ABSTRACT
GENERALIZED COUETTE FLOW OF A
HERSCHEL - BULKLEY FLUID
THROUGH ECCENTRIC ANNULUS - AN APPROXIMATE SOLUTION
Seyidoglu, Tijen
M.S., Department of Chemical Engineering
Supervisor: ismail Tosun
Co-Supervisor: Ahmet N. Eraslan
January 2006, 134 pages
Generalized Couette flow of a Herschel-Bulkley fluid in an eccentric annulus is analyzed by approximating the flow geometry as a slit of variable height. Besides an imposed pressure gradient, one of the plates is considered non-stationary to take into account the axial and/or angular motion of the inner pipe in an eccentric annulus system.
Depending on the magnitude and the direction of the applied pressure gradient with respect to the plate velocity, three separate flow cases are studied in which the velocity reaches its maximum value either within the plug flow region or at the moving boundary. Velocity distributions are obtained for each case by solving the equations of continuity and motion. Volumetric flow rate expressions are obtained by integrating the velocity distribution over the cross-sectional area. At a given pressure gradient, the results indicate an increase in volumetric flow rate with an increase in eccentricity ratio. Criteria for each flow type is developed in terms of a dimensionless parameter & / #923 / , which takes into account the ratio of the imposed pressure gradient to the plate velocity. Volumetric flow rate expressions for Newtonian, Bingham and power-law fluids are obtained by considering the limiting values of the fluid index and yield stress. The validity of the equations are checked by considering the slit height to be a constant, i.e., flow between parallel plates.
Surge/swab pressure calculations are carried out for Herschel-Bulkley, power-law and Bingham fluids and the results are expressed as a function of eccentricity ratio, radius ratio, fluid index and yield stress. The results indicate that when the fluid index and the eccentricity ratio are fixed, a slight increase in the radius ratio causes a tremendous increase in surge/swab pressure, especially for low values of fluid index. On the other hand, displacement of the inner pipe from a concentric position causes a decrease in swab/surge pressure when other parameters are held constant.
Comparison with the literature values reveals the fact that flow in an eccentric annulus can be modeled as flow between a slit of variable height as long as the radius ratio is greater than 0.5 and the eccentricity ratio is less than 0.3. The results for other values of radius ratio and eccentricity ratio can be used as initial guess values in carrying out numerical calculations.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/2/12607087/index.pdf |
| Date | 01 January 2006 |
| Creators | Seyidoglu, Tijen |
| Contributors | Tosun, Ismail |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for METU campus |
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