Numerical Analysis of Flow through Shrouded Turbine Cascade

(1)

ISSN : 2319 – 3182, Volume-2, Issue-3, 2013

1

Numerical Analysis of Flow through Shrouded Turbine Cascade

Vinoth Kumar Annamalai & S. Thanigaiarasu

Department of aerospace engineering, MIT Anna University Chennai.

E-mail : [email protected], [email protected]

Abstract – The aim of the work is to estimate the secondary flow losses through the gap between the shrouded turbine rotor blades. Aerodynamic losses occurring in flow such as profile, secondary flow and leakage were analyzed. The numerical results of flow over a single shrouded turbine rotor blade, cascade analysis of two shrouded turbine rotor blade with zero gap and leakage analysis through the 2mm z-gap of the shrouded turbine rotor blade are presented.

First, a single shrouded turbine rotor blade was analyzed and the pressure coefficient on the surface of the blade at midsection of blade is taken as reference. For this, the geometry of a shrouded HP turbine rotor is chosen.

GAMBIT software is used for designing and analyzed using FLUENT software. Secondly cascade analysis was also carried out using the same procedure and the pressure coefficient is compared with the reference pressure coefficient profile and found that changes in the pressure coefficient on the blade surface. Finally the two shrouded turbine rotor blades with 2mm z-gap between the shrouds are created and analyzed using the same procedure and the pressure coefficient was compared with the reference pressure coefficient profile and found that decrease in the pressure coefficient on the blade surface near the shroud is because of the leakage of flow through the z-gap between the shrouds. The leakage lessens the end wall boundary layer separation near shroud of the turbine rotor blade with 2mm z-gap.

Keywords – shroud, cascade, end-wall boundary layer, wall Y+

I. INTRODUCTION

In modem gas turbine engines, the gap between rotating turbine blade shrouds are small, and sometimes are even smaller than 1 mm. The shroud gap of turbine rotor causes the leakage through the gap, and it is important to be able to predict static pressure coefficients on the blade surface to optimize the gap between shrouds so the performance does not suffer too great a loss. The rapid development of high-temperature turbines has vastly suppressed the fundamental research of the flow field in the gap between the shrouded rotor blades. The first turbine stage, has the most extreme fluid-thermal conditions in the entire turbine, and is

characterized by a periodically unsteady three- dimensional flow field.

The HP turbine airfoil profile coordinates [6] were taken for the design of shrouded turbine blade. The shrouded HP turbine blade airfoil profile coordinates are in the form of XYZ coordinate system. A single stage high-pressure turbine blade includes an airfoil having a profile substantially agree at least an intermediate portion of the Cartesian coordinate values of X, Y and Z. The X and Y values are distances, which when smoothly connected by an appropriate continuing curve, define airfoil profile sections at each distance Z. The profile sections at each distance Z are joined smoothly to one another to form an airfoil shape. The airfoil profile of HP turbine blade at mid-span is shown in the fig 1.

Fig. 1: HP Turbine Blade Airfoil

The shape of z-notch shroud profile coordinates [5]

were taken for design of z- notch shroud at the tip of the HP turbine blade. In one embodiment, a turbine bucket includes: a tip shroud with a front edge and a following edge, including a Z-Notch profile according to the Cartesian coordinate values of X, Y and Z are used. In which the coordinate values are dimensional values representing a distance from an origin of an internal coordinate system for the bucket; and in which the X and Y values are connected by smooth continuing arcs, the Z-Notch profile is defined as shown in the fig 2.

(2)

2 Fig. 2: z-notch shaped shroud profile

II. COMPUTATIONALMETHODOLOGY A. Physical Model

The 3D modeling scheme was adopted in GAMBIT and it was analyzed using FLUENT. A turbine cascade model with zero degree flow angle of incidence was designed. The physical model is defined as follows:

Parameters Dimensions Blade height h = 28.72475mm

Chord C = 20.65586mm hub radius R_b = 75.44975mm Number of blades, n = 3

Blade to blade angle = 8.7321 deg Blade profile = Pratt and Whitney

turbine airfoil

The blade dimensions are taken from Ref. [6]. The model is shown in figure-3.

Fig. 3 : Turbo Volume Model for Cascade Analysis B. Numerical Approach

The computational grid used for the simulation of turbine blade cascade is shown in Figure-4. By using the periodic function of the blades, only two blades of turbine disc with required mesh refinements is created.

A nominal three dimensional structured grid with 4.26

lakh cells is selected. Dry air using ideal gas approximation is used as the working fluid with constant specific heats with γ =1.4. k-Ѡ turbulence model is chosen.

Fig. 4 : Meshed Turbo Volume Model for Cascade Analysis

C. Boundary Conditions

The turbo volume was considered as a flow domain.

The air flow comes into the flow domain (turbo volume) from the inlet face and exit through the outlet face and the gap between the shrouds. The face ahead of the pressure and suction side of the blade was given as periodic face. The top and bottom face was considered as shroud and hub so wall boundary type was given to it.

The pressure and suction side of the blade is also given the wall boundary type.

D. Solving Procedure

The FLUENT software was used for computational analysis of flow over the turbine blade. The density based solver was used since we have to analyze the compressible flow over the turbine blade. The flow over the blade was assumed as inviscid to find pressure coefficient of the blade only because of the profile shape. The density of the gas was taken as ideal gas. The inlet and outlet boundary conditions were given as mentioned in the boundary conditions. The solution was initialized by computing from inlet with the x-velocity of 136m/s. The iterations were carried out for convergence of the solution.

The grid independence test is done which involves transforming the generated physical model into a mesh with number of node points depending on the fineness of the mesh. The various flow properties were evaluated at these node points. The extent of accuracy of result depended to a great extent on how fine the physical domain was meshed.

After a particular refining limit the results changes no more. At this point it is said that grid independence is achieved. The results obtained for

(3)

3 this mesh is considered to be the best. This mesh formation was done with GAMBIT

III. RESULTSANDDISCUSSION A. Pressure Coefficient Of Turbine Blades

The pressure coefficient of over the blades of the turbine rotor stage is shown in the figure-5. The turbine rotor stage consists of 43 blades arranged with the angular orientation of 8.73 degrees between each blade.

From the figure-5 it is observed that, the pressure coefficient is maximum at the leading edge of the blade which represents the stagnation point of the blade. The pressure coefficient is minimum at the suction side which represents the velocity is maximum at that location.

Fig. 5 pressure coefficient distribution along the span of the blade

The pressure coefficient variation along the span of the blade is plotted in figure-5. It is observed the pressure coefficient decreases near the hub and shroud of the blade. It is observed that the decrement in the pressure is due end wall boundary layer creation near the hub and shroud of the blades.

Fig. 6: Pressure Coefficient at the Mid-Section of the Blade The pressure coefficient variation over the blade surface at the midsection of the blade is shown in figure-

6. From the figure, it is observed that, the pressure coefficient is maximum at the leading edge of the blade which represents the stagnation point of the blade. The pressure coefficient is minimum at the suction side and near the trailing edge which represents the velocity is maximum at that location.

The contour of pressure coefficient on the suction side of the blade is shown in the figure-7. It is observed form the contour that the pressure coefficient is minimum and there is a small variation in the pressure coefficient near the hub and shroud of the blade, due to end wall boundary layer formation and wake formation because of the highly curved surface of the blade. The contour of pressure coefficient on the pressure side of the blade is shown in the figure-8.

Fig. 7 : Pressure Coefficients on Suction Surface of the Blade

Fig. 8 : Pressure Coefficient On The Pressure Surface Of The Blade

It is observed form the contour that the pressure coefficient is higher than that of suction side and there is a small variation in the pressure coefficient near the hub and shroud of the blade, because of end wall boundary layer formation and wake formation because of the highly curved surface of the blade.

(4)

4 B. Cascade Analysis Of Turbine Blade Pressure

Coefficients On Surface Of Blade

The pressure coefficient variation over the cascaded blade surface at the midsection of the blade is shown in figure-9. From the figure, it is observed that the pressure coefficient is maximum at the leading edge of the blade which represents the stagnation point of the blade. The pressure coefficient is minimum at the suction side and near the trailing edge which represents the velocity is maximum at that location.

Fig. 9 : Pressure Coefficient On The Cascaded Blade Surface The contour of pressure coefficient on the pressure side of the blade is shown in the figure-10. It is observed form the contour the pressure coefficient is minimum at the center of the blade because of wake formation on the blade and there is a small variation in the pressure coefficient near the hub and shroud of the blade, because of end wall boundary layer formation on the surface of the blade. The contour of pressure coefficient on the suction side of the blade is shown in the figure- 10. It is observed form the contour the pressure coefficient is lower than that of pressure side and there is a small variation in the pressure coefficient near the hub and shroud of the blade, because of end wall boundary layer formation and wake formation because of the highly curved surface of the blade.

Fig. 10(b) : Cp distribution on suction surface

Fig. 10(b) : Cp distribution on pressure surface C. End Wall Boundary Layer Separation On Cascaded

Blades

End-wall loss is also known as secondary loss, and is related to the passage and the horseshoe vortices. Due to these loses, the pressure coefficient near the hub and shroud of the blade decreases as shown in the figure-11.

Fig. 11 : End Wall Boundary Layer Separation D. Leakage Analysis Through Shroud Z-Gap Pressure

Coefficients On Surface Of Blade

The pressure coefficient variation over the surface of shrouded turbine blade with 2mm z-gap at the midsection of the blade is shown in figure-12. From the figure, it is observed that, the pressure coefficient decreases on the suction side of first blade because of the gap between shrouds.

(5)

5 Fig. 12 : Pressure Coefficient of shrouded blade with

2mm z-gap (mid-section)

Due to the gap near the shroud, the end wall boundary layer separation decreases as shown in the pressure coefficient contour in figure-13. The first fig shows the Cp contour on pressure surface and second fig shows the Cp contour on suction surface.

Fig. 13 Cp distribution on blade surface

E. Comparison Of Shrouded Blades With Gap And Without Gap

From the above fig 14 it is observed the pressure coefficient on pressure side of blade 1 lowers because of the large end wall boundary layer formation on the cascaded blades without gap but on the shrouded blade with 2mm gap the pressure coefficient is same as that of the reference pressure. It is also observed the pressure coefficient on suction side of blade 1 increases due to the large end wall boundary layer formation on the cascaded blades without gap but on the shrouded blade with 2mm gap the pressure coefficient is same as that of the reference pressure. Thus due to 2mm z-shroud gap on the turbine blades shrouds the end wall boundary layer is reduced by the leakage of primary airflow through the 2mm gap between the shrouds.

Fig. 14: Cp Of Blade With Gap And Without Gap IV. CONCLUSION

The effect of the turbine rotor blade shroud z-gap on the pressure coefficient distribution on the surface of the blades is analysed. It is found there is decrease in the pressure coefficient near the shroud of the turbine blade.

Although there is a decrease in the pressure coefficient on the surface of the blade but it reduces effect of end wall boundary layer separation near the shroud of the turbine blade because of the leakage of primary flow through the gap between the shrouds.

V. FUTUREWORK

The present computational work has to carried out on the models with different shroud gaps such as 0.25 mm, 0.5mm, 0.75mm, 1mm, 1.25mm, 1.5mm and 1.75mm to find out the optimum gap size for better performance of the blade in the engine. Experimental work has to be done by creating the model and analyze the model with the same conditions as that of computational analysis. The experimental results can be analyzed with the computational results for verification of results. If both the results are same it can be implemented in turbine engines for various applications

VI. REFERENCES

[1] Villiers, J. D., & Govender, S. (2003). validation of a CFD Static Pressure Distribution against Experimental Data for a Turbine. R & D Journal, 19(3), 3–5.

[2] Ameri, A. A., Park, B., & Steinthorsson, E.

(1996). Analysis of Gas Turbine Rotor and Shroud Heat Transfer Blade Tip (p. 10).

[3] Maier et al, inventor; 1991 Jan.11. Gas turbine blade shroud support. United States patent US 5,022,816.

(6)

6 [4] Remo Marini, inventor; 2012 Jan. 31.

Compressor Turbine Blade Airfoil Profile. United States patent US 8,108,044 B2.

[5] Wilmortt G. Brown, inventor; 1989 Mar. 28.

Shroud gap control for integral shrouded blades.

United States patent US 4,815,938.

[6] US 7,306,436 B2 by Sami Girgis, Montreal (CA) and Constantinos Ravanis, Brossard (CA), March 2.2006.

NOMENCLATURE M_a Mach number P₀ Total pressure (kPa) T0 Total temperature (K) P_i inlet static pressure (kPa) C_P Pressure coefficient C chord

H Blade height R_b Hub radius

γ ratio of specific heats

