Stresses and deformations in impulse water turbines

Macduff, Iain B (1969) Stresses and deformations in impulse water turbines. PhD thesis, University of Glasgow.

Abstract

This thesis concerns the theoretical and experimental investigation of the working stresses and deformations in the Turgo impulse wheel and, to a lesser extent, in the Pelton wheel. These wheels are the only impulse water turbines in common use. Directly relevant publications are very few. The most recent significant paper, which discusses a limited experimental analysis of the approximate jet loading stresses in a Pelton bucket, was issued in 1934. A much more recent Russian publication is much less informative. It appears that no theory has been advanced to explain the working stress behaviour of the buckets of these water wheels, and that no attempt has been made at rational theoretical stress analyses for their strength design. Impulse water turbine buckets are of shell form, and are critical component from the strength aspect. An Introduction sketches the background to the investigation and indicates that potential advantages in respect of design and performance are attendant on a realistic knowledge of the working stresses. The literature is reviewed and a cursory glance given at indirectly pertinent publications relating to the stress analyses of other types of water turbine. The Turgo impulse wheel, which is a side-jet wheel incorporating a rim round the buckets, is described in Chapter 2, and the bucket geometry is discussed. It is shown that the bucket shape approximates reasonably to that of part of a shell of revolution of varying thickness. Assuming an idealised but realistic bucket and rim geometry, approximate theoretical analyses are developed in Chapter 3, to determine the order-of-magnitude of the centrifugal and jet loading stresses in a working/working Turgo wheel. These analyses are based mainly on elementary energy methods, and assume that the buckets behave as beams. Albeit approximate, the calculations reliably reveal the dominance of centrifugal action, the maximum approximate centrifugal stress being about twice the corresponding maximum approximate jet loading stress. Both maxima occur on the bucket edges. Chapter 4 presents the experimental stress analyses of a Turgo wheel. The strain measurements comprise static loading tests on separate single buckets, centilfugal tests using slip rings, with the wheel spinning in the dry condition, and approximate jet loading tests on the stationary wheel, the loading being simulated by mechanical means. Most of the important predictions of the approximate theoretical analyses are confirmed. It is demonstrated that the stress behaviour of a bucket under working conditions, approximates reasonably to that of a toroidal shell subjected to in-plane bending. An approximate theoretical solution is derived in Chapter 5, for the stresses and deformations in a varying-thickness open toroidal shell under in-plane bending, a case which does not seem to have been treated. This derivation is founded on the work of R. A. Clark, dealing with theoretical stress analyses of pipe-bends and thin toroidal shells. Clark's approximate non-homogeneous complex differential equation and a given approximate particular integral are relevant. An asymptotic solution for the complementary function is then found, using a method developed by R. E. Langer. Applications of the genera] solution to simplified cases are performed using the special functions tabulated by L. N. Osipova and S. A. Tumarkin. The stress behaviour indicated by this shell theory, fits well with the working stress behaviour measured on Turgo wheel buckets. In Chapter 6 comparison is made between theoretical and experimental results for the working Turgo impulse wheel. An approximate rigidity factor from the shell theory of Chapter 5, is applied to some of the calculations of Chapter 3 to modify the beam analyses to take shell behaviour into account. Reasonably good correspondence is found between theory and experiment. In Chapter 7 shell theory is applied in an approximate manner to the case of the Pelton bucket subjected to jet loading. The solution derived in Chapter 5 is used in conjunction with existing toroidal shell solutions due to Clark. The results compare quite well with results from strain measurements on a Pelton bucket subjected to simulated jet loading by mechanical means. The implications of the results of the investigation are considered in Chapter 8, in relation to the designs and duties of these two types of impulse water turbine.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Mechanical engineering, Fluid mechanics
• Date of Award: 1969
• Depositing User: Enlighten Team
• Unique ID: glathesis:1969-73902
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:56
• Last Modified: 14 Jun 2019 08:56
• URI: https://theses.gla.ac.uk/id/eprint/73902