cooling air blending of the rotor at mean radius.

Table 1 .
Stator and rotor blade profile at mean radius.

Table 3 .
Main flux and injected cooling air fluid model mass fraction as boundary conditions.The balance flow of the 100%NG fuel is 593.18kg/s, of 50%NG+50%H2 fuel is 589.56kg/s,decreased by 0.61%, of 100%H2 fuel is 577.59kg/s,decreased by 2.63% compared to 100%NG fuel.
4.1.Thermodynamic performanceAfter the calculation converged, the thermodynamic performance of the turbine stage could be acquired, the isentropic stage efficiency of 100%NG fuel is 92.86%, of 50%NG+50%H2 fuel is 92.67%, decreased by 0.19%, of 100%H2 fuel is 92.03%, decreased by 0.83% compared to 100%NG fuel.The pressure ratio of the stage under different fuel are almost the same.

Table 4 .
Thermodynamic performance of the turbine stage under different fuel.

Table 5 .
Flow parameter at rotor stage 1 inlet.