Links Return to the Detailed Guide for ChE 815.08 - Advanced Momentum Transfer Introductory Guide for ChE815.08 - Advanced Momentum Transfer The Home Page for the Fluid Mechanics Group Selection of the Fluent Project You need to select your own FLUENT project! The problem must be interesting from a fluids viewpoint and challenging from the numerics viewpoint of grid generation. There are a number of example fluid flow pictures and explanations below. This material is from Milton van Dyke's book An Album of Fluid Motion,published by The Parabolic Press. The pictures are only meant to be suggestions.You may select anything you want! It does not have to be based on the suggestions below. These are only for your help. You may use the pictures as a basis and make the calculation more interesting by selecting a somewhat different geometry and/or conditions. It is i mportant to run more than one set of conditions so you can establish the development of the flow as a function of Reynolds number or even turbulence. The instructor has a copy of van Dyke's book in his office for you to view. Once you have selected the flow you want to study, turn in two copies with your name and a sketch with flow direction,boundaries etc. clearly marked. One copy will be retained by the instructor and the other will b e posed to help other not to select the same geometry. Make sure you clearly point out what you are going to do and what changes you are going to make from the those suggested below. Note that a solution using either Cartesian or cylindrical coordinates within Fluent will not be satisfactory, you must use Gambit. Remember, each of you will be running your own problem, but do not interpret this to mean that you should not work t ogether in your learning process. It will help you greatly if you team up in doing the tutorials and preliminary tests. It will also help you to interact with each other (and me) during the period you set up your grid using the boundary fitted coordinates (BFC) system. 10. Creeping flow in a wedge. The motion is driven by steady clockwise rotation of a circular cylinder whose bottom is seen just below the free surface at the top of the photograph. Visualization is by aluminum dust in water. The Reynolds number is 0.17 based on peripheral speed and wedge height. A 90-minute exposure shows the first two of what are in theory an infinite sequence of successively smaller eddies extending down into the corner. For this wedge, of total angle 28.5 , each eddy is 100 times weaker than its neighbor above. The third eddy is al ways so weak that it is not certain that anyone has ever observed it. Taneda 1979, J. Phys. Soc. Jpn., 46,1935-1942. 13. Streamlines around a semicircular arc. At this Reynolds number of 0.031 the streamline pattern is not perceptibly altered by reversing the direction of flow. The centers of the pair of eddies in the cavity are separated by 0.52 diameter, in good agreement wit h a solution of the Stokes approximation. Aluminum powder dispersed in glycerine is illuminated by a slit of light. Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942. 15.Creeping flow past two circles in tandem. The gap is one diameter, and The Reynolds number is 0.01. Streamlines are shown by aluminum dust in glycerine. The interaction prod uces separation at any speed, whereas flow past an isolated circular cylinder separates only above a Reynolds number of 5. Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942. 18. Creeping flow past two spheres in tandem. With the same spacing and approximately the same Reynolds number as the circles opposite, spheres show no sign of separation. T his is consistent with the fact that separation on an isolated sphere appears only above a Reynolds number of 20, compared with 5 for a circle. Aluminum dust is illuminated in glycerine. Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942. 19. Creeping flow past closer spheres. At a spacing of 0.7 diameter, spheres in tandem show separation much li ke that between the circles spaced one diameter apart (see flow picture 15). The diameter is 1.6 cm, and the Reynolds number 0.013. Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942. 20. Creeping flow past tangent spheres. At the same Reynolds number of 0.013 The two pairs of vortex rings above have now merged into a single pair. Theory predicts,much as for the wedge in figure 10 , an infinite sequence of vortex rings nested toward the contact point. Taneda 1979, J. Phys. Soc. Jpn.,46, 1935-1942. For further information you can contact Robert S. Brodkey at (614) 292-2609; brodkey.1@osu.edu

Selection of the Fluent Project (continued) 16. Creeping flow past two circles side-by-side. The Reynolds number is 0.01, and the gap between the cylinders is 0.2 of their diameter. Aluminum dust in glycerine shows that there is no-apparent separation. Taneda 1979, J. Phys. Soc. Jpn.,46, 1935-1942. 17. Circle in slow linear shear near a plate. The cylinder is 0.1 diameter from the plate,or 0.2 diameter from its hydrodynamic image, which is actual ly visible as an optical image. The Reynolds number is 0.011 based on the shear rate.Large recirculating eddies form because the glycerine must stick to the plate, in contrast to the photograph above, where it flows along the symmetry plane. Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942. 38. Laminar separation from a curved wall. Air bubbles i n water show the separation of a laminar boundary layer whose Reynolds number is 20,000 based on distance from the leading edge (not shown). Because it is free of bubbles, the boundary layer appears as a thin dark line at the left. It separates tangentially near the start of the convex surface, remaining laminar for the distance to which the dark line persists, and then becomes unstable and turbulent. ONERA photograph, Werlé 1974, Le Tunnel Hydrodynamique au Servicede la Recherche Ae rospatiale, Publ. No. 156, ONERA, France. 39. Turbulent separation over a rectangular block on a plate. The step height is large compared with the thickness of the oncoming laminar boundary layer. The flow is effectively plane, so that the recirculating region ahead of the step is closed, whereas in the corresponding three-dimensional flow it is op en and drains around the sides,ONERA photograph, Werlé 1974, Le Tunnel Hydrodynamiqueau Service de la Recherche Aerospatiale, Publ. No. 156, ONERA, France. 40. Circular cylinder at R=9.6. Here, the flow has clearly separated to form a pair of recirculating eddies. The cylinder is moving through a tank of water containing aluminum powder, and is illuminated by a sh eet of light below the free surface.Extrapolation of such experiments to unbounded flow suggests separation at R=4 or 5, whereas most numerical computations give R=5 to 7. Photograph by Sadatoshi Taneda. 41. Circular cylinder at R=13.1. The standing eddies become elongated in the flow directional the speed increases. Their length is found to increase linearly with Reynolds number until the flow becomes unstable above R=40. Taneda 1956a, J. Phys. Soc. Jpn., 11, 302-307. 42.Circular cylinder at R=26. The downstream distance to the cores of the eddies also increases linearly with Reynolds number. However, the lateral distance between the cores appears to grow more nearly as the square root. Photograph by Sadatoshi Taneda. 47. Circular cylinder at R=2000. At this Reynolds number one may properly speak of a boundary layer. It is laminar over the front, separates, and breaks up into a turbulent wake. The separation points, moving forward as the Reynolds number is increased, have now attained their upstream limit,ahead of maximum thickness. Visualization is by air bubbles in water. ONERA pho tograph, Werlé Gallon 1972, Aeronaut. Astronaut.,no. 34, 21-33. 48. Circular cylinder at R=10,000. At five times the speed of the photograph at the top of the page, the flow pattern is scarcely changed. The drag coefficient consequently remains almost constant in the range of Reynolds number spanned by these two photographs. It drop s later when the boundary layer becomes turbulent at separation. Photograph by Thomas Corke and Hassan Nagib. 51.Sphere at R=56.5. The sphere is falling steadily down the axis of a tube filled with oil, but here so large that the influence of the walls is negligible.Magnesium cuttings are illuminated by a sheet of light, which casts the shadow of the sphere. Archives de l'Académie de s Sciences de Paris, Payard Coutanceau 1974, C.R. Acad. Sci. Ser. B, 278, 369-372. 53. Sphere at R=118. The wake grows more slowly in axisymmetric than plane flow. These photographs have shown that the length of the recirculating region is proportional to the logarithm of the Reynolds number, whereas it gro ws linearly with Reynolds number for a cylinder. Aluminum dust shows the flow of water. Taneda 1956a, J. Phys. Soc. Jpn., 11, 302-307.