PROJECTILE WITH REDUCED BASE DRAG

Abstract: A projectile having a downstream extending sur­ face of revolution (306) which terminates as a blunt base (304) has a plurality of circumferentially spaced apart U-shaped, downstream extending troughs in its sur­ face. Each trough is essentially aligned with the di­ rection of the bulk fluid flow adjacent the surface (306) in the vicinity of the trough, and intersects the blunt. base (304) to form a trough outlet therein. The troughs are appropriately spaced apart, sized and configured to flow full over their entire length and to cause fluid to flow into the space immediately behind the blunt base (304), thereby reducing base drag on the projectile.

Description: The present invention relates to reducing base drag of projectiles adapted to travel through a fluid in an upstream direction. Drag is the result of skin friction and surface pressure variations induced by viscous effects, especially those due to separation bubbles or regions (i. e., low pressure wakes). Separation regions occur when two and three dimensional boundary layers depart from the surface of the body. Bluff or blunt bodies have shapes which tend to promote a rapidly increasing downstream pressure gradient in the streamline flow around it which can cause the bulk flow to break loose from the surface of the body. This is particularly true for projectiles having blunt end surfaces. The separation bubbles created behind these projectiles as they move through the air produce high base drag. A projectile as recited in the precharacterizing portion of claim 1 is disclosed in the "Journal of Spacecraft and Rockets", vol. 12, no. 12, December 1975, pages 727-732, in an article entitled "Improved Projectile Boattail" by Anders S. Platou, and in US-A-3,873,048 wherein it is stated that a conical projectile boattail has reduced drag compared to a cylindrical projectile boattail, but that especially the conical boattails generate large Magnus forces and moments at transonic velocities, which can adversely affect the dynamic stability of the projectile. The boattail is provided with flat surfaces to stabilize the projectile. Fin-like portions extending only over a portion of the flat surfaces can be provided between adjacent flat surfaces. As used in the specification and appended claims, "streamwise, two-dimensional boundary layer separation" means the breaking loose of the bulk fluid from the surface of a body, resulting in flow near the wall moving in a direction opposite the bulk fluid flow direction. It has been a constant goal of aerodynamicists to reduce the drag and improve lift and stall characteristics (if appropriate) on bodies disposed in a fluid moving relative thereto. A common way to avoid boundary layer separation on an airfoil (or other streamlined body) or to at least delay separation such that it occurs as far downstream along the surface of the airfoil as possible so as to minimize drag, is to reduce the pressure rise downstream such as by tailoring the surface contour along the length of the airfoil in the direction of bulk fluid flow. Another well known method for reducing the drag on airfoils is to create turbulence in the boundary layer so as to impart a greater average momentum of the boundary layer fluid, which carries it further downstream along the surface against an adverse pressure gradient, thereby delaying the separation point. For example, US-A-4,455,045 describes elongated, expanding channels in the flow surface. The channels have sharp, lengthwise edges. The boundary layer on the surface flows into the channels, and the channel edges create streamwise vortices below the level of the normal flow surface which energize the flow in the channel to maintain boundary layer attachment of the flow along the floor of the channel. Similarly, US-A-2,800,291 creates a plurality of adjacent streamwise extending channels in the flow surface. The channels continuously expand laterally from a narrow inlet to a wide outlet. A generally triangular ramp is formed between adjacent channels. US-A-2 800 291 explains that the boundary layer flow is split between the ramps and the channels. The flow within the channels spreads out and the boundary layer becomes thinner and remains attached to the surface longer. The ramp flow is diverted into the general flow. One application (Fig. 6 of US-A-2,800,291) is between the roof and rear window of an automobile to maintain the flow attached to the curved surface for a greater distance than normal. In US-A-1,773,280 increased lift without increased drag is created for an aircraft wing by placing a plurality of side-by-side chordwise extending ridges along the top of the wing from its leading to its trailing edge, the ridges having their highest point near the thickest portion of the wing. The ridges themselves are airfoil shaped when viewed from above, tapering to a point at the trailing edge of the wing. This concept does not take into account viscous induced boundary layer separation effects and therefore could not be expected to avoid separation at high lift conditions. US-A-3,588,005 uses chordwise extending ridges in the upper surface of an airfoil to delay the onset of separation by providing "channels of accelerated flow in the free stream flow direction to add energy to the boundary layer and maintain laminar flow in the region of normally adverse pressure gradient". The ridges protrude from the surface "to a height of the order of the boundary layer thickness". Cross flow components "are accelerated over the ridges and may reduce the likelihood of separation near the aft end...of the body by allowing the flow to 'corkscrew' smoothly off the aft end rather than encounter the abrupt adverse pressure gradient in the free stream direction caused by a blunted aft end". As with the ridges of US-A-1,773,280 discussed above, flow is also accelerated between the ridges which further helps maintain laminar flow over the airfoil surface. In US-A-3,741,285 and 3,578,264 separation is delayed by creating vortices using a series of crests or concave depressions which extend substantially transverse to the streamwise flow direction. The maximum height of a crest or depth of a depression is preferably less than the boundary layer thickness. In a paper titled "The Reduction of Drag by Corrugating Trailing Edges" by D. L. Whitehead, M. Kodz, and P. M. Hield published by Cambridge University, England in 1982, blunt base drag of a blade [having a 508 mm (20-inch) span, 508 mm (20-inch) chord length, a constant thickness of 38 mm (1.5 inches) and a blunt trailing edge] is reduced by forming the last 177 mm (seven inches) of its chordwise length into streamwise extending, alternating troughs and ridges (corrugations). The trailing edge and any upstream cross-section across the corrugations has the shape of a sine wave with an 203 mm (8.0 inch) wavelength. The thickness of the blade material is maintained constant over the length of each trough and ridge, although the trough depth or ridge height (i.e., wave amplitude) transitions from a maximum of 50 mm (2.0 inches) at the trailing edge to zero upstream. The total trough outlet area is more than 50% of the blunt base area. Figs. 21 - 23 show the blade described therein, with dimensions given in terms of a unit length "a". A reduction of base drag of about one-third was realized when compared with a reference blade without corrugation. It is explained that spanwise vortices which were shed alternately from the top and bottom rear edges of the non-corrugated reference blade were eliminated by the corrugations. In general, it is believed that the separation delaying devices of the prior art create significant drag in their own right, thereby negating some of the benefits they would otherwise provide. This sometimes limits their effectiveness. While many of the devices of the prior art have proved to be effective in reducing drag, further improvement is still desired, such as with respect to reducing base drag on blunt based projectiles. The object of the present invention is to provide a blunt ended projectile having a reduced size separation bubble downstream of a blunt end surface of the projectile to provide reduced base drag. According to the present invention, to achieve this, there is provided a projectile adapted to travel through a fluid in an upstream direction, said projectile having an external surface which is substantially a surface of revolution about an axis extending in the upstream direction, said projectile having a blunt, downstream facing end surface, said surface of revolution terminating at said end surface, a plurality of circumferentially spaced apart downstream extending troughs formed in said surface of revolution, each trough having zero depth at its upstream end and intersecting said end surface to form a trough outlet, and each of said troughs increasing in depth to a maximum depth at its outlet, characterized in that each trough is smoothly U-shaped in cross-section along its length and that the contour and dimensions of said troughs are selected to ensure that each trough flows full throughout its length and causes fluid to flow into the space immediately downstream of said blunt end surface to reduce base drag. The fluid flowing into the space immediately behind the blunt end surface reduces the size of the separation bubble which would otherwise be formed. In other words, the intensity of the low pressure wake formed immediately behind the blunt end surface is reduced. The blunt end surface may be either a downstream facing end surface formed by a rapidly increasing rate of curvature of a generally streamwise extending surface, or the downstream facing end surface at which a streamwise extending surface terminates abruptly, such as when the end surface is essentially perpendicular to the streamwise surface. The troughs must be contoured and sloped such that they flow full (i. e., no streamwise, two-dimensional boundary layer separation occurs within the troughs). Thus, the troughs must extend from a point upstream of where boundary layer separation would normally occur. Due to the U-shaped smoothly curved troughs no sharp angles are formed where trough sidewall surfaces meet the trough floor to minimize losses. Most preferably the troughs form a smoothly undulating surface which is wave-shaped in cross section perpendicular to the downstream direction. In EP-A-0 244 344 there is described an airfoil trailing edge region with streamwise troughs and ridges formed therein defining a wave-like, thin trailing edge. The troughs in one surface define the ridges in the opposing surface. The troughs and the ridges help delay or prevent the catastrophic effects of two-dimensional boundary layer separation on the airfoil suction surface, by providing three-dimensional relief for the low momentum boundary layer flow. The present invention, however, is directed to reducing the base drag created behind a blunt based projectile. One distinction between EP-A-0 244 344 and the present invention is that in the present invention the troughs need only be formed in one surface. Additionally, the troughs can have a significant effect when the blunt end surface area is much greater than the sum of the trough outlet areas, even twenty times greater or more. It is believed that the fluid leaves the troughs with a direction of momentum that carries it over the blunt end surface into the normally stagnant region behind the blunt end surface (i.e., a downwash is created). Additionally, it is believed that each trough generates a single, large-scale axial vortex from each side wall surface at the trough outlet. (By "large-scale" it is meant the vortices have a diameter about the size of the overall trough depth.) These two vortices rotate in opposite directions and create a flow field which tends to cause fluid from the trough and also from the nearby bulk fluid to move into the region behind the blunt surface. The net effect of this phenomenon either alone or coupled with the downwash effect, is to reduce the size of the stagnation bubble normally formed behind a blunt end surface, thereby reducing base drag. Additionally, in cases where the shedding of spanwise vortices is an additional contributor to base drag, it is believed that the troughs suppress such shedding. Adjacent troughs should be spaced far enough apart such that the counter-rotating axial vortices tending to be generated from the sidewall surfaces of adjacent troughs have enough space to become fully developed. If the troughs are too close together the counter-rotating vortices will interfere with each other or cancel each other out (claim 3). It is preferred that the fluid exiting from each trough have a minimum lateral component of velocity to minimize secondary flow losses. For this reason the trough sidewalls, for a significant distance upstream of the outlet, are preferably parallel to the direction of bulk fluid flow adjacent the surface in the vicinity of the trough (claims 6 and 8). Further, it is preferred that the trough sidewalls at the outlet be steep, most preferably substantially perpendicular to the streamwise extending surface. This is believed to increase the intensity of the vortex generated by the sidewall. The word "steep" as used herein and in the claims means that, in cross section perpendicular to the direction of trough length, lines tangent to the steepest point on each sidewall intersect to form an included angle of no more than about 120° (claim 5). Other advantageous features of the projectile are recited in additional dependent claims. The foregoing and other features and advantages of the present invention will become more apparent in the light of the following detailed description of preferred embodiments thereof as illustrated in the accompanying drawing, wherein: Fig. 1 illustrates the fluid dynamics associated with a blunt based body moving relative to a fluid stream. Fig. 2 is a perspective view of a blunt based article having troughs in oppositely facing surfaces thereof. Fig. 3 is a sectional view taken along the line 3 - 3 of Fig. 2. Fig. 4 is a view taken generally in the direction of the line 4 - 4 of Fig. 3. Fig. 5 is a sectional view taken generally in the direction of the line 5 - 5 of Fig. 4. Fig. 6 is an enlarged view of the area designated Y in Fig. 4. Fig. 7 is a partial perspective view of a blunt ended body having a downstream facing end surface formed by a rapidly increasing rate of curvature of a generally streamwise extending surface provided with troughs. Fig. 8 is a sectional view taken along the line 8 - 8 of Fig. 7. Fig. 9 is an end view taken in the direction of the line 9 - 9 of Fig. 8. Fig. 10 is a side elevation view of a projectile incorporating the troughs of the present invention. Fig. 11 is an end view of the projectile of Fig. 10 taken generally in the direction of the line 11 - 11 of Fig. 10. Fig. 12 is a perspective view of a "blade" in accordance with the prior art. Fig. 13 is a cross sectional view taken along the line 13 - 13 of prior art Fig. 12. Fig. 14 is a cross sectional view taken along the line 14 - 14 of prior art Fig. 12. Fig. 1 illustrates what occurs when fluid flows over the surface of a body which terminates at a blunt downstream end. In this figure the body is represented by the reference numeral 10, and includes upper and lower smooth, flat surfaces 12, 14, respectively, over which fluid is flowing. The wide arrows 16 represent the downstream direction, while the lines 18 represent streamlines of the bulk fluid flowing adjacent the surfaces 12, 14. As is well known in the art, although the fluid may stay attached to the smooth surfaces 12, 14 under a wide range of conditions, it cannot turn the corner when it reaches the blunt end surface 20, resulting in separation at or near the upper and lower edges 22, 24. The flow off the upper and lower surfaces rejoin each other at some point downstream of the surface 20. Upstream of that point there is a low pressure region 21 (or "separation bubble") between the upper and lower streamlines immediately downstream of the blunt end surface 20. If the fluid flow is the result of the body 10 moving through the fluid in an upstream direction, this low pressure stagnation region results in a force in the downstream direction which resists or is opposite to any force attempting to move the body in the upstream direction. This force is referred to as the base drag, and can be substantial. The present invention is concerned with base drag reduction while introducing minimal other losses which counteract the benefits of reduced base drag. The general concept of the invention will now described with reference to Figs. 2 - 6. As shown in Fig. 2, an article incorporating the troughs of the present invention is generally represented by the numeral 30. The article has an upper surface 32 and a lower surface 34. It is assumed that the article is moving through a fluid, such as air, in an upstream direction generally represented by the arrow 36. The downstream direction is represented by the arrow 38. A plurality of downstream extending troughs 40 are formed in the upper surface 32; and a plurality of downstream extending troughs 42 are formed in the lower surface 34. The troughs are generally U-shaped in cross section taken perpendicular to the downstream direction. Each trough extends from its respective inlet 43 to a blunt end surface 44 which joins the upper and lower surfaces 32, 34 and faces substantially downstream. The troughs must be contoured, sized and shaped to flow full over their entire length such that streamwise boundary layer separation does not occur within the troughs. In this regard, the fluid flowing along the surfaces 32, 34 must be attached to such surfaces (i.e., no streamwise boundary layer separation) as it enters the trough inlets. The trough outlets 45 in the end surface 44 have an amplitude or depth A (Fig. 6). They have zero depth at their upstream ends and blend smoothly into their respective upper and lower surfaces at their upstream ends and along their length. In this preferred embodiment each trough increases in depth from its upstream end to its outlet. However, this is not required. For example, the depth could reach a maximum upstream of the trough outlet and then remain constant to the outlet. In this exemplary embodiment the troughs are smoothly U-shaped along their length in cross section perpendicular to the downstream direction and define a smoothly undulating surface which is wave shaped in cross section perpendicular to the downstream direction. Each trough has a pair of facing sidewall surfaces 46 which terminate as side edges 48 of the trough outlet 45. Preferably the sidewall surfaces 46 are substantially parallel to the direction of bulk fluid flow over the surface in which they are disposed over a substantial continuous portion of the length of the trough, which includes the trough outlet. The parallel nature of the sidewall surfaces 48 is best shown in Fig. 5. It is undesirable that the sidewalls diverge since it contributes to streamwise separation within the troughs and introduces lateral velocity components in the fluid leaving the trough, which create undesirable secondary flow losses. It is believed that a couple of different fluid dynamic mechanisms are responsible for the reduced base drag resulting from the troughs of the present invention, although these mechanisms are not fully understood. It is felt, for example, that there is a bulk motion of the fluid leaving the troughs which motion is into the space immediately behind and adjacent the blunt end surface as if it were, to some extent, remaining attached to the blunt end surface of the article after it exits the troughs. Second, it is believed that each trough generates a pair of large-scale axial vortices, the axial direction being the downstream direction. Each vortex is generated off of a respective one of the two trough side edges 48. The vortices of each pair rotate in opposite directions. These vortices create a flow field which tends to cause fluid from the trough and from the nearby bulk fluid to move into the region behind and adjacent the blunt surface. In order that the vortex generated off of the side edge 48 of one outlet is not interfered with (i.e., cancelled out) by a counterrotating vortex generated off the side edge of the next adjacent trough it is necessary that the side edges of adjacent troughs be spaced apart by a sufficient distance. Thus, it is necessary that a portion of the area of the blunt end surface 44 extend laterally from the side edge 48 of each trough outlet to the side edge 48 of an adjacent trough outlet over the full length of each of the side edges. This area of the blunt end surface is represented by the cross hatched area 50 of Fig. 6 disposed between the trough side edges designated by the reference numerals 48A and 48B. In general, the downstream projection of the area 50 between the side edges of adjacent troughs should be at least about one quarter (1/4) of the downstream projected outlet area of a trough. It is further believed that best results are obtained when the side wall surfaces 48 at the outlet are steep. Preferably, in a cross section perpendicular to the downstream direction, which is the direction of trough length, lines 52 tangent to the steepest points along the side edges 48 should form an included angle C (Fig. 6) of no greater than about 120°. The closer angle C is to zero degrees (0°), the better. The troughs should be large enough in downstream projected cross-sectional area at their outlets, relative to the total downstream projected area of the blunt end surface to have a worthwhile impact on the base drag. For some applications a total trough outlet area which is only a few percent of the total blunt base area may produce a measureable reduction in base drag. For most applications a trough outlet area no more than 30% of the total blunt base area would be used due to practical considerations. It is also believed that the troughs should not be too narrow relative to their depth, otherwise appropriate flow patterns within the trough will not develop and the desired base drag reduction will not occur. With reference to Fig. 6, the trough width at its outlet is considered to be the peak to peak wave length P, and the trough depth at the outlet is considered to be the peak to peak wave amplitude A. The ratio P/A should be greater than about 0.25 and preferably at least 0.5. Additionally, the ratio P/A should be less than about 4.0. The results will also not be very effective if the trough is too long relative to its outlet depth (amplitude) since the appropriate flow fields generated within the trough will dampen out before reaching the outlet. It is believed that the ratio of trough length to outlet amplitude should be no greater than about 12 to 1.0. Although in the embodiment of Figs. 2 - 6 the end surface 44 is flat and perpendicular to the downstream direction, the invention may be applied to blunt ends of other shapes (see Figs. 7 - 9). Another embodiment of the present invention is illustrated in Figs. 7 - 9. Note that there are troughs 200 only in one surface. Also, the troughs 200 are semicircular in cross section at all points along their length and form relatively sharp edges 202 with the smooth, flat surface 204 in which they are disposed. Although sharp edges are not preferred since they induce losses, it is believed that a significant net benefit may still be obtained with such a configuration. As best seen in Fig. 8, the bottom surface 206 of each trough blends smoothly with the surface 204 at the upstream end 205 of the trough and has its outlet 210 in the curved blunt end surface 209. The outlets 210 are located upstream of where boundary layer separation from the surface 204 would normally occur (i.e., without troughs). As discussed with respect to the embodiment of Figs. 2 - 6, the downstream projection of the blunt surface area portion 211 (shaded) disposed laterally between each pair of adjacent troughs should have an area which is at least one quarter (1/4) of the downstream projected area of a trough outlet. A projectile, such as the ballistic shell 300, having troughs of the present invention to reduce base drag, is shown in Figs. 10 and 11. Projectiles of this type typically rotate in flight about their longitudinal axis, such as the axis 302 of the shell 300, for purposes of aerodynamic stability. The direction of rotation is represented by the arrow R. The shell 300 has an axial velocity V represented by the vector V ₁. The vector V ₂, which is tangent to the shell surface 306, represents the rotational velocity of the shell external surface 306 at the shell downstream end 304. Each trough 305 extends generally parallel to the direction of the sum of the vectors V ₁ and V ₂. This trough orientation is required in order that the fluid flows into the troughs in a direction substantially parallel to the trough length. Although troughs 305 of generally semicircular cross section (like those described with respect to Figs. 7 - 9) are shown in this embodiment, the troughs could also be configured as shown in the embodiment of Figs. 4 - 6 (i.e., U-shaped troughs formed by a smoothly undulating surface, wave-shaped in cross section perpendicular to the downstream direction).

Claims: Projectile adapted to travel through a fluid in an upstream direction, said projectile (300) having an external surface (306) which is substantially a surface of revolution about an axis (302) extending in the upstream direction, said projectile having a blunt, downstream facing end surface (304), said surface of revolution terminating at said end surface (304), a plurality of circumferentially spaced apart downstream extending troughs (305) formed in said surface of revolution, each trough (305) having zero depth at its upstream end and intersecting said end surface (304) to form a trough outlet, and each of said troughs increasing in depth to a maximum depth at its outlet, characterized in that each trough (305) is smoothly U-shaped in cross-section along its length and that the contour and dimensions of said troughs (305) are selected to ensure that each trough (305) flows full throughout its length and causes fluid to flow into the space immediately downstream of said blunt end surface (304) to reduce base drag. Projectile according to claim 1, characterized in that the projectile (300) is adapted to simultaneously rotate about its axis (302) when travelling upstream, and that each of said troughs (305) extends downstream substantially parallel to the direction of a vector which is the sum of a vector ( V ₁) representing the axial velocity of the projectile (300) and a vector ( V ₂) representing the rotational velocity of said external surface (306) at said trough outlet. Projectile according to claim 1, characterized in that each of said troughs (300) includes a pair of sidewall surfaces which face each other and which intersect said end surface (304) to form side edges of said trough outlets, and the downstream projected area of the portion of the blunt end surface (304) disposed circumferentially between said side edges of each pair of adjacent trough outlets is at least one quarter (1/4) of the downstream projected area of one of said adjacent trough outlets. Projectile according to claim 3, characterized in that said plurality of troughs define a smoothly undulating surface which is wave-shaped in cross section perpendicular to the axial direction. Projectile according to claim 4, characterized in that in cross section perpendicular to the axial direction, lines tangent to each side wall of said pair of trough side walls at their steepest point at said trough outlet form an included angle of no more than 120°. Projectile according to claim 1, characterized in that each of said troughs (305) includes a pair of sidewall surfaces which terminate as side edges at said trough outlet, said sidewall surfaces being substantially parallel to the direction of bulk fluid flow over the external surface (306), in which said trough (305) is disposed, along a substantially continuous portion of the length of said trough (305), including said trough outlet. Projectile according to claim 4, characterized in that each of said troughs (305) includes a pair of sidewall surfaces which terminate as side edges at said trough outlet, said sidewall surfaces being substantially parallel to each other at said trough outlet. Projectile according to claim 7, characterized in that said sidewall surfaces are substantially parallel to the direction of bulk fluid flow over the external surface (306), in which said trough (305) is disposed, along a substantial continuous portion of the length of said trough, including said trough outlet.

Inventors: PATERSON, ROBERT W., PRESZ, WALTER MICHAEL JR., WERLE, MICHAEL J.
Applicants: UNITED TECHNOLOGIES CORPORATION
Application year: 1987
Main classification: F42B10
IPC codes: F42B10, B62D35, F04D29, B64C21