Page 120 - 48Fundamentals of Compressible Fluid Mechanics

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. This approach had major significance and
CHAPTER 5. NORMAL SHOCK
5.2.1 The Limitations of The Shock Wave
When the upstream Mach number becomes very large, the downstream Mach
number (see equation (5.22) is limited by
(5.38)
%
This results is shown in Figure (5.3). The limits of of the pressure ratio can be
%
%
obtained by looking at equation (5.16) and utilizing the limit that was obtained in
equation (5.38).
5.2.2 Small Perturbation Solution
The Small perturbation solution referred to an analytical solution in a case where
only small change occurs. In this case, it refers to a case where only a “small
usefulness at a time when personal computers were not available. Now, during
shock” occurs, which is up to
the writing of this version of the book, this technique mostly has usage in obtaining
analytical expressions for simplified models. This technique also has academic
value, and therefore will be described in the next version (0.5 series).
The strength of the shock wave defined as
(5.39)
Using the equation (5.23) transformed equation (5.39) into
(5.40)
Or utilizing equation
(5.41)
%
%
%
5.2.3 Shock Thickness
The issue of the shock thickness is presented (will be presented in version 0.45)
here for completeness. This issue has very limited practical application for most
students, however, to have the student convinced that indeed the assumption of
very thin shock is validated by analytical and experimental study, the issue must
be presented.
The shock thickness has several way to defined it. The most common
definition is passing a tangent to the velocity at the center and finding where is the
theoretical upstream and downstream condition are meet.