Experimental study of flow past turbine blades

Experimental study of flow past turbine blades


Material Information

Experimental study of flow past turbine blades
Series Title:
Physical Description:
29 p. : ill. ; 27 cm.
Eckert, E
Vanier, J
Vietinghoff-Scheel, K. von
United States -- National Advisory Committee for Aeronautics
Place of Publication:
Washington, D.C
Publication Date:


Subjects / Keywords:
Aerodynamics   ( lcsh )
Gas-turbines   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Turbine-blade-section tests were made in a low-speed two-dimensional cascade tunnel using a Mach-Zehnder interferometer. Pressure distributions and forces were calculated from density gradients given by the interference patterns. The central blade was heated to improve the definition of boundary layer separation. Reynolds number was varied from 11,800 to 54,000 and spacing ration from 0.687 to 1.141.
Includes bibliographic references (p. 14).
Sponsored by National Advisory Committee for Aeronautics
Statement of Responsibility:
by E. Eckert and K. von Vietinghoff-Scheel
General Note:
"Report date June 1949."
General Note:
"Translation of "Versuche über die Strömung durch Turbinenschaufelgitter" Vorabdrucke aus jahrbuch 1942 der deutschen Luftfahrtforschung, 6. Lieferung."
General Note:
"Translated by J. Vanier."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003804235
oclc - 123505043
sobekcm - AA00006224_00001
System ID:

Full Text




By E. Eckert and K. v. Vietinghoff-Scheel




The requirements on gas turbines for aircraft power units, namely,
adequate efficiency, operation at high gas temperatures, low weight, and
small dimensions, must be taken into consideration during the design of
the blading. To secure good efficiency, it is necessary that the gas
flow past the blades as smoothly as possible without separation. This
is relatively easily obtainable in the accelerated flow of turbine
blading, if the blade spacing is chosen small enough. A small blade
spacing, however, is detrimental to the other requirements outlined above.
Operation at high gas temperatures usually calls for blade cooling. This
cooling is associated with a power input that lowers the turbine effi-
ciency. Since the amount of heat that must be carried off for cooling a
blade can be influenced rather little, the gross power input for a tur-
bine stage can be reduced by keeping the number of blades to a minimum,
that is, with blades of high spacing ratio. But here also a limit is
imposed, the exceeding of which is followed by separation of flow. Hence
the requirement of finding blade forms on which the flow separates at
rather high spacing ratios.

Small dimensions of the turbine are essentially obtained by keeping
the outside diameter of the blading as small as possible. This is made
possible by choosing a high tip speed and making the width of the annular
space of the turbine stage available for the passage of the gas great,
that is, the inside diameter as small as possible. But on such long
blades the flow at the inside diameter is appreciably different from that
at the outside diameter. The flow strikes the rotor blades inside at a

*"Versuche Uber die Str8mung durch Turbinenschaufelgitter."
.Vorabdrucke aus Jalrbuch 1942 der deutschen Luftfalrtforschung,
S-6.. Lieferung, pp. 2-10.

NACA TM No. 1209

much flatter angle than outside. The turbine blades must therefore ensure
a flow free from separation throughout the whole available range of flow

Since the visualization of the separation phenomena on a running
turbine involves considerable difficulties, it is appropriate to study
the flow first on blade grids at rest. Direct application of such
findings to the guide vanes of a turbine is probably possible. Greater
care is advised in application to rotor blades. On these the boundary
layer, which forms at the surface of the blades, is under the influence
of the centrifugal force. This should not affect the separation phenomena
on axial turbines very much, where the centrifugal force is perpendicular
to the direction of motion. A greater effect is to be expected on radial
turbines, where the centrifugal force acts against the separation when
the gas flows through the turbine from the inside toward the outside. In
the reversed flow direction the centrifugal-force effects favor separation
of flow.

The use of the interference method for the study of flow past the
blade grids (references 1 and 2) has the advantage that the tests can be
run at Reynolds and Mach numbers encountered on actual turbines. On top
of that, interference photographs not only afford a qualitative picture
of the flow process, but also can be interpreted quantitatively, such as
the determination of the pressure distribution over the blades and with
it the torque exerted on the rotor, for instance.


To the torque exerted by the flowing gas on the rotor there corre-
sponds a force on each blade in circumferential direction. This force
is introduced by low pressure at the back of the blade and by high pres-
sure at the face of the blade, in the same manner as the lift on an air-
foil. Weinig (reference 3) computed the pressure distribution caused
by the flow of a frictionless fluid for several blade forms, one of which
is represented in figure 1, by the pressure distribution curve for a
blade grid with spacing ratio = 0.96 and flow direction wl. The
viscosity of the flowing gas causes a boundary layer along the blade
surface, and it is this, as is known, that effects the separation at
the blade as .oon as the pressure rise in flow direction along the blade
surface exceeds a certain value. To be feared most of all is a sepa-
ration at the back in the area between A and B, although it can occur
equally on the face at C. The amount of pressure rise which a boundary
layer can overcome without separation depends upon whether the layer is
laminar or turbulent. It is therefore to be expected that the separation
phenomena discussed hereinafter are affected by the Reynolds number.

The order of magnitude of the pressure rise to be overcome by the
flow past a turbine blade is readily estimated when the entrance and exit

NACA TM No. 1209 3

angle of flow for the blading are known. Weinig's calculations (fig. 1)
as well as the test data on wings and cascades of airfoils (references 4
and 5) give the pressure distribution curve an approximately triangular
form. Giving the pressure distribution projected on a straight line
(width of grid b in fig. 2) perpendicular to the grid direction the
shape of a triangle as represented in figure 3, the magnitude of the
force U per unit blade length exerted by the flow in grid direction is

U= (1)

where Apm is the maximum pressure difference between front and back of
blade, and b the width of the blade grid. On the other hand, by the
momentum theorem with the notation of figure 2A this force U follows
the equation

U = paw(wu2 wul) (2)

the flow velocities being assumed so small that constant gas density p
can be assumed. Since an estimate is involved, this is possible up to
the speed of about two thirds the velocity of sound. This assumption
simplifies the calculation, which, of course, can be carried out for
variable density just as well. The velocity components w are intro-
duced vectorially in equation (2), that is, subtracted when in the same
direction, but added when directed oppositely. Determining the maximum
pressure difference from equations (1) and (2) gives

Pm = 2p-m (u2 Wul) (3)

The stage pressure drop Lpst is the difference of the static pressures
pi and p2 upstream and downstream from the blade grid as

Pst = Pl P2 = (w2 = wu) (4)

The dynamic pressure of the flow velocity is

P= p2 (5)
ql =e 2

With these quantities the pressure distribution triangle can be plotted
S to scale, as exemplified in figure 3A, because the pressure at the blade

NACA TM No. 1209

trailing edge, that is, at the tip of the triangle, is practically p2.
The amount of the pressure rise at the back of the blade follows then as
the difference between p2 and the lowest pressure p3 as

P2 3 = pm q1 Apst (6)

Whether the boundary layer is able to overcome this pressure rise without
separation depends upon the magnitude of the kinetic flow energy relative
to this pressure rise. The velocity increases from wI to w2 during
the flow through the blade grid. For the present estimate, therefore,
it is best and perhaps accurate enough as well to refer the pressure
rise P9 p3 to the average kinetic energy of flow

2 = "- L + (7)
q12i 2 2 ) (7)

With equation (6) we then get

P2 P3 aw u2 vu 2w2 wu22 ul
= 8 2 (8)
q Vb 2 + 2 2 2+ + W2

as measure for the danger of separation.

The pressure distribution triangle in figure 3A relates to a turbine
stage with axial entry Wul = 0) and an exit angle 02 of 200
(m/wu2 = tan 02 = 0.364) measured against the circumferential direction.
Rtfersing the flow through the blade grid involves a pressure rise
from 2, toward pi. The blades must then, of course, be shaped a little
differently, the pointed tip of the blade being placed on the exit side
again, as exemplified in figure 2B. Equations (3), (4), and (7) remain
valid for this direction of flow. But the dynamic pressure of the flow
velocity is

2 ="22 (9)

NACA TM No. 1209 5

The pressure distribution triangle assumes the form represented in
figure 3B, and the referred pressure rise at the blade back amounts to

P2 P3 a "m("u2 ul) 2w2 u22 Wul2
~ + 2 (10)
q b 2 2 2 2 2
q W2 + Wl Wl + w2 Wl + Wo
w2 +w1 +w2 12

The flow directions of figure 3B are the same as in figure 3A. A compari-
son of these two triangles indicates that the pressure rise, referred to
the average kinetic energy of flow which the boundary layer has to over-
come, is substantially higher for the blower blade than for the turbine
blade. This is the reason such marked deflection as assumed in figure 3
can apparently not be achieved at all in a blower blading without sepa-
ration. According to equations (8) and (10) the danger of separation is
so much greater as the flow is more deflected and the length ratio a/b
is greater. The result is that a turbine stage can be operated with a
greater ratio a/b, hence with a greater spacing rati- a/t or with a
greater deflection of flow, than a blower stage.

The present estimate gives obviously only an approximate picture of
the separation danger since the effect of blade formal and profile chord,
for example, are not mentioned at all. But even so it serves as a guide
for the evaluation of grids of highly cambered blades, for which there are
practically no test data available.

The preparation of more accurate data on profile form is the purpose
of the present report. The maximum lift coefficient ca max is not suit-
able for evaluating the separation danger on highly curved blades in
cascade arrangement, because existing constant pressure turbines operate
at lift values up to 6, while the flow over an airplane wing already
separates at ca max 1.5.

On the airplane wing there exists a definite relationship between
P2 9
lift coefficient ca and the parameter inti duced here. On

*Reviewer's note: This equation does not agree with Figure 3B.
P2 F3 PI P3
In order to do so, P- should be changed to -
q q
1That closely spaced, highly curved blades, for which the flow
is very considerably dependent upon the blade form, can result in a pres-
sure distribution other than triangular is shown in figure 9.
2 a "u2 "ul
The relation for blade grids is = 2 where

W is the value of the vectorial mean of the two velocities wl and wp.

6 NACA TM No. 1209

substituting a triangle for the pressure distribution plotted against
the profile chord t, the lift A per unit of span is A = Apm while,
by definition, A = ca tq. Lastly:

Sp2 ii
P2 p3 = APm q; hence 2 = 2c 1.
q ..l

P2 P3
The parameter 2 2 is therefore equivalent to the maximum

lift coefficient of wings ca N 1.5


The tests were made with a Mach-Zehnder interferometer (reference 6)
manufactured by Zeiss, (fig. 4). It consists essentially of four plane
mirrors, two of them (al and a2) being "half-silvered," and the other
two (bl and b2) with opaque silver coating. Every beam of light from
the light source c, is split into two parts at the half-silvered plate al,
and reaches the screen e by different paths. One part is reflected at al,
reaches mirror b2, passes through mirror a2 and reaches screen e with
a portion of its intensity. The beam going through mirror al arrives
after reflection at the mirrors bi and a2 at the screen e. The two
light rays passing through the interferometer when superimposed produce
interference fringes at the point of intersection (reference 1). If the
four mirrors are perfectly parallel the two light rays leaving plate a2
intersect at infinity. Thus the interference fringes would occur at
infinity. Since the wave fronts of the two light rays are parallel to each
other, however, the width of the interference bands is infinitely great.
Bands of finite width at infinity are obtained when the two mirrors a1
and a are turned through a small angle al and m2 out of their
neutral position. The plane in which the interference bands originate can
be shifted to any position at infinity and the width itself can be adjusted
as desired by corresponding choice of angle a1 and a2. At the setting
of the mirrors shown in figure 4, the two light rays move in divergent
directions from plate a2. Their extension backward meets in the plane
1 2, however, so in this plane a virtual interference pattern is produced.
This picture can be made visible on screen e by a converging lens d and
photographed. In reality, a more complicated optical device takes the
place of the lens. For the subsequent application of the interferometer
the plane 1 2 must be placed in the position between mirrors a2 and al

*Reviewer's note: This equation is correct only if q is
changed to q2. If that is done the lift coefficient ca is based
on q2 which is unusual but not necessarily incorrect.

i `41

NACA TM No. 1209

shown in figure 4. If the axes of rotation of'mirrors al and a2 are
normal to the plane of the drawing, the interference fringes thrown on
the screen are parallel to the axes of rotation. By swinging mirror a2
about a second axis which lies in the mirror plane and is normal to the
first axis, the direction of the bands can be varied at will. Their
relative spacing is varied by the adjustment of the angles cl and a2.
Monochromatic light produces contrasting interference fringes in a larger
field. For the present purpose a mercury vapor lamp with a monochromatic
filter which lets through light of the wavelength Xk = 0.561 x 10-3 milli-
meter was employed.

Placing a chamber f closed by two flat parallel windows g and
filled with a gas in the path of the rays and varying the density p of
the gas in the chamber by a value p', the interference pattern shows a
shift of the bands. The density variation in the chamber Ap = p' p
can be computed from the observed band shift by the formula (reference 1)

Ap = --pX (11)
L(n 1)

0 is the wavelength of the light in vacuum, E the band shift measured
in widths (one width equals the distance of the center lines of two suc-
cessive light and dark bands), n the index of refraction of the gas of
density, p and L the path-length of the light rays in the medium of
n 1
density p'. The expression has a constant value for every gas.
For air = 0.002265 The path length L for the setup used
P kg s2
is given by the inside distance between the two windows g. It amounts
to 199.8 millimeters. These values entered in equation (11) give

kg s
Ap = 0.001246c k -- (12)

Given the type of change of state by which the density variation
p' p of the gas in the chamber f was obtained, all the other conditions
of state can be computed from the fringe displacement. For the isentropic
change of state of an ideal gas It is p'/p = (p'/p) and T'/T = (p'/p)-"
for example. Through the density p' computed by equation (1l) the

NACA TM No. 1209

pressure p' and the temperature T' are defined. Likewise, for an
isobaric change of state the gas equation = RT gives the

temperature T' = T-P).

In place of chamber f the test section of a flow channel closed
at both sides by parallel windows g is placed in the path of the rays.
The blades to be studied are fitted into this channel in such a way that
the light rays pass parallel to the generating axis of the blades.
Through the air flow a density field is formed around the blades. Now
the density has a different value for the path of each light ray through
the channel. The result is a distortion of the interference fringes.

The blade grid, itself, together with the interference fringes
originating in the plane 1 2, is reflected on the screen e. Therefore,
the density field around the blades can be determined by measuring the
deflections of the interference fringes at each point of the screen. As
is seen from the subsequent photographs the density field of the flowing
air made thus visible brings out the extent of the boundary layer as well
as its separation.


The flow channel into which the blade grid was mounted is shown in
two sections in figure 5, and in photograph figure 6. The air is induced
by a blower through the rectangular inlet cone a and flows past the
blading b. The air jet leaving the screen is intercepted by the exit
cone c and returned to the blower by way of the diffuser d and a
pipe line connected by a flexible leather collar. The blower is driven
by a direct-current motor so that its speed can be controlled within wide
limits. It produces a maximum pressure difference of 260 millimeters of
water. Since the flow through the blades was to be explored at different
flow angles, the front and back wall f of the air channel before the
blading are pivotable about the two rotational axes g. The blade grid
could be investigated for six flow directions. Every setting called for
a different entrance cone a. The two parallel windows i were mounted
in the heavy side walls h of the channel. The front and back wall f
was sealed from the sides h by rubber collars and plasticine. The
blades b are suspended from two tension wires k of 2 millimeter gage
and sealed from the glass windows by glued on rubber washers I. To
prevent the exit direction of the air flow from the blading from being
Influenced by the position of the exit cone c, the dead air regions m
and n existing at either side of the jet were joined by two strong pipe
lines, by which a pressure balance is maintained between the dead air
regions. In spite of this the uniformity of the air jet behind the blade
grid 13 so far still not quite satisfactory, and is to be improved on the
newly designed set-up by larger dead air regions m and n. The blades

NACA TM No. 1209

were impregnated beech wood. Great care was taken to ensure the best
possible two-dimensional blade form, (flat, parallel generating line),
because the light rays must pass parallel to the blade as exactly as
possible over its entire length if an observation of the flow processes
in the thin boundary layer of the blade surface is to be possible. Appr>-
priate gages ensure exact parallel setting of the blades during assembly
on the tension wires. The grid spacing was varied by changing the number
of blades. The surfaces were finished with shellac to ensure smoothness.
In figure 7 two blades together with the tension wires are reproduced.
In the majority of the tests described hereinafter the middle blade of the
screen was heated. To this end the blade was provided with two holes o
into which a chromium-nickel heating coil on a ceramic tube was inserted.
Owing to the low thermal conductivity of the wood it was, of course, not
to be expected that the blade surface would reach a constant temperature,
which, however, did not matter in the present tests. The exact alinement
in the light rays of the interferometer was obtained by means of three
set screws p. From the 146 millimeter diameter circle presented by the
window for inspection, the interferometer covers a rectangular field of
view of 8 x 10 centimeters. The position of the field can be changed by
shifting the test section.

The flow velocity wo of the blades is computed from the negative
pressure Ap measured at the orifice r relative to the test room, by
the equation

'p = X (13)

X = density of air. The upper wall f of the channel contains further
three orifices s closed by threaded plugs, into which a small pitot tube
can be inserted, for checking the uniformity of air flow in front of the
blades. Up to a thin boundary layer at the side walls the velocity over
the cross section was practically constant and agreed with the figure
obtained by equation (13) to a few tenths of one percent. A check of the
flow behind the blades by pitot tube is afforded by a flange, shown in
figure 5, replacing one of the two glass windows. The flange consists
of a ring t and a concentric disk u which can be turned by means of
a handle v. Its setting is read from a scale w. This disk carries a
hole x for inserting a pitot tube. By moving the pitot tube in this
orifice and turning the disk u the flow in the section behind the blades
can be measured. This is important, in order to ascertain whether the
flow separates from the side walls h. This phenomenon was repeatedly
observed on blower blade grids (references 5 and 7). It is also intended
to use this method to measure the wake defect behind the blades, and thus
to establish the blade drag and the energy loss of the air at passage
S through the grid.

HACA TM No. 1209


A section of flow photographs for different spacing ratios and flow
angles is represented in figures 8 and 10 to 30. The shape of the blades
tested, visible from the pictures, was suggested from other tests. The
blade exit angle, measured between the bisectrix of the blade trailing
edge and the cascade direction, is 150 for these blades. Aside from the
two end pieces, which at the side facing the inside of the channel, were
shaped to conform to the blade profile, figure 5, two to four blades were
mounted in the working section. This made spacing ratios a/t, (fig..2),
of 0.687, 0.859, and 1.141 possible. The chord of the blade profile is
58.2 millimeters. It was measured, as for a wing, as projection of the blade;::l.
profile on a straight line touching the lower surface of the blade, figure 1...
Through the different settings of the channel walls f and the related
entrance cones flow angles of 20, 34, 48, 62, 76, and 900 were obtained.

Figure 8 shows an interference photograph at 0.687 spacing and 340
flow angle. The deflection of the interference fringes caused by the
density field in the flowing air is plainly visible. Directly at the
blade surface the interference lines have a bend, that is, an especially
great density gradient exists at the surface3 which is due to the fact
that the boundary layer of the flow is heated as a result of the heat
(heat of dissipation) liberated by internal friction. This phenomenon
makes it possible, as already indicated by Th. Zobel, to render the bound-
ary layer visible by interference photographs. Even the dead air region
behind the blade trailing edge, which is formed by the warmer air in the
boundary layer, is clearly shown. Outside of the boundary layer and the
dead-air region the air flow is, of course, free from loss, the change of
state of the air in this area is therefore isentropic, hence the pressure
field within the flow can be computed from the density field defined by
the interference photographs by means of the previously cited relations.
This method also yields the pressure distribution along the blade surface
from the fringe displacements at the border of the boundary layer, as
exemplified by the pressure area, figure 9, where the pressure distribution
is plotted against the grid width b (fig. 2), hence against the blade
projection on a normal'to the grid direction. The area of the pressure
surface indicates the tangential force acting on the blade. The photograph,
figure 8, was made at 21.7 meters per second air speed. The mean exit
velocity at the end of the blade channel computed from the continuity
equation was 89.5 meters per second. The mean velocity at the same point
from the interference record is 91.6 meters per second. The blower operated
at its maximum speed. The fringe movements (fig. 8) are not yet very great
at these velocities, and the accuracy with which the tangential force on
the blade can be determined from the interference photographs is, as a
result, not quite satisfactory. This drawback is easily removed by
addition of a stronger blower. The boundary layers at the blade inlet side
where the velocities are comparatively low, are not clearly visible in
figure 8.

3Unfortunately, many details on the photographs are not as clear
as on the originals.

NACA TM No. 1209 1

Since for the study in question, however, it is important to
observe the separation of the boundary layer, even at the low velocities,
S the temperature of the boundary layer was raised artificially by heating
the blade. According to the Navier-Stokes differential equations for
frictional fluid flow the field of flow is not affected by temperature
differences if the fluid properties (density, viscosity) are not dependent
upon the temperature and the lifting forces in the flow introduced by the
temperature differences disappear with respect to the inertia forces. And
this is certainly the case at the speeds and low increases of temperature
of 250 at the most produced within the boundary layer by the heating.
Figures 10 to 30 represent interference photographs with such blade heating.
The two heavy parallel lines are the shadows of the current supply wires,
carried in thin insulating tubing along the upright side walls of the
entrance cone, figure 6. The flow direction is nearly the same as the
direction of these wires.

Figures 10 to 15 show the flow at the smallest spacing
ratio a/t = 0.687, figures 16 to 21 at a/t = 0.859, and figures 22
to 27 at the greatest spacing ratio a/t = 1.141. Reverting to figures 10
to 15 it is seen that for this smallest flow angle the flow already breaks
down near the stagnation point on the back of the blade. According to
figure 10 the interference fringes at a certain distance from the blade's
surface disappear completely after a bend. That the area actually indicates
the dead air behind a separation zone is plainly seen in figure 27. The
bend of the interference fringes at the back of the blade somewhat down-
stream from the support wire breaks away from the surface of the blade.
This indicates the surface of discontinuity which always emanates from an
area of separation of flow. Such a surface of discontinuity dissolves
in vortices. Thio is manifested in the washed out fringes as soon as the
vortex frequency is sufficiently great. This is particularly plain from
the separation at the face of the blade of figure 27. Larger vortices of
correspondingly lower frequency are no longer seen in the photograph; but
they can be observed on the ground-glass plate by oscillation of the inter-
ference fringes in the dead-air regions. The disappearance of the inter-
ference lines inside a narrow strip along the face of the blade in
figure 10 is probably due to the deflected interference fringes being
extremely thin at this point and not reproduced on the photograph. The

4Figures 10 to 30 indicate that the interference fringes in the
boundary layer have a maximum deflection of eight interference Cringe
widths. Thus the maximum density difference in the boundary layer between
kg s
blade wall and free flow is, by equation (12), Lp =0.00997 k The
k s2 m4
air density in the tests was about p = 0.12 g- Since the change of
m4 AT Ap
state in the boundary layer can be regarded as isobaric, we get = -
as it follows immediately from the equation of state for a small change of
state. Therefore the maximum temperature difference inside the boundary
layer is IT = 24. The displacement by eight widths, however, occurs
only in very isolated cases. On the average it, and hence the temperature
differences inside the boundary layer, are substantially less.

NACA TM No. 1209

dead-air zone at the back of the blade disappears again downstream. It is
readily seen how, starting from the suspension wire, a new boundary layer
is formed in the accelerated flow. At the next greater flow angle,
figure 11, however, the separation at the back of the blade has already
disappeared. But at the great angles of setting, figures 14 and 15, the
flow breaks down at the front side in the vicinity of the stagnation
point. The flow adheres again farther downstream. In figure 13 a slight
breakaway is probably under way.

The same phenomena recur for greater spacing ratios. At a/t = 0.859,
figures 16 to 21, a second region of separation is observed, at the back
of the blade downstream from the end of the blade passage. In figure 16
this second breakdown is not quite so conspicuous. A variation of the
interference fringe right next to the blade surface is noticed at the
same place as in the subsequent photographs. Behind this region the flow
remains separated. The result is an expansion of the wake behind the
blade trailing edge. The exiting velocity direction, as shown by the
direction of the wake, is no longer exactly the same as the direction of
the blade trailing edge. The blade grid is, at this spacing, no longer
capable of completely deflecting the flow as far as the blade exit angle.

The separation phenomena at a/t = 1.141, figures 22 to 27, are
very pronounced. The wake behind the blades is very wide, as evidenced
from the direction of the discontinuity surfaces arising from the regions
of separation, and the direction of the outgoing flow is far from the
blade exit angle. The blading is impractical for a turbine at this
extremely large spacing ratio.

According to the photographs the blading can be used up to a/t = 0.859
and at flow angles ranging between 34 and 62. The slight separation on
the back of the blde at a/t = 0.859 should not cause perceptible impair-
ment of the efficiency, since the width ratio of the wake given by the
rounding of the blade trailing edge to the width of the undisturbed air
stream at the blade exit decreases with increasing spacing ratio. A
sharp exit edge would reduce the width of the wake, so that the flow condi-
tions would certainly be improved through the grid.

Since there is a possibility that the separation phenomena at the
blades are affected by the Reynolds number, the blading was investigated
with a/t = 0.859 at various flow velocities. Three photographs from this
test series are represented in figures 28 to 30. It is seen that the
separation is diminished at the higher speeds. If the Reynolds number is
calculated using the axial component, wm, of the flow velocity and the
blade chord t, its magnitude for figure 28 is 11800, for figure 29,
22300 and for figure 30, 35400. The axial component was used for calcu-
lating the Reynolds number because it can be precisely calculated on the
actual turbine from the discharge volume and the flow cross sections. Gas
or steam turbines operate with blades of from 1 to 3 centimeters chord and
flow velocities in axial direction w, of from 100 to 300 meters per second

NACA TM No. 1209 13

The gas or vapor temperatures range between 1000 and 200 degrees and the
pressures between 10 and 1 atmosphere, except fqr maximum pressure turbines.
This gives a Reynolds number ranging between 10i and 100. In consequence
the present test range lies approximately midway in the practical range.
One condition for the applicability of these data is, of course, that the
Mach number does not exceed the value 0.6 to 0.7, which usually is the
case on gas turbines.


To provide basic data for the design of turbine blading the flow
through a blade grid of highly curved profiles was analyzed by the inter-
ference method. The density of the air passing through the grid was
determined from the records and the pressure distribution past the blades
and the force produced by the pressures on the blade were obtained. Since
the boundary layer of the flow at the blade surface is plainly visible on
the interference records, any separation of flow is readily recognized.
These separation phenomena were studied first. It is expedient to use
comparatively large model blades in the tests. Limiting the Reynolds
numbers to values usual for turbine operation, therefore, gives propor-
tionally low airspeeds. One of the blades was slightly heated in order
to make the boundary layer visible at these speeds also.

The flow through a turbine blade grid with good (advantageous)
blade profiles was examined at different spacing ratios and flow angles.
The interference photographs of the flow through this grid as represented
in figures 10 to 27 indicate that at the smallest flow angle (200) the
flow has already separated from the back surface of the blade just behind
the inlet stagnation point. The flow separates likewise on the face of
the blade at great flow angles (600 to 900). In both cases, however, the
flow follows the blade closely again when the spacing ratio is small. At
greater ratio (say from a/t = 0.859 on), separation occurs again at the
back of the blade near the trailing edge. Behind this region of sepa-
ration, however, the flow no longer follows the blade surface. Thus the
separation leads to expansion of the wake behind the blade and so certainly
to a substantial impairment in efficiency. The described separation
phenomena are affected by the Reynolus number, as was determined in a
special test series (figs. 28 to 30).

The tests are at present being extended to other blade forms, with
the aim of developing suitable blade forms that ensure separation-free
flow within a wide range of flow angles and spacing ratios. The tests are
also to be extended to include blower blades. The flow losses can be
determined by momentum measurements in the wakes behind the blades and the
efficiency of the blading defined numerically. Since the temperature
conditions in the boundary layer on the blade surface can be determined
S from the interference photographs, this method is particularly suitable

NACA TM No. 1209

for the study of the efficiency of the different methods for blade cooling.
The effect of the Mach number on the flow is to be investigated also.

Translation by J. Vanier,
National Advisory Committee
for Aeronautics.


1. Schardin, H.: Z. Instrumentenkde. Bd. 53, 1933, pp. 396-403
and pp. 424-436.

2. Zobel, Th.: Z. VDI, Bd. 81, 1937, pp. 619-624.

3. Weinig, F.: Die Stromung um die Schaufeln von Turbomaschinen.
(Leipzig), 1935, PP. 125-137.

4. Ergebnisse der aerodynamischen Versuchsanstalt, GCttingen,
III. Lieferung, 1935, PP- 132-137.

5. Christiani, K.: Luftfahrtforschung Bd. 2, 1928, pp. 91-100.

6. Hansen, G.: Z. techn. Physik. Bd. 12, 1931, pp. 436-440.

7. Keller, C.: AxialgeblKse vom Standpunkt der Tragfligeltheorie.
Mitteilg. a.d. Inst. f. Aerodynamik. ETH (Zurich) 1934.

NACA TM No. 1209


Figure 1.- Pressure distribution around a turbine blade (Weinig).
t = blade chord, a = spacing, w1 = flow velocity.

NACA TM No. 1209



a. a

o s

S n








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NACA TM No. 1209 17

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NACA TM No. 1209

a, b

9 I 9

Figure 4.- Plan of the Mach-Zehnder interferometer.
Figure 4.- Plan of the Mach-Zehnder interferometer.

half-silvered mirrors
full-silvered mirror
light source

parallel glass windows
angle of inclination

NACA TM No. 1209



0a t.

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NACA TM No. 1209 21




0 0

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NACA TM No. 1209

Figure 9.- Pressure distribution around a turbine blade according to
figure 8.
b width of blade grid
Ap difference between local pressure and static pressure of flow
ql dynamic pressure of flow




NACA TM No. 1209 25















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NACA TM No. 1209 27


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NACA TM No. 1209 29





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