Shock wave propagation into a valley

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dc.contributor.author Whitehouse, Joanne
dc.date.accessioned 2006-10-30T12:16:13Z
dc.date.available 2006-10-30T12:16:13Z
dc.date.issued 2006-10-30T12:16:13Z
dc.identifier.uri http://hdl.handle.net/10539/1500
dc.description Student Number: 0008522F Master of Science Faculty of Engineering & The Built Environment School of Mechanical, Industrial & Aeronautical Engineering en
dc.description.abstract An aircraft travelling at supersonic speeds close to the ground generates a bow wave, which is reflected off the ground surface. When the aircraft enters a valley, the three-dimensional bow wave is reflected off the valley walls, such that it could focus behind the aircraft. Complex threedimensional wave surfaces will result. The real situation of an aircraft entering a valley can be modelled and tested experimentally in a shock tube. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to identify the resulting complex three-dimensional wave structures and then verified by three-dimensional CFD. The valley geometries investigated are rectangular, triangular, parabolic and conical. Three hill geometries were also investigated. The three-dimensional reflected surfaces from the rectangular valleys were found to vary only slightly as the valley floor inclination is increased. As the incident wave interacts with both the wedge and valley floor surfaces two prominent reflections occur. A primary reflected wave surface is generated from regular reflection off the wedge. This surface flows over into the valley contacting the incident wave at a second contact point. A secondary reflected wave is found underneath the primary reflected wave, generated due to Mach reflection occurring over the full width off the valley floor. The area of the incident wave between the second contact point and the triple point is seen to bow out into the downstream flow. The Mach stem of the reflection off the valley floor tends to become less pronounced for the larger valley floor inclination angles. In all the rectangular valleys, a shear layer is present, cascading down the valley wall and then along the valley entrance. The shear layer tends to decrease in size as the valley floor inclination increases. Both prominent reflected shock surfaces are almost conical in nature at close proximity to the valley wall. The triangular valleys show similar reflection patterns as the rectangular valleys. As the incident shock wave initially interacts with the wedge surface only regular reflection occurs. The resulting reflected wave forms the primary reflected surface which flows over into the valley. The reflection changes to Mach reflection as the incident wave interacts with the valley floor. The Mach stem of the reflection off the valley floor increases in characteristic height as one moves from the valley entrance wall to the plane of symmetry. The Mach stem is much smaller for the higher valley floor inclinations. A secondary reflected wave is found underneath the primary reflected surface. The secondary wave is Mach reflection near the plane of symmetry which turns iii to regular reflection closer to the valley wall. The primary and secondary reflected surfaces merge near the plane of symmetry and again along the wedge surface. A shear layer is found to cascade down the valley entrance wall for all geometries, decreasing in strength as the valley inclination angle increases. The parabolic valleys show similar reflection patterns as the triangular valleys. As the incident wave interacts with both the wedge and valley surfaces two reflections occur. The reflection off the wedge surface is regular. As the incident wave flows over into the valley the initial reflection off the valley floor is regular. This regular reflection then turns into Mach reflection the closer one moves to the symmetry plane. The Mach reflection off the valley floor forms a secondary reflected wave underneath the primary reflected wave that is found to flow over into the valley. The primary reflected wave contacts the incident wave at a second contract point found above the triple point. This contact point moves closer to the triple point and eventually along the secondary reflected wave as the incident wave advances downstream. The second contact point at a single time instant is also seen to move closer to the triple point as one moves closer to the plane of symmetry. A shear layer is found cascading down the valley entrance wall. The secondary reflected wave of the Mach reflection off valley floor forms a semi-circular surface which contacts the floor just after the shear layer. The Mach reflection off the valley floor changes to regular reflection as the surface begins to climb up along the valley entrance wall. The conical valleys once again show similar reflection patterns as those found in the other valley geometries. As the incident wave interacts with both the wedge and valley surfaces two reflections occur. Regular reflection occurs off the wedge surface with the resulting primary reflected wave flowing over into the valley. This primary reflected wave contacts the incident shock at a second contact point in the valley. The reflection off the valley floor is regular close to the valley entrance wall changing to Mach reflection nearer the symmetry plane. The reflected wave from the Mach reflection forms the secondary reflected surface found beneath the primary reflected wave. The secondary reflected Mach wave changes to regular reflection as the surface nears the valley wall, with the reflection point travelling along the valley floor until coincident with the valley entrance wall, where it then travels along the entrance wall. The second contact point found on the incident wave is found above the triple point and moves down the incident shock to eventually coincide with the triple point. A weak shear layer is found to cascade down the valley entrance wall. A weak separation also occurs at the entry point of the valley. iv The three hill geometries, triangular, parabolic and conical, all display similar reflection patterns. As the incident wave advances downstream regular reflection occurs off both the wedge and hill surfaces. The reflected waves come together at a point off the surface. At this point a double triple point occurs with two resulting Mach stems. One Mach stem contacts the wedge surface while the other contacts the hill surface. The resulting double Mach stem surface wraps around the base of the hill getting progressively tighter the closer it gets to the incident wave. The only major differences between all three geometries is the shape of the resulting reflected wave off the hill surface (which tends to follow the same geometric shape as the hill) and the distance between the two triple points for the conical and parabolic hills tends to be larger than that found for the triangular hill. en
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dc.language.iso en en
dc.subject Shock Wave Reflection en
dc.subject 2D and 3D Reflection Phenomenon en
dc.subject Double Wedge en
dc.title Shock wave propagation into a valley en
dc.type Thesis en


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    Thesis (Ph.D.)--University of the Witwatersrand, 1972.

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