Vortical Analysis of Secondary Flows in Turbine Cascades

P M V SubbaraoProfessor

Mechanical Engineering Department

A Pictorial Fluid Mechanics for Complex Flows……

Formation & Evolution of Endwall Flows

• The picture of endwall flows in turbine blade-to-blade passages is 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?

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.

Theory of Formation of endwall flows

• The main type of secondary flow is the induced recirculating flow, which leads to the formation of a passage vortex.

• The source of the induced recirculating flow is the cross flow in the endwall boundary layer.

The passage vortex forms as a result of force equilibrium in curvilinear motion. The momentum equation in the cross-stream direction can be written in the form:

n

p

R

vcf

2

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.

Secondary flow models in turbine cascades

Model (a) : model of Hawthorne (1955)

Secondary flow models in turbine cascades

Model (b) : Model of Langston (1980)

Secondary flow models in turbine cascades

Model (c) : model of Sharma and Butler (1987)

Secondary flow models in turbine cascades

Model (d) : model of Goldstein and Spores (1988)

Secondary flow models in turbine cascades

Model (e) : model of Doerffer and Amecke (1994)

Secondary flow models in turbine cascades

Model (f) : model of Wang et al. (1997)

Secondary whirl

Describe Secondary Flow as An Elephant !?!?!

The main type of secondary flow is the induced recirculating flow, which leads to the formation of a passage vortex.

Generation of Secondary Flow System

Horse-shoe vortex

• Another element of secondary flows is a horse-shoe vortex.

• The process of formation of the horse-shoe vortex upstream of the leading edge and its downstream transport was explained by many researchers.

• The models of the process of formation of horse shoe presented in these papers differ from one another in details only.