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CHAPTER 5. SUMMARY AND DISCUSSION

5.2 Conclusions

The present investigation provides clear evidence in a number of properties of asymptotic be- havior in cases of strong interaction between the attached leading edge shock wave and boundary layer on plate geometries in laminar–hypersonic flow. Plate force coefficients, such as those shown in Figures 4.4, 4.12, and 4.20 - 4.24 are one example of this behavior. As the hypersonic inter- action parameter becomes large, these force values show signs of leveling off to a constant value, independent of interaction parameter.

This asymptotic behavior is also seen in the characterized behavior of the shock wave and boundary layer profiles. For both constant temperature and constant heat flux, the shock wave

consistently lowers toward the boundary layer, while the boundary layer rises toward the shock wave. This behavior is best demonstrated in Figures4.8 and 4.16. Another notable trait of these profiles is the asymptotic behavior of the power law exponents in Figures 4.6b, 4.7b, 4.14b and

4.15b. This behavior shows general agreement with the theory presented in Dorrance (1962) that for sharp leading edge bodies, in the strong interaction limit ofM∞ → ∞, the laminar boundary

layer takes on the power law form ofy=bx3/4as the shock wave and boundary layer come together. This helps better conclude that the models in use are capable of recreating the asymptotic trends predicted in the strong interaction theory.

When comparing effects of heat transfer, considering the Stanton number provides valuable information for boundary layer theories. The order–of–magnitude study for constant dimensional heat flux on the flat plate finds that unless the flat plate heat flux is a sizeable portion of the freestream thermal capacity, behavior will mimic that of an adiabatic wall. This observed behavior can help inform modeling assumptions in future studies.

Finally, isothermal compression ramps also show signs of asymptotic behavior in regard to upstream influence and separation occurring at the plate-ramp junction. Both of these properties show independence from interaction parameter at interactions ofχ >2. This behavior can be used to inform lower order models for prediction of upstream influence and separation for sufficiently strong shock wave – boundary layer interactions.

Several signs of asymptotic behavior are observed in the present study. This behavior provides validation to hypersonic boundary layer theories which are built on the premise of this asymptotic behavior, when the shock wave and boundary layer tend towards a single boundary.

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