BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain aspects of the instant invention and together with the description, serve to explain, without limitation, the principles of the invention. Like reference characters used therein indicate like parts throughout the several drawings.
FIG. 1 shows a schematic flow model for a drag enhancing d-type surface roughness, in which downwash is shown between the counter-rotating vertex pair and upwash, that would occur on either side, is shown on the front region of the surface roughness.
FIG. 2 shows a schematic flow model for a drag reducing d-type surface roughness, in which outflow, as depicted by the arrows, from the upstream cavity to the adjacent neighboring downstream cavity occurs through the valleys in the saw tooth geometry of the formed ridges.
FIG. 3 shows a schematic front elevational view of one embodiment of a ridge of an array of roughness elements of the present invention. In one aspect, for drag reduction, the elements can be aligned such that the peaks of the roughness elements of each adjacent ridge can be staggered and can be spaced at about half the peak height of the roughness element. In this view, flow will encounter the ridge by moving into the figure. In one exemplary aspect, the spacing between the peaks of the adjoined roughness elements is on the order of about 30 viscous length scales at close to maximum velocity for the fluid passing over the wall surface.
FIG. 4 is a side elevational schematic view of the exemplary micro-array of roughness elements shown in FIG. 3, showing the tops of the roughness elements of FIG. 3 and showing the formation of counter-rotating streamwise vortices due to the staggered alignment of adjacent rows of the roughness elements in the drag enhancing case. The flow of fluid is directed into the figure.
FIG. 5 is a top elevational schematic view of exemplary vertex structures that form within the transversely extending cavities of an exemplary micro-array of roughness elements of FIG. 3 of the present invention, showing fluid flow moving from the bottom to the top of the figure and showing dark short lines correspond to the peaks of the roughness element in FIG. 3.
FIG. 6 is a perspective view of one embodiment of a roughness element of a micro-array of the present invention, showing riblets formed on a front, upstream surface of the roughness element.
FIG. 7 is a side elevational view of the roughness element of FIG. 6.
FIG. 8 is a top elevational view of the roughness element of FIG. 6.
FIG. 9 is front, upstream elevational view of a plurality of adjoined roughness elements of FIG. 6 that form a ridge, and showing a plurality of channels formed between portions of the respective bases and the bottom portions of the peripheral edges of the respective adjoined roughness elements.
FIG. 10 is a perspective view of a portion of a micro-array of the present invention, showing a plurality of staggered rows of the formed ridges of adjoined roughness element of FIG. 8, and showing the approximate spacing between the rows of ridges to be approximately half the height of a roughness element.
FIG. 11 is a schematic diagram of cavity flow of representative fluid flow between the tops of roughness elements of FIG. 6 and across one “valley,” the roughness elements being positioned in adjacent ridges or rows. In this diagram, fluid flow over the surface is from left to right.
FIG. 12 is a top elevational schematic view of exemplary vertex structures that form on an exemplary micro-array of roughness elements of FIG. 6 of the present invention, showing fluid flow moving from the left to the right of the figure. The orange vortices represent the outer vortices shown in FIG. 11 and may have small counter-rotating vortices superimposed on the outer-vortices that make the flow field consistent to its neighboring vortices. In the exemplified aspect with three riblets on the front face of the roughness element, two counter-rotating vortices would form with an upwelling between them and a downwash to the flow at the sides. These vortices are also known as Taylor-Gortler vortices. The blue vortex tubes represent the vortex cores to the vortex array that link all the individual outer cavity vortices together.
FIG. 13 is a graphical illustration of a two-dimensional computational fluid dynamics (CFD) numerical calculation through a line of symmetry over the peaks and valleys; of the roughness elements in drag reduction mode. The cavity Re for this calculation is 2000, and the formation of stable cavity vortices is observed.
FIG. 14 is a graphical illustration of the velocity profiles in the boundary layer forming over the surface in FIG. 13 above the third and eighth cavities. These profiles are compared to that of a flat plate boundary layer, known as the Blasius solution. One can observe the non-zero velocity over the surface of the cavities due to the embedded cavity vortex. One skilled in the art will appreciate that one can obtain the momentum thickness of the two boundary layers, which is proportional to the total drag coefficient on the plate from the leading edge to that corresponding downstream distance, by integrating these velocity profiles. In one example, the momentum thickness over the third cavity is 16.09% of the momentum thickness of the flat plate Blasius solution, while at the eighth cavity the percentage of the momentum thickness of the surface with cavities with respect to the flat plate solution is 23.91%. Thus, at the third and eighth cavity, the drag coefficient is reduced by 84% and 76% correspondingly.
Patent Application
20070194178
