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Flow of a non-Newtonian Bingham plastic fluid over a rotating disk



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Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress “Bingham number”, By, which is the ratio of the yield and viscous stresses. Using von Kármán’s similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.



Rheology, PIV., Bingham fluid, Bingham model, Rotating disk, Non-Newtonian fluid



Doctor of Philosophy (Ph.D.)


Mechanical Engineering


Mechanical Engineering


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