2 Aerodynamics
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attached to the tip of the object. This kind of shock is different from
the normal shock in form. Its wave front is obliquely intersected with
the flow direction, which is called the oblique shock. In oblique shock
wave, the angle β between the front of shock wave and the direction
of incoming flow is called shock angle. Similarly, the airflow direction after the oblique shock wave is not perpendicular to the shock
wave surface, nor parallel to the airflow direction before the wave, but
parallel to the sharp split plane. The included angle δ is called the
airflow angle, which means the angle of the airflow after the oblique
shock wave (as shown in Fig. 2.69).
Compared with normal shock, oblique shock belongs to weak
shock, and the smaller the wedge angle is, the weaker the shock is.
If the half apex angle δ of the wedge is infinitesimal, it is obvious
that the disturbance of the very thin wedge to the supersonic flow
must be weak, the disturbance wave must be the Mach wave, and
the disturbance angle must be the Mach angle. With the increase in
wedge angle δ, the shock wave β increases. The larger δ is, the larger
β is. Therefore, for a positive shock, as long as Ma 1 is determined, the
increment of other parameters is determined; for an oblique shock, it
is necessary to determine the shock slope angle β by Ma 1 and δ, and
then other physical quantities can be solved according to the shock
intensity determined by β. Figure 2.70 shows the relationship between
oblique shock angle and wedge angle at different Mach numbers.
(3) Internal structure of shock wave
It is possible to treat the shock wave as a sudden jump surface (discontinuity) without thickness in dealing with the general flow problems
without causing large errors. However, when considering the effect
of viscosity, shock waves cannot be regarded as thickness free. In
fact, the velocity gradient is infinite when the thickness of the shock
wave is zero, and the viscosity has a great influence. Under the action
of viscosity, the velocity cannot decelerate suddenly from V 1 to V 2
without thickness, that is to say, there must be a transition zone, and
the thickness of this transition zone is the thickness of shock wave. It
is found that the thickness of shock wave is a small quantity, which
is the same order of magnitude as the average free path of molecule.
In the sea atmosphere, the molecular free path is 70 × 10 −6 mm. In
the case of Ma = 3, the shock thickness calculated by continuum
theory is 66 × 10 −6 mm. Some people use the equation of continuous medium considering viscosity and heat transfer to analyze the
change process of airflow parameters in the shock wave. It is found
133
attached to the tip of the object. This kind of shock is different from
the normal shock in form. Its wave front is obliquely intersected with
the flow direction, which is called the oblique shock. In oblique shock
wave, the angle β between the front of shock wave and the direction
of incoming flow is called shock angle. Similarly, the airflow direction after the oblique shock wave is not perpendicular to the shock
wave surface, nor parallel to the airflow direction before the wave, but
parallel to the sharp split plane. The included angle δ is called the
airflow angle, which means the angle of the airflow after the oblique
shock wave (as shown in Fig. 2.69).
Compared with normal shock, oblique shock belongs to weak
shock, and the smaller the wedge angle is, the weaker the shock is.
If the half apex angle δ of the wedge is infinitesimal, it is obvious
that the disturbance of the very thin wedge to the supersonic flow
must be weak, the disturbance wave must be the Mach wave, and
the disturbance angle must be the Mach angle. With the increase in
wedge angle δ, the shock wave β increases. The larger δ is, the larger
β is. Therefore, for a positive shock, as long as Ma 1 is determined, the
increment of other parameters is determined; for an oblique shock, it
is necessary to determine the shock slope angle β by Ma 1 and δ, and
then other physical quantities can be solved according to the shock
intensity determined by β. Figure 2.70 shows the relationship between
oblique shock angle and wedge angle at different Mach numbers.
(3) Internal structure of shock wave
It is possible to treat the shock wave as a sudden jump surface (discontinuity) without thickness in dealing with the general flow problems
without causing large errors. However, when considering the effect
of viscosity, shock waves cannot be regarded as thickness free. In
fact, the velocity gradient is infinite when the thickness of the shock
wave is zero, and the viscosity has a great influence. Under the action
of viscosity, the velocity cannot decelerate suddenly from V 1 to V 2
without thickness, that is to say, there must be a transition zone, and
the thickness of this transition zone is the thickness of shock wave. It
is found that the thickness of shock wave is a small quantity, which
is the same order of magnitude as the average free path of molecule.
In the sea atmosphere, the molecular free path is 70 × 10 −6 mm. In
the case of Ma = 3, the shock thickness calculated by continuum
theory is 66 × 10 −6 mm. Some people use the equation of continuous medium considering viscosity and heat transfer to analyze the
change process of airflow parameters in the shock wave. It is found