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Flujo hipersónico sobre misiles
rEsumEn
Entre otras técnicas, las técnicas para resolver problemas de
ujo sobre misiles hipersónicos modernos que están en el
régimen de ujo hipersónico son las soluciones exactas. La
primera solución exacta se basa en las relaciones de ondas
de choque oblicuas y se mantiene para todos los números de
Mach superiores a la unidad, supersónicos o hipersónicos,
suponiendo gases perfectamente calóricos. El segundo método
de solución exacta es el método de inclinación de supercie
local basado en la teoría newtoniana. El tercer método
de solución exacta es el método de pequeña perturbación
hipersónica que se basa en los supuestos de que la pendiente
de la supercie local del cuerpo en la dirección de la corriente
es pequeña en todas partes en comparación con la unidad;
las perturbaciones de velocidad son pequeñas en comparación
con la velocidad de ujo libre, y la perturbación de presión
es pequeña en comparación con la presión dinámica de ujo
libre.
Palabras clave: hipersónico, onda de choque, numero
mach, supersónico, gases calóricos, teoría newtoniana, presión
dinámica
aBstraCt
Among others, the techniques to solve problems of the
modern hypersonic missiles which are in the hypersonic ow
regime are the exact solutions. e rst exact solution is based
on the oblique shock wave relations and hold for all Mach
numbers greater than unity, supersonic or hypersonic ows
assuming perfectly caloric gases. e second exact solution
method, is the local surface inclination method based on
Newtonian theory. e third exact solution method is the
small hypersonic disturbance method which is based on the
assumptions that the slope of the local surface of the body in
the stream wise direction is everywhere small compared with
unity; the velocity perturbations are small compared with
the freestream velocity, and the pressure perturbation is small
compared with the freestream dynamic pressure.
Key words: hypersonic, shock wave, Mach numbers,
supersonic, caloric gases, Newtonian theory, dynamic pressure
L A. A
1 Aerospace Enmgineer, B.Sc., M. Sc
Facultad de Ingeniería y Arquitectura,
Escuela Profesional de Ciencias
Aeronáuticas
Universidad de San Martín de Porres,
Lima Perú
larriolag@usmp.pe
Hipersonic ow over missiles
Recibido: noviembre 20 de 2019 | Revisado: diciembre 12 de 2019 | Aceptado: enero 06 de 2020
https://doi.org/10.24265/campus.2020.v25n29.09
| C | V. XX IV | N. 28 | PP. - | - | || C | V. XX IV | N. 28 | PP. - | - | || C | V. XX V | N. 29 | PP. - | - | |
© Los autores. Este artículo es publicado por la Revista Campus de la Facultad de Ingeniería y Arquitectura de la Universidad
de San Martín de Porres. Este artículo se distribuye en los términos de la Licencia Creative Commons Atribución No-comercial
– Compartir-Igual 4.0 Internacional (https://creativecommons.org/licenses/ CC-BY), que permite el uso no comercial,
distribución y reproducción en cualquier medio siempre que la obra original sea debidamente citada. Para uso comercial
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Introduction
When the space shuttle enters the
earth´s atmosphere form near-earth
orbit, it is ying at Mach 25. When the
Apollo spacecraft returned from the
moon, it entered the atmosphere at
Mach 36. Today, there are new concepts
of space vehicles such as hypersonic
missiles as shown in Figure 1 but which
are based on the concept of the 1980s
and experiments that took place in the
1959s and 1960s.
Figure 1. Hypersonic Missile
ese high values of Mach numbers
are associated with the extreme portion
of high values of the ight spectrum
which is referred as Hypersonic Flight.
From the aerodynamic point of view, it
is necessary to understand the principles
and fundamentals in a ow whose
velocity is extremely high as in the
hypersonic range. is can happen just
around space vehicles, as it is the case of
hypersonic missiles of the present years
and later 2020s.
Discussion
In spaceight, and generally in high-
speed ights it is common to refer to the
Mach number as a measure of vehicle
speed compared to the speed of sound.
ere is a conventional rule of thumb
that denes hypersonic aerodynamics
as those ows where the Mach number
is greater than 5 as dened by Zucrow
& Homan (1976). However, this is no
more than just a rule of thumb; when
a ow is accelerated from Mach 4.99
to 5.01, there is no “clash of thunder”
and the ow does not “instantly turn
from green to red”. Rather, a hypersonic
ow is better dened as that regime
where certain physical ow phenomena
become progressively more important
as the Mach number is increased to
higher values. Among the concepts
and principles that arise in this type of
hypersonic ow regime are the following
according to Shapiro (1953).
in Shock Layers
Considering the theory of oblique
shock waves that, for a given ow
L A. A
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deection angle, the density increase
across the shock wave becomes
progressively larger as the Mach number
is increased. At higher density, the mass
ow behind the shock wave can more
easily “squeeze through” smaller areas.
For a ow over a hypersonic body such
as a missile, this means that the distance
between the body and the shock wave
can be small.
Entropy Layer
ere are some options in forms of
hypersonic vehicles. e sharp tip and
the blunt nose tip. Unlike those with a
sharp tip, in those with a blunt nose and
hypersonic Mach numbers, a shock layer
over the blunt nose is formed which is
also very thin (compared to that with a
sharp tip) and with a small separation
distance in the nose called “detachment”.
Entropy is energy, and the entropy of
the ow is increased through a shock
wave, and thus, the stronger the shock
wave, the larger the entropy increase.
is layer which contains the energy,
called entropy layer causes analytical
problems when you want to perform
standard boundary layer (boundary layer
phenomena) calculations on the surface
of the vehicle.
Viscous Interaction
A high-speed hypersonic ow contains
a large amount of kinetic energy. When
this ow is decelerated by the viscous
eects within the boundary layer, the lost
kinetic energy is transformed (in part)
into internal energy of the gas, so call
viscous dissipation. us, the temperature
is increased within the boundary layer
and heat can be transferred to the vehicle
if protective measures of aerodynamic,
thermal and structural design are not
taken in consideration.
High Temperature Flows
Extreme viscous dissipation that
occurs within hypersonic boundary
layers can create very high temperatures.
So high, as to energize or stimulate
vibrational energy internally between
molecules, and cause dissociation and
even more, ionization within the gas.
If the surface of the hypersonic vehicle
is protected by an ablative heat shield,
the ablation products are also present in
the boundary layer, leading to complex
chemical reactions of hydrocarbons. In
this way, we can see that the surface of
a hypersonic vehicle can be aected by a
boundary layer reacting chemically.
Among the techniques to solve
this type of high-speed ows are
the exact solutions. e rst exact
solution is based on the oblique shock
wave relations and hold for all Mach
numbers greater than unity, supersonic
or hypersonic ows assuming perfectly
caloric gases. However, some interesting
approximations and simplied forms of
this type of oblique shock wave relations
are obtained at the limit of high Mach
number values. ere is a second exact
solution that is based on the local surface
inclination method which is a method
based on Newtonian theory; and a
third exact solution method is based
on the relations of small hypersonic
disturbances. e pressure distribution
Cp, is particularly important since it
is a measure of how much can stand
the vehicle under pressure due to
higher values of speed. For the rst
exact solution method, which is based
on the oblique shock wave relations
F
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and occurring in the hypersonic limit
(Mach number →∞), the relation for
the pressure distribution as dened by
Anderson (2003) is the following: Cp =
(4 / (γ+1))sin
2
𝛽. Where γ is a constant
value of 1.4 for dry air, the Mach
number is in the hypersonic limit, β is
the shock angle, and θ is the deection
angle where theta and β are small as
indicated in Figure 2.
Figure 2. Oblique shock wave geometry
en, according to Anderson, Jr.
(2003), the relation between β and θ for
the hypersonic limit and under these small
angles case is:
𝛽
=
𝛾 +1
.
2
For the second exact solution method,
which is the oldest and most widely used
local surface inclination method based on
Newtonian theory, the surface pressure
distribution for hypersonic bodies is also
dened by Anderson (2003) as: Cp =
2sin
2
.
In the Newtonian model of uid ow,
the particles in the free stream impact only
on the frontal area of the body; they cannot
curl around the body and impact on the
back surface. Hence, for that portion of
a body which is in the “shadow” of the
incident ow, such as the shaded region
sketched in Figure 2, no impact pressure
is felt. Hence, over this shadow region it
is
consistent to assume that p = p
∞,
where p
is the pressure variation around the body
and p
∞
is the
free stream pressure, and
therefore Cp = 0, as indicated in Figure 3.
Figure 3. Shadow region on the leeward side of a body, from Newtonian
theory
L A. A
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Finally, the third and last exact solution
method of small hypersonic disturbances
is based on the assumptions that the
slope of the local surface of the body in
the stream wise direction is everywhere
small compared with unity; the velocity
perturbations are small compared with
the freestream velocity, and the pressure
perturbation is small compared with the
freestream dynamic pressure. However,
the “modern” hypersonic aerodynamics
is characterized by applications of
computational uid dynamics (CFD)
which is based on numerical methods.
CFD had an impact due mainly to the
lack of hypersonic ground test facilities
for experimental studies, especially at
the extreme ends of the spectrum where
the Mach number greater than 20 and
the stagnation temperatures are high
enough to cause substantial chemical
dissociation of the gas. In lieu of such
high-performance facilities, the design of
hypersonic vehicles such as the hypersonic
missiles must rely heavily on the results
of computational uid dynamics.
Conclusions
It is important to understand the
physical phenomenon in this type of
high speed regime since a dierent
behavior of the ow around the space
vehicle occurs. is behavior of particles
that we have described as dissociation
of molecules and ionization of particles
from the ow around the vehicle
greatly aect the material over the
entire surface of the vehicle. However,
if the vehicle is not properly protected
to withstand high temperatures and
heat transfer and ions, then damage
to the structure of the vehicle and its
avionics is imminent. In general, it is
the shape of the surface of the vehicle
which is shaped in order to mitigate
these eects of hypersonic ow as well
as using protection such as the surface
protective thermal shields. In order
to shape the surface of the vehicle in
question, any of the methods briey
described here can be applied.
References
Anderson, Jr. (2003). Modern
Compressible Flow with Historical
Perspective. NY: McGraw
Hill Shapiro, A. (1953). e
Dynamics and ermodynamics
of Compressible Fluid Flow. N.Y
Zucrow, M.& Homan J. (1976).
Gas Dynamics. New York: Wiley
F
