Student Number: 0008522F
Master of Science
Faculty of Engineering & The Built Environment
School of Mechanical, Industrial & Aeronautical Engineering / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/1500 |
| Date | 30 October 2006 |
| Creators | Whitehouse, Joanne |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 35239991 bytes, 20411764 bytes, 3432 bytes, 9536 bytes, 12598 bytes, 8595212 bytes, 20937 bytes, 851755 bytes, 183783 bytes, 95600 bytes, 2056 bytes, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf |
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