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Introduction

Internship at Aero-Thermal department for a month
Experience about axial turbine design
Utilizing MS Excel as a tool for theoretical turbine design
From thermodynamic parameters to blade geometries
Results with physical possibility

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Outline

How does an Axial Turbine work?
Turbine model calculations
Loss calculations
Free Vortex Design
Streamline shift
Visualization and diagrams
Degree of reaction’s effect
Blade geometry profiling

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How does an Axial Turbine work?

Generating energy by fluid flowing through passage
Air expands, static pressure drops, increase of kinetic energy being used
Used in air-breathing jet engines to generate rotation for compressor
Two sections of a turbine stage;

Stator row – Increasing kinetic energy of fluid
Rotor row – Converting fluid kinetic energy to shaft kinetic energy

Figure 1 – Single stage axial turbine [1]

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Turbine model calculations

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Velocity diagrams at stator and rotor,

Figure 2 – Turbine stage velocity diagram [2]

C = V : Absolute velocity

W : Relative velocity

U : Peripheral velocity (by shaft rotation)

Stators and rotors angle the flow, creating relative velocities
No work is done by stator and rotor, in absolute and relative parameter aspects, respectively
The following notations are used for a turbine stage,

(1) – Stator inlet
(2) – Stator exit / Rotor inlet
(3) – Rotor exit

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T-s diagram of a turbine stage,

Figure 3 – Turbine stage T-s diagram [3]

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(St. : Stator, Ro. : Rotor)

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In stator inlet, axial flow passes, no relative velocity or flow angle
Total parameters higher than static parameters, as their definition
Inlet Mach number has been assumed as a boundary condition

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Model’s parameters match with design control guidelines mostly
The difference showing values don’t vary much from their targets

Figure 4 – Axial turbine stage design control guidelines [3]

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Loss calculations

For a turbine model, using blading efficiencies is necessary for an accurate design
Blading efficiencies show losses occurring at blade rows and estimate realistic results
4 types of losses can occur for a blade row in a turbine stage (according to Kacker & Okapuu [5]),

Profile losses
Secondary losses
Trailing edge losses
Tip clearance losses

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Figure 5 – Losses in a turbine stage’s blade row [4]

Profile losses, result of boundary layer growth over the blade surface in a fluid flow. Additionally, includes flow separation losses if occurs
Secondary losses, caused by secondary flow arising from boundary layers on curved blade surfaces being turned by the rotating shaft
Trailing edge losses, resulting from inside (pressure side) and outside (suction side) of blade profiles’ boundary layers having different pressure coefficients
Tip clearance losses, caused by fluid flow being disturbed and interacting with the outer (casing) boundary layer at blade tips

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Results obtained by this correlation,

All the particular losses have increased at rotor row. Caused by rotor blade profiles being designed for the angled flow in opposite direction, transferring flow’s kinetic energy to shaft by reaction
Higher Mach numbers present between rotor inlet and exit, contributes to higher losses
Inputting resulting efficiencies, obtaining new better accuracy efficiencies, creating a converging iterative process, which resulted with above values after several steps

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Turbine stage efficiency (total-to-total) been calculated as 85.1%, which is around enough for a high pressure turbine. This number can be improved by further optimization
The flow coefficient for stator row higher than usual (casually max 1.3) which can be a result of low row efficiency or inaccurate peripheral velocity assumption
We have obtained a 24.6 MW high pressure turbine with results on average levels

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Free Vortex Design

Figure 6 – Free & forced vortex velocity distributions [6]

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Streamline shift

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Flow Mach numbers increase from tip to hub
Peripheral velocity only affects relative velocities
Relative velocities increase more, cause of changing peripheral velocity

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Total temperature at (2) constant, cause of no work
Generally, temperatures increase from hub to tip
Relative total temperatures are close but different, cause of shifting streamlines

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Visualisation and diagrams

Charts of,

Velocity diagrams
T-s diagram
Meridional view of the model

By blade heights
By blade radiuses

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Velocity diagrams for blade tips, mean lines and hubs

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T-s diagram

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Calculation of stagger angles for meridional views
Estimated by Kacker & Okapuu’s chart,

Figure 7 – Stagger angle geometric definition [5]

Figure 8 – Stagger angle estimation chart [5]

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Meridional views

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Degree of reaction’s effect

Figure 9 – Degree of reaction’s effect on rows [3]

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Blade geometry profiling

Profiling stator and rotor rows’ blades
Geometries optimized for specific cases
Better understanding of manufacturability visually
Blade profile ready for computational fluid dynamics analyses
Utilized Pritchard’s [7] axial turbine airfoil geometry model

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Figure 10 – Independent geometric parameters of Pritchard’s model [7]

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Integrating of algorithm into MS Excel
Difficulties,

Circular arc function not given and is over-defined with two points and two local blade angles (Point No. 1 & Point No. 2)
At axial inlet flows, Point No. 2 too close to Point No. 3, resulting extreme curvature for third order polynomial and local blade angle
Difficult to profile for high turning angles
Can create non-continuous surface joinings

Improvements done for those reasons,

Calculating two under-defined circular arcs at Point No. 1 & Point No. 2 and adjusting exit half-wedge angle for a single circular arc
When Point No. 2 & Point No. 3 are really close,

Linear surface profiling between Point No. 2 & Point No. 3
Local blade angle correction at Point No. 2

Figure 11 – Five key points and surface functions of Pritchard’s model [7]

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Targets for stator and rotor blade profiles,

Inlet local blade angle ~ inlet flow angle
Exit local blade angle ~ exit flow angle
Exit half-wedge angle ~ 0.5 * Unguided turning angle
Unguided turning angle ~ 0-16 degrees, 8 degrees optimum
Radiuses of leading edges ~ 5% chord lengths
Radius of trailing edge for,

Stator ~ 0.6-0.9 mm
Rotor ~ 0.25 mm

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Modelled blade geometries

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Resulting parameters for blade models

Most of the performance targets been reached
The non-reached values vary only a small amount from their targets

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Conclusion

Creation of a 1D-2D axial turbine modelling tool on MS Excel
Plotting parameters and inspecting their behaviours from hub to tip
Creating diagrams of important aspects
Plotting degree of reaction’s effect
Visualizing turbine’s meridional view
Profiling blade geometries

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References

[1] Gambini, M., Vellini, M. (2021). Preliminary Design of Axial Flow Turbines. In: Turbomachinery. Springer Tracts in Mechanical Engineering. Springer, Cham.

[2] Adhikari, Pradhumna & Budhathoki, Umesh & Timilsina, Shiva & Manandhar, Saurav & Bajracharya, Tri. (2014). A Study on Developing Pico Propeller Turbine for Low Head Micro Hydropower Plants in Nepal. Journal of the Institute of Engineering. 9.

[3] Sieverding, C. (January, 2013). Advanced Course on Turbines – Course Note 221. von Karman Institute for Fluid Dynamics.

[4] Bahr Ennil, Ali (2017). Optimization of small-scale axial turbine for distributed compressed air energy storage system. University of Birmingham. Ph.D.

[5] Kacker, S. C., and Okapuu, U. (January 1, 1982). "A Mean Line Prediction Method for Axial Flow Turbine Efficiency." ASME. J. Eng. Power. January 1982; 104(1): 111–119.

[6] Q. H. Nagpurwala. Axial Turbines. M.S. Ramaiah School of Advanced Studies

[7] Pritchard, L. J. (1985). "An Eleven Parameter Axial Turbine Airfoil Geometry Model. The American Society Of Mechanical Engineers

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