There are two kinds of inlets that could possibly be used in supersonic flight, especially in their simplest forms for ramjet-propelled vehicles. One is the so-called “pitot/normal shock” inlet, useful from subsonic speeds all the way up to about Mach 1.5, maybe even 2.0. The other is the “supersonic inlet” that features external compression surfaces ahead of its cowl lip capture station. These are only useful in their simplest forms from roughly Mach 1.5 to high supersonic, even low hypersonic speeds. That would be Mach 6+.
That brings up the definition of “capture area”. It is defined as the area that is swept-out
by the inlet structure as it moves at flight speed. That varies with inlet type, because of the varying requirements for
external compression structures and cowl lip shapes. However,
Figure 0 may help the reader to better understand how these
things are defined.
Figure 0 – Definitions of Capture Area for the Various
Inlets
Shock waves are inherent once supersonic flight speed is
attained. Shock waves come in two basic
forms: the “normal shock” and the
“oblique shock”. They have different
characteristics and effects. This is
illustrated in Figure 1. The
normal shock occurs when a supersonic streamtube must go straight into a region
of sufficiently-higher pressure. The
oblique shock forms when an angled surface forces the streamtube to divert to a
new direction. The math behind this is
complex, and given in the indicated
source (Ref. 1). The normal shock
is the “stronger”, in that flow behind
it is subsonic, and at a lower total (stagnation)
pressure. Flow behind an oblique shock
is still supersonic, with less loss of
total pressure. Total is larger than the
static pressure, reflecting high speed
flow energy.
Figure 1 – Basic Characteristics of the Two Kinds of Shock
Waves
The pitot/normal shock inlet is just a pitot inlet flying
supersonic. A bow wave shock begins to
form out in front (“subcritical” operation) if the outlet is obstructed. If the pressure at the outlet of the duct reduces
to just the right pressure, the shock
moves to the min area right at the cowl lip.
This is the “critical” operation point.
If the pressure at the outlet (“the backpressure”) is reduced
further, the shock will move downstream
further into the divergent passage of the inlet duct (“supercritical”
operation). The pitot/normal shock inlet
has no “shock-on-lip” design point, it
simply “is”. This is illustrated to the left
side in Figure 2 at critical operation.
The supersonic inlet has a compression surface exposed in
front of the cowl lip capture station.
This surface is a spike if circular in cross section, or is a flat ramp if rectangular in cross
section. It works by diverting the air
stream’s direction, thus creating
oblique shocks. At the design
“shock-on-lip” speed, these shock waves
converge upon the cowl lip, as
illustrated for the two slightly-different designs on the right side of Figure
2.
There is always a minimum channel area in a supersonic
inlet, as noted in the figure, termed the “inlet throat”. If the inlet throat is downstream of the cowl
lip capture station, there is also
internal compression in the contracting channel. That is the “mixed compression” design, bottom of the two illustrations. The cowl lip can be close to parallel with
the oncoming flow for lowest drag, and
sheds an internal oblique shock, which
at design should be focused upon the inlet throat station. At critical operation, the terminal normal shock is also located at
that inlet throat, which is still
somewhat supersonic.
Figure 2 – How the Various Inlets Incorporate Shock Waves in
Their Compression Process
If the cowl lip is angled more parallel to the external
compression surface, the inlet throat
can be located right at the cowl capture station. The cowl lip does cause higher cowl lip drag,
oriented that way. There is no internal compression by any
contracting channel, and thus no
internal oblique shock shed by the cowl.
This is the “all-external compression” inlet design. At critical operation, the final terminal normal shock is right
there at the inlet throat, which is the
min flow area at the cowl capture point.
In either supersonic design,
the sequence of oblique shocks slows the flow speed in steps, at each oblique shock shed by a surface
feature. The diversion angles generate the
oblique shock waves that the flow encounters.
Done “right” (that math is also very complex), there is about the same total pressure ratio (a
number less than 1) across each shock,
which can also be made about equal to the total pressure ratio of the
terminal normal shock. That last is because
the terminal shock occurs at a quite low supersonic flow speed, instead of full flight speed.
The product of these total pressure ratios is essentially (but
not entirely, because of friction in its
various forms) the “critical pressure recovery ratio” of the inlet (a number
less than 1). That product of ratios is
higher than the total pressure recovery ratio across the single normal shock of
the pitot/normal shock inlet. That higher
total pressure recovery ratio is why these supersonic inlet types are much
preferred beyond Mach 1.5 to 2 flight speeds.
There is a classic problem in fluid mechanics texts, dealing with using a converging-diverging
passage as a supersonic inlet diffuser to slow a flow down, instead of as a nozzle to speed it up. At the “design” speed, flow slows in the contraction to a speed just
above Mach 1, and then tries to expand
again supersonically just as the channel starts to diverge, but then shocks down subsonic with a normal
shock, for (ideally) final subsonic
diffusion.
When one attempts this experimentally, the shock forms out front as a bow
shock, and the subsonic flow behind it
tries to pass through the min area at flow speeds up to Mach 1. But the subsonic massflow passable at Mach
1 is less than the supersonic massflow that is being swept out! One has to speed-up the oncoming flow to
considerably higher speed than the “design” speed, in order to “swallow” the bow shock, in
order for it to become that terminal normal shock.
This is the Kantrowitz-Donaldson problem (Ref. 2), and mixed-compression inlets inherently suffer
from it, because such a
converging-diverging passage is a part of the inlet’s design. The only way to get the shock system
swallowed is either (1) by very significant overspeed, or (2) by adding very significant throat
bleed slots that lead overboard, in
order to pass the requisite supersonic massflow rate. The subsonic flow can make the turn to go out
through the bleed slots easily! Once
supersonic, the flow cannot easily make
the turn, so the slot bleed flow is very
much lower, once supersonic internally.
The all-external compression inlet does not have this
“starting” (shock-swallowing) problem!
That is because there is only a diverging channel, once the flow is inside the cowl. These inlets start easily without need of
overspeed, or any need of significant
throat bleed slots. They simply have no
contracting channel with which to suffer the Kantrowitz-Donaldson problem. That leads to the list of pros and cons for
the two types of supersonic inlets in Table 1. The pitot inlet is included for completeness.
All these inlets share the behaviors that we call
subcritical, critical, and supercritical flow. This is driven by the “backpressure” the
inlet “sees” at its subsonic outlet. In
effect, this backpressure is a
resistance to swallowing the shock system and keeping it swallowed. In both critical and supercritical flow, the shock system is swallowed. At critical,
the terminal normal shock is right at the inlet throat. Supercritical, it is located further down in the divergent
diffuser and is thus stronger, taking place
at a higher flow speed, and thus
creating a lower total pressure in the subsonic flow downstream of it.
In subcritical flow the entire shock system is
unswallowed, located out on the external
compression surfaces. Its position along
that surface determines how much air is spilled around the cowl lip and not
ingested at all, even after passing
through the oblique shocks and terminal normal shock and getting the max
possible final total pressure. This behavior
is shown in Figure 3 just below for all three inlets, at their design speeds (excepting pitot, which is simply shown in supersonic flow). Subsonically,
the pitot always effectively operates “subcritically” by spilling air, it’s just that there is no shock wave at all.
Only the supersonic inlets have a design speed, the pitot does not. There is the possibility of operating below
design speed, at design speed, and above design speed, quite independently of the possibilities of
operating sub- or supercritical. At or
above design speed, the ingested
streamtube is its full swept-out size.
Below it, the ingested streamtube
is smaller for geometric reasons,
because the local flow behind each oblique shock must be parallel to the
surfaces of the external compression features.
This behavior is shown only at critical,
for simplicity, in Figure 4. The shock and spillage patterns are more
complex supercritical, and simply
different subcritical.
Figure 3 – Subcritical,
Critical, and Supercritical
Operation at Design Speed
Figure 4 – Below vs At or Above Design Speed with Supersonic
Inlets at Critical
The net effect of all this is (1) subcritical spillage
reduces air ingestion while maintaining full pressure recovery, while supercritical operation ingests full
air flow while reducing pressure recovery.
The point where both ingestion and recovery are their max possible values
is the critical point. This has the
effect that at any one flight speed Mach number, the operation of the inlet is per Figure 5
below. In that figure, the notation PRCR is the critical total
pressure recovery, which is that maximum
recovery. The notation ARCR is the
critical area ratio of the captured streamtube, to that which could be swept out by the
inlet’s capture area. It is maximum at
critical.
That “any one flight Mach number” could be below, at, or
above the design shock-on-lip Mach number for the supersonic-type inlets. There is no such design shock-on-lip Mach
number for a pitot/normal shock inlet.
Below design, the possible ARCR
ratio of the supersonic-type inlets is reduced by the geometries involved, while above it, ARCR is not reduced. The pitot has no such effect.
Figure 5 – How All Supersonic Inlets Operate at Any One
Flight Mach Number
Pressure recovery is aways reduced at higher speeds, but it reduces faster above design than below
it, with the supersonic-type
inlets. Pitot has no slope break at
design because it has no design speed,
but it always has lower pressure recovery than the supersonic types, just because of the stronger single normal
shock. That gives rise to the recovery
curve shapes shown generically in Figure 6.
Figure 6 – Generic Representation of Typical Inlet Curve
Shapes with Mach number
There are drags associated with the air that is either
spilled subcritically, or not ingested
for being below design speed, among many
other reasons. These vary with the
details of the inlet designs, and where
they are positioned on the vehicle. That
is a very complicated item, beyond scope
here.
The use of these inlets on turbojet and turbofan aircraft is
another very large separate topic. These
inlets, especially the supersonic
types, require a myriad of “band-aids”
like spring-loaded blow-in doors admitting extra air, with the duct sucked down below local
atmospheric by the turbine engine, in
order to function well when below design speed.
The pitot inlet may need some of these “band-aids” for low subsonic and
ground-run operation. Even so, the very same components get used quite
differently for turbojet or turbofan, as
compared to ramjet! That is also beyond
scope here, except to say that ramjet
needs supercritical operation, and
turbojet/turbofan needs subcritical operation.
References
#1. NACA Technical
Report 1135 “Equations, Tables, and Charts for Compressible Flow”, Ames Research Staff, 1953.
#2. Kantrowitz, A.,
and Donaldson, C., “Preliminary
Investigation of Supersonic Diffusers”,
NACA TR L5D20, 1945.
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