NACA
RESEARCH MEMORANDUM
CHARACTERISTICS OF FLOW ABOUT AXIALLY SYMMETRIC
ISENTROPIC SPIKES FOR NOSE INLETS AT
MACH NUMBER 3.85
By James F. Connor s and Richard R. Woollett
,
Lewis Flight Propulsion Laboratory
Cleveland, Ohio
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASHINGTON
NACA RM E54F08
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESEARCH MEMORANDUM
CHARACTERISTICS OF FLOW ABOUT AXIALLY SYMMETRIC ISENTROPIC
SPIKES FOR NOSE INLETS AT MACH NUMBER 3.85
By James F. Connors and Richard R. Woollett
SUMMARY
An experimental study of the compression fields around axially symmetric isentropic spikes with varying degrees of compressive flow turning
was made at a Mach number of 3. 85 in order to analyze the basic shock
structures and thereby establish further design crit eria for supersonicinlet applications. Pi tot-probe surveys and static-pressure distributions
along the sur face were used in conjunct i on with extensive schlieren photographs a nd shadowgraphs to i nterpr et t he flow. For zero-angle-of-attack
conditions, re sults are presented for spikes both wi th and without tip
roughness .
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For inlet s ut ilizlng al l - external compres sion, t here appeared t o be
a pract ical design limitation on t he degree of compressive turning that
could be effi cient ly imposed on t he flow . This limit was the amount of
turni ng required to produce a s tatic - press ure rise equal t o that a cros s
a free -stream normal shock. Over a wide range of Mach number s (2.0 to
6.0), this criterion satisfactorily predicted t he shape and t he s l ope of
a curve of current experimental maximum inlet - pres sure rec overies. At a
Ma ch number of 3 . 85, the limiting va lue corresponded to a f inal Mach
number out side of the boundary layer of 1.95 and a theoreti cal maximum
pres s ure recovery of 0.74 . The difference between this and the exper i mental maximum inlet recovery (0.62) is largely assignable t o fr icti onal
a nd sub s onic diffuser losses.
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Is entropic survey-spike configurations which exceeded thi s limit of
compressive tur ning resulted in a reorientation of the shock structure
whereby either a bow wave moved out forward of t he mai n shock intersection,
or a double-inters ection pattern w~s formed with a st rong shock followe d
by a subsonic expansion fi eld occurring between t he t~o .
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INTRODUCTION
A rather extensive investigation of annular nose inlets at Mach number 3.85 has been undertaken at the NACA Lewis laboratory. Earlier results on the performance (pres~ure, mass-flOW, and force data) of several axially symmetric inlet configurations have been analyzed and reported
in references 1 and 2. Of those studied, the isentropic inlet indicated
the best over-all performance at zero angle of attack as a result of attaining the highest total-pressure recovery without prohibitive external
drag. This conclusion was based on a comparison of the specific fuel
consumptions and propulsive thrusts of hypothetical ram-jet engines utilizing the various inlet geometries. For the isentropic inlet, a maximum
recovery as high as 0.625, corresponding to a kinetic energy efficiency
of 0.95, was realized. However, this value was still far below a theoretical maximum recovery of 0.92 which was based solely on normal shock
losses after assuming inviscid flow and isentropic compression to Mach
number 1.5.
In view of the large discrepancy between experiment and theory, the
present investigation was undertaken to ascertain the basic underlying
factors contributing to such a difference. Specifically, the objectives
of this study were (1) to survey and analyze the basic shock structures
and the flow fields around the isentropic spike at Mach number 3.85; (2)
to establish, at least qualitatively, a breakdown of the losses associated
with this particular type of design; and (3) to indicate possible direction in changing the design procedure in order to attain further improve ments in over-all performance.
Experimentally, the flow fields of isentropic spikes with various
degrees of compressive flow turning were surveyed by means of a traversing pitot probe and wall static-pressure distributions. The results of
these pressure data were supported by both schlieren photographs and
shadowgraphs of the corresponding shock patterns. In addition, the investigation w~s conducted both with and without the application of roughness to the spike tips, and only zero angle of attack was considered.
SYMBOLS
The following symbols are used in this report:
M
Mach number
P
total pressure
p
static pressure
- - - - -
-
-
-
- - --
-
- -
- -
NACA RM E54FOS
K.E.
3
kinetic energy efficiency defined as ratio of kinetic energy
available after diffusion to kinetic energy in free stream,
1 - (y _
Y
ratio of specific heats fnr air
y
A
~)Mo2 ~~
y - 1
max
maximum two-dimensional flow turning
~ngle
for attached flow
Subscripts:
o
free-stream conditions
1
conditions in survey plane at main shock intersection
3
conditions at end of subsonic diffuser
B
conditions behind normal shock
f
final conditions outside of boundary layer
x
local condition
APPARATUS AND PROCEDURE
The experimental program was conducted at a Mach number of 3.S5 in
the Lewis 2- by 2-foot supersonic wind tunnel. Test-section conditions
corresponded to a simulated pressure altitude of approximately 108,000
feet and a Reynolds number per foot of approximately 1.03 xl0 6 . Tunnel
air was maintained at a stagnation temperature of 200±5° F and at a dewpoint temperature of -20±lOo F.
In figure l(a), a photograph is presented to show a general over-all
view of the isentropic inlet (5-in. maximum cowl diameter) installed in
the tunnel test chamber. The entire configuration is the same as that of
references 1 and 2. In table I pertinent dimensions of the isentropic
inlet and survey spikes are listed. For the survey study, the inlet cowl
was removed and the exposed blunt lap-joint was concealed behind a sharpedged ring. A close-up photograph showing the isentropic spike and pitotprobe survey arrangement is given in figure l(b). Probe tip dimensions
are presented in the schematic sketches of figure l(c). For convenience
the isentropic spike of reference 1 will hereinafter be referred to as
the original spike, as contrasted with the survey-spike configurations.
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NACA RM E54F08
As illustrated in the drawing of figure l(d)) the contours of the original
and survey spikes were somewhat different in scale; however) the two spikes
were otherwi se geometricall y similar.
The contours of the isentropic spikes were designed by the method of
characteristics (ref . 3 ) to focus all the compression waves at a point
located out on the conical tip shock. At this focal point) a twodimensional compressive flow turning (reverse Prandtl - Meyer streamline)
was assumed to occur. The initial cone had an 8 0 half-angle} and the
surface was not corrected for boundary-layer growth. The calculation
upon which the experimental contours was based emp l oyed a two-dimensional
turning of fini te radius and did not involve any iterations in the solution . In the subsequent analysis of the survey data} some discrepancy
existed between the experimental and theoretical final Mach numbers after
compression occurred . To check this discrepancy) a more refined calculation was made wherein several iterations were made in the solution for
each point in the characteristics network and a zero - radius point - turning
was assumed on the initial tip shock. The results of these two methods
are indicated in figures l(e) and (f). As shown} there was a negligibly
small differ ence involved between the geometric contours but rather appreciable changes in the local Mach number distributions along the spike}
particularly at the larger surface angles . Since the later refined calculation was corr oborated by the data} this Mach number distribution (fig .
l ( f)) will be used in the subsequent discussion. Thus) the original spike
instead of having a theoretical final Mach number of 1.5 was theoretically
capable of compressing the flow only down to a Mach number of 1.75) and a
corr espondi ng total-pressure recovery of 0 . 826.
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Similarly the survey spike was based on the same theoretical contour
and was designed to carry the compression initially down to a Mach number
of 1 . 73 . With successive maching operations to modify the spike shoulder
(fig . l(g))) several amo~nts of compressive flow turning were obtained.
These various steps corresponded to theoretical final Mach numbers of
1 . 73} 1 . 77 } 1 . 89) 2 . 06) 2 . 25) and 2 .45 and were designated as configurations A through F} respectively . As illustrated in figure l(f)} two
survey spikes were fabricated with different types of shoulder modfication
downstream of the design point . The first employed an immediate constantradius expansion after the design point (configuration designation unprimed) ; the second had a small - pressure - gradient conical surface following the design point (configuration designation primed) . The second
type was used in the pitot - probe survey study .
In order to study further the effects of an artificially induced
transition from laminar to turbulent boundary layer upon the main flow
f i elds } the isentropic spikes were also investigated with roughness.
This was done by applying a 1/2 - inch band of (No . 60) carborundum grit
to the spike tip . Configurations with tip roughness are designated by
the letter R .
To actuate the pitot probe} a small electric motor and screw arrange·
ment was used. As shown in the photograph of figure l(b)} the probe
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NACA RM E54F08
5
traversed a survey line perpendicular to the spike axis of symmetry. An
electric contact indicator was employed to establish the vertical zero
reference position of the probe. Manual adjustment for axial location
was also provided.
Additional pressure instrumentation consisted of approximately 25
static-pressure taps distributed axially along the spike surface. At the
exit of the subsonic diffuser of the isentropic inlet, an extensive pressure rake was used to indicate the inlet total-pressure recovery (see
ref. 1). Optical provisions for observing the shock patterns in the flow
included a twin-mirror spark schlieren system and a spark shadowgraph
system.
For probing along a spec ific line in the flow field, for example,
one passing through a particular shock intersection, the axial station
was determined through observation with the schlieren or shadowgraph apparatus. The inclination of the probe-tip was determined by the surface
angle of the spike at the survey station. Data were recorded as the probe
traversed between the spike surface and a point well outside the compres sion field. For use in the analysis, measurements of the various flow
angles were taken from schlieren and shadowgraph pictures enlarged to
approximately four times full scale.
RESULTS AND DISCUSSION
For clarity and continuity of development, this section of the report has been subdivided under three major headings. The first, "Original Isentropi c Spike and Cowl, " considers the flow characteristics of a
current high-performance isentropic inlet. The secon'Cl, "Isentropic
Survey- Spike Configurations ," presents the results of an extended study
of the compression characteristics of a family of isentropic spikes having
various amounts of turning above and below that of the original inlet configuration. Finally, the third subdivision, "External-Compression Limitations," concerns the conclusions or deductions derived from these studies
and their extrapolation to other Mach numbers. This last section includes
a new viewpoint which indicates that the performance capabilities of
external - compression inlets may be limited to values much lower than
heretofore anticipated.
Original Isentropic Spike and Cowl
Inlet performance. - Static - pressure distributions along the center body surfaces of the isentropic inlet during supercritical operation are
presented in figure 2. As the back pressure was increased by progressively restricting the sonic exit area, the diffuser shock moved forward
and the total-pressure recovery increased to a maximum of 0.574. At this
condit i on the shock was located c lose to the cowl lip as demonstrated by
the static pressures. The distributions, in general, indicated that the
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NACA RM E54F08
subsonic diffuser was performing satisfactorily insofar as there was no
evidence of local separations of the flow that might limit the forward
positioning of the normal shock configuration. However, the staticpressure level at the minimum area (entrance) was somewhat below that
expected from the theoretical design (theoretical px/P O = 0.18; experimental px/P O = 0.16). Approximately 5 to 6 inches from the spike tip,
there was a flat (zero pressure gradient) portion in the distribution
curve, indicating laminar boundary-layer separation and subsequent reattachment. A corresponding schlieren photograph of the inlet-flow pattern
(shown as an insert on the figure) illustrates further the extent of separation and its effect on shock structure and also the location of the
various shOCKS relative to both the spike and cowl. These shocks will be
described in more detail in the subsequent discussion.
Visual flow observations for spike alone. - In order to isolate the
supersonic portion of the diffuser for detailed study and to evaluate the
performance of the external - compression surface independent of the remaining inlet geometry, the cowl was removed. Resultant flow patterns of
the compression fields are presented in figure 3 for the spike with and
without tip roughness. For clarity, the nomenclature to be used throughout this paper is given in figure 3(a). Shock S for the no roughness
case is the shock which appears to form in the vicinity of the separation
point and is strengthened by the coalescence with weaker upstream shocks.
As shown here and in all the subse~uent photographs, the application of
tip roughness apparently eliminated boundary-layer separation. The shock
configurations in the vicinity of the main intersection were ~uite similar
for the roughness and no roughness cases.
Photographic enlargements of the main shock intersections are presented in figure 4. The shock formation consisted of a single-intersection
branch shock structure, the upper leg being of the strong shock family.
In order to satisfy the condition of a pressure balance across the vortex
sheet, a shock reflection was necessary.
The angles of the vortex sheets immediately behind the main shock
intersections were measured as being e~ual to or slightly greater (up to
approximately 60 ) than the maximum deflection angle corresponding to the
free-stream Mach number (Amax = 38.2 0 ) . A solution compatible with such
angular measurements (in excess of Amax) is that the upper leg of the
branch configuration was actually a bow wave. This possibility was checked
against the approximation of reference 4 by conSidering the contour of the
vortex sheet analogous to that of a blunt body in a flow at free-stream
Mach number . Agreement was only fair, but probably within the accuracies
of the method and the angular measurements. However, there also exist ed
the possibility that, since the main shock intersection itself was not
preci sely defined in the photographs, all the shock waves may not have
fallen exactly on a single focal point of intersection. Thus, knowledge
of the flow structure may have been obscured and limited by the resolving
power of the optical system .
NACA RM E54FOB
7
To illustrate the extent of the influence of probe disturbances on
the flow fields, typical photographs of the largest pitot probe in survey
positions are shown in figure 5. The effect appeared small. Subsequent
surveys were made with probe tips of one half this size.
Pressure and Mach number profiles. - Profiles of the flow along a
survey line through the main shock intersection and perpendicular to the
spike axis are presented in figure 6 . The pitot-pressure profile (fig.
6(a)) indicated a maximum pressure recovery (Px,B/Po) of 0.73 with a mean
value obtained through an area integration from the wall out to the main
shock intersection of 0.64. This value of 0.64 roughly checked with the
maximum over-all inlet recovery of 0.574 by allowing the difference to be
attributed to subsonic diffuser losses.
Mach number and total-pressure profiles (fig. 6(b)) were calculated
by applying the Rayleigh and other normal-shock equations to the measured
pitot pressures and a static pressure, which was assumed to hold constant
from the spike surface out to the main shock int·e rsection. This assumption was deemed to be reasonably valid after an inspection of the theoretical characteristics diagram revealed very small changes in Mach number from
the surface to the intersection - in this case, approximately 1.75 to 1.74.
Outside of the boundary layer, the final Mach number was approximately 2.0
with nearly isentropic compression being indicated by total-pressure
ratios close to unity. This Mach number was well abOVe the 'design value
of 1.75. However, these conditions plus an approximate 20 compression
(as a shock reflection) roughly satisfied the strong shock pressure rise
across the upper leg of the branch shock configuration, thus providing
the required pressure balance across the vortex sheet.
In order to investigate further the extent of the boundary-layer
separation off the spike and its effect on the main flow field, a pitotpressure survey was made through the separation zone at a. station 5.B
inches from the spike tip. Without tip roughness (fig. 7(a)), the thickness of the separated region was clearly defined and was approximately
0.035 inch as indicated by the cross-hatched band. With the application
of tip roughness (fig . 7(b)), this separation was eliminated. It was
also observed that the mean values of the pressure ratio px,Bipo at
this station were approximately the same for both the roughness and no
roughness cases even though the distributions across the flow field were
quite, different.
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In analyzing the branch- shock configurations of the original isentropic spike, it was evident, from the viewpoint of inlet application,
that further systematic research should be directed toward studying
various amounts of external compressive turning for the purpose of optimizing the performance of this type of inlet. With this aim, the
isentropic spike survey program was undertaken .
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8
Isentropic Survey-Spike Configura tio ns
Visual flow observations. - Based solely on isentropic compres s ive
fl ow turni ng with characteri sti c s focusse d at a pOint on the initial tip
shock, the theoretical design variables of fi nal Mach number and s urfac e
a ngle are tabulated on figure l(e). Varying degre es of compression above
and below that of the original spike were incorporated in the des i gn . The
re s ulting flow patterns obta ined for the various configurations with and
wit hout r oughness are shown i n the schlieren photogr aphs and shadowgraphs
of figur e 8 . For configurations A, B', and C' wi t hout roughness (f igs .
8 (a), (b), and ( c), respectively) , double- intersecti on solutions were
obtained wherein the upper one was designated as the shock- S intersection
and the lower one as the main sho ck i ntersection . As can be observed in
the photographs, the vortex sheet from the shock- S intersect ion had a
pronounced curvature immediat e ly downstream of the intersect ion before
it parall eled t h e lower vortex she et . The angles of t hese t railing vortex
l i nes attained maximum val ues of approximately 45 0 with the axis of the
spi ke (~ax = 38 .2 0 ). Wi t h decreasi ng turning, t hat is, pr ogressing from
A toward C', the annula r di stance between t he two i nter sections was ob served to decrea se.
With the appli cati on of roughness to the spi ke tip , configurations
A( R), B' (R), and C'(R) were f ound to have definite bow waves f ormed out
ahead of t he main shock intersect ion. Again , the bow-wave relations
given by t he approximation of ref erence 4 were applied a nd f ound to hold
reasonably well . I n addition, i t was not ed that the upstream displa ce ment of the bow wave ahead of the main shock i nter s ection decreas ed with
de creased t urning f rom A(R) t o C'(R).
I n figures 8 (d) , (e), and (f) the flow patterns ubtained with conf igurations D', E', and F', respectiv e ly, wi th and without tip roughne s s
are s hown. In each case, Single- i nt ers e ct i on weak t wo- dimensional branch
shock formations resul ted . As woul d be expected, the angles of the vortex
sheets a nd the shocks downstream of the intersection decreased with de creased t urning . The appli cat ion of tip roughness did not appr eciab l y
alter the basi c s hock structures i mmediat ely downstream of the main-shock
intersecti ons .
For t he configurat ions with cons t a nt - radius shoulder, expansion
waves emanat i ng from the spike surfac e immediately after the design point
produced a mar ked change in the shock pat tern when compared with that
obtained with a conical section after the design point. This change is
illustrated quite clearly by comparing the patterns for configuration C
with and without roughness (fig. 8(g)) to those of configuration C' (fig.
8(c)). This e~fect precluded the accurate interpretation of the survey
da ,a in that the traverse line of the probe would then have to pass
through a nonuniform stat·c-pressure field. Consequently, all pressuresurvey data were take!. with configuration modifications of the conical
small-pressure-gradient type.
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NACA RM E54FOS
9
Pressure and Mach number profiles. - Pitot-pressure profiles in a
survey line perpendicular to the axis and passing through the main-shock
intersections (indicated in fig. S(a)) are presented for the various
isentropic survey-spike configurations in figure 9. The vertical lines
and arrows on the figures indicate the shock intersections as measured
from corresponding shadowgraphs. Generally, it was found that the application of tip roughness resulted in slightly higher pitot pressures.
With the exception of configuration A, the maximum values of px,B/P o
decreased with decreased turning. The highest value of 0.S4 was attained
with configuration BI(R). For the double-intersection solutions (configurations A, B', and C'), low-pressure-recovery ~ir was encountered
be~ween the mai n and shock
S-intersections. In every case, the thickness of the boundary layer at the survey plane was approximately 1/8
inch and represented a large portion of the annulus o~ ail (in some cases
more than one third of the height) between the spike surface and the
main shock intersection. Within this boundary layer, an irregularity in
the profile (approximately 0.05-in. from the surface) became evident with
configuration CI and became more pronounced with decreased compression
from CI to Fl. The reason for this irregularity is at present unknown.
In figure la , the static -pressure distributions along the surfaces
of the various isentropic survey-spike configurations with and without tip
roughness are presented. Enough data points were plotted to establish
the experimental curves and to indicate the order of scatter. Also included is the theoretical distribution based on the characteristics solution. Generally fair agreement between experiment and theory was obtained with regard to the shape of the curve; however, all the experimental data tended to fall somewhat higher than the theory except for
a short range in the no-roughness case immediately following the laminarboundary-layer separation region. Slightly higher pressure levels were
realized along the spike for the tip roughness cases, except in the
separation region of the no roughness case., This separation zone was
clearly defined, for the no roughness configurations, by a flat section
in the distribution curve. The angle between this separation boundary
and the axis of symmetry was approximately 19 0 as determined by measurements from a large number of schlieren photographs. As seen from the
data, pressures upstream of the design points were unaffected by downstream shoulder modifications.
Mach number and total-pressure profiles (fig. 11) were again calculated from the survey pitot pressures and the wall-static pressure
which was assumed to hold constant throughout the compression field.
Outside the boundary layer , the Mach numbers conformed adequately to the
theory for all survey-spike configurations. In general, the data indicated nearly isentropic compreSSion in the center of the highcompression fields with total-pressure ratios near unity. For
NACA RM E54F08
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configurations A, B', and C', subsonic-flow fields were indicated
between the main and shock S-intersectiollS; however, the static-pressure
used in the calculation of Mach number in this region was somewhat
high.
Flow analysis of double-intersection shock structure. - Based on the
pressure-survey data and angular measurements from enlarged schlieren
photographs, a two-dimensional flow analysis was made of a typical doubleintersection shock structure (configuration A). A schematic representation of the flow is given in figure 12. The static-pressure levels in
the various fields and also the basis for calculation of the different
values are indicated in the inserted table.
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The requirement of a pressure balance across the vortex lines led
to the following conclusions: The flow field between the vortex lines
downstream of the main and shock S-intersections was essentially a
subsonic flow behind a strong (normal) shock reaccelerating to choking
at station 5, as labeled on the sketch. This interpretation was supported by the curvature o~ the upper vortex line before it became parallel to the lower one and by the area contraction in the channel formed
between the two vortex lines, as seen in the schlieren photograph (fig.
8(a)). To satisfy the pressure requirement at the upper vortex line
just behind the shock S-intersection, the normal shock between zones 2
and 4 could bifurcate somewhat in the manner shown. This effect cannot
be distinguished in the photographs except as a blurred region since it
occurred in a very small area. Theoretically at least, the flow from
zone 3 would pass through the downstream leg of the branch shock and
enter zone 4 to 5 at near sonic velocity. A 50 to 60 compression wave
(as a shock reflection) served to provide the necessary pressure balance
across the lower vortex line. Thus, in this rather complicated shock
structure, the following static-pressure levels were encountered: in
the survey plane outside the boundary layer (P7/PO 23.5), downstream
of main shock intersection (P4/PO = P6/PO
30), and downstream of the
shock S-intersection (Pl/PO = P3/P O = P5/P O N 17.5). Although this largely qualitative discussion appears to describe this type of ShOCK structure,
no satisfactory description exists for the theoretical inviscid flow case
of high compressive turning with resulting mixed-flow fields.
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As observed earlier in the discussion of the shock patterns (fig. 8),
the two intersections tended to approach each other with decreased compressive turning. Thus, in the limit, superposition of the main and shock
S-intersections might be attained. This condition appeared to be nearly
achieved with the original isentropic spike.
Shock-intersection locations. - The relative positions of the shock
intersections encountered in the survey plane for the various configurations are presented in figure 13. Main shock intersections appeared to
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fall along a 45 0 line with a trend to move back from the tip and out from
the axis with decreased compressive turning. This 45 0 line tippeared to
be approximately at the angle of the final coalesced shock waves. As
shown on figure 13, the design focal point of the compression waves also
fell on this line and close to that of configuration A. With decreased
turning, the decrease in the annular distance between the main and shock
S-intersections for configurations A, B', and C' is again illustrated.
Potential inlet-pressure recoveries. - A summary of the potential
pressure recoveries available for all-external-compression inlets designed to accommodate the flow fields of these various isentropic survey
spikes is presented in figure 14. All the experimental data points represent values obtained through area-weighted integrations of the survey
profiles given in figure 9. The solid-line values are indicative of the
performance capabilities of hypothetical inlets having cowls located at
the main-shock intersections of configurations D', E', and F' with and
without tip roughness. As such, these inlets would have relatively uniform profiles at the entrance and no supercritical flow spillage (capture
mass-flow ratio of unity). The single-dashed-line values are for hypothetical inlets having cowls located at the main shock intersections of
configurations A, B', and C' with and without tip roughness. Although
benefitting from pressure recoveries higher than the solid-line values,
these inlets would be penalized by mass-floW spillage and attendant additive drag. For the no-roughness cases, this mass-flow spillage was
estimated at 5 to 6 percent of the maximum capt ure mass flow. With configurations A, B', and CI, there was the alternative of avoiding this
mass-flow spillage by locating the inlet cowls at the shock Sintersections; the resulting available pressure recoveries are indicated
by the double-dashed line values on figure 14 . Although there would be
no supercritical spill age, t hese latter i nlet s would be penalized by nonuniform profiles at the entrance with concomitant mixing losses and, more
importantly, with no gain in recovery above the solid-line values.
External-Compress ion Limitations
Mach number 3.85. - In the analys i s of thes e various shock structures,
it was observed that the required condi tion of balancing the static pressures across the vortex sheets (negl e cting flow direction) might impose
a limit upon the amount of external compre s sion attainable, this limit
being set by t he maxi mum pre ssure ri se through a single shock, that is,
the normal shock. This proposed limitation was converted int o a limiting final Mach number along the compression sur fac e ( see appendix) and
superimposed on the data of f i gure 14. As illustrat ed, this Mach number
l i mit (Mf = 1. 95) subdi vided the experimental data quite well in that
the c onfi gurations with excess compressive turning inc urred penalties
of mas s - flow spillage and additive drag which appeared to offset the gains
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NACA RM E54F08
in pressure recovery above that at the limiting value. For a free - stream
Mach number of 3.85, this limiting condition for all-external - compression
inlets corresponded to a final Mach number outside the boundary layer of
approximately 1 . 95 and a theoretical pressure recovery of 0.74. This
concept, derived from experimental observations, may then constitute a
practical design limitation, applicable to all-external-compression inlets
where mass - flow spillage and attendant additive drag are weighed in overall performance. An adequate theoretical description of the shock structures and mixed-flow fields when this limit is exceeded has not yet been
devised.
Variation with Mach number. - This proposed limitation for allexternal - compression inlets has been computed for free-stream Mach numbers from 2.0 to 6.0. Details of the relations used in the calculation
of the compression limits are outlined in the appendix. In figure 15,
a comparison is made between the total-pressure recoveries corresponding
to the compression limit and current experimental maximum recoveries obtained from a survey of the existing literature (refs. 1, 5, 6, and 7).
For the theoretical calculations of this limit, it was assumed that the
flow was compressed isentropically after an initial tip shock (totalpressure recovery, 0.99) to a static pressure equal to that behind a
normal shock at free-stream Mach number and then followed by a normal
shock located at the entrance to the diffuser (the cowl-lip station).
This process is schematically illustrated by the insert sketch of the
shock pattern shown on figure 15. Frictional or subsonic diffuser losses
were not included in the calculations. At a free-stream Mach number of
approximately 2.2, this limitation first came into effect. The theoretical maximum recovery then fell off quite rapidly with increasing Mach
number and at the same time crossed over lines of constant kinetic energy
efficiency ~ K.E. as shown on the figure.
This empirical limitation satisfactorily predicted the general shape
and slope of the experimental curve shown in figure 15. The displacement
between the two curves is, for the most part, assignable to the frictional
or subsonic diffuser losses Which the calculation did not take into ac count. For Mach numbers from 3 .0 to 5.6, this difference between the
limiting values and the current experimental maxima was approximately
0 . 15.
The variation of the final Mach number limit with free-stream Mach
number is presented in figure 16. Below Mach number 2.2, this compression
limitation does not exist; however, above this value the final Mach number limit increases almost linearly. At MQ = 6.0 this final Mach number limit is equal to 3.0.
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CONCLUDING REMARKS
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N
o
It has, thus, been observed that the performance capabilities of
high Mach number nose inlets employing conventional all-externalcompression surfaces may be li~ited to levels much lower than heretofore
believed possible. With conventional design, then, any future gains in
over-all inlet-pressure recovery are apt to be small and come from the
direction of improved boundary-layer control and improved subsonic diffusion. On the other hand, there may be some promise in the use of different design procedures such as the utilization of internal contraction
with adequate boundary-layer control and means for coping with the initial
starting problem (such as perforations or variable geometry.) However,
for these a loss in terms of drag or complex mechanisms, again, may more
than offset any gains in recovery.
SUMMARY OF RESULTS
An experimental analysis of the compression fields around axially
symmetric isentropic spikes with varying degrees of compressive turning
was conducted at a Mach number of 3.85. Results were extended to other
Mach numbers and are as follows:
1. For all-external-compression inlets above a Mach number of 2.2,
there appeared to be a practical design limitation on the degree of compressive flow turning which corresponded to that producing a staticpressure rise equal to that across a free-stream normal shock. Over a
wide range of Mach numbers (2.0 to 6.0), thlS limiting condit ion satisfactorily predicted the shape and the slope of a curve of current experimental maximum recoveries.
2. At a Mach number of 3. 85, the limiting condition corresponded to
a final Mach number outside of the boundary layer of 1.95 and a theoretical maximum total-pressure recovery of 0.74. The difference between this
and a previously reported inlet-pressure recovery of 0.62 is lar gely
assignable to frictional and subsonic diffuser losses.
3. Isentropic survey-spike configurations which exceeded t his limit
of compressive turning resulted in a reorientation of the shock structure
whereby either a bow wave moved out forward of the main shock intersection, or a double-intersection solution was formed with a subsonic
expansion field occurring between the two.
,
Lewis Flight Propulsion Laboratory
National Advisory Committee for Aeronautics
Clevp.land, Ohio June 23, 1954
L
14
NACA RM E54F08
APPENDIX - CALCULATION OF COMPRESSION LIMITS
Details of the calculations used in the determination of compression limits as a function of free-stream Mach number are as follows:
o
C\J
to
to
Po
Po
where
~/PO = Pa/P O
static-pressure ratio across a free-stream normal shock
PO/PO
ratio of static to total pressure at free-stream Mach
number
0.99 (initial shock loss)
where
total-pressure ratio across a normal shock at
~
,
NACA RM E54F08
15
REFERENCES
1. Connors, James F., and Woollett, Richard R.: Performance Character~
istics of Several Types of Axially Symmetric Nose Inlets at Mach
Number 3.85. NACA RM E52I15, 1952.
2. Connors, James F., and Woollett, Richard R.: Force, Moment, and Pressure Characteristics of Several Annular Nose Inlets at Mach Number
3.85. NACA RM E53J09, 1954.
3. Ferri, Antonio: Application of the Method of Characteristics to Supersonic Rotational Flow. NACA Rep. 841, 1946. (Supersedes NACA TN
1135. )
4 . Moeckel, W. E.: Approximate Method for Predicting Form and Location
of Detached Shock Waves Ahead of Plane or Axially Symmetric Bodies.
NACA TN 1921, 1949.
5. Hunczak, Henry R.: Pressure Recovery and Mass-Flow Performance of
Four Annular Nose Inlets Operating in Mach Number Region of 3.1
and Reynolds Number Range of Approximately 0.45 x l0 6 to 2.20xl0 6 •
NACA RM E54A07, 1954.
6. Bernstein, Harry, and Haefeli, Rudolph C.: Performance of Isentropic
Nose Inlets at Mach Number of 5.6. NACA RM E54B24, 1954.
7. Anon.: Fifth Quarterly Progress Report on Ram Jet Development. Rep.
No. 1521, Wright Ae:i:onautical Corp., Apr. 13, 1951. (Contract· AF
33 ( 038 ) - 9000 • )
NACA EM E54F08
16
TABLE I. - MODEL DIMENSIONS
(a) Isentropic inlet details. A, length of spike from tip to point of attachment to aft
body. in ; B, length of cowl from l i p to point of attachment to outer shell, i n .
~z
VI
VI
N
o
Oute r shell
~------- A --~----~
X
Spike
Outer shell
Aft body
X
y
Z
A
1. 82
B
Straight
taper
A + 4.50
A + 9 .1 3
A+14.25
1.22
Straight
taper
1. 00
B + 7 .1 86
B + 7 .6 25
Straight
cyl1nder
1.00
Isentropic
2 . 30
V
2 . 50
Straight
taper
Cyl1ndrical
U
B + 12 . 75
(A , 14 . 741)
Z
U
V
0
0
. 075
.145
. 216
. 284
. 357
.436
.528
.624
.742
.876
1.031
1.210
1.433
1.746
1.830
1 . 922
2 .025
2 .100
2 .1 37
2 . 159
2 .170
2 .17 8
2.180
2 . 174
2 .1 70
2.153
2 .113
2 . 060
1.994
1.906
1.820
.025
. 050
.100
.200
. 300
.400
.500
. 800
1.000
2.240
2.262
2 . 277
2.299
2.328
2.346
2.358
2 . 370
2 . 376
2.378
2.240
2 . 2 72
2.291
2 . 323
2.370
2 .404
2 . 432
2 . 469
2.492
2 . 500
Cyl1ndr i cal
Cyl1ndrical
X
0
2 . 06
l - in.rad . arc
.500
1.000
1.500
2.000
2 . 500
3.000
3.500
4.000
4.500
5.000
5.500
6.000
6 . 500
7.000
7.100
7.200
7 . 300
7.400
7 . 500
7 .600
7 . 700
8 . 000
8 . 230
9.000
9 .1 88
10.000
11.000
12.000
13 . 000
14 . 000
14.741
2 . 085
Straight
taper
2.375
Cowl
(B, 7.750)
Spike
2 . 50
Y
5 . 300
5 . 500
5.750
6 . 000
2.378
2 .3 76
2 .3 70
2 . 360
Straight
taper
7 . 760
2 .300
2 . 500
(b) Isentropic survey spike.
..l
1.820"
------1.1,.
14.75''--'
X
Y
X
Y
1.000
2.000
3 .000
4 .000
4 . 500
5.000
5 .500
6.000
6.500
7.000
7.250
0.143
.2 84
. 431
. 590
.683
.786
.904
1.033
1.178
1 . 342
1.433
7.500
7.750
8 . 000
8 . 055
8.274
8 .450
8 . 607
8 .770
8 . 860
8 .973
9 .040
1 . 529
1.636
1.754
1.781
1.898
2 .002
2 .108
2 . 232
2 .315
2.437
2 . 516
Design
points
F
E
D
C
B
A
I
-Ii
•
~
~
~
t:tj
~
o
OJ
( a) Isentropic inlet installed in 2- by 2-foot supersonic tunnel.
Figure 1. - Experimental apparatus.
t-'
--..J
I
I
L
NAeA RM E54F 08
18
!
vertical probe
traverse
(b) Isentropic spike and pitot-probe survey mechanism in tunnel test section.
c· 0401~
0.015"
tc::)-r
Used only for original spike configuration
Used on all configurations except F' and
original spike configuration
C·016'~ 0 .004
fc.:::::=-f
UBed with configuration F '
(c) Pitot-probe tip dimensions.
Figure 1. - Continued.
Experimental apparatus .
•
•
~
~
~
t:r:j
CJ1
~
o
CD
:3
C_~\
I:l
~
2
~
.
Survey-spike contour~
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'd
&!
1
or
,,,,,,,,.,
,,.,
o
1
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~
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Original-spike contour
\ \ \\
\ \ \ \
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,
lE
,,
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,
j
~
'F;/~ ~,..
2
j
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)
3
4
5
6
7
8
9
10
Axial distance from spike tip, in.
(d) Scale variation between original and survey spikes.
Figure 1 . - Continued.
Experimental apparatus.
t-'
to
t\)
o
20
Experimental contour
Theor etical contour given
by r efinements
0
en
~
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al
;.,
10
V
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1 __
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I
I
I
I
I
20
30
40
60
50
Axial distance
( e ) Isentropic spike contours plotted in arbitrary units ,
4
I
~"
';:<.><
~
;.,
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3
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2
---{}--- Original calculation
- - - Refined calculation
r-...
Design points,c
F
..c:()
.--I
......
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§
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al
()
Ii ~
C
0
>-l
1
o
10
20
30
40
~At -...
50
~
~
60
Local angle of spike surface with axis of symmetry, deg
~
t?::I
(f ) Local Mach number distribution fo r isentr opic spike contours.
Figure 1. - Continued.
•
Experimental apparatus .
CJl
~
o
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3320
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~
2.8
Configuration
I
A
B
2 .6
C
D
E
F
Theoretical
Mach
number
1. 73
1.77
1.89
2.06
2 . 25
2.45
&;
Surface
angle ,
deg
49.5
48.5
45.0
40 . 0
35.0
29 . 5
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Original contour A
-Unprimed ; immediate expansion;
constant radius
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conical surface
8 .3
8 .5
8.7
8.9
Axial distance from spike tip, in.
9 .1
9.3
9 .5
( g ) Isentropic survey spike configurations .
Figure 1 . - Concluded .
Experimental apparatus .
N
t-'
r
r
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....,.
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2
3
4
5
6
7
B
9
14
10
Axial distance from spike tip . in.
Figure 2. - Static-pressure distributions along spike of isentropic inlet for several supercritical operating conditions.
attack and no tip roughness.
Zero angle of
~
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•
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NAeA RM E54F08
23
(8) No roughness.
(b) With tip roughness.
Figure 3. - Shadowgraphs of flow patterns obtained with original
isentropic spike with inlet-cowl removed.
•
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Schlieren
(a ) No roughne s s.
Shadowgraph
~
~
Schlieren
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Shadowgraph
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Figure 4. - Enl arged schl i eren photographs and shadowgraphs of f low in .vicinity of main shock intersection for original isentropic spike .
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--~
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~
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Figure 5. - Typical photographs showing probe in flow field of original isentropic spike.
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NACA EM E54F08
26
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Distance from spike surface, in.
(a) Pitot-pressure profil e .
Figure 6 . - Profiles of flow in plane of main shock intersection for
original isentropic spike .
•
27
NACA RM E54F08
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Distance from spike surface, i n.
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(b) Mach number and t otal-pressure profiles.
•
Figure 6. - Concluded. Prof i les of flow in plane of main
shock intersection for original isentropic spike •
.--~
NACA EM E54F08
28
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Separ atiol1 zone
r She ar layer
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. 24
p.,0
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Di s tance fro m spike surf a ce , in .
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(b ) With tip r oughness .
t
Figure 7 . - Effect of r oughness on boundar y layer and main flow fi eld of
or iginal isentropic spike ( survey station, 5 . 8 in . fro m ti p) .
~---
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..
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en
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With tip roughn ess
(a) Config uration A.
Figure 8. - Flow pattern s for the variou s isentro pic
.survey spike configu ration. s.
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No r oughness
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with tip roughness
Figure 8. - Continued.
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(b) Configuration B'.
Flow patterns for various isentropic survey-spike configurations.
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fi!
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No roughness
With tip roughness
(c) Configuration C' •
Figure 8. - Continued.
Flow patterns for various isentropic survey-spike configurations.
C>l
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~
~
Figure 8. - Continued.
With tip roughness
~
(d) Configuration D' •
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Flow patterns for various isentropic survey-spike configurations.
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o
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Figure 8. - Continued. "Flow patterns for various isentropic survey-spike configurations.
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~
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(f) Configuration F' •
Figure 8 . - Continued.
Flow patterns for various isentropic survey-spike configurations.
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oQ)
~
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~
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g
No roughness
With tip roughness
C-3603l
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Figure 8. - Concluded.
Flow patterns ror various isentrop:1c survey-spike configurations.
CA
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36
NACA RM E54F08
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With rougbness
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Distance from spi ke surface, in.
(a ) Configur ations A and A(R ) .
Figur e 9 . - Pitot - pr essure profil es of flow in plane of main shock inter s ection for various is ent r opic survey-spike configurations .
.8
37
NACA EM E54F08
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Distance f r om spi ke s urface , in.
(b ) Confi gurations B' and B'{R).
Figure 9 . - Continued. Pitot - pre ssur e profi~es of f~ow i n pl ane of main
s hock i nt ers ecti on f or various isentr opi c s urvey - spike configurations.
J
NAeA RM E54F 08
38
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With roughness
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~
~
Q)
'"'
+'
co
Q)
Q)
Q)
1
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o
o
\
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,
b.'{
~
-rl
i;l
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til
Q)
-rl
al
~
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.,-i
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o
0
CJ
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.1
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-....
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i-
",..0-
~...1
CJ
til
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Q)
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Distance from spike surface, in.
u.
'n
~b.
h....
Q)l~
Q)
Q)
HI'"'
rs.+,
i~
.7
(c) Configurations C' and C'(R).
Figure 9. - Continued. Pitqt-pressure profiles of flow in plane of main
shock intersection for various isentropic survey-spike configurations.
.8
I~NACA RM E54F08
39
---<>--
No roughness
With roughness
--0-s:l
0
·rl
+>
()
Q)
to
H
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Q)
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Q)
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Q)
8
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11
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......
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1"1..
~..L
o
II
.1
.2
.3
.4
.5
.6
.7
Distance from spike surface, in.
(d) Configurations D' and D'(R).
Figure 9. - Continued. Pitot-pressure profiles o f flow in plane of main
shock intersection for various isentropic survey-spike configurations.
.8
NACA RM E54F08
40
~
- - 0--
No r ou ghness
With r oughness
.
tN
tN
N
o
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0
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.3
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OJ
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C)
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U)
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I
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::;::
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pc;
o
.1
.5
.4
.2
.3
Distance fr om spike surface, in .
.6
.7
(e) Configurations E' and E'(R) .
Figur e 9 . - Continued. Pitot - pressure profiles of flow in plane of
main shock inters ection f or vari ous isentropic survey- spike
configur ations .
~~---
--
-
41
NACA RM E54F08
--0---[)--
No roughness
With roughness
'r-
-
s::
0
ori
+>
()
11>
({J
f...t
Q)
+>
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..!<1
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4)
.5
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~
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--
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/
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+>~.3
Q)
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+>
C)
({J
({J
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Q)
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Pi
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o
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C)
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Q)
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I
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o
o
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p:;
o
.1
.2
.3
.4
.5
.6
.7
Distance from spike surface, in.
(f) Configurations F' and F'(R).
Figure 9. - Concluded. Pitot-pressure profi l es of fl ow in plane of
main sho ck inter section for various isentropic survey-spike
configurati ons .
~
. 20
BI(R1-- ~.
.
N
IA'(R
+-~.~
_ A'
,
8'
.18
o
I
'),
'"
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..."'"
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-'=
Theoretical based on characteristics solution
- -0- - Wi thout tip roughness } Experituental
~-~-~--~i--1[}-- -Wi th tip roughness
Horizontal arrows indicate values at design
point for each configuration. .
.16
9m c'
. 14
.,o
--.C
~(R)'D'
e
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. 12
"
...''""
I
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2
II
. 10
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. 04
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r.:;
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r ~"
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&;
1~--+--+---i--4---1~--b~-t--=E~~~~~~;;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~
~
o
o
1
2
3
5
6
78
Axial distance along spike, in.
9
10
11
12
Figure 10 . - Static-pressure distributions along surfaces of various isentropic survey-spike configurations .
..
13
l:rJ
14
(}l
~
o
en
NACA RM E54F08
1.0
p....0
,
rd
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..........
..
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1-1
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Main shock
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~
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o
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1.6
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tJ
0
H
~
r\
.4
o
.1
.4
.2
.3
Distance from spike surface, in.
.5
(a) Configurations A and A(R).
Figure 11. - Total-pressure and Mach number profiles for'isentropic
survey-spike configurations.
NACA RM :E54F0 8
44
1.0
:~
~
~
~
d
.8
~
0
p.,.
.........
p.,><
0
.6
+>oj
--0--
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With r oughness
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Q)
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til
Q)
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H
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o
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1. 6
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rl
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0
H
.4
o
~"""'C
'"
.2
.4
.1
.3
Distance from spike surface, in .
(b ) Configurati ons B' and B' (R) .
Figur e 11 . - Continued . Total- pressure and Mach number prof i l e s
fo r isentr opic sur vey- s pike configura tions .
45
NACA EM E54F08
1. 2
fhn ,ron..,
1.0
0
C\J
t()
t()
0
p.,
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_0
~
.8
~
p.,><
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H
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.6
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QJ
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I~
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I
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(
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Shock S inter section
o
Main shock
2.0
Theory
~
I--mIr
1.6
I
inte r sections~.
p
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r~
(?
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1.2
\
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\
0
'b
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\
\
Cl
o
.1
-
--
-
r-u-
.4
.5
.2
.3
Distance from spike surface, in.
o[
"0
.6
(c) Configurations C' and C' (R) .
Figure 11 . - Cont inued . Tota l -pre s s ure and Mach numbe r profiles
f or isent r opic s urvey-spike conf igurations .
.7
NACA RM E54F08
46
1.0
roo
~
<~
-
~ - - &8 ~
"J.,J.
p.,><
0
.r<
~
C
.6
\J
Q)
~
Q)
--0--
1
9
.4
~
IQ>
H
P<
I
rl
\~
oj
+'
0
8
With roughness
,[\
H
Ul
Ul
--0--- No rou ghness
1\ I~
b.l
p.,0
+'
oj
t
~
;!;;
.8
<J.
.2
Ii t j1J.~ ~I
I
o
2.4
I
~
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jJ t9""
~
""D-'(
~
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J
1. 6
Main shock intersections
t
..,..,
I-
~
r
Theor y
2.0
r
~
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\
Ie
1.2
\
J.,
1II
\
.8
u~
.4
o
\F
.1
.2
.3
.4
.5
Distance f r om spike surface, in .
(d ) Configurations D' and D'(R) .
Figur e 11 . - Continued . Total-pressure and Mach number profiles
f or i s entropic survey-spike configuratio ns .
(fl
()L
N
o
NAeA EM E54F08
47
1.1
0
C\l
I'f)
I'f)
..c~..lJ
.9
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p..0
P-t><
Lf':]
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al
'-~ 'q
No roughness
- - 0 - - With roughness
~
)
!-t
--<>--
1\.\C
I
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0
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- U', 5h:
c~
;J
........
..,
-.
Q)
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w
II
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Q)
I
!-t
PI
..,
..-I
al
0
8
.3
.,
\
1\ \
)
l't~
.1
Main shock intersectionb - ..
2.4
Theory
2.0
-.
f1 ~
-
-
.Q'1..J 11:1'
L
ULl
'~ ~
~~
)
\
;:s><
1.6
...
1
J
1
!-t
(I)
]
Q
.c:
CJ
1\
1.2
\ <~
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\ 1\
..-I
al
CJ
0
H
.8
~
I).,~
"-
•4
o
1'\
~ ..........
~
""
.1
.4
.5
.2
.3
Distance from spike surface, in .
(e)
.6
Configuration E' and E'(R) .
Figure 11. - Continued. Total-pressure and Mach number profiles
for isentropic s~vey-spike configurations.
_J
.8
NACA RM E54F08
1.2
?~
~ I~
1.0
-/"lor
'"""""-(
....
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rl
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- - 0 - - Wi th r oughness
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o
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shock intersections
2.8
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H
.8
.4
o
.1
.2
.4
.5
.3
Distance from spike surface, in.
.6
.7
(f) Configurations F' and F'(R).
Figure 11 . - Concluded. Total-pressure and Mach number profiles for isent r opic survey- spike confi gurations.
1
I
~
&;
~
~Vortex line~
y~ I I \1r
~
t>:I
~
Pressure
Order of
magnitude
Pl/PO
17.5
P2/PO
3.0
5.8
Strong shock
turnin~mprelssive
~ /PO
17.5
P4/P2
10
p/Po
p/Po
30
(P 4 / P 2 ) (pipo)
I .
Main shock
P 6/P 7
23.5
1.3
P6/PO
P4/ P3
P4/P s
30
PS / P o
18
1.7
1.65
o
CD
Free-stream normal
Measured shock angle
Required for P = P
l
3
(P2 / PO) ( P3 / P2 )
Normal at M = 3 . 0
P3 /P2
Shack r ef'l
.
ectlo n
5 -6 a C
Basis
Survey pressures
Measured flow angles
(P 6 /P 7 ) (P7/PO)
Required
Subsonic acceleration
to choking
(p4 / PO) (p4 / PS )
~
Figure 12 . - Experimental and analytical approximation of shock structure and flow fields obtained for confi~ation A of
isentropic survey spike.
~
to
NACA EM E54F08
50
No roughness
With roughness
Solid symbols represent
shock structures with
single intersections
0
0
3.0
~in
ShiCk
intersections;
Shock S interseetions;
2.9
S-:)
AcI t~-'
IF ,'(Rhll
2.8
!
VD' :;::
Z
V'
E'
-e
~D'(R)
r'
Design focal pOint,
C; and C' (R)
and
~'(R)
A and A(R)
2.7
/
2.6
8.8
9.1
8.9
9.0
Axial distance from spike tip, in.
Figure 13. - Relative positions of shock intersections encountered in survey plane.
9.2
51
NAeA RM E54F08
No r oughness
With roughness
No spillage; uniform profile
= = Nonuniform profile; mixing
losses
- - - - Spillage; additive drag
0
0
1.0
o
= =
C\l
to
to
~
.9
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.....
~
" "-
.8
Estimated mass flow ratio = 0.94-
~,[ ~~
AR
1'.
.950-
A
p.,O
...........
p.,t0
.7
~ Theoretical based
~~
normal shock loss
.965~
solely on
and assuming
nearly isentropic compression _
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c,J " ,
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7
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..c:()
~
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1.4
1.8
2 .0
2. 2
2.4
Final Mach number outside boundary layer, Mf
2.6
1.6
Figure 14. - Summary of potential pressure reco veries available for all external-compression inlets designed to accommodate flow fields of various isentropic spikes.
-
52
NAeA RM E54F08
I
1'JK.E.=l.OO
l.O
limit based
r----.. ~TheOretical
on normal shock pressure
tN .
tN
N
rise (no friction or sub"sonic diffuser losses)
.9
'~
1\
1
1
~Experimental
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\.
\
.8
, ~" "~
\
\.
p..
...........
p"10
\
.7
\
t-
H
- = Normal shock
Po = Po
pressure rise
-
Schematic diagram of shock
configuration
"-
\" , , ,
\ '\ \ " ,
1\ , ,
\'\ ~L\,
,
\ \
\ '\
,
\,
'\.
\.
Reference
\
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5
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6
V
7
1
,
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\
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~~.
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\
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2
3
CL
pt
\ T]K.E.=O.97
til
rl
al
-.......
\~
\
8to
Pa
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p = O.~9 Across
0
tip shock
-
'\
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.6
-
~3
\
[\
Q)
>
0
()
Q)
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...
0
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\
0
a
maxima for
inlets
/
\
o
,
1\
\
""
5
Free-stream Mach number,
4
1\
\
~
Me
6
7
Figure 15. - Comparison of current experimental maximum recoveries
with theoretical limits for all-external-compression isentr opic
inlets at several Mach numbers.
53
NACA RM E54F08
3 .4
I
3.0
-£
...
/
2. 6
+>
0..-1
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/
(!)
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1.8
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/
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1.4
1.0
2
/
/
V
/
/
/
V
/
II
3
4
5
Free - stream Mach numbe r,
Mo
6
7
Figure 16 o - Effect of free - stream Mach number on final Mach
numbe r limit .
_J
