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104. BACKGROUND THEORY 4.1 Introduction This section will begin by explaining the theory of windmill damage due to high-speed, low-altitude aircraft, which encompasses many theoretical issues. Most obvious is the nature of the vortex created by an aircraft, particularly the B-1B bomber, during high-speed, low-altitude flight. Due to the high degree of sweep of the B-1B’s wings, two types of vortices actually have to be addressed. Another important issue is the generation of supersonic flow regions created by the B-1B bomber at transonic Mach numbers. After that, the theory behind the vortex windmill interaction is discussed. Once the physics of the problem are understood, methods of simulating the problem can be investigated. Three vortex generation methods are introduced, followed by a method of simulating the vortex loading in this problem. The theory section concludes with an explanation of the measurements that need to be collected in any experiment and a brief discussion of vortex scaling. 4.2 Wingtip Vortices Early in the history of powered flight, the presence of wingtip vortices was discovered and explained. The vortex theory of an airfoil’s lift was developed in the early 1900’s and most notably by Prandtl in 1918 [3]. The specific equations and their derivations are not particularly relevant to this semester’s project, but the details can be found in a number of different sources [3]. The general theory, however, is very relevant. A wing can be modeled as a collection of line vortices lying across the span of the wing. When a line vortex hits either the edge of the wing, or another line vortex, it turns and11propagates downstream. The vortices from each side of the wing merge and create a single pair of wingtip vortices slightly downstream of the trailing edge as seen in figure 4.1. Prandtl’s lifting line theory is an excellent approximation for conventional subsonic aircraft, but the theory involves some assumptions. One is a low sweep angle and another is that the air is incompressible. Neither assumption is true for a B-1B bomber flying at a speed of approximately Mach 0.7 – 0.9. At those transonic Mach numbers, the bomber’s wings will be swept back at an angle of about 67º and the air is certainly not incompressible [3]. Modifications to the Prandtl theory have somewhat accounted for these problems. The Prandtl theory can predict the presence and strength of wingtip vortices to an extent, but it is not capable of fully explaining the wake of the B-1B bomber [4]. Figure 4.1: Diagram of a pair of wingtip vortices shed off a conventional wing [2] 4.3 Leading Edge Vortices One of the clearest examples of a leading edge vortex is air flow over a delta wing. An excellent diagram of this type of vortex can be seen in figure 4.2(a) [3]. In addition, a12photograph taken here at UT using smoke-wire flow visualization shows an excellent example of a leading edge vortex figure 4.2(b) [5]. (a) (b) Figure 4.2: (a) Schematic diagram of the leading edge vortices generated on top of a delta wing [3]. (b) Photograph of the leading edge vortex of a cropped delta wing [5]. The basic theory behind the leading edge vortex is that the pressure on the upper side of the plate is much lower than that on the lower side of the plate, causing the air to tend to move from the bottom to the top. However, once the flow rolls up from the bottom, it cannot stay attached to the plate, so it separates. The air is still attracted to the low pressure on the top of the plate, so it reattaches, creating a circular vortex motion which is carried downstream by the flow, as shown in figure 4.2(b). Leading edge strakes, used to increase lift, can also create leading edge vortices as seen in figure 4.3(a) [6]. Similarly, the highly swept wings of the B-1B bomber generate significant leading edge vortices. In fact, at high transonic Mach numbers, the B-1B bomber is capable of generating two strong leading edge vortices, shown in figure 4.3(b) [6].13 (a) (b) Figure 4.3: (a) Vortices caused by the leading edge strakes of an F-16 [6]. (b) Diagram of the leading edge vortices on a B-1 bomber at high transonic speeds [6]. Another issue related to the generation of leading edge vortices is vortex interaction. Because of the presence of wingtip vortices and possibly two leading edge vortices, vortex interaction could drastically change the character of the vortex or vortices shed from the B-1B bomber. In a declaration written in defense of the US Air Force regarding the issue of vortex-windmill interaction, Dr. Skujins states that the leading edge vortex would actually increase the rate at which the vortex dissipated [7]. Unfortunately, he gives no reference to support that assertion. In contrast, a reference found by this group seems to contradict his statement, showing that vortices turning in the same direction will tend to move closer to one another and possibly even merge, as shown in figure 4.4 [8]. Although figure 4.4 only shows the interaction of wingtip vortices, the report goes on to state that leading edge vortices behave similarly.14 Figure 4.4: Diagram of the merging of two wingtip vortices [8]. Despite this possible inconsistency, the numbers that were obtained by Dr. Skujins in the Air Force Report were verified by Dr. Stearman and are being used to characterize the vortex. The analysis appears to be a good one, but it was made in 1979, before the B-1B was even built. A better analysis of the vortex would be preferable, but not absolutely necessary. 4.4 Supersonic Damage Although the B-1B bomber is incapable of supersonic speeds at the altitudes being investigated in this project, it can fly at rather high transonic speeds [7]. Figure 4.5 shows how supersonic flow disturbances, even at transonic airspeeds, can have very significant effects far away from the aircraft. In figure 4.5 the F-14 fighter is creating15winds of over 50 mph on the ocean’s surface at an altitude of about 100 ft, which is an altitude of about three wingspans (38 ft. span) [2]. Figure 4.5: Supersonic flow disturbances around an F-14A over the ocean [1]. Similar supersonic flow regions have been seen on the B-1A bomber, which is very similar to the B-1B.


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UT ASE 463Q - BACKGROUND THEORY

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