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NATIONAL ADVISORY COMMITTEE F'OR AERONAUTICS
ADVANCE CONFIDENTIAL REPORT
i" PHB :MIINARY INVESTIGATION OF SUPERSONIC DIFPSERS
AT: Art: ur Kantrowlts and Coleman duP. Donaldson
I .*" o -:; ... .,*. :.. i.. .. : '.:
: i" J iw .: '. .- .
i..: .i .
i. 'j; 1 dee leration of air from supersonic velocities
S la i sannelsh has been. studied. It has become apparent
tha: a normal ahook in the diverging part of the diffuser
s' s.pehaibay. necessary for stable flow, and ways of min'i-
m sing. the intensity of this shook have been developed.
: The frfet of various geometrical parameters, especially
eantac tion ratio in the entrance region, on the performs
A. e of.supersonic diffusers has been investigated.
:By the use of these results, diffusers were designed
itoehi starting without initial boundary layer, recovered
90 percent of the kinetic energy in supersonic air streams,
uai4to a Mach number of 1.85.
.The deceleration of air from supersonic to subsonic
Vicitieas is a problem that is encountered in the design
of-highwapeed rotary compressors and supersonic air intakes.
Th&effictency of the supersonic diffusers used to accom-
plish third deceleration has an important effect on the
:performance of these machines. The present study is
i Qltaded to provide information upon whioh to design.
eflaoient spersonic diffusers for use in cases in which
the-flow starts without initial boundary layer.
S The available .data on supersonic diffusers are very
lheager and are reviewedd by Crocco in reference 1. This
Sreiew indicates that, in the deceleration of air from
supersonia velocities, the total-heed losses are:so large
as to: aimpa a seriously the efficiency of machines employing
this: -rodes.. The experiments reported in reference 1 were
primarily daspgned to serve the needs of supersonic wind
Stabel, l Ae therefore only diffusers starting with initial
boundary layer were considered.
2 CONFIDENTIAL NACA ACR No. L5D20
FLOW IN A SUPERSOIIO-DIFFUSER
Stability.- In a Laval-nozzle the gases start at a
low velocity, are accelerated to the velocity of soubiain
the converging part of the nozzle, and are accelerated to
supersonic velocities in the diverging-part.of th. noathle.
The supersonic velocities reached can be calculated approx-
imately from the isentropic-mass-flow curve of figure 1 and
the geometry of the nozzle. It is well known that, for
shock-free flow, experiment is in good agreement with this
one-dimensional isentropic theory although, since the
boundary layer thickens in the diverging part. of thesozsle,
the Mach numbers'reached may be a little lower thbat.-.tWE% ,l
values calculated. (For example, see referenc.e'2.) (wf:ih
dimensional nozzles can be designed by the Prandtl-B3~Aeafn
method (reference 3) to give essentially shockfefree s apfl
sions, which can be obtained experimentally provid-dt'.O asf"
moisture-condensation effects are present (tefsreneeid"t:40
It might be supposed that the flow in a nozzle designed
by the Prandtl*Busemann method could be reversed. atdif
proper allowance were made for.boundary-layer dieplmeoftl
thickness, a smooth deceleration through the speed. ;. ;:.i ?
sound obtained. A flow of this type is, however, uinatefla
in the sense that it is unattainable in practice. Consider
that a flow of this type has been established. (See
fig. 2(a),) In this flow pattern the mass flow per unit
area through the throat is the maximum possible for the
given state and velocity of the gas entering the diffusers
As long as the flow entering the diffuser is supers.eaito,:
the entering mass flow would be unaffected by even4taiJ4ai.
.stream. A transient disturbance propagated upstreamE:iltdm::
'the subsonic region would, however, reduce the masa "It-ft~ r
at least temporarily in the velocity-of-sound regieozt fIJ.
Thus, a disturbance would result in an acduiulation saf:.i:l1
air ahead of the throat. The 'perturbation of the. oritgbjlt
isentropic flow produced by this accumulation of alr t:ll9tt.;
prevent the mass flow from returning to its initial..mntl-
imum value; thus, air would continue to accumulate ahead
of the throat until the mass flow entering.the:dtffu* i r
was reduced. In the case of a supersonic diffuser..immea.se
in a supersonic stream as in the experimental arrangemeGq't
described later, this would.necessitate the formation :.I ar:
a normal shock ahead of thb diffuser and, in other f'r'tg*0
ments, would likewise necessitate drastic changes &snj*h'U'Ii.
flow pattern. From the .discussion of the .tear itg,: ,?*ti.":
supersonic flows in diffusers given later, it will be *d .
that these changes are irreversible (certainly in the
experimental arrangement described later and probably in
mbst other arrangements). It therefore appears that
isentrople deceleration through the speed of sound in
channels is unstable end unattainable in practice.
In a series of preliminary attempts to produce an
approximation to isentropic deceleration through the speed
of sound, it was found that supersonic flow could not be
started into diffusers designed to produce this flow. In
diffusers with a larger throat area, the normal shock
jumped from a position ahead of the diffuser to a position
in the diverging part.of the diffuser. Flows of the type
shown in figure 2(b), which involve a normal shock in the
diverging part of the diffuser, were found to be stable.
S Contraction ratio and losses. An important part of
the losses in. a supersonic diffuser are associated with
the- dissipation accompanying the normal shock in the
div:erging part of the diffuser. It is therefore important
"'~o consider the factors that determine-its intensity. As
in a Laval nozzle, the position of the shock wave is
controlled by the back pressure on the diffuser and moves
upstream as the back pressure is increased. When the back
pressure forces the shock to a point close to the minimum
area of the diffuser, the shock Mach number approaches
its lowest value and the associated losses are minimized.
The magnitude of these minimum losses depends upon how
much the air entering the diffuser is slowed up by the
'time it reaches the minimum cross section. The more the
entrance area of the diffuser can be contracted, the lower
the :ach number of the normal shock and the greater the
efficiency of the diffuser. It is therefore valuable to
.npiider what determines the maximum contraction ratio
that can be used. (Contraction ratio is defined as the
"ratio of the area at the entrance of a diffuser to the area
at its minimum section. See fig. 2(b).)
In most applications, the establishment of supersonic
flow is preceded by a normal shock traveling downstream.,.
If this normal shock is to move into the diffuser at a
given entrance Mech number and thus establish supersonic
flow, the throat of the diffuser must be large enough to
permit the passage of the mass flow in a stream tube
having an area that corresponds to the entrance area of
the diffuser and a total head that corresponds to the
value behind a normal shock at the entrance Mach number.
Thus, if the throat area-has .minimum value for a given
NAOA 'AR .N. L5DRO
NACA ACR No. L5D20.,
entrance Mach.number, the Mach-'number at the. throat will
be close to 1 when there is a normal shock ahead of the
diffuser. An approximation"td the contraction ratt.' that
produces this condition can be found from conventional .
one-dimensional-flow theory. The conditions after th4
normal shock are known from the usual normal-shock equations
and it is necessary merely to find.the stream tube eentrac-
tion, which increases the Mach number-at the .throat .t'l.
Since the mass flow per unit area at th.e. Mach..numbeP.'f 1 `
for a given stagnation temperature is proportional 6; the
total head,.the maximum permissible contraction rati IsV.''
equal to the contraction ratio that would be require,.:fa :'
an isentropic compression to the Mach number of ,1 (frji'i'
the initial supersonic conditions) multiplied by the.
total-head ratio across the normal shock. The maxiamlJ'L
theoretical contraction ratio that permits starting of'''
supersonic flow is computed in this way in appendix .A and
is shown-in figure 3. If the throat area were redudWi
after supersonic flow had been established or if the ilo'
through-the diffuser were started by temporarily incbansNig
the entrance Mach number to a value greater than t&. "
design value, a less intense shock and lower losses "mcid ;
probably be obtained. In these cases, the lowest limit
of the shock intensity would be provided by stability
For diffusers in which the geometry (particularly
the throat area) cannot be variad..and i-n which the.'`per-
sonic flow cannot be started by temporarily. increa'sfn'g tlh
entrance Mach number, the minimumwloss diffusion occuivra
with the shock just downstream fr-on -the minimum seclt'dbon..
The .Mach number preceding such a.-shock (with isantr-p. d.
flow assumed) can be found from-the computed contraf6tiS
ratio (fig. 3) and equation (2):of .appendix-.A., ~el tdtiBl6
heed loss across a normal shock at this Mech.number,
(equation (4), appendix A) is then an approximation to
the minimum losses (with boundary-layer losses neglected)
in a supersonic diffuser subject to the foregoing'starting
restrictions. The performances of diffusers obtained in
this way are given in figure 4. .
It should be pointed out that these theoretical '
considerations are derived with the tacit assumption thatL
conditions in a plane perpendicular to the axis of the'..:
channel are constant; that is, one-dimensional flow is,""
assumed.. For example, the occurrence.-of oblique shocks
at the entrance of a diffuser would lightly a4ter thes4i;:.
conditions; in'particular, the normal shock.in'the diver tag
NAtA kCRNo. LSD20O CONFIDENTIAL 5
part of the diffuser would have a somewhat reduced
intensity and the theoretical efficiency would be some-
what higher. It is considered, however, that the general
features would not be much altered by the departures from
one-dimensional flow that would occur in diffusers such
as those discussed in the experimental part of this report,
In order to investigate experimentally the properties
of constant-geometry supersonic diffusers, the apparatus
shown schematically in figure 5 was designed .and con-
structed. The settling chamber was connected to a supply
of dry compressed air controlled by a valve in such a way
that the chamber pressure could be held constant -at any
desired value, The air left the chamber through inter-
changeable two-dimensional nozzles that were designed to
give parallel flow at various desired Mach numbers. The
feather-edge tip of the diffuser (fig. 6) was held in the
center of, the supersonic jet at the exit of the nozzle.
The experimental arrangement was designed to study the
operation of supersonic diffusers that started without
initial boundary layer. This condition was studied for
two reasons: (1) It is the simplest defined boundary-
layer condition to obtain experimentally, and (2)'it is
considered to approximate more closely than any other the
boundary-layer conditions that occur at the entrance to
supersonic diffusers used in compressors. A long sub-,
sonic diffuser cone behind the supersonic diffuser tip
was provided to complete the diffusion process. The valve
behind'the cone was used to control the back pressure in
the subsonic portion of the diffuser and an orifice was
used to measure the mess flow through the diffuser. The
surface in the supersonic diffuser tips was machined
steel, whereas the cone in the subsonic portion was rolled
and finished heavy sheet steel.
In order to compare the efficiencies of the various
diffuser combinations tested, two quantities were required:
(1) the percentage of the total head that the diffuser
recovered and (2) the entrance Mech number at which the
diffuser attained this recovery.
Because the losses in well-designed supersonic
nozzles are small, the absolute pressure in the settling
chamber was assumed to be the total heed before diffusion.
|m j ...
NACA ACR No, ;]ia,
This pressure was measured with a large mercury manometer.
The total head after diffusion can be assumed equal to tbh
static pressure'at the end bf the subsonic diffuser cone.
without appreciable error, inasmuch as the kinetic energy
at the end of the cones was of the order of 0.16 percent
of the entering kinetic energy. A mercury manometer was...
used to measure the difference between the total heads
before and after diffusion. These two measurements were
sufficient to determine the percentage of total head
The mass flow per unit area and the stagnation con-
ditions are sufficient to determine the Mach number at.
any point. (See equation (2), appendix A.) The Mach
number at which a diffuser was operating was determined
by measuring the mass flow through the diffuser, which
had a known entrance areas, and by measuring the settling
chamber pressure and temperature that correspond to
Two other observations were made. The pressure just
inside the supersonic tip of the diffuser was measured to
make sure that the shock had passed down the diffuser and
that supersonic flow existed in the contracting portion.
The flow in the nozzle and into the diffuser was observed
with a schlieren system to check visually whether the
shock had entered the diffuser.
In order to make a test, the nozzle was brought up"-
to design speed by increasing the pressure in the settling.
chamber po to some value that was held constant thtftAjgh
out the test. The throttling valve behind the diffuser'
cone was open and the shock passed down the .diffuser, if
the contraction ratio permitted, and stopped at some-plioe
in the diffuser cone. The throttling valve was then
slowly closed, thus increasing the pressure at the end of
the cone pf and pushing the shock upstream to lower and
lower Mach numbers. When the shock had been moved upstream
as far as possible, that is, just downstream from the
minimum section of the diffuser, pf reached its maximum,
value. Although pf was increased during this process,
the mass flow through the diffuser was not affected be.%uae
the flow was supersonic into the diffuser tip, When theI
valve was closed farther, the shock wave passed the mini-
mum section and suddenly moved out in front of the diffqser.
NJA AiR.N6. 5 20O CONFIDENTIAL 7
.r steass flow immediately dropped (and continued to drop
as Jhe valve was closed farther) and the pressure' inside
the diffuser tip immediately jumped to a subsonic value.
.The results of a typical test are presented in fig-
.ui: 7. The breaks in the mass-flow and tip-pressure
curves give an excellent indication'of when the diffuser
was operating at maximum efficiency and when it failed
to ant as a supersonic diffuser. The slight change in
mass flow while the diffuser was operating was due to the
fact that the pressure in the settling chamber Varied
slightly. from the beginning to the end of the test run.
The curves indicate that a given diffuser may have any
,WjaLue of total-head recovery, up to a certain maximum,
depending upon the position of the shock. Therefore, the
e' .,bous method of comparing the performance of a number
. slo:diffusers is to compare their maximum recoveries.
-:. RESULTS AND DISCUSSION
',"The primary design parameter-of a supersonic diffuser
is Its contraction rptio, which determines the minimum
K4a0..number-.~ which the supersonic diffuser operates and
the nounti.of compression that the entering air undergoes
before it must.negotiate the normal shock. If the con- .
traction ratio of a diffuser is increased, the minimum
Mach.number at which it operates theoretically increases
as shown in figure 3. The minimum Mach-numbers at which
a number of diffusers were observed to operate and the
Mach numbers at which they first failed to operate are
shown in figure 3. The points so plotted give excellent
agreement with the theoretical contraction-ratio curve.
As was pointed out previously, the effect of contrac-
tioa ratio uoon the performance of a supersonic diffuser
should be approximately as shown in figure 4. The observed
performances of three diffusers with different contraction
ratios are plotted in figure 8. The effect of contraction
ratio is very similar to the approximate theoretical
results shown in figure 4. The indicated discrepancy-
betw.ween experimental and theoretical results is probably
chiefly due to losses in the subsonic portion of the
Aftdr, the contraction .ratio of a supiersonic diffuser
Shas been:fixed according to the minimum Mach number at
NACA ACR No. L5~iE :
which it must operate, two other parameters the entraiob-
cone angle -and the exit-cone angle may be considered :f
Owing to the difficulty of measuring the exact
entrance angles .on the small diffusers tested, the data
evaluating the effect of the entrance-cone angle are-not"
considered quantitative and are not presented herein,*'-./
The trend observed, however, was that the larger the
entrance-cone angle, the better the performance of tht .
diffuser. Further experiment is needed to determine the.-
optimum entrance-cone angles although, for the three
diffusers of figure 8, the entrance-cone angles are
probably so close to the optimum that no large gain inh
recovery could be expected from a change in this paramef~r .
In the diffusers tested, the internal shape was faired@ --
a smooth curve between the entrance cone and the exit n0i.
The curve was close to a circular arc and started ve9r nSter
the leading edge of the entrance cone.
Two diffusers of equal contraction ratio and entrance-
cone angle but different exit-cone angle were tested, The
performances of the two diffusers with exit-cone angles
of 50 and 30 are plotted in figure 9. The diffuser With
an exitecone angle of 30 was found to give consistently
higher recoveries. As is pointed out in reference 14 the'
boundary layer.is thick after a normal shock and th*efl06
the pressure recovery in the subsonic cone must be s~tW"~1'
to prevent separation. The slightly different shepe.t ..
the performance curve of these diffusers when compa*bd:
with the other diffusers reported (fig. 8) may be dB to':--:-
the fact that, although the two diffusers correspond '
closely to each other except for exit-cone angles, they
do not correspond to the other three diffusers.
The total-head recoveries measured in the experiments
were transformed into energy efficiencies. The energy
efficiency n is defined as the percentage of available
kinetic energy recovered in the diffusion process or the-
kinetic energy of an expansion from the pressure at Vest
after diffusion pf to the pressure at the entrance :of
the diffuser Pe divided by the kinetic energy of an
expansion from the initial chamber pressure po to g.i:.
Because no external work is done, the whole process of i.;
expansion and diffusion is a throttling process' and the 1J'
stagnation temperature To is the same after diffusion
NAOBath 1,4 Z0 ... *CONFIDSMTIAL 9
as ,a ....t.he settling Sasmber4 The equation for the energy
et~o&siseny may be. written.
*2op [To T "
The symbols are defined in appendix B. When = 5.5,
where M is the Mach number of the flow entering the
The efficiencies obtained by equEtion (1) are compared
in figure 10 with the typical efficiencies (converted to
efficiency as defined in equation (1))of the work previously
done with supersonic diffusers presented by Crocco in
reference 1, the efficiency of a normal shock (combined
with compression to rest without further loss), and the
approximate maximum theoretical efficiency .for constant-
geometry diffusers previously derived. Figure 10 shows
that the normal-shock efficiency may be exceeded and that
energy recoveries of over 90 percent can be obtained up
to a Mach number of 1.85; thus, the results presented for
supersonic diffusers in reference 1 are far too conservative
for diffusers that have no initial boundary layer.
An investigation of the deceleration of air in channels
from supersonic to subsonic velocities was conducted. A
channel flow involving the shock-free deceleration of a
gas stream through the local speed of sound was found to
be unstable. A stable flow probably involves a normal
shock in the diverging part of the diffuser. The losses
10 CONFIDENTIAL NACA AOR No. LSDW S .
involved in this normal shock can- be minimized by makingl-
the throat area as small as possible for a given entrana.i :
Mach number. The maximum contraction ratio that permits
starting of supersonic flow at a given entrance Mach
number has been calculated and checked very closely by
With the use of these results, diffusers were designed
which, starting without initial boundary layer, recovered
over 90 percent of the kinetic energy in supersonic air
streams up to a Mach number of 1.85.
Langley Memorial Aeronautical Laboratory
National Advisory Committee for Aeronautics
Langley Field, Va.
NAWA AR W~. L5D20
CALCULATION OF MAXIMUM PERMISSIBLE CONTRACTION RATIO
It can be shown that the mass flow per unit area at
Mach number M is
= M + --2M) (2)
where the symbols are defined in appendix B.
The isentropic area-contraction ratio from a Mach
number M to the local velocity of sound is then
where pV is computed from equation (2).
When air crosses a shock wave, its stagnation
temperature is unchanged; hence, the reduction in possible
mass flow per unit area, from equation (2) and the perfect
gas law, is proportional to the total-head loss across
the shock. The total-head ratio p3/Po across a normal
shock wave can be shown to be
P3 (\ 1)
Po Y 1
+ .M2 1)
-0 -1 1 -
Multiplying equation (4) by expression (3) gives the
maximum contraction ratio that permits supersonic flow to
start in a diffuser. This, quantity is plotted in figure 2.
NACA ACR.No. L5DiQ
y ratio of specific heat at constant pressure to
specific heat at constant volume
a velocity of sound
M Mach number
Cp specific heat at constant pressure
R gas constant
pe pressure at entrance of diffuser
pf pressure at rest after diffusion
Po initial chamber pressure
p3 total head after normal shock wave '' ''
Pd pressure at internal leading-edge of supersanic
diffuser (see fig. 7)
Md design Mach number of supersonic diffuser; that
is, minimum starting Mach number of diffuser
with given contraction ratio
T entrance angle of diffuser (see fig. 6)
8 exit angle of diffuser
b, c dimensions used in .ig. '2
CR contraction ratio (see fig. 2(b))
NACA ACR No. L5D20
S passage area
The subscript o refers to initial stagnation conditions.
1. Crocco, Luigi: Gallerie aerodynamiche oer alte velocity.
L'Aerotecnica, vol. XV, fasc. 5, March 1955, pp. 237-
275 end vol. XV, fasc. 7 and 8, July and Aug. 1935,
2. Kantrowitz, Arthur, Street, Robert E., and Erwin,
John R.: Study of the Two-Dimensional Flow through
a Converging-Diverging Nozzle. NACA CB No. 3D24,
3. Busemann, A.: Oasdynamik. Handb. d. Experimentalphys.,
Bd. IV, 1. Tail, Akad. Verlrgsgesellschaft m. b. H.
(Leipzig), 1951, pp. 421-541 end 447-449.
4. Doneldson, Coleman duP.: Effects of Interaction
between Normrl Shock and Boundary Leyer. NACA CB
No. 4A27, 1944.
0'0dS 'oiP mOiJ- s9l-3o0Tdoa1uasI
NACA ACR No. L5D20
! o -i
NACA ACR No. L5D20
COMMITTEE FOR AERONAUTICS
(a) Reversed Laval nozzle with isentropic flow (unstable).
(b) Stable supersonic diffuser flow. (For circular
diffuser = CR, where CR is contraction
Figure 2.- Flow in a converging-diverging diffuser.
NACA ACR No. L5D20 Fig. 3
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NACA ACR No. L5D20
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NACA ACR No. L5D20
OZ __ _
COMMITTEE FOR AERONAUTICS
Figure 6.- Interchangeable circular diffuser tips for which performances
are shown in figures 8 and 10. These different tips were screwed into
a permanent cone having an exit angle of 30. r, entrance-cone angle.
NACA ACR No. L5D20 Fig. 7
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NACA ACR No. L5D20
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UNIVERSITY OF FLORIDA
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