Measurements of drag forces an spheres end a cylinder in open rectangular channels in liquid helium II heat flow and superflow wore mode at temperatures between 1.3°K and the λ-point. The drag forces were measured by the deflection of a torsion system suspended above the free surface of the liquid from a quarts fibre. In the heat flow experiments, the drag vas found to be similar to that which would be exerted by a classical fluid with the same velocity, viscosity and density as the norma1 component. Correlations of the drag coefficient D/( 1⁄2 ρ[sub]n2A) with the Reynolds numbers ρnvηd/ηn and ρvnd/ηn show that the former is much more suitable both in tor of eliminating temperature dependence and agreement with the classical value. Above 1.6°K, a small decrease in drag with increasing velocity was usually noticed; this was attributed to the onset of turbulence in the superfluid, giving rise to a component of drag in the direction of superfluid flow. Describing the turbulent superfluid so a laminarly flowing fluid with an effective viscosity ηs makes possible an ardor of magnitude estimate of ηs the decrease in drag; it is found to lie between 10 and 100 micropoise. At temperatures nearer the λ -point, the simple two fluid description appears to become lies adequate. In the superflow experiments, sphere an the cylinder arc dragged in the direction of the superfluid flow. Correlations of drag coefficient with Reynolds number suggest value for the effective viscosity of between 20 and 100 micropoise. In the cylinder superflow experiments, below a velocity of 2±1 am sec−1, no drag was observable. This is attributed to an ideal flow regime and is bellowed to be the first direct demonstration of D'Alembert's wades, rely that an inviscid fluid can exert no drag on a body.

The stability of wall driven and thermally driven cavity flow is investigated for a wide range of viscous and viscoelastic fluids. The effect of inertia, elasticity, temperature gradients, viscous heating and Biot boundary conditions are of particular interest. Both destabilisation and bifurcation phenomenon are found. For Newtonian constant viscosity flow the instabilities are characterised by a critical Reynolds number which represents the ratio of inertial forces to viscous forces, and instability occurs when the inertial forces become large. For non-Newtonian viscoelastic fluids the instability is characterised by a critical Weissenberg number, which represents the ratio of elastic forces to viscous forces, and instability also occurs when elastic forces dominate the viscous forces. For thermally driven flow the instability is characterised by a critical Rayleigh number, which represents the ratio of temperature gradient to viscosity, and instability occurs when the Rayleigh number become large. In this case the instability is also characterised by both Eckert and Biot number. The work has relevance to thermal convection and mixing processes which occur in the viscous and viscoelastic fluid within the Earth's mantle. Three-dimensional steady and transient flow in a cylindrical cavity and three dimensional steady flow in a spherical cavity, are also considered for both viscous and viscoelastic fluids. Instabilities in these three-dimensional flow depend on the same parameters as the flow in square cavity.

Obtaining accurate solutions to flows that involve discontinuous features still re- mains one of the most difficult tasks in computational fluid dynamics today. Some discontinuous features, such as shear waves and material interfaces, are quite deli- cate, yet they have a profound effect on the rest of the flow field. The accuracy of the numerical scheme and the quality of the grid discretisation of the flow domain, are both critical when computing multi-dimensional discontinuous solutions. Here, the second order WAF scheme is used in conjuction with an adaptive grid algorithm, which is able to automatically modify the grid in regions of discontinuous features and solid boundaries. The grid algorithm is a combination of two successful ap- proaches, namely Chimera and Cartesian grid Adaptive Mesh Refinement (AMR). The Chimera approach is able to accurately represent non-Cartesian boundaries, whilst the AMR approach yields significant savings in memory storage and cPu time. The combined algorithm has been thoroughly validated for convection test problems in gas dynamics. The computed solutions compare well with other numerical and experimental results. These tests have also been used to assess the efficiency of the grid adaption algorithms. Finally, the approach is applied to axi-symmetric, two- dimensional, two-phase, reactive flows in the context of internal ballistics problems. Again, the computed results are compared with other numerical and experimental results.

Effective and robust high resolution schemes are of vital importance for simulation of viscous and inviscid flows. Since second-order high resolution schemes in practice are inadquate for many applications, large efforts have been put towards developing higher- order accurate schemes in the past. Although some progress has been made, the efforts were frustrated by the lack of effective and robust new schemes. Therefore this thesis is aimed at challenging this difficult but very important issue. Some new theories and methodologies were established during this research, which covers the linear stability analysis for high-order numerical schemes; the fully discrete techniques for model equations; the formulation of conservative high-order schemes and the high-order Total Variation Diminishing (TVD) schemes. According to these theories arbitrary-order high resolution schemes can be developed. To illustrate the methodologies second-, third-, fourth-, and 20th-order schemes are presented. These high resolution schemes were tested and validated by solving some popular test problems for one and two dimensional Euler and incompressible Navier-Stokes equations. The efficiency and robustness are the features of these high-order schemes.

Thesis (DTech (Chemical Engineering))--Cape Technikon, Cape Town, 2004 / Despite efforts since the 1950s, laminar flow through pipe fittings is still a topic that needs investigation (Jacobs, 1993). Most experimental studies on this topic include fittings such as contractions, expansions, elbows, valves and orifices (Edwards et aI., 1985; Turian et al., 1998; Pal & Hwang, 1999). Although sudden contractions are not often found in industry, most researchers included these fittings as part of their experimental investigation. The volume of work done on flow through sudden contractions over the last 50 years (e.g. Bogue, 1959; Christian et aI., 1972; Vrentas & Duda, 1973; Boger, 1987; Bullen et aI., 1996; Sisavath et aI., 2002), establishes its place of importance in the fundamental understanding offluid flow and fluid mechanics. There are inconsistent reports on the status ofthe study ofNewtonian fluids flowing through sudden contractions, i.e., that "it is a solved problem" (Boger, 1987) and "that it is far from being resolved" (Sisavath et aI., 2002). One reason for this apparent contradiction is the fact that most experimental studies do not agree with one another or with analytical and numerical studies. A state-of-the-art literature review by Pienaar et al. (2001) confirmed this and that further investigation of this topic is required. To explore these contradictions, it was necessary for one study to do both an experimental and numerical investigation and compare the results with existing literature. It was also important to find some basis for agreement of experimental work and not just add another data set to the existing scattered database. A test facility was built for testing three contraction ratios, i.e., ~ = 0.22, 0.50 and 0.85. A range ofNewtonian and non-Newtonian fluids was tested over a wide range ofReynolds number (Re = 0.01 - 100 000).

M.Ing. / There are two advantages of enhanced heat transfer. Firstly a decrease in the heat exchanger size and secondly an increase in the heat transfer coefficient. A method of increasing the heat transfer coefficient is to insert spiralled wires in the annulus of a tube-in-tube heat exchanger. It was decided to investigate this method further and therefore the objectives of the investigation are twofold. First to determine what the optimum spiral angle of the wires is, and secondly what mechanism causes the enhanced heat transfer. Specifically to determine if it is an increase in the turbulence or an increase in the flow rotation. A numerical model that was experimentally verified was used to do the investigation. It was concluded from the numerical results that for optimum heat transfer, the spiral angle of the wires should be 30°. It was also found that the mechanism for enhanced heat transfer is an increase in the rotation of the flow in the annulus.

No description available.

The purpose of this thesis is to study the problem of a low Reynolds number swimmer that is in very close proximity to a wall or solid boundary in a non- Newtonian fluid. We assume that it moves by propagating waves down its length in one direction, creating a thrust and therefore propelling it in the opposite direction. We model the swimmer as an infinite, inextensible waving sheet. We consider two main cases of this swimming sheet problem. In the first case, the type of wave being propagated down the length of the swimmer is specified. We compare the swimming speeds of viscoelastic shear thinning, shear thickening and Newtonian fluids for a fixed propagating wave speed. We then compare the swimming speeds of these same fluids for a fixed rate of work per wavelength. In the latter situation, we find that a shear thinning fluid always yields the fastest swimming speed regardless of the amplitude of the propagating waves. We conclude that a shear thinning fluid is optimal for the swimmer. Analytical results are obtained for various limiting cases. Next, we consider the problem with a Bingham fluid. Yield surfaces and flow profiles are obtained. In the second case, the forcing along the length of the swimmer is specified, but the shape of the swimmer is unknown. First, we solve this problem for a Newtonian fluid. Large amplitude forcing yields a swimmer shape that has a plateau region following by a large spike region. It is found that there exists an optimal forcing that will yield a maximum swimming speed. Next, we solve the problem for moderate forcing amplitudes for viscoelastic shear thickening and shear thinning fluids. For a given forcing, it is found that a shear thinning fluid yields the fastest swimming speed when compared to a shear thickening fluid and a Newtonian fluid. The difference in swimming speeds decreases as the bending stiffness of the swimmer increases. / Science, Faculty of / Mathematics, Department of / Graduate

In the analysis of thermoacoustic systems, a flame is usually characterised by the way its heat release responds to acoustic forcing. This response depends on the hydrodynamic stability of the flame. Some flames, such as a premixed bunsen flame, are hydrodynamically globally stable. They respond only at the forcing frequency. Other flames, such as a jet diffusion flame, are hydrodynamically globally unstable. They oscillate at their own natural frequencies and are often assumed to be insensitive to low-amplitude forcing at other frequencies. If a hydrodynamically globally unstable flame really is insensitive to forcing at other frequencies, then it should be possible to weaken thermoacoustic oscillations by detuning the frequency of the natural hydrodynamic mode from that of the natural acoustic modes. This would be very beneficial for industrial combustors. In this thesis, that assumption of insensitivity to forcing is tested experimentally. This is done by acoustically forcing two different self-excited flows: a non-reacting jet and a reacting jet. Both jets have regions of absolute instability at their base and this causes them to exhibit varicose oscillations at discrete natural frequencies. The forcing is applied around these frequencies, at varying amplitudes, and the response examined over a range of frequencies (not just at the forcing frequency). The overall system is then modelled as a forced van der Pol oscillator. The results show that, contrary to some expectations, a hydrodynamically self-excited jet oscillating at one frequency is sensitive to forcing at other frequencies. When forced at low amplitudes, the jet responds at both frequencies as well as at several nearby frequencies, and there is beating, indicating quasi-periodicity. When forced at high amplitudes, however, it locks into the forcing. The critical forcing amplitude required for lock-in increases with the deviation of the forcing frequency from the natural frequency. This increase is linear, indicating a Hopf bifurcation to a global mode. The lock-in curve has a characteristic ∨ shape, but with two subtle asymmetries about the natural frequency. The first asymmetry concerns the forcing amplitude required for lock-in. In the non-reacting jet, higher amplitudes are required when the forcing frequency is above the natural frequency. In the reacting jet, lower amplitudes are required when the forcing frequency is above the natural frequency. The second asymmetry concerns the broadband response at lock-in. In the non-reacting jet, this response is always weaker than the unforced response, regardless of whether the forcing frequency is above or below the natural frequency. In the reacting jet, that response is weaker than the unforced response when the forcing frequency is above the natural frequency, but is stronger than it when the forcing frequency is below the natural frequency. In the reacting jet, weakening the global instability – by adding coflow or by diluting the fuel mixture – causes the flame to lock in at lower forcing amplitudes. This finding, however, cannot be detected in the flame describing function. That is because the flame describing function captures the response at only the forcing frequency and ignores all other frequencies, most notably those arising from the natural mode and from its interactions with the forcing. Nevertheless, the flame describing function does show a rise in gain below the natural frequency and a drop above it, consistent with the broadband response. Many of these features can be predicted by the forced van der Pol oscillator. They include (i) the coexistence of the natural and forcing frequencies before lock-in; (ii) the presence of multiple spectral peaks around these competing frequencies, indicating quasi-periodicity; (iii)the occurrence of lock-in above a critical forcing amplitude; (iv) the ∨-shaped lock-in curve; and (v) the reduced broadband response at lock-in. There are, however, some features that cannot be predicted. They include (i) the asymmetry of the forcing amplitude required for lock-in, found in both jets; (ii) the asymmetry of the response at lock-in, found in the reacting jet; and (iii) the interactions between the fundamental and harmonics of both the natural and forcing frequencies, found in both jets.

No description available.