Hence, maximum blade efficiency is when entrance angle is at 0o and when the blade is rotating at 1/2 the speed of the jet stream
As the steam must enter at an angle ao
Optimum value for U / Ci = 1/2 cos a ( 0.45 to 0.48 )
Maximum blade efficiency = Cos2 a (14o to 20o)
Impulse blading may have up to 20% reaction effect at mean blade height.
Astern turbines generally consist of a single wheel on which are mounted a tow stage velocity compound followed by a single stage wheel
Properties required of the blade material
Typical blade material is
Low tensile stainless steel preferred to high tensile stainless iron due to better fatigue resistance. Where lacing wires are to be brazed in special care must be made as to the intergrannular penetration effects of the braze
Bull nosed blades
Standard blades have the same inlet and outlet angles.
Bull nosed blades are capable of accepting a wide range of steam angles without serious increase in blade losses.
The cross sectional area is increases and hence the blade is stronger and better resistant to vibration. The increase thickness also allows a circular tang to be fitted for attaching a shroud. Non circular such as square tangs require the shroud to be punched rather than drilled which introduces residual stress, micro-cracking etc.
De Laval Impulse Turbine-Single Stage
Optimum efficiency occurs when the blade is moving at half the speed of the jet stream. To achieve this very high rotational speeds would be required ( in the order of 15000 rpm). High centrifugal stress, high journal speed and excessive gearing requirements prohibits the use of such system for propulsion by itself.
This system is often found as the first stage of a HP turbine were a large pressure drop is required to allow for a smaller turbine. Only the nozzle box has to cope with full boiler pressure and temperatures simplifying design especially of gland boxes. Special material requirements are again restricted to nozzle box. Reduced pressure within the following stages reduces tip leakage
The steam leaving the blades has a high kinetic energy indicating high leaving loss.
Pressure Compounding (Rateau)
The overall heat and pressure drop is divided between the stages. The U/Ci ratio is 0.5 for each stage. By careful design the rotor mean diameter may be kept to a minimum.
Excessive number of stages produces an overly long rotor, these leads to problems of critical vibration, increased rotor diameter, increased stage losses due friction and windage and increased gland leakage both at the main glands and the diaphragm plate glands. This due to the increased number of glands and the increased rotor diameter.
Stage mean diameter and nozzle height are increased at the LP end as the steam expands to the limits of centrifugal stress. Nozzle and/or blade angles may be altered to accommodate the increase in volume reducing the requirement to increase blade height excessively.This is referred to as taper-twisting
The blade height increase towards the LP end means that the rotational velocity also increases. Hence for the same value of U/Ci they can deal with higher inlet steam velocities and hence higher enthalpy drops p>The design produces a short lightweight turbine used where size, weight and strength are more important than efficiency. E.G. feed pumps , astern turbines and the inlet portion of HP turbines where it provides a large initial drop in temperature and pressure lightening the rotor and reducing the need for high grade alloys for remaining stages
Velocity Compounded (Curtis)
For a two stage system U/Ci = 1/4, for a three stage system U/Ci = 1/6
There is no pressure drop except in the nozzle ( although in practice some drop occurs due to losses as the steam passes over the blade). Dividing the velocity drop across the stages leads to a loss of efficiency but gives a more acceptable blade speed reducing centrifugal stress and simplifying gearing arrangement.
For a three row system, the steam speed at inlet to the first row is 6 times the blade speed, reducing the velocity makes the conditions at the final stages close to ideal.
To maintain the same mass flow for the reducing velocity, blade height is increased to the limit of centrifugal forces. Taper-twisting and flattening of the blade angle is then given to the final stage blades.
Some reheating occurs due to friction of the fixed blades associated with a loss of velocity of about 12%
Theoretically efficiency is independent of the row number. However in practice efficiency and work done in final stages reduces and therefore overall efficiency drops with increase rows.
This system gives the advantage of producing a shortened rotor compared to pure velocity compounding. In addition it also removes the problem of very high inlet steam velocities and the reduction in efficiency and work done in the final stages.
In this design steam velocity at exit to the nozzles is kept reasonable and thus the blade speed (hence rotor rpm) reduced.
Typical applications are large astern turbines
Ci= velocity of steam at inlet to blade, i.e. leaving nozzle( giving nozzle angle)
Ci rel= velocity of steam relative to the blade( giving blade inlet angle)
Co= Velocity of steam at outlet of blade
The original blade design was thin section with a convergent path. Blohm & voss designed blades similar to bull nose impulse blades which allowed for a convergent-divergent path. However due to the greater number of stages the system did not find favour over impulse systems
U/Ci = 0.9
If the heat drop across the fixed and moving blades are equal the design is known as half degree reaction.
Steam velocity was kept small on early designs, this allowed the turbine to be directly coupled to the prop shaft.
Increased boiler pressure and temperature meant that the expansion had to take place over multiple rotors and gearset.
As there is full admission over the initial stage, blade height is kept low. This feature alone causes a decrease in blade and nozzle efficiency at part loading.
In addition, although clearances at the blade tips are kept as small as practical, steam leakage causes a proportionally higher loss of work extracted per unit steam
Blade tip clearances may be kept very tight so long as the rotor is kept at steady state.
Manoeuvring, however, introduces variable pressures and temperatures and hence an allowance must be made.
End tightening for blades is normally used. This refers to an axial extension of the blade shroud forming a labyrinth. When the rotor is warmed through a constant check is made on the axial position of the rotor. Only when the rotor has reached its normal working length may load be introduced. Alternatively tip tightening may be used referring to the use of the tips of the blade to form a labyrinth against the casing/rotor. This system is requires a greater allowance for loading and is not now generally used.
To keep annular leakage as small as possible these rotors tend to have a smaller diameter than impulse turbines.
To keep the mass flow the same with the increasing specific volume related to the drop in pressure requires an increase in axial velocity, blade height or both -see above. Altering the blade angle will also give the desired effect but if adopted would cause increased manufacturing cost as each stage would have to be individual. Generally the rotor and blading is stepped in batches with each batch identical.
The gland at the HP end is subjected to full boiler conditions and is susceptible to rub. The casing must be suitably designed and manufactured from relevant materials.
A velocity compounded wheel is often used as the first stage(s) giving a large drop in conditions allowing simpler construction of casing and rotor and reducing length. Special steels are limited to the nozzle box.
Dummy piston arrangement on Parsons Turbines
In parsons reaction turbines there is always an end thrust due to the steam at inlet being higher than the exhaust. This leads to high thrust bearing loading. The dummy piston arrangement is a wheel or drum integral to the rotor. Forces are balanced by the drum offering a greater surface area to the low pressure balancing steam than to the HP steam.Note the drawing above is not to scale.
A labyrinth arrangement is fitted to seal the drum.
Double Flow Turbines
These are found mainly on large LP turbines. Here steam enters mid rotor and passes axially towards both ends. The advantages are;
The main disadvantage of this system is increase rotor length leading to increased risk of sagging
May be end or tip tightening
This is seen particularly on reaction turbines. It requires accurate positioning of the turbine rotor and is normally associated with lengthy warm up periods during which the position of the rotor is carefully monitored. Operational limitations on rapid power changes may be in place. The author has seen this system in use on very large but compact turbo alternators which required a warm up period consisting of increaseing the rotor speed in stages over one hour
Clearance is governed by maximum blade centrifugal stretch
The predominant stress in turbine blades is centrifugal and concentrated at the root
Vibration is set up in blades due to fluctuations in steam flow. Particularly in impulse turbines where partial admission is used
Further stress is caused by expansion and contraction as well as bending stresses due to the action of the steam
In addition to these stresses occur during manoeuvring due to speed changes.
Although not subjected to centrifugal force, the fixed blades of curtis velocity compounded turbines are subjected to vibration in a similar way to the rotating blades. The root fixture must, by necessity, be secure to prevent fretting
Blades are rolled to correct shape then cut to length.
Up to 50 blades are then assembled in a jig of correct radius with a distance piece to give the correct spacing.
The root is drilled and the upper part machined so as to accept shrouding fro end-tightening, or thinned for tip tightening.
After assembly on the jig a hole is drilled though the base and a wire passed through. The whole assembly may then be removed and brazed or spot welded to form a solid curved section.
The arc is then machined to the desired root form. Shown below is a single blade section of the arc showing typical root form.
The segment is dropped into position pushed axially and a caulking piece fixed
A gate is formed in the final blade which receives a further thin section piece made of copper which is caulked in.
The fixed blades in reaction turbines are made in a similar fashion except that the end blades as held in by a screw and locking strip as the horizontal joint. Also the root may be of a simpler design due to the lack of centrifugal stress.
For higher speed, higher rated turbines the built up method may not be acceptable due to the stresses.
These blades may then be made of solid individual sections. The blades enter through a gate with the final blade being caulked into position.
The gates for each groove are staggered to assist balancing. The lacing wire/shrouding is then fitted.
The most common form is the dove tail.
The groove is cut away to form a gate to allow the fitting of the blades. The final blade is riveted in position.
Blades subjected to higher centrifugal stresses, for example the longer tapered blades found in the final stages of the LP turbine, may have the fir tree root method which allows increased contact area without weakening root or wheel rim.
To reduce centrifugal stress on the wheel straddle root form of blade fixing may be used thinning the wheel rim. The straddle may be a simple fork design or of fir tree root. Rivets are added for strength.
Inverted Fir tree
Fir tree root attachment is very strong but requires accurate machining and manual blade fixing is not possible. The gate is filled with a machined block with no blade and then riveted to secure.
For very large blades, say at the end if the LP turbine, the root, and thus wheel rim, would be required to be very large. Multiple forks may be used which are comparatively easier to machine.
Straddle 'T' used rather than inverted 'T' so that the holding faces on the rim can be easily inspected for defects.
Stal Laval bulb root
The main advantage of this system is that the blades are introduced into the rim axially. Therefore the individual fitting of the blades required with circumferential root arrangements is unnecessary
Where the distances between the bulb becomes so small as to risk failure of the rim, staggered bulb root depths are used with alternating short and long shank lengths.
For these types of blades the shrouds are part of the blade. On this shroud are two tabs. A shrouding wire is passed around the circumference over the shroud and the tanbs are bent over. This has the advantage that in the event of root failure some support is given to the blade. Multiple shroud wires are filled rather than a singe one for ease of manufacture allowing smaller tabs, and also to reduce mechanical stress. On more modern designs the groove is moved to the end of the shroud and a welded shroud wire fitted.
Sizing the rim
When the rim is first cut and the entrance gate formed, a test blade with slightly too large root ( or feet) is carefully filed and then tapped around the rim. This blade is then discarded. The real blades are then carefully filed and fitted taking into account the wear on the rim. The mating face of the blades are filed to ensure even blade pitch. A tight fit is essential with a steam turbine, if not then severe fretting and failure will occur
Turbine blade vibration
Damping wires, Lacing wires and shrouding are fitted to
The vibration associated with turbine blades is referred to as the ' clamp-pin' type and is determined by viewing the blades in their packets i.e. blade groups attached by their shroud.
The lowest frequency is of the whole packet vibrating
Higher frequency is where as equal number of blades bow in opposite directions
Higher still frequencies occur where each blade vibrates
Lacing, Damping and Binding wires
There are four sources of vibration damping under normal operating conditions
Lacing wires fitted at an antinode provide a very effective form of dampening. However, the antinode may exist at different positions for the different types of vibration so a compromise on the position has to be reached.
A Damping wire which is 'free fitting' is free to move within the holes. Centrifugal force throws the wire to the outside of the hole where frictional effects help dampen the vibration. The disadvantage of damping wires is that heavy fretting can eventually cause the holes to widen to an extent that the rotor has to be re-bladed.
Lacing wires are brazed in and are therefore strengthening and hence are not necessarily placed at an antinode but rather where the blade is thickest.
Binding wire is used to strengthen the trailing edge of the blade. This is a very old fashioned technique and is little used.
The use of round wire can lead to aerodynamic losses
Snubber or bumbing blocks may be cast or forged into the blade. These have a highly
The damping is then achieved by both the bumbing of the blades and the following resistance to breaking as a vacuum formed at the joined faces tries to hold them together. A certain amount of fluid damping also occurs.
May be fitted by brazing, welding or riveting.
The shrouding is fitted over the blade, the tenon is then either riveted with 4 or 5 blows or welded. Care must be taken either method of fixing as it can lead to crack formation. Once the shrouding is fitted the surveyor may request a pull off test. The pull is determined by calculation and governed by the expected centrifugal stress on the shroud during normal operations.
For blade batches where the centrifugal stress on the shroud of very large LP blades is significant, then centenary shrouding is employed.
Taper-Twisting of blades
Reasons for taper-twisting of the final stages of LP turbines
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 its 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
Loss of efficiency due to recirculation
Balance holes may be drilled in the blade wheel to reduce the loading caused by this effect. This has the effect of increasing the amount of recirculation, introduces a stress raiser and increases windage losses. To try to alleviate some of this the bore is carefully radiused and polished
A certain amount of reaction is put on the blade by casuing a pressure drop across the blade to equal that caused by the eduction effect-approximately 10% ( Degree of reaction = Enthalpy drop over blade/enthalpy drop over stage)