Secondary Flows in Turbine Cascades

1. Secondary Flows in Turbine Cascades P M V Subbarao Professor Mechanical Engineering Department Finite Length Blades Generate More Entropy.……

2. Euler’s Vision of Flow in A Turbo-machine

3. Complex Blade design for Occurrence of 2D Flow

4. Modular (Conventional) Concept of Blade Design

5. Change Flow field due to 2D to 3D nature of Turbine Blade

6. The Profile of A 3D Blade • A 3D blade works along with its endwalls. • Endwall flows originate from specifically developing endwall boundary layers. • These are associated with the presence of longitudinal vortices with a dominant streamwise component of the vorticity. • These are generally known as and secondary flows. • They are driven by transverse static pressure gradients and mass forces acting on fluid elements in curvilinear motion through the blade-to-blade passage. Understanding the complex development of endwall flows is a part of betterment of blade profile !!!

7. Impact of Endwall Flows • Endwall flows are also an important source of losses in turbines. • More serious impact on cascades with short-height blading and high flow turning. • Due to the complex nature of endwall boundary layer flows, the evaluation of endwall losses is a tough task.

8. Description of Secondary Flows • The picture of Secondary Flows generated by endwall boundary layers in a turbine blade-to-blade passages is seen to be extremely complex. • The secondary flows also modify the shape of endwall boundary layers from which they originate. • Demands a set of creative thinking to understand the development of secondary flows. • A creative thinker will always tend to propose a geometrical solution the complex problem. • How to proceed to understand this phenomena? “Action at a distance" has stymied many of the great minds

9. Action at a Distance : The Field Nature of Fluid Mechanics

10. Hans Albert Einstein (May 14, 1904 – July 26, 1973) • Hans Albert Einstein was a Swiss-American engineer and educator • He was an avid sailor, frequently taking colleagues and family out for excursions on the San Francisco Bay. • On his many field trips and academic excursions, he took thousands of pictures, many of which he developed himself and presented as slide shows. • In tribute to Einstein's lifelong contributions to the field, his former graduate students published a book of research in his honor in 1972, Sedimentation: Symposium to Honor Professor H.A. Einstein. • In 1988, the American Society of Civil Engineers created the Hans Albert Einstein Award to recognize outstanding achievements in erosion control, sedimentation and/or waterway development.

11. Theory of Formation of Secondary flows • The strongest vortex seen in a secondary flow is known as Induced Recirculating Flow (IRF). • The mother of IRF of is the cross flow in the endwall boundary layer. A passage vortex forms as a reaction to the force created by IRF. This is an equilibrium condition in curvilinear motion. The momentum equation in the cross-stream direction can be written in the form:

12. The Reaction • With a decrease of the radial velocity in the boundary layer, a reduction of the streamline curvature radius in the boundary layer flow is required in order to balance the pitch-wise pressure gradient formed in the channel. • As a consequence, the boundary layer flow is turned more than the main flow in the blade-to-blade channel, leading to a crossflow from the pressure to suction surface in the endwall boundary layer. • A compensating return flow must then occur at a certain distance from the endwall, giving rise to the recirculating flow. • The action is science but reaction is an engineering art.

13. Secondary flow models in turbine cascades Model (a) : model of Hawthorne (1955)

14. Secondary flow models in turbine cascades Model (b) : Model of Langston (1980)

15. Secondary flow models in turbine cascades Model (c) : model of Sharma and Butler (1987)

16. Secondary flow models in turbine cascades Model (d) : model of Goldstein and Spores (1988)

17. Secondary flow models in turbine cascades Model (e) : model of Doerffer and Amecke (1994)