3. Electronic Theses and Dissertations (ETDs) - All submissions

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The discharge capacity and design of curb inlets with and without clogging
(2019) Dube, Ntombikayise
Prolonged surface runoff on streets contributes to flooding, thus compromising the structural integrity of roads, increasing the probability of accidents and traffic stagnation, and as such drainage structures such as the Pretoria type curb inlet are integrated into the road infrastructure to facilitate conveyance of surface runoff into conduits. The Pretoria type inlet is popular in South Africa, but there is limited literature on its hydraulic performance. Therefore, this research is aimed at expanding the existing literature by assessing the behavior of the Pretoria type curb inlet and, developing design tools. Various configurations of the model of the Pretoria type curb inlet were fabricated in the Hydraulics laboratory of the School of Civil and Environmental Engineering at Witwatersrand University, and tests were carried out in a flume that simulated flow on the roadway with model a curb inlet that intercepted a portion of the flow. The tests were carried out on three longitudinal slopes of 0.25%, 0.5% and 0.75%, two cross-section slopes of 2% and 3%, with an undepressed and depressed gutter, and the mouth of the inlet free from any clog material and with clog material. To confirm the uniqueness of the Pretoria type curb inlet, we found that the Hydraulic Engineering Circular No. 22 (HEC-22) and Izzard methods did not give good prediction of the discharge capacity of the Pretoria type curb inlet. In contrast to previous work on the Pretoria type curb inlet which was restricted to 80% and 100% interception, this study explores a wider a range of interception efficiencies which make it more useful for design. Further, this work is the first known research investigation in South Africa that examines the influence of clogging on the performance of the Pretoria type curb inlet. We found that the discharge capacity of the curb inlet increases with the length of the opening, and an upstream transition section improves its efficiency. The efficiency of the inlet favors steep crosssectional slopes and gentle longitudinal slopes; depression of the gutter enhances the interception efficiency and this supports why the Pretoria type curb inlet is now synonymous with the depressed gutter. The reduced performance of the inlet due to clogging calls for concerted efforts at better solid waste management in South Africa.
Expansion fan/shock wave interactions between bodies in close proximity
(2019) Nel, Lara Joy
Shearing Interferometer Study of Shock Wave Impact on Membranes
(2019) Schulz, Jennifer
A study was conducted to investigate the flow eld characteristics that form for a shock wave propagating through a membrane. Analysis was also done to determine the strength of the shock wave reflected back into the system as well as the strength of the shock wave that was transmitted through the membrane. Multiple tests were done to analyse the e ects of di erent material types as well as di erent back pressures. Six di erent materials were used, each with three di erent back pressures. The flow field visualisation was done using both schlieren fow visualisation and shearing interferometry flow visualisation using a Sanderson prism. A comparison between the two forms of visualisation was done to determine which would provide the best qualitative understanding of the flow field. From this it was found that the shearing interferometry flow visualisation gave better insight into the density gradients as well as provided a clearer view of the flow characteristics. When analysing the flow eld characteristics for the early development of the transmitted shock wave, there were three principal characteristics that were present in all of the tests; a di racted shock wave, an expansion wave and a recompression shock wave. It was found that the prominence of these features varied depending on the material type as well as the type of back pressure. For the later ow development and membrane rupture, there were ve principal characteristics; small vortices, secondary shock waves, a vortex ring, expansion waves and a Mach disk. When analysing the strength of the re ected and transmitted shock waves, it was found that their strengths did not vary signi cantly for the di erent back pressures. The only exception was found when conducting tests using a balloon as a membrane. This was because the balloon de ected further into and out of the shock tube. The balloon tests were therefore done for a wider range of vacuum back pressures. It was found that the more the balloon de ected the stronger the transmitted shock wave produced, while the re ected shock wave remained approximately the same. A relationship between the strength of the re ected and transmitted shock wave was formed. It was found that as the strength of the re ected shock wave increased the strength of the transmitted shock wave decreased.
Three-dimensional shock wave reflection transition in steady flow
(2018) Surujhlal, Divek
This work details ﬁndings of an analytical, numerical and experimental investigation into the physical nature of three-dimensional shock reﬂection transition. Steady ﬂow shock reﬂections comprise two types: regular reﬂection and Mach reﬂection. Reﬂection studies have previously been conducted using double-wedge symmetrical test piece conﬁgurations. It had been found by previous researchers that the expansion waves resulting from the side edges of the wedges would inﬂuence the reﬂection plane. The three-dimensional nature of real experimental ﬂows gives rise to there generally being a coexistence of regular reﬂection (at the central portions) and Mach reﬂection (towards the outer peripheral portions) in between which transition occurs. It is the object of this work to understand three-dimensional transition for ﬂow ﬁelds in which edge eﬀects do not inﬂuence the reﬂection plane. Specially modiﬁed test piece geometry was developed for this purpose. Experimental tests were required for validation of the numerical models of the ﬂow ﬁeld. This was achieved by obtaining oblique shadowgraphs with optical orientation in both yaw and roll to assist in visualising the three-dimensional features of the ﬂow ﬁeld. These were compared with numerically reconstructed images at the same oblique orientations using a novel reconstruction technique. The main objective of this work was to identify the degree of correspondence of the threedimensional transition conditions to those of two-dimensional ﬂows. This was facilitated by means of reducing the three-dimensional analysis to an eﬀective two-dimensional one. It was found that the three-dimensional transition points occur at a higher eﬀective angle than predicted by twodimensional criteria, and tend towards two-dimensional criteria at reduced free-stream Mach numbers and increased model geometrical spreads. Another important aspect of this work was the nature of the intersection line in the vicinity of the transition point, i.e., the point of impingement of the incident wave and its Mach surface on the horizontal symmetry plane in between the test pieces. Here it was found that a cusp exists in the sweep proﬁle of the intersection line at the transition point. This was proved from a theoretical standpoint based on a model developed for the analysis of the ﬂow in the vicinity of transition. Evidence of this from the numerical and experimental results is given as well. Higher geometrical spreads and lower free-stream Mach numbers were found to create ﬂatter intersection line proﬁles at the horizontal symmetry plane on which the transition points were located further forward towards the apex of this line and which gave rise to greater transverse deﬂections for the streamlines passing through the regular reﬂection portions. Further discussion revolves around the nature of the shear and Mach surfaces. The Mach surface heights (representative of the triple line trajectories) are shown to increase monotonically. The shear layer edge trajectory, which originates at the sweep cusp, was found to show considerable transverse divergence but in keeping with the nature and extent of the transition cusp sweep differential, which in some cases was found to be large enough to cause a strong shock solution for the Mach reﬂection portion. In this case the shear surface edge trajectory diverted from trends seen for other models. The nature of the shear surface as a whole revealed interesting insights into the negative triple conﬁguration of the Mach reﬂection portions which comprised of convex Mach surfaces. This is in contrast to the geometry obtained for the Mach surface for full Mach reﬂection numerically studied with a highly-spread geometry. Here, the ﬂat Mach surface was found to increase monotonically towards the periphery in contrast to what was found for ﬂows with edge inﬂuences on the Mach surface. It is suggested that this is what precludes complex reﬂection (central Mach reﬂection, transitioning to regular reﬂection further out, with a further transition to Mach reﬂection at the periphery) from being obtained in such ﬂow ﬁelds
Laminar wake ﬂow behind a hump on a wall
(2018) Julyan, Jonathan
The laminar wake ﬂow behind a hump on a solid wall boundary is investigated. A Blasius boundary layer ﬂow is perturbed by the hump and a wake forms directly downstream. Triple deck theory is applied to the wake region and the ﬂow is divided into three decks. The governing equations are derived for each deck for both the near and the far wake. Particular attention is paid to the role of the boundary layer displacement eﬀect. The conservation laws and conserved quantities for the governing equations are derived. The multiplier method is applied to the linearised governing equations for small humps and a basis of conserved vectors is constructed. Since, in general, the problem contains an unknown non-homogeneous boundary condition, each conserved vector needs to be carefully chosen and additional restrictions need to be applied to ensure that each conserved quantity, which is obtained by integrating the corresponding conservation law across the wake and imposing the relevant boundary conditions, has a ﬁnite value. Four non-trivial conserved quantities are found; three of which have only now been identiﬁed. The four conserved quantities relate to the conservation of mass, drag and the ﬁrst and second moments of the momentum deﬁcit. For each case the existence of a solution that satisﬁes the governing equations, boundary conditions and a ﬁnite valued conserved quantity is discussed. The solution corresponding to the near wall-wake ﬂow is further discussed. Although the far wall-wake does not satisfy a conserved quantity, for completeness, it is included in this work.
Blast wave generation and interactions
(2018) Demby, David Marc
The design, construction and validation of a non-explosively driven blast tube was undertaken in order to reduce the cost and time of blast wave experimentation as well as to enable the study of blast waves in the test laboratory environment. The design of the blast tube was performed numerically using commercially available CFD software. Numerous di erent driver shapes and con gurations were analysed during the design process including linearly diverging drivers, straight drivers and polynomial drivers. Based on the results and analysis performed in it was deduced that a driver section required a few key features in order to generate a blast wave with a realistic Friedlander pressure pro le namely, the driver section must end in a sharp corner in order to enable expansion focusing to occur, the walls of the driver section must be divergent to cause the expansion waves to re ect downstream almost immediately after the diaphragm bursts as well to drive the expansion focusing, the walls of the driver section must transition smoothly, that is without a corner, into the expansion section walls and the walls of the driver section must be curved in order to induce smooth and continuous expansion wave re ection and focusing. After some tests were carried out on a few iterations of driver section shapes, three shapes were settled on, namely a concave driver, a linear driver and a convex driver. Once the nal design of the blast tube was settled upon, a working prototype was manufactured and assembled in the North West Engineering Laboratories and the prototype was tested. During testing of the blast tube it was found that, despite issues arising due to choice of mechanism employed to pressurise the driver being awed, there being notches and steps at the joints along the tube length and the downstream end of the test section being closed, the blast tube did in fact generate blast waves with realistic pressure decay pro les and good visual quality. After being validated the blast tube was used to examine the di raction of the blast wave around a 90 corner and the re ection of the blast wave induced upon impinging wedges having angles of 15 , 30 and 45 . The blast wave di raction and re ection experimentation were carried out in the 1:2 < Ms < 1:4 range.
Expansion wave diffraction around sharp convex corners
(2017) Shaikh, Zahra
Much work has been previously invested towards the study of shock wave phenomena. However, little or no literature can be found involving studies of expansion waves undergoing similar effects. The study of expansion wave diffraction was rst considered by Mohamed and Skews [1]. The investigation focussed on studying expansion wave diffraction around a 90 corner by using both experimental and computational methods. While a good agreement between the results was found there were several features which were apparent in the experimental imaging but could not be resolved by a numerical model. This included the large-scale turbulent structures in the separation bubble, shear layer instability and vortex shedding as well as a large wake region which was noted downstream of the bubble. In the current work, expansion wave di raction is examined using Large Eddy Simulation in an attempt to provide a better description of the ow eld. To make the analysis more feasible the Embedded LES hybrid technique was employed. Several subgrid-scale LES models were tested and the Wall Modelled LES technique showed the most promising results. The LES solution showed much improvement to the RANS solutions from the previous work. Turbulence in the separation bubble was evident and shear-layer instability and vortex shedding was observed. Due to the very low velocity uctuations the LES model did not resolve the wake region although, in certain cases, evidence of a wake region beginning to form could be seen. Using these results a further analysis into the structure of the bubble through the depth of the ow was conducted. As an extension of previous work the current study also examined expansion wave diffraction around other convex corners. The study involved an experimental as well as RANS and LES computational methods. The wedge angles investigated were 45 , 15 and 5 . The effects of changing the initial diaphragm pressure ratio and the diaphragm distance from the di raction corner were analysed. The results showed a high resemblance to what was found previously for the 90 case. However, signifi cant differences were noted in the shape of the bubble due to the inclination angle of the ow along vertical wall and the much higher velocity gradients of the ow at the diffraction corner and surrounding the bubble.
On shock wave diffraction from non-orthogonal apertures
(2018) Paton, Randall Tyrone
The diffraction of shock waves has been explored in many contexts in which either the shock wave is plane and the confi ning volume has complex geometry or where the shock wave has some non-plane geometry, typically something like spherical since this is the approximate shape of the waves generated by blasts. However, these studies have not considered more complex initial wave shapes or exit geometries. This study therefore addresses this de ciency in two ways. The dynamic conical shock wave was originally proposed as a mechanism for the initiation of fusion whereby the focusing of the shock wave near the axis of symmetry would produce the high temperatures and pressures required. This was explored numerically and theoretically, as no experimental method was considered viable, and it was found that the regular re ection of a shock wave de ned by conical wave geometry is not stable and will revert to an irregular re ection pattern at the axis. Three primary geometries were identi ed distinguished by the number of irregular re ections formed and in uenced by the induced vortical ow. The current study used a developed experimental apparatus to study conical shock waves and an additional, new re ection pattern, named the von Neumann type (vN-type) for the similarity to the von Neumann re ection of weak plane waves, was identi ed. In addition, instability of the conical shear layer present as a result of the irregular re ection at the axis of the shock wave was identi ed experimentally which resembles the Kelvin-Helmholtz instability previously only studied in two-dimensional con gurations of compressible ow. Dynamic bending of the central jet from the re ection axis was also tested as a function of upstream occlusion in the shock tube and this suggests possible future work in compressible jet actuation. The current study also considered the diffraction of plane shock waves at the inclined or curved exits of shock tubes, which are more general examples of duct interaction of the sort that might be found in engines or ventilation systems. This was done experimentally using novel, open test sections for a conventional shock tube and for a limited number of computational cases. These ows are characteristically different from the diffraction of shock waves from tubes of complex cross-section studied to date where the exit plane is still normal to the direction of travel of the wave. This is because the shock wave still undergoes simultaneous diffraction at all points around the edge of the tube in such a case while in this study the wave diffracts at different times around the tube periphery. This affects the strength of both the emerging incident wave and the diffraction and thus an atypical formation of the jet and vortex takes place. In the case of the inclined plane exit of the shock tube, two primary phenomena were noted: de ection of the jet and change of the jet cone angle; and variations in the vortex diffraction behaviour. For the former effect a large inclination of the exit from the normal increased the spread of the jet and the inclination away from the tube axis. Also, a system of secondary shock waves forms in the jet due to the expansion fans formed at the diffraction edge, typical of under expanded jets but becomes weaker as exit surface inclination increases. The second effect noted is of the increased curvature as a function of time after diffraction for higher inclinations, due to the much stronger induced velocities for the portion of the vortex shed on the obtuse upstream edge. The vortex loop also loses coherence with increasing inclination because of the weak vortex shedding at the downstream edge of the tube. The results for the curved exit are similar although the effects are not as extreme since the limiting diffraction angles are lower than for the extreme plane cases due to the characteristics of circular geometry. In the extreme case of part of the shock tube exit being tangent to the exit surface, the vortex again does not form a closed loop but rather terminates in the exit surface. This was particularly tested here with a plane section at the tangent point. However, the secondary re ection of the diffracted shock wave due to the curvature of the surface toward the diffracted wave, which tends to disrupt the vortex, means that an internal diffraction with a fully closed tube would result in a short-lived vortex loop. In both of the latter cases the vortex loop, or arch if it cannot close into a loop, is part of the physical mechanism whereby a jet ow exiting a pipe adjusts to being a di use ow along the exit surface. This is accomplished by the spreading of the sheet of vorticity, which is the boundary layer in the pipe and the jet boundary outside of it, by the origination of turbulence in the breakdown of the vortex arch or loop. The diffraction of shock waves from non-orthogonal apertures demonstrates features previously unidenti ed and suggests complex ow patterns which simpli ed two-dimensional analysis cannot describe.
The eﬀect of wall thermal conductivity on shock wave reﬂection
(2017) Berry, Richard
In traditional two-dimensional shock wave theory the reﬂection of a shock wave oﬀ a surface is treated as an adiabatic process and that the reﬂection surface is perfectly rigid and smooth with an inviscid ﬂow of the ﬂuid. In reality it has been found that these assumptions are not entirely accurate, and that although they are a good indication in the regular and irregular reﬂection domains of shock waves over the surface, viscous and thermal eﬀects are present within the ﬂow ﬁeld. It has been experimentally shown that the transition of regular reﬂection to irregular reﬂection exceeds the theoretical limit, which is known as the von Neumann paradox. This paradox has largely been accounted for in the formation of a viscous boundary layer behind the reﬂected shock wave, based on numerous experimental and computational studies. However, the thermal eﬀects in the reﬂection process have largely been neglected as the assumption of heat transfer between the post-shock wave gas and the reﬂection surfaces is assumed to be invalid. These thermal eﬀects were investigated by testing materials with a varying range of thermal conductivities (1.13 to 401 W/mK) and similar surface roughness’s below the suggested limit for hydraulic smoothness. Each experiment placed two test pieces at the same incidence angle, symmetrically in the shock tube. This allowed ﬂow properties to be exactly the same for the two materials being tested with a single plane shock wave. Test Mach numbers ranged from 1.2790 to 1.3986, with tests conducted at shock wave incidence angles of 36◦, 40◦, 60◦ and 70◦. This allowed both the regular and irregular reﬂection domains to be tested. Shadowgraph images were created using a z-conﬁguration optical set up. These shadowgraph images were analysed quantitatively based on the angles measured as well as qualitatively based on ﬂow features and symmetry. Both the quantitative and qualitative tests indicated that there was a diﬀerence in the angles between the reﬂected shock waves and surfaces based on the material thermal conductivity. In the quantitative tests the value of this angle was larger for materials with a lower thermal conductivity, and smaller for ones with a higher thermal conductivity for the regular reﬂection cases. In the irregular reﬂection cases the angle between the reﬂected and incident shock waves was larger for materials with a higher thermal conductivity. The materials with midrange thermal conductivities had reﬂection angles that lay within the bounds of the glass and copper angle values. The qualitative images supported these ﬁndings showing asymmetry in materials with diﬀerent thermal conductivities with the intersection of reﬂected shock waves lying closer to the material with a higher thermal conductivity. Control experiments using test pieces made from an identical material showed no bias due to the location of the test piece in the shock tube
Eﬀect of internal surface curvature on steady axisymmetric shock waves
(2017) Filippi, Alessandro Antonio
The cardinal aspects of supersonic and hypersonic propulsion intake design involve understanding the internal shock wave structures forming therein. A study was conducted to explore the eﬀects of internal surface curvature and entry deﬂection angle on steady axisymmetric shock waves. Very little is known about these inﬂuences with only Curved Shock Theory, produced by M¨ older, providing analytical insight directly after a curved shock wave. The shock waves and accompanying ﬂow ﬁelds which were generated were studied via experimental and numerical means. Radius normalised internal radii of curvature of 1, 1.5 and 2 with entry deﬂection angles of 0◦, 4◦ and 8◦ were investigated between a Mach number range of Mach 2.4 and 3.6. Experimental results were produced using a blow down supersonic wind tunnel facility and were captured via shadowgraph and schlieren ﬂow visualisation techniques. The numerical simulations were validated using the experimental results. A self similar curved shock wave shape equation was presented with an empirical model which uses ﬂow Mach number and internal radius of curvature in order to produce the resulting curved shock shape. Curved Shock Theory streamlines were used to try predict the internal surfaces that produced the curved shocks but results did not correlate. This was due to extreme streamline curvature curving the streamlines when the shock angle approached the Mach angle. Very good agreement was however found between the theoretical and numerical streamlines at lower curvatures. The higher the internal surface curvature and entry deﬂection angle, the greater the ﬂow ﬁelds were impacted. Steeper characteristics formed as a result, curving the shock wave more noticeably. Both the internal surface curvature and entry deﬂection angle were found to have an eﬀect on the trailing edge expansion fans which then altered the shape of downstream shock wave structures. The highest curvature models produced steady double reﬂection patterns due the ﬂow being turned in onto itself by the imposed internal surface curvature. The eﬀects of conical and curved internal surfaces were explored for additional insight into the presence of ﬂow-normal curvature and the curving of the attached shock waves.

3. Electronic Theses and Dissertations (ETDs) - All submissions

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