Bailey, Bruce M

Persh, Jerome

English

NASA Technical Reports Server

NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
TECHNICAL NOTE 3124
A METHOD FOR ESTIMATING THE EFFECT OF TURBULENT
VELOCITY FLUCTUATIONS IN THE BOUNDARY LAYER ON
DIFFUSER TOTAL-PRESSURE -LOSS MEASUREMENTS
By Jerome Persh and Bruce M. Bailey
Langley Aeronautical Laboratory
Langley Field, Va.
Washington
January 1954
AFM2C
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL NOTE 3wk
llllb5983
A METHOD FOR ESTIMATING THE EFFECT OF TURBULENT
VTZCK!ITYFLUCTUATIONS IN THE BOUNDARY LAYER ON
DIFFUSER TOTAL-PRESSURE-LOSS MEASUREMENTS
~ Jercme Persh and Bruce M. Bailey
SUMMARY
A method is presented for estimating the effect of turbulent
velocity fluctuations on diffuser total-pressure-loss measurements.
This method stipulates continuity of flow and is based on the assmption
that the diffuser dimensions, inlet conditions, and the approximate dis-
tance from the wall, if finite, to the point of zero velocity are known,
that the flow is symmetrical, and that the velocity outside the boundary
layer at the downstream measuring stations is not measurably influenced
9 by the turbulent velocity fluctuations.
.
Only the case of the conical
diffuser with incompressible flow is considered.
4 When the longitudinal velocity fluctuations are large, as etidenced
by discrepancies between the inlet and exit weight flows, the method com-
pensates for the discrepancies by adjusting the boundary-layer profile.
Total-pressure-loss coefficients estimated by the proposed method produce
substantially higher (more pessimistic) values than those obtained from
uncorrected impact-pressure-tube surveys. Application of this method to
the experimental data for cases of negligible
shows that the calculated total-pressure-loss
with the experimental value.
INTRODUCTION
weight-flow discrepancies
coefficient is in agreement
The extensive application of subsonic diffusers to modern aircraft
powerplant installations and the desirability of effective space utiliza-
tion have prompted the direction of considerable research toward devel-
1 oping efficient, short, wide-angle diffusers. The steep longitudinal
static-pressure gradients occurring in components of this @_pe, however,
#: result in highly distorted boundary-layer velocity profiles at the dif-
fuser exit. Such profiles are characterized by the presence of turbu-
lent fluctuating velocities which may significantly affect impact-
. pressure-tube measurements.
2 NACATN 3124
9
Boundary-layer control devices which accelerate the turbulent
exchange of momentum may intensify this effect. In the investigation
reported in reference 1, in which triangular.ledgeswere installed cir-
cumf’erentiallyin a 23° conical diffuser in an effort to increase the
momentum transfer, exit weight-flow values computed from impact-pressure
data were found to be 10 to 15 percent higher.than those at the inlet.
Consequently, values of total-pressure-loss coefficient calculated from
the exit data were incorrect. A study was therefore made to determine
whether the weight-flow discrepancies could be attributed to the influ-
ence on the impact-~ressuremeasurements of the turbulent fluctuating
..-
velocities in the boundary layer.
The purpose of this paper is to present a method for estimating the
magnitude of the effect of turbulent fluctuating velocities in the bound-
ary layer on diffuser total-pressure-lossmeasurements. In the develop-
ment of this method, continuity of flow is stipulated, and it is assumed
that the inlet conditions and the diffuser dtiensions are accurately
known, that the flow is symmetrical, and that the velocity outside the
130’undarylayer at the downstream measuring stations is not measurably
influenced by the turbulent fluctuating velocities. Only the case of a
conical diffuser with incompressible flow is considered; however, the
method can be readily extended to compressible flow.
13
H
h
Ii
P
qc
R
r
.
Is
TJ
SYMBOLS
v
gravitational force per unit mass
boundary-layer shape parameter, ~*/e
total pressure
mean total pressure
local mean static pressure
impact pressure, K - p r..
radius of diffuser
radial distance from center line
distance from diffuser wall, if finite, to point of zero
velocity
velocity outside boundary layer
—
—
—
.—
.
.
NACA TN 3124 3
u,V,w local mean velocity components
—— —
U’2,V’2,W’2 mean-square components of fluctuating velocity
~2 square of mean velocities, Up +$+$
V12 mean square of turbulent fluctuating velocities,
I’7
Y
P
e
Subscripts:
o
1
2
exp
L
T
—— —
U’2 2 2+ v’ + w’
weight rate of flow, lb/see
distance from wall measured
ais
mass density
boundary-layer
boundary-layer
boundary-layer
thiclmess
displacement
perpendicular to longitudinal
thickness,
~’p - ;)*
momentum thickness,
1’31- :)w
reference station
diffuser inlet station
diffuser exit station
experimental
linear velocity distribution
true
.
--- .
“
4 NACA TN 31.24
ANALYTIC RASIS Ol?lMl?I’HOD
9
d
The efficiency of a diffuser is usually expressed in terms of the
static-pressure-riseand total-pressure-loss coefficients. Both of ““
these quantities are generally determined fro-m-aseries of conventional
wall static- and stream to~l-pressure measurements at the diffuser inlet
and exit stations. .—
The rise in static pressure is computed_as the difference between
the mean static-pressuremeasurements at the diffuser inlet and the “- ‘“” —
diffuser exit; that is,
.-.
..,— .—
(1)Q2J = P2 - PI
The loss in mean total pressure between inlet and exit stations is
generally determined by the following relati_o_nsfor symmetrical flow: —
—
J waro
(3)
and
Equations (1) and (4) are usually nondimensionalizedby dividing by
the inlet impact pressure qcl.
(4)
Results shown in reference 2 indicate that hpact-tube measurements
are influenced by turbulent fluctuating velocities. The total pressure
recorded by an impact tube in an airstream containing fluctuating
velocities may be expressed by the following relation (ref. 2):
.
NACA TN 3124 5
(5)
(In
the
this relation the static pressure is assumed to be unifozm across
measuring station.) Because V;2 is always positive, the measured
total pressure will always be greater than the effective total pressure
by the amount A V12*2P
Since the turbulent velocities do not contribute
to the mean wei@t flow, weight flows computed from impact-tube measure-
ments will be greater than the true mean weight flows. A correction to
the computed total-pressure loss based on continuity of mean weight flow
therefore is proper since the effective total-pressure loss is based on
mean quantities only.
If the boundary layer at the diffuser inlet is not distorted and
therefore approaches the usual l/7-power-law velocity distribution, the
= component of equation (5) is negligible compared to the V2 compo-
nent, and accurate impact-tube measurements and, therefore, accurate
mean weight-flow values are obtainable. At the exit of a wide-angle
diffuser, however, the boundary layer is usually distorted and mean
a weight flows computed from impact-tube measurements, contmry to the
law of conservation of mass, are greater at the exit than at the inlet.
* When this condition exists it is reasonable to assume that the V’2
component in the boundary layer at the diffuser exit is not negligible.
In the experiments of reference 1, for some of the O.10-inch-high
rough-ledge configurations the weight flows measured at the exit were
found to be appreciably greater than those at the inlet. The data
plotted in fi~e 1, which shows the variation of weight flow with inlet
airspeed, were taken from this reference and illustrate that discrep-
ancies of the order of 10 to 15 percent were found. Consequently, total-
pressure-loss coefficients calculated from these data would be incorrect.
METHOD FOR ESTIMATING CORRECTED TOTAL-PRESSURE-LOSS COEFFICIENTS
If the actual weight flow at any given velocity, the dimensions
of the diffuser, and the velocity outside the boundary layer at the
diffuser exit are known, a boundary-layer thickness which will satisfy
continuity of the mean weight flow can be determined by making a suit-
able assumption for the velocity distribution and assigning a specific
. value for the velocity at some particular distance from the diffuser
wall. By assuming tkt the point of zero velocity near the diffuser
wall is Mown, a boundary-layer thickness may be calculated by this
.
.
6procedure
ured one,
and it should not be
provided the assumed
NACA TN 3124
substantially different from the meas-
velocity distribution fits fairly accu-
rately the probable mean distribution. (In the analysis made herein of
the data of reference 1, a linear velocity distribution was assumed.
However, for those cases for which the velocity profiles cannot be rea-
sonably matched by a linear velocity distribution, another assumption
as to the nature of the profile shape.may be made.)
In order to find the corrected total-pressure-loss coefficients,
the actual weight flow at any given velocity is first equated to the
integral expression for the weight flow at the diffuser exit:
(6)
If the velocity outside the boundary layer
‘2 is assumed to be meas-
ured accurately by an impact tube and to be constant over that region,
equation (6) may be transformed to
%fl$-$-j (7) :
which gives the boundary-layer thickness as a function of the mean
.
weight flow, the diffuser radius, and the velocity and density outside
the boundary layer at the diffuser exit for the assumed linear velocity
distribution. The counterpart of equation (7) for separated flow is
f )
Application of method. - Typical results of the application of the
preceding assumptions and equations to the data of reference 1 are given
in figure 2. Inasmuch as the point of zero velocity near the wall is
assumed to be known,”anotherpoint on the linear profile (the boundary-
layer thickness) can”be calculated through use of continuity and the
revised values of velocity may be detemined at any point. This infor-
mation, used in conjunction with the density of the free stream at the
exit, permits the computation of ~
indicatedby equation (3). Values of
the result computed from equation (k)
and %,2 through the integration
%J qc~ are obtained by dividing -
by tie inlet impact pressure.
.
NACA TN 3124 7
Values of total-pressure-loss coefficient &- qcl determined in
. /
this manner for the three configurations in figure 1 are shown in fig-
ure 3. Examination of this figure reveals that the esthated values
/
of m q= are greater than values computed from the experimental data
1
over the ,speedrange. This result was anticipated because, as noted in
a preceding section, the values of total pressure recorded by the impact
tubes are higher than the mean values and therefore, when integrated
/
across the stream, values of h— qcl which tend to be low result.
Error introduced by assmption of linear veloci~ prefile. - A
check was made with additional data from reference 1 to determine the
error introduced by the assmnption of a linear velocity profile. Another
configuration from reference 1 was selected for which negligibly small
discrepancies between tilet and exit weight flows were noted. This
configuration, identified as d-l in reference 1, has four rough ledges
of dissimilar heights. The procedure described was applied to the data
for this configuration and the results are shown in figure 4. The esti-
mated coefficients are, for this case, almost the same as the values of
/
~- qc~ computed from the original experimental data.
.
A comparison between the experimentally measured velocity profiles
and the assumed linear profiles for this configuration is given in fig-
ure 5. The assumed linear distributions are seen to compare reasonably
well with the measured profiles for configuration d-1. The values of
/~- qc~
estimated by the proposed procedure would therefore be
expected to be no more than slightly different from those computed from
the uncorrected data for this configuration.
The order of magnitude of the error obtainedby the linear-profile
assumption was determined for several cases for which the linear profile
did not provide a good fit to the actual velocity profile. Several veloc-
ity profiles were selected from data in references 1 and 3 as typical
of those occurring at the exit of diffuser-t~e components. Figure 6
shows a comparison between the true mean velocity profiles selected for
this analysis and the corresponding linear profiles. The linear profile
if seen to be a fair approximation to the true profiles for values of H
from about 2.6 to 3.4.
/
Values of b- qcl were calculated for all the profiles shown in
—
.
figure 6. For th~ profiles shown in figures 6(a) to 6(d) the calculations
were made for the arbitrary case of 5 = R/2 and a representative set
.
8of streem conditions from reference 1. Because the
fixed, it was necessary to allow the weight flow to
NACA TN 3124
value of 5 was
change for each
assumed value of
are indicated in
(fwq,
(W,c+ ‘i’h
H. The values of W obtained for each of the profiles
figure 6. Figure 7 shows the variation of the ratio
H for the cases investigated.
.
A further estimate of the order of magnitude of the error obtained
by the linear-profile assumption was made for the profiles shown in
figures 6(e) and 6(f). For these cases the experimental exit weight
flows were greater.than those at the diffuser inlet. Accordingly, the
velocities near the edge of the boundary layer were assumed to be reason-
ably accurate and velocity profiles were arbitrarily faired by a trial-
and-error process such that the inlet weight-flow values agreed. Values
of &-/qcl were calculated for both this faired velocity profile and
(G/,cl),
the linear profile and the values of
~l~c= ~
()
are indicated in
figure 7. It shouldbe noted that this procedure implies that the arbi-
trarily faired curve for the velocity profile is we true profile, and
the values of E against which
figure 7 were obtained from the
shown in figure 7 indicate that
(fa,cJT
the ratio
(G/,cl)L
are plotted in
faired velocity profiles. The results
the values of total-pressure-loss coef-
ficient estimatedby the proposed method are accurate to within 3 per-
cent over a range of boundary-layer shape factors from 1.8 to 4.0.
Remark on application of method. - It shouldbe emphasized that
the method proposed is not intended as a substitute for boundary-layer
surveys in the experimental determination of diffuser total-pressure-
10SS coefficients. It shouldbe used as a check for only those cases
in which turbulent fluctuating velocities sufficiently influence the
diffuser-exit total-pressure observations to result in weight-flow
discrepancies.
CONCLUDING REMARKS
A method has been devised for estimating the effect of turbulent
velocity fluctuations on diffuser total-pressure-loss measurements as
.
.
2K
NACA TN 3124 9
.
obtained by impact-pressure-tubereadings. In the development of this
u method, continuity of flow is stipulated, and it is assumed that the
inlet conditions, the diffuser dimensions, an~ the width of a separated
region, if any, are accurately known, that the flow is symmetrical, and
that the velocity outside the boundary layer at the downstream measuring
stations is not measurably influenced by the turbulent velocity fluctu-
ations. Only the case of a conical diffuser with incompressible flow
is considered, although the method may be readily madlfied to include
effects of compressible-flow conditions.
For cases where the effect of turbulent velocity fluctuations is
found to be large, as evidencedby discrepancies between inlet and exit
weight flows, the values of total-pressure-loss coefficient calculated
from the impact-pressure-tube data are shown to be incorrect. The method
co?gpensatesfor these discrepancies by ad~usting the baundary-layer
profile. The values of total-pressure-loss coefficient esthatedby the
proposed yethod are compatible wtth flow continuity and are higher than
the results obtained from the experimental data. For cases where the
effect of velocity fluctuations is small, estimated values of totil-
pressure-los~ coefficient agree well with values obtained directly from
experimental data.
. The method presented is not intended as a substitute for experi-
mental determination of diffuser total-pressure losses by boundary-layer
surveys. It shouldbe used as a check for only ”thosecases in which
. fluctuating velocities sufficiently influence the total-pressure measure-
ments to produce weight-flow discrepancies.
Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley-Field, Vs., July 30, 1953.
REFERENCES
1. Persh, Jerome, and Bailey, Bruce M.: Effect of Various Arrangements
of Triangular L6dges on the Performance of a 23° Conical Diffuser
at Subsonic Mach Nmnbers. NACATN 3X23, 1954.
2. Fluid Motion Panel of the Aeronautical Research Committee and Others:
Modern Developments in Fluid Dynamics. Vol. I, S. Goldstein, cd.,
The Clarendon Press (Oxford), 1938.
3. Von Doenhoff, Albert E., and Tetervin, Neal: Determination of
. General Relations for the Behavior of Turbulent Boundary Layers.
NACA Rep.’n2, 1943. (Supersedes NACAWR L-382.)
-.
80
70
63
50
W, lb/see
40
w
20
10
. #
I
Number of equally
uration spaced O. 10-inch-hi@
rough ledges
{
T
40 80 120 160 m 240 2%0 3XI 360 400
~
Ul, fps
g
El
Figure 1.-
2
Example of discrepanciesbetween weight flows ccmputed from
inlet and exit bp.2ct-pressure measurements (data of ref. 1) . E
1
1.2
1.0
.8
.6
g
.4
.2
0
, b .
I
Exp3rJental proifilea qat~= 2.5 gat~= 2.7 EL }.33
— --- Linear distribution
(8L computed from / / tH
m= (7)) /
J~
/
/
/’
,/
/
/
/ / /
/ / /
/
,//
% / /
, / / /
/
/ / /
/y
A , /
o .2 .4
~ “,
-=3&V
Uo .2 .4.. .6 .8 1.0
u
ii
I I I I I J
o .2 .4 .6 .8 1.0
Figure 2,- Compurison of experimental profiles with linenr distributions
for cuses in which observed inlet-exit weight-flow discrepancies were
considerable. ul =s250 fp9.
12 NAC!ATN 3124
—-- Estimated
— Experimental
.
.
xii
qcl
6
.15
.10
(a) 2 ledges.
.05
180 220 260 300 340 380 42o
u~; ms
.15-
—
- . —- ——
l 10 ~
I
(b) 3 ledges.
.05 l I I
180 220 260 300 340 380 42o
MO 220 260 300 340 380 420
U1, fps
.
Mgure 3.- Total-pressure-loss coefficients ccmputed by conventional interpre-
tation of impa~t-pressuredata compared wi%h-values-estimated by the me~hod -
of this paper.
, ,
, l &
,2
I I
0 Experimental
--- Est Mated
.1 . tL
—-. -—. -+% —- n - —.
0 I
120 160 2(33 2h0 2%0 320 360 400
Ul) fps
Figure 4.- Totd.-presmre-loss coefficients computed from pressure data
and estimated by present. method. (Case of neg.li,gibleweigM-flow
dj.Q~e~cies, configuration d-1 of r@f. 1.)
P
c
1.0
.8
.6
f
.4
.2
0
II
Experimental profiles - ~ “
~m” --- c.,
E R /
Line= distribution E
= 2.7
----
0(detenuined from eq. (8)) H /
,.
/ /
/ /
r’-’ r
A ‘
/’ul -282 *
p
h U1 . *8 fps
s
I
=S$=
. 1. c n
.C .4 .0 .U 1.0
;~
o .2 .4 .6 .8 1.0
u I I I I 1 J
tio .2 .4 .6 .8 1.0
:
u
Figure 5.- Comparison of experimental profiles with linear distribution
Por n cuae in which observed effects of fluctuating velocities were
negligible. (Configuration d-l of ref. 1.)
4 J # .
1
,,, ,
NACA TN 3124
— True profile
—.— Linear profile
1.2
0 Experi~nt&
I
.
I
w = 63 lbjsec w = 52 lbjsec II
.4>
.471 I LA’ I
o .4 .8 1.2 0 .4 .. .8 1.2
1.2
.8
~
a
.4
l
g
(a)H = 1!8(ref.3).
1
W = 49 Ib/sec
o .4 u .8 1.2
—
(c] H :3.0 (ref. 1).
1.:
.8
g
.4
0
I
/R
--6
= 2.5
.4 ~ .8 1.2
8
(e)H = 4.5(ref’.1).
1.2
.8
0
Figure 6.- Comparison of true, linear,
:
(b) H = 2.6(ref.3).
I
w = 46lb~sec
/
i
o .4 ,, .8 1.2
ii
(d) H = 3.4 (ref.1).
I 8
.4 .8 I
:
(f) H = 6.2(ref.1).
2
and experimental profiles for
—
several values of H.
16
.
.
1.2
1.0
.8
.2
0
1.0 2.0 3.0 4.0 5.0 6.0 7.0
H
I’igm-e7.-
(-)/()
Variation of A ~
%~T qc ~
with boundary-layer shape parameter H.
.
.
NACA-Lmgley - 1-11-64- moo


A method for estimating the effect of turbulent velocity fluctuations in the boundary layer on diffuser total-pressure-loss measurements

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