In transonic flow conditions, buffeting associated with finite-amplitude lift fluctuations can limit the operational envelope of an aircraft. For both airfoils and wings, these oscillations have been linked to global flow instabilities that arise from a Hopf bifurcation. We employ a combination of numerical simulations and global stability analysis to investigate the near-critical behaviour of the oscillatory buffet-onset instability on airfoils. The flow is governed by the unsteady Reynolds-averaged Navier-Stokes equations, with a basic state provided by a steady-state solution. In the weakly nonlinear formulation, the disturbance amplitude is described by the Landau equation. The linear growth rate can be determined from either the simulations or the stability analysis, and the Landau constant is derived from simulations resulting in finite-amplitude equilibrium states. The results show that the Landau constant is nearly independent of Mach number and angle of attack for a given airfoil. Using the Landau constant derived from a small number of simulations, the stability analysis can be employed to efficiently capture the essential finite-amplitude behaviour needed to estimate the buffet-onset boundary. The stability analysis is shown to capture the envelope of lift oscillations during a continuous pitch of an airfoil, from pre-buffet through post-buffet lift levels.

Approaches to transition prediction are considered within the context of applications to aircraft, where surface-induced distortions are an integral part of the boundary-layer flow. Different routes to transition are discussed as a function of the type and level of surface irregularity perturbing the flow. Amplitude methods offer the best potential for predicting the gradual movement of transition with increasing levels of flow distortion. Global stability analysis offers the potential for capturing abrupt transition near the source of the flow distortion (typically characterized as bypass transition). A semi-empirical amplitude method, based on a combination of stability theory and experiments, is considered for a-priori predictions to capture gradual changes to transition for realistic surface irregularities. This predictive framework is then used to characterize the different mechanisms and flow regimes responsible for boundary-layer transition in the presence of surface steps and gaps.

Global instability analysis is used to investigate the effects of extended regions of laminar flow on both unswept and swept infinite-span wings. The formulation is based on the Reynolds-averaged Navier-Stokes equations and differs from earlier studies on fully turbulent flows in the activation of the trip term in the Spalart-Allmaras eddy-viscosity transport equation. The trip term ensures a rapid transition to turbulence at an arbitrary-specified location on the wing surface, analogous a trip strip in an experiment. A parametric study is conducted for the ONERA OAT15A extruded airfoil, as an example. Results show that an extended region of laminar flow leads to a reduction in the critical angle of attack for the buffet onset, as compared with the fully turbulent conditions. All modes of instability show enhanced growth as a result of the laminar flow. However, increased lift (at fixed angle of attack) associated with an extended region of laminar flow results in a higher lift coefficient at buffet onset as compared with the fully turbulent case. Results show that the laminar flow effects on the buffet onset are linked to the suction-side laminar flow and are largely independent of the boundary-layer state on the pressure side of the wing.

Gap effects on boundary-layer transition are investigated using a combination of experiments and linear stability theory. The data and analysis is focused on nominally two-dimensional flows in quiet environmental conditions, where the transition is nominally the result of Tollmien-Schlichting (TS) instability. Results cover a large array of gap characteristics, with the resulting transition locations varying from the smooth-surface location all the way forward to the gap. Transition downstream of the gap is linked to TS instabilities with modified growth characteristics, while cases with transition at the gap appear to result from some form of bypass mechanism. The transition movement is well characterized by a variable N-factor NTS that depends on the gap width w/* and depth d/* normalized by the boundary-layer displacement thickness at the gap location. Results show the influence on transition depends on the ratio of the d/w. For shallow gaps, d/w<0.028, NTS depends only on the gap depth and varies similar to a backward-facing step. For deep gaps, d/w>0.028, NTS depends only on the gap width. A model for the NTS variation is shown to be very effective for predicting the change in transition location, up to a limit where bypass transition results in transition at the gap location.

Effects of gaps (rectangular surface cavities) on boundary-layer transition are investigated using a combination of linear stability theory and experiments, for boundary layers where the smooth-surface transition results from Tollmien–Schlichting (TS) instability. Results are presented for a wide range of gap characteristics, with the associated transition locations ranging from the smooth-surface location all the way forward to the gap location. The transition movement is well described by a variable $N$ -factor, which links the gap characteristics to the level of instability amplification $e^N$ leading to transition. The gap effects on TS-wave transition are characterized by two limiting behaviours. For shallow gaps $d/w < 0.017$ , the reduction in $N$ -factor is a function of the gap depth $d$ and is independent of the gap width $w$ . For deep gaps $d/w > 0.028$ , the reduction in $N$ -factor is a function of the gap width and is independent of the gap depth. When both the gap width and depth are sufficiently large relative to the displacement thickness $\delta ^*$ , the TS-wave transition is bypassed, resulting in transition at the gap location. These behaviours are mapped out in terms of ( $w/ \delta ^*$ , $d/ \delta ^*$ ), providing a predictive model for gap effects on transition.

Global stability analysis is used to analyse the onset of transonic buffet on infinite swept and unswept wings. This high-Reynolds-number flow is governed by the unsteady Reynolds averaged Navier–Stokes equations. The analysis generalizes earlier studies focused on two-dimensional airfoils. For the unswept wing, results show spanwise-periodic stationary modes in addition to the earlier-observed oscillatory mode. The oscillatory mode is nominally two-dimensional with a spanwise wavelength greater than ten wing chords. The stationary modes of instability exist over two bands of spanwise wavelengths centred around an intermediate wavelength of one wing chord, and around a short wavelength of one tenth of a wing chord. The intermediate-wavelength modes have a flow structure characteristic of airfoil buffeting modes, concentrated at the shock and in the shear layer downstream of the shock. The short-wavelength modes are only concentrated in the shear layer downstream of the shock. These stationary modes can lead to spanwise-periodic flow structures for the unswept wing. For the swept wing, these stationary modes become unsteady travelling modes and contribute to the more complex buffeting-flow structures observed on swept wings as compared with unswept wings. The spanwise-wavelength bands of the travelling modes translate to different frequencies, resulting in a broad-banded unsteady response for the swept wing. For a $30^{\circ }$ swept wing, the frequencies associated with the intermediate-wavelength modes are approximately 10 times higher than the swept-wing generalization of the long-wavelength oscillatory mode, and approximately 6 times higher than the long-wavelength mode for the unswept wing. These instability characteristics are in good agreement with experimental observations.

Insect fouling during takeoff, climb and landing can result in increased drag and fuel consumption for aircrafts with laminar-flow surfaces. This study investigates the effectiveness of various hydrophobic and superhydrophobic surfaces in reducing residue of insects on an aerodynamic surface at relatively high impact speeds (about 45 m/s). An experimental setup consisting of a wind tunnel and a method to inject live flightless fruit flies was used to test the effectiveness of various surfaces against insect fouling. Insect fouling was analyzed based on residue area and height from multiple impacts. In general most of the residue area was due to the hemolymph spreading while most of the residue height was due to adhesion of exoskeleton parts. Hydrophobic and especially superhydrophobic surfaces performed better than a hydrophilic aluminum surface in terms of minimizing the residue area of various insect components (exoskeleton, hemolymph, and red fluid). Surfaces with reduced wettability and short lateral length scales tended to have the smallest residue area. Residue height was not as strongly influenced by surface wettability since even a single exoskeleton adhered to the surface upon impact was enough to produce a residue height of the order of one mm. In general, the results indicate that hemolymph spread needs to be avoided (e.g. by having reduced wettability and short lateral correlation lengths) in order to minimize the residue area, while exoskeleton adherence needs to be avoided (e.g. by having oleophobic properties and micro/nano roughness) in order to minimize the residue height. In particular, two of the superhydrophobic coatings produced substantial reduction in residue height and area, relative to the baseline surface of aluminum. However, the surfaces also showed poor mechanical durability on the high-speed insect impact location. This suggests that although low wettability materials show great insect anti-fouling behavior, their durability needs to be substantially improved in order to withstand harsh aerospace conditions. (C) 2016 Elsevier B.V. All rights reserved.

Insect residue adhesion to moving surfaces such as turbine blades and aircraft not only causes surface contamination problems but also increases drag on these surfaces. Insect fouling during takeoff, climb and landing can result in increased drag and fuel consumption for aircraft with laminar-flow surfaces. Hence, certain topographical and chemical features of non-wettable surfaces need to be designed properly for preventing insect residue accumulation on surfaces. In this work, we developed a superhydrophobic coating that is able to maintain negligible levels of insect residue after 100 high speed (50 m/s) insect impact events produced in a wind tunnel. The coating comprises alternating layers of a hydrophobic, perfluorinated acrylic copolymer and hydrophobic surface functional silicon dioxide nanoparticles that are infused into one another by successive thermal treatments. The design of this coating was achieved as a result of various experiments conducted in the wind tunnel by using a series of superhydrophobic surfaces made by the combination of the same polymer and nanoparticles in the form of nanocomposites with varying surface texture and self-cleaning hydrophobicity properties. Moreover, the coating demonstrated acceptable levels of wear abrasion and substrate adhesion resistance against pencil hardness, dry/wet scribed tape peel adhesion and 17.5 kPa Taber linear abraser tests.

Surface-roughness and free-stream-turbulence effects on crossflow-instability transition are investigated experimentally and theoretically. A model baseflow is established and shown to be well predicted by boundary-layer analysis. Surface roughness is systematically introduced, with a factor-of-50 variation in r.m.s. levels. Free-stream turbulence levels are varied using grids across the test section, providing roughly a factor-of-10 variation in the turbulence intensity. For low turbulence levels, the transition is dominated by stationary crossflow instabilities. As the free-stream turbulence is increased, the traveling crossflow instabilities become increasingly relevant. For higher-turbulence and lower-roughness levels the transition appears to be dominated by the traveling crossflow instabilities. The results are linked to a variable N-factor method, which is shown to provide a good basis for estimating the transition location for low turbulence levels. The variable N-factor method is used to interpret the results and infer causality between roughness, turbulence and transition.

Certain interesting flow features involving multiple transition/relaminarization cycles on the leading edge of a swept wing at low speeds are reported here. The wing geometry tested had a circular nose and a leading edge sweep of 60°. Tests were made at a chord Reynolds number of 1.3 × 106 with model incidence α varied in the range of 3°−18° in discrete steps. Measurements made included wing chord-wise surface pressure distributions and wall shear stress fluctuations (using hot-film gages) within about 10 % of the chord in the leading edge zone. Results at α = 16° and 18° showed that several (often incomplete) transition cycles between laminar-like and turbulent-like flows occurred. These rather surprising results are attributable chiefly to the fact that the Launder acceleration parameter K (appropriately modified for swept wings) can exceed a critical range more than once along the contour of the airfoil in the leading edge region. Each such crossing results in a relaminarization followed by direct retransition to turbulence as K drops to sufficiently low values. It is further shown that the extent of each observed transition zone (of either type) is consistent with earlier data acquired in more detailed studies of direct transition and relaminarization. Swept leading edge boundary layers therefore pose strong challenges to numerical modelling.

In this paper the global-stability theory is extended to account for weak spanwise-flow variations using a quasi-three-dimensional framework. The analysis considers the onset of vortex shedding behind a circular cylinder with a spanwise-varying diameter. The quasi-three-dimensional approach models the fully three-dimensional flow structure as a series of two-dimensional eigenvalue problems representing the sectional-flow behaviour. The sectional results are coupled together using the Ginzburg–Landau equation, which models the diffusive coupling and provides the global response. The onset of global instability (and thus vortex shedding) is linked to both the sectional growth rates (characterized by the maximum-diameter location) and the spanwise extent of the zone of instability. Unsteady numerical simulations are used to guide the global-stability analysis and to assess the fidelity of the predictions. Results from the stability analysis are shown to be in good agreement with the numerical simulations, which are in close agreement with experiments.

A study is conducted to investigate the initial movement of transition downstream of protruding and recessed surface irregularities. Experimental data is provided on the transition movement, and on the steady and unsteady boundary-layer characteristics leading to the transition movement. The transition Reynolds numbers collapse reasonable well when plotted in terms of the roughness height non-dimensionalized by the boundary-layer displacement thickness. Local stability analysis is shown to capture many of the features of the pre-transitional flow The upstream movement of the transition can be represented by a reduction in the critical N-factor, similar to earlier studies on surface roughness or two-dimensional steps.

The flow field associated with transonic airfoil buffet is investigated using a combination of global-stability theory and experimental data. The theory is based on perturbing a steady flow field obtained from the Reynolds-averaged Navier-Stokes equations. Linearized perturbations are described by an eigenvalue problem, with the frequency and growth rate given by the eigenvalue and global-flow structure provided by the eigen function. The experiments provide both steady and unsteady information on the airfoil surface and in the flow downstream of the shock. The theory and experiment show good agreement for the buffet onset conditions including the critical angle of attack and the buffet-onset frequency. The post-buffet flow structure is also in good agreement, and shows a shock oscillation phase locked to an oscillating shear layer downstream of the shock.

The key missile defense questions facing policymakers today are what kind of systems should be fielded and to what extent should investments be made in future missile defense technologies. In recent years, some have argued that more investments are needed to counter theater-range missile threats, even if such investments come at the expense of developing future capabilities. On the surface, this approach seems reasonable given the sizable increase in the number of short-range ballistic missiles around the world. However, such an approach could undermine the U.S.' ability to defend against an adversary that might not be deterred by offensive forces alone. Moreover, it would not provide a meaningful capability in the long term that could dissuade an adversary from investing in ballistic missiles in the first place. This paper argues that the United States can achieve the deterrence and defense objectives set out for its missile defense forces only by sustaining a program that is balanced between the deployment of nearterm defenses and the development of advanced technologies, and between the fielding of defenses against theater-range threats and long-range threats to the American homeland. Notes 1. Lt. Gen. Trey Obering, "Missile Defense Hits Mark," Defense News, July 23, 2007, p. 21. 2. Draft Memorandum from Secretary of Defense McNamara to President Kennedy, November 14, 1963, U.S. Department of State, Foreign Relations of the United States, 1961–1963, vol. 8, National Security Policy (Washington, DC: USGPO, 1996), Document 145. 3. Kenneth Waltz, "Waltz Responds to Sagan," in Scott D. Sagan and Kenneth N. Waltz, The Spread of Nuclear Weapons (New York: W.W. Norton, 2003), p. 153. 4. Text of the report of the 1998 Congressionally mandated Commission to Assess the Ballistic Missile Threat to the United States, also called the Rumsfeld Commission after its chair Donald H. Rumsfeld, is available at: http://www.fas.org/irp/threat/bm-threat.htm. 5. As quoted form the unclassified NSPD-23, "National Policy on Ballistic Missile Defense," issued by the president on December 16, 2002. 6. Bertil Lintner, "The long reach of North Korea's missiles." Asia Times, June 21, 2006. 7. Bradley Graham, "Withdrawal Gives U.S. More Latitude in Defense Tests," Washington Post, December 14, 2001. 8. Fiscal Year 2007 National Defense Authorization Act, Sec 223 (b). 9. Michael Bruno, "HASC Panel Targets Missile Defense, Milspace," Aviation Week, May 3, 2007. 10. United States, White House, "Fact Sheet: Defending America and Its Allies Against Ballistic Missile Attack," October 23, 2007. 11. David C. Wright and Timur Kadyshev, "An Analysis of the North Korean Nodong Missile," Science and Global Security, November 1993. 12. David S. Cloud and David Sanger, "U.S. Aide Sees Arms Advance by North Korea," April 29, 2005. 13. Craig Covault, "Iran Tests Safir Space Booster," Aviation Week, August 18, 2008. 14. See, U.S. Department of State, International Security Advisory Board, Report on Discouraging a Cascade of Nuclear Weapons States (Washington, DC: U.S. Department of State, October 19, 2007). 15. Kurt Campbell and Robert Einhorn, "Avoiding the Tipping Point: Concluding Observations," in Kurt Campbell, Robert Einhorn, and Mitchell Reiss, eds., The Nuclear Tipping Point (Washington, DC: Brookings Institution Press, 2004), p. 321 (emphasis in original).

occurs. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The unstable modes provide insight into the basic character of bueting flow at near-critical conditions.