[Footnote: Paper read before the British Association at Montreal.]
By Mr. ARTHUR RIGG, C.E.
Literature relating to turbines probably stands unrivaled among all that
concerns questions of hydraulic engineering, not so much in its voluminous
character as in the extent to which purely theoretical writers have ignored
facts, or practical writers have relied upon empirical rules rather than
upon any sound theory. In relation to this view, it may suffice to note
that theoretical deductions have frequently been based upon a
generalization that "streams of water must enter the buckets of a turbine
without shock, and leave them without velocity." Both these assumed
conditions are misleading, and it is now well known that in every good
turbine both are carefully disobeyed. So-called practical writers, as a
rule, fail to give much useful information, and their task seems rather in
praise of one description of turbine above another. But generally, it is of
no consequence whatever how a stream of water may be led through the
buckets of any form of turbine, so long as its velocity gradually becomes
reduced to the smallest amount that will carry it freely clear of the
machine.
The character of theoretical information imparted by some _Chicago Journal
of Commerce_, dated 20th February, 1884. There we are informed that "the
height of the fall is one of the most important considerations, as the same
stream of water will furnish five times the horse power at ten ft. that it
will at five ft. fall." By general consent twice two are four, but it has
been reserved for this imaginative writer to make the useful discovery that
sometimes twice two are ten. Not until after the translation of Captain
Morris' work on turbines by Mr. E. Morris in 1844, was attention in America
directed to the advantages which these motors possessed over the gravity
wheels then in use. A duty of 75 per cent. was then obtained, and a further
study of the subject by a most acute and practical engineer, Mr. Boyden,
led to various improvements upon Mr. Fauneyron's model, by which his
experiments indicated the high duty of 88 per cent. The most conspicuous
addition made by Mr. Boyden was the diffuser. The ingenious contrivance had
the effect of transforming part of whatever velocity remained in the stream
after passing out of a turbine into an atmospheric pressure, by which the
corresponding lost head became effective, and added about 3 per cent. to
the duty obtained. It may be worth noticing that, by an accidental
application of these principles to some inward flow turbines, there is
obtained most, if not all, of whatever advantage they are supposed to
possess, but oddly enough this genuine advantage is never mentioned by any
of the writers who are interested in their introduction or sale. The
well-known experiments of Mr. James B. Francis in 1857, and his elaborate
report, gave to hydraulic engineers a vast store of useful data, and since
that period much progress has been made in the construction of turbines,
and literature on the subject has become very complete.
In the limits of a short paper it is impossible to do justice to more than
one aspect of the considerations relating to turbines, and it is now
proposed to bring before the Mechanical Section of the British Association
some conclusions drawn from the behavior of jets of water discharged under
pressure, more particularly in the hope that, as water power is extremely
abundant in Canada, any remarks relating to the subject may not fail to
prove interesting.
Between the action of turbines and that of screw propellers exists an exact
parallelism, although in one case water imparts motion to the buckets of a
turbine, while in the other case blades of a screw give spiral movement to
a column of water driven aft from the vessel it propels forward. Turbines
have been driven sometimes by impact alone, sometimes by reaction above,
though generally by a combination of impact and reaction, and it is by the
last named system that the best results are now known to be obtained.
The ordinary paddles of a steamer impel a mass of water horizontally
backward by impact alone, but screw propellers use reaction somewhat
disguised, and only to a limited extent. The full use and advantages of
reaction for screw propellers were not generally known until after the
publication of papers by the present writer in the "Proceedings" of the
Institution of Naval Architects for 1867 and 1868, and more fully in the
"Transactions" of the Society of Engineers for 1868. Since that time, by
the author of these investigations then described, by the English
Admiralty, and by private firms, further experiments have been carried out,
some on a considerable scale, and all corroborative of the results
published in 1868. But nothing further has been done in utilizing these
discoveries until the recent exigencies of modern naval warfare have led
foreign nations to place a high value upon speed. Some makers of torpedo
boats have thus been induced to slacken the trammels of an older theory and
to apply a somewhat incomplete form of the author's reaction propeller for
gaining some portion of the notable performance of these hornets of the
deep. Just as in turbines a combination of impact and reaction produces the
maximum practical result, so in screw propellers does a corresponding gain
accompany the same construction.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
_Turbines_.--While studying those effects produced by jets of water
impinging upon plain or concave surfaces corresponding to buckets of
turbines, it simplifies matters to separate these results due to impact
from others due to reaction. And it will be well at the outset to draw a
distinction between the nature of these two pressures, and to remind
ourselves of the laws which lie at the root and govern the whole question
under present consideration. Water obeys the laws of gravity, exactly like
every other body; and the velocity with which any quantity may be falling
is an expression of the full amount of work it contains. By a sufficiently
accurate practical rule this velocity is eight times the square root of the
head or vertical column measured in feet. Velocity per second = 8 sqrt
(head in feet), therefore, for a head of 100 ft. as an example, V = 8 sqrt
(100) = 80 ft. per second. The graphic method of showing velocities or
pressures has many advantages, and is used in all the following diagrams.
Beginning with purely theoretical considerations, we must first recollect
that there is no such thing as absolute motion. All movements are relative
to something else, and what we have to do with a stream of water in a
turbine is to reduce its velocity relatively to the earth, quite a
different thing to its velocity in relation to the turbine; for while the
one may be zero, the other may be anything we please. ABCD in Fig. 1
represents a parallelogram of velocities, wherein AC gives the direction of
a jet of water starting at A, and arriving at C at the end of one second or
any other division of time. At a scale of 1/40 in. to 1 ft., AC represents
80 ft., the fall due to 100 ft. head, or at a scale of 1 in. to 1 ft., AC
gives 2 ft., or the distance traveled by the same stream in 1/40 of a
second. The velocity AC may be resolved into two others, namely, AB and AD,
or BC, which are found to be 69.28 ft. and 40 ft. respectively, when the
angle BAC--generally called _x_ in treatises on turbines--is 30 deg. If,
however, AC is taken at 2 ft., then A B will be found = 20.78 in., and BC =
12 in. for a time of 1/40 or 0.025 of a second. Supposing now a flat plate,
BC = 12 in. wide move from DA to CB during 0.025 second, it will be readily
seen that a drop of water starting from A will have arrived at C in 0.025
second, having been flowing along the surface BC from B to C without either
friction or loss of velocity. If now, instead of a straight plate, BC, we
substitute one having a concave surface, such as BK in Fig. 2, it will be
found necessary to move it from A to L in 0.025 second, in order to allow a
stream to arrive at C, that is K, without, in transit, friction or loss of
velocity. This concave surface may represent one bucket of a turbine.
Supposing now a resistance to be applied to that it can only move from A to
B instead of to L. Then, as we have already resolved the velocity A C into
AB and BC, so far as the former (AB) is concerned, no alteration occurs
whether BK be straight or curved. But the other portion, BC, pressing
vertically against the concave surface, BK, becomes gradually diminished in
its velocity in relation to the earth, and produces and effect known as
"reaction." A combined operation of impact and reaction occurs by further
diminishing the distance which the bucket is allowed to travel, as, for
examples, to EF. Here the jet is impelled against the lower edge of the
bucket, B, and gives a pressure by its impact; then following the curve BK,
with a diminishing velocity, it is finally discharged at K, retaining only
sufficient movement to carry the water clear out of the machine. Thus far
we have considered the movement of jets and buckets along AB as straight
lines, but this can only occur, so far as buckets are concerned, when their
radius in infinite. In practice these latter movements are always curves of
more or less complicated form, which effect a considerable modification in
the forms of buckets, etc., but not in the general principles, and it is
the duty of the designer of any form of turbine to give this consideration
its due importance. Having thus cleared away any ambiguity from the terms
"impact," and "reaction," and shown how they can act independently or
together, we shall be able to follow the course and behavior of streams in
a turbine, and by treating their effects as arising from two separate
causes, we shall be able to regard the problem without that inevitable
confusion which arises when they are considered as acting conjointly.
Turbines, though driven by vast volumes of water, are in reality impelled
by countless isolated jets, or streams, all acting together, and a clear
understanding of the behavior of any one of these facilitates and concludes
a solution of the whole problem.
_Experimental researches_.--All experiments referred to in this paper were
made by jets of water under an actual vertical head of 45 ft., but as the
supply came through a considerable length of ½ in. bore lead piping, and
many bends, a large and constant loss occurred through friction and bends,
so that the actual working head was only known by measuring the velocity of
discharge. This was easily done by allowing all the water to flow into a
tank of known capacity. The stop cock had a clear circular passage through
it, and two different jets were used. One oblong measured 0.5 in. by 0.15
in., giving an area of 0.075 square inch. The other jet was circular, and
just so much larger than ¼ in. to be 0.05 of a square inch area, and the
stream flowed with a velocity of 40 ft. per second, corresponding to a head
of 25 ft. Either nozzle could be attached to the same universal joint, and
directed at any desired inclination upon the horizontal surface of a
special well-adjusted compound weighing machine, or into various bent tubes
and other attachments, so that all pressures, whether vertical or
horizontal, could be accurately ascertained and reduced to the unit, which
was the quarter of an ounce. The vertical component _p_ of any pressure P
may be ascertained by the formula--
_p_ = P sin alpha,
where alpha is the angle made by a jet against a surface; and in order to
test the accuracy of the simple machinery employed for these researches,
the oblong jet which gave 71 unit when impinging vertically upon a circular
plate, was directed at 60 deg. and 45 deg. thereon, with results shown in
Table I., and these, it will be observed, are sufficiently close to theory
to warrant reliance being placed on data obtained from the simple weighing
machinery used in the experiment.
_Table I.--Impact on Level Plate._
--------------+--------------------+----------+----------+----------
| Inclination of jet | | |
Distance. | to the horizonal. | 90 deg. | 60 deg. | 45 deg.
--------------+--------------------+----------+----------+----------
| | Pressure | Pressure | Pressure
| | | |
/ | Experiment \ | / | 61.00 | 49.00
1½ in. < | > | 71.00 < | |
\ | Theory / | \ | 61.48 | 50.10
| | | |
| | | |
/ | Experiment \ | / | 55.00 | 45.00
1 in. < | > | 63.00 < | |
\ | Theory / | \ | 54.00 | 45.00
| | | |
--------------+--------------------+----------+----------+----------
In each case the unit of pressure is ¼ oz.
In the first trial there was a distance of 1½ in. between the jet and point
of its contact with the plate, while in the second trial this space was
diminished to ½ in. It will be noticed that as this distance increases we
have augmented pressures, and these are not due, as might be supposed, to
increase of head, which is practically nothing, but they are due to the
recoil of a portion of the stream, which occurs increasingly as it becomes
more and more broken up. These alterations in pressure can only be
eliminated when care is taken to measure that only due to impact, without
at the same time adding the effect of an imperfect reaction. Any stream
that can run off at all points from a smooth surface gives the minimum of
pressure thereon, for then the least resistance is offered to the
destruction of the vertical element of its velocity, but this freedom
becomes lost when a stream is diverted into a confined channel. As pressure
is an indication and measure of lost velocity, we may then reasonably look
for greater pressure on the scale when a stream is confined after impact
than when it discharges freely in every direction. Experimentally this is
shown to be the case, for when the same oblong jet, discharged under the
same conditions, impinged vertically upon a smooth plate, and gave a
pressure of 71 units, gave 87 units when discharged into a confined
right-angled channel. This result emphasizes the necessity for confining
streams of water whenever it is desired to receive the greatest pressure by
arresting their velocity. Such streams will always endeavor to escape in
the directions of least resistance, and, therefore, in a turbine means
should be provided to prevent any lateral deviation of the streams while
passing through their buckets. So with screw propellers the great mass of
surrounding water may be regarded as acting like a channel with elastic
sides, which permits the area enlarging as the velocity of a current
passing diminishes. The experiments thus far described have been made with
jets of an oblong shape, and they give results differing in some degree
from those obtained with circular jets. Yet as the general conclusions from
both are found the same, it will avoid unnecessary prolixity by using the
data from experiments made with a circular jet of 0.05 square inch area,
discharging a stream at the rate of 40 ft. per second. This amounts to 52
lb. of water per minute with an available head of 25 ft., or 1,300
foot-pounds per minute. The tubes which received and directed the course of
this jet were generally of lead, having a perfectly smooth internal
surface, for it was found that with a rougher surface the flow of water is
retarded, and changes occur in the data obtained. Any stream having its
course changed presses against the body causing such change, this pressure
increasing in proportion to the angle through which the change is made, and
also according to the radius of a curve around which it flows. This fact
has long been known to hydraulic engineers, and formulæ exist by which such
pressures can be determined; nevertheless, it will be useful to study these
relations from a somewhat different point of view than has been hitherto
adopted, more particularly as they bear upon the construction of screw
propellers and turbines; and by directing the stream, AB, Fig. 3,
vertically into a tube 3/8 in. internal diameter and bent so as to turn the
jet horizontally, and placing the whole arrangement upon a compound
weighing machine, it is easy to ascertain the downward pressure, AB, due to
impact, and the horizontal pressures, CB, due to reaction. In theoretical
investigations it may be convenient to assume both these pressures exactly
equal, and this has been done in the paper "On Screw Propellers" already
referred to; but this brings in an error of no importance so far as general
principles are involved, but one which destroys much of the value such
researches might, otherwise possess for those who are engaged in the
practical construction of screw propellers or turbines. The downward impact
pressure, AB, is always somewhat greater than the horizontal reaction, BC,
and any proportions between these two can only be accurately ascertained by
trials. In these particular experiments the jet of water flowed 40 ft. per
second through an orifice of 0.05 square inch area, and in every case its
course was bent to a right angle. The pressures for impact and reaction
were weighed coincidently, with results given by columns 1 and 2, Table II.
[Illustration: FIG. 3]
[Illustration: FIG. 4]
_Table II.--Impact and Reaction in Confined Channels._
-----------------------------+-------+---------+----------+-------
Number of column. | 1 | 2 | 3 | 4
-----------------------------+-------+---------+----------+-------
Description of experiments. |Impact.|Reaction.|Resultant.| Angles
| | | | ABS.
-----------------------------+-------+---------+----------+-------
Smooth London tube, 1¾ in. | 71 | 62 | 94.25 | 49°
mean radius. | | | |
| | | |
Rough wrought iron tube, | 78 | 52 | 98.75 | 56.5°
1¾ in. | | | |
| | | |
Smooth leaden tube bent to a | 71 | 40 | 81.5 | 60
sharp right angle. | | | |
-----------------------------+-------+---------+----------+------
The third column is obtained by constructing a parallelogram of forces,
where impact and reaction form the measures of opposing sides, and it
furnishes the resultant due to both forces. The fourth column gives the
inclination ABS, at which the line of impact must incline toward a plane
surface RS, Fig. 3, so as to produce this maximum resultant perpendicularly
upon it; as the resultant given in column 3 indicates the full practical
effect of impact and reaction. When a stream has its direction changed to
one at right angles to its original course, and as such a changed direction
is all that can be hoped for by ordinary screw propellers, the figures in
column 3 should bear some relationship to such cases. Therefore, it becomes
an inquiry of some interest as to what angle of impact has been found best
in those screw propellers which have given the best results in practical
work. Taking one of the most improved propellers made by the late Mr.
Robert Griffiths, its blades do not conform to the lines of a true screw,
but it is an oblique paddle, where the acting portions of its blades were
set at 48 deg. to the keel of the ship or 42 deg. to the plane of rotation.
Again, taking a screw tug boat on the river Thames, with blades of a
totally different form to those used by Mr. Griffiths, we still find them
set at the same angle, namely, 48 deg. to the keel or 42 deg. to the plane
of rotation. An examination of other screws tends only to confirm these
figures, and they justify the conclusion that the inclinations of blades
found out by practice ought to be arrived at, or at any rate approached, by
any sound and reliable theory; and that blades of whatever form must not
transgress far from this inclination if they are to develop any
considerable efficiency. Indeed, many favorable results obtained by
propellers are not due to their peculiarities, but only to the fact that
they have been made with an inclination of blade not far from 42 deg. to
the plan of rotation. Referring to column 4, and accepting the case of
water flowing through a smooth tube as analogous to that of a current
flowing within a large body of water, it appears that the inclination
necessary to give the highest resultant pressure is an angle of 49 deg.,
and this corresponds closely enough with the angle which practical
constructors of screw propellers have found to give the best results.
Until, therefore, we can deal with currents after they have been
discharged from the blades of a propeller, it seems unlikely that anything
can be done by alterations in the pitch of a propeller. So far as concerns
theory, the older turbines were restricted to such imperfect results of
impact and reaction as might be obtained by turning a stream at right
angles to its original course; and the more scientific of modern turbine
constructors may fairly claim credit for an innovation by which practice
gave better results than theory seemed to warrant; and the consideration of
this aspect of the question will form the concluding subject of the present
paper. Referring again to Fig. 3, when a current passes round such a curve
as the quadrant of a circle, its horizontal reaction appears as a pressure
along _c_ B, which is the result of the natural integration of all the
horizontal components of pressures, all of which act perpendicularly to
each element of the concave surface along which the current flows. If, now,
we add another quadrant of a circle to the curve, and so turn the stream
through two right angles, or 180 deg., as shown by Fig. 4, then such a
complete reversal of the original direction represents the carrying of it
back again to the highest point; it means the entire destruction of its
velocity, and it gives the maximum pressure obtainable from a jet of water
impinging upon a surface of any form whatsoever. The reaction noticed in
Fig. 3 as acting along _c_ B is now confronted by an impact of the now
horizontal stream as it is turned round the second 90 deg. of curvature,
and reacts also vertically downward. It would almost seem as if the first
reaction from B to F should be exactly neutralized by the second impact
from F to D. But such is not the case, as experiment shows an excess of the
second impact over the first reaction amounting to six units, and shows
also that the behavior of the stream through its second quadrant is
precisely similar in kind to the first, only less in degree. Also the
impact takes place vertically in one case and horizontally in the other.
The total downward pressure given by the stream when turned 180 deg. is
found by experiment thus: Total impact and reaction from 180 deg. change in
direction of current = 132 units; and by deducting the impact 71 units, as
previously measured, the new reaction corresponds with an increase of 61
units above the first impact. It also shows an increase of 37.75 units
above the greatest resultant obtained by the same stream turned through 90
deg. only. Therefore, in designing a screw propeller or turbine, it would
seem from these experiments desirable to aim at changing the direction of
the stream, so far as possible, into one at 180 deg. to its original
course, and it is by carrying out this view, so far as the necessities of
construction will permit, that the scientifically designed modern turbine
has attained to that prominence which it holds at present over all
hydraulic motors. Much more might be written to extend and amplify the
conclusions that can be drawn from the experiments described in the present
paper, and from many others made by the writer, but the exigencies of time
and your patience alike preclude further consideration of this interesting
and important subject.
* * * * *