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Next: Small ``Weak Oblique shock'' Up: Solution of Mach Angle Previous:   Index

Flow in a Semi-2D Shape

Figure 13.10: Schematic of finite wedge with zero angle of attack.
Image wedgeEnd
The discussion so far was about the straight infinite long wedge13.21 which is a ``pure'' 2-D configuration. Clearly, for any finite length of the wedge, the analysis needs to account for edge effects. The end of the wedge must have a different configuration (see Figure (13.10)). Yet, the analysis for the middle section produces a close result to reality (because of symmetry). The section where the current analysis is close to reality can be estimated from a dimensional analysis for the required accuracy or by a numerical method. The dimensional analysis shows that only the doted area to be area where current solution can be assumed as correct13.22. In spite of the small area were the current solution can be assumed, this solution is also act as a ``reality check'' to any numerical analysis. The analysis also provides additional value of the expected range.

Another geometry that can be considered as two-dimensional is the cone (some referred to it as Taylor-Maccoll flow). Even though, the cone is a three-dimensional problem, the symmetrical nature of the cone creates a semi-2D problem. In this case there are no edge effects and the geometry dictates slightly different results. The mathematics is much more complicated but there are three solutions. As before, the first solution is thermodynamical unstable. Experimental and analytical work shows that the weak solution is the stable solution and a discussion is provided in the appendix of this chapter. As opposed to the weak shock, the strong shock is unstable, at least, for steady state and no known experiments showing that it exist can be found in the literature. All the literature, known to the author, reports that only a weak shock is possible.

next up previous index
Next: Small ``Weak Oblique shock'' Up: Solution of Mach Angle Previous:   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21