DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A Trapped Bubble Array

[0017] Described in this section is the Trapped Bubble Array (TBA) concept with numerical and experimental results to date. It should be understood, however, that the principals of the TBA concept may be extended to other applications.

[0018] Consider the following gedanken experiment. We submerge a horizontal flat plate in a water channel and measure the drag on it. We may use a mechanical force balance or measure the velocity profile and perform a momentum balance computation. The flow develops a simple growing boundary layer from the leading edge.

[0019] Now suppose we drill a hole up into the bottom of the plate (but not all the way through) and, using a syringe, inject enough air into the hole so that the bubble capping the hole is virtually flush with the flat plate surface. Will the drag on the plate with the hole be larger or smaller or the same as the drag on the smooth plate? It is suggested here that since the air/water interface is nearly free of shear stress in the water, the net drag will be lower. That being the case, one can dramatically reduce the viscous drag on a surface by boring many such holes and filling each with an air bubble.

Could the Drag Reduction be Large?

[0020] Suppose the flow were slow and the hole area were really large, nearly the size of the plate itself. Moreover, suppose the hole was very deep into the plate so even though there is some air circulation in the (huge) bubble cavity, it would create negligible drag on the water surface. Since the viscous drag on the plate would be roughly proportional to the SOLID plate area exposed to the water flow (raised to some suitable exponent), the drag would be much reduced.

[0021] Of course, having a huge hole in the bottom of, say, a ship to reduce drag is not suitable. But the argument does serve to illustrate that at one extreme, drag reduction should be appreciable. Presumably small holes would be necessary under a high speed boundary layer since for large bubbles the bubble interface will become unstable and splash around. A small bubble, however, should be held stiffly in place by surface tension.

[0022] Moreover, since the bubbles are held in place at their perimeters by surface tension, the bubble radius of curvature is large. With a large radius of curvature, the internal pressure should be small and gas loss due to diffusion consequently weak.

[0023] The inventor has completed some preliminary computational studies which suggest that large drag reductions are possible. Turbulent channel flow was directly simulated on a computer. One channel wall is an ordinary flat no-slip surface while the opposing no-slip wall has a circular hole over which a shear-free boundary condition is applied. Since the flow is doubly periodic in the streamwise and cross-flow directions, the simulation can be used to directly compare the flow over a periodic array of shear-free bubble caps against that over a simple flat surface.

[0024] FIG. 1 shows an instantaneous realization, denoted generally as 10 , of the streamwise velocity, indicated in table 20 , just above a bubble 12 in a bubble array. Ordinary low speed streaks are seen beside the bubble 12 . Directly over the bubble 12 the flow rapidly accelerates from rest at the (left) upstream edge to a maximum value just upstream of the trailing edge. Upon re-attaching to the solid surface 14 , the flow again comes to rest. That flow deceleration upon reattachment leads to large local viscous drag. Over all, however, this particular simulation produced a drag reduction of about 25% on the bubble wall 12 as compared to the opposing flat wall 14 .

[0025] Preliminary experiments in a low speed water channel have been done of laminar flow over a 0.75 inch bubble in a flat plate. The air flow within the bubble was visualized with smoke and found to exhibit weak three-dimensional circulation patterns. Flow of the water over the bubble surface was visualized with dye injected into the water. It appeared that the dye did in fact move more swiftly over the bubble than over the surrounding flat wall. This suggests that there was less drag over the bubble. Finally, the water velocity profile was examined in great detail over the bubble using a laser Doppler anemometer capable of high spatial resolution.

[0026] There was clear evidence of velocity slip over the bubble surface as initially suggested by the earlier numerical simulations.

[0027] Further experiments are presently underway to actually measure the viscous drag on a flat plate having hundreds of bubbles. In a different experiment a 15″×22″ Lucite plate with an array of 210 half inch holes on the lower surface is suspended from a trapeze and the plate deflection is measured to determine the net drag. The LDA is also used to obtain the drag via a momentum balance. In the best case, perhaps an 11% drag reduction compared to the plate with the holes covered was obtained. 11% was also the area of the exposed bubble surface. However, there were too many experimental uncertainties and a better machine 15″×40″ plate with a perforated stainless steel insert having O (10 ⁴ ) ⅛″ bubbles on the lower side is just now being tested. The trapeze can again by used or, by taping over one side of the bubble surface, the LDA can be used to obtain a side-by-side direct comparison of the boundary layers and wakes. Very preliminary results indicate a 30% drag reduction but that number may need to be revised over the next few weeks.

But would the Generic Concept really Produce Lower Drag? What could Prevent a Drag Reduction?

[0028] First, the bubble surface might not be sufficiently flush so that there develops net pressure drag on the bubble. Second, since the bubble surface will be moving, it will induce an internal flow in the air in the hole. This internal flow will be viscously damped and that will lead to an interface which is not shear free. Third, for small bubbles, surface contamination may accumulate and lead to a non-shear-free interface. Fourth, even if the bubbles create an effective shear-free interface, a periodic array of shear-free spots on the surface may alter the turbulent boundary layer in such a way as to hugely increase the drag on the remaining exposed metal structure. These objections all are worth investigating.

Can we Obtain a Quantitative Idea of how much Drag Reduction may be Possible?

[0029] With reference to FIGS. 2 A- 2 F, a simple experiment with holes in a solid (Lucite) block 50 demonstrates that a small bubble 52 can be suitably made to lie nearly flush with a flat surface 54 bounding a flow. The inventor has examined a few different cavity shapes. A cavity depth, “h”, about equal to or somewhat greater than the bubble diameter, “d”, is believed to be optimal as shown in FIG. 2 . If h is too small there will be appreciable gas drag on the bubble film. Cavities deeper than d do not provide much more benefit in terms of lower gas drag but do weaken the substrate. According to one known class of embodiments, the cavity depth h is 40% as large as the cavity diameter d. If the cavity width, w, is much greater than d, the bubbles must be far apart and more solid material is exposed to the flow. More exposed solid reduces the overall drag benefit which comes from having a large part of the surface covered by bubbles. Hence, d˜I˜w is expected to produce the lowest drag surface.

[0030] FIGS. 2 a and 2 b indicate two configurations of round, flat-bottomed cavities 60 holding a bubble when there is no flow: the bubbles 52 , 64 are simply shaped and convex downward as one would expect. Note that the figures are drawn roughly to the scale of the experiment performed. If the lucite sample is turned upside down so the bubble is hydrostatically unstable, the large bubble quickly escapes from its cavity while the small bubble remains in place, held there by surface tension at the cavity lip.

[0031] FIGS. 3 and 4 are photographs of a TBA in an aluminum plate, denoted generally as 100 , in a similar configuration illustrating bubble stability and shape. If the lucite sample is held bubble-side down as shown in FIG. 2 c, and there is a flow below the surface of ˜3 ft/s, little is seen to happen to a small bubble. The large bubble becomes distinctly humped. This hump likely results from the speeding up of the flow over the slip bubble interface and the resulting relative pressure drop. There is no hump obvious over the smaller cavity bubble but perhaps it requires closer examination.

[0032] Small holes are able to retain their bubbles quite well. A clean sharp cavity lip is important and the preferred cavity types seen in FIGS. 2 d and 2 e seem able to hold the bubbles better than the square-sided cavities of FIGS. 2 a, 2 b, and 2 c. This improvement in the preferred type may occur since, for the bubble to retreat slightly into the FIG. 2 d or FIG. 2 e cavity, its perimeter must increase dramatically and surface tension inhibits this.

[0033] Small holes of these configurations retain their bubbles whether the sample is held inverted or even under separated turbulent flow. Moreover, many smaller bubbles are to be preferred over fewer large ones because large bubbles are more subject to shear- and fluctuation-induced oscillation and instability. Surface tension holds smaller bubbles rigid. Smaller holes of a size ˜1 mm will likely be necessary under the most turbulent, high-shear, applications. Such small bubbles are better retained under separated flows as well.

[0034] It is anticipated, however, that the TBA technique will be most profitably applied on the forward portion of a submerged body where the boundary layers are thin and the shear stress greatest. The TBA concept is expected to be most useful for reducing friction drag and not to greatly effect the wave drag and form drag which, together, are usually less than the friction drag on fast clean surface ships. Hence, if the TBA reduces the friction drag by half, the total drag on the submerged portion of a surface ship will drop by ˜25% while on a submarine or torpedo the drag would drop ˜50%. Moreover, if the TBA concept reduces friction losses in the hull boundary layer, the flow near the solid surface will have greater momentum and an aft-mounted propellor working in the hull slipstream will become more efficient.

[0035] Regardless of cavity or hole size, the bubbles will eventually be lost if for no other reason than gas diffusion into the water. The bubbles must then be replaced. The inventor has tested a concept using a metal or conductive metalized plastic film 70 with a hole 72 centered over the cavity 60 as shown in FIG. 2 f. Essentially, a voltage is applied to the conductive metal layer 80 so that if any water enters the cavity 60 , it will be electrolyzed and the cavity gas pressure will rise until the bubble 52 is restored and the water pushed out past the opening 72 . Once the bubble interface returns to the cavity lip, no further power is used as there is no longer water in contact with the metal film 80 . The overall idea is to create a self-refilling bubble cavity having no moving parts (e.g., no valves or tubing in the supporting substrate).

[0036] Preliminary tests with painted aluminum surfaces show that electrolysis can clearly fill the cavity. Better control of the paint distribution about the lips of the cavity will likely be important to maintaining a low profile bubble shape. One way the TBA may be used is as a multi-layer flexible panel adhered to a vessel hull in regions of high shear. Such a panel would consist at least of a substrate having cavities and an outer perforated non-conductive film. The number of holes on a given panel may vary although it is contemplated that a range of numbers may be utilized from, for example, 10 to 100 to 10000 holes per square centimeter. The back of the film and/or the interiors of the cavities would be made conductive (metalized) and electrically energized to create the trapped bubbles. Otherwise some form of MEMS feedback control of the filling process may be desirable.

[0037] It may be that non-circular holes would be optimal in that they could be more closely packed than circles. Since each of these small holes could be isolated and held dynamically at a different internal pressure, the low-drag surface could be curved around the hull of a ship on which the mean and fluctuating surface pressures vary.

[0038] The device has dramatic advantages compared to previous concepts involving an air film held in the valleys of a ribbed surface with a continuous air feed at the upstream edge (U.S. Pat. No. 5,054,412). With the present invention, since each bubble cavity is self-contained, there is no need to continuously feed air into the cavity to replace gas swept away by the water flow. Additionally, since each discrete hole is small, surface tension is sufficient to retain the bubble cap even in the presence of strong shear. Finally, the discrete holes prevent the overlying air film from becoming unstable.

[0039] While the invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. It is intended that modifications and variations of the invention will be apparent to those of ordinary skill in the art and that such modifications and variations be part of the present invention.

[0040] For example, the technique of using gas bubbles held in small pits in a solid bounding a liquid flow may be of use in reducing the pumping power required to drive a liquid such as oil through a pipeline or to drive plastic through a forming die. Moreover, it may be suitable to form the pits simply by placing a perforated non-conductive layer simply over a conductive flat surface. Liquid thus entering the perforation pits would contact the underlying conductive bottom of the pit and be electrolysed. That is, it may not be critical exactly where in the cavity the conductor lies. All that would seem to matter would be that the electrolysis process produces fairly flat bubble surfaces and that the bubble, once suitably formed, prevents liquid contact with the electrode so that electrolysis stops and no further electrical power is consumed.