Master's degrees completed 2011

Mr I.Mathebula 2011. " Friction Factor Correlations for Perforated Tubes at Low Injection Rates"
Perforated tubes are widely used in industry for various applications. They can be found in commercial buildings or homes with stylish perforation patterns for aesthetic purposes while some perforation patterns are designed for suppressing specific frequencies in exhaust mufflers. Common pipes are sometimes customised into perforated pipes by simply drilling multiple holes along the length of the pipe for a cost effective irrigation system. An interesting application for perforated tubes arises when fluid injection is introduced through the perforations. Such a case arises when perforated tubes are used for horizontal oil well drilling, French drains or other draining applications. The pressure losses experienced under these conditions has led to the development of friction factor correlations, which consider the effects of the perforations and fluid injection. However, most of these correlations do not quantify the influence of fluid acceleration caused by injection in the familiar friction factor form. The present study reports friction factor correlations measured at low injection rate when the additional kinetic energy from the fluid injection process is considered. The friction factor measurements were conducted in copper tubes with an internal diameter of 20 mm and a wall thickness of 1 mm at three non-dimensional pitches of 0.375, 0.75 and 1.5. A perforated length-to-diameter ratio of 40:1 was used and each perforation row contained seven small perforation holes with a diameter of 1.5 mm spaced evenly around the perimeter of the tube. The perforations were staggered row to row, resulting in triangular perforation patterns. Water was used as a test medium and the Reynolds numbers at the tube outlet ranged from 20 000 to 60 000. Injection ratios were varied from 0 to 5% in increments of 1% to obtain a total of 135 unique combinations of perforated tube friction factor data at different injection ratios, Reynolds numbers and non-dimensional perforation pitches. The experiments were condensed into simple friction factor correlations, which can be used to predict the pressure losses expected across perforated tubes when fluid injection is present.

Supervisor: Prof J.P. Meyer

 Miss L.Smith 2011."An Interactive Boundary Layer Modelling Methodology for Aerodynamic flows"

Computational fluid dynamics (CFD) simulation is a computational tool for exploring flow applications in science and technology. Of central importance in many flow scenarios is the accurate modelling of the boundary layer phenomenon. This is particularly true in the aerospace industry, where it is central to the prediction of drag.

Modern CFD codes as applied to modelling aerodynamic flows have to be fast and efficient in order to model complex realistic geometries. When considering viscous flows, the boundary layer typically requires the largest part of computational resources. To simulate boundary layer flow with most current CFD codes, requires extremely fine mesh spacing normal to the wall and is consequently computationally very expensive. Boundary layer modelling approaches offer considerable computational cost savings.

One boundary layer method which proved to be very accurate is the two-integral method of Drela (1985). Coupling the boundary layer solution to inviscid external flow, however, is a challenge due to the Goldstein singularity, which occurs as separation is approached.

This research proposed to develop a new method to couple Drela’s two-integral equations to a generic outer flow solver in an iterative fashion. The study introduced an auxiliary equation, which was solved along with the displacement thickness to overcome the Goldstein singularity without the need to solve the entire flow domain simultaneously. In this work, the incompressible Navier-Stokes equations were used for the outer flow. 

In the majority of previous studies, the boundary layer thickness was simulated using a wall transpiration boundary condition at the interface between viscous and inviscid flows. This boundary condition was inherently non-physical since it added extra mass into the system to simulate the effects of the boundary layer. Here, this drawback was circumvented by the use of a mesh movement algorithm to shift the surface of the body outward without regridding the entire mesh. This replaced the transpiration boundary condition.

The results obtained show that accurate modelling is possible for laminar incompressible flow. The predicted solutions obtained compare well with similarity solutions in the case of flat and inclined plates, and with the results of a NACA0012 airfoil produced by the validated XFOIL code (Drela and Youngren, 2001).

Supervisor: Prof J.P. Meyer, Dr O.F. Oxtoby and Dr A.G. Malan

Mr A.G.B. Mowat 2011 "Modelling of non-linear aeroelastic systems using a strongly coupled fluid-structure-interaction methodology"

The purpose of this study was to develop a robust fluid-structure-interaction (FSI) technology that can accurately model non-linear flutter responses for sub- and transonic fluid flow. The Euler equation set governs the fluid domain, which was spatially discretised by a vertex-centred edge-based finite volume method. 

A dual-timestepping method was employed for the purpose of temporal discretisation. Three upwind schemes were compared in terms of accuracy, effciency and robustness, viz. Roe, HLLC (Harten-Lax-Van Leer with contact) and AUSM+ -up (Advection Up-stream Splitting Method). For this purpose, a second order unstructured MUSCL (Monotonic Upstream-centred Scheme for Conservation Laws) scheme, with van Albada limiter, was employed. The non-linear solid domain was resolved by a quadratic modal reduced order model (ROM), which was compared to a semi-analytical and linear modal ROM. The ROM equations were solved by a fourth order Runge-Kutta method. The fluid and solid were strongly coupled in a partitioned fashion with the information being passed at solver sub-iteration level. The developed FSI technology was verified and validated by applying it to test cases found in literature. 

It was demonstrated that accurate results may be obtained, with the HLLC upwind scheme offering the best balance between accuracy and robustness. Further, the quadratic ROM offered significantly improved accuracy when compared to the linear method.

Supervisors: Prof. A.G. Malan and Prof. J.P. Meyer 


Mr L Prinsloo  2011 "A critical evaluation of the design of removable cover-plate header boxes for air-cooled heat exchangers "

Large air-cooled heat exchangers (ACHEs) are most popularly implemented in the petrochemical and power industries at arid locations. They operate on a simple concept of convective heat transfer, whereby air in the surrounding atmosphere is caused to flow across a tube bundle, which in turn transports a process fluid. The distribution and direction of the process fluid flow may furthermore be guided via a set of appropriately located header boxes, which essentially consist of a collection of welded flat plates and nozzle attachments. Perforations on one of the faces of these boxes serve as an interface to the tube bundle.

The overall design and construction of an ACHE is commonly regulated by an American Petroleum Institute (API) standard, which is required to be used in conjunction with acceptable design codes. In spite of this, the design of certain header box configurations remains of prominent concern. It is the focus of the present study to investigate the approach adopted for a header box variant labelled as the removable cover type. In this configuration, one of the plates used to construct the header box is left removable. This plate is fastened and sealed by a collection of bolted joints and gasket.

One appropriate design code for the header box equipment is the ASME (American Society of Mechanical Engineers) boiler and pressure vessel code, although it provides no specific approach pertaining to the removable cover design. Instead it has been commonplace in industry for a number of aspects from this code to be synthesized, together with a collection of assumptions surrounding the header box behaviour, into an all encompassing design by rule approach. In this approach, the header box behaviour is accepted as being planar, whilst circumstances such as nozzle attachments and associated loading would suggest that a more comprehensive approach should be undertaken.

The aim of the present study is therefore to critically evaluate the current practice, and establish its adequacy. To do so, a finite element model (FEM) of an example header box design is developed. Subsequent comparisons with the stress distribution predicted via current practice are performed, and problems identified. An alternative analytical approach developed from rigid frame theory is further shown to provide improved results. According to Norris et al. [1], a rigid frame may be defined as ‘... a structure composed of a number of members all lying in one plane and connected so as to form a rigid configuration by joints, some or all of which are moment-resisting (rigid) instead of hinged ...’.

The linear elastic design by analysis approach, presented in the ASME code, is also utilised as a method for establishing design adequacy, whereby the finite element method is adopted. This approach is implemented in a more detailed investigation of nozzle placement and external loading. Design results obtained via the respective design by rule, and design by analysis methods are compared throughout the study.

Supervisors: Ms H.M. Inglis and Dr S. Kok

Mr J van den Bergh  2011 "An Algebraic Multigrid Solution Strategy for Efficient Solution of Free-Surface Flows "

Free-surface modelling (FSM) is a highly relevant and computationally intensive area of study in modern computational fluid dynamics. The Elemental software suite currently under development offers FSM capability, and employs a preconditioned GMRES solver in an attempt to effect fast solution times. In terms of potential solver performance however, multigrid methods can be considered state-of-the-art.

This work details the investigation into the use of Algebraic Multigrid (AMG) as a high performance solver tool for use as black box plug-in for Elemental FSM. Special attention was given to the development of novel and robust methods of addressing AMG setup costs in addition to transcribing the solver to efficient C++ object-oriented code. This led to the development of the so-called Freeze
extension of the basic algebraic multigrid method in an object-oriented C++ programming environment. The newly developed Freeze method reduces setup costs by periodically performing the setup procedure in an automatic and robust manner. 

The developed technology was evaluated in terms of robustness, stability and speed by applying it to benchmark FSM problems on structured and unstructured meshes of various sizes. This evaluation yielded a number of conclusive findings. First, the developed Freeze method reduced setup times by an order of magnitude. Second, the developed AMG solver offered substantial performance increases over the preconditioned GMRES method. In this way, it is proposed that this work has furthered the state-of-the-art of algebraic multigrid methods applied in the context of free-surface modelling.

Supervisors: Prof. A.G. Malan and Dr. D.N. Wilke

Mr D.D. Ndenguma  2011 "Computational fluid dynamics model for controlling dust and methane in underground coalmines "

Airborne dust and methane are common problems in the underground coalmines. They pose health and safety risk to mining personnel, and a safety risk to mining equipment as well. In order to prevent these risks, air borne dust and methane concentrations must be reduced to within the acceptable levels. In South Africa, the dust and methane concentration in coalmines should not exceed 2.0 mg/m³ and 0.5% per volume, respectively.

Different ventilation systems have been designed since the history of underground coal mining. Unfortunately, none provides an ultimate solution to the dust and methane problem, especially in the most critical areas of the underground coalmine, like blind-end of the heading and last through road. 

By changing airflow patterns and air velocity, it is possible to obtain an optimum ventilation design that can keep dust and methane within the acceptable levels. Mine ventilation is one of the popular ways of controlling both dust and methane. 

Since it is very difficult to conduct experiments in the underground coalmine due to harsh environmental conditions and tight production schedules, the investigator made use of a Computational Fluid Dynamics (CFD) modelling technique. The models were then experimentally verified and validated using a scaled down model at University of Pretoria.

After verification, further numerical analysis was done to in order to obtain a method for determining optimum fan positions for different heading dimensions.

This study proves that CFD can be used to model ventilation system of a scaled down coalmine model. Therefore chances that this might be true for the actual mine are very high but it needs to be investigated. If this is found to be true, then CFD modelling will be a very useful tool in coalmine ventilation system research and development.

Supervisors: Dr   J. Dirker  and Prof N.D.L. Burger

Mr J Jansen van Rensburg 2011 "Selective feature preserved elastic surface registration in complex geometric morphology "

In the study of functional morphology, evolutionary biologists, paleontologists and anthropologists use numerical tools to enquire into the adaptation of organic form to accommodate the relevant physics. The effect of a chosen elastic registration procedure, uncertainty of the mapping and discretisation of geometries are inspected within a contextual study using two complex skull geometries. Non-rigid registration offers a researcher interested in aspects of functional morphology the opportunity to do direct comparisons and statistics when digital geometries of related subject shapes are available. A finite element analysis is done on the two skulls to simulate masticatory induced stress. These results obtained are elegantly compared during the post-processing stage using the non-rigid mapping between the relevant computational domains. As shown in the study, exact difference values are not necessarily obtained but a non-rigid map between subject shapes and numerical results could give a good indication on the location of differences.

Supervisors: Dr. S. Kok, Dr. D.N. Wilke

Mr WG le Roux 2011 "Maximum net power output from an integrated design of a small-scale open and direct solar thermal Brayton cycle "

The geometry of the receiver and recuperator in a small-scale open and direct recuperative solar thermal Brayton cycle can be optimised in such a way that the system produces maximum net power output. The purpose of this work was to apply the second law of thermodynamics and entropy generation minimisation to optimise these geometries using an optimisation method. The dynamic trajectory optimisation method was used and off-the-shelf micro-turbines and a range of parabolic dish concentrator diameters were considered. A modified cavity receiver was used in the analysis with an assumed cavity wall construction method of either a circular tube or a rectangular channel. A maximum temperature constraint of 1 200 K was set for the receiver surface temperature. A counterflow plate-type recuperator was considered and the recuperator length was constrained to the length of the radius of the concentrator. Systems producing a steady-state net power output of 2 – 100 kW were analysed. The effect of various conditions, such as wind, receiver inclination and concentrator rim angle on the maximum net power output, and optimum geometry of the system were investigated. Forty-five different micro-turbines and seven concentrator diameters between 6 and 18 metres were considered. Results show the optimum geometries, optimum operating conditions and minimum entropy generation as a function of the system mass flow rate. The optimum receiver tube diameter was relatively large when compared with the receiver size. The optimum counterflow plate-type recuperator channel aspect ratio is a linear function of the optimum system mass flow rate for a constant recuperator height. The optimum recuperator length and optimum NTU are small at small system mass flow rates but increase as the system mass flow rate increases until the length constraint is reached. For the optimised systems with maximum net power output, the solar receiver is the main contributor to the total rate of minimum entropy generation. The contributions from the recuperator, compressor and turbine are next in line. Results show that the irreversibilities were spread throughout the system in such a way that the minimum internal irreversibility rate was almost three times the minimum external irreversibility rate for all optimum system geometries and for different concentrator diameters. For a specific environment and parameters, there exists an optimum receiver and recuperator geometry so that the system can produce maximum net power output.

Supervisors: Dr T. Bello-Ochende and Prof J. P. Meyer

Mr T Botha 2011 "High Speed Autonomous Off-Road Vehicle Steering "

High speed cornering of an off-road vehicle poses considerable challenges to the development of an autonomous vehicle due to the non-linear dynamics of the tyre road interface as well as those of the vehicle as a whole during high lateral accelerations. Most driver models are developed for low speed applications using linear control methods under the assumption of linear vehicle dynamics. The dynamics of a vehicle however become highly non-linear as the lateral acceleration increases, thus rendering these linear models unusable during high speed manoeuvres.

In this study, two robust driver models for use in an autonomous vehicle capable of path following at both low and high speeds are presented. Both models make use of the relationship between the yaw acceleration and steering rate to control the yaw angle of the vehicle. The first driver model is derived from the simulation of a full non-linear vehicle model in ADAMS. The Magic Tyre Formula is used to model the relationship between the vehicle's yaw acceleration and steer rate as a function of vehicle speed. The second driver model is a mathematical model which incorporates a form of sliding control. The model includes the lateral tyre dynamics as modelled by the Pacejka '89 tyre model.

Both driver models are coupled with a gain scheduling proportional derivative controller to reduce the cross-track error.

The two driver models were implemented on a Land Rover Defender and experimentally validated by performing a double lane change manoeuvre at speeds up to 80km/h. The vehicle remained stable even though the lateral accelerations experienced were 80% of the vehicle limits.

The result is a robust controller capable of path following at various speeds and at high lateral accelerations.

Supervisor: Prof S Els

Mr AC Hohls 2011 "Investigation into Phase Transformation of Yttria Stabilized Zirconia Femoral Heads."

27 Retrieved Yttria Stabilised Tetragonal Zirconia (Y-TZP) femoral heads were studied for the occurrence of tetragonal to monoclinic phase transformation and the effects that such transformation has on the bearing surface. The mean monoclinic percentage found is 53.6% with 25 of the samples having transformed more than 20%. This finding nullifies earlier predictions that it would take 25 to 30 years to transform to a monoclinic content of 30 to 40% inside the human body (Chevalier, Drouin & Calés 1997). It was however shown that Hot Isostatic Pressed (HIP’ed) Y-TZP femoral heads have a better, though still not adequate, resistance to phase transformation in the human body than non-HIP’ed femoral heads. 

Results of various investigations show that this transformation degrades the surface condition of the femoral heads, which in turn increases wear and subsequently decreases the survival rate of the prosthesis due to a greater risk of aseptic loosening. 

It is postulated that a great contributing factor to the phase transformation is increased temperatures inside the bearing couple, due to inadequate lubrication between the two bearing surfaces. 

Tetragonal to monoclinic phase transformation and its associated effects renders Y-TZP femoral heads less attractive for hip replacements.

Supervisor: Dr NDL Burger 

Mr ASD Dymond 2011 "Multiple objective optimization of an airfoil shape."

An airfoil shape optimization problem with conflicting objectives is handled using two different multi-objective approaches. These are a an 'a priori' scalarization approach where the conflicting objectives are assigned weights and summed together to form a single objective, and the direct multi-objective approach.

The optimization formulations for both approaches contain challenging numerical characteristics which include noise, multi-modality and undefined regions. Gradient-, surrogate- and population-based single objective optimization methods are applied to the `a priori' formulations. The gradient methods are modified to improve their performance on noisy problems as well as to handle undefined regions in the design space. The modifications are successful but the modified methods are outperformed by the surrogate methods and population based methods.

Population-based techniques are used for the direct multi-objective approach. Two established optimization algorithms and two custom algorithms are implemented. The custom algorithms use fitted unrotated hyper ellipses and linear aggregating functions to search the design space for non-dominated designs. Various multi-objective formulations are posed to investigate different aspects of the airfoil design problem. The non-dominated designs found by the direct multi-objective optimization algorithms are then presented.

Supervisor: Dr Schalk Kok
Co-Supervisor: Dr Bennie Broughton   

Mr F U Ighalo 2011 "Optimisation of Microchannels and Micropin-fin Heat Sinks with Computational Fluid Dynamics in Combination with a Mathematical Optimisation Algorithm."

In recent times, high power density trends and temperature constraints in integrated circuits have led to conventional cooling techniques not being sufficient to meet the thermal requirements. The ever-increasing desire to overcome this problem has led to worldwide interest in micro heat sink design of electronic components. It has been found that geometric configurations of micro heat sinks play a vital role in heat transfer performance. Therefore, an effective means of optimally designing these heat sinks is required. Experimentation has extensively been used in the past to understand the behaviour of these heat extraction devices. Computational fluid dynamics (CFD) has more recently provided a more cost-effective and less time-consuming means of achieving the same objective. However, in order to achieve optimal designs of micro heat sinks using CFD, the designer has to be well experienced and carry out a number of trial-and-error simulations. Unfortunately, this will still not always guarantee an accurate optimal design. In this dissertation, a design methodology which combines CFD with a mathematical optimisation algorithm (a leapfrog optimisation program and DYNAMIC-Q algorithm) is proposed. This automated process is applied to three design cases. In the first design case, the peak wall temperature of a microchannel embedded in a highly conductive solid is minimised. The second case involves the optimisation of a double row micropin-fin heat sink. In this case, the objective is to maximise the total rate of heat transfer with the effect of the thermal conductivity also being investigated. The third case extends the micropin-fin optimisation to a heat sink with three rows. In all three cases, fixed volume constraint and manufacturing restraints are enforced to ensure industrial applicability. Lastly, the trends of the three cases are compared. It is concluded that optimal design can be achieved with a combination of CFD and mathematical optimisation.

Supervisors: Dr T Bello-Ochende and Prof Josua Meyer

Mr S Smitt 2011 "Contraction heat transfer coefficient correlation for rectangular pin fin heat"

The demand for smaller but more powerful electronic components is ever increasing. This demand puts a strain on engineers to produce optimal cooling designs for these electronic components. One method for cooling these electronic components is with heat sinks which effectively increase the surface area available for extracting the heat from the electronic components. Computational Fluid Dynamics (CFD) software is sometimes used to aid in the design process, but CFD simulations are computationally expensive and take long to complete. This causes the design engineer to test only a few proposed designs based on his/her experience and select the design that performs the best out of the tested designs, which might not be the optimum.

The temperature distribution inside the heat sink can be solved relatively quickly with the diffusion equation, but the flow around the heat sink complicates the CFD simulation and increases the solving time significantly. Therefore, applications have been developed where the interaction between the heat sink and the flow around the heat sink is replaced by heat transfer coefficients. These coefficients are calculated from correlated equations which contain the flow properties. The flow properties are extracted from a flow network solver, which solves the flow around the heat sink. This procedure results in less expensive simulations, which can be used together with an optimisation procedure to develop an optimum cooling design.

In this dissertation, a correlation for the contraction heat transfer coefficients of rectangular pin fin heat sinks was developed. A methodology was developed where consecutive regression lines were fitted to a large set of data extracted from numerous CFD simulations. The combination of these regression lines formed the basis of the correlation, which was divided into two correlations; one for laminar flow and another for turbulent flow. The correlations were tested against CFD simulations as well as experimental data. The results indicate that these correlations can be effectively used to calculate the contraction heat transfer coefficients on pin fin heat sinks.

Supervisors: dr DJ de Kock and Prof Josua Meyer


The flexibility in the region of the crack is different from an uncracked section. A finite element model of a shaft is built and investigated. The damaged model is the same except that the nodes in the location of the crack are not equivalenced in order to represent the crack. A simple constant cross-sectional shaft with semi-circular transverse surface cracks varying in size have been modelled on the Patran finite element software and a normal modes analysis was done using the Nastran solver. The results revealed a change in the natural frequencies due to the variation in the size of the crack.

The experimental investigation involved creating sample shafts with damage positioned in them that would closely resemble what one may find in actual real-life situations and the dynamics during rotation with various torsional loadings are investigated and monitored using three methods. A fibre-optical sensor, Digital image correlation system and telemetry strain gauges were used. Undersampling techniques were used for the DIC system. Results showed that the fibre-optic sensor is by far the most favourable as it is able to detect damage under constant operation. The finite element model was updated by re-modelling the geometry, damage and material properties. The solution of the analysis matched the experimental results closely and model verification was achieved.

Supervisor: Professor P.S Heyns

Published by Bradley Bock

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