Thursday, 24 May 2012

Negative Reaction

The degree of reaction R is defined as the ratio of the heat drop in the moving blades to the sum of the heat drop in the nozzles and the moving blades i.e.
R = hb/hn + hb
The heat drop across the moving blades is manifest as an expansion of the steam during ites passage through the moving blades and thus as increase in steam velocity.
If a compression takes place at the same section along the blade length instead of an expansion thus being equivalent to work done then the term becomes negative, and provided hn > hb the expression becomes negative at the section considered.
The actual mechanism where by this occurs is linked to the vortex flow theory.
Simplified this states that because of the oblique angle of the steam flow out of the nozzle the flow path in the gap between the nozzle outlet and moving blade inlet follows a line of flow something like a spiral and that there must be therefore inertial forces set up which cause a variation in steam pressure in the radial direction to the gap.
Where the nozzle height ratio (ratio radial height L of the nozzles to the mean diameter D) is small the effect is limited, but in those stages where the nozzle height ratio is large it has a profound effect on the distribution of heat drop in the nozzles and blades.
Calculation of steam conditions at mean blade height (as be used in the preceding stages) is no longer indicative of flow characteristics.

Shown is a section of nozzle and blade. It is assumed the pressure is sensibly constant in a radial direction i.e. the flow lines are entirely axial in direction relative to the casing. However,there is a pressure gradient in the radial direction in the gap between the nozzles and moving blades so that if the blade profile were calculated on the conditions prevailing at the mean height of the nozzles and blades, based on a pressure drop through the moving blades of P2 - P3, the pressure in the gap near the tip (P2T) would be greater than the mean height inlet pressure (P2) and the pressure near the root (P2R) would be less than the mean height inlet pressure (P2).
If the degree of reaction at the moving blade height were small so that the expansion in the moving blades were small, then P2 would be only slightly greater than P3 and the inlet pressure at the root P2R could in fact be less than P3. This would lead to an apparent increase in pressure through a part of the moving blades or negative reaction. Also, the pressure difference P2T-P3 at the tip could be greater than at the mean height. So the degree of reaction would be positive but larger at the mean height.
Thus, the degree of reaction may increase from negative to positive from root to tip.
In reality, there is not necessarily a flow reversal at the section where negative reactions occur as would expect but simply an over-expansion of the steam at exit from the nozzles.
Such a blade would be highly inefficient, not only due to the high losses associated with negative reaction but also due to shock losses at entry to the moving blades.
Modern designs ensure a degree of positive reaction at the root of every moving blade and design conditions to avoid negative reaction at all other off design conditions.

1 comment:

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